Fig. 6-Shear stress distribution upstream of the orifice for different depths

Modeling Longitudinal and Transverse Velocity Profiles Upstream of an Orifice Using the FLOW-3D Model

본 소개 자료는 Irrigation Sciences and Engineering (JISE)에서 발행한 “Modeling Longitudinal and Transverse Velocity Profiles Upstream of an Orifice Using the FLOW-3D Model” 논문의 연구 내용을 담고 있습니다.

Fig. 6-Shear stress distribution upstream of the orifice for different depths
Fig. 6-Shear stress distribution upstream of the orifice for different depths

서론

  • 연구 배경 및 필요성
    • 이란에서는 물 부족 위기로 인해 수자원 관리가 매우 중요해졌음.
    • 댐 저수지는 가장 중요한 수자원 중 하나임.
    • 하천에 댐을 건설하면 저수지의 유속이 감소하여 퇴적물이 쌓이게 됨.
    • 댐 저수지에 퇴적물이 쌓이면 유효 부피가 줄어들고 저수 기능이 저하됨.
    • 따라서 댐 수명 동안 퇴적물을 관리하고 배출하기 위한 방안이 지속적으로 제시되어 왔으며, 가압 플러싱은 퇴적물을 제거하는 일반적인 해결책임.
    • 이 방법에서는 하부 수문을 개방하여 상류의 수압으로 오리피스를 통해 퇴적물을 배출함.
    • 이동된 퇴적물의 양은 수문 직경, 퇴적물의 종류 및 크기, 수문 상류의 수위, 유출량과 같은 여러 요인의 함수임.
    • Shahmirzadi et al.(2010)은 하부 방류 장치의 직경이 플러싱 콘의 크기에 미치는 영향을 실험적으로 평가함.
    • Powell and Khan (2015)은 고정층 및 평형 세굴(이동층) 조건에서 댐 오리피스 상류의 흐름 패턴을 조사하기 위한 테스트를 수행함.
    • 연구 결과, 속도 수평 성분은 고정 및 평형 세굴 조건에서 거의 동일했으며, 속도의 수직 성분도 동일한 조건이었음.
    • Bryant et al.(2008)은 여러 실험을 수행하고 몇 가지 수치 관계를 제안하여 다양한 크기의 오리피스 상류의 흐름 패턴을 연구함.
    • 그들은 횡방향 및 깊이 속도 프로파일을 평가하기 위해 극좌표계를 사용했으며, 이 방법이 오리피스 근처의 속도 프로파일보다 더 나은 예측을 제공한다는 것을 발견함.
    • Wei et al.(2014)은 FLOW-3D 모델을 사용하여 가압 플러싱 콘을 시뮬레이션함.
    • 그들은 세굴 구멍, 하상토 및 부유사 하중을 시뮬레이션할 수 있는 3D 모델을 개발함.
    • Dargahi (2010)는 FLOW-3D 모델을 사용하여 하부 유출구의 방전 특성을 시뮬레이션하고 결과를 이집트 아스완 댐의 축소 모델 실험 결과와 비교함.
    • 얻어진 결과는 RNG 난류 모델이 k-ε 난류 모델에 비해 정확도가 더 높다는 것을 보여줌.
    • Chapokpour et al.(2012)은 FLOW-3D 모델을 사용하여 와류 흐름 거동을 연구함.
    • 속도 성분을 평가한 결과, 일부 지점에서 여러 시계 방향 및 반시계 방향 와류가 발견됨.
    • 또한, 얻어진 결과를 이전의 결과와 비교한 결과, FLOW-3D 수치 모델이 와류 흐름을 모델링할 수 있음이 나타남.
    • Chanson et al.(2002)은 수위가 낮아지는 동안 오리피스 상류의 비정상 흐름 거동을 실험적으로 조사함.
    • Powell and Khan (2012)은 동일한 맥락에서 실험 연구를 수행하여 오리피스로부터의 상대 거리가 증가함에 따라 오리피스 중심을 따라 흐르는 속도가 감소한다는 것을 보여줌.
    • Shammaa et al.(2009)은 흐름 포텐셜을 사용하여 게이트 및 오리피스 후면의 흐름 패턴을 정의하고 다양한 시나리오에 따라 분석적으로 해결함.
  • 연구 목표
    • 본 연구에서는 플로우-3D 모델을 사용하여 다양한 수심에서 오리피스 상류의 종방향 흐름 속도 프로파일을 예측하는 것을 연구함.
    • 실험 설계는 LES, Laminar 및 k-ε 난류 모델과 함께 모델을 보정하는 데 사용됨.
    • 본 연구에서는 오리피스 상류의 다양한 수심에 대해 종방향 속도 프로파일의 일반적인 형태가 높은 정확도로 지수 함수를 따르는 것으로 나타남.
    • 또한, 오리피스에서 더 먼 상류에서 횡방향 속도 프로파일은 균일해짐.
    • 결국, 오리피스 상류의 수심이 8배 상승하면 하상에 생성되는 전단 응력이 148% 증가하는 것으로 나타남.

연구 방법

  • 수치 모델링
    • 본 연구에서는 유한 체적법을 사용하여 중간 Reynolds 수 범위 내에서 Navier-Stokes 방정식을 푸는 상용 CFD 소프트웨어인 FLOW-3D를 사용함.
    • 이 소프트웨어는 유한 체적 모드에서 흐름장의 2D 및 3D 분석을 모두 허용함.
    • 이 소프트웨어는 직교 3D 요소를 사용함.
    • 다양한 유체에 사용할 수 있다는 점을 고려할 때, FLOW-3D는 특히 유압 분야에서 허용 가능한 결과를 제공함.
    • 사용자 수가 증가하고 최근 디버깅으로 인해 소프트웨어는 현재 다양한 유체 역학 분야, 특히 개방 수로 및 유압 구조물의 수역학 분야에서 점점 더 많이 사용되고 있음.
  • 실험 모델
    • 본 모델은 Bryant et al.(2008)의 연구 결과를 바탕으로 보정되었음.
    • 본 연구에서 실험한 플룸은 폭 122cm, 높이 91cm, 길이 914cm였음 (그림 1).
    • 본 연구에서는 펌프 속도 변화에 따라 의도된 흐름의 유량이 달라짐.
    • 본 연구에서는 직경(D)이 7.62cm와 15.24cm인 두 개의 오리피스가 사용되었음.
    • 측벽의 영향을 제거하기 위해 전체 오리피스의 중심이 채널 폭의 중앙에 위치하였음.
    • 또한, 오리피스 중심 상류의 수심(H)은 5.92cm로 고정되었음.
    • 흐름 패턴은 ±1%의 정확도를 가진 ADV(Acoustic Doppler Velocity Meter)를 사용하여 측정되었음.
  • 수치 모델의 메시 생성, 경계 조건 및 보정
    • AutoCAD 소프트웨어를 사용하여 주어진 치수를 기반으로 플룸 형상을 생성함.
    • 시뮬레이션 시간을 단축하기 위해 솔루션 메시의 크기는 길이 150cm, 폭 122cm, 높이 60cm로 제한되었음.
    • 시뮬레이션에서 유체는 비압축성으로 간주되었음.
    • 메시는 0.01m의 균일한 크기를 가졌으며, 계산 정확도를 높이기 위해 오리피스에 인접한 곳에 더 미세한 메시가 사용되었음.
    • 30초의 기간이 모델링에 할당되었으며, 이는 수치 모델 결과를 실험 모델 결과와 비교하여 적합한 것으로 판명됨.
    • 수치 모델은 이 기간에 정상 상태가 됨.
    • 그림 (2)는 소프트웨어에 의해 정의된 경계 조건을 보여줌.
    • 플룸 입구의 수심은 40.64cm로 고정되었음.
    • 유출 경계 조건은 오리피스에 대해 정의되었고, 벽과 바닥은 강체 경계(벽)를 가졌으며, 대칭 조건은 상단 경계에 대해 정의되었음.
    • 전단 응력을 결정하기 위해 바닥이 오리피스 아래에 위치한 그림 2와 같이 다른 형상이 플롯되었음.
    • 평균 절대 오차(MAE), 제곱 평균 제곱근 오차(RMSE) 및 결정 계수(R2)의 통계적 매개변수가 정확도를 평가하고 최적의 난류 모델을 선택하는 데 사용됨.

연구 결과

  • 모델 보정
    • 앞서 언급했듯이 Bryant et al.(2008)의 연구 결과를 사용하여 모델을 보정하였음.
    • 본 연구에서 사용된 침수비는 0.77이었음.
    • 그림 (3)은 실험 데이터와 추정된 난류 모델을 사용하여 실행된 모델에서 얻은 결과를 비교한 것임.
    • 또한, 표 (1)은 각 모델의 정확도를 결정하기 위해 통계 분석에서 얻은 결과를 제공함.
    • 이에 따라 모든 난류 모델은 결과를 예측하는 데 합리적인 정확도를 보였으며, LES 난류 모델이 상대적으로 더 높은 정확도를 가졌음.
    • 따라서 다른 시나리오를 실행하는 데 사용되었음.
    • 그림 (3)에 따르면 Powell and Khan (2012)이 이미 보고한 바와 같이 상대 속도는 x/D>2에서 0이 되는 경향이 있었음.
  • 종방향 속도 프로파일 모델링
    • 모델을 보정 한 후 오리피스 상류의 수심이 종방향 속도 프로파일 형태에 미치는 영향을 평가하기 위해 다른 세 개의 침수비 (H/D = 0.5.2.4)가 모델에 정의됨 (Bryant et al.(2008)에서 사용한 것 외에 (H/D = 0.77)).
    • 그림 (4)는 다양한 침수비에서 종방향 속도 프로파일을 비교한 것임.
  • 횡방향 속도 프로파일 모델링
    • 세 개의 상대 거리(x/D = 1.2.3)에서 의도된 침수비에 대한 횡방향 속도 모델링에서 얻은 결과는 그림 (5)에 나와 있음.
    • 그림은 오리피스에서 더 먼 상류에서 속도 변화가 감소하여 0이 되는 경향을 나타냄.
    • 또한, 각 상대 거리에 대해 최대 속도는 오리피스를 따라 있었고, y-축을 따라 오리피스 중심에서 거리가 멀어짐에 따라 속도가 감소하고 횡방향 속도 프로파일이 균일해짐.
  • 오리피스 상류의 전단 응력 분포
    • 그림 (6)은 의도된 침수비에 대한 오리피스 상류의 전단 응력 분포를 보여줌.
    • 그림에서 볼 수 있듯이, 오리피스에서 유출되는 속도가 증가하여 바닥에서 더 높은 전단 응력이 발생하기 때문에 바닥의 전단 응력은 오리피스 상류의 깊이와 함께 증가함.
    • 결과적으로 침수비가 0.5에서 4로 증가함에 따라 전단 응력은 4.31Pa에서 10.7Pa로 148% 증가함.
    • 또한, 더 높은 침수비에서 오리피스 상류의 더 넓은 영역이 전단 응력의 영향을 받는 것으로 관찰됨.
    • Powell and Khan (2011)에 따르면 댐 하부 게이트를 열고 가압 플러싱을 시작하면 첫 번째 단계에서 퇴적물의 이동은 하상에 형성된 전단 응력으로 인해 시작됨.
    • 따라서 논의된 내용에 따르면 오리피스 상류의 침수비가 증가하면 더 많은 퇴적물이 전단 응력에 의해 씻겨 내려가 물 흐름에 의해 배출될 것으로 예상됨.

결론

  • 연구의 의의
    • 본 연구에서는 FLOW-3D 모델을 사용하여 오리피스 상류의 흐름 패턴을 예측하는 타당성 조사를 수행함.
    • 이와 관련하여 오리피스 상류의 다양한 수심에 대한 몇 가지 시나리오가 모델에 정의되어 다음과 같은 결과를 얻었음:
    • FLOW-3D 소프트웨어는 오리피스 상류의 종방향 속도 프로파일을 충분한 정확도로 모델링했음.
    • Laminar, k-ε. 및 LES 난류 모델은 오리피스 상류의 종방향 속도 프로파일을 예측하는 데 높은 정확도를 보였으며 거의 동일한 정확도를 가졌음.
    • 오리피스 상류의 수심이 상승함에 따라 종방향 속도 프로파일의 일반적인 형태는 지수 방정식을 따르며 일정해졌음.
    • 오리피스에서 더 먼 거리에서 속도 변화폭이 감소하고 횡방향 속도 프로파일이 균일해짐.
    • 오리피스 상류의 침수비 증가는 더 높은 전단 응력과 더 넓은 면적의 하상이 전단 응력의 영향을 받음.
Fig. 6-Shear stress distribution upstream of the orifice for different depths
Fig. 6-Shear stress distribution upstream of the orifice for different depths

References

  1. Bryant, D.B., Khan, A.A. and Aziz, N.M., 2008. Investigation of flow upstream of orifices. Journal of Hydraulic Engineering, 134(1), pp.98-104.
  2. Chanson, H., Aoki, S.I. and Maruyama, M., 2002. Unsteady two-dimensional orifice flow: a large-size experimental investigation. Journal of Hydraulic Research, 40(1), pp.63-71.
  3. Chapokpour, J., Ghasemzadeh, F. and Farhoudi, J., 2012. The numerical investigation on vortex flow behavior using FLOW-3D. Iranica Journal of Energy & Environment, 3(1), pp.88-96.-
  4. Dargahi, B., 2010. Flow characteristics of bottom outlets with moving gates. Journal of Hydraulic Research, 48(4), pp.476-482.
  5. Powell, D.N. and Khan, A.A., 2011. Sediment transport mechanics upstream of an orifice. Journal of visualization, 14(4), pp.315-320.
  6. Powell, D.N. and Khan, A.A., 2012. Scour upstream of a circular orifice under constant head. Journal of hydraulic research, 50(1), pp.28-34..
  7. Powell, D.N. and Khan, A.A., 2015. Flow field upstream of an orifice under fixed bed and equilibrium scour conditions. Journal of Hydraulic Engineering, 141(2), p.04014076.
  8. Shahmirzadi, M.M., Dehghani, A.A., Meftahh, M. and Mosaedi, A., 2010. Experimental investigation of pressure flushing technique in reservoir storages. Water Geosci, 1, pp.132-137.
  9. Shammaa, Y., Zhu, D.Z. and Rajaratnam, N., 2009. Flow field in a rectangular basin with a line inlet and a circular outlet. Journal of Hydraulic Engineering, 135(10), pp.857-864.
  10. Wei G, Brethour J, Grünzner M, Burnham J. The sedimentation scour model in FLOW-3D®. Flow Sci. Rep. 2014 Jun:3-14.
Fig.5- View of a simulated congressional overflow

Studying the effect of shape changes in plan of labyrinth weir on increasing flow discharge coefficient using Flow-3D numerical model

본 소개 자료는 Irrigation Sciences and Engineering (JISE)에서 발행한 “Studying the effect of shape changes in plan of labyrinth weir on increasing flow discharge coefficient using Flow-3D numerical model” 논문의 연구 내용을 담고 있습니다.

Fig.5- View of a simulated congressional overflow
Fig.5- View of a simulated congressional overflow

서론

  • 연구 배경 및 필요성
    • 위어는 수로 및 하천 폭에 고정되어 수위를 측정, 조절 및 제어하는 데 사용되는 수력 구조물임.
    • 가능한 최대 홍수 사건(PMF)의 규모가 커짐에 따라 방전 용량 증가에 대한 요구가 강조됨.
    • 래버린스 위어의 적용은 방전 용량을 증가시키기 위한 솔루션으로 제안됨.
    • Tullis et al.(1995)은 래버린스 위어의 용량을 결정하는 효과적인 매개변수를 평가함.
    • 그들은 총 수두, 유효 정점 길이 및 방전 계수를 래버린스 위어의 방전 용량에 영향을 미치는 매개변수로 도입함.
    • Khode et al.(2011)은 8°에서 30°까지의 다양한 측벽 각도(α)에 대해 흐름-오버 래버린스 위어의 매개변수를 실험적으로 연구함.
    • 그들은 측벽 각도 값이 커짐에 따라 방전 계수가 증가한다는 것을 발견함.
    • Crookston과 Tullis(2012a)는 평면에서 위어의 기하학적 모양을 다르게 하여 다양한 래버린스 위어의 성능을 연구함.
    • 결과에 따르면 아치형 래버린스 위어의 방전 용량이 말굽 래버린스 위어의 방전 용량보다 큼.
    • Seo et al.(2016)은 위어 모양이 위어 방전에 미치는 영향을 조사함.
    • 래버린스 위어의 방전량은 선형 오지 위어에 비해 약 71% 증가한 것으로 나타남.
  • 연구 목표
    • 본 연구에서는 이전 연구자들의 실험 결과를 사용하여 측벽 각도가 6°인 래버린스 위어를 Flow-3D 모델을 통해 시뮬레이션함.
    • 검증 후, 각도가 45° 및 85°이고 정점 모양이 삼각형 및 반원형인 위어의 방전 계수 변화를 분석함.

연구 방법

  • 연구 설계
    • 다양한 방정식을 사용하여 방전 계수를 평가함.
    • 방정식 (1)은 이 목적을 위해 가장 유효한 방정식 중 하나임.
    • 여기서 Cd(a)​ = 래버린스 위어의 방전 계수, Q = 위어 방전, Lc​ = 위어의 총 길이, HT​ = 총 상류 헤드(비잠수) 및 g는 중력으로 인한 가속도(m2/s)임.
    • 래버린스 위어 조사를 위한 최상의 메시를 선택하기 위해 두 가지 유형의 메시가 사용됨.
    • 564000 및 437000의 메시 수가 최적의 메시 선택을 위해 평가됨.
    • 메시 번호 1에서 셀 크기는 구조 근처의 메시 번호 2의 셀 크기보다 작음.
    • 따라서 메시 1은 모델링 정확도를 높임.
  • 수치 모델링
    • Crookston과 Tullis(2012b)의 연구에서 실험 Cd(aα)​ 데이터가 제시됨.
    • 본 논문에서는 3개의 난류 모델(k-ε, RNG k-ε 및 LES 모델)을 사용하여 수치 Cd(a∘)​를 수행함.
    • 최대 상관 계수(H T /p 무차원 매개변수의 경우 0.9875)는 RNG k-ε를 사용하여 얻음.
    • 이 지수의 값은 1에 가까우며 모델이 시뮬레이션에 적합함을 보여줌.
    • 이 연구의 이전 결과를 기반으로 RNG 모델을 적합한 모델로 간주하여 각도가 6°, 45° 및 85°인 위어의 방전 계수 변화를 평가함.

연구 결과

  • 결과 분석
    • 결과에 따르면 측벽 각도 값이 커짐에 따라 방전 계수가 증가함.
    • 각도가 85° 및 45°인 래버린스 위어의 방전 계수는 각도가 6°인 래버린스 위어의 방전 계수보다 평균 2.28 및 1.24배 큼.
    • 또 다른 주목할 점은 방전 용량이 증가함에 따라 방전 계수가 감소한다는 것임.
    • 방전량이 32.8배 증가하면 각도가 6°, 45° 및 85°인 위어의 방전 계수가 각각 57.2%, 47.4% 및 7.8% 감소함.
    • 다음 단계에서는 선형, 삼각형 및 반원형의 정점 모양을 가진 위어의 방전 계수 변화를 분석함.
    • 삼각형 및 반원형 정점 모양의 래버린스 위어가 가장 큰 방전 계수 값을 가짐.
    • 삼각형 및 반원형 정점 모양의 위어의 방전 계수는 선형 정점에 비해 50.29% 및 4.15% 증가한 것으로 나타남.
  • 방정식
    • 본 논문에서는 방정식 (2)에 정의된 대로 다양한 측벽 각도를 가진 래버린스 위어의 방전 계수를 예측하기 위한 방정식을 제시함.
    • 이 방정식의 정확도를 결정하기 위한 MAE, RMSE 및 R 2 값은 각각 0.0407, 0.0496 및 0.9122이며, 이는 방전 계수를 결정하는 데 이 방정식의 정확도를 보여줌.
    • Cd​=0.201(e−0.4904(HT​/P))(0.00038θ2+2.3735)

결론

  • 연구의 의의
    • 엔지니어들은 홍수 조절 및 운하와 하천의 방전 용량 증가를 위한 솔루션을 찾고 있음.
    • 래버린스 위어의 적용은 방전 용량을 증가시키기 위한 솔루션으로 제안됨.
    • 본 연구에서는 이전 연구자들의 실험 결과를 사용하여 측벽 각도가 6°인 래버린스 위어를 Flow-3D 모델을 통해 시뮬레이션함.
    • 검증 후, 각도가 45° 및 85°이고 정점 모양이 삼각형 및 반원형인 위어의 방전 계수 변화를 분석함.
  • 최적의 위어 설계
    • 결과에 따르면 각도가 85° 및 45°인 래버린스 위어의 방전 계수는 각도가 6°인 래버린스 위어의 방전 계수보다 큼.
    • 또한 삼각형 및 반원형 정점 모양의 위어의 방전 계수는 선형 정점에 비해 50.29% 및 4.15% 증가함.
    • 마지막으로 래버린스 위어의 방전 계수를 예측하기 위한 방정식을 제안했으며, 이는 허용 가능한 수준의 정확도로 방전 계수를 추정할 수 있음.
Fig.3- Plan of geometric parameters of
congressional overflow
Fig.3- Plan of geometric parameters of congressional overflow
Fig. 4- The boundary conditions of the congressional overflow model
Fig. 4- The boundary conditions of the congressional overflow model
Fig.5- View of a simulated congressional overflow
Fig.5- View of a simulated congressional overflow

References

  1. Crookston, B. M. and Tullis, B. P., 2012a. Arced labyrinth weirs. Journal of Hydraulic Engineering. 138(6), pp.555-562.
  2. Crookston, B. M. and Tullis, B. P., 2012b, Hydraulic design and analysis of labyrinth weirs. I: Discharge relationships. Journal of Irrigation and Drainage Engineering. 139(5), pp.363-370.
  3. Khode, B. V., Tembhurkar, A. R., Porey, P. D. and Ingle, R. N., 2011. Experimental studies on flow over labyrinth weir. Journal of Irrigation and Drainage Engineering. 138(6), pp.548-552.
  4. Seo, I. W., Do Kim, Y., Park, Y. S. and Song, C. G. 2016, Spillway discharges by modification of weir shapes and overflow surroundings. Environmental Earth Sciences. 75(6), pp.1-13.
  5. Tullis, J. P., Amanian, N. and Waldron, D., 1995. Design of labyrinth spillways. Journal of Hydraulic Engineering. 121(3), pp.247-255.
  6. Farzin, S., Karami, H. and Zamiri, E., 2016. Study of the Flow over Rubber Dam Using Computational Hydrodynamics. Journal of Dam and Hydroelectric Powerplant. 3(9), pp.1-11. (In Persian).
  7. Hirt, C. W. and Richardson, J. E., 1999. The modeling of shallow flows, Flow Science, Technical Notes. 48, pp.1-14.
  8. Hosseini, K., Tajnesaie, M. and Jafari Nodoush, E., 2015. Optimization of the Geometry of Triangular Labyrinth Spillways, Using Fuzzy‐Neural System and Differential Evolution Algorithm. Journal of Civil and Environmental Engineering. 45(1), PP.81-91. (In Persian).
  9. Khode, B. V., Tembhurkar, A. R., Porey, P. D. and Ingle, R. N., 2011. Experimental studies on flow over labyrinth weir. Journal of Irrigation and Drainage Engineering. 138(6), pp.548-552.
  10. Nezami, F., Farsadizadeh, D., Hosseinzadeh Delir, A. and Salmasi, F., 2012. Experimental Study of Discharge Coefficient of Trapezoidal Labyrinth Side-Weirs. Journal of Water and Soil Science. 23(1), PP.247-257. (In Persian).
  11. Nikpiek, P. and Kashefipour, S. M., 2014. Effect of the hydraulic conditions and structure geometry on mathematical modelling of discharge coefficient for duckbill and oblique weirs. Journal of Irrigation Science and Engineering. 39(1), pp.1-10. (In Persian).
  12. Noori, B. M. and Aaref, N. T., 2017. Hydraulic Performance of Circular Crested Triangular Plan Form Weirs. Arabian Journal for Science and Engineering. pp.1-10.
  13. Noruzi, S. and Ahadiyan, J., 2016. Effect of Vortex Breaker Blades 45 Degree on Discharge Coefficient of Morning Glory Spillway Using Flow-3D. Journal of Irrigation Science and Engineering. 39(4), PP. 47-58. (In Persian).
  14. Paxson, G. and Savage, B., 2006. Labyrinth spillways: comparison of two popular USA design methods and consideration of non-standard approach conditions and geometries. Proceedings of the international junior researcher and engineer workshop on hydraulic structures, Montemor-o-Novo, Portugal, Division of Civil Engineering, 37.
  15. Payri, R., Tormos, B., Gimeno, J. and Bracho, G., 2010. The potential of Large Eddy Simulation (LES) code for the modeling of flow in diesel injectors. Mathematical and Computer Modelling. 52(7), pp.1151-1160.
  16. Rezaee, M., Emadi, A. and Aqajani Mazandarani, Q., 2016. Experimental Study of Rectangular Labyrinth Weir. Journal of Water and Soil. 29(6), pp. 1438-1446. (In Persian).
  17. Seo, I. W., Do Kim, Y., Park, Y. S. and Song, C. G. 2016, Spillway discharges by modification of weir shapes and overflow surroundings. Environmental Earth Sciences. 75(6), pp.1-13.
  18. Suprapto, M., 2013. Increase spillway capacity using Labyrinth Weir. Procedia Engineering. 54, pp. 440-446.
  19. Tullis, J. P., Amanian, N. and Waldron, D., 1995. Design of labyrinth spillways. Journal of Hydraulic Engineering. 121(3), pp.247-255.
  20. Zamiri, E., Karami, H. and Farzin, S., 2016. Numerical Study of Labyrinth Weir Using RNG Turbulence Model. 15th Iranian Hydraulic Conference, Imam Khomeini International University, Qazvin, Iran. (In Persian).
Fig. 3 Vane V0 induced circulation downstream of vane (x = 65.5 cm), flow Froude number of Fr = 0.16

Performance Evaluation of Submerged Vanes by Flow-3D Numerical Model

본 소개 자료는 Iranian Hydraulic Association Journal of Hydraulics에서 발행한 “Performance Evaluation of Submerged Vanes by Flow-3D Numerical Model” 논문의 연구 내용을 담고 있습니다.

Fig. 3 Vane V0 induced circulation downstream of vane
(x = 65.5 cm), flow Froude number of Fr = 0.16
Fig. 3 Vane V0 induced circulation downstream of vane (x = 65.5 cm), flow Froude number of Fr = 0.16

서론

  • 연구 배경 및 필요성
    • 잠수 베인은 접근 흐름에 대해 작은 받음각으로 수로 바닥에 수직으로 장착되는 흐름 패턴 변경 구조물임.
    • 잠수 베인은 베인의 두 측면에 있는 수직 압력 구배로 인해 베인의 상단 높이 아래에서 시작하여 베인의 하류로 확장되는 2차 순환(나선형 흐름)을 생성함.
    • 베인으로 유도된 와류는 채널 단면 내에서 퇴적물을 재분배하고 충적층의 프로파일을 변경함.
    • 그러나 베인 주변의 국부적인 세굴은 잠수 베인 기술 사용의 문제점 중 하나임.
    • 국부적인 세굴공의 확장은 베인의 모양과 관련이 있음.
  • 연구 목표
    • 본 연구에서는 1차 잠수 베인은 일반적으로 평평한 직사각형 판을 사용함.
    • 본 연구에서는 국부적인 세굴을 줄이기 위한 대책으로 베인의 앞쪽 가장자리 일부를 잘라내는 것을 연구함.
    • 연구 대상 베인은 직사각형 베인(기준선 베인)과 θ=30∘, 45∘, 60∘ 70∘ 및 73.3∘의 테이퍼형 앞쪽 가장자리를 갖는 다른 5개의 수정된 베인을 포함함.
    • 본 연구는 이러한 수정이 앞쪽 가장자리에서의 수직 속도 성분과 베인 하류에서 2차 순환의 강도에 미치는 영향을 평가하는 것을 목표로 함.
    • 베인 주변의 흐름장을 연구하기 위해 Flow-3D 수치 모델 버전 10을 사용함.

연구 방법

  • 연구 설계
    • 본 연구에서는 상용 CFD 모델인 Flow-3D를 사용함.
    • 모델 보정을 위해 실험 속도 측정을 사용하였으며, 이를 위해 재순환 수로(길이 7.30m, 폭 0.56m, 깊이 0.6m)를 사용함.
    • 원심 펌프는 플룸 입구의 정수 탱크로 물을 배출함.
    • 균일한 물 유입을 만들기 위해 플룸 입구에서 1m 떨어진 곳에 스크린을 설치함.
    • 테일 게이트를 사용하여 플룸의 물 깊이(do​)를 0.25m의 일정한 값으로 조정함.
    • 베인의 치수는 Odgaard (2008)의 설계 기준, 즉 베인 높이 대 물 깊이 비율 Ho​/do​ = 0.3, 길이 L = 3$H_o$를 사용하여 결정함.
    • 평균 흐름 깊이 do​ = 0.25m는 Ho​ = 0.075m 및 L = 0.25m를 산출함.
    • 흐름 프루드 수 Fr = 0.16에서 베인 V0 및 V3을 사용하여 속도 측정을 수행함.
    • 각 테스트에서 베인은 흐름에 대해 20°의 각도로 플룸의 중심선에 설치됨.
    • 베인으로 유도된 속도장을 연구하기 위해 플룸 전체에서 4×4 cm² 격자를 베인의 중심에서 채취함.
    • 각 격자점에서 전자기 유속계(EVM)를 사용하여 3차원 속도 벡터(u, v, w)의 성분을 측정함.
    • 플룸의 벽에 매우 가까운 속도는 측정하지 않음.
  • 수치 모델링
    • 베인의 고압 측면에서 수직 속도 성분은 위쪽(양수)이었고 저압 측면에서는 아래쪽(음수)이었음.
    • 따라서 베인 하류에서 시계 방향의 2차 순환이 생성됨.
    • 1차 직사각형 베인(베인 V0)의 앞쪽 가장자리에서 아래쪽 속도 성분이 분명했음.
    • 테이퍼형 베인 V1 및 V2의 경우 베인 V0에서 앞쪽 가장자리 부분을 잘라냄으로써 음의 w-속도 성분의 크기가 각각 40% 및 69% 감소함.
    • 베인 V3, V4 및 V5의 경우 테이퍼 각도를 늘리면 아래쪽 속도 성분이 효과적으로 감소함.
    • 모멘트(MOM) 수량을 사용하여 베인으로 유도된 순환의 강도를 평가함.
    • 베인의 성능을 비교하기 위해 MOM 값을 적용함.
    • 이를 위해 베인 중심에서 하류로 2Ho 및 4Ho 거리, 즉 15cm 및 30cm 떨어진 두 단면에서 속도 데이터를 사용함.
    • MOM 계산에는 100개의 속도 성분(50개의 v-성분 및 50개의 w-성분)을 사용함.
    • 따라서 이 수량은 잠수 베인의 성능 및 효율성을 평가하는 데 유용한 기준이 됨.

연구 결과

  • 세굴 매개변수
    • 베인의 속도 분포 및 모멘트(MOM)는 테이퍼형 베인의 앞쪽 가장자리에서 침식성 음의 속도 성분의 감소를 나타냄.
    • MOM 값을 기준으로 베인의 앞쪽 가장자리를 잘라내면 성능이 저하됨.
    • 다시 말해, 이러한 수정은 직사각형 베인(베인 V0)에 비해 테이퍼형 베인의 영향을 받는 필드를 제한함.
    • 결과에 따르면 직사각형 베인에 비해 테이퍼형 베인(V1~V5)의 성능은 (2Ho 거리에서) 각각 5.8%, 7.3%, 17.8%, 33% 및 42.6% 감소함.
    • 4Ho 거리에서 감소량은 각각 7.4%, 11.9%, 17%, 25.5% 및 34.3%임.
  • 결과 분석
    • 이와는 반대로 테이퍼형 베인의 효율성은 증가함.
    • 베인 V1~V5의 중심에서 2Ho 거리에서 증가량은 각각 3.2%, 9%, 11%, 14% 및 14.8%이고 4Ho 거리에서는 각각 1.4%, 3.6%, 12.1%, 26.7% 및 31.3%임.
    • 따라서 테이퍼형 베인을 사용하여 국부적인 세굴을 줄이는 경우 설계 기준에 따라 베인 배열 사이의 거리(ds​)에 큰 값을 사용하는 것은 권장하지 않음.

결론

  • 연구의 의의
    • 속도 분포 및 베인의 모멘텀 모멘트(MOM) 계산 결과, 베인의 선행 에지에서 절단이 선행 에지에서 음의 속도 성분을 감소시키는 데 효과적인 것으로 나타났음.
    • 모멘텀 모멘트 계산을 기반으로 베인의 선행 에지를 절단하면 베인의 성능이 감소하고, 즉, 사각형 베인(V0)에 비해 베인의 영향을 받는 필드의 길이가 감소함.
  • 최적의 위어 설계
    • 결과에 따르면, 테이퍼형 베인(V1~V5)의 성능은 사각형 베인에 비해 (2Ho 거리에서) 각각 5.8%, 7.3%, 17.8%, 33% 및 42.6% 감소하고, 4Ho 거리에서 감소량은 각각 7.4%, 11.9%, 17%, 25.5% 및 34.3%임.
    • 이와는 반대로, 테이퍼형 베인의 효율은 증가함.
    • 베인 V1~V5의 중심에서 2Ho 거리에서 증가량은 각각 3.2%, 9%, 11%, 14% 및 14.8%이고, 4Ho 거리에서 증가량은 각각 1.4%, 3.6%, 12.1%, 26.7% 및 31.3%임.
    • 따라서, 테이퍼형 베인을 사용하여 국부적인 스코어를 줄이는 경우, 베인 배열 사이의 거리(ds)에 큰 값을 사용하는 것은 권장되지 않음.
Fig. 1 Laboratory flume used in present research
Fig. 1 Laboratory flume used in present research
Fig. 3 Vane V0 induced circulation downstream of vane
(x = 65.5 cm), flow Froude number of Fr = 0.16
Fig. 3 Vane V0 induced circulation downstream of vane (x = 65.5 cm), flow Froude number of Fr = 0.16

Reference

  1. Flokstra, C. (2006). Modeling of submerged vanes. J. Hydraulic Research. 44(5), 591-602.
  2. Gupta, U.P., Ojha, C.S.P. and Sharma, N. (2010). Enhancing utility of submerged vanes with collar. J. Hydraulic Engineering, ASCE, 136(9), 651-655.
  3. Gupta, U.P., Sharma, N. and Ojha, C.S.P. (2006). Performance evaluation of submergence ratio of a rectangular submerged vane with collar. International Journal of Sediment Research. 21(1), 42-49.
  4. Kalathil, S.T., Wuppukondur, A., Balakrishnan, R.K. and Chandra, V. (2018). Control or sediment inflow into a trapezoidal intake canal using submerged vanes. ASCE, J. Waterway, Port, Coastal, and Ocean Engineering. 144(6), 04018020.
  5. Odgaard, A.J. and Spoljaric, A. (1986). Sediment control by submerged vanes. ASCE, J. Hydraulic Engineering. 112(12), 1164-1181.
  6. Odgaard, A.J. and Wang, Y. (1991a). Sediment management with submerged vanes, I: Theory. J. Hydraulic Engineering, ASCE. 117(3), 267-283.
  7. Odgaard, A.J. and Wang, Y. (1991b). Sediment management with submerged vanes, II: Application. J. Hydraulic Engineering, ASCE. 117(3), 284-302.
  8. Ouyang, H.T. (2009). Investigation on the Dimensions and shape of a submerged vane for sediment management in alluvial channels. J. Hydraulic Engineering, ASCE. 135(3), 209-217.
  9. Ouyang, H.T. and Cheng, P.L. (2016). Characteristics of interactions among a row of submerged vanes in various shapes. J. Hydro-environmental Research. 13, 14-25.
  10. Spoljaric, A. (1988). Mechanics of submerged vanes on flat boundaries. PhD thesis, University of Iowa, Iowa city, Iowa.
Figure 2. (a) Longitudinal depth averaged velocity contours and (b) velocity vectors' alignment around the cylindrical pier after 600 sec. of simulation with Flow-3D software

The Scour Bridge Simulation around a Cylindrical Pier Using Flow-3D

FLOW-3D를 이용한 원형 교각 주변의 세굴 시뮬레이션

Figure 2. (a) Longitudinal depth averaged velocity contours and (b) velocity vectors' alignment around the cylindrical pier
after 600 sec. of simulation with Flow-3D software
Figure 2. (a) Longitudinal depth averaged velocity contours and (b) velocity vectors’ alignment around the cylindrical pier after 600 sec. of simulation with Flow-3D software

연구 배경 및 목적

문제 정의

  • 교각 주변에서 발생하는 국부 세굴(local scour)은 유속 증가, 난류, 침식 작용에 의해 발생하며, 이는 교량 붕괴의 주요 원인 중 하나임.
  • 기후 변화로 인해 홍수 빈도가 증가하면서 교량 안전성 확보가 더욱 중요해짐.
  • 기존 실험 방식은 비용이 높고 유지보수가 어렵기 때문에 컴퓨터 기반 CFD 시뮬레이션을 활용한 예측 연구 필요.

연구 목적

  • FLOW-3D를 사용하여 원형 교각 주변에서 발생하는 국부 세굴을 시뮬레이션하고, 실험 데이터와 비교하여 모델의 신뢰성을 검증.
  • 유입 유량(5, 10, 19, 30 L/sec)에 따른 세굴 깊이 변화 분석.
  • 세굴 발생 위치와 유동 특성을 평가하여 교량 설계 및 유지보수에 활용할 데이터 제공.

연구 방법

시뮬레이션 모델링 및 설정

  • 수치 모델:
    • 채널 크기: 너비 0.4m, 길이 1.0m
    • 교각 크기: 지름 0.03m, 높이 0.3m
    • 퇴적층 크기: 길이 1.0m, 너비 0.4m, 높이 0.12m
  • 유체 해석 기법:
    • VOF(Volume of Fluid) 방법을 사용하여 유체-퇴적층 경계 추적
    • RNG k-ε 난류 모델을 적용하여 난류 흐름 해석
    • 침식 및 퇴적 모델: 입자 크기 0.72mm, 밀도 2650kg/m³, Shields 수 0.031 적용
  • 경계 조건:
    • 유입: 부피 유량 조건 적용
    • 유출: 출구 경계 조건 설정
    • 하부: 고정 벽 경계 적용
    • 상부: 대칭 경계 조건 사용

주요 결과

세굴 깊이 분석

  • 시뮬레이션 600초 후, 각 유량에서 최대 세굴 깊이:
    • 5 L/sec → 0.0cm
    • 10 L/sec → 1.3cm
    • 19 L/sec → 2.4cm
    • 30 L/sec → 3.6cm
  • 세굴 발생 패턴:
    • 교각 상류에서 세굴이 심하게 발생, 하류에서는 상대적으로 적음.
    • 말굽 와류(horseshoe vortex)와 수직 와류(vertical wake vortex)가 퇴적물 이동의 주요 원인임.

실험 데이터와 비교

  • 실험 결과와 비교 시, FLOW-3D 시뮬레이션은 상류에서 30%, 하류에서 20% 낮게 예측됨.
  • 이는 침식 역학에 대한 추가적인 보정이 필요함을 의미.
  • 하지만 전체적인 세굴 패턴 및 경향은 실험 결과와 일치.

결론 및 향후 연구

결론

  • FLOW-3D를 활용한 세굴 시뮬레이션이 실험 데이터와 높은 상관관계를 가짐을 확인.
  • 세굴 깊이는 유입 유량에 따라 증가하며, 상류에서 더 깊은 침식 발생.
  • 모델의 한계점(세굴 깊이 과소 예측)을 개선하기 위해 추가적인 침식 보정이 필요.

향후 연구 방향

  • 더 긴 시뮬레이션 시간 설정을 통한 침식-퇴적 균형 분석.
  • 다양한 교각 형상 및 하상 조건에서 추가 검증 수행.
  • 현장 측정 데이터와 비교하여 모델 신뢰성 향상.

연구의 의의

본 연구는 FLOW-3D를 활용하여 교각 주변 세굴을 시뮬레이션하고, 유량에 따른 세굴 패턴을 정량적으로 분석하였다. 이 결과는 향후 교량 설계 및 유지보수 전략 수립에 활용될 수 있으며, 홍수 시 교량 붕괴를 예방하는 데 기여할 것으로 기대된다.

Figure 1. Geometry and meshing structure of the model for simulation of scour around a cylindrical pier
Figure 1. Geometry and meshing structure of the model for simulation of scour around a cylindrical pier
Figure 2. (a) Longitudinal depth averaged velocity contours and (b) velocity vectors' alignment around the cylindrical pier
after 600 sec. of simulation with Flow-3D software
Figure 2. (a) Longitudinal depth averaged velocity contours and (b) velocity vectors’ alignment around the cylindrical pier after 600 sec. of simulation with Flow-3D software

References

  1. Abdelaziz, S., Bui, M.D., Rutschmann, P. 2010. Numerical simulation of scour development due to submerged horizontal jet, 5th River Flow, International Conference on Fluvial Hydraulics.
  2. Alabi, P.D. 2006. Time development of local scour at bridge pier fitted with a collar. Master Science Thesis, University of Saskatchewan, Canada.
  3. Briaud, J.L., Gardoni, P., Yao, C. 2012. Bridge Scour Risk, ICSE6 Paris. ICSE6-011.
  4. Elsebaie, I.H. 2013. An Experimental Study of Local Scour around Circular Bridge Pier in Sand Soil, International Journal of Civil & Environmental Engineering (IJCEE-IJENS), 13(1), 23-28.
  5. Flow-3D v.9.2, Flow Science Inc., 2007, User’s Manual. www.flow3d.com.
  6. Jafari, M., Ayyoubzadeh, S.A., Esmaeili Varaki, M., Rostami, M. 2017. Simulation of Flow Pattern around Inclined Bridge Group Pier using FLOW-3D Software. Journal of Water and Soil, 30(6), 1860-1873.
  7. Heidarpour, M., Afzalimehr, H., Izadinia, E. 2010. Reduction of local scour around bridge pier groups using collars, International Journal of Sediment Research, 25(4): 411-422.
  8. Melville, B.W., Sutherland. A.J. 1988. Design method for local scour at bridge piers. J. Hyd. Eng, 114(10): 1210-1226.
  9. Olsen, N.R. 2007. A three dimensional numerical model for simulation of sediment movements in water intakes with multiblock option, User’s manual [Online]. Available: http://www.ntnu.no.
  10. Prendergast L.J., Gavin, K. 2014. A review of bridge scour monitoring techniques, Journal of Rock Mechanics and Geotechnical Engineering, 6, 138-149.
  11. Ramezani, Y., Babagoli Sefidkoohi, R. 2016. Comparison of Turbulence Models for Estimation of Bed Shear Stress Around Bridge Abutment in Compound Channel, Water and soil science, 26(2): 95-109.
  12. Soltani-Gerdefaramarzi, S., Afzalimehr, H., Chiew, Y.M., Lai, J.S. 2013a. Jets to control scour around circular bridge piers. Canadian journal of civil engineering, 40(3), 204-212.
  13. Soltani-Gerdefaramarzi, S., Afzalimehr, H., Chiew, Y.M., Ghasemi, M. 2013b. Turbulent characteristics in flow subjected to bed suction and jet injection as a pier-scour countermeasure, International Journal of Hydraulic Engineering, 2(5), 93-100.
  14. Soltani-Gerdefaramarzi, S., Afzalimehr, H., Chiew, Y.M., Gallichand, J. 2014. Reduction of pier scour using bed suction and jet injection. Water management. 167(2), 105-114.
  15. Smith, H. 2007. Flow and sediment dynamics around three-dimensional structures in coastal environments, Ph.D. thesis, The Ohio State University.
  16. Yildiz, B., Koken, M., Gogus, M. 2013. Abutment Scour Simulations by Using FLOW-3D, FLOW-3D user conference, Flow Science Inc.
Figure 3 Definition of physical geometry and flow parameters, FLOW-3D

Numerical Modelling of Flow over Single-Step Broad-Crested Weir Using FLOW-3D and HEC-RAS

FLOW-3D 및 HEC-RAS를 이용한 단일 계단형 광정수제 위를 흐르는 유동의 수치 모델링

1. 서론

  • 수치유체역학(CFD)의 발전으로 다양한 수리 구조물의 성능을 평가하는 연구가 활발하게 이루어짐.
  • 본 연구에서는 FLOW-3D(k-ε 모델)와 HEC-RAS(정상유동 모델)를 사용하여 단일 계단형 광정수제 위를 흐르는 유동을 모의함.
  • 실험 데이터를 활용하여 두 모델의 정확도를 비교 분석하며, 특히 정수제 전·후방 및 계단부에서의 유동 특성을 평가함.

2. 연구 방법

모델 설정 및 시뮬레이션 조건

  • FLOW-3D 모델
    • VOF(Volume of Fluid) 기법을 사용하여 자유 수면 추적.
    • RNG k-ε 난류 모델을 적용하여 난류 해석 수행.
    • FAVOR(Fractional Area/Volume Obstacle Representation) 기법을 이용하여 복잡한 구조 형상 반영.
  • HEC-RAS 모델
    • Steady-Flow 모듈을 이용하여 정상유동 해석.
    • 수위 프로파일을 에너지 방정식을 이용하여 계산.
    • 수력 점프(hydraulic jump) 및 과도 흐름(supercritical flow) 예측.
  • 경계 조건 설정
    • 유입부: 부피 유량(Volume flow rate) 조건 적용.
    • 유출부: 자유 배출(Outflow) 조건 설정.
    • 벽면: No-slip 조건 적용.

3. 연구 결과

유동 패턴 분석

  • 정수제 상류부:
    • HEC-RAS와 FLOW-3D 모두 상류부에서의 수위 분포를 정확하게 예측(평균 오차: 0.52%, 0.59%).
  • 정수제 상부 흐름:
    • HEC-RAS는 점진적인 흐름을 정확히 계산하지 못하고 불연속적인 프로파일을 생성함.
    • FLOW-3D는 점진적인 흐름 변화를 보다 정확하게 시뮬레이션(평균 오차: 1.57%, HEC-RAS: 2.48%).
  • 낙수(nape flow) 및 수력 점프(hydraulic jump) 형성:
    • HEC-RAS는 수직면을 지나가는 흐름을 제대로 시뮬레이션하지 못함.
    • FLOW-3D는 수력 점프 위치를 보다 정확하게 예측.
  • 임계수심(yc) 및 전면수심(yb) 분석
    • FLOW-3D 예측 값(yc/yb 비율 = 1.5687)이 실험값(1.5)과 가장 유사.
    • HEC-RAS는 yb를 과대 예측하여 yc/yb 비율이 1.0193으로 나타남.

4. 결론 및 제안

결론

  • FLOW-3D는 점진적 흐름, 난류, 수력 점프의 위치 등을 보다 정밀하게 예측하는데 유리함.
  • HEC-RAS는 장거리 채널에서 정상유동을 빠르게 분석하는 데 효과적이나, 급격한 흐름 변화가 있는 경우 부정확할 수 있음.
  • 낙수 영역에서 HEC-RAS는 곡면 흐름을 제대로 재현하지 못하지만, FLOW-3D는 이를 보다 현실적으로 모의.

향후 연구 방향

  • 다양한 계단 형상 및 유량 조건에서의 추가 연구 필요.
  • 실제 현장 데이터를 이용한 모델 검증 연구 진행.
  • LES(Large Eddy Simulation) 모델과의 비교 연구 수행.

5. 연구의 의의

본 연구는 FLOW-3D와 HEC-RAS를 활용하여 단일 계단형 광정수제 위를 흐르는 유동을 수치적으로 분석하고, 두 모델의 성능을 비교하였다. FLOW-3D는 난류 흐름과 수력 점프를 보다 정밀하게 예측하는 데 유용하며, HEC-RAS는 정상 유동 조건에서 경제적인 해석이 가능함을 확인하였다.

6. 참고 문헌

  1. Akan, A. O. (2006), Open Channel Hydraulics, First edition, Elsevier.
  2. Akbar, Z.A.; Habib, M.J.S.; Hassan, L.: Simulation of Hydraulic Jump through Channels Junction Using the FLOW-3D and Flunent Models, Research Journal of Recent Sciences, 4(1), 129-134 (2015).
  3. Babaali, H.; Shamsai, A.; Vosoughifar, H.: Computational Modeling of the Hydraulic Jump in the Stilling Basin with Convergence Walls Using CFD Codes, Arabian Journal for Science and Engineering, 4(2), 381–395 (2015).
  4. Chanson, H.: The Hydraulics of Open Channel Flow: An Introduction, Second edition, Elsevier (2004).
  5. Chow, V.T.: Open-Channel Hydraulics, McGraw-Hill (1959).
  6. Cook, A.C.: Comparison of One-Dimensional HEC-RAS with Two-Dimensional FESWMS Model in Flood Inundation Mapping, MSc thesis, Purdue University, USA (2008).
  7. Crookston, B.M.; Paxson, G.S.; Savage, B.M.: Hydraulic Performance of Labyrinth Weirs for High Headwater Ratios, The 4th IAHR International Symposium on Hydraulic Structures, Porto, Portugal, 1-8 (2012).
  8. FLOW-3D Documentation, Release 10.1.0, Flow Science, Inc. (2012).
  9. Graebel, W.P.: Advanced Fluid Mechanics, Elsevier (2007).
  10. Gonzalez, N.S.: Two-Dimensional Modeling of the Red River Floodway, MSc thesis, University of Manitoba, Canada (1999).
  11. Hoseini, S.H.: 3D Simulation of Flow over a Triangular Broad-Crested Weir, Journal of River Engineering, 2(2), 1-7 (2014).
  12. Khazaee, I.; Mohammadiun, M.: Effect of flow field on open channel flow properties using numerical investigation and experimental comparison, International Journal of Energy and Environment, 3(4), 617-628 (2012).
  13. Mohammed, J.R.; Qasim, J.M.: Comparison of One-Dimensional HEC-RAS with Two-Dimensional ADH for Flow over Trapezoidal Profile Weirs, Caspian Journal of Applied Sciences Research, 1(6), 1-12 (2012).
  14. Rady, R.M.: 2D-3D Modeling of Flow over Sharp-Crested Weirs, Journal of Applied Sciences Research, 7(12), 2495-2505 (2011).
  15. Siddique-E-Akbor, A.H.M.; Hossain, F.; Lee, H.; Shum, C.K.: Inter-comparison study of water level estimates derived from hydrodynamic–hydrologic model and satellite altimetry for a complex deltaic environment, Remote Sensing of Environment, Vol. 115, 1522–1531 (2011).
  16. Subramanya, K.: Flow in Open Channels, McGraw-Hill (1986).
  17. Toombes, L.; Chanson, H.: Numerical Limitations of Hydraulic Models, The 34th International
    Association for Hydraulic Research World Congress, Brisbane, Australia, 2322-2329 (2011).
Fig. 6. Results of RMA-2 & FLOW-3D Model.(Flow vector)

2D 및 3D 모델을 이용한 자연하도의 만곡부에서의 흐름 특성 연구

Fig. 6. Results of RMA-2 & FLOW-3D Model.(Flow vector)

1. 서론

  • 최근 기상이변으로 인한 국지적 홍수가 빈번해지면서 하천 만곡부에서의 흐름 특성을 정확하게 분석하는 것이 중요해짐.
  • 자연하천의 만곡부는 곡률 변화에 따라 유동 특성이 크게 변하며, 홍수 시 통수능 저하 및 범람 가능성을 증가시킴.
  • 본 연구에서는 2D RMA-2 모델과 3D FLOW-3D 모델을 이용하여 낙동강 본류의 만곡부 흐름 특성을 비교 분석함.

2. 연구 방법

연구 대상 지역

  • 연구 대상 구간: 낙동강 본류 중 낙동수위표 기준 하류 14km 구간.
  • 만곡비(Curve Ratio) = 1.044 (연구 대상 구간의 곡률).
  • 100년 빈도 홍수량을 적용하여 2D 및 3D 모델의 수치해석 수행.

FLOW-3D 기반 3D 모델링

  • VOF(Volume of Fluid) 기법을 이용하여 자유 수면 추적.
  • RNG k-ε 난류 모델을 적용하여 난류 해석 수행.
  • FAVOR(Fractional Area/Volume Obstacle Representation) 기법을 사용하여 복잡한 지형을 반영.
  • 경계 조건 설정:
    • 유입부: 부피 유량(Volume flow rate) 조건 적용.
    • 유출부: 자유 배출(Outflow) 조건 설정.
    • 벽면: No-slip 조건 적용.

3. 연구 결과

유속 특성 비교

  • 2D 모델(RMA-2)의 평균 유속이 3D 모델(FLOW-3D)보다 약 1.3배 높게 나타남.
  • 만곡부 외측에서 3D 모델은 수충(erosion)으로 인해 와류(Vortex)가 발생하였지만, 2D 모델에서는 발생하지 않음.
  • 내측으로 갈수록 두 모델 간 유속 차이가 점차 감소.
  • 최대 유속이 발생하는 위치는 두 모델에서 동일하게 나타남.

편수위(Super Elevation) 특성 비교

  • 만곡부 외측에서 최대 수위 발생, 내측에서는 상대적으로 낮은 수위 확인.
  • 2D 모델: 내측의 수위 감소율이 외측의 증가율보다 큼.
  • 3D 모델: 외측의 수위 증가율이 내측의 감소율보다 큼.
  • 3D 모델에서 외측 수위가 더 높아진 이유는 수충의 영향으로 인한 추가적인 난류 효과 때문으로 분석됨.

4. 결론 및 제안

결론

  • FLOW-3D 기반 3D 모델은 만곡부의 유동 특성을 보다 정밀하게 반영함.
  • 2D 모델은 상대적으로 계산 속도가 빠르지만, 수충 영향과 와류 발생 등의 복잡한 흐름을 정확하게 예측하기 어려움.
  • 3D 모델의 경우 복잡한 지형 및 난류 효과를 정밀하게 고려할 수 있어 하천 정비 및 홍수 예측에 유용함.

향후 연구 방향

  • 3D 모델을 활용한 다양한 곡률 및 하폭 조건에서의 흐름 특성 분석 필요.
  • 하천 내 식생 및 지형 변화가 흐름 특성에 미치는 영향 연구.
  • 실제 현장 관측 데이터를 기반으로 모델 검증 연구 수행.

5. 연구의 의의

본 연구는 FLOW-3D를 활용하여 자연하천 만곡부에서의 유동 특성을 수치적으로 분석하고, 2D 및 3D 모델 간의 차이를 비교하였다. 향후 홍수 예방 및 하천 정비 계획 수립에 기여할 수 있는 데이터 및 분석 방법을 제공한다.

6. 참고 문헌

  1. 건설교통부, 1993, 낙동강하천정비기본계획.
  2. 김창성, 2005, FLOW-3D를 이용한 교각 주변 흐름의 수치해석, 석사학위논문, 명지대학교.
  3. 박기범, 2007, 급경사 만곡부 하도의 2차원 수리특성 해석, 한국환경과학회지, 16(9), 1039-1049.
  4. 서일원, 백경오, 성기훈, 2002, S자형 만곡 수로의 흐름 특성에 관한 실험적 연구, 대한토목학회 학술대회, 11, 115-118.
  5. 안승섭, 이상일, 김정기, 박동일, 2011, 하도만곡부의 흐름특성 연구를 위한 실험적 고찰, 한국환경기술학회지, 12(1), 7-14.
  6. 안승섭, 이상일, 박동일, 김위석, 2011, 하도만곡형상에 따른 수리특성분석, 한국환경과학회지, 20(10), 1309-1317.
  7. 윤선권, 2007, FLOW-3D를 이용한 하천흐름 해석에 관한 연구, 석사학위논문, 서울시립대학교.
  8. 정재욱, 정현수, 이종설, 윤세의, 2000, RMA-2모형을 이용한 만곡수로의 흐름특성 분석, 대한토목학회논문집, 20(4-B), 479-489.
  9. 최보람, 2010, FLOW-3D를 이용한 댐 여수로 흐름현상 검토, 석사학위논문, 동아대학교.
  10. EMRL(Environmental Modeling Research Laboratory), 2000, SMS (Surface-water modeling System) RMA-2 User’s Manual, Brigham Young University, Utah, 110-240.
Fig. 6. Vector plot of turbulent energy.

FLOW-3D 모형을 이용한 용승류 모의

Fig. 6. Vector plot of turbulent energy.

1. 서론

  • 최근 일본과 한국에서 대규모 해양구조물을 이용하여 인공적으로 용승류를 발생시키는 연구가 활발히 진행되고 있음.
  • 용승류는 심층수의 영양염을 표층으로 이동시켜 어장 환경을 개선하는 효과를 가짐.
  • 본 연구에서는 FLOW-3D를 이용하여 용승류의 흐름을 수치적으로 모의하고, Marker 기법을 활용하여 영양염의 이동을 분석하는 방법을 탐색함.

2. 연구 방법

FLOW-3D 기반 CFD 모델링

  • VOF(Volume of Fluid) 기법을 사용하여 자유 수면 추적.
  • RNG k-ε 난류 모델을 적용하여 유동 해석 수행.
  • FAVOR(Fractional Area/Volume Obstacle Representation) 기법을 활용하여 복잡한 해저 구조 반영.
  • 경계 조건 설정:
    • 유입부: 일정 유량(Volume flow rate) 조건 적용.
    • 유출부: 자유 배출(Outflow) 조건 설정.
    • 벽면: No-slip 조건 적용.
  • 검사단면(Observation section) 설정
    • 검사단면에서의 영양염 농도 변화를 추적하여 용승효과를 정량적으로 분석.

3. 연구 결과

용승류 흐름 분석

  • 용승 구조물 설치 전후 비교 결과, 구조물 설치 후 수직 유속이 증가하여 영양염이 상층으로 이동함.
  • 구조물 높이에 따른 용승류의 강도 변화 확인:
    • 높이 14m: 최대 연직 유속 0.204 m/s.
    • 높이 17m: 최대 연직 유속 0.210 m/s.
  • 난류 강도 및 유동 패턴
    • 용승류가 발생하는 위치에서 난류 에너지가 증가하며, 영양염이 효과적으로 이동하는 것으로 나타남.
  • Marker 기법을 이용한 영양염 이동 분석
    • 해저에 분포한 Marker가 구조물의 용승 효과로 인해 표층으로 이동하는 것을 확인함.

4. 결론 및 제안

결론

  • FLOW-3D 기반 수치 모델이 용승류 효과를 정성적으로 분석하는 데 유용함.
  • 구조물의 높이가 증가할수록 용승류가 강해지고, 영양염의 이동 효과가 뚜렷해짐.
  • 검사단면에서의 영양염 농도 변화를 분석하면 용승효과를 사전에 평가할 수 있음.

향후 연구 방향

  • 다양한 구조물 형상과 배치 조건에서 용승효과 최적화 연구.
  • LES(Large Eddy Simulation) 모델과의 비교 연구 수행.
  • 현장 데이터를 기반으로 실험적 검증 진행.

5. 연구의 의의

본 연구는 FLOW-3D를 활용하여 인공 용승류의 유동 특성을 수치적으로 분석하고, Marker 기법을 이용하여 영양염의 이동을 정량적으로 평가하였다. 이를 통해 어장 조성 사업의 효과를 사전에 예측할 수 있는 방법론을 제시한다.

6. 참고 문헌

  1. 신정교, 김규한, 편종근 (2004). 인공리프의 용승류 발생효과에 관한 연구, 대한토목학회 정기학술대회논문집, 5548-5551.
  2. 해양수산부 (2005). 인공용승류를 이용한 어장환경 개선 연구 1차년도 보고서.
  3. 해양수산부 (2006). 인공용승류를 이용한 어장환경 개선 연구 2차년도 보고서.
  4. 해양수산부 (2007). 인공용승류를 이용한 어장환경 개선 연구 3차년도 보고서.
  5. 金卷精一, 鈴木達雄 (2001). 沖合域における漁場造成の課題, 水産工學關係試驗硏究推進會議水産基盤部會報告書, 水産工學硏究所, 23-41.
  6. 武田眞典, 左タ木洋之 (2006). 人工海底山脈漁場造成現狀課題, 全國漁港漁場整備技術硏究發表會講演集, 5, 105-120.
  7. 中島敏光 (2002). 海洋深層水の利用, 綠書房.
Fig. 2. CWP chamber

논문 요약: FLOW-3D 모형을 이용한 순환수취수펌프장 내 흐름현상 연구

FLOW-3D 모델을 이용한 순환수취수펌프장 내 흐름 현상 연구

Fig. 2. CWP chamber
Fig. 2. CWP chamber

1. 서론

  • 인도네시아는 전력 공급이 부족하여 화력발전소 건설이 증가하는 추세임.
  • 화력발전소의 안정적 운영을 위해 순환수취수펌프장(CWP Chamber)의 설계가 필수적임.
  • ANSI(1998) 설계기준에 따르면 확산각(Spreading Angle)은 20° 이내여야 하나, 현장 조건상 이를 만족할 수 없는 경우가 존재함.
  • 본 연구는 FLOW-3D를 활용한 3D 수치해석을 수행하여, 안정적인 유동 조건을 확보할 수 있는 최적의 설계를 검토하는 것이 목적임.

2. 연구 방법

FLOW-3D 기반 CFD 모델링

  • VOF(Volume of Fluid) 기법을 이용하여 자유 수면 추적.
  • RNG k-ε 난류 모델을 적용하여 유동 해석 수행.
  • FAVOR(Fractional Area/Volume Obstacle Representation) 기법을 사용하여 복잡한 구조물 형상을 정확하게 반영.
  • 경계 조건:
    • 유입부: 부피 유량(Volume flow rate) 조건 적용.
    • 유출부: 자유 배출(Outflow) 조건 적용.
    • 벽면: No-slip 조건 적용.

수치 모델 검증

  • Rodi(1997)의 사각형 구조물 주위 흐름 실험 데이터와 비교하여 모델 검증 수행.
  • 실험과의 비교 결과, 종방향 유속 분포가 잘 일치함을 확인함.

3. 연구 결과

순환수취수펌프장 내 흐름 분석

  • 유입 유속: 1.5 m/s ~ 2.5 m/s 범위에서 변화.
  • 배플(Baffle) 적용 시 유속 저감 및 유동 균등화 효과 확인.
  • 배플에서 발생하는 분리 흐름 각도는 약 15° ~ 20°이며, 이를 고려하여 하류에 배플을 배치함으로써 설계 유속(0.5 m/s 이하)을 만족시킴.

4. 결론 및 제안

결론

  • FLOW-3D를 이용한 수치 모델이 실험 결과와 높은 신뢰도를 보이며, 안정적인 유동 조건을 예측하는 데 유용함.
  • 배플을 적용한 설계를 통해 유속을 효과적으로 감소시킬 수 있음.
  • 순환수취수펌프장 설계 시, 배플의 배치와 크기를 고려하는 것이 중요함.

향후 연구 방향

  • 다양한 유량 조건에서 배플 형상 및 배열 최적화 연구.
  • LES(Large Eddy Simulation) 모델과의 비교 연구 수행.
  • 실제 현장 데이터를 활용한 검증 연구 진행.

5. 연구의 의의

본 연구는 FLOW-3D를 활용하여 순환수취수펌프장의 유동 및 난류 특성을 정량적으로 분석하고, 실험 데이터를 통해 모델의 신뢰성을 검증하였다. 이를 통해 최적의 설계를 도출하여 화력발전소의 안정적 운영을 지원할 수 있는 데이터를 제공한다.

Fig. 2. CWP chamber
Fig. 2. CWP chamber
Fig. 8. Velocity development around column (unit : m/s)
Fig. 8. Velocity development around column (unit : m/s)

6. 참고 문헌

  1. J. P. Tullis, “Modeling in Design of Pumping Pits”, Journal of the Hydraulic Division, Vol. 105 (HY9), pp. 1053-1063, 1979.
  2. C. E. Sweeney, R. A. Elder, D. Hay, “Pump Sump Design Experience: Summary”, Journal of the Hydraulic Division, Vol. 108 (HY3), pp. 361-377, 1982.
  3. G. E. Hecker, “Scale Effects in Modeling Vortices”, Symposium on Scale Effects in Modeling Hydraulic Structures, International Association for Hydraulic Research, 1984.
  4. ANSI, Pump Intake Design, New Jersey, USA, 1998. Available From: https://webstore.ansi.org/standards/hi/ansihi1998
  5. KEPRI, Design of Structure of the Thermal and Nuclear Power Plant, 1997.
  6. Y. K. Yi, S. h. Cheong, C. W. Kim, “Hydraulic and Numerical Model Experiments of Flows in Circulation Water Pump Chambers”, Journal of KWRA, Vol. 38, No. 8, pp. 631-643, 2005. DOI: http://dx.doi.org/10.3741/JKWRA.2005.38.8.631
  7. Daewoo E&C, Benghazi North Combined Cycle Power Plant, Libya – Hydraulic Calculation for C.W System, 2004.
  8. Hyundai E&C, Tripoli West 4×350 MW Power Plant Project – Calculation for Circ. Water Intake Structure, 2014.
  9. Hyundai E&C, Kalselteng 2 CFSPP (2×100 MW), 2018.
  10. Daelim, Pagbilao 420 MW Unit 3 Coal-Fired Power Project – Hydraulic Analysis for Intake and Discharge System, 2015.
  11. Hyundai E&C, Talimarjan Thermal Power Plant Expansion Project, 2014.
  12. Posco E&C, Hassyan 1 Clean Coal Project, 2015.
  13. Hyundai E&C, Mirfa Independent Water and Power Project – Hydraulic Calculation for Cooling Water System, 2015.
  14. Kepco E&C, Gangneung Anin Thermal Power Plant Units 1 & 2 (1,040 MW×2), 2016.
  15. Samsung C&T, S-Oil Distillation Recovered Heat Generation Project, 2015.
  16. Korea Western Power, The 2nd PyeongTaek Combined Cycle Power Plant 950 MW×1, 2013.
  17. Y. K. Yi, S. h. Cheong, C. W. Kim, J. G. Kim. “Hydraulic and Numerical Model Experiments of Circulation Water Intake for Boryeong Thermal Power Plant No. 7 and No. 8”, Journal of KSCE, Vol. 26, No. 5B, pp. 459-467, 2006.
  18. B. J. Park, H. K. Song, Y. H. Hur, S. W. Kang, Y. G. Park, “Estimation of Hydraulic Status on Intake Structure at Gunsan Combined Cycle Power Plant by Numerical and Physical Model Test”, Proceedings of KWRA, pp. 1884-1888, 2009.
  19. Flow Science. Flow-3D User’s Manual. Los Alamos, NM, USA, 2016.
  20. W. Rodi, “Comparison of LES and RANS calculations of the flow around bluff bodies”, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 69, No. 71, pp. 55-75, 1997. DOI: https://doi.org/10.1016/S0167-6105(97)00147-5
Fig.3. Wave profile for probe distance at 46m

Numerical Modeling for Wave Attenuation by Coastal Vegetation using FLOW-3D

FLOW-3D를 이용한 해안 식생의 파랑 감쇠에 대한 수치 모델링

1. 서론

  • 해안 식생(예: 해초)은 파랑 저감, 토양 침식 방지 및 해저 안정화 등 다양한 생태적 기능을 수행함.
  • 본 연구는 침수된 식생이 파랑 감쇠 역할을 수행하는 효율성을 수치적으로 분석함.
  • FLOW-3D®를 이용하여 파랑-식생 상호작용을 3차원 모델링하고, 기존 실험 데이터(Manca et al., 2012)와 비교하여 검증함.

2. 연구 방법

FLOW-3D 기반 CFD 모델링

  • VOF(Volume of Fluid) 기법을 이용하여 자유 수면 추적.
  • Reynolds-Averaged Navier-Stokes(RANS) 방정식을 사용하여 유동 해석 수행.
  • 난류 모델: RNG k-ε 모델 적용.
  • 경계 조건:
    • 유입: 유량 조건(volume flow rate).
    • 유출: 자유 배출(outflow) 조건.
    • 벽면: No-slip 조건 적용.
  • 식생 특성 변수:
    • 해초 초장의 길이(L), 개체 간 간격(SP), 밀도(N), 식물 높이(hs), 식물 두께(t) 반영.
  • 파랑 특성 변수:
    • 파고(H), 수심(h), 주기(T) 적용.

3. 연구 결과

파랑 감쇠 특성 분석

  • FLOW-3D 시뮬레이션 결과와 실험 데이터(Manca et al., 2012) 비교 시 오차율 10% 이내로 확인됨.
  • 파랑 감쇠율(H/H₀)은 식생 밀도가 높을수록 증가.
  • 서브머전스 비율(submergence ratio, hs/h)이 0.32일 때 식생 밀도(N=180 stems/m², 360 stems/m²) 증가에 따른 감쇠율 차이 2% 내외.
  • 파랑 감쇠는 중간 밀도의 식생에서 가장 효과적이며, 너무 높은 밀도에서는 유체 흐름이 차단되어 감쇠 효과가 감소함.

4. 결론 및 제안

결론

  • FLOW-3D 모델을 활용한 해안 식생의 파랑 감쇠 분석이 높은 신뢰성을 가짐.
  • 파랑 감쇠율은 식생 밀도 및 식생 초장에 영향을 받으며, 적절한 밀도 조절이 중요함.
  • CFD 기법을 활용한 모델링이 지속 가능한 연안 보호 설계에 유용한 정보를 제공할 수 있음.

향후 연구 방향

  • 다양한 파랑 조건에서 추가적인 실험 및 시뮬레이션 수행.
  • LES(Large Eddy Simulation) 난류 모델과 비교 연구.
  • 실제 현장 데이터를 활용한 모델 검증.

5. 연구의 의의

본 연구는 FLOW-3D를 활용하여 해안 식생의 파랑 감쇠 효과를 정량적으로 분석하고, 실험 데이터를 통해 모델의 신뢰성을 검증하였다. 연안 보호 및 지속 가능한 해양 환경 설계에 기여할 수 있는 데이터 및 분석 방법을 제공한다.

6. 참고 문헌

  1. Suzuki T, Zijlema M, Burger B, Meijer MC, Narayan S. Wave dissipation by vegetation with layer schematization in SWAN. Coast Eng [Internet]. 2012;59(1):64–71. Available from: http://dx.doi.org/10.1016/j.coastaleng.2011.07.006
  2. Knutson PL, Brochu RA, See WN. 1982. Wave damping in Spartina alterniflora marshes. 1982;(1978):87–104.
  3. Möller I, Spencer T, French JR, Leggett DJ, Dixon M. Wave transformation over saltmarshes: a field and numerical modelling study from North Norfolk, England. Estuar Coast Shelf Sci. 1999;49:411–26.
  4. Bradley K, Houser C. Relative velocity of seagrass blades: Implications for wave attenuation in low-energy environments. J Geophys Res Earth Surf. 2009;114(1):1–13.
  5. Fonseca MS, Cahalan JA. A preliminary evaluation of wave attenuation by four species of seagrass. Estuar Coast Shelf Sci. 1992;35(6):565–76.
  6. Augustin LN, Irish JL, Lynett P. Laboratory and numerical studies of wave damping by emergent and near-emergent wetland vegetation. Coast Eng [Internet]. 2009;56(3):332–40. Available from: http://dx.doi.org/10.1016/j.coastaleng.2008.09.004
  7. Stratigaki V, Manca E, Prinos P, Losada IJ, Lara JL, Sclavo M, et al. Large-scale experiments on wave propagation over Posidonia oceanica. J Hydraul Res. 2011;49(SUPPL.1):31–43.
  8. Anderson ME, Smith JM. Wave attenuation by flexible, idealized salt marsh vegetation. Coast Eng [Internet]. 2014;83:82–92. Available from: http://dx.doi.org/10.1016/j.coastaleng.2013.10.004
  9. YIPING L, ANIM DO, WANG Y, TANG C, DU W, LIXIAO N, et al. Laboratory Simulations of Wave Attenuation By an Emergent Vegetation of Artificial Phragmites Australis: an Experimental Study of an Open-Channel Wave Flume. J Environ Eng Landsc Manag [Internet]. 2015;23(4):251–66. Available from: https://journals.vgtu.lt/index.php/JEELM/article/view/1398
  10. Dalrymple RA, Kirby JT, Hwang PA. Wave Diffraction Due to Areas of Energy Dissipation. J Waterw Port, Coastal, Ocean Eng. 1984;110(1):67–79.
  11. FORMULATION z Wave Gages. 1993;119(1):30–48.
  12. Maza M, Lara JL, Losada IJ. A coupled model of submerged vegetation under oscillatory flow using Navier-Stokes equations. Coast Eng [Internet]. 2013;80:16–34. Available from: http://dx.doi.org/10.1016/j.coastaleng.2013.04.009
  13. Mendez FJ, Losada IJ. An empirical model to estimate the propagation of random breaking and nonbreaking waves over vegetation fields. Coast Eng. 2004;51(2):103–18.
  14. Zink JM, Jennings GD. Channel roughness in North Carolina mountain streams. J Am Water Resour Assoc. 2014;50(5):1354–8.
  15. Lara JL, Maza M, Ondiviela B, Trinogga J, Losada IJ, Bouma TJ, et al. Large-scale 3-D experiments of wave and current interaction with real vegetation. Part 1: Guidelines for physical modeling. Coast Eng [Internet]. 2016;107:70–83. Available from: http://dx.doi.org/10.1016/j.coastaleng.2015.09.010
  16. Christensen ED, Deigaard R. Large eddy simulation of breaking waves. Coast Eng. 2001;42(1):53–86.
  17. Choi BH, Pelinovsky E, Kim DC, Didenkulova I, Woo S. Nonlinear Processes in Geophysics: Two- and three-dimensional computation of solitary wave runup on non-plane beach. Nonlin Process Geophys. 2008;15(2006):489–502.
  18. CHEN X bin, ZHAN J min, CHEN Q. Numerical simulations of 2-D floating body driven by regular waves. J Hydrodyn [Internet]. 2016;28(5):821–931. Available from: http://dx.doi.org/10.1016/S1001-6058(16)60682-0
  19. King AT, Tinoco RO, Cowen EA. A k-ε turbulence model based on the scales of vertical shear and stem wakes valid for emergent and submerged vegetated flows. J Fluid Mech. 2012;701:1–39.
  20. Seagrasses of India. Jagtap, T.G.; Komarpant, D.S.; Rodrigues, R. Citation: World Atlas of Seagrasses, eds. Green, E.P.; Short, F.T. 101-108pp. 2003.
  21. Manca E, Cáceres I, Alsina JM, Stratigaki V, Townend I, Amos CL. Wave energy and wave-induced flow reduction by full-scale model Posidonia oceanica seagrass. Cont Shelf Res. 2012;50–51:100–16.
  22. Zhao Q, Armfield S, Tanimoto K. Numerical simulation of breaking waves by a multi-scale turbulence model. Coast Eng. 2004;51(1):53–80.
  23. Nepf H, Ghisalberti M. Flow and transport in channels with submerged vegetation. Acta Geophys. 2008;56(3):753–77.
  24. Raupach MR, Shaw RH. Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol. 1982;22(1):79–90.
  25. Folkard AM. Hydrodynamics of model Posidonia oceanica patches in shallow water. Limnol Oceanogr. 2005;50(5):1592–600.

Fig. 8 Computation of (TKE) in horizontal sections of basin at end time of simulation

The Numerical Investigation on Vortex Flow Behavior Using FLOW-3D

FLOW-3D를 이용한 와류 유동 거동에 대한 수치적 연구

1. 서론

  • 와류 침전지(Vortex Settling Basin, VSB)는 유동의 와류 현상을 이용하여 침전물을 분리하는 장치로, 기존 침전지보다 비용이 적게 들고 공간 활용도가 높음.
  • VSB 내의 유동은 강제 와류(Forced Vortex)와 자유 와류(Free Vortex)로 구성되며, 이들의 형성과 거동을 정확히 이해하는 것이 중요함.
  • 본 연구는 FLOW-3D를 이용하여 와류 침전지 내부의 3차원 난류 유동을 수치적으로 분석하고, 실험 데이터를 통해 모델의 신뢰성을 검증하는 것을 목표로 함.

2. 연구 방법

실험 및 수치 모델 개요

  • 실험 장치
    • 직경 0.7m, 깊이 1.5m의 원형 와류 침전지 사용.
    • 중앙 배출구(Flush Pipe) 직경: 0.075m.
    • 입구 및 배출구 배치는 Paul et al.(1991)의 설계 권장사항을 따름.
  • FLOW-3D 기반 CFD 시뮬레이션 설정
    • VOF(Volume of Fluid) 기법을 사용하여 자유 수면 추적.
    • RNG k-ε 난류 모델을 적용하여 난류 해석 수행.
    • 격자(Grid) 설정: 중심부 0.5cm, 벽면 주변 1cm, 나머지 영역 2cm.
    • 경계 조건:
      • 유입: 부피 유량 조건(volume flow rate).
      • 유출: 자유 배출(outflow) 경계 조건.
      • 벽면: No-slip 조건 적용.

3. 연구 결과

유동 패턴 및 와류 형성

  • 강제 와류와 자유 와류가 동시에 존재하며, 시간이 지나면서 와류 강도가 변화함.
  • 중앙부에서 강한 와류 코어 형성 후, Overflow Jet에 의해 변형되는 현상 확인.
  • 와류 중심(Core)이 초기에는 유지되다가 시간이 지나면서 점차 소멸되는 현상 관찰.

난류 강도 및 에너지 해석

  • 침전지 중앙부에서 난류 강도가 가장 높고, 벽면에서는 상대적으로 낮음.
  • 시간이 경과할수록 에너지가 감소하며, Overflow Jet이 난류 강도를 증가시키는 역할을 함.
  • 실험 결과와 비교했을 때, 수치 모델이 높은 정확도를 보이며, 최대 5% 이내의 오차율 확인.

4. 결론 및 제안

결론

  • FLOW-3D 기반 시뮬레이션이 실험 결과와 높은 신뢰도로 일치하며, 와류 침전지의 유동 거동을 정밀하게 분석할 수 있음.
  • 중앙부에서 형성된 강한 와류가 시간이 지남에 따라 소멸되며, Overflow Jet이 유동 패턴을 크게 변화시킴.
  • 기존 이론 모델(Rankine Combined Vortex)과 비교 시, 실제 유동에서는 난류 효과로 인해 와류 코어가 변형됨.

향후 연구 방향

  • 다양한 입구 및 배출구 배치 조건에서의 추가 실험 및 시뮬레이션 수행.
  • LES(Large Eddy Simulation) 모델과의 비교 연구.
  • 실제 현장 데이터를 활용한 검증 연구 진행.

5. 연구의 의의

본 연구는 FLOW-3D를 활용하여 와류 침전지의 유동 및 난류 특성을 정량적으로 분석하고, 실험 데이터를 통해 모델의 신뢰성을 검증하였다. 수처리 시스템 및 하천 공학 분야에서 VSB 설계 최적화에 기여할 수 있는 데이터 및 분석 방법을 제공한다.

6. 참고 문헌

  1. Paul, T.C., S.K. Sayal, V.S. Sakhanja and G.S. Dhillon, 1991. Vortex settling chamber design considerations. J. Hyd. Engng., 117(2): 172-189.
  2. Mashauri, D.A., 1986. Modeling of vortex settling chamber for primary clarification of water. PhD thesis, Tampere University of Technology, Tampere, Finland, pp: 217.
  3. Salakhov, F.S., 1975. Rotational design and methods of hydraulic calculation of load-controlling water intake structures for Mountain Rivers. Proceedings of Ninth Congress of the ICID, Moscow, Soviet Union, pp: 151-161.
  4. Cecen, K., 1977. Hydraulic criteria of settling basins for water treatment, hydro-power and irrigation. Proc. 17th Congress of the Int. Assoc, of Hydr. Res., BadenBaden, West Germany, pp: 275-294.
  5. Cecen, K. and N. Akmandor, 1973. Circular settling basins with horizontal floor. MAG Report No 183, TETAK, Ankara, Turkey.
  6. Cecen, K. and M. Bayazit, 1975. Some laboratory studies of sediment controlling structures calculation of load-controlling water intake structures for Mountain Rivers. Proceedings of the Ninth Congress of the ICID, Moscow, Soviet Union, pp: 107-110.
  7. Mashauri, D.A., 1986. Modeling of vortex settling chamber for primary clarification of water, PhD thesis, Tampere University of Technology, Tampere, Finland, pp: 217.
  8. Anwar, H.O., 1969. Turbulent flow in a vortex. J. Hydr. Res., 7(1): 1-29.
  9. http://www.flow3d.com/resources/flow3d-technical-papers-1.html.
  10. Chapokpour, J. and J. Farhoudi, 2011. Sediment extraction and flow structure of vortex settling basin. WASJ., 14(5): 782-793.
  11. Isfahani, A.H.G. and J.M. Brethour, 2009. On the Implementation of Two-equation Turbulence Models in FLOW-3D, Flow Science, FSI-09-TN86.
Fig. 8. Three-dimensional modeling of a serrated stepped spillway

Numerical Study of Energy Dissipation in Baffled Stepped Spillway Using Flow-3D

FLOW-3D를 이용한 배플형 계단식 여수로의 에너지 소산에 대한 수치 연구

1. 서론

  • 댐 건설은 효율적인 저수지 조성, 저장 및 최적 활용을 목표로 하며, 이에 따라 수리학적 설계가 중요함.
  • 여수로(spillway)는 댐의 보조 구조물로서 초과 유량을 안전하게 하류로 방출하는 역할을 수행하며, 이 과정에서 잠재적 에너지를 운동 에너지로 변환하여 하류부 침식을 초래할 수 있음.
  • 계단식 여수로(stepped spillway)는 유입 공기를 증가시키고 흐름 속도를 줄여 운동 에너지 소산을 향상시키는 효과가 있음.
  • 본 연구는 FLOW-3D를 이용한 배플형 계단식 여수로의 유동 및 에너지 소산 특성을 수치적으로 분석하고, 실험 결과와 비교하여 신뢰성을 평가하는 것을 목표로 함.

2. 실험 모델

  • 실험 장치 개요:
    • 계단식 여수로 모델과 모래 바닥을 포함한 수조로 구성.
    • 다양한 유량과 경사 조건에서 실험 수행.
    • 배플 블록(Block A~E)은 거친 표면을 가지며, 인접한 블록과 90° 회전된 형태로 배치됨.
  • 기존 연구(Kamyab Moghaddam et al.)에서 사용된 실험 방법론을 적용하여 모델 검증 수행.

3. 수치 모델링

  • FLOW-3D 모델 설정:
    • VOF(Volume of Fluid) 기법을 사용하여 자유 수면 추적.
    • RNG k-ε 난류 모델을 적용하여 난류 해석 수행.
    • FAVOR(Fractional Area/Volume Obstacle Representation) 기법을 적용하여 복잡한 형상을 해석 가능하게 함.
  • 경계 조건 설정:
    • 유입부(X min): 부피 유량 조건(Volume flow rate) 적용.
    • 유출부(X max): 자유 배출(Outflow) 경계 조건 설정.
    • 벽면(Y min, Y max): 대칭 경계 조건(Symmetry) 적용.
    • 상단(Z max) 및 바닥(Z min): 각각 자유 수면 및 고체 경계 설정.

4. 모델링 결과

  • FLOW-3D 시뮬레이션과 실험 비교 결과:
    • 평균 제곱근 오차(RMSE) = 0.02, 즉 실험 결과와 매우 높은 일치도 확인.
    • 배플 블록이 유동 난류를 증가시켜 전체 에너지의 77%를 소산하는 것으로 나타남.
  • 상대적 에너지 소산율(∆E/E₀) 분석:
    • 유량이 증가할수록 에너지 소산율은 감소하지만, 배플 블록이 없는 경우보다 높은 소산 효과 유지.
    • 실험 및 수치 해석 결과의 에너지 소산율 차이는 최대 2% 이내로 매우 낮음.

5. 결론 및 제안

결론

  • 배플형 계단식 여수로는 기존 계단식 여수로보다 높은 에너지 소산 효과를 가짐.
  • FLOW-3D 기반 시뮬레이션이 실험 데이터와 높은 신뢰도로 일치하며, 수리학적 거동 분석에 효과적임.
  • 배플 블록의 배열과 형상이 유동 난류 및 에너지 소산에 중요한 영향을 미침.

향후 연구 방향

  • 장기적인 캐비테이션(cavitation) 및 구조적 안전성 분석 필요.
  • 실제 현장 데이터를 기반으로 추가적인 최적 설계 연구 진행.
  • 다양한 배플 블록 형상 및 배치 조건에서의 추가 실험 수행.

6. 연구의 의의

본 연구는 FLOW-3D를 활용하여 배플형 계단식 여수로의 유동 및 에너지 소산 특성을 정량적으로 분석하고, 수치 모델의 신뢰성을 실험적으로 검증하였다. 향후 여수로 설계 최적화 및 홍수 방지 인프라 구축에 기여할 수 있는 데이터 및 분석 방법을 제공한다.

7. 참고 문헌

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Figure 10. Three-dimensional illustration of Froude number in various tailwaters. (a) 129.10 m, (b) 129.40 m, (c) 129.70 m, (d) 129.99 m, and (e) 130.30 m

Hydraulic Characteristic Analysis of Buoyant Flap Typed Storm Surge Barrier using FLOW-3D Model

FLOW-3D 모델을 이용한 부유 플랩형 폭풍 해일 방어벽의 수리 특성 분석

1. 서론

  • 본 연구는 부유 플랩형 폭풍 해일 방어벽의 수리학적 특성을 수치적으로 분석하는 것을 목적으로 함.
  • 폭풍 해일 제어 및 연안 홍수 완화에서 방어벽의 효과를 평가하기 위해 수행됨.
  • FLOW-3D 소프트웨어를 이용하여 방어벽의 유체역학적 거동을 모델링함.

2. 연구 방법

  • 전산유체역학(CFD) 기법을 적용하여 부유 플랩형 방어벽을 모델링함.
  • 수치 모델의 주요 구성 요소:
    • 레이놀즈 평균 나비에-스토크스(RANS) 방정식을 이용한 난류 모델링.
    • VOF(Volume of Fluid) 기법을 사용하여 자유 수면 추적.
    • 실제 조석(tidal) 및 폭풍 해일(storm surge) 조건을 반영한 경계 조건 적용.
  • 기존 실험 데이터를 활용하여 모델 검증 수행.

3. 연구 결과

  • 주요 연구 결과:
    • 방어벽이 수위 감소 및 파랑 에너지 저감에 효과적임을 확인.
    • 방어벽 각도에 따라 와류(vortex) 형성 및 난류 강도가 변화함.
    • 파고, 방어벽 유연성, 유속에 따라 구조적 안정성이 영향을 받음.
  • 실험 데이터와의 비교를 통해 모델의 예측 정확성이 높음을 확인함.

4. 결론

  • 부유 플랩형 폭풍 해일 방어벽은 연안 홍수 완화에 효과적인 대안이 될 수 있음.
  • CFD 시뮬레이션을 통해 방어벽 설계 최적화에 유용한 정보를 제공할 수 있음.
  • 향후 연구에서는 장기적인 구조적 내구성 및 실제 환경에서의 적용 가능성을 중점적으로 다뤄야 함.
Figure 1. Location of the study area
Figure 1. Location of the study area

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Graphical Abstract

Flow-3D Numerical Modeling of Converged Side Weir

수렴형 측방 위어의 FLOW-3D 수치 모델링

연구 배경 및 목적

문제 정의

  • 측방 위어(side weir)는 수로 및 하천에서 홍수 조절, 유량 분배 및 관개 시스템에서 중요한 역할을 함.
  • 기존 연구는 주로 단순한 프리즘형(prismatic) 채널에서 수행되었으며, 수렴형(converged) 채널에서의 측방 위어 성능 연구는 부족함.
  • 수렴형 채널에서 위어의 효율성 증대 가능성을 검토하고, FLOW-3D를 이용한 정량적 분석이 필요함.

연구 목적

  • FLOW-3D를 사용하여 수렴형 채널에서 측방 위어의 유동 특성을 수치적으로 분석.
  • 실험 모델과 비교하여 FLOW-3D의 신뢰성을 검증.
  • 수렴각 및 하류 채널 폭 변화가 위어 성능(유량 분배, 수위 변화, 에너지 손실 등)에 미치는 영향 평가.

연구 방법

실험 및 수치 모델 개요

  • 실험 환경:
    • 실험실 규모 수로(길이 700mm, 폭 310mm, 높이 480mm).
    • 다양한 위어 길이(5개), 위어 크레스트 높이(4개), 수렴각(2개), 하류 채널 폭(3개) 조건에서 총 33개 실험 수행.
    • 유량 범위: 10~100m³/h.
  • FLOW-3D 기반 CFD 시뮬레이션 설정:
    • VOF(Volume of Fluid) 기법을 사용하여 자유 수면 추적.
    • RNG k-ε 난류 모델 적용.
    • 격자(Grid) 설정: 메쉬 크기 1cm, 전체 셀 수 모델 크기에 따라 조정.
    • 경계 조건:
      • 유입: 부피 유량 조건(volume flow rate).
      • 유출: 자유 배출(outflow) 경계 조건.
      • 벽면: No-slip 조건 적용.

주요 결과

수렴형 vs. 프리즘형 채널 비교

  • 수렴형 채널에서 하류 폭을 감소시키면 위어 상류 수심이 증가하여 위어를 통한 유량 분배 증가.
  • 수렴각이 클수록 수위 및 특정 에너지가 증가하여 유출량(Qw/Q0) 비율 향상.
  • 프리즘형 채널 대비 수렴형 채널이 동일한 유량에서도 더 높은 위어 크레스트 수위를 형성하여 방류 효율성이 증가.

수위 및 유속 분포 분석

  • 위어 상류 및 중간부에서 수면 경사가 하강하는 경향, 그러나 위어 끝에서는 상승하는 패턴 확인.
  • 최대 유속이 수렴 채널에서 위어 시작점 근처에서 발생, 반면 횡방향 유속은 위어 중앙부에서 최대값 도달.
  • 에너지 손실 분석 결과, 하류 채널 폭 감소(b/B ↓)에 따라 에너지 손실 감소, 이는 유량 분배 효율 증가로 연결됨.

결론 및 향후 연구

결론

  • FLOW-3D 시뮬레이션 결과와 실험 데이터가 높은 일치도를 보이며(R² = 0.98), 수렴형 측방 위어의 유동 특성을 효과적으로 예측 가능.
  • 수렴형 채널에서 위어의 효율성이 증가하며, 하류 채널 폭이 줄어들수록 위어 상류 수위가 상승하여 방류량이 증가.
  • b/B 비율이 작을수록(즉, 하류 채널이 좁을수록) 위어의 성능이 개선됨.

향후 연구 방향

  • LES(Large Eddy Simulation) 모델과의 비교 분석 수행.
  • 다양한 채널 형상 및 유량 조건에서 추가적인 검증 수행.
  • 실제 하천 및 관개 시스템 적용을 위한 최적 설계 모델 연구.

연구의 의의

이 연구는 FLOW-3D를 활용하여 수렴형 측방 위어의 유동 및 에너지 특성을 분석하고, 실험 데이터를 통해 모델의 신뢰성을 검증하였다. 수렴형 채널 설계를 통해 위어 성능을 최적화할 수 있음을 입증하며, 실무 적용 가능성이 높음.

References

  1. Abbasi S, Fatemi S, Ghaderi A, Di Francesco S (2021). “The Effect of Geometric Parameters of the Antivortex on a Triangular Labyrinth Side Weir.” Water, 13(1), 14. https://doi.org/10.3390/w13010014
  2. Ackers P (1957). “A Theoretical Consideration of Side-weirs as Storm Water Overflows.” Proceeding of Institute of Civil Engineers, 6, 250–269.
  3. Afshar H, Hoseini SH (2013). “Experimental and 3-D Numerical Simulation of Flow Over a Rectangular Broad-Crested Weir.” International Journal of Engineering and Advanced Technology (IJEAT), 2(6), 214–219.
  4. Al-Hashimi AS, Madhloom MH, Nahi NT (2017). “Experimental and Numerical Simulation of Flow Over Broad Crested Weir and Stepped Weir Using Different Turbulence Models.” Journal of Engineering and Sustainable Development, 21(2), 28–45.
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  7. Bagheri S, Heidarpour M (2011). “Characteristics of Flow Over Rectangular Sharp Crested Side Weirs.” J Irrig Drain Eng, 138(6), 541–547. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000433
  8. Borghei SM, Parvaneh A (2011). “Discharge Characteristics of a Modified Oblique Side Weir in Subcritical Flow.” Flow Meas Instrum, 22(5), 370–376. https://doi.org/10.1016/j.flowmeasinstr.2011.04.009
  9. Granata F, Di Nunno F, Gargano R, de Marinis G (2019). “Equivalent Discharge Coefficient of Side Weirs in Circular Channel—A Lazy Machine Learning Approach.” Water, 11(11), 2406. https://doi.org/10.3390/w11112406
  10. Hager WH (1987). “Lateral Outflow Over Side Weirs.” J Hydraulic Engineering, 113(4), 491–504. https://doi.org/10.1061/(ASCE)07339429(1987)113:4(491)
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Figure 4. Bed bathymetry of the developed scour hole at Q = 0.035 m3 s

Three Dimensional Simulation of Flow Field around Series of Spur Dikes

Spur Dikes 주변의 3차원 유동장 시뮬레이션

Figure 4. Bed bathymetry of the developed scour hole at Q = 0.035 m3 s
Figure 4. Bed bathymetry of the developed scour hole at Q = 0.035 m3 s

연구 배경 및 목적

문제 정의

  • Spur Dikes는 하천 제방 보호 및 유로 조절을 위해 사용되며, 국부적인 세굴(scour)과 유동장 변화가 발생함.
  • 기존의 물리 실험은 시간과 비용이 많이 소요되므로 컴퓨터 기반 CFD(전산유체역학) 시뮬레이션을 활용한 연구가 필요함.

연구 목적

  • FLOW-3D를 이용하여 Spur Dikes 주변 유동 특성을 3차원적으로 분석.
  • 실험 데이터와 비교하여 FLOW-3D 모델의 정확성을 검증.
  • 다양한 난류 모델(RNG k-ε, LES 등)의 성능을 비교하여 최적의 난류 모델 선정.

연구 방법

실험 및 수치 모델 개요

  • 연구 대상: 연속된 세 개의 Spur Dikes가 있는 수로.
  • 실험 조건:
    • 수로 길이 12.2m, 폭 0.6m, 깊이 1.2m.
    • Sontek ADV를 이용하여 유속 측정.
    • 실험 후 세굴 형상 측정 및 모델 검증 수행.

FLOW-3D 기반 CFD 시뮬레이션 설정

  • VOF(Volume of Fluid) 기법을 사용하여 자유 수면 추적.
  • RNG k-ε, LES 및 표준 k-ε 난류 모델 비교.
  • 격자(Grid) 민감도 분석을 통해 최적의 격자 크기 결정(3mm).
  • 경계 조건:
    • 유입: 평균 속도 0.29m/s 적용.
    • 유출: 자유 배출(outflow) 경계 설정.
    • 바닥: No-slip 조건 적용, 이동 가능한 퇴적층 설정.

주요 결과

유동 및 세굴 특성 분석

  • Spur Dikes 전면에서 강한 와류(vortex) 발생 → 세굴 형성의 주요 원인.
  • RNG k-ε 모델이 실험 데이터와 가장 높은 정확도를 보임.
  • LES 모델은 고난류 영역에서 비교적 정확하지만 계산 비용이 높음.
  • 표준 k-ε 모델은 난류 에너지를 과대평가(50% 이상의 오차).

결론 및 향후 연구

결론

  • FLOW-3D 기반 시뮬레이션이 실험 결과와 높은 일치도를 보이며, Spur Dikes 주변의 유동 및 세굴 현상을 효과적으로 예측 가능.
  • RNG k-ε 모델이 가장 적합한 난류 모델로 평가됨.
  • 세굴 깊이는 초기 및 주요 세굴 단계에서 대부분 결정되며, 이후 큰 변화 없음.

향후 연구 방향

  • LES(Large Eddy Simulation) 적용 범위 확대 및 정확도 비교.
  • 실제 하천 환경과의 비교 연구 수행.
  • 세굴 예측 모델 개선을 위한 추가적인 실험 검증 수행.

연구의 의의

이 연구는 FLOW-3D를 활용하여 Spur Dikes 주변의 유동 및 세굴 현상을 정량적으로 분석하고, 수치 모델의 정확성을 실험적으로 검증하였다. 하천 관리 및 구조물 설계의 최적화에 기여할 수 있는 데이터와 분석 방법을 제공한다.

References

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  2. R.A. Kuhnle, Y. Jia, and C.V. Alonso, Measured and simulated flow near a submerged spur dike, J. Hydraul. Eng., 1348(7), 2008, 916–924.
  3. R.J. Garde, K. Subramanya, and K.D. Nambudripad, Study of scour around spur-dikes, J. Hydraul. Div., ASCE, 87(6), 1961, 23–37.
  4. E.M. Laursen, Analysis of relief bridge scour, J. Hydraul. Div., Am. Soc. Civ. Eng., 89(3), 1963, 93–118.
  5. M.A. Gill, Erosion of sand beds around spur dikes, J. Hydraul. Div., ASCE, 98(9), 1972, 1587–1602.
  6. T.F. Kwan, and B.W. Melville, Local scour and flow measurements at bridge abutments, J. Hydraul. Res., 32(5), 1994, 661–673.
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  8. M.M. Rahman, N. Nagata, Y. Muramoto, and H. Murata, Effect of side slope on flow and scouring around spur-dike-like structures, Proc., 7th Int. Symp. on River Sedimentation, Hong Kong, China, 1998, 165–171.
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  12. B. Dargahi, Flow field and local scouring around a pier. Bulletin No. TRITA-VBI-137, Hydraulic Laboratory, Royal Institute of Technology, Stockholm, Sweden, 1988.
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Figure 4 Velocity distributions around the spur dike at middle section (a) velocity contours

3D Numerical Simulation of Flow and Local Scour around a Spur Dike

Spur Dike 주변 유동 및 국부 세굴의 3차원 수치 시뮬레이션

Figure 4 Velocity distributions around the spur dike at middle section (a) velocity contours
Figure 4 Velocity distributions around the spur dike at middle section (a) velocity contours

연구 배경 및 목적

문제 정의: Spur Dike(수로 둑)는 강변 보호 및 수로 흐름 조절을 위해 사용되며, 구조물 주변의 복잡한 난류 및 세굴 현상이 발생한다. 이는 구조물의 안정성과 유지보수에 큰 영향을 미친다.
연구 목적:

  • FLOW-3D를 이용하여 Spur Dike 주변 유동장 및 세굴 과정을 수치적으로 분석.
  • 난류 모델(RNG k-ε)과 세굴 모델(Shields number 기반) 적용하여 세굴 깊이 및 흐름 변화 예측.
  • 실험 데이터와 비교하여 모델의 정확도를 검증하고, 세굴 메커니즘을 이해.

연구 방법

Spur Dike 및 유동 모델링

  • Spur Dike는 비침수(non-submerged) 조건으로 설정.
  • 연속 방정식 및 Navier-Stokes 방정식을 사용하여 유동 해석 수행.
  • VOF(Volume of Fluid) 기법을 이용하여 자유 수면 추적.
  • 세굴 모델: Shields number를 적용한 이동 가능 하상 모델.
  • 난류 모델: RNG k-ε 모델 사용.

경계 조건 및 격자 설정

  • 유입: 0.29m/s 속도의 입구 유동 경계 조건 적용.
  • 유출: 자유 유출(outflow) 경계 설정.
  • 하천 바닥: 이동 가능한 침전층으로 설정(평균 입자 크기 0.145cm, 비중 1.9g/cm³).
  • 격자 수: 약 600,000개 비균일(non-uniform) 격자 사용.

주요 결과

유동장 및 난류 특성 분석

  • Spur Dike 후류(wake zone)에서 시계방향 와류(clockwise vortex) 발생, 이는 불규칙한 타원형 형태를 보임.
  • 유속 분포 분석 결과:
    • Spur Dike 전면에서 최대 유속 0.56m/s까지 증가 후 급감.
    • Dike 후방에서 속도 회복 및 역류(backflow) 형성.
    • Horseshoe Vortex(말굽 와류)가 세굴 형성의 주요 원인.

세굴 과정 및 형상 변화

  • 세굴 과정은 초기 단계 → 주요 세굴 단계 → 균형 단계의 3단계로 구분.
  • 주요 세굴 단계에서 침수 유동과 말굽 와류가 강하게 형성, 세굴 깊이 급격히 증가.
  • 균형 단계에서는 유속이 감소하며 세굴 진행이 멈춤.
  • 실험과 비교 시 최대 세굴 깊이 7.8cm, 경사 35°로 유사한 결과 도출.

결론 및 향후 연구

결론

  • FLOW-3D 기반 세굴 시뮬레이션이 실험 결과와 높은 정확도로 일치함을 확인.
  • Spur Dike 주변 침수 유동과 말굽 와류가 주요 세굴 요인임을 입증.
  • 세굴 깊이는 초기 및 주요 세굴 단계에서 대부분 결정되며, 이후 큰 변화 없음.
  • 난류 및 퇴적물 이동의 복잡성으로 인해 실험값과의 완벽한 일치는 어렵지만, 전반적으로 유사한 패턴을 보임.

향후 연구 방향

  • 다양한 Spur Dike 형상 및 배치에 따른 유동 변화 분석.
  • LES(Large Eddy Simulation) 난류 모델과 비교 검토.
  • 세굴 예측 모델 개선을 위한 추가적인 실험 검증 수행.

연구의 의의

이 연구는 Spur Dike 주변 세굴의 수치적 분석을 수행하여, 유동 및 세굴 형상의 변화 원인을 규명하였다. 하천 구조물의 안정성 평가 및 설계 최적화에 기여할 수 있는 실용적 모델을 제시하였다​.

Figure 4 Velocity distributions around the spur dike at middle section (a) velocity contours
Figure 4 Velocity distributions around the spur dike at middle section (a) velocity contours
Figure 7 Scour development around spur dike in different times (d) 80min
Figure 7 Scour development around spur dike in different times (d) 80min
Figure 8 Scour development at section y=0.1m in different times (d) 80min
Figure 8 Scour development at section y=0.1m in different times (d) 80min

Reference

  1. Chen B. The numerical simulation of local scour in front of a vertical-wall breakwater[J]. Journal of Hydrodynamics, Ser. B. 2006, 18(3): 134-138.
  2. Duan, J. G.Mean flow and turbulence around an experimental spur dike. J. Hydraul. Eng., 2009,134 (3), 315-327.
  3. Engelund F, Fredsøe J. A sediment transport model for straight alluvial channels [J]. Nordic Hydrology. 1976, 7(5): 293-306.
  4. LI Zhong-we, YU Ming-hui. Numerical simulation of local flow field around spur dike. Wuhan university journal of hydraulic and electric engineering, 2000, 33(3): 18-22.
  5. Michiue, M., and Hinokidani, O., Calculation of 2dimensional Bed Evolution around S pur-dike, Annual Journal of Hydraulic Engineering, JSCE, 1992, Vol. 36: 61-66.
  6. Pan Qing-shen, Yu Wen-chou et al., Research summary of spur dike in foreign [J]. Yangtze River, 1979, (3):51-61. Peng ling, Nobuyuki Tamai, Y oshihisa K awahara. Numerical modeling of local scour around spur dikes. Journal of Sediment Research, 2002(1):25-29.
  7. Tingsanchali T, Maheswaran S. 2-D depth-averaged flow computation near groyne. Joumal of Hydraulic Engineering, ASCE, 1990, 116(1): 71-86.
  8. Yakhot V. Orszag S A. Renormalization-group analyses of turbulence [J]. Physical review letters. 1986, 57(14): 1722-1724.
  9. Ying Qiang. Jiao Zhi-bin. Hydraulic Properties of Groyne [M] Bingjing: Maritime Press, 2004. Zhang Han, Hajime NAKAGAWA et al. Experiment and simulation of turbulent flow in local scour around a spur dyke. International Journal of Sediment Research, Vol. 24, No. 1, 2009-33-45.  
  10. Zhang Rui-jin. River sediment dynamics. [M].Beijing: China Water Power Press, 1998. Zhang, H., Nakagawa, H., Ishigaki, T, and Muto, Y. Prediction of 3D flow field and local scouring around spur dikes. Ann. J. Hydraul. Eng., 2005, 49, 1003-1008.
Flow 3D outputs of flow depth and velocity of H =0.15m

Numerical Analysis of Hydraulic Behavior of Vertical Drop Structures Using FLOW-3D

FLOW-3D를 활용한 수직 낙차 구조물의 수리학적 거동 수치 해석

FIG8FL~4
Figure 8.FLOW-3D outputs of flow depth and velocity of H =0.15m

연구 목적

  • 본 연구는 수직 낙차 구조물(vertical drop structure)의 유동 특성을 분석하기 위해 CFD(Computational Fluid Dynamics) 모델을 활용함.
  • FLOW-3D 소프트웨어를 이용하여 자유 표면 흐름을 시뮬레이션하고, 실험 데이터와 비교하여 모델의 정확성을 검증함.
  • 수로 경사, 유입 속도, 난류 모델 선택이 낙차 구조 내 유동 패턴 및 에너지 손실에 미치는 영향을 평가함.
  • 수치 해석 결과를 기반으로 낙차 구조물의 최적 설계 조건을 도출하여 수력학적 효율성을 개선하고자 함.

연구 방법

  1. FLOW-3D 기반 수치 모델링
    • VOF(Volume of Fluid) 기법을 적용하여 자유 표면 흐름을 추적하고, 표준 k-ε 난류 모델을 사용하여 난류 효과를 분석함.
    • 격자(grid) 크기 최적화를 통해 해석 정확도를 향상시킴.
    • 수직 낙차 구조물의 유동 특성을 분석하기 위해 다양한 수로 길이 및 낙차 높이 조건을 설정함.
  2. 실험 데이터와 비교 검증
    • 실제 실험에서 측정된 하류 수심 및 에너지 손실 데이터를 CFD 결과와 비교하여 모델의 신뢰성을 평가함.
    • 낙차 구조 내 유동 속도 분포 및 충격력(impact force)을 수치적으로 분석함.
    • 다양한 격자 크기 및 난류 모델을 비교하여 최적 해석 방법을 도출함.

주요 결과

  1. 유동 거동 분석
    • 낙차 구조물에서 수류가 낙하하면서 난류 강도가 증가하며, 하류에서 수심이 증가하는 패턴을 보임.
    • 낙차 높이가 증가할수록 충격력이 증가하고, 이에 따른 에너지 손실도 커짐.
    • 하류 채널 길이가 충분할 경우 난류 효과가 감소하며, 유동이 안정화되는 경향을 보임.
  2. CFD 시뮬레이션과 실험 데이터 비교
    • FLOW-3D 모델이 실험 결과와 높은 일치도를 보이며, 평균 오차율이 5% 이하로 나타남.
    • 격자 크기가 20,000개 이상일 때 모델 정확도가 최적화됨.
    • 낙차 구조의 형상 및 유입 조건에 따라 난류 강도가 다르게 나타남.
  3. 에너지 손실 및 하류 유동 특성
    • 수로 길이가 증가할수록 에너지 손실이 감소하며, 하류 수심이 증가함.
    • 낙차 구조 설계에 따라 난류 강도가 달라지며, 이를 고려한 최적 설계가 필요함.
    • 낙차 구조 후단부에 역류(backflow)가 발생할 수 있으며, 이를 방지하기 위한 추가 설계가 요구됨.

결론

  • FLOW-3D를 활용한 수치 해석이 수직 낙차 구조물의 유동 특성을 정확하게 예측할 수 있음을 확인함.
  • 하류 수심, 유입 속도 및 난류 모델이 유동 특성 및 에너지 손실에 미치는 영향을 분석함.
  • CFD 시뮬레이션 결과와 실험 데이터가 높은 상관관계를 보이며, 낙차 구조물 설계 최적화를 위한 유용한 도구임을 입증함.
  • 향후 연구에서는 다양한 수리학적 조건을 반영한 추가적인 검증이 필요함.

Reference

  1. RAND, W.: Flow Geometry at Straight Drop Spillways. In Proceedings of the Proceedings ofthe American Society of Civil Engineers; ASCE, 1955; Vol. 81, pp. 1–13.
  2. Akram Gill, M.: Hydraulics of Rectangular Vertical Drop Structures. Journal of HydraulicResearch 1979, 17, 289–302.
  3. RAJARATNAM, N. – CHAMANI, M.R.: Energy Loss at Drops. Journal of Hydraulic Research1995, 33, 373–384.
  4. ESEN, I.I. – ALHUMOUD, J.M.; HANNAN, K.A.: Energy Loss at a Drop Structure with a Step atthe Base. Water international 2004, 29, 523–529.
  5. HONG, Y.-M. – HUANG, H.-S. – WAN, S.: Drop Characteristics of Free-Falling Nappe forAerated Straight-Drop Spillway. Journal of hydraulic research 2010, 48, 125–129.
  6. FAROUK, M. – ELGAMAL, M.: Investigation of the Performance of Single and Multi-DropHydraulic Structures. International Journal of Hydrology Science and Technology 2012, 2, 48–74.
  7. LIU, S.I. – CHEN, J.Y. – HONG, Y.M. – HUANG, H.S. – RAIKAR, R. V.: Impact Characteristics ofFree Over-Fall in Pool Zone with Upstream Bed Slope. Journal of Marine Science andTechnology 2014, 22, 9.
  8. AL-SHAIKHLI, H.I. – KHASSAF, S.I.: CFD Simulation of Waves over Mound Breakwater.Journal of Global Scientific Research 2022, 7, 2283–2291.
  9. KHASSAF, S.I. – ABBAS, H.A. Study of the Local Scour around L-Shape Groynes in ClearWater Conditions. International Journal of Engineering & Technology 2018, 7, 271–276.
  10. GESSLER, D. CFD Modeling of Spillway Performance. In Impacts of Global Climate Change;2005; pp. 1–10.
  11. RAJAB, H. – Elgizawy, A. Design of Spill Tube with Features for Controlling Air BubbleGenerated for Aircraft Applicaitons. Mechanical and Aerospace Engineering presentations2012.
  12. BERGA, L. – BUIL, J.M. – BOFILL, E. – DE CEA, J.C. – PEREZ, J.A.G.; MAÑUECO, G. -POLIMON, J. – SORIANO, A. – YAGÜE, J. Dams and Reservoirs, Societies and Environment inthe 21st Century, Two Volume Set: Proceedings of the International Symposium on Dams inthe Societies of the 21st Century, 22nd International Congress on Large Dams (ICOLD),Barcelona, Spain, 18 June 2006; CRC Press, 2006; ISBN 1482262916.
  13. AL SHAIKHLI, H.I. – KHASSAF, S.I. Using of Flow 3d as CFD Materials Approach in WavesGeneration. Materials Today: Proceedings 2022, 49, 2907–2911.
  14. CHANEL, P.G. An Evaluation of Computational Fluid Dynamics for Spillway Modeling 2009.
  15. Flow-Science FLOW-3D User Manual, Version 11 2014.
  16. MIA, M.F. – NAGO, H. Design Method of Time-Dependent Local Scour at Circular Bridge Pier.Journal of Hydraulic Engineering 2003, 129, 420–427.
  17. AL SHAIKHLI, H.I. – KHASSAF, S.I. Stepped Mound Breakwater Simulation by Using Flow 3D.Eurasian Journal of Engineering and Technology 2022, 6, 60–68.
  18. STEHLIK-BARRY, K. – BABINEC, A.J. Data Analysis with IBM SPSS Statistics; PacktPublishing Ltd, 2017; ISBN 1787280705.

Study on the Water Surge Height Line of Landslide Surge of Linear River Course Reservoir Based on FLOW-3D

FLOW-3D를 활용한 선형 하천 저수지의 산사태 파고 선 연구

Fig. 3 Geometric numerical model
Fig. 3 Geometric numerical model

연구 목적

  • 본 연구는 산사태로 인해 발생하는 해일(surge)의 전파 특성과 감쇠 과정을 분석하는 데 초점을 맞춤.
  • FLOW-3D® 시뮬레이션을 활용하여 선형 하천 저수지에서 산사태 해일이 발생하는 기작을 규명함.
  • 산사태 유입각, 하천 깊이, 하천 형상 및 산사태 질량 등 다양한 요소가 해일 높이 및 전파에 미치는 영향을 평가함.
  • 해일의 전파 과정 및 감쇠 메커니즘을 규명하여 수력학적 안정성 평가 및 방재 대책 수립에 기여하고자 함.

연구 방법

  1. FLOW-3D® 기반 수치 해석 모델 구축
    • 산사태로 인해 발생하는 해일의 거동을 모델링하기 위해 VOF(Volume of Fluid) 기법을 사용함.
    • 산사태의 초기 속도, 질량 및 유입각에 따른 해일 생성 및 전파 특성을 분석함.
    • 하천 폭 및 수심 변화에 따른 해일 감쇠 특성을 평가함.
  2. 시뮬레이션 실험 설계
    • 산사태 질량을 0.4 m × 0.2 m × 0.15 m로 고정하고, 유입각을 40°~80° 범위에서 변화시킴.
    • 다양한 수심 조건(0.5 m ~ 0.9 m)에서 해일 전파 특성을 분석함.
    • 5개 주요 측정 지점을 설정하여 해일의 초기 파고 및 전파 과정 데이터를 수집함.
  3. 결과 비교 및 검증
    • 각 실험 조건에서 해일의 최대 파고 및 전파 속도를 측정하고, 시뮬레이션 결과를 실험 데이터와 비교함.
    • 기존 연구 결과 및 실험 모델과의 비교를 통해 시뮬레이션 신뢰도를 검토함.

주요 결과

  1. 산사태 유입각에 따른 해일 발생 특성
    • 해일의 초기 파고는 유입각 60°에서 최대값을 기록하며, 이후 유입각 증가에 따라 감소하는 경향을 보임.
    • 유입각이 80° 이상일 경우, 슬라이딩 블록의 수직 충돌로 인해 에너지 손실이 증가하여 해일 높이가 감소함.
    • 유입각이 작을 경우(40° 이하), 해일 발생 에너지가 낮아지고 전파 속도도 감소함.
  2. 수심 변화에 따른 해일 전파 및 감쇠 특성
    • 동일한 조건에서 초기 해일 높이는 수심이 깊을수록 감소하는 경향을 보임.
    • 수심이 0.5 m에서 0.9 m로 증가하면, 최대 파고가 49 mm에서 33 mm로 감소함.
    • 이는 깊은 수심에서는 에너지가 더 많은 수체에 분산되기 때문으로 분석됨.
  3. 해일 전파 속도 및 감쇠 패턴
    • 해일의 전파 속도는 초기 파고 및 하천 형상에 따라 달라지며, 좁은 수로에서 감쇠가 느려지는 경향을 보임.
    • 측정 지점별 파고 감소율을 분석한 결과, 해일 감쇠율이 비선형적으로 나타남.
    • 이는 수면 저항 및 흐름 분산에 따른 에너지 손실이 비균일하게 발생하기 때문으로 해석됨.

결론

  • 산사태 유입각이 해일 발생의 주요 변수이며, 60°에서 최대 파고가 발생함.
  • 수심이 깊을수록 해일 감쇠가 더 빠르게 진행되며, 초기 파고가 낮아짐.
  • FLOW-3D® 기반 시뮬레이션을 통해 선형 하천 저수지에서의 산사태 해일 전파 및 감쇠 메커니즘을 규명할 수 있음.
  • 향후 연구에서는 다양한 하천 형상 및 실제 지형 조건을 반영한 추가 분석이 필요함.

Reference

  1. Kiersch, G. A. 1964. “Vajont Reservoir Disaster.” Civil Engineering (ASCE) 34 (3): 32-39.
  2. Hunan Hydro & Power Design Institute. 1983. Slope Engineering Geology. Beijing: Water Conservancy and Electric Power press.
  3. Wiegel, R. L. 1995. “Laboratory Studies of Gravity Waves Generated by the Movement of A Submerged Body.” Transactions-American Geophysical Union 36 (5): 759-774.
  4. Fritz, H. M., Moster, P. 2003. “Pneumatic Landslide Generator.” International Journal of Fluid Power 173 (2): 223-233.
  5. Sander, J., Hutter, K. 1992. “Evolution of Weakly Non-linear Channelized Shallow Water Waves Generated by A Moving Boundary.”Acta Mechanic 91: 119-155.
  6. Sander, J., Hutter, K. 1996. “Multiple Pulsed Debris Avalanche Emplacement at Mount St. Helens in 1980: Evidence form Numerical Continuum Flow Simulation.” Acta Mechanic 115:133-149.
  7. Heinrich, Ph. 1992. “Nonlinear Water Waves Generated by Submarine and Aerial Landslides.” Journal of Waterway, Port, Coast, and Ocean Engineering, ASCE 118: 249-266.
  8. Ataie-Ashtiani, B., Farhadi, I. A. 2006. “Stable Moving-particle Semi-implicit Method for Free Surface Flow.” Fluid Dynamic Research 38 (4): 241-256.
  9. Monaghan, J. J. 1994. “Simulating Free Surface Flows with SPH.” Journal of Computational Physics 110: 399-406.
  10. Ataie-Ashtiani, B., Shobeyri, G. 2001. “Numerical Simulation of Landslide Impulsive Waves by Incompressible Smoothed Particle Hydrodynamic.” International Journal for Numerical Method in Fluids 56: 209-232.
high froude number

Using the Calculated Froude Number for Quantifying Flow Conditions in Hydraulic Structures

수력 구조물의 유동 조건 정량화를 위한 계산된 프로우드 수(Froude Number) 활용

연구 목적

  • 본 논문은 프로우드 수(Froude Number, Fr)를 활용하여 수력 구조물 내 유동 조건을 정량적으로 평가하는 방법을 제안함.
  • 기존 실험 및 수치 해석 데이터를 분석하여, Fr이 유량, 수심, 구조물 기하학적 특성과 어떻게 연관되는지 검토함.
  • 다양한 수력 구조물(여수로, 수로, 도수로 등)에 적용할 수 있는 일반화된 Fr 기반 해석 기법을 개발함.
  • 수력 구조물 설계 및 해석에서 Fr을 활용한 예측 정확도를 향상하는 방안을 모색함.

연구 방법

  1. 프로우드 수 이론 및 모델링
    • 프로우드 수는 유동의 관성력과 중력력 간의 비율을 나타내며, 수력학적 흐름 상태(사류, 임계류, 부류)를 평가하는 중요한 매개변수임.
    • Fr 계산을 위해 기본 식을 적용함:
  • V : 유체 속도
  • g : 중력 가속도
  • L : 대표 길이(수심 또는 수력 구조물의 특성 길이)
  1. 수치 해석 및 실험 검증
    • 다양한 수력 구조물에서 유동 해석을 수행하고, Fr 값과 유동 특성 간의 관계를 분석함.
    • CFD(전산유체역학) 시뮬레이션을 통해 여수로 및 개방 수로에서 Fr 변화를 평가함.
    • 기존 문헌의 실험 데이터를 활용하여 시뮬레이션 결과를 검증하고, Fr 기반 예측 모델의 신뢰성을 평가함.
  2. Fr 값에 따른 유동 패턴 분석
    • Fr 값에 따라 흐름이 어떻게 변화하는지 정량적으로 평가함.
    • Fr < 1: 부류(subcritical flow) → 중력파 전파 가능, 유동 안정적.
    • Fr = 1: 임계류(critical flow) → 최소 에너지를 가지며, 설계에서 중요한 기준이 됨.
    • Fr > 1: 사류(supercritical flow) → 난류가 강하며, 에너지 소산이 필요함.
  3. Fr 기반 설계 적용 가능성 평가
    • Fr을 활용한 설계 기준을 도출하여, 수력 구조물 설계 및 유지관리에서 활용 가능성을 검토함.
    • 실무 엔지니어링에서 Fr을 효과적으로 적용할 수 있는 방법을 제안함.

주요 결과

  1. Fr과 유동 특성의 관계
    • Fr 값이 증가할수록 난류 강도가 증가하고, 에너지 소산이 필요함.
    • Fr 값이 1에 가까울수록 유동 안정성이 높아지며, 최적 설계 조건으로 고려 가능함.
    • 여수로와 같은 급경사 흐름에서는 높은 Fr 값이 관찰되었으며, 에너지 소산 구조물 필요성이 확인됨.
  2. CFD 및 실험 검증 결과
    • CFD 시뮬레이션 결과와 실험 데이터 간 평균 오차율은 5% 이내로 나타나 신뢰성이 높음.
    • Fr을 기반으로 유량 및 속도를 예측하는 모델이 실험값과 높은 상관성을 보임.
    • 다양한 수력 구조물에서 Fr을 활용한 해석 기법이 적용 가능함을 확인함.
  3. Fr 기반 설계 적용 가능성
    • Fr을 활용하면 구조물의 최적 유동 조건을 도출할 수 있으며, 기존 설계 기준을 보완할 수 있음.
    • 수로 및 여수로 설계에서 Fr을 고려한 흐름 안정화 기법이 필요함.
    • 유지관리 측면에서도 Fr을 활용하면 유동 상태를 빠르게 평가할 수 있음.
  4. 산업적 적용 및 향후 연구 방향
    • Fr을 활용한 설계 최적화는 수력 구조물의 효율성과 안정성을 높이는 데 기여할 수 있음.
    • 향후 연구에서는 다양한 흐름 조건에서 Fr을 적용한 추가 실험 및 해석이 필요함.
    • 실무 적용성을 높이기 위해 Fr 기반 설계 가이드라인을 개발할 필요가 있음.

결론

  • 프로우드 수(Fr)는 수력 구조물의 유동 조건을 정량적으로 평가하는 데 효과적임.
  • Fr 값이 1에 가까울수록 유동 안정성이 높아지며, 설계 기준으로 활용 가능함.
  • CFD 및 실험 데이터 검증 결과, Fr을 이용한 해석 기법이 높은 신뢰성을 보임.
  • 향후 연구에서는 다양한 수력 구조물에서 Fr 기반 설계 최적화 연구가 필요함.

Reference

  1. Flow-3D, www.flow3d.com.
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Water-Rock interaction

Using Computational Fluid Dynamics (CFD) Simulation with FLOW-3D to Reveal the Origin of the Mushroom Stone in the Xiqiao Mountain of Guangdong, China

FLOW-3D 기반 CFD 시뮬레이션을 통한 광둥성 시차오산 버섯 돌 형성 원인 분석

연구 목적

  • 본 연구는 FLOW-3D® CFD 시뮬레이션을 활용하여 Xiqiao Mountain(시차오산)의 버섯 돌(Mushroom Stone) 형성 과정을 규명함.
  • 기존 연구에서는 유수 침식(stream water erosion)이 주요 형성 원인으로 제시되었으나, 본 연구에서는 CFD 분석을 통해 침식 외에도 화학적 및 물리적 풍화 작용이 결정적인 역할을 했음을 입증하고자 함.
  • 광물 분석 및 현장 조사와 함께 컴퓨터 시뮬레이션을 수행하여 물리적, 화학적 풍화 작용과 유동 역학 간의 관계를 평가함.

연구 방법

  1. 현장 조사 및 샘플링
    • 드론(DJI Phantom 4 RTK)을 활용하여 버섯 돌의 3D 지형 데이터를 정밀 측정.
    • 암석 시료 7개를 서로 다른 위치에서 채취하여 **광물 분석(mineralogical analysis)**을 수행함.
    • 지질 나침반을 사용하여 버섯 돌 곡면의 방향 및 침식 패턴을 기록함.
  2. FLOW-3D® 기반 CFD 시뮬레이션
    • 자유 표면 유동(Free Surface Flow)을 모델링하여 홍수 시 버섯 돌 주변의 유속 및 압력 분포를 분석.
    • 난류 모델 적용: RANS(Reynolds-Averaged Navier-Stokes) 방정식을 사용하여 난류 효과를 고려함.
    • 모의 홍수 실험을 진행하여 홍수 시기 물의 흐름이 버섯 돌에 미치는 영향을 평가함.
  3. 결과 비교 및 검증
    • 광물 분석 데이터 및 현장 조사 결과를 CFD 시뮬레이션과 비교하여 풍화 및 침식 기작을 검증.
    • 침식 패턴, 유속, 압력 분포 등을 종합 분석하여 버섯 돌 형성의 주요 기작을 도출함.

주요 결과

  1. 홍수 시 버섯 돌 주변 유동 특성
    • 시뮬레이션 결과, 최고 유속은 버섯 돌의 측면에서 발생하며, 전·후면에서는 상대적으로 낮은 유속을 보임.
    • 버섯 돌의 전면(상류 방향)에서는 고압력이 발생하여 아래쪽으로 흐름이 집중됨, 이는 하부 침식을 유도함.
    • 그러나 시뮬레이션 결과, 버섯 돌의 좁은 하부 구조는 단순한 유수 침식만으로 형성될 수 없음을 보여줌.
  2. 버섯 돌 침식 패턴 및 풍화 작용
    • CFD 분석 결과, 버섯 돌 하부(풍하측)에 퇴적물이 집중적으로 형성되며, 이는 침식보다 퇴적 과정이 더 중요한 역할을 했음을 시사함.
    • 실험 데이터와 비교 시, 유수 침식만으로는 현장에서 관찰된 곡면 구조를 재현할 수 없음.
    • 대신, 장기간 퇴적물이 축적되면서 화학적 및 물리적 풍화 작용이 진행되었을 가능성이 높음.
  3. 광물 분석 결과 및 풍화 작용
    • XRD(X-ray diffraction) 분석 결과, 버섯 돌 하부의 암석은 석고(gypsum) 및 점토 광물 함량이 높으며, 이는 화학적 풍화가 활발하게 진행되었음을 의미함.
    • 석고 크리스탈이 성장하면서 암석 내부 균열을 유발하는 할로클래스티(haloclasty) 현상이 관찰됨.
    • 장기간 퇴적층 내에 존재했던 암석이 화학적 풍화 및 수분에 의한 연화 작용으로 약해진 후, 외부 퇴적물이 제거되면서 버섯 돌 하부의 곡면이 형성됨.
  4. 버섯 돌 형성 과정 및 주요 기작 정리
    • 1단계: 버섯 돌이 퇴적물 속에 매립됨 → 장기간 퇴적물 내에서 화학적 풍화가 진행됨.
    • 2단계: 퇴적물 제거 후, 풍화된 암석이 노출되면서 내부 곡면이 형성됨.
    • 3단계: 추가적인 기계적 풍화 및 석고 결정 성장이 내부 균열을 유발하며 현재의 버섯 돌 형태가 완성됨.

결론

  • 유수 침식만으로 버섯 돌이 형성되었다는 기존 가설은 CFD 시뮬레이션 결과와 일치하지 않음.
  • 광물 분석 및 화학적 풍화 모델링 결과, 할로클래스티(haloclasty) 및 습윤 연화(softening due to moisture) 작용이 버섯 돌 형성의 주요 기작으로 확인됨.
  • CFD 시뮬레이션을 통한 수력학적 해석과 광물 분석을 결합하여 자연 암석 형성 기작을 정량적으로 분석하는 새로운 접근법을 제시함.
  • 향후 연구에서는 장기적인 풍화 속도 및 추가적인 유체-암석 상호작용 모델링을 수행해야 함.

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Way

Three-dimensional numerical simulation of flow in trapezoidal cutthroat flumes based on FLOW-3D

FLOW-3D를 이용한 사다리꼴 컷스로트 플룸(Trapezoidal Cutthroat Flume) 내 유동의 3차원 수치 시뮬레이션

연구 배경 및 목적

  • 문제 정의: 물 부족 문제가 심화됨에 따라 농업용 관개 시스템에서의 효율적인 물 배분이 필수적이다.
    • 플룸(Flume)은 개방 수로(Open Channel)에서 유량을 측정하는 장치로, 기존의 직사각형 컷스로트 플룸(Rectangular Cutthroat Flume)은 큰 수두 손실(Head Loss)과 시공의 어려움을 가지고 있다.
    • 사다리꼴 채널(Trapezoidal Channel)에 적합한 유량 측정 구조물의 부재로 인해, 정확한 유량 측정이 어려운 문제가 존재한다.
  • 연구 목적:
    • FLOW-3D 소프트웨어를 사용하여 사다리꼴 컷스로트 플룸의 3차원 수치 시뮬레이션을 통해 유동 특성(속도 분포, Froude 수, 수두 손실) 분석.
    • RNG k-ε 난류 모델TruVOF 기법을 활용하여 다양한 유량 조건에서의 수치 모델 검증 및 성능 평가.
    • 실험 데이터를 바탕으로 시뮬레이션 결과 검증 및 회귀 분석을 통한 방류식 개발.

연구 방법

  1. 물리 모델 및 실험 설정
    • 사다리꼴 컷스로트 플룸 설계:
      • 길이 1.80m, 높이 0.5m, 사다리꼴 목부(Throat)의 바닥 폭 0.18m, 측벽 기울기 75°.
      • 수렴부(Converging Section), 목부(Throat Section), 발산부(Diverging Section)의 14개 측정 단면을 통해 수리학적 매개변수 측정.
    • 실험 시스템 구성:
      • 저수조, 펌핑 스테이션, 전자기 유량계, 조절 밸브, 안정화 연못, 공급 파이프, 테일게이트, 90° V-notch 위어(Weir)로 구성.
      • 낮은 수두 손실과 높은 측정 정확도를 목표로 설계.
  2. 수치 시뮬레이션 및 모델링
    • FLOW-3D의 RNG k-ε 난류 모델TruVOF 기법을 사용하여 유동 시뮬레이션.
    • 연속 방정식(Continuity Equation) 및 Navier-Stokes 방정식을 통해 비압축성 뉴턴 유체 흐름 모델링.
    • 격자 설정:
      • 격자 크기 0.02m × 0.02m × 0.02m, 총 78만 3천 개의 격자 사용.
      • FAVOR(Fractional Area Volume Obstacle Representation) 방법을 활용하여 복잡한 형상에서도 높은 정확도 보장.
    • 경계 조건 설정:
      • 입출구 경계: 유량 조건에 따른 자동 유체 높이 조절.
      • 벽면(Wall Boundary): 비투과성(Impermeable) 경계 조건.
      • 상단(Top Boundary): 대칭 경계(Symmetry Boundary).

주요 결과

  1. 모델 검증 및 속도 분포 분석
    • FLOW-3D 시뮬레이션 결과실험 데이터 간의 평균 속도 비교에서 상대 오차 10% 미만.
    • 수렴부에서는 Froude 수가 0.5 미만, 목부에서 임계 흐름(Critical Flow)이 나타남.
    • 발산부에서는 Froude 수가 감소, 수두 손실이 기존 직사각형 플룸 대비 약 9% 감소.
  2. 수두 손실(Head Loss) 비교
    • 사다리꼴 컷스로트 플룸의 수두 손실은 최대 8.955%로, 직사각형 플룸의 11.097%보다 낮음.
    • 유량 증가에 따른 수두 손실 변화 분석에서 0.045 m³/s 이상의 유량에서는 수두 손실 증가율이 감소.
  3. 방류 계산식(Discharge Calculation Formula) 도출
    • 자유 흐름(Free Flow)침수 흐름(Submerged Flow) 조건에서의 회귀 분석을 통해 방류 계산식 개발.
    • 상류 깊이와 방류량 간의 상관계수 0.992, 5% 이내의 오차율을 보이며 농업용 관개 시스템의 정확도 요건 충족.

결론 및 향후 연구

  • 결론:
    • FLOW-3D 시뮬레이션을 통해 사다리꼴 컷스로트 플룸이 직사각형 플룸 대비 높은 측정 정확도와 낮은 수두 손실을 제공.
    • 단순한 구조, 저비용, 다양한 수자원 조건에서의 적용 가능성을 입증.
    • 특히 고침전물 환경에서도 우수한 성능을 보임.
  • 향후 연구 방향:
    • 다양한 사다리꼴 채널 기울기 및 유량 조건에서의 성능 평가.
    • AI 및 머신러닝을 활용한 실시간 유량 예측 모델 개발.
    • 장기적인 현장 실험을 통한 모델의 신뢰성 강화.

연구의 의의

이 연구는 FLOW-3D를 활용하여 사다리꼴 컷스로트 플룸의 유동 특성을 정량적으로 분석하고, 정확한 유량 측정 및 수자원 관리 효율성을 높이는 설계 기준을 제시하며, 농업용 관개 시스템의 물 절약 및 생산성 향상에 기여할 수 있다​.

Reference

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Velocity Magnitude

Study of Velocity, Flow Depth and Froude Number of HDPE Diagonal Modular Pavement Using FLOW-3D

FLOW-3D를 이용한 HDPE 대각선 모듈러 포장(HDP Diagonal Modular Pavement)의 속도, 유동 깊이 및 Froude 수 연구

연구 배경 및 목적

  • 문제 정의: 기존의 아스팔트 포장 도로물의 자연스러운 흐름을 방해하고 홍수 위험을 증가시키는 환경적 문제를 초래한다.
    • 모듈러 포장 시스템(Modular Pavement System)은 투수성 재료와 중첩된 빈 공간 구조를 통해 강우 유출을 줄이고 지하수 재충전을 촉진할 수 있다.
    • 그러나 물리적 실험 방법은 비용이 많이 들고 시간 소모적이기 때문에, 수치 시뮬레이션을 통한 효율적 설계 방법이 필요하다.
  • 연구 목적:
    • FLOW-3D 소프트웨어를 활용하여 대각선 HDPE 모듈러 포장 시스템의 수리적 특성(속도, 유동 깊이, Froude 수)을 분석.
    • 말레이시아 실제 강우 데이터를 사용하여 다양한 강우 강도(5 mm/h 및 85 mm/h)에 따른 포장의 물 흡수 능력 평가.
    • 예비 설계 방법으로서의 FLOW-3D 사용 가능성 검증.

연구 방법

  1. 포장 모델 설계 및 시뮬레이션 설정
    • AutoCAD를 이용해 모듈러 포장 모델링을 수행하고, FLOW-3D 소프트웨어에서 수치 시뮬레이션을 진행.
    • 포장 모델 구성:
      • 모듈러 포장층, 자갈층, 모래층의 3가지 레이어로 구성.
      • HDPE 모듈러 포장80 mm 직경, 5 mm 두께의 얇은 대각선 기둥 구조.
      • Jabatan Kerja Raya 표준에 따라 설계.
    • 수치 모델 설정:
      • FLOW-3D의 VOF(Volume of Fluid) 기법을 사용하여 유체 흐름 및 유동 깊이 예측.
      • Navier-Stokes 방정식을 사용하여 3차원 불압축성 유동(Incompressible Flow) 시뮬레이션.
      • 모듈러 포장 모델의 경계 조건대칭(Symmetry), 연속(Continuative), 체적 유량(Volume Flow Rate), 벽(Wall) 경계로 설정.
  2. 시뮬레이션 시나리오 및 변수 설정
    • 강우 강도 시나리오:
      • 낮은 강우(5 mm/h)높은 강우(85 mm/h) 조건을 설정하여 모듈러 포장의 유동 특성 분석.
    • 측정 변수:
      • 속도(속도의 x, y, z 성분), 유동 깊이(Flow Depth), Froude 수(Fr)를 측정.
      • Froude 유속과 관성력의 비율을 나타내며, 유동 상태(서브크리티컬 또는 슈퍼크리티컬) 평가에 사용.

주요 결과

  1. 속도(X-, Y-, Z-방향) 분석
    • 시뮬레이션 결과:
      • x, y 속도z 속도보다 크게 나타남.
      • 200초 초기 단계에서 x 속도는 122.40 ~ 125.28 cm/h, 6000초 후에는 68.04 ~ 78.12 cm/h로 감소.
      • z 속도는 40.68 ~ 44.28 cm/h(200초)에서 22.32 ~ 30.6 cm/h(6000초)로 다소 적은 변화를 보임.
    • 속도 감소 원인 분석:
      • 낮은 토양 투수성으로 인해 강우 강도가 유속에 미치는 영향 미미.
      • 모듈러 포장 구조 내 작은 기공(Pore Space)과 모세관 현상(Capillarity) 제한으로 유속 감소.
  2. 유동 깊이(Flow Depth) 변화 분석
    • 모든 강우 강도 조건(5 mm/h, 85 mm/h)에서 유동 깊이는 425.65 mm로 일정하게 유지.
    • 포장 내 물의 유입 및 유출이 균형을 이루어 정상 상태(Steady State) 도달.
    • 포장 구조의 투수성 덕분에 강우 강도가 증가해도 표면 유출(Surface Runoff)이 발생하지 않음.
  3. Froude 수(Fr) 평가
    • 모든 강우 조건에서 Froude 수는 0으로 유지, 서브크리티컬 흐름(Subcritical Flow, Fr < 1) 상태.
    • 모듈러 포장이 물 저장 및 투수 역할을 수행하여 흐름 에너지를 낮추고 난류(Turbulence) 감소 효과.
    • 높은 Froude 수낮은 전단력 방출(Shear Force Discharge) 및 높은 침전물 운반 용량을 의미하지만, 본 연구에서는 낮은 Fr 값으로 침전물 운반 감소 효과 확인.

결론 및 향후 연구

  • 결론:
    • FLOW-3D 소프트웨어를 활용하여 HDPE 모듈러 포장의 수리적 특성을 정확히 분석 가능.
    • 모듈러 포장이 강우 유출을 줄이고 지하수 충전에 효과적임을 입증.
    • 말레이시아 실제 강우 데이터를 활용하여 현지 조건에서도 적합성을 보임.
    • FLOW-3D는 모듈러 포장 설계 시 예비 평가 도구로 활용 가능.
  • 향후 연구 방향:
    • 다양한 경사(Slope) 조건에서의 모듈러 포장 성능 분석 필요.
    • 최적 강우 강도 및 침투 효율성 평가를 위한 시뮬레이션 확장.
    • AI 및 머신러닝을 활용한 실시간 수리적 성능 예측 모델 개발.

연구의 의의

이 연구는 FLOW-3D를 활용하여 HDPE 대각선 모듈러 포장의 수리적 성능을 정량적으로 평가하고, 비용 효율적인 강우 관리 및 침수 예방을 위한 설계 가이드라인을 제공하며, 도시 홍수 위험을 줄이고 지속 가능한 물 관리 정책 수립에 기여할 수 있다​.

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  15. Liu et al. (2019) Laboratory Analysis on the Surface Runoff Pollution Reduction Performance ofPermeable Pavements Science of the Total Environment 691 1–8.
  16. Khan et al. (2016) Effect of Slope, Rainfall Intensity and Mulch on Erosion and Infiltrationunder Simulated Rain on Purple Soil of South-Western Sichuan Province, China Water(Switzerland) 8 (11) 1–18.
  17. Lee et al (2013) Modelling the Hydrologic Process of a Permeable Pavement System Journal ofHydrologic Engineering 20 (5) 04014070
  18. Wolff, A. (2012) Simulation of Pavement Surface Runoff using the Depth-Averaged ShallowWater Equations. 93(März), 149.
  19. Lei et al. (2020) Study on Runoff and Infiltration for Expansive Soil Slopes in Simulated RainfallWater 12 (1) 222.
  20. Inn et al. (2020) Features of the Flow Velocity and Pressure Gradient of an Undular Bore on aHorizontal Bed Physics of fluids 32 (4) 043603.
Dam

Numerical Simulation of Dam Failure Process Based on FLOW-3D

FLOW-3D를 이용한 댐 붕괴 과정의 수치 시뮬레이션

연구 배경 및 목적

  • 문제 정의: 댐 붕괴(Dam Failure)는 하류 지역의 인명 및 재산 안전에 심각한 위협을 가할 수 있다.
    • 댐 붕괴 시 발생하는 홍수예측이 어렵고 복잡한 수리학적 현상을 동반하며, 긴급 구조 및 대응 계획 마련이 필수적이다.
    • 특히 Tangjiashan 산사태 댐(Tangjiashan Landslide Dam)과 같은 장애호수(Barrier Lake)의 붕괴는 갑작스러운 월류 및 사면 불안정(Slope Instability)을 초래할 수 있다.
  • 연구 목적:
    • FLOW-3D 소프트웨어를 활용하여 Tangjiashan 산사태 댐의 붕괴 과정3차원 수치 모델링을 통해 시뮬레이션.
    • 초기 붕괴 수위(Initial Breach Water Level)의 민감도 분석을 통해 붕괴 유량 및 최종 붕괴 폭(Breach Width)에 미치는 영향 평가.
    • 비상 계획 수립 및 재난 대응을 위한 기술적 참조 자료 제공.

연구 방법

  1. 댐 모델링 및 시뮬레이션 설정
    • 모델 구축:
      • Autodesk Civil3D 소프트웨어를 사용하여 위성 원격 감지 데이터를 바탕으로 Tangjiashan 댐의 3D 모델 생성.
      • 댐의 실제 지형 데이터를 1:1 비율로 반영하여 복잡한 월류 및 붕괴 과정을 시뮬레이션.
    • FLOW-3D를 이용한 시뮬레이션:
      • 3차원 수치 모델을 통해 월류(Ovetopping) 및 붕괴 과정 재현.
      • 계산 효율성을 높이기 위해:
        • 모델 크기: 1100m × 700m × 150m.
        • 붕괴 영역(Breach Area)에는 세밀한 격자(2.5m × 2.5m × 2.5m) 사용.
        • 총 유효 격자 수: 약 390만 개.
    • 경계 조건(Boundary Condition) 설정:
      • 상류(Upstream): 압력 경계(Pressure Boundary).
      • 하류(Downstream): 자유 유출(Outflow) 경계.
      • 측면(Sides): 대칭 경계(Symmetrical Boundary).
      • 바닥(Bottom): 벽(Wall) 경계.
      • 상단(Top): 대기압과 동일한 압력 경계(Atmospheric Pressure).
  2. 민감도 분석(Sensitivity Analysis)
    • 초기 붕괴 수위 변화 시나리오:
      • 742m, 745m, 748m의 세 가지 초기 수위 조건을 설정.
      • 각각의 초기 수위에 따른 최대 붕괴 유량(Peak Breach Flow) 및 붕괴 폭 변화 분석.
    • 침식 및 퇴적 모델링:
      • 댐 재료의 물리적 특성(예: 건조 벌크 밀도 2200 kg/m³, 임계 Froude 수 0.05)을 반영.
      • 모델 입력 파라미터는 기존 연구 및 현장 측정 데이터를 활용.

주요 결과

  1. 시뮬레이션 결과 분석
    • 최대 붕괴 유량(Peak Breach Flow):
      • 742m 초기 수위에서 6937 m³/s 도달.
      • 745m 초기 수위에서는 7597 m³/s, 9.5% 증가.
      • 748m 초기 수위에서는 8542 m³/s, 23.1% 증가.
    • 최종 붕괴 폭(Breach Width):
      • 초기 수위 증가에 따라 150m → 220.8m47.2% 증가.
    • 유량 도달 시간(Time to Peak Flow):
      • 초기 수위 증가 시 도달 시간이 단축:
        • 742m 수위에서는 5.83시간, 748m에서는 3.55시간(39.1% 감소).
    • 모델 검증(Validation):
      • 시뮬레이션 결과와 현장 측정 데이터 비교:
        • 최대 붕괴 유량상대 오차 7.05%.
        • 최종 붕괴 폭의 상대 오차 4.16%.
        • 유량 도달 시간은 실제보다 약 40분 빠름.
  2. 민감도 분석 결과
    • 초기 붕괴 수위는 붕괴 과정에 매우 민감:
      • 수위가 높아질수록 붕괴 유량 및 하류 방출 유량이 급격히 증가.
      • 정확한 초기 수위 측정의 중요성 강조.

결론 및 향후 연구

  • 결론:
    • FLOW-3D 소프트웨어를 통한 Tangjiashan 댐 붕괴 시뮬레이션이 실제 현상과 높은 일치도를 보임.
    • 초기 붕괴 수위는 붕괴 유량, 최종 붕괴 폭 및 붕괴 과정 전반에 큰 영향을 미침.
    • 긴급 구조 및 대응 계획 수립 시 초기 수위 데이터를 정확히 반영할 필요.
    • 본 연구 결과는 향후 장애호수 붕괴 대응 및 재난 관리 정책 수립에 중요한 기술적 참조 자료 제공.
  • 향후 연구 방향:
    • 수치 시뮬레이션의 정확도 향상을 위해 물의 밀도 변화(퇴적물 침식에 따른 영향) 고려.
    • 다양한 초기 조건(예: 강우 패턴, 하천 유량 변화)에 따른 시나리오 분석.
    • AI 및 머신러닝을 활용한 실시간 댐 붕괴 예측 모델 개발.

연구의 의의

이 연구는 FLOW-3D를 활용하여 Tangjiashan 산사태 댐의 붕괴 과정을 정량적으로 평가하고, 재난 대응 및 비상 계획 수립을 위한 실질적인 데이터와 설계 기준을 제공하며, 장애호수 붕괴 시 인명 및 재산 피해를 최소화하는 데 기여할 수 있다​.

Reference

  1. Zuwen Yan , Yingqi Wei, Hong Cai. Formation mechanism and stability analysis of barrier dam [J].Chinese Journal of geological hazards and prevention, 2009,20(04) : 55-59.
  2. Costa J E,Schuster R L. The formation and failure of natural dams [J]. Geological Society of AmericaBulletin,1988,100 (7):1054 – 1068.
  3. Schuster R L, Costa J E,Rl S. A perspective on landslide Dams. Lands1ide Dams: processes, risk andmitigation [J]. Geotechnical Special Publication,1986,(3):1 – 20.
  4. Jianguo Zhang,Cheng Wang,Xuejun Xu . Numerical simulation of Tangjiashan Lake Flow [J] . People’sYangtze River, 2009,40(22) : 60-62.
  5. Yonghui Zhu, Beilin Fan, Jinyou Lu, Xibing Zhang, Wenjun Yang, Geng Qu. Analysis of TangjiashanLake dam-break flood and simulation of discharge scour [J]. People’s Yangtze River, 2008,39(22):79-82.DOI: 10.16232/J. CNKI. 1001-4179.2008.22.023.
  6. Tianlong Zhao, Shengshui Chen, Junjie Wang, qiming zhong,Changjing Fu. Centrifuge model test onovertopping failure of barrier dam [J] . Geotechnical engineering, 2016,38(11) : 1965-1972.
  7. Liu N,Chen Z Y,Zhang J X,et al. Draining the Tangjiashan barrier lake [J]. Journal of HydraulicEngineering,2010,136 (11 ):914-923.
  8. Shufei Li, Weizhong Hu. Possible Tangjiashan Lake of water level [J] . People’s Yangtze River,2008,39(22) : 73-75.
mornig glory test

Numerical Modelling of Flow in Morning Glory Spillways Using FLOW-3D

FLOW-3D를 이용한 모닝 글로리(Morning Glory) 월류수문에서의 유동 수치 모델링

연구 배경 및 목적

  • 문제 정의: 모닝 글로리(Morning Glory) Spillway는 댐의 수위 조절 및 홍수 방지를 위해 사용되는 원형 월류수문이다.
    • 기존 설계에서는 부유물(Suspended Load)의 영향을 간과하는 경우가 많았으며, 이는 설계 가정에 큰 변화를 초래할 수 있다.
    • 부유물 함유 흐름물의 밀도를 변화시켜 수문 성능에 영향을 미칠 수 있다.
  • 연구 목적:
    • FLOW-3D 소프트웨어를 사용하여 모닝 글로리 수문에서의 부유물 농도 변화가 유량(Flow Discharge)에 미치는 영향을 평가.
    • 3000, 6000, 9000, 12000 ppm의 부유물 농도를 적용하여 수문 상부에서 다양한 수위 조건에서의 유량 변화를 분석.
    • 수치 모델 결과를 물리적 모델 실험 데이터와 비교하여 FLOW-3D의 예측 성능을 검증.

연구 방법

  1. 수치 모델링 및 시뮬레이션 설정
    • FLOW-3D 소프트웨어VOF(Volume of Fluid) 기법FAVOR(Fractional Area-Volume Obstacle Representation) 기법을 사용하여 유동 및 고체 경계 시뮬레이션.
    • k-ε 및 RNG 난류 모델을 사용하여 난류 효과를 모델링.
    • 모닝 글로리 수문 설계:
      • 해라즈(Haraz) 댐의 모닝 글로리 Spillway를 모델링.
      • Solidworks 소프트웨어를 이용해 3D 모델링을 수행하고, FLOW-3D에 가져와 수치 시뮬레이션을 설정.
    • 부유물 농도 설정:
      • 3000, 6000, 9000, 12000 ppm의 부유물을 흐름에 추가하여 유량 변화 분석.
      • 부유물 농도가 증가함에 따라 점도 및 유체의 물리적 특성이 변화함을 고려.
  2. 경계 조건 설정
    • 입출구 및 벽면 경계 조건:
      • 입구(Inlet): 유량 조건을 일정하게 유지.
      • 출구(Outlet): 자유 유출 조건을 적용.
      • 벽면(Wall): 비투과성(Impermeable) 경계 조건 설정.
    • 공기-물 경계:
      • 자유 수면(Free Surface) 조건을 적용하여 공기와의 접촉을 고려.

주요 결과

  1. 부유물 농도 증가에 따른 유량 변화
    • 순수 물(부유물 없음) 상태에서의 평균 유량: 600 m³/s.
    • 부유물 농도에 따른 유량 감소 효과:
      • 3000 ppm: 평균 유량 605 m³/s, 유량 감소 3.8%.
      • 6000 ppm: 평균 유량 575 m³/s, 유량 감소 87.12%.
      • 9000 ppm: 평균 유량 575 m³/s, 유량 감소 7.18%.
      • 12000 ppm: 평균 유량 483 m³/s, 유량 감소 26%.
    • 부유물 농도가 증가할수록 수문을 통과하는 유량이 감소하며, 이는 부유물이 물의 점도 증가밀도 변화에 따른 흐름 저항 증가에 기인.
  2. 유동 패턴 및 수문 성능 변화
    • FLOW-3D 시뮬레이션에서 부유물 농도가 증가할수록 유동의 안정성이 감소.
    • 특히 터널 및 월류수문 목(Throat) 부분에서의 유량 변화가 뚜렷하게 나타남.
    • 수문 상부에서의 월류 유속 감소혼합 층의 두께 증가가 관찰됨.
  3. FLOW-3D 모델의 신뢰성 평가
    • FLOW-3D 시뮬레이션 결과와 실험 결과 간 높은 일치도 확인.
    • 모델 검증 결과, 예측된 유량 변화가 물리적 실험과 평균 5% 이내의 오차율을 보임.
    • 이는 FLOW-3D가 복잡한 부유물 흐름을 정확하게 모델링할 수 있음을 의미.

결론 및 향후 연구

  • 결론:
    • FLOW-3D 소프트웨어는 모닝 글로리 월류수문의 부유물 농도 변화에 따른 유량 감소를 정확히 예측할 수 있음.
    • 부유물 농도가 높을수록 유량 감소율이 증가하며, 특히 12000 ppm에서는 평균 26%의 유량 감소가 나타남.
    • 이는 댐 설계 및 운영 시 부유물 농도를 고려해야 함을 시사하며, 월류수문의 성능을 보장하기 위한 설계 기준 마련 필요.
  • 향후 연구 방향:
    • 다양한 부유물 크기 및 형태에 따른 유량 변화 추가 연구 필요.
    • 다양한 수문 형상 및 경사 조건에서 FLOW-3D 모델 검증.
    • AI 및 머신러닝을 활용한 부유물 농도 변화에 따른 유량 예측 모델 개발.

연구의 의의

이 연구는 FLOW-3D를 활용하여 모닝 글로리 월류수문의 부유물 농도 변화가 유량에 미치는 영향을 정량적으로 평가하고, 댐 안전성 및 수문 설계 최적화에 기여할 수 있는 실질적인 데이터를 제공한다​.

Reference

  1. Kavan, Jan, Jakub Ondruch, Daniel Nývlt, Filip Hrbáček, Jonathan L. Carrivick, and Kamil Láska. “Seasonal hydrological andsuspended sediment transport dynamics in proglacial streams, James Ross Island, Antarctica.” Geografiska Annaler: Series A,Physical Geography 99, no. 1 (2017): 38-55.
  2. Ervine, D. A., and A. A. Ahmed. “A Scaling relationship for a two-dimensional vertical dropshaft.” In Proc. Intl. Conf. onHydraulic Modelling of Civil Engineering Structures, pp. 195-214. 1982.
  3. Zhao, Can-Hua, David Z. Zhu, Shuang-Ke Sun, and Zhi-Ping Liu. “Experimental study of flow in a vortex drop shaft.” Journalof Hydraulic Engineering 132, no. 1 (2006): 61-68.
  4. Emamgheis, Reza Jamali, and Ebrahim Nohani. “Review of the efficiency of shaft spillway discharge influenced by sharptriangular vortex breaker blades with rectangular body.” Advances in Environmental Biology (2014): 285-290.
  5. Shemshi, Roya, and Abdorreza Kabiri-Samani. “Swirling flow at vertical shaft spillways with circular piano-key inlets.” Journalof Hydraulic Research 55, no. 2 (2017): 248-258.
  6. Coleman, H. Wayne, C. Y. Wei, and James E. Lindell. “Hydraulic design of spillways.” Hydraulic design handbook (2004): 17-41.
  7. Xianqi, Zhang. “Hydraulic characteristics of rotational flow shaft spillway for high dams.” International Journal of Heat andTechnology 33, no. 1 (2015): 167-174.
  8. Petaccia, G., and A. Fenocchi. “Experimental assessment of the stage–discharge relationship of the Heyn siphons of Bric Zerbinodam.” Flow Measurement and Instrumentation 41 (2015): 36-40.
  9. Houichi L, Ibrahim G, Achour B. Experiments for the discharge capacity of the siphon spillway having the Creager Ofitserovprofile. Int J Fluid Mech Res 2006; 33(5):395–406. http://dx.doi.org/10.1615/InterJFluidMechRes.v33.i5.10.
  10. Houichi L, Ibrahim G, Achour B. Experimental comparative study of siphon spillway and overflow spillway. Cour Savoir 2009;9:95–100.
  11. Gramatky, Ferdinand Gunner, and Kenneth Hall Robinson. “Siphon spillway.” PhD diss., California Institute of Technology,1929.
  12. Nohani, Ebrahim. “An experimental study on the effect of vortex breakers thickness on discharge efficiency for the shaftspillways.” Science International 27, no. 3 (2015).
  13. Hirt, C. W., and B. Nichols. “Flow-3D User’s Manual.” Flow Science Inc (1988).
  14. Lenzi, Mario A., and Lorenzo Marchi. “Suspended sediment load during floods in a small stream of the Dolomites (northeasternItaly).” Catena 39, no. 4 (2000): 267-282.
  15. Fokema, M. D., S. M. Kresta, and P. E. Wood. “Importance of using the correct impeller boundary conditions for CFDsimulations of stirred tanks.” The Canadian Journal of Chemical Engineering 72, no. 2 (1994): 177-183

kinetic energy

Numerical Investigation of the Effect Dimensions of Rectangular Sedimentation Tanks on Its Hydraulic Efficiency Using Flow-3D Software

FLOW-3D 소프트웨어를 이용한 직사각형 침전지(Rectangular Sedimentation Tank) 치수가 수리 효율(Hydraulic Efficiency)에 미치는 영향에 대한 수치적 연구

연구 배경 및 목적

  • 문제 정의: 침전지(Settling Basin)는 수처리 및 폐수 처리 공정에서 입자 침전(Sediment Separation)을 위해 중요한 역할을 한다.
    • 침전지의 효율을 높이기 위해서는 원활하고 균일한 흐름을 유지하고, 순환 영역(Circulation Zone)을 최소화해야 한다.
    • 기존 설계 방법은 경험적 공식에 의존하여 유체의 역학적 세부 사항을 충분히 고려하지 못하는 한계가 있다.
  • 연구 목적:
    • FLOW-3D 소프트웨어를 사용하여 직사각형 침전지의 치수(Length/Width 및 Length/Depth 비율)가 흐름 패턴과 수리 효율에 미치는 영향을 분석.
    • 침전지의 순환 영역 감소 및 침전 효율 최적화를 목표로 함.
    • L/W(길이/너비) 및 L/d(길이/깊이) 비율 변화를 통한 최적의 침전지 설계 조건 도출.

연구 방법

  1. 수치 모델링 및 시뮬레이션 설정
    • FLOW-3D 소프트웨어VOF(Volume of Fluid) 기법FAVOR(Fractional Area/Volume Obstacle Representation) 기법을 사용하여 유동 및 지형 모델링.
    • k-ε 난류 모델을 사용하여 유동 패턴을 시뮬레이션.
    • 침전지 설계:
      • 입구(Inlet) 및 출구(Outlet) 위치와 부피모든 시나리오에서 동일하게 유지.
      • 직사각형 침전지의 L/W 비율: 1, 2, 4, 8 (Case 1~4)
      • L/d 비율: 5, 7, 10 (Case 5, 3, 6)
    • 모델 검증:
      • Shahrokhi et al. 실험 데이터와 비교하여 수치 모델의 신뢰성 평가.
  2. 침전지 치수 시나리오
    • L/W 비율 시나리오:
      • 길이 증가와 너비 감소를 동시에 적용하여 순환 영역의 부피 변화 분석.
      • Case 1(정사각형, L/W = 1)부터 Case 4(L/W = 8)까지 비교.
    • L/d 비율 시나리오:
      • 깊이 감소와 함께 길이 고정(2 m) 조건에서 순환 영역 및 에너지 분포 분석.
      • Case 5(L/d = 5), Case 3(L/d = 7), Case 6(L/d = 10) 비교.

주요 결과

  1. L/W 비율 변화에 따른 영향
    • 순환 영역 부피 감소 효과:
      • L/W 비율 증가 시, 순환 영역 부피가 53% → 22%로 감소.
      • 정사각형 탱크(L/W = 1)에서 순환 영역 부피는 53%, L/W = 8에서는 22%로 감소.
    • 유속 및 에너지 분포 변화:
      • 최대 운동 에너지(red zone)가 80% → 30%로 감소.
      • 이는 입자 침전 효율을 크게 개선함을 의미.
  2. L/d 비율 변화에 따른 영향
    • 순환 영역 감소 효과:
      • L/d 비율 증가(5 → 10) 시, 순환 영역 부피 54% → 16%로 감소.
      • 깊이 감소(0.4m → 0.2m) 시, 순환 영역 감소유속 균일화 효과 발생.
    • 운동 에너지 분포 개선:
      • 최대 운동 에너지 영역 길이1.5m → 0.9m로 감소.
      • 이는 침전지 바닥에 부드럽고 균일한 흐름을 형성하여 침전 효율을 향상시킴.
  3. 모델 검증 결과
    • FLOW-3D 시뮬레이션 결과실험 데이터 간 높은 일치도 확인.
    • 속도 프로파일의 평균 제곱근 오차(RMSE)가 x 방향 0.11, 0.07, 0.08, z 방향 0.13, 0.10, 0.19로 분석됨.
    • 이는 유동 패턴 예측 정확도가 높음을 의미.

결론 및 향후 연구

  • 결론:
    • FLOW-3D를 활용한 침전지 설계 최적화 가능성 입증.
    • L/W 비율이 4 이상, L/d 비율이 7 이상일 때 최적의 침전 효율을 제공.
    • 순환 영역 부피를 감소시켜 입자 침전 성능을 개선할 수 있음.
    • 최적화된 설계건설 및 유지보수 비용 절감에도 기여할 수 있음.
  • 향후 연구 방향:
    • 다양한 형태의 침전지(L자형 등)를 대상으로 L/W 및 L/d 비율에 따른 추가 연구 필요.
    • 다양한 유동 조건 및 입자 특성을 고려한 수치 모델 고도화.
    • AI 및 머신러닝을 활용한 실시간 침전지 성능 예측 모델 개발.

연구의 의의

이 연구는 FLOW-3D 소프트웨어를 통해 직사각형 침전지의 치수 최적화를 위한 설계 가이드라인을 제공하며, 수처리 및 폐수 처리 공정의 효율을 극대화할 수 있는 실질적인 데이터와 설계 기준을 제시한다​.

Reference

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  21. A. Ghaderi, M. Dasineh, F. Aristodemo, A.Ghahramanzadeh, Characteristics of free andsubmerged hydraulic jumps over differentmacroroughnesses, Journal of Hydroinformatics, 22 (6) (2020) pp. 1554-1572.https://doi.org/10.2166/hydro.2020.298
  22. M. Ahmadi, A. Ghaderi, H. MohammadNezhad, A. Kuriqi, S. D. Francesco, NumericalInvestigation of Hydraulics in a Vertical SlotFishway with Upgraded Configurations,Water, 13 (19) (2021) pp. 1-23.https://doi.org/10.3390/w13192711
  23. S. Abbasi, S. Fatemi, A. Ghaderi, S. D. Francesco, The Effect of Geometric Parameters of the Antivortex on a Triangular Labyrinth SideWeir, Water, 13 (1) (2020) pp. 2-25. https://doi.org/10.3390/w13010014
  24. Flow-3D, Help, V.11.2, Flow Science Inc
Domain

Validation of the CFD Code Flow-3D for the Free Surface Flow Around Ship Hulls

선체 주위 자유 표면 유동을 위한 CFD 코드 Flow-3D 검증

연구 목적

  • 본 논문은 FLOW-3D®를 사용하여 선체 주변의 자유 표면 유동을 수치적으로 분석하고 실험 데이터를 기반으로 검증함.
  • DTNSRDC 5415 전투함 모델을 사용하여 난류 모델 및 수치 해석 기법을 검토함.
  • 총 저항 예측, 파형 분석 및 난류 해석을 수행하여 모델의 신뢰성을 평가함.
  • CFD 시뮬레이션의 한계를 확인하고 메쉬 민감도 및 수치 기법 최적화 방향을 제시함.

연구 방법

  1. 실험 데이터 및 모델 선정
    • 미국 해군이 개발한 DTNSRDC 5415 전투함 모델을 사용하여 수치 해석을 수행함.
    • 프루드 수(Froude Number) 범위: 0.17 ~ 0.4로 설정하여 자유 표면 유동을 시뮬레이션함.
    • 실험 데이터와 비교하여 시뮬레이션 결과의 정확성을 평가함.
  2. FLOW-3D® 시뮬레이션 설정
    • VOF(Volume of Fluid) 방법을 사용하여 자유 표면 추적을 수행함.
    • 난류 모델로 Reynolds-Averaged Navier-Stokes(RANS) 및 다양한 이류(advection) 기법을 비교 분석함.
    • 메쉬 독립성 연구를 통해 최적의 격자 해상도를 결정함.
  3. 결과 비교 및 검증
    • 실험 데이터와 비교하여 총 저항(Total Resistance) 예측 정확도를 평가함.
    • 파형 분포 및 자유 표면 형상이 실험과 얼마나 일치하는지 분석함.
    • 프루드 수(Froude Number)에 따른 저항 변화 및 난류 모델의 영향을 검토함.

주요 결과

  1. 총 저항 예측 및 비교 분석
    • 1차 이류 기법(1st order upwind advection scheme) 사용 시, 실험 대비 총 저항이 약 3배 과대 예측됨.
    • ITTC-57 방법을 적용하여 마찰 저항을 보정하면, 실험과의 오차가 절반 수준으로 감소함.
    • 2차 이류 기법(2nd order scheme)을 적용하면 총 저항 예측이 개선되었으나 여전히 약 2배 과대 평가됨.
  2. 파형 및 자유 표면 분석
    • 시뮬레이션에서 자유 표면 형상 및 파형 패턴은 실험과 유사하게 나타남.
    • 파랑 저항(Wave Resistance)은 메쉬 해상도가 높아질수록 실험값과 더 가까워짐.
    • 그러나 경계층 해석이 부족하여 마찰 저항(Frictional Resistance) 예측이 부정확함.
  3. 메쉬 민감도 연구 결과
    • 메쉬 독립성을 완전히 확보하지 못한 상태에서 총 저항이 65%까지 과대 평가됨.
    • 메쉬 해상도를 증가시킬수록 저항값이 감소하지만, 연산 비용이 크게 증가함.
    • 추가적인 연구를 통해 완전한 메쉬 독립성 확보 필요.
  4. 난류 모델 및 수치 기법 평가
    • 2차 이류 기법 + 단조 유지(Monotonicity Preserving) 조합이 가장 적절한 결과를 제공함.
    • 다중 블록 격자(Multi-Block Gridding)와 추가적인 난류 모델 적용이 필요함.
    • 향후 연구에서는 경계층 및 마찰 저항 개선을 위한 고급 난류 모델 적용이 필수적임.

결론

  • FLOW-3D®는 선체 주변 자유 표면 유동의 질적(qualitative) 분석에 적합함.
  • 총 저항 예측은 과대 평가되며, 마찰 저항 해석 능력이 제한적임.
  • 2차 이류 기법 + 단조 유지 기법 적용 시, 실험과의 상관성이 가장 높음.
  • 메쉬 독립성 확보 및 난류 모델 최적화가 추가 연구의 핵심 과제임.

Reference

  1. Barkhudarov, M., “Multi-Block GriddingTechnique for FLOW-3D”, Technical Note #59-R2, FSI-00-TN59-R2, Flow Science Inc., 2004
  2. Ferziger, H. J., and Peric, M., “ComputationalMethods for Fluid Dynamics”, 2001, SpringerVerlag
  3. Lewis, E. V., “Principles of NavalArchitecture” SNAME, USA, 1989
  4. Lin, A. C., “Bare Hull Effective PowerPredictions and Bilge Keel Orientation forDDG51 Hull Represented by Model 5415,”DTNSRDC/SPD-0200-03, 1982(http://conan.dt.navy.mil/5415/)
  5. Ratcliffe, T. J., Muntick, I., Rice, J., “SternWave Topography and Longitudinal Wave Cutsobtained on Model 5415, With and WithoutPropulsion”, DTM, USA, 2001
  6. Yao, G. F., “Development of New PressureVelocity Solvers in FLOW-3D”, Flow Science,Inc., USA, 2004
Wave

Using FLOW-3D as a CFD Materials Approach in Waves Generation

FLOW-3D를 이용한 파랑 생성의 CFD 재료 접근법

연구 목적

  • 본 연구는 FLOW-3D®를 이용하여 파랑 생성 및 파랑 붕괴 현상을 수치적으로 분석함.
  • 실험적인 접근법과 비교하여 CFD 기반 시뮬레이션의 정확도 및 적용 가능성을 평가함.
  • 포리어 급수(Fourier series) 및 CFD 모델을 적용하여 다양한 파랑 조건을 해석함.
  • 해양 구조물 및 파력 발전 설계를 위한 정확한 파랑 모델링 가능성을 탐색함.

연구 방법

  1. 파랑 수치 모델링 및 설정
    • FLOW-3D®의 자유 표면 모델(Free-Surface Model)을 활용하여 파랑 형성을 시뮬레이션함.
    • 포리어 급수(Fourier Series) 방법을 적용하여 수치적으로 파랑의 기본 형태를 정의함.
    • 난류 모델 적용: Reynolds-Averaged Navier-Stokes(RANS) 모델을 사용하여 난류 효과를 고려함.
  2. FLOW-3D® 시뮬레이션 설정
    • 초기 및 경계 조건을 설정하여 파랑의 전파 및 붕괴 과정을 분석함.
    • 다양한 파고 및 주기를 적용하여 파랑의 다양한 특성(높이, 주기, 속도 등)을 평가함.
    • 실험 데이터와 비교하여 모델의 신뢰성을 검증함.
  3. 결과 비교 및 검증
    • 시뮬레이션 결과를 실험적 연구 및 기존 문헌 데이터와 비교 분석함.
    • 파랑 생성 및 붕괴 과정에서 발생하는 동역학적 변화를 평가함.
    • 해양 구조물 및 파력 발전과의 적용 가능성을 논의함.

주요 결과

  1. 파랑 생성 및 붕괴 특성 분석
    • FLOW-3D® 시뮬레이션을 통해 다양한 높이와 주기의 파랑을 생성할 수 있음.
    • 높은 주파수의 파랑에서는 강한 붕괴(breaking) 현상이 발생하며, 저주파 파랑은 안정적인 진행성을 유지함.
    • 파랑 붕괴 시 에너지 소산 및 흐름 변화가 명확하게 나타남.
  2. 수치 모델의 신뢰성 평가
    • 실험 결과와 비교했을 때 시뮬레이션의 평균 오차율이 5~10% 수준으로 확인됨.
    • 높은 파고(high wave height)에서는 실험값보다 약간 낮은 수치를 예측하는 경향이 있음.
    • 추가적인 모델 보정 및 난류 효과 개선이 필요함.
  3. 해양 공학 및 에너지 적용 가능성
    • FLOW-3D®를 활용하면 파력 발전 시스템의 설계 최적화 가능.
    • 해양 구조물(방파제, 해상 플랫폼 등) 설계 시 파랑 하중 분석에 유용하게 적용 가능.
    • 향후 연구에서는 다양한 환경 조건에서 추가적인 시뮬레이션 검증 필요.

결론

  • FLOW-3D®를 활용한 CFD 시뮬레이션은 파랑 생성 및 붕괴 분석에 효과적임.
  • 실험 데이터와 비교했을 때 높은 신뢰성을 보이며, 일부 난류 모델 개선이 필요함.
  • 해양 공학 및 파력 발전 설계에 적용할 수 있는 가능성을 확인함.
  • 향후 연구에서는 다양한 파랑 조건 및 실제 환경 적용성을 추가로 검토해야 함.

Reference

  1. Abd Alall, Mostafa. ‘‘Numerical Investigation of hydrodynamic Performance ofDouble Submerged Breakwaters”, International Journal of Scientific &Engineering Research 11(3), (2020). ISSN 2229-5518
  2. Ahmed, Hany and Abo-Taha, M. ‘‘Numerical Investigation of Regular WavesInteraction with Submerged Breakwater”, International Journal of Scientific &Engineering Research 10(11), (2019). ISSN 2229-5518.
  3. S.T. Grilli, M.A. Losada, F. Martin, Characteristics of solitary wave breakinginduced by breakwaters, J. Waterway, Port, Coastal, Ocean Eng. 120 (1) (1994)74–92.
  4. F. Hajivalie, A. Yeganeh-Bakhtiary, Numerical study of breakwater steepnesseffect on the hydrodynamics of standing waves and steady streaming, J.Coastal Res. (2009) 658–662.
  5. F. Hajivalie, A. Yeganeh-Bakhtiary, J.D. Bricker, Numerical study of theeffect of submerged vertical breakwater dimension on wave hydrodynamicsand vortex generation, Coastal Eng. J. 57 (3) (2015) 1550009-1–1550009-21.
  6. Hayakawa, Norio, Tokuzo Hosoyamada, Shigeru Yoshida, and GozoTsujimoto. ‘‘Numerical simulation of wave fields around the submergedbreakwater with SOLA-SURF method.” In Coastal Engieering 1998, pp. 843-852. (1999).
  7. D.-S. Hur, C.-H. Kim, D.-S. Kim, J.-S. Yoon, Simulation of the nonlinear dynamicinteractions between waves, a submerged breakwater and the seabed, OceanEng. 35 (5-6) (2008) 511–522.
  8. D.-S. Hur, K.-H. Lee, D.-S. Choi, Effect of the slope gradient of submergedbreakwaters on wave energy dissipation, Eng. Appl. Comput. Fluid Mechanics 5(1) (2011) 83–98.
  9. K. Kawasaki, Numerical simulation of breaking and post-breaking wavedeformation process around a submerged breakwater, Coastal Eng. J. 41 (3-4) (1999) 201–223.
  10. B. Liang, G. Wu, F. Liu, H. Fan, H. Li, Numerical study of wave transmission overdouble submerged breakwaters using non-hydrostatic wave model,Oceanologia 57 (4) (2015) 308–317.
  11. H.A.H. Petit, P. Tönjes, M.R.A. Van Gent, P. Van Den Bosch, Numericalsimulation and validation of plunging breakers using a 2D Navier-Stokesmodel, Coastal Eng. 1994 (1995) 511–524.
  12. A. Sasikumar, A. Kamath, O. Musch, A. Erling Lothe, H. Bihs, Numerical studyon the effect of a submerged breakwater seaward of an existing breakwater forclimate change adaptation, ASME 2018 37th International Conference onOcean, Offshore and Arctic Engineering, American Society of MechanicalEngineers Digital Collection, 2018.
  13. Takahiro Uemura, A numerical simulation of the shape of submergedbreakwater to minimize mean water level rise and wave transmission,TVVR13/5004 (2013).
FLOW Vector

Analysis of Flow in the Pool of Fishway Using FLOW-3D Model

FLOW-3D 모형을 이용한 어도(Fishway) Pool 내 흐름 해석

연구 배경 및 목적

  • 문제 정의: 어도(Fishway)는 댐이나 하천에 설치되어 어류가 상류로 이동할 수 있도록 돕는 수리구조물이다. 하지만 기존 어도의 설계는 어류의 생태적 특성과 물리적 환경을 충분히 반영하지 못해 기능이 미흡한 경우가 많았다.
  • 연구 목적:
    • FLOW-3D CFD 모델을 활용하여 어도 내 Pool(휴식 공간)의 유동 특성을 분석.
    • 어류의 소상(Migration) 환경을 최적화하기 위해 월류 수심(Overflow Depth)과 유속 분포를 평가.
    • 군남홍수조절지를 대상으로 어도의 설계 조건을 검증하고 최적화 방안을 제시.

연구 방법

  1. 수치 모델링 및 시뮬레이션 설정
    • FLOW-3D 소프트웨어를 활용하여 3차원 CFD 해석 수행.
    • VOF(Volume of Fluid) 기법을 사용하여 자유 수면을 정확히 모델링.
    • RNG k-ε 난류 모델을 적용하여 난류 흐름을 해석.
    • 격자 설정:
      • 계산 영역은 4m × 4m 크기, 격자는 200 × 120 × 30 (총 720,000개) 사용.
      • 격자 간격은 x 방향 0.18m, y 방향 0.14m ~ 0.88m, z 방향 0.07m.
  2. 어도 설계 및 실험 조건
    • 대상지: 군남홍수조절지 내 Pool식 어도.
    • 수치 모델 검증:
      • 기존 잠실수중보 어도의 최적 월류 수심인 10 cm를 적용.
      • 초기 조건:
        • 풀 내 물의 흐름이 정지된 상태에서 격벽 상단부의 월류를 시작으로 계산.
        • 물의 물리적 성질:
          • 온도 20℃, 밀도 1,000 kg/m³, 동점성계수 1.005 × 10⁻⁶ m²/s, 중력가속도 9.81 m/s², 조도계수 0.05.
  3. 분석 항목
    • 유속 및 유동 패턴:
      • Pool 내 유입어도 노치(Notch)와 잠공(Orifice) 부분에서의 최대 유속 분석.
      • 순환류 발생 여부유속의 범위 평가.
    • 월류 수심 변화에 따른 영향:
      • 월류 수심 10 cm를 기준으로, 유입 유속 증가 시 어류의 소상 환경 변화를 분석.

주요 결과

  1. 유속 및 순환류 분석
    • 월류 수심이 10 cm인 경우:
      • Pool 내 최대 유속 0.4 m/s 이하 유지.
      • 국부적 집중 유속에 의해 순환류 발생.
      • 유속의 최대 범위 0.15 m/s를 넘지 않음.
      • 이는 어류의 중간 휴식처로서 적절한 환경을 제공.
  2. 월류 수심 증가 시 어류 소상 환경 변화
    • 월류 수심이 10 cm를 초과할 경우:
      • 풀 내 유입 유속 증가로 어류의 소상 환경이 불량해질 것으로 예상.
      • 특히 어류의 돌진 속도를 초과하는 유속 발생이동 어려움이 발생할 수 있음.
  3. FLOW-3D 모델의 신뢰성 평가
    • 정상 상태 도달 시간운동에너지가 일정하게 유지되는 시점으로 간주하여 효율적인 해석을 수행.
    • 모델 결과와 기존 연구 비교:
      • 기존 잠실수중보 어도의 최적 수심 결과와 일치.
      • 어류 이동을 위한 안전하고 안정적인 유속 분포를 확보.

결론 및 향후 연구

  • 결론:
    • FLOW-3D를 활용한 어도 내 유동 해석이 실질적인 어류 소상 환경 평가에 유용함을 입증.
    • 월류 수심 10 cm를 유지할 때 어류의 휴식처로 최적의 환경을 제공할 수 있음.
    • 월류 수심이 증가할 경우 유입 유속이 증가하여 어류 이동에 부정적인 영향을 미칠 수 있음.
    • 격벽부의 월류 수심을 10 cm로 유지하여 어류의 소상 환경을 최적화할 필요가 있음.
  • 향후 연구 방향:
    • 다양한 어류의 종류 및 크기에 따른 최적 유속 및 수심 조건 추가 검토.
    • 다양한 난류 모델(예: LES, k-ω 모델) 적용 및 비교.
    • AI 및 머신러닝을 활용한 어도 내 유동 예측 모델 개발.
    • 계절 및 유량 변화에 따른 어도 설계 최적화 연구.

연구의 의의

이 연구는 FLOW-3D를 활용하여 어도 내 유동 특성을 정량적으로 평가하고, 어류 소상 환경을 최적화할 수 있는 설계 지침을 제시하며, 자연 생태계 보전 및 수산자원 보호에 기여할 수 있다​.

Reference

  1. 김혜성, 윤용진, 이동훈, 이은태(2007).어도 및 유인수로의 공간적 배치와 흐름 한국수자원학회 학술 발표회논문집 ,한국수자원학회 , pp. 602-606.
  2. 이진원, 강창수, 이삼희(2000). 혼합형 어도 개발 및 FLUENT 수치모형에 의한 적정성 검토 한국수
    자원학회 학술발표회논문집 한국수자원학회 , pp. 667-672.
  3. 한국수자원학회 (2005). 댐설계기준, 한국수자원학회 .
Numerical-modelling

A Study of the Conditions of Energy Dissipation in Stepped Spillways with Λ-shaped step Using FLOW-3D

FLOW-3D를 이용한 Λ자형 계단식 여수로의 에너지 소산 조건 연구

연구 목적

  • 본 논문은 FLOW-3D를 활용하여 Λ자형 계단식 여수로(stepped spillway)의 에너지 소산 효과를 분석함.
  • 기존 계단식 여수로와 Λ자형 계단식 여수로의 유동 특성을 비교하여 에너지 소산 성능을 평가함.
  • 다양한 유량 조건에서 난류 구조 및 수력 특성을 해석하여 최적의 설계 조건을 탐색함.
  • 수치 해석을 통해 실험적 연구의 한계를 보완하고, 여수로 설계 최적화 가능성을 검토함.

연구 방법

  1. 여수로 모델링 및 실험 설정
    • Λ자형 계단식 여수로와 기존 계단식 여수로를 비교하기 위해 3D 모델을 구축함.
    • 다양한 유량 조건에서 수면 형상, 속도 분포, 공기 혼입 효과 등을 평가함.
    • 실험 데이터를 통해 시뮬레이션 결과를 검증하고, 모델의 신뢰성을 평가함.
  2. FLOW-3D 시뮬레이션 설정
    • VOF(Volume of Fluid) 기법을 적용하여 자유수면 흐름을 해석함.
    • 난류 모델로 RNG k−εk-\varepsilonk−ε 방정식을 사용하여 유동 특성을 분석함.
    • 메쉬 독립성 검토를 통해 최적의 해상도를 설정하고 계산 정확도를 높임.
  3. 결과 비교 및 검증
    • 실험 데이터를 바탕으로 에너지 소산율 및 유동 패턴을 비교 분석함.
    • Λ자형 계단식 여수로와 기존 계단식 여수로 간의 차이를 정량적으로 평가함.
    • 시뮬레이션 결과와 실험 데이터 간의 평균 오차율을 계산하여 모델의 정확성을 검증함.
  4. 추가 분석
    • 유량 변화가 여수로 내 유동 특성 및 에너지 소산에 미치는 영향을 연구함.
    • 공기 혼입 현상이 여수로 성능에 미치는 영향을 평가함.
    • 향후 연구 방향으로 추가적인 실험적 검증 및 최적 설계 기법을 제안함.

주요 결과

  1. 에너지 소산 성능 비교
    • Λ자형 계단식 여수로는 기존 계단식 여수로보다 평균 12~18% 높은 에너지 소산율을 보임.
    • 높은 유량 조건에서도 안정적인 유동을 유지하며, 월류(overflow) 및 난류 강도가 감소함.
    • 기존 계단식 여수로에 비해 낙하한 물이 계단 표면에서 분산되면서 충격 에너지가 감소함.
  2. 유동 패턴 및 난류 구조
    • Λ자형 계단식 여수로에서는 물이 계단 측면으로 확산되면서 유동이 균등하게 분포됨.
    • 기존 계단식 여수로에서는 수직 방향 난류가 강하게 발생하며, 불균형한 흐름이 형성됨.
    • 계단 형상이 난류 구조 및 에너지 소산 효율에 중요한 영향을 미침.
  3. 공기 혼입 효과
    • Λ자형 계단식 여수로에서는 공기 혼입이 균일하게 발생하여 압력 변화가 완화됨.
    • 기존 계단식 여수로보다 기포 형성이 균일하며, 수압 변동이 줄어들어 구조적 안정성이 향상됨.
    • 공기 함유량이 증가하면 에너지 소산 효과가 더욱 높아지는 경향을 보임.
  4. 시뮬레이션과 실험 비교
    • 실험 데이터와 시뮬레이션 결과 간 평균 오차율은 4~7% 수준으로 나타남.
    • 특정 유량 조건에서 시뮬레이션 결과가 실험값보다 다소 낮게 예측되는 경향이 있음.
    • 메쉬 해상도 및 난류 모델 보정을 통해 예측 정확도를 향상시킬 수 있음.

결론

  • Λ자형 계단식 여수로는 기존 계단식 여수로보다 높은 에너지 소산 효과를 보임.
  • 공기 혼입이 균일하게 발생하여 수압 변동이 줄어들고 구조적 안정성이 증가함.
  • 실험과 시뮬레이션 결과 간의 높은 상관성을 확인함.
  • 향후 연구에서는 다양한 계단 형상과 추가적인 실험적 검증이 필요함.

Reference

  1. Chanson, Hubert. Hydraulics of stepped chutes and spillways. CRC Press, 2002.
  2. Cassidy, John J. “Irrotational flow over spillways of finite height.” Journal of the Engineering Mechanics Division 91, no. 6(1965): 155-176.
  3. Sorensen, Robert M. “Stepped spillway hydraulic model investigation.” Journal of Hydraulic Engineering 111, no. 12 (1985):1461-1472.
  4. Pegram, Geoffrey GS, Andrew K. Officer, and Samuel R. Mottram. “Hydraulics of skimming flow on modeled stepped spillways.”Journal of hydraulic engineering 125, no. 5 (1999): 500-510.
  5. Tabbara, Mazen, Jean Chatila, and Rita Awwad. “Computational simulation of flow over stepped spillways.” Computers &structures 83, no. 27 (2005): 2215-2224.
  6. Pedram, A and Mansoori, A. “Study on the end sill stepped spillway energy dissipation”, Seventh Iranian Hydraulic Conference,Power and Water University of Technology, Tehran, Iran, (2008) (In Persian).
  7. Naderi Rad, A et al. “Energy dissipation in various types of stepped spillways including simple, sills, and sloped ones usingFLUENT numerical model”, journal of civil and environmental engineering 39, no 1 (2009) (In Persian).
  8. Stephenson, D. “Energy dissipation down stepped spillways.” International water power & dam construction 43, no. 9 (1991):27-30.
  9. Soori, S and Mansoori, A. “compared energy dissipation in Nappe flow and Skimming flow regime using FLOW-3D”,International Conference on Civil, Architecture and Urban Development, Islamic Azad University, Tabriz, Iran, (2013) (In Persian).
  10. Pfister, Michael, Willi H. Hager, and Hans-Erwin Minor. “Bottom aeration of stepped spillways.” Journal of HydraulicEngineering 132, no. 8 (2006): 850-853.
  11. Pfister, Michael, and Willi H. Hager. “Self-entrainment of air on stepped spillways.” International Journal of Multiphase Flow37, no. 2 (2011): 99-107.
  12. Hamedi, Amirmasoud, Mohammad Hajigholizadeh, and Abbas Mansoori. “Flow Simulation and Energy Loss Estimation in theNappe Flow Regime of Stepped Spillways with Inclined Steps and End Sill: A Numerical Approach.” Civil Engineering Journal 2,no. 9 (2016): 426-437.
  13. Sedaghatnejad, S. “Investigation of energy dissipation in the end sill stepped spillways”, Master thesis, Sharif University ofTechnology, (2009)..
Comparison-of-waves-overtopping-discharge

Study on Wave Overtopping Discharge Affected by Guiding Wall Angle of Wave Dragon Device Using FLOW-3D Software

FLOW-3D 소프트웨어를 이용한 Wave Dragon 장치의 안내벽 각도가 월류 유량에 미치는 영향 연구


연구 배경 및 목적

  • 문제 정의: 파력 에너지 변환 장치(Wave Energy Converter, WEC)는 파도의 에너지를 전기로 변환하는 장치로, 그중 Wave Dragon은 월류 방식(overtopping)을 이용하는 대표적인 WEC 중 하나이다.
  • 연구 목적: Wave Dragon 장치의 안내벽(Reflector) 각도가 월류 유량(overtopping discharge)에 미치는 영향을 분석하고, 최적의 안내벽 각도를 도출하는 것.
  • 접근법: CFD(Computational Fluid Dynamics) 소프트웨어인 FLOW-3D를 활용하여 안내벽 각도와 파고(wave height) 변화에 따른 월류 유량을 시뮬레이션하고 실험 데이터와 비교 분석.

연구 방법

  1. Wave Dragon 장치 개요
    • Wave Dragon은 세 가지 주요 구성 요소로 이루어짐:
      1. 안내벽(Guiding Walls): 파도를 유도하여 경사면(Ramp)으로 향하게 함.
      2. 경사면(Ramp): 파도를 저수조(Reservoir)로 유입시킴.
      3. 수력 터빈(Hydro Turbines): 저수조에 저장된 물이 터빈을 통과하면서 전기를 생산.
  2. FLOW-3D 기반 수치 모델링
    • Navier-Stokes 방정식 및 연속 방정식을 사용하여 유체 흐름을 모델링.
    • VOF(Volume of Fluid) 기법을 활용하여 자유 수면을 해석.
    • 메쉬 설정: 격자 독립성 검토를 통해 최적의 해상도를 확보.
    • 실험 데이터 검증: 기존 연구 및 실험 결과와 시뮬레이션 결과를 비교하여 모델 신뢰성 평가.
  3. 시뮬레이션 변수
    • 파고(Wave Height): 0.2m ~ 1.5m 범위에서 변화.
    • 안내벽 각도(Guiding Wall Angle): 50°, 60°, 70°, 80°, 90°.
    • 월류량 측정: 안내벽 각도 및 파고에 따른 월류 유량을 비교 분석.

주요 결과

  1. 안내벽 각도와 월류량의 관계
    • 안내벽 각도가 80°에서 최대 월류량을 기록.
    • 50°, 60°, 70°에서는 월류량이 감소하며, 90°에서는 파도의 속도가 낮아져 월류량이 다소 감소.
  2. 파고와 월류량의 관계
    • 파고가 증가할수록 월류량이 증가하는 경향을 보임.
    • 1.5m 파고에서 가장 높은 월류량이 발생.
  3. 시뮬레이션과 실험 데이터 비교
    • FLOW-3D 시뮬레이션 결과와 실험 데이터 간 오차는 평균 15% 이내로, 모델이 신뢰할 만한 정확도를 보임.

결론 및 향후 연구

  • 결론:
    • Wave Dragon 장치의 안내벽 각도가 월류 유량에 중요한 영향을 미치며, 80°가 최적의 각도로 나타남.
    • 90° 이상에서는 파도 반사가 줄어들어 효율이 낮아지고, 50°~70°에서는 월류 유량이 감소함.
  • 향후 연구 방향:
    • 실험적 검증을 확장하여 다양한 해양 조건에서의 성능 평가.
    • 터빈 효율을 고려한 최적의 수력 에너지 변환 설계 연구.
    • 다중 안내벽 설계 및 추가적인 CFD 기법 적용을 통한 성능 개선.

연구의 의의

이 연구는 Wave Dragon과 같은 월류형 WEC의 성능을 최적화하기 위한 CFD 기반 설계 평가 방법을 제시하며, 파력 발전 시스템의 효율성을 향상시키기 위한 실용적인 가이드라인을 제공한다.

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setting

Predicting and Optimizing the Infuenced Parameters for CulvertOutlet Scouring Utilizing Coupled FLOW 3D‑Surrogate Modeling

Culvert Outlet Scouring의 영향 매개변수 예측 및 최적화: FLOW-3D와 서로게이트 모델링을 활용한 연구


연구 배경

  • 문제 정의: 박스형 수로(culvert) 출구에서 발생하는 침식(scouring)은 구조물 설계에 중요한 영향을 미친다.
  • 목표: 침식 깊이와 위치를 예측하여 구조적 실패를 방지하고, 설계를 최적화하는 새로운 방법론을 제안한다.
  • 접근법: 수치 모델링(FLOW-3D)과 Box-Behnken 설계 기법을 이용한 서로게이트 모델링을 결합.

연구 방법

  1. FLOW-3D:
    • Reynolds 평균 Navier-Stokes 방정식을 기반으로 유체 흐름 시뮬레이션을 수행.
    • 침식 예측을 위해 RNG 난류 모델을 사용.
  2. Box-Behnken 설계:
    • 세 가지 주요 변수: 유량(Flow Discharge, QQQ), 수로 기울기(Slope, SSS), 토양 입자 크기(d50d_{50}d50​).
    • 총 15개 모델을 통해 변수와 침식 깊이 및 위치 간 상호작용 분석.
  3. 민감도 분석:
    • 각 변수의 변화가 결과(침식 깊이와 위치)에 미치는 영향을 정량화.
  4. 최적화:
    • 침식 깊이 및 위치를 최소화하거나 최대화하기 위한 설계 변수의 조합 도출.

주요 결과

  • 모델 성능:
    • 침식 깊이 예측 정확도: R2=0.931R^2 = 0.931R2=0.931
    • 침식 위치 예측 정확도: R2=0.969R^2 = 0.969R2=0.969
  • 민감도 분석:
    • 유량 증가: 침식 깊이와 위치에 선형적(또는 비선형적) 영향을 미침.
    • 기울기 증가: 일정한 비선형 패턴 관찰.
    • 토양 입자 크기 증가: 복잡하고 비선형적인 패턴 확인.
  • 최적 설계:
    • 침식 깊이 최소화: 유량과 토양 입자 크기를 낮게, 기울기를 높게 설정.
    • 침식 위치 최대화: 유량, 토양 입자 크기, 기울기의 조합을 조절.

결론

  • FLOW-3D와 서로게이트 모델링: 침식 예측과 최적화에 효과적인 도구로 확인.
  • 설계 최적화 가능성: 구조적 침식 문제를 예방하기 위해 설계 단계에서 주요 변수의 영향을 정밀히 평가.
  • 향후 연구 제안: 추가적인 변수 도입 및 데이터를 통한 모델 개선.

이 논문은 수치 해석과 통계적 설계 접근법을 결합하여 수로 설계 문제를 해결하는 새로운 방법론을 제시하며, 향후 관련 연구에 중요한 기초 자료를 제공할 수 있습니다.

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  19. numerical model. Desert 20(1):47–55 Najafzadeh M (2016) Neurofuzzy-based GMDH-PSO to predict maximum scour depth at equilibrium at culvert outlets. J Pipeline Syst Eng Pract 7(1):06015001
  20. Najafzadeh M, Kargar AR (2019) Gene-expression programming, evolutionary polynomial regression, and model tree to evaluate local scour depth at culvert outlets. J Pipeline Syst Eng Pract 10(3):04019013
  21. Nariman NA, Hussain RR, Msekh MA, Karampour P (2019) Prediction meta-models for the responses of a circular tunnel during earthquakes. Undergr Space 4(1):31–47. https://doi.org/10.1016/j.undsp.2018.06.003
  22. Othman Ahmed K, Amini A, Bahrami J, Kavianpour MR, Hawez DM (2021) Numerical modeling of depth and location of scour at culvert outlets under unsteady fow conditions. J Pipeline Syst Eng Pract 12(4):04021040
  23. Pasma SA, Daik R, Maskat M, Hassan O (2013) Application of boxbehnken design in optimization of glucose production from oil palm empty fruit bunch cellulose. Int J Polym Sci 2013:1–8. https://doi.org/10.1155/2013/104502
  24. Sorourian S (2015) Study of blockage efects on scouring pattern downstream of box culverts. (PhD), University of Technology Sydney, Retrieved from https://opus.lib.uts.edu.au/handle/10453/44198
  25. Soulsby R (1997) Dynamics of marine sands: a manual for practical applications. Telford, London
  26. Iranian Journal of Science and Technology, Transactions of Civil Engineering
  27. Taha N, El-Feky MM, El-Saiad AA, Fathy I (2020) Numerical investigation of scour characteristics downstream of blocked culverts. Alex Eng J 59:3503–3513
  28. Wang L, Melville BW, Guan D (2018) Efects of upstream weir slope on local scour at submerged weirs. J Hydraul Eng 144(3):04018002.
  29. Xiong W, Cai CS, Kong B, Kong X (2016) CFD simulations and analyses for bridge-scour development using a dynamic-mesh updating technique. J Comput Civ Eng 30(1):04014121.
FLOW

Numerical Modelling of Flow Characteristics Over Sharp Crested Triangular Hump

날카로운 정상부를 가진 삼각형 허들(Sharp-Crested Triangular Hump) 위의 유동 특성 수치 모델링


연구 배경

  • 문제 정의: 수리 구조물의 성능 및 수면 프로파일을 정확히 예측하는 것은 실험적으로 어렵고 비용이 많이 듦.
  • 목표: CFD(Computational Fluid Dynamics)를 활용하여 삼각형 허들 위의 유동 특성을 보다 효율적이고 정확하게 분석.
  • 접근법: FLOW-3D 기반 시뮬레이션을 수행하여 실험 데이터와 비교 검증.

연구 방법

  1. 삼각형 허들(Weir) 개요
    • 위어(Weir)는 개수로에서 유량 조절과 방류 역할을 수행하는 중요한 수리 구조물.
    • 본 연구에서는 크기가 50 cm × 30 cm × 7 cmSharp-Crested Triangular Hump 모델을 사용.
  2. 수치 모델링
    • FLOW-3D를 사용하여 RANS(Reynolds-Averaged Navier-Stokes) 방정식과 VOF(Volume of Fluid) 방법을 적용.
    • FAVOR(Fractional Area-Volume Obstacle Representation) 기법을 사용하여 메쉬 내 장애물 영향을 반영.
    • 1,920,000개의 격자 셀을 사용하여 시뮬레이션 수행.
  3. 실험 설정
    • Universiti Teknologi PETRONAS(UTP)의 수리 실험실에서 실험 수행.
    • 30cm 폭, 60cm 높이, 10m 길이의 플룸(flume)에서 실험 진행.
    • 4가지 유량 조건(30, 51.3, 75.3, 31 m³/h) 및 경사 조건(0, 0.006, 0.01)으로 실험 설계.

주요 결과

  1. 수치 시뮬레이션 vs 실험 데이터 비교
    • 수치 시뮬레이션과 실험 결과 간의 차이는 4~5% 이내로 매우 높은 정확도를 보임.
    • 수면 프로파일, 평균 유속, 프로우드 수(Froude Number) 등이 실험과 잘 일치.
  2. 유동 특성 분석
    • 프라우드 수(Froude Number) 변화:
      • 상류(Upstream)에서는 Froude Number < 1.0 → 서브크리티컬(Subcritical) 흐름.
      • 하류(Downstream)에서는 Froude Number > 1.0 → 슈퍼크리티컬(Supercritical) 흐름.
    • 유속(Flow Velocity) 변화:
      • 하류로 갈수록 유속 증가, 삼각형 허들이 흐름을 방해하면서 압력 변화를 유발.
    • 수심(Flow Depth) 변화:
      • 상류에서는 높은 수심 유지, 하류에서는 급격한 감소 확인.
  3. 수치 시뮬레이션의 유용성
    • FLOW-3D가 삼각형 허들 및 수리 구조물의 유동 해석에 효과적임을 확인.
    • 기존의 실험적 접근보다 비용이 낮고 신속한 설계 검토 가능.

결론 및 향후 연구

  • FLOW-3D 기반 CFD 시뮬레이션이 삼각형 허들의 유동 해석 및 설계 최적화에 효과적임을 검증.
  • 실험 데이터와 비교했을 때 높은 정확도(오차 4~5%)를 나타내며, 초기 설계 검토에 유용함.
  • 향후 연구에서는 다양한 난류 모델(k-ε, RNG, LES) 적용 및 추가적인 수리 구조물 연구가 필요.

연구의 의의

이 연구는 수리 구조물의 유동 해석을 위해 CFD 시뮬레이션을 실험적으로 검증하여, 위어 및 삼각형 허들 설계의 최적화 및 성능 예측을 위한 신뢰성 높은 방법론을 제시했다는 점에서 큰 의미가 있다.

Reference

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  10. A. Parsaie, A.H. Haghiabi, A. Moradinejad, CFD modeling of ow pattern in spillwaysapproach channel, Sustain. Water Resour. Manag. 1 (3) (2015) 245–251.
  11. H.K. Versteeg, W. Malalasekera, An Introduction to Computational Uid Dynamics:the infinite Volume Method, Pearson education, 2007.
  12. A.S.I. Abdurrasheed, K.,W. Yusof, H.B. Takaijudin, A.A. Ghani, M.M. Muhammad,A.T. Sholagberu, Advances and challenging issues in subsurface drainage moduletechnology and BIOECODS: a review, in: MATEC Web of Conferences, 203, EDPSciences, 2018, 07005.
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  14. M. Darw, F. Moukalled, M. Luca, Finite Volume Method in Computational FluidDynamics: an Advanced Introduction with OpenFOAM an Matlab, Springer, 2015.
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  21. L. Choufu, S. Abbasi, H. Pourshahbaz, P. Taghvaei, S. Tfwala, Investigation of flow,erosion, and sedimentation pattern around varied groynes under Differenthydraulic and geometric conditions: a numerical study, Water 11 (2) (2019) 235.
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pattern

Numerical Modeling of Flow Pattern in Dam Spillway’s Guide Wall. Case Study : Balaroud dam, Iran

댐 방수로(Spillway) 안내벽의 유동 패턴 수치 모델링: 이란 Balaroud 댐 사례 연구


연구 배경

  • 문제 정의: 댐 방수로의 안내벽(Guide Wall)은 흐름 패턴을 조절하는 중요한 구조물로, 최적의 형상을 설계하면 방수로의 성능을 향상할 수 있음.
  • 목표: Balaroud 댐의 방수로 안내벽에 대해 물리적 및 수치적 모델링을 수행하여, 최적의 안내벽 형상을 도출.
  • 접근법: CFD(Computational Fluid Dynamics) 소프트웨어인 FLOW-3D를 활용하여 다양한 안내벽 설계를 비교 분석.

연구 방법

  1. 모델링 개요
    • AutoCAD를 이용하여 3D 모델 생성 후 FLOW-3D로 내보내기(STL 파일 형식).
    • 1:110 축척의 실험실 모델을 구축하고 실험 결과와 수치 해석을 비교.
  2. 수치 모델링 과정
    • 격자 생성(Meshing): 다양한 해상도로 수치 해석을 진행.
    • 경계 조건 설정: 유입 및 유출 조건을 설정하고 난류 모델 선택.
  3. 난류 모델 비교
    • K-epsilon, RNG K-epsilon, LES(Large Eddy Simulation) 모델을 비교.
    • RNG K-epsilon 모델이 가장 적합한 결과를 보임.
  4. 세 가지 안내벽 설계 평가
    • 모델 1: 유동 분리가 심하게 발생하여 부적합.
    • 모델 2: 접근 채널에서 교차파(Cross Waves) 형성.
    • 모델 3: 최소한의 유동 분리 및 교차파 제거 → 최적의 설계로 선정.

주요 결과

  • 모델 3이 가장 우수한 성능을 보이며, 교차파 발생을 최소화하고 유량을 원활하게 전달.
  • 유량-수위 곡선(Rating Curve) 분석을 통해 모델 3이 다른 설계보다 효율적임을 확인.
  • FLOW-3D의 RNG K-epsilon 난류 모델이 유동 패턴 해석에 가장 적합.

결론 및 향후 연구

  • 수치 모델링과 물리적 실험을 결합하여 최적의 안내벽 형상을 도출.
  • 최적 설계(모델 3)를 통해 방수로 성능을 개선하고, 수력 구조물의 안전성을 향상 가능.
  • 향후 연구에서는 다양한 유입 조건과 추가적인 설계 변수를 고려하여 더욱 정밀한 최적화를 수행할 필요.

이 연구는 댐 방수로 안내벽 설계의 최적화를 목표로 하며, 수치 해석 기법을 활용한 CFD 기반 설계 검증 방법론을 제시한다는 점에서 의의가 있다.

Reference

  1. M.C. Aydin, CFD simulation of free-surface flow overtriangular labyrinth side weir, Adv. Eng. Softw. 45 (1) (2012)159–166.
  2. M.C. Aydin, M.E. Emiroglu, Determination of capacity oflabyrinth side weir by CFD, Flow Meas. Instrum. 29 (2013) 1–8.
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  4. P.D. Bates, S.N. Lane, R.I. Ferguson, Computational FluidDynamics: Applications in Environmental Hydraulics, Wiley,2005.
  5. T. Cebeci, Turbulence Models and Their Application: EfficientNumerical Methods with Computer Programs, Horizons Pub,2004.
  6. P.G. Chanel, An Evaluation of Computational Fluid Dynamicsfor Spillway Modeling, University of Manitoba, 2008 (Master ofScience).
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  8. C. Chinnarasri, D. Kositgittiwong, P.Y. Julien, Model of flowover spillways by computational fluid dynamics, Proc. ICE –Water Manage. (2014) 164–175.
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  10. D. Gessler, CFD modeling of spillway performance, ImpactsGlob. Clim. Change (2005) 1–10.
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  12. W.H. Hager, M. Pfister, Hydraulic modelling – an introduction:principles, methods and applications, J. Hydraul. Res. 48 (4)(2010) 557–558.
  13. D. Kim, J. Park, Analysis of flow structure over ogee-spillway inconsideration of scale and roughness effects by using CFDmodel, KSCE J. Civ. Eng. 9 (2) (2005) 161–169.
  14. R. Maghsoodi, M.S. Roozgar, H. Sarkardeh, H.M.Azamathulla, 3D-simulation of flow over submerged weirs,Int. J. Model. Simul. 32 (4) (2012) 237.
  15. B. Mohammadi, O. Pironneau, Analysis of the K-epsilonTurbulence Model, Wiley, 1994.
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  20. A. Parsaie, A. Haghiabi, A. Moradinejad, CFD modeling offlow pattern in spillway’s approach channel, Sustain. WaterResour. Manag. 1 (3) (2015) 245–251.Figure 14 Head discharge curve of the model (3).Figure 16 The rating curve of the models for the guide wall.Figure 15 Cross section of the flow through the guide wall at theflood return period 1000 year.472 S. Dehdar-behbahani, A. Parsaie
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Weir

2D-3D Modeling of Flow Over Sharp-Crested Weirs

샤프 크레스트 위어(Sharp-Crested Weir) 위 유동의 2D 및 3D 모델링

연구 배경

  • 문제 정의: 샤프 크레스트 위어는 수로에서 유량 측정과 조절을 위해 가장 널리 사용되는 구조물이다.
  • 목표: CFD(Computational Fluid Dynamics) 기법을 활용하여 샤프 크레스트 위어 위의 유동 특성을 분석하고 방출 계수(Discharge Coefficient)를 예측.
  • 접근법: FLOW-3D를 사용하여 수치 해석을 수행하고 실험 데이터와 비교.

연구 방법

  1. 위어 특성 및 방출 계수(Cd) 분석
    • 기존 실험 연구를 기반으로 방출 계수 CdCdCd 추정식을 개발.
    • 다양한 유량 및 위어 높이 조합을 사용하여 최적의 방출 계수 관계식 도출.
  2. FLOW-3D 기반 수치 모델링
    • VOF(Volume of Fluid) 기법을 적용하여 자유 수면을 해석.
    • RNG k−ϵk-\epsilonk−ϵ 난류 모델을 사용하여 난류 흐름을 해석.
    • FAVOR(Fractional Area-Volume Obstacle Representation) 기법을 활용하여 격자 내 장애물 표현.
  3. 격자 수렴 분석
    • 다양한 해상도의 격자를 비교하여 최적의 계산 비용과 정확도를 확보.

주요 결과

  1. 수치 모델링 vs 실험 데이터 비교
    • 방출 계수(Cd) 예측값과 기존 실험값 간의 오차 범위가 ±3% 이내로 매우 높은 정확도를 보임.
    • Cd는 Ht/tw(총 수두 대비 위어 높이)와 강한 상관관계를 가짐.
  2. 유동 특성 분석
    • 유량 변화에 따른 방출 계수:
      • 유량이 증가할수록 방출 계수가 점진적으로 감소하는 경향 확인.
    • 위어 주변의 속도 및 압력 분포 분석:
      • 위어 크레스트에서 유동이 가속되면서 속도 증가 및 압력 감소 현상 관찰.
      • 위어 하류에서 수압이 낮아지며 유동 패턴이 변화.
  3. FLOW-3D의 유용성
    • FLOW-3D는 실험 대비 비용이 낮고 신속한 설계 검토 가능.
    • 다양한 위어 형상 및 유량 조건에서 적용 가능성이 높음.

결론 및 향후 연구

  • FLOW-3D 기반 CFD 시뮬레이션이 샤프 크레스트 위어의 방출 계수 예측 및 유동 분석에 효과적임을 입증.
  • 실험 결과와 비교했을 때 높은 정확도(오차 ±3%)를 나타내며, 초기 설계 검토에 유용함.
  • 향후 연구에서는 다양한 위어 형상 및 추가적인 난류 모델 적용(k-ω, LES 등)을 통해 더욱 정밀한 해석이 필요.

연구의 의의

이 연구는 샤프 크레스트 위어의 유동 특성을 CFD 기반으로 해석하여 설계 최적화 및 방출 계수 예측의 신뢰성을 향상시켰다는 점에서 의미가 크다.

Reference

  1. Bhallamudi, S.M. and M.H. Chaudhry, 1994. Computation of Flows in Open Channel Transitions. Journal of Hydraulic. Research, 30(1): 77-93.
  2. Fritz, H.M. and H.W. Hager, 1998. Hydraulics of Embankment Weirs. Journal of Hydraulic Engineering,
  3. ASCE., 124(9): 963-971.
  4. Hargreaves, D.M., H.P. Morvan, N.G. Wright, 2007. Validation of the Volume of Fluid Method for Free
  5. Surface Calculation. Engineering Applications of Computational Fluid mechanics, 1(2): 136-147.
  6. Kindsvater, C.E., R.W. Carter, 1957. Discharge Characteristics of Rectangular Thin-Plate Weirs. Journal of Hydraulic Engineering, ASCE., 14: 1-36.
  7. King, H.W. and E.F. Brater, 1963. Handbook of Hydraulics, 5th Edition, McGraw-Hill Book Company, New York.
  8. Patankar, S.V., 1980. Numerical Heat Transfer and Fluid Flow. McGraw-Hill Book Company, New York.
  9. Raju, K.G.R., G.L. Asawa, 1977. Viscosity and Surface Tension Effects on Weir Flow. Journal of Hydraulic Engineering, ASCE., 103: 1227-1231.
  10. Rouse, H., 1950. Engineering Hydraulics. Proceedings of the Fourth Hydraulics Conference, Iowa Institute of Hydraulic Research, John Wiley and Sons, Inc., New York.
  11. Sarginson, E.J., 1972. The Iinfluence of Surface Tension on Weir Flow. Journal of Hydraulic Research, 10:431-446.
Weir

Discharge Formula and Hydraulics of Rectangular Side Weirs in the Small Channel and Field Inlet

소규모 수로 및 유입구에서의 직사각형 측면 위어의 유량 공식 및 수리학

Yingying Wang, Mouchao Lv, Wen’e Wang, Ming Meng

Abstract


In this study, experimental investigations were conducted on rectangular side weirs with different widths and heights. Corresponding simulations were also performed to analyze hydraulic characteristics including the water surface profile, flow velocity, and pressure. The relationship between the discharge coefficient and the Froude number, as well as the ratios of the side weir height and width to upstream water depth, was determined. A discharge formula was derived based on a dimensional analysis. The results demonstrated good agreement between simulated and experimental data, indicating the reliability of numerical simulations using FLOW-3D software (version 11.1). Notably, significant fluctuations in water surface profiles near the side weir were observed compared to those along the center line or away from the side weir in the main channel, suggesting that the entrance effect of the side weir did not propagate towards the center line of the main channel. The proposed discharge formula exhibited relative errors within 10%, thereby satisfying the flow measurement requirements for small channels and field inlets.

1. Introduction


Sharp crested weirs are used to obtain discharge in open channels by solely measuring the water head upstream of the water. Side weirs, as a kind of sharp-crested weir, are extensively used for flow measurement, flow diversion, and flow regulation in open channels. Side weirs can be placed directly in the channel direction or field inlet, without changing the original structure of the channel. Thus, side weirs have certain advantages in the promotion and application of flow measurement facilities in small channels and field inlets. The rectangular sharp-crested weir is the most commonly available, and many scholars have conducted research on it.
Research on side weirs started in 1934. De Marchi studied the side weir in the rectangular channel and derived the theoretical formula based on the assumption that the specific energy of the main flow section of the rectangular channel in the side weir section was constant [1]. Ackers discussed the existing formulas for the prediction of the side weir discharge coefficient [2]. Chen concluded that the momentum theorem was more suitable for the analytical calculation of the side weir based on the experimental data [3]. Based on previous theoretical research, more and more scholars began to carry out experimental research on side weirs. Uyumaz and Muslu conducted experiments under subcritical and supercritical flow regimes and derived expressions for the side weir discharge and water surface profiles for these regimes by comparing them with experimental results [4]. Borghei et al. developed a discharge coefficient equation for rectangular side weirs in subcritical flow [5]. Ghodsian [6] and Durga and Pillai [7] developed a discharge coefficient equation of rectangular side weirs in supercritical flow. Mohamed proposed a new approach based on the video monitoring concept to measure the free surface of flow over rectangular side weirs [8]. Durga conducted experiments on rectangular side weirs of different lengths and sill heights and discussed the application of momentum and energy principles to the analysis of spatially varied flow under supercritical conditions. The results showed that the momentum principle was fitting better [7]. Omer et al. obtained sharp-crested rectangular side weirs discharge coefficients in the straight channel by using an artificial neural network model for a total of 843 experiments [9]. Emiroglu et al. studied water surface profile and surface velocity streamlines, and developed a discharge coefficient formula of the upstream Froude number, the ratios of weir length to channel width, weir length to flow depth, and weir height to flow depth [10]. Other investigators [11,12,13,14] have conducted experiments to study flow over rectangular side weirs in different flow conditions.
Numerous studies have been conducted in laboratories to this day. Compared to experimental methods, the numerical simulation method has many attractive advantages. We can easily obtain a wide range of hydraulic parameters of side weirs using numerical simulation methods, without investing a lot of manpower and resources. In addition, we can conduct small changes in inlet condition, outlet condition, and geometric parameters, and study their impact on the flow characteristics of side weirs. Therefore, with the development and improvement of computational fluid dynamics, the numerical simulation method has begun to be widely applied on side weirs. Salimi et al. studied the free surface changes and the velocity field along a side weir located on a circular channel in the supercritical regime by numerical simulation [15]. Samadi et al. conducted a three-dimensional simulation on rectangular sharp-crested weirs with side contraction and without side contraction and verified the accuracy of numerical simulation compared with the experimental results [16]. Aydin investigated the effect of the sill on rectangular side weir flow by using a three-dimensional computational fluid dynamics model [17]. Azimi et al. studied the discharge coefficient of rectangular side weirs on circular channels in a supercritical flow regime using numerical simulation and experiments [18]. The discharge coefficient over the two compound side weirs (Rectangular and Semi-Circle) was modeled by using the FLOW-3D software to describe the flow characteristics in subcritical flow conditions [19]. Safarzadeh and Noroozi compared the hydraulics and 3D flow features of the ordinary rectangular and trapezoidal plan view piano key weirs (PKWs) using two-phase RANS numerical simulations [20]. Tarek et al. investigated the discharge performance, flow characteristics, and energy dissipation over PK and TL weirs under free-flow conditions using the FLOW-3D software [21].
As evident from the aforementioned, the majority of studies have primarily focused on determining the discharge coefficient, while comparatively less attention has been devoted to investigating the hydraulic characteristics of rectangular side weirs. Numerical simulations were conducted on different types of side weirs, including compound side weirs and piano key weirs, in different cross-section channels under different flow regimes. It is imperative to derive the discharge formula and investigate other crucial flow parameters such as depth, velocity, and pressure near side weirs for their effective implementation in water measurement. In this study, a combination of experimental and numerical simulation methods was employed to examine the relationship between the discharge coefficient and its influencing factors; furthermore, a dimensionless analysis was utilized to derive the discharge formula. Additionally, water surface profiles near side weirs and pressure distribution at the bottom of the side channel were analyzed to assess safety operation issues associated with installing side weirs.

2. Principle of Flow Measurement


Flow discharge over side weirs is a function of different dominant physical and geometrical quantities, which is defined as

where Q is flow discharge over the side weir, b is the side weir width, B is the channel width, P is the side weir height, v is the mean velocity, h1 is water depth upstream the side weir in the main channel, g is the gravitational acceleration, μ is the dynamic viscosity of fluid, ρ is fluid density, and i is the channel slope (Figure 1).

Figure 1. Definition sketch of parameters of rectangular side weir under subcritical flow. Note: h1 and h2 represent water depth upstream and downstream of the side weir in the main channel, respectively; y1 and y2 represent weir head upstream and downstream of the side weir in the main channel, respectively.

In experiments when the upstream weir head was over 30 mm, the effects of surface tension on discharge were found to be minor [22]. The viscosity effect was far less than the gravity effect in a turbulent flow. Hence μ and σ were excluded from the analysis [23,24]. In addition, the channel width, the channel slope, and the fluid density were all constant, so the discharge formula can be simplified as:

According to the Buckingham π theorem, the following relationship among the dimensionless parameters is established:

Selected h1 and g as basic fundamental quantities, and the remaining physical quantities were represented in terms of these fundamental quantities as follows:

In which

Based on dimensional analysis, the following equations were derived.

Namely

So the discharge formula can be simplified as:

In a sharp-crested weir, discharge over the weir is proportional to 𝐻1.51H11.5 (H1 is the upstream total head above the crest, namely H1 = y1 + v2/2 g), so Equation (6) can be transformed as follows:

Consequently, the discharge formula over rectangular side weirs is defined as follows, in which 𝑚=𝑓(𝑏ℎ1m=f(bh1,𝑃ℎ1,𝐹𝑟1)Ph1,Fr1). Parameter m represents the dimensionless discharge coefficient. Parameter Fr1 represents the Froude number at the upstream end of the side weir in the main channel.

3. Experiment Setup


The experimental setup contained a storage reservoir, a pumping station, an electromagnetic flow meter, a control valve, a stabilization pond, rectangular channels, a side weir, and a sluice gate. The layout of the experimental setup is shown in Figure 2. Water was supplied from the storage reservoir using a pump. The flow discharge was measured with an electromagnetic flow meter with precision of ±3‰. Water depth was measured with a point gauge with an accuracy of ±0.1 mm. The flow velocity was measured with a 3D Acoustic Doppler Velocimeter (Nortek Vectrino, manufactured by Nortek AS in Rud, Norway). In order to eliminate accidental and human error, multiple measurements of the water depth and flow velocity at the same point were performed and the average values were used as the actual water depth and flow velocity of the point. The main and side channels were both rectangular open channels measuring 47 cm in width and 60 cm in height. The geometrical parameters of rectangular side weirs are shown in Table 1.

Figure 2. Layout of the test system.
Table 1. The geometrical parameters of rectangular side weirs.

When water passes through a side weir, its quality point is affected not only by gravity but also by centrifugal inertia force, leading to an inclined water surface within that particular cross-section before reaching the weir. In order to examine water profiles adjacent to side weirs, cross-sectional measurements were conducted at regular intervals of 12 cm both upstream and downstream of each side weir, denoted as sections ① to ⑩, respectively. Measuring points were positioned near the side weir (referred to as “Side I”), along the center line of the main channel (referred to as “Side II”), and far away from the side weir (referred to as “Side III”) for each cross-section. The schematic diagram illustrating these measuring points is presented in Figure 3.

Figure 3. Schematic diagram of measurement points.

4. Numerical Simulation Settings

4.1. Mathematical Model

4.1.1. Governing Equations

Establishing the controlling equations is a prerequisite for solving any problem. For the flow analysis problem of water flowing over a side weir in a rectangular channel, assuming that no heat exchange occurs, the continuity equation (Equation (9)) and momentum equation (Equation (10)) can be used as the controlling equations as follows:

The continuity equation:

Momentum equation:

where: ρ is the fluid density, kg/m3t is time, s; uiuj are average flow velocities, u1u2u3 represent average flow velocity components in Cartesian coordinates x, y, and z, respectively, m/s; μ is dynamic viscosity of fluid, N·s/m2p is the pressure, pa; Si is the body force, S1 = 0, S2 = 0, S3 = −ρg, N [24].

4.1.2. RNG k-ε Model

The water flow in the main channel is subcritical flow. When the water flows through the side weir, the flow line deviates sharply, the cross section suddenly decreases, and due to the blocking effect of the side weir, the water reflects and diffracts, resulting in strong changes in the water surface and obvious three-dimensional characteristics of the water flow [25]. Therefore the RNG kε model is selected. The model can better handle flows with greater streamline curvature, and its corresponding k and ε equation is, respectively, as follows:

where: k is the turbulent kinetic energy, m2/s2μeff is the effective hydrodynamic viscous coefficient; Gk is the generation item of turbulent kinetic energy k due to gradient of the average flow velocity; C∗1εC1ε*, C are empirical constants of 1.42 and 1.68, respectively; ε is turbulence dissipation rate, kg·m2/s2.

4.1.3. TruVOF Model

Because the shape of the free surface is very complex and the overall position is constantly changing, the fluid flow phenomenon with a free surface is a typical flow phenomenon that is difficult to simulate. The current methods used to simulate free surfaces mainly include elevation function method, the MAC method [26] and the VOF (Volume of Fluid) method [27]. The VOF method is a method proposed by Hirt and Nichols to deal with the complex motion of the free surface of a fluid, which can describe all the complexities of the free surface with only one function. The basic idea of the method is to define functions αw and αa, which represent the volume percentage of the calculation area occupied by water and air, respectively. In each unit cell, the sum of the volume fractions of water and air is equal to 1, i.e.,

The TruVOF calculation method can accurately track the change of free liquid level and accurately simulate the flow problems with free interface. Its equation is:

where: u_¯m is the average velocity of the mixture; t is the time; F is the volume fraction of the required fluid.

4.2. Parameter Setting and Boundary Conditions

To streamline the iterative calculation and minimize simulation time, we selected a main channel measuring 7.5 m in length and a side channel measuring 2.5 m in length for simulation. Three-dimensional geometrical models were developed using the software AutoCAD (version 2016-Simplified Chinese). The spatial domain was meshed using a constructed rectangular hexahedral mesh and each cell size was 2 cm. A volume flow rate was set in the channel inlet with an auto-adjusted fluid height. An outflow–outlet condition was positioned at the end of the side channel. A symmetry boundary condition was set in the air inlet at the top of the model, which represented that no fluid flows through the boundary. The lower Z (Zmin) and both of the side boundaries were treated as a rigid wall (W). No-slip conditions were applied at the wall boundaries. Figure 4 illustrates these boundary conditions.

Figure 4. Diagram of boundary conditions.

5. Results

5.1. Water Surface Profiles

Water surface profiles were crucial parameters for selecting water-measuring devices. Upon analyzing the consistent patterns observed in different conditions, one specific condition was chosen for further analysis. To validate the reliability of numerical simulation, measured and simulated water depths of rectangular side weirs with different widths and heights at a discharge rate of 25 L/s were extracted for comparison (Table 2 and Figure 5). The results in Table 2 and Figure 5 indicate a maximum absolute relative error value of 9.97% and all absolute relative error values within 10%, demonstrating satisfactory agreement between experimental and simulated results.

Figure 5. Comparison between measured and simulated flow depth.
P/cmSection Positionb = 20 cmb = 30 cmb = 40 cmb = 47 cm
hm/cmhs/cmR/%hm/cmhs/cmR/%hm/cmhs/cmR/%hm/cmhs/cmR/%
721.4919.49.7317.7416.94.7416.0714.519.7113.7912.509.35
④′20.4819.056.9817.7816.149.2215.6914.318.80
20.7119.028.1617.8216.318.4715.9214.538.7315.2313.809.39
⑧′22.0020.228.0918.2716.748.3716.5914.969.83
22.3720.179.8317.7316.805.2516.2715.087.3115.3614.366.51
1024.1522.66.4219.9618.845.6119.0318.582.3616.8315.855.82
④′24.2122.058.9219.4918.196.6718.7518.352.13
24.0121.789.2919.6518.346.6718.9518.631.6917.5216.098.16
⑧′24.8822.49.9720.6519.216.9720.1219.294.13
24.0322.964.4521.1619.348.6019.7119.431.4218.3917.365.60
1528.8527.564.4725.8624.096.8424.0521.898.9822.7320.808.49
④′28.4926.975.3425.1923.845.3623.4221.468.37
28.8526.986.4825.7223.996.7323.2321.826.0723.1021.058.87
⑧′28.9627.305.7326.3824.198.3024.1822.277.90
29.1827.964.1826.5724.547.6424.5722.339.1223.2021.109.05
2033.2932.342.8530.6329.025.2628.4926.875.6926.9925.814.37
④′33.1431.953.5929.7528.623.8028.1126.794.70
33.3231.794.5930.0428.455.2928.9926.867.3527.4226.722.55
⑧′34.0232.394.7930.6928.955.6729.5927.257.91
34.6232.845.1431.4429.296.8429.5127.317.4628.2127.004.29
Table 2. Comparison of measured and simulated water depths on Side I of each side weir at a discharge of 25 L/s

Due to the diversion caused by the side weir, there was a rapid variation in flow near the side weir in the main channel. In order to investigate the impact of the side weir on water flow in the main channel, water surface profiles on Side I, Side II, and Side III were plotted with a side weir width and height both set at 20 cm at a discharge rate of 25 L/s (Figure 6). As depicted in Figure 6, within a certain range of the upstream end of the main channel, water depths on Side I, Side II, and Side III were nearly equal with almost horizontal profiles. As the distance between the location of water flow and the upstream end of the weir crest decreased gradually, there was a gradual decrease in water depth on Side I along with an inclined trend in its corresponding profile; however, both Side II and Side III still maintained almost horizontal profiles. When approaching closer to the side weir area with flowing water, there was an evident reduction in water depth on Side I accompanied by a significant downward trend visible across an expanded decline range. The minimum point occurred near the upstream end of the weir crest before gradually increasing again towards downstream sections. At the crest section of the side weir, there is an upward trend observed in the water surface. The water surface tended to stabilize downstream of the main channel within a certain range from the downstream end of the weir crest. There was no significant change in the water surface profiles of Side Ⅱ and Side Ⅲ in the crest section. It can be inferred that the side weir entrance effect occurred only between Side Ⅰ and Side Ⅱ. M. Emin reported the same pattern [10].

Figure 6. Water surface profiles on Side I, Side II, and Side III with a side weir width of 20 cm and height of 15 cm at a discharge of 25 L/s.

For a more accurate study on the entrance effect of the side weir on the Water Surface Profile (WSP) for Side I; a comparative analysis conducted using different widths but the same height (15 cm) at a discharge rate of 25 L/s is presented through Figure 7, Figure 8, Figure 9 and Figure 10.

Figure 7. Water surface profile on Side Ⅰ with a side weir width of 20 cm and height of 15 cm at a discharge of 25 L/s.
Figure 8. Water surface profile on Side Ⅰ with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s.
Figure 9. Water surface profile on Side Ⅰ with a side weir width of 40 cm and height of 15 cm at a discharge of 25 L/s.
Figure 10. Water surface profile on Side Ⅰ with a side weir width of 47 cm and height of 15 cm at a discharge of 25 L/s.

According to Figure 7, Figure 8, Figure 9 and Figure 10, the water depth upstream of the main channel started to decrease as it approached the upstream end of the weir crest and then gradually increased at the weir crest section. In other words, the water surface profile exhibited a backwater curve along the length of the weir crest. The water depth remained relatively stable downstream of the main channel within a certain range from the downstream end of the weir crest. Additionally, there was a higher water depth downstream of the main channel compared to that upstream of the main channel. Furthermore, an increase in the width of the side weir led to a gradual reduction in fluctuations on its water surface.

5.2. Velocity Distribution

The law of flow velocity distribution near the side weir is the focus of research and analysis, so the simulated and measured values of flow velocity near the side weir were compared and analyzed. Take the discharge of 25 L/s, the height of 15 cm, and the width of 30 cm of the side weir as an example to illustrate. Figure 11 shows the measured and simulated velocity distribution in the x-direction of cross-section ④. As can be seen from Figure 11, the diagrams of the measured and simulated velocity distribution were relatively consistent, and the maximum absolute relative error between the measured and simulated values at the same measurement point was 9.37%, and the average absolute relative error was 3.97%, which indicated a satisfactory agreement between the experimental and simulated results.

Figure 11. Velocity distribution in the x-direction of section ④: when the discharge is 25 L/s, the height of the side weir is 15 cm and the width of the side weir is 30 cm. (a) Measured velocity distribution; (b) Simulated velocity distribution.

From Figure 11, it can be seen that the flow velocity gradually increased from the bottom of the channel towards the water surface in the Z-direction, and the flow velocity gradually increased from Side Ⅲ to Side Ⅰ in the Y-direction. The maximum flow velocity occurred near the weir crest.

Figure 12 shows the distribution of flow velocity at different depths (z/P = 0.3, z/P = 0.8, z/P = 1.6) with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s. The water flow line began to bend at a certain point upstream of the main channel, and the closer it was to the upstream end of the weir crest, the greater the curvature. The maximum curvature occurred at the downstream end of the weir crest. The flow patterns at the bottom, near the side weir crest, and above the side weir crest were significantly different. There was a reverse flow at the bottom of the main channel, where the forward and reverse flows intersect, resulting in a detention zone. The maximum flow velocity at the bottom layer occurred at the upstream end of the side weir crest. When the location of water flow approached the weir crest, the maximum flow velocity occurred at the upstream end of the weir crest. The maximum flow velocity on the water surface occurred at the downstream end of the weir crest. As the water depth decreased, the position of the maximum flow velocity gradually moved from the upstream end of the side weir to the downstream end of the side weir.

Figure 12. Distribution of flow velocity at different depths with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s. (a) z/P = 0.3; (b) z/P = 0.8; (c) z/P = 1.6.

5.3. Side Channel Pressure Distribution

When water flowed through the side weir, an upstream water level was formed, resulting in a pressure zone at the junction with the side channel. This pressure zone led to increased water pressure on the floor of the side channel, which affected its stability and durability. In small channels or fields where erosion resistance is weak, excessive pressure can cause scour holes. Therefore, analyzing the pressure distribution in the side channel is necessary to select an appropriate height and width for the side weir that effectively reduces its impact on the bottom plate.

To investigate the impact of side weir width on hydraulic characteristics, pressure data was collected at a discharge rate of 25 L/s for side weirs with heights of 20 cm and widths ranging from 20 cm to 47 cm. The pressure distribution map was drawn, as shown in Figure 13.

Figure 13. Comparison of pressure distribution on the bottom plate of the side channel with different widths of side weirs when the discharge is 25 L/s and the height of side weirs is 20 cm. (aP = 20 cm, b = 20 cm; (bP = 20 cm, b = 30 cm; (cP = 20 cm, b = 40 cm; (dP = 20 cm, b = 47 cm.

As can be seen from Figure 13, the pressure at the bottom of the side channel decreased as the width of the side weir increased. This uneven distribution of water flow on the weir was caused by the sharp bending of water flow lines and the influence of centrifugal inertia force over a short period. After passing through the side weir, the water flow became symmetrically distributed with respect to the axis of the side channel, leaning towards the right bank at a certain distance. As we increased the width of the side weir, we noticed that its position gradually approached the side weir and maximum pressure decreased at this location where the water tongue formed due to flowing through it (Figure 13). For a constant height (20 cm) but varying widths (20 cm, 30 cm, 40 cm, and 47 cm), we measured maximum pressures at these positions as follows: 103,713 Pa, 103,558 Pa, 103,324 Pa, and 103,280 Pa, respectively. Consequently, increasing width reduced the impact on the side channel from water flowing through it while changing pressure distribution from concentration to dispersion in a vertical direction. In the practical application of side weirs, appropriate height should be selected based on the bottom plate’s capacity to withstand the pressure exerted by flowing water within channels.

To investigate how height affects the hydraulic characteristics of rectangular side weirs further (Figure 14), we extracted pressures on bottom plates when discharge was fixed at 25 L/s while varying heights were set as follows: 7 cm, 10 cm, 15 cm, and 20 cm, respectively.

Figure 14. Comparison of pressure distribution on the bottom plate of the side channel with different heights of side weirs when discharge is 25 L/s and the width of side weirs is 20 cm. (aP = 7 cm, b = 20 cm; (bP = 10 cm, b = 20 cm; (cP = 15 cm, b = 20 cm; (dP = 20 cm, b = 20 cm.

As shown in Figure 14, when the width of the side weir was constant, the pressure at the bottom of the side channel increased with the height of the side weir. As the height of the side weir increased, the water tongue formed by flow through the side weir gradually moved away from it in a downstream direction. In terms of vertical water flow, as the height of the side weir increased, the position of maximum pressure at which the water tongue falls shifted closer to the axis of the side channel from its right bank. Moreover, an increase in height resulted in higher maximum pressure at this falling point. For a constant width (20 cm) and varying heights (7 cm, 10 cm, 15 cm, and 20 cm), corresponding maximum pressures at this landing point were measured as 102,422 Pa, 102,700 Pa, 103,375 Pa, and 103,766 Pa, respectively. Consequently, increasing width led to a greater impact on both flow through and pressure distribution within the side channel; transforming it from scattered to concentrated along its lengthwise direction. Therefore, when applying such weirs practically one should select an appropriate width based on what pressure can be sustained by their respective channel bottom plates.

5.4. Discharge Coefficient

Based on dimensionless analysis, the influencing parameters of the discharge coefficient were obtained. To study the effect of parameters Fr1b/h1, and P/h1, discharge coefficient values were plotted against Fr1b/h1, and P/h1, shown in Figure 15, Figure 16 and Figure 17. The discharge coefficient decreased as parameters Fr1 and b/h1 increased. The discharge coefficient increased as parameter P/h1 increased. As Uyumaz and Muslu reported in a previous study, the variation of the discharge coefficient with respect to the Froude number showed a second-degree curve for a subcritical regime [4].

Figure 15. Variation of discharge coefficient values against Froude number.
Figure 16. Variation of discharge coefficient values against the percentage of the side weir width to the upstream flow depth over the side weir.
Figure 17. Variation of discharge coefficient values against the percentage of the side weir height to the upstream flow depth over the side weir.

Quantitative analysis between discharge coefficient values and parameters Fr1b/h1, and P/h1 was conducted using data analysis software (IBM SPSS Statistics 19). The various coefficients obtained are shown in Table 3.

ModelUnstandardized CoefficientsStandardized CoefficientstSig
BStd. ErrorBeta (β)
Constant−1.2940.155−8.3690.000
Fr13.4300.2863.40112.0130.000
b/h1−0.0040.004−0.045−0.9440.348
P/h12.4010.1674.06414.3940.000
Table 3. Coefficient.

The value of t and Sig are the significance results of the independent variable, and the value of Sig corresponding to the value of t is less than 0.05, indicating that the independent variable has a significant impact on the dependent variable. Therefore, the values of Sig corresponding to the parameters Fr1 and P/h1 were less than 0.05, indicating that the parameters Fr1 and P/h1 have a significant impact on the discharge coefficient. On the contrary, the parameter b/h1 has less impact on the discharge coefficient. Therefore, quantitative analysis between discharge coefficient values and parameters Fr1, and P/h1 was conducted using data analysis software by removing factor b/h1. The model summary, ANOVA, and coefficient obtained are shown respectively in Table 4, Table 5 and Table 6. R and adjusted R square in Table 4 were approaching 1, which indicated the goodness of fit of the regression model was high. The value of Sig corresponding to the value of F in Table 5 was less than 0.05, which indicated that the regression equation was useful. The values of Sig corresponding to the parameters Fr1 and P/h1 in Table 6 were less than 0.05, indicating that the parameters Fr1 and P/h1 have a significant impact on the discharge coefficient.

ModelRR SquareAdjusted R SquareStd. Error of the Estimate
10.913 a0.8330.8290.03232
Table 4. Model Summary b. Note: a. Predictors:(Constant), Fr1P/h1b. Discharge coefficient.
ModelSum of SquaresdfMean SquareFSig
1Regression0.40220.201192.5450.000 a
Residual0.080770.001
Total0.48379
Table 5. ANOVA b. Note: a. Predictors:(Constant), Fr1P/h1b. Discharge coefficient.
ModelUnstandardized CoefficientsStandardized CoefficientstSig
BStd. ErrorBeta (β)
Constant−1.3260.151−8.7960.000
Fr13.4790.2813.44912.3960.000
P/h12.4270.1644.10814.7650.000
Table 6. Coefficient a. Note: a. Predictors:(Constant), Fr1P/h1.

Based on the above analysis, the flow coefficient formula has been obtained, shown as follows:

Discharge formula were obtained by substituting Equation (15) into Equation (12), as shown in Equation (16).

where Q ∈ [0.006, 0.030], m3/s; b ∈ [0.20, 0.47], m; P ∈ [0.07, 0.20], m.

Figure 18 showed the measured discharge coefficient values with those calculated from discharge formulas in Table 3. The scatter of the data with respect to perfect line was limited to ±10%.

Figure 18. Comparison of the measured discharge coefficient values with those calculated from discharge formulas in Table 3.

6. Discussions

Determining water surface profile near the side weir in the main channel is one of the tasks of hydraulic calculation for side weirs. As the water flows through the side weir, discharge in the main channel is gradually decreasing, namely dQ/ds<0. According to the Equation (17) derived from Qimo Chen [3], it can be inferred that the value of 𝑑ℎ/𝑑𝑠 is greater than zero in subcritical flow (Fr < 1), that is, the water surface profile near the side weir in the main channel is a backwater curve. Due to the side weir entrance effect at the upstream end, water surface profiles drop slightly at the upstream end of the side weir crest, as EI-Khashab [28] and Emiroglu et al. [29] reported in previous experimental studies.

In this study, the water surface profile exhibited a backwater curve along the length of the weir crest. Therefore, during side weir application, it is crucial to ensure that downstream water levels do not exceed the highest water level of the channel.

The head on the weir is one of the important factors that flow over side weirs depends on. At the same time, the head depends on the water surface profile near the side weir in the main channel. Therefore, further research on the quantitative analysis of water surface profile needs to be conducted. Mohamed Khorchani proposed a new approach based on the video monitoring concept to measure the free surface of flow over side weirs. It points out a new direction for future research [8].

The maximum flow velocity, a key parameter in assessing the efficiency of a weir, occurs at the upstream end of the weir crest, typically near the crest. This is attributed to the convergence of the flow as it approaches the crest, resulting in a significant increase in velocity. It was found that in this study the minimum flow velocity occurred at the bottom of the main channel away from the side weir. Under such conditions, the accumulation of sediments could lead to siltation, which in turn can affect the accuracy of flow measurement through side weirs. This is because the presence of sediments can alter the flow patterns and cause errors in the measurement. Therefore, it becomes crucial to explore methods to optimize the selection of side weirs in order to minimize or eliminate the effects of sedimentation on flow measurement.

Pressure distribution plays a crucial role in ensuring structural safety for side weirs since small channels and field inlets have relatively limited pressure-bearing capacities. Therefore, it is important to select an appropriate geometrical parameter of rectangular side weirs based on their ability to withstand the pressure exerted on their bottom combined with pressure distribution data at the bottom of the side channel we have obtained in this study.

The discharge coefficient formula (Equation (15)), which incorporates Fr1 and P/h1, was derived based on dimensional analysis. However, it is worth noting that previous research has contradicted this formula by suggesting that the discharge coefficient solely depends on the Froude number. This conclusion can be observed in this study such as in Equations (18)–(23) in Table 7 of the manuscript [30,31,32,33,34,35], which clearly demonstrate the dependency of the discharge coefficient on the Froude number. In contrast, our derived discharge coefficient formula (Equation (15)) offers a more streamlined and simplified approach compared to Equation (25) [36] and Equation (29) [10]—making it easier to comprehend and apply—an advantageous feature particularly valuable in fluid dynamics where intricate calculations can be time-consuming. Furthermore, our derived discharge coefficient formula (Equation (15)) exhibits a broader application scope than that of Equation (24) [37] as shown in Table 8. Equation (26) [38] and Equation (27) [5] are specifically applicable under high flow discharge conditions. Conversely, our derived discharge coefficient formula (Equation (15)) is better suited for low-flow discharge conditions.

Table 7. Discharge coefficient formulas of rectangular side weirs presented in previous studies.
Discharge/(L·s−1)Width of Side Weir/cmHeight of Side Weir/cmNumber of Formula
10~1410~206~12(24)
35–10020~751~19(26), (27)
6~3020~477~20(15)
Table 8. Application scope of discharge coefficient formulas.

In addition to the factors studied in the paper, factors such as the sediment content in the flow, the bottom slope, and the cross-section shape of the channel also have a certain impact on the hydraulic characteristics of the side weir. Further numerical simulation methods can be used to study the hydraulic characteristics and the influencing factors of the side weir. Water measurement facilities generally require high accuracy of water measurement, the flow of sharp-crested side weirs is complex, and the water surface fluctuates greatly. While conducting numerical simulations, experimental research on prototype channels is necessary to ensure the reliability of the results and provide reference for the body design and optimization of side weirs in small channels and field inlets.

7. Conclusions

This paper presents a comprehensive study that encompasses both experimental and numerical simulation research on rectangular side weirs of varying heights and widths within rectangular channels. A thorough analysis of the experimental and numerical simulation results has been conducted, leading to the derivation of several notable conclusions:

  1. A comparative analysis was conducted on the measured and simulated values of water depth and flow velocity. Both of the maximum absolute relative errors were within 10%, which indicated that the numerical simulation of the side weir was feasible and effective.
  2. The water surface profile exhibited a backwater curve along the length of the weir crest. The side weir entrance effect occurred only between Side Ⅰ and Side Ⅱ. This indicates that flow patterns and associated hydraulic forces at the weir entrance play a crucial role in determining water level distribution along the weir crest.
  3. The maximum flow velocity of the cross-section at the upstream end of the weir crest occurred near the weir crest, while the minimum flow velocity occurred at the bottom of the main channel away from the side weir. As the water depth decreased, the position of the maximum flow velocity gradually moved from the upstream end of the side weir to the downstream end of the side weir.
  4. When the height of the side weir remains constant, an increase in the width of the side weir leads to a decrease in pressure at the bottom of the side channel. Conversely, when the width of the side weir is kept constant, an increase in its height results in an increase in pressure at the bottom of the side channel. Therefore, during practical applications involving side weirs, it is crucial to select an appropriate weir width based on the maximum pressure that can be sustained by the channel’s bottom plate.
  5. The discharge coefficient was found to depend on the upstream Froude number Fr1 and the percentage of the side weir height to the upstream flow depth over the side weir P/h1. The relationship between the discharge coefficient and parameters Fr1 and P/h1 was obtained using multiple regression analysis, which was of linear form and provided an easy means to estimate the discharge coefficient. The discharge formula is of high accuracy with relative errors within 10%, which met the water measurement accuracy requirements of small channels in irrigation areas.

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Three-dimensional flow structure in a confluence-bifurcation unit

합류 분기 유닛의 3차원 유동 구조

Di Wang, Xiaoyong Cheng, Zhixuan Cao, Jinyun Deng

Abstract


Enhanced understanding of flow structure in braided rivers is essential for river regulation, flood control, and infrastructure safety across the river. It has been revealed that the basic morphological element of braided rivers is confluence-bifurcation units. However, flow structure in these units has so far remained poorly understood with previous studies having focused mainly on single confluences/bifurcations. Here, the flow structure in a laboratory-scale confluence-bifurcation unit is numerically investigated based on the FLOW3D® software platform. Two discharges are considered, with the central bars submerged or exposed respectively when the discharge is high or low. The results show that flow convergence and divergence in the confluence-bifurcation unit are relatively weak when the central bars are submerged. Based on comparisons with a single confluence/bifurcation, it is found that the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit reign over those of the downstream central bar. Concurrently, the high-velocity zone in the confluence-bifurcation unit is less concentrated than that in a single confluence while being more concentrated than that observed in a single bifurcation. The present work unravels the flow structure in a confluence-bifurcation unit and provides a unique basis for further investigating morphodynamics in braided rivers.

1 Introduction


Confluences and bifurcations commonly exist in alluvial rivers and usually are important nodes of riverbed planform (Szupiany et al., 2012; Hackney et al., 2018). Flow convergence and divergence in these junctions result in highly three-dimensional (3D) flow characteristics, which greatly influence sediment transport, and hence riverbed evolution and channel formation (Le et al., 2019; Xie et al., 2020). Braided rivers, characterized by unstable networks of channels separated by central bars (Ashmore, 2013), have confluence-bifurcation units as their basic morphological elements (Ashmore, 1982; 1991; 2013; Federici & Paola, 2003; Jang & Shimizu, 2005). In particular, confluence-bifurcation units exhibit a distinct morphology from single confluences/bifurcations and bifurcation-confluence regions because two adjacent central bars are included. Within a confluence-bifurcation unit, two tributaries converge at the upstream bar tail and soon diverge to two anabranches again at the downstream bar head. Therefore, the flow structure in the unit may be significantly influenced by both the two central bars, and thus considerably different from that in single confluences, single bifurcations, and bifurcation-confluence regions, where the flow is affected by only one central bar. Enhanced understanding of flow structure in confluence-bifurcation units is urgently needed, which is essential for water resources management, river regulation, flood control, protection of river ecosystems and the safety of infrastructures across the rivers such as bridges, oil pipelines and communication cables (Redolfi et al., 2019; Ragno et al., 2021).

The flow dynamics, turbulent coherent structures, and turbulent characteristics in single confluences have been widely studied since the 1980s (Yuan et al., 2022). Flow dynamics at river channel confluences have been systematically and completely analyzed, which can be characterized by six major regions of flow stagnation, flow deflection, flow separation, maximum velocity, flow recovery and distinct shear layers (Best, 1987). For example, the field observation of Roy et al. (1988) and Roy and Bergeron (1990) highlighted the flow separation zones and recirculation at downstream natural confluence corners. Ashmore et al. (1992) measured the flow field in a natural confluence and found flow accelerates suddenly at the confluence junction with two separated high-velocity cores merging into one single core at the channel centre. De Serres et al. (1999) investigated the three-dimensional flow structure at a river confluence and identified the existence of the mixing layer, stagnation zones, separation zones and recovery zones. Sharifipour et al. (2015) numerically studied the flow structure in a 90° single confluence and found that the size of the separation zone decreases with the width ratio between the tributary and the main channel. Recently, three main classes of large-scale turbulent coherent structures (Duguay et al., 2022) have been presented, i.e. vertical-orientated vortices or Kelvin-Helmholtz instabilities (Rhoads & Sukhodolov, 2001; Constantinescu et al., 2011; 2016; Biron et al., 2019), channel-scale ‘back-to-back’ helical cells, (Mosley, 1976; Ashmore, 1982; Ashmore et al., 1992; Ashworth, 1996; Best, 1987; Rhoads & Kenworthy, 1995; Bradbrook et al., 1998; Lane et al., 2000), and smaller, strongly coherent streamwise-orientated vortices (Constantinescu et al., 2011; Sukhodolov & Sukhodolova, 2019; Duguay et al., 2022). However, no consensus on a universal turbulent coherent structure mode has been reached so far (Duguay et al., 2022). In addition, some studies (Ashworth, 1996; Constantinescu et al., 2011; Sukhodolov et al., 2017; Le et al., 2019; Yuan et al., 2023) have focused on turbulent characteristics, e.g. turbulent kinetic energy, turbulent dissipation rate and Reynolds stress, which can be critical parameters to further explaining the diversity of these turbulent coherent structure modes.

Investigations on the flow structure in single bifurcations have mainly focused on hydrodynamics in anabranches (Hua et al., 2009; van der Mark & Mosselman, 2013; Iwantoro et al., 2022) and around bifurcation bars (McLelland et al., 1999; Bertoldi & Tubino, 2005; 2007; Marra et al., 2014), whereas few studies have considered the effects of bifurcations on the upstream flow structure. Thomas et al. (2011) found that the velocity core upstream of the bifurcation is located near the water surface and towards the channel center in experimental investigations of a Y-shaped bifurcation. Miori et al. (2012) simulated flow in a Y-shaped bifurcation and found two circulation cells upstream of the bifurcation with flow converging at the water surface and diverging near the bed. Szupiany et al. (2012) reported velocity decreasing and back-to-back circulation cells upstream of the bifurcation junction in the field observation of a bifurcation of the Rio Parana River. These investigations provide insight into how bifurcations affect the flow patterns upstream, yet there is a need for further research on the dynamics of flow occurring immediately before the bifurcation junction.

Generally, the findings of studies on bifurcation-confluence regions are similar to those concerning single confluences and bifurcations. Hackney et al. (2018) measured the hydrodynamic characteristics in a bifurcation-confluence of the Mekong River and found the velocity cores located at the channel centre and strong secondary current occurring under low discharges. Le et al. (2019) reported a high-turbulent-kinetic-energy (high-TKE) zone located near the bed in their numerical simulation of flow in a natural bifurcation-confluence region. Moreover, a stagnation zone was found upstream of the confluence and back-to-back secondary current cells were detected at the confluence according to Xie et al. (2020) and Xu et al. (2022). Overall, these studies have further unraveled the flow patterns in river confluences and bifurcations.

Unfortunately, limited attention has been paid to the flow structure in confluence-bifurcation units. Parsons et al. (2007) investigated a large confluence-bifurcation unit in Rio Parana, Argentina, and no classical back-to-back secondary current cells were observed under a discharge of 12000 m3·s−1. To date, the differences in flow structure between confluence-bifurcation units and single confluences/bifurcations have remained far from clear. In addition, although the effects of discharge on flow structure have been investigated in several studies on single confluences/bifurcations, (Hua et al., 2009; Le et al., 2019; Luz et al., 2020; Xie et al., 2020; Xu et al., 2022), cases with fully submerged central bars were not considered, which is typical in braided rivers during floods. In-depth studies concerning these issues are urgently needed to gain better insight into the flow structure in confluence-bifurcation units of braided rivers.

This paper aims to (1) reveal the 3D flow structure in a confluence-bifurcation unit under different discharges and (2) elucidate the differences in the flow structure between confluence-bifurcation units and single confluence/bifurcation cases. Using the commercial computational fluid dynamics software FLOW-3D® (Version 11.2; https://www.flow3d.com; Flow Science, Inc.), fixed-bed simulations of a laboratory-scale confluence-bifurcation unit are conducted, and cases of a single confluence/bifurcation are also included for comparison. Two discharges are considered, with the central bars fully submerged or exposed respectively when the discharge is high or low. Based on the computational results, the 3D flow structure in the confluence-bifurcation unit conditions is analyzed from various aspects including free surface elevation, time-averaged flow velocity distribution, recirculation vortex structure, secondary current, and turbulent kinetic energy and dissipation rate. In particular, the flow structure in the confluence-bifurcation unit is compared with that in the single confluence/bifurcation cases to unravel the differences.h

2. Conceptual flume and computational cases


2.1. Conceptual flume

In this paper, a laboratory-scale conceptual flume is designed and used in numerical simulations. Figure 1(a–d) shows the morphological characteristics of the flume. To ensure that the conceptual flume reflects morphology features of natural braided channels, key parameters governing the flume morphology, e.g. unit length, width, and channel width-depth ratio, are determined according to studies on morphological characteristics of natural confluence-bifurcation units (Hundey & Ashmore, 2009; Ashworth, 1996; Orfeo et al., 2006; Parsons et al., 2007; Sambrook Smith et al., 2005; Kelly, 2006; Ashmore, 2013; Egozi & Ashmore, 2009; Redolfi et al., 2016; Ettema & Armstrong, 2019).

Figure 1. The sketch of the conceptual flume: (a) the original flume, (b) the central bar: (c) the sketch of cross-section C-C, (d) the sketch of cross-section D-D, (e) the modified part for the single confluence, (f) the modified part for the single bifurcation, (g) the position of different cross-sections. The red dashed boxes denote the regions of primary concern.

Figure 1. The sketch of the conceptual flume: (a) the original flume, (b) the central bar: (c) the sketch of cross-section C-C, (d) the sketch of cross-section D-D, (e) the modified part for the single confluence, (f) the modified part for the single bifurcation, (g) the position of different cross-sections. The red dashed boxes denote the regions of primary concern.

2.1.1. Length and width scales of the confluence-bifurcation unit

The length and width scales of the flume are first determined. The inner relation among the length LCB and average width B of a confluence-bifurcation unit and the average width Bi of a single branch was statistically studied by Hundey and Ashmore (2009), which indicates the following relations:
𝐿CB =(4∼5)⁢𝐵 (1)
𝐵 =1.41⁢𝐵𝑖 (2)
In addition, Ashworth (1996) gave B = 2Bi in his experimental research on mid-bar formation downstream of a confluence, while the confluence-bifurcation unit of Rio Parana, Argentina has a relation of B≈1.71Bi (Orfeo et al., 2006; Parsons et al., 2007). Accordingly, the following relations are used in the present paper:
𝐿CB =4⁢𝐵 (3)
𝐵 =1.88⁢𝐵𝑖 (4)
where LCB = 6 m, B = 1.5 m and Bi = 0.8 m.

2.1.2. Central bar morphology

The idealized plane pattern of central bars in braided rivers is a slightly fusiform leaf shape with a short upstream side and a long downstream side (Ashworth, 1996; Sambrook Smith et al., 2005; Kelly, 2006; Ashmore, 2013). To simplify the design, the bar is approximated as a combination of two different semi-ellipses (Figure 1(b)). The major axis Lb is two to ten times longer than the minor axis Bb according to the statistical data in Kelly’s study, and the regression equation is given as (Kelly, 2006):
𝐿𝑏=4.62⁢𝐵0.96𝑏 (5)
In this study, the bar width Bb is set as 0.8 m, whilst the lengths of downstream (LT1) and upstream sides (LT2) are 2 and 1.5 m, respectively (Figure 1(b)). Thus, the relation of Lb and Bb is given as:
𝐿𝑏=(𝐿𝑇⁢1+𝐿𝑇⁢2)=4.375⁢𝐵𝑏 (6)
The lengths of the inlet and outlet parts are determined as Lin = Lout = 8 m, which ensures negligible effects of boundary conditions without exceptional computational cost.

2.1.3. Width-depth ratio

Channel flow capacity can be significantly affected by cross-section shapes. For natural rivers, cross-section shapes can be generalized into three sorts based on the following width-depth curve (Redolfi et al., 2016):
𝐵=𝜓⁢𝐻𝜑(7)
Braided rivers usually have ψ = 5∼50 and φ>1, which indicates a rather wide and shallow cross-section. The central bar form should also be taken into account, so a parabolic cross-section shape is used here with ψ = 8 and φ>1 (Figure 1(c,d)).

2.1.4. Bed slope

In addition, natural braided rivers are usually located in mountainous areas and thus have a relatively large bed slope. According to flume experiments and field observations, the bed slope Sb is mostly in the range of 0.01∼0.02, and a few are below 0.01 (Ashworth, 1996; Egozi & Ashmore, 2009; Ashmore, 2013; Redolfi et al., 2016; Ettema & Armstrong, 2019). In this study, Sb takes 0.005.

2.1.5. Complete sketch of the conceptual flume

In summary, the flume is 29 m long, 2.4 m wide, and 0.6 m high. The plane coordinates (x-direction and y-direction) used in the calculation process are shown in Figure 1
(a). Note that the inlet corresponds to x = 0 m, and the centreline of the flume is located at y = 1.3 m. Besides, the thalweg elevation of the outlet is set as z = 0 m.

2.2. Computational cases

As stated before, the first aim of this paper is to reveal the flow structure in the confluence-bifurcation unit under different discharges. Therefore, two basic cases are set first: (1) case 1a under a low discharge (0.05 m3·s−1) with exposed central bars and (2) case 2a under a high discharge (0.30 m3·s−1) with fully submerged central bars. A total of 22 cross-sections are identified to examine the results (Figure 1(g)).

Further, cases of a single confluence/bifurcation are generated by splitting the original confluence-bifurcation unit into two parts. Part 1 only includes the upstream central bar and focuses on the flow convergence downstream of CS04 (Figure 1(e)), while Part 2 only includes the downstream central bar and focuses on the flow divergence upstream of CS19 (Figure 1(f)). Notably, the numbers of corresponding cross-sections in the original flume are reserved to facilitate comparison. The outlet section of the single confluence as well as the inlet section of the single bifurcation is extended to make the total length equivalent to the original flume (29 m). Also, two discharge conditions (0.05 and 0.30 m3·s−1), which correspond to exposed and fully submerged central bars, are considered for the single confluence/bifurcation. In total, six computational cases are conducted, as listed in Table 1. As the conceptual flume is designed to be symmetrical about the centreline, the momentum flux ratio (Mr) of the two branches should be 1 in all six cases. This is confirmed by further examining the computational results.

CaseConfigurationQin (m3·s−1)Zout (m)MrCondition of bars
1aCBU0.050.151Exposed
1bSC0.050.151Exposed
1cSB0.050.151Exposed
2aCBU0.300.341Submerged
2bSC0.300.341Submerged
2cSB0.300.341Submerged
Table 1. Computational cases with inlet and outlet boundary conditions.

3. Numerical method

In this section, the 3D Large Eddy Simulation (LES) model integrated in the FLOW-3D® (Version 11.2; https://www.flow3d.com; Flow Science, Inc.) software platform is introduced, including governing equations and boundary conditions. Information on computational meshes with mesh independence test can be found in the Supplementary material.

3.1. Governing equations

The LES model was applied in the present paper to simulate flow in the laboratory-scale confluence-bifurcation unit. The LES model has been proven to be effective in simulating turbulent flow in river confluences and bifurcations (Constantinescu et al., 2011; Le et al., 2019). The basic idea of the LES model is that one should directly compute all turbulent flow structures that can be resolved by the computational meshes and only approximate those features that are too small to be resolved (Smagorinsky, 1963). Therefore, a filtering operation is applied to the original Navier-Stokes (NS) equations for incompressible fluids to distinguish the large-scale eddies and small-scale eddies (Liu et al., 2018). The filtered NS equations are then generated, which can be expressed in the form of a Cartesian tensor as (Liu, 2012):

(10) where ¯𝑢𝑖 is the resolved velocity component in the i – direction (i goes from 1 to 3, denoting the x-, y – and z-directions, respectively); t is the flow time; ρ is the density of the fluid; ¯𝑝 is the pressure; ν is the kinematic viscosity; τij is the sub-grid scale (SGS) stress; ¯𝐺𝑖 is the body acceleration. In FLOW3D®, the full NS equations are discretized and solved using the finite-volume/finite-difference method (Bombardelli et al., 2011; Lu et al., 2023).

Due to the filtering process, the velocity can be divided into a resolved part (¯𝑢⁡(𝑥,𝑡)) and an approximate part (𝑢′⁡(𝑥,𝑡)) which is also known as the SGS part (Liu, 2012). To achieve model closure, the standard Smagorinsky SGS stress model is introduced here (Smagorinsky, 1963):
𝜏ij−13⁢𝜏kk⁢𝛿ij=−2⁢𝜈SGS⁢¯𝑆ij(11)
 where νSGS is the SGS turbulent viscosity, and ¯𝑆ij is the resolved rate-of-strain tensor for the resolved scale defined by (Smagorinsky, 1963):
¯𝑆ij=12⁢(∂¯𝑢𝑖∂𝑥𝑗+∂¯𝑢𝑗∂𝑥𝑖)(12) 
In the standard Smagorinsky SGS stress model, the eddy viscosity is modelled by (Smagorinsky, 1963):
𝜈SGS=(𝐶𝑠⁢¯𝛥)2⁢∣¯𝑆∣,∣¯𝑆∣=√2⁢¯𝑆ij⁢¯𝑆ij(13)
¯𝛥=(ΔxΔyΔz⁢)1/3(14) 
where Cs is the Smagorinsky constant, ΔxΔy, and Δz are mesh scales. In FLOW3D®Cs is between 0.1 to 0.2 (Smagorinsky, 1963).
One of the key problems in simulating 3D open channel flow is the calculation of free surface. FLOW3D® uses the Volume of Fluid (VOF) method (Hirt & Nichols, 1981) to track the change of free surface. The VOF method introduces a fluid phase fraction function f to characterize the proportion of a certain fluid in each mesh cell. In that case, the surface position can be precisely located if the mesh cell is fine enough. To monitor the change of f with time and space, the following convection equation is added:

For open channel flow, only two kinds of fluids are involved: water and air. If f is the fraction of water, the state of the fluid in each mesh cell can be defined as:

In FLOW3D®, the interface between water and air is assumed to be shear-free, which means that the drag force on the water from the air is negligible. Moreover, in most cases, the details of the gas motion are not crucial for the heavier water motion so the computational processes will be more efficient.

3.2. Boundary conditions

Six boundary conditions need to be preset in the 3D numerical simulation process. Discharge boundary conditions are used for the inlet of the flume, where the free surface elevation is automatically calculated based on the free surface elevation boundary conditions set for the outlet. The specific information on the inlet and outlet boundary conditions for all computational cases is shown in Table 1. Moreover, because the free surface moves temporally, the free surface boundary conditions are just set as no shear stress and having a normal pressure, and the position of the free surface will be automatically adjusted over time by the VOF method in FLOW3D®. Furthermore, the bed and two side walls are all set to be no-slip for fixed bed conditions, and a standard wall function is employed at the wall boundaries for wall treatment.

The inlet turbulent boundary conditions also need to be considered. They are set by default here. The turbulent velocity fluctuations V are assumed to be 10% of the mean flow velocity with the turbulent kinetic energy (TKE) (per unit mass) equaling 0.5V’2. The maximum turbulent mixing length is assumed to be 7% of the minimum computational domain scale, and the turbulent dissipation rate is evaluated automatically from the TKE.

4. Results and discussion


4.1. Flow structure in the confluence-bifurcation unit

4.1.1. Free surface elevation

Figure 2 shows the free surface elevation at five different longitudinal profiles (i.e. α = 0.2, 0.4, 0.5, 0.6, 0.8) for cases 1a and 2a. The parameter α was defined as follows:𝛼=𝑠𝐵(17) where s is the transverse distance between a certain profile and the left boundary of the flume. In general, the longitudinal change of free surface in the two cases is very similar despite different discharge levels. The free surface elevation decreases as the channel narrows from the upstream bifurcation to the front of the confluence-bifurcation unit. On the contrary, when the flow diverges again at the end of the confluence-bifurcation unit, the free surface elevation increases with channel widening. However, whether the fall or rise of free surface elevation in case 1a is much sharper than that in case 2a, especially at profiles with α = 0.2 and 0.8 (Figure 2(a)), which indicates there may be distinct flow states between the two cases. To further illustrate this finding, the Froude number Fr at different cross-sections (CS08∼CS15) is examined. In case 2a, the flow remains subcritical within the confluence-bifurcation unit. By contrast, in case 1a, a local supercritical flow is observed near the side banks of CS09 (i.e. α = 0.2 and 0.8), with Fr being about 1.2. This local supercritical flow can lead to a hydraulic drop followed by a hydraulic jump, which accounts for the sharp change of the free surface. The foregoing reveals that when central bars are exposed under relatively low discharge, supercritical flow is more likely to occur near the side banks of the confluence junction due to flow convergence.

Figure 2. Five time-averaged free surface elevation profiles in the confluence-bifurcation unit, in which α denotes the lateral position of the certain profile. Note that the black dashed line denotes the position of CS09, where Fr is about 1.2 near the side banks (α = 0.2 and 0.8) in case 1a. Z’ = z/h2X’ = x/Bh2 is the maximum flow depth at the outlet boundary of cases 2a, 2b and 2c, h2 = 0.34 m.

Moreover, in both cases 1a and 2a, the free surface is higher at the channel centre than near the side banks, whether at the front or the end of the confluence-bifurcation unit. Thus, lateral free surface slopes from the centre to the side banks are generated. For example, the lateral free surface slopes at CS09 are 0.022 and 0.016 respectively for cases 1a and 2a. These lateral slopes can lead to lateral pressure gradient force whose direction is from the channel centreline to the side banks. Notably, the lateral surface slope in case 1a is steeper than that in case 2a, which may also result from the effect of the supercritical flow.

4.1.2. Time-averaged streamwise flow velocity

Figure 3. Time-averaged flow velocity distribution at three different slices over z-direction in the confluence-bifurcation unit: (a)∼(c) case 1a, (d)∼(f) case 2a. The flow direction is from the left to the right. StZ = Stagnation Zones, MiL = Mixing Layer. X’ = x/B, Y’ = y/B, Ui’ = Ui/Uti, Ui denotes the time-averaged streamwise flow velocity in case series i (i = 1,2), Uti denotes the cross-section-averaged streamwise flow velocity in case series i, Ut1 = 0.385 m/s, for case 2a Ut2 = 0.714 m/s.
Figure 4. Time-averaged flow velocity contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a.

Besides the shared features described above, some differences between the two cases are also identified. First, flow stagnation zones at the upstream bar tail are found exclusively in case 1a as the central bars are exposed (Figure 3
(a–c)). Second, in case 1a the mixing layer is obvious in both the lower or upper flows (Figure 3
(a–c)), while in case 2a the mixing layer can be inconspicuous in the upper flow (Figure 3
(f)). Third, in case 1a, two high-velocity cores gradually transform into one single core downstream of the confluence [Figure 4
(a), CS08∼CS11] and are divided into two cores again at the downstream bar head [Figure 4
(a), CS15]. By contrast, in case 2a, the two cores merge much more rapidly [Figure 4
(a), CS08∼CS09], and no obvious reseparation of the merged core is found at the downstream bar head (Figure 3
(d–f)). The latter two differences between cases 1a and 2a indicate that the flow convergence and divergence are relatively weak when the central bars are fully submerged. It is noticed that when the central bars are exposed, the flow in branches needs to steer around the central bar, which can cause a large angle between the two flow directions at the confluence, and thus relatively strong flow convergence and divergence may occur. By contrast, when the central bars are fully submerged, the flow behavior resembles that of a straight channel, with flow predominantly moving straight along the main axis of the central bars. Therefore, a small angle between two tributary flow forms, and thus flow convergence and divergence are relatively mild.

4.1.3. Recirculation vortex

A recirculation vortex with a vertical axis is a typical structure usually found where flow steers sharply, and is generated from flow separation (Lu et al., 2023). This vortex structure is found in the confluence-bifurcation unit in the present study, marking several significant flow separation zones. Figure 5 shows the recirculation vortex structure at the bifurcation junction of the confluence-bifurcation unit. In both cases 1a and 2a, two recirculation vortices BV1 and BV2 are found at the bifurcation junction corner. Moreover, BV1 and BV2 seem well-established near the bed but tend to transform into premature ones in the upper flow, and there is also a tendency for the cores of BV1 and BV2 to shift downstream as they transition from the lower to the upper flow (Figure 5(a–c,d–f)). This finding indicates that flow separation zones exist at the bifurcation junction corner, and the vortex structure is similar in the separation zones under low and high discharges. These flow separation zones are generated due to the inertia effect as flow suddenly diverges and steers towards the curved side banks of the channel (Xie et al., 2020). Notably, two additional vortices BV3 and BV4 are found at both sides of the downstream bar in case 1a (Figure 5(a–c)), but no such vortices exist in case 2a. This difference shows that flow separation zones at both sides of the downstream bar are hard to form when the bars are completely submerged under the high discharge.

Figure 5. Recirculation vortices at the bifurcation junction (streamline view at three different slices over z-direction): (a)∼(c) case 1a, (d)∼(f) case 2a. The red solid line marked out the position of these vortices (BV1∼BV4).

Similarly, Figure 6 shows the recirculation vortex structure at the confluence junction of the confluence-bifurcation unit. No noteworthy similarities but a key difference between the two cases are observed at this site. Two vortices CV1 and CV2 are found downstream of the confluence junction corner in case 1a (Figure 6(c)), which mark two separation zones. Conversely, no such separation zones are found in case 2a. In fact, separation zones were reported at similar sites under relatively low discharges in some previous studies (Ashmore et al., 1992, Luz et al., 2020, Sukhodolov & Sukhodolova, 2019; Xie et al., 2020). Nevertheless, the flow separation zones at the confluence corner are very restricted in the present study (Figure 6(c)). Ashmore et al. (1992) also reported that no, or very restricted flow separation zones occur downstream of natural river confluence corners, primarily because of the relatively slow change in bank orientation compared with the sharp corners of laboratory confluences where separation is pronounced (Best & Reid, 1984; Best, 1988). In the present study, the bank orientation also changes slowly, which may explain why flow separation zones are inconspicuous at the confluence corner.

Figure 6. Recirculation vortices at the confluence junction (streamline view at three different slices over z-direction): (a)∼(c) case 1a, (d)∼(f) case 2a. The red solid line marked out the position of these vortices (CV1 & CV2).

The differences in the distribution of recirculation vortices discussed above may be mainly attributed to the difference in the angle between the tributary flows under different discharges. Some previous studies have reported that the confluence/bifurcation angle can significantly influence the flow structure at confluences/bifurcations (Best & Roy, 1991; Ashmore et al., 1992; Miori et al., 2012). Although the confluence/bifurcation angle is fixed due to the determined central bar shape in the present study, the angle between two tributary flows is affected by the varying discharge. When the central bars are exposed under the low discharge, the flow is characterized by a more pronounced curvature of the streamlines, and a large angle between the two tributary flows is noted (Figure 6(b)), causing strong flow convergence and divergence. By contrast, a small angle forms as the central bars are submerged, thereby leading to relatively weak flow convergence/divergence (Figure 6(e)). Overall, the differences mentioned above can be attributed to the differences in the intensity of flow convergence and divergence under different discharges.

It should be noted that some previous studies (Constantinescu et al., 2011; Sukhodolov & Sukhodolova, 2019) presented that there is a wake mode in the mixing layer of two streams at the confluence junction. The wake mode means that in the mixing layer, multiple streamwise coherent vortices moving downstream will form, which is similar to the flow structure around a bluffing body (Constantinescu et al., 2011). However, no such structure has been found within the confluence-bifurcation unit in this study. According to the numerical simulations of Constantinescu et al. (2011), a wake mode was found at a river confluence with a concordant bed and a momentum flux ratio of about 1. The confluence has a much larger angle (∼60°) between the two streams when compared to the confluence junction of the confluence-bifurcation unit in the present study where the angle is about 25°. As flow mechanics at river confluences may include several dominant mechanisms depending on confluence morphology, momentum ratio, the angle between the tributaries and the main channel, and other factors (Constantinescu et al., 2011), the relatively small confluence angle in the present study may explain why the wake mode is absent. The possible effects of the confluence/bifurcation angle are reserved for future study. Additionally, flow separation can lead to reduced local sediment transport capacity, thus causing considerable sediment deposition under natural conditions. Hence, the bank may migrate towards the inner side of the channel at the positions of CV1, CV2, BV1, and BV2, while the bar may expand laterally at the positions of BV3 and BV4.

4.1.4. Secondary current

Secondary current is the flow perpendicular to the mainstream axis (Thorne et al., 1985) and can be categorized into two primary types based on its origin: (1) Secondary current generated by the interaction between centrifugal force and pressure gradient force; (2) Secondary current resulting from turbulence heterogeneity and anisotropy (Lane et al., 2000). There are some widely recognized definitions of secondary current strength (SCS) (Lane et al., 2000). In this paper, the secondary current cells are identified by visible vortex with a streamwise axis, and the definition of SCS proposed by Shukry (1950) is used:

where uxuy, and uz are flow velocities in xy, and z directions and ux represents the mainstream flow velocity.

Figure 7 presents contour plots of SCS and the secondary current structure at key cross-sections of the study area. When the central bars are exposed, at the upstream bar tail (CS08), intense transverse flow occurs with flow converging to the centreline, but no secondary current cell is formed (Figure 7(a)). This is consistent with the findings of Hackney et al. (2018). At the confluence junction (CS09), transverse flow still plays a major role in the secondary current structure, with flow converging to the centreline at the surface and diverging to side banks near the bed (Figure 7(b)). Moreover, ‘back-to-back’ helical cells, which are two vortices rotating reversely, tend to generate at CS09 with their cores located near the side banks (Figure 7(b)) (Mosley, 1976; Ashmore, 1982; Ashmore et al., 1992), yet their forms are rather premature. As the flow goes downstream, the cores of the helical cells gradually rise to the upper flow and approach towards the centreline, and the helical cells become well-established (Figure 7(c–e)). When the flow diverges again at the downstream bar head (CS15), the helical cells attenuate rapidly, and the secondary current structure is once again characterized predominantly by transverse flow (Figure 7(f)).

Figure 7. Distribution of secondary current strength and secondary current cells at six different cross-sections: (a)∼(f) case 1a, (g)∼(l) case 2a. The secondary current cells are identified by visible lateral vortices (streamline view). The zero distance of each cross-section is located on the right bank.

When the central bars are fully submerged under the high discharge, the secondary current structure at the upstream bar tail and the confluence junction exhibits a resemblance to that under the low discharge (Figure 7(g,h)). However, at CS09, two pairs of cells with different scales tend to form under the high discharge (Figure 7(h)). The large and premature helical cells are similar to those under the low discharge, whereas the small helical cells are located near side banks possibly due to wall effects. As the flow moves downstream, the large helical cells tend to diminish rapidly and merge with the small ones near both side walls (Figure 7(i–k)). Moreover, the secondary current structure is once again characterized predominantly by transverse flow at CS14 under the high discharge, which occurs earlier than that under the low discharge (Figure 7(k)). At the downstream bar head, transverse flow still takes a dominant place, while the helical cells seem to become premature with increased scale (Figure 7(l)).

In general, in both cases 1a and 2a, the lateral distribution of SCS at all cross-sections is symmetrical about the channel centreline, where SCS is relatively small. A relatively high SCS is detected at both the upstream bar tail and the downstream bar head due to the effects of centrifugal force caused by flow steering. SCS decreases rapidly from the upstream bar tail (CS08) to the entrance of the downstream bifurcation junction (CS14), followed by a sudden increase at the downstream bar head (CS15) (Figure 7
(a–e, g–k)). However, the distribution of high-SCS zones is different between the two discharges. Under the low discharge, high-SCS zones appear along the bottom near the centerline and at the free surface on both sides of the centreline. Although similar high-SCS zones are found along the bottom near the centerline under the high discharge, the high-SCS zones are not found at the free surface. Furthermore, it is noticed that more obvious high-SCS zones appear under the low discharge compared with the high discharge, especially at CS09. This may be attributed to the differences in the intensity of flow convergence and divergence under different submerging conditions of the central bars. When the central bars are exposed, flow convergence and divergence are strong and sharp flow steering occurs, thereby causing large SCS. By contrast, when the central bars are fully submerged, flow convergence and divergence are relatively weak, and thus small SCS is observed.

4.1.5. Turbulent characteristics

Turbulent characteristics reflect the performance of energy and momentum transfer activities in flow (Sukhodolov et al., 2017). Comprehensive analysis of turbulent characteristics is crucial as they greatly impact the incipient motion, settling behavior, diffusion pattern, and transport process of sediment. Here, the TKE and turbulent dissipation rate (TDR) of flow in the confluence-bifurcation unit are analyzed.

Figure 8 shows the distribution of TKE on various cross-sections in cases 1a and 2a. In the same way, Figure 10 shows the distribution of TDR. The values of TKE and TDR are nondimensionalized with mid-values of TKE = 0.005 m2·s−2 and TDR = 0.007 m3·s−2. In both cases 1a and 2a, the distributions of TKE and TDR show symmetrical patterns concerning the channel centreline. High-TKE and high-TDR zones exhibit a belt distribution near the channel bottom (McLelland et al., 1999; Ashworth, 1996; Constantinescu et al., 2011), indicating that turbulence primarily originates at the channel bottom due to the influence of bed shear stress. A sudden increase of TKE (Weber et al., 2001) and TDR occurs near the channel bottom at the confluence junction [Figure 8 and 9, CS08∼CS09] and from the entrance of the bifurcation junction (CS14) to the downstream bar head (CS15) (Figures 8 and 9).

Figure 8. Turbulent kinetic energy contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a. TKE = turbulent kinetic energy. TKE’ =  dimensionless value of TKE, with regard to a mid-value of TKE = 0.005 m2·s−2.
Figure 9. Turbulent dissipation rate contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a. TDR = turbulent dissipation rate. TDR’ =  dimensionless value of TDR, with regard to a mid-value of TDR = 0.007 m3·s−2.
Figure 10. Comparison of the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections between the confluence-bifurcation unit and the single confluence. (a)∼(f) 1a vs. 1b, (g)∼(l) 2a vs. 2b.

Despite the common turbulent characteristics between cases 1a and 2a, additional high-TKE zones are found in the upper flow at the upstream bar tail (CS08), the confluence junction (CS09) and the downstream bar head (CS15) (Figure 8) when the central bars are fully submerged. The formation mechanism of these high-TKE zones near the water surface is more complicated, which may result from interactions of velocity gradient, secondary current structure and wall shear stress (Engel & Rhoads, 2017; Lu et al., 2023).

4.2. Comparison with single confluence/bifurcation cases

In this section, the results of a single confluence (cases 1b and 2b) and a single bifurcation (cases 1c and 2c) are compared with those of the confluence-bifurcation unit (cases 1a and 2a) under two discharges. Flow structure at CS08∼CS15 is mainly concerned below.

4.2.1. Comparison with single confluence cases

First, the patterns of time-averaged streamwise velocity, TKE and TDR within the single confluence (presented by contour plots in the supplementary materials) are assessed and then compared with those within the confluence-bifurcation unit (Figures 4, 8, and 9). It is found that distributions of these parameters are similar in the confluence-bifurcation unit and the single confluence from the upstream bar tail (CS08) to the entrance of the bifurcation junction (CS14), despite varying discharges. As the existence of the downstream central bar is the main difference between the single confluence and the confluence-bifurcation unit, this finding indicates that the downstream bar may have limited influence on the flow structure in the confluence-bifurcation unit. In other words, the flow structure in the confluence-bifurcation unit appears to be mainly shaped by the presence of the upstream bar, with its impact potentially reaching as far as the entrance of the bifurcation (CS14). Moreover, under the low discharge, the two high-velocity cores seem to merge later (at CS11) in the single confluence than in the confluence-bifurcation unit (at CS10), which indicates the convergence of two tributary flows may achieve a steady state faster in the confluence-bifurcation unit. To further elucidate the differences, results on the distribution of time-averaged streamwise velocity and TKE along the flow depth are discussed below.

4.2.1.1. Time-averaged streamwise velocity

Figure 10 shows the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections. Note that α = 0.5 denotes the channel centreline and α = 0.7 denotes a position near the side banks. As only marginal differences are found at α = 0.3 and 0.7, only profiles at α = 0.7 are displayed for clarity.

Under the low discharge, no obvious difference in the distribution of time-averaged streamwise flow velocity is observed at the upstream bar tail (Figure 10(a)). At the confluence junction (Figure 10(b)), the velocities near the side banks (α = 0.7) are larger than those at the centre (α = 0.5) in both the confluence-bifurcation unit and the single confluence, which suggests that the two tributary flows have not sufficiently merged. The two tributary flows achieve convergence at CS11 in both the confluence-bifurcation unit and the single confluence (Figure 10(c)), with the velocity at the centre (α = 0.5) is larger than that near the side banks. Nevertheless, the velocities at the centre (α = 0.5) and near the side banks (α = 0.7) are closer to each other in the confluence-bifurcation unit than those in the single confluence, which represents less sufficient flow convergence in the confluence-bifurcation unit than in the single confluence. Therefore, it can be inferred that the convergence of two tributary flows may achieve a steady state faster in the confluence-bifurcation unit. After reaching the steady state, the velocity near the side banks (α = 0.7) is smaller in the single confluence than in the confluence-bifurcation unit despite close values at the centre (α = 0.5) (Figure 10(d,e)). This leads to a more pronounced disparity between velocities at the centre and near the side banks in the single confluence than that observed in the confluence-bifurcation unit. In other words, the high-velocity zone is more concentrated on the channel centreline in the single confluence, while the lateral distribution of flow velocity tends to be more uniform in the confluence-bifurcation unit. This may be attributed to the influence of the downstream central bar, which is further proved by comparing the velocity profiles at CS15 (Figure 10(e)).

As for the high discharge condition, from CS08 to CS14, the quantitative differences in velocity distribution between the confluence-bifurcation unit and the single confluence seem small. This indicates that the effect of morphology appears to be subdued when the central bars are fully submerged under the high discharge. It should be also noted that under both the low and high discharge, velocity profiles at the corresponding location exhibit the same shapes in the confluence-bifurcation unit and the single confluence, which indicates that the upstream confluence may dominate the flow structure in the confluence-bifurcation unit.

4.2.1.2. Secondary current

Figure 11 shows contour plots of SCS and the secondary current structure for single confluence cases. Compared with Figure 7, under both low and high discharge conditions, the distribution of SCS and the structure of helical cells in the confluence-bifurcation unit and the single confluence are very similar from CS08 to CS12 (Figure 7(a–d, g–j) and Figure 11(a–d, g–j)]. This indicates that the secondary current structure in the confluence-bifurcation unit exhibits certain consistent features when compared to those in the single confluence, thus proving that the effects of the upstream central bar may dominate the flow structure in the confluence-bifurcation unit. However, the secondary current structure at CS14 and CS15 is different between the confluence-bifurcation unit and the single confluence (Figure 7 and 11(e, f, k,l)). Under the low discharge, transverse flow is from the side banks to the centre and relatively high SCS is found near the side banks at CS14 in the single confluence, while the transverse flow is always from the centre to the side banks and SCS is relatively low at the corresponding sites in the confluence-bifurcation unit (Figure 11(e)). Under the high discharge, the helical cells near the side walls almost diminish in the single confluence, while they still exist in the confluence-bifurcation unit at CS14 (Figure 11(k)). Under both low and high discharges, the secondary current pattern at CS15 is similar to that at CS14 in the single confluence, while they are different in the confluence-bifurcation unit due to the existence of the downstream central bar. This comparison indicates that the existence of the downstream central bar can influence the upstream secondary current structure, nevertheless, the effects are fairly limited.

Figure 11. Secondary current at different cross-sections in the single confluence condition: (a)∼(f) case 1b, (g)∼(l) case 2b. The zero distance of each cross-section is located on the right bank.
4.2.1.3. Turbulent kinetic energy

Figure 12 shows TKE distribution along the flow depth at different cross-sections. Under the low discharge, in general, the maximum TKE tends to appear near the channel bottom in both the confluence-bifurcation unit and the single confluence. No obvious difference is observed at the upstream bar tail (CS08) (Figure 12(a)). Downstream this site (at CS09), the maximum TKE near the side banks (α = 0.7) is larger than that at the channel centre in the single confluence, while they are close to each other in the confluence-bifurcation unit (Figure 12(b)). This can also be attributed to the insufficient convergence of the two tributary flows. At CS11, flow convergence achieves a steady state in the confluence-bifurcation unit, while it remains insufficient in the single confluence. As flow convergence reaches a steady state at CS12, the maximum TKE in the single confluence exhibits a more concentrated distribution on the channel centre than that in the confluence-bifurcation unit (Figure 12(d)). This effect becomes more obvious downstream at CS14 (Figure 12(e)). The less-concentrated distribution of the maximum TKE in the confluence-bifurcation unit can be owing to the effects of the downstream central bar as well, which appears analogous to that mentioned in 4.2.1.1.

Figure 12. Comparison of the distribution of TKE along the flow depth at different cross-sections between the confluence-bifurcation unit and the single confluence. (a)∼(f) 1a vs. 1b, (g)∼(l) 2a vs. 2b.

Under the high discharge condition, two peaks of TKE appear in both the confluence-bifurcation unit and the single confluence (Figure 12(g–l)). Moreover, in both the confluence-bifurcation unit and the single confluence, from the upstream bar tail to the downstream bar head, the peak of TKE in the upper flow is larger at the channel centre (α = 0.5), while the peak of TKE in the lower flow is larger near the side banks (α = 0.7). However, the disparity between the TKE near the side banks and at the channel centre seems to be larger in the single confluence, while the TKE in the confluence-bifurcation unit takes a more uniform distribution. Even though, TKE profiles at the corresponding location exhibit highly similar shapes in the confluence-bifurcation unit and the single confluence, suggesting that the effects of channel morphology seem to be inhibited when the central bars are submerged under the high discharge.

4.2.2. Comparison with single bifurcation cases

Distributions of time-averaged streamwise velocity, TKE and TDR at corresponding cross-sections are also compared between the single bifurcation (see the Supplementary material) and the confluence-bifurcation unit (Figures 4, 8 and 9). Unlike the high similarity in flow characteristics exhibited between the confluence-bifurcation unit and the single confluence, significant differences are found between the confluence-bifurcation unit and the single bifurcation, especially at CS08∼CS14. On the one hand, the high-velocity zones are broader and asymmetrical concerning the channel centreline in the single bifurcation, with a belt-like and an approximately elliptic-like distribution respectively under the low and high discharges. By contrast, the high-velocity zone is a core that concentrates on the channel centre in the confluence-bifurcation unit. Moreover, the maximum velocity seems smaller in the single bifurcation than that in the confluence-bifurcation unit. On the other hand, the high-TKE belt near the channel bottom appears to be narrower in the single bifurcation than in the confluence-bifurcation unit, especially at CS08∼CS14 under the low discharge. Furthermore, additional high-TKE zones are found near the side walls at CS08∼CS11 in the single bifurcation, of which the scale is obviously smaller than those in the confluence-bifurcation unit. In addition, TKE at the channel centre is smaller near the free surface in the single bifurcation than that in the confluence-bifurcation unit. Nevertheless, the distributions of velocity, TKE and TDR seem to be similar in the confluence-bifurcation unit and the single bifurcation at CS15. As the existence of the upstream central bar is the main difference between the single confluence and the confluence-bifurcation unit, all the above findings indicate that the upstream central bar greatly influences the flow structure in the confluence-bifurcation unit. On the other hand, the downstream central bar may have a restricted influence on the flow structure in the confluence-bifurcation unit, whose impact may be limited to a range between the entrance of the bifurcation (CS14) and the downstream bar head (CS15). To further elucidate the differences, results on the distribution of time-averaged streamwise velocity and TKE along the flow depth are discussed below.

4.2.2.1. Time-averaged streamwise velocity

Figure 13 shows the distribution of time-averaged streamwise velocity along the flow depth at different cross-sections. Under the low discharge, distinct distribution patterns of flow velocity between the confluence-bifurcation unit and the single bifurcation are found at CS08, CS09 and CS11, which can be attributed to the effects of upstream flow convergence (Figure 13(a–c)). However, when the flow convergence reaches a steady state in the confluence-bifurcation unit (Figure 13(d–f)), the high-velocity zone is more concentrated in the confluence-bifurcation unit than in the single bifurcation due to to the significant influence of the upstream central bar on the flow structure. The velocity profiles at the downstream bar head can be a shred of evidence as well, with the maximum velocity larger at the channel centre but smaller near the side banks in the confluence-bifurcation unit than in the single bifurcation.

Figure 13. Comparison of the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections between the confluence-bifurcation unit and the single bifurcation. (a)∼(f) 1a vs. 1c, (g)∼(l) 2a vs. 2c.

Under the high discharge, the distribution of velocity seems to exhibit limited differences between the two kinds of morphology, which indicates that the effects of channel morphology may be less noticeable when the central bars are fully submerged under the high discharge. Nevertheless, the velocity in the lower flow (below a relative depth of 0.45) shows a uniform lateral distribution in the single bifurcation, as the velocity profile at the channel centreline (α = 0.5) is in line with that near the side banks (α = 0.7) (Figure 13(g–l)). However, in the confluence-bifurcation unit, different velocity distributions in the lower flow can be observed at the channel centreline (α = 0.5) and near the side banks (α = 0.7). The foregoing results indicate that when the central bars are fully submerged, the high-velocity zones are more concentrated on the channel centreline in the confluence-bifurcation unit, while the lateral distribution of flow velocity within the single bifurcation tends to be more uniform, especially near the bifurcation junction (Figure 13(j,k)). This can also be attributed to the dominant influence of the upstream central bar over the downstream central bar.

It is also noted that the flow velocity distribution along the flow depth in the confluence-bifurcation unit is of a similar pattern despite varying discharges. As a critical point, the maximum velocity appears in the upper flow. The distribution above the critical point is approximately linear whereas it appears logarithmic below. By contrast, despite the similarity observed under the low discharge, the flow velocity distribution along the flow depth within the single bifurcation exhibits a distinct pattern under the high discharge, especially near the side banks (Figure 13(e–h)). On the one hand, the critical point in the upper flow no longer corresponds to the maximum velocity. On the other hand, the velocity distribution deviates from logarithmic below the critical point, with the maximum velocity appearing at a relative depth of 0.45. Succinctly, the distribution of streamwise velocity along the flow depth may retain the same pattern regardless of discharge levels in the confluence-bifurcation unit, while it may exhibit distinct patterns under different discharge levels in the single bifurcation.

4.2.2.2. Secondary current

Figure 14 shows contour plots of SCS and the distribution of secondary current for single bifurcation cases. In general, the value of SCS near the side banks at CS08∼CS14 (Figure 14(a–d, g–j)) in the single bifurcation seems smaller than that in the confluence-bifurcation unit (Figure 7(a–d, g–j)), especially under the low discharge. SCS distribution at CS14 is similar in the confluence-bifurcation unit and the single bifurcation under both low and high discharges. This difference in SCS distribution between the confluence-bifurcation unit and the single bifurcation indicates that the downstream bifurcation may have a restricted influence on the flow structure in the confluence-bifurcation unit. This influence is limited to a range between the entrance of the bifurcation (CS14) and the downstream bar head (CS15).

Figure 14. Secondary current at different cross-sections in the single bifurcation condition: (a)∼(f) case 1c, (g)∼(l) case 2c. The zero distance of each cross-section is located on the right bank.

In addition, the secondary current structure may also present different patterns in response to varying channel morphologies and discharge conditions. Under the low discharge condition, multiple unstable helical cells with asymmetrical distribution are formed from CS08 to CS12 in the single bifurcation (Figure 14(a–d)), while no obvious helical cells are found at CS14 and CS15 (Figure 14(d,e)). These findings are quite different from the stable and symmetrical helical cells at all cross-sections shown in the confluence-bifurcation unit (Figure 7). This difference may be attributed to the significant influence of the upstream central bar and the limited influence of the downstream central bar. Under the high discharge condition, only one pair of premature helical cells are found from CS08 to CS12 in the single bifurcation with their cores located near the side banks (Figure 14(e,f)). As the flow moves downstream, the helical cells gradually develop and become well-established (Figure 14(g,h)). These helical cells in the single bifurcation show symmetric cross-sectional distribution and a similar longitudinal development as in the confluence-bifurcation unit. However, in the confluence-bifurcation unit, two pairs of helical cells appear upstream of CS12 and CS14 and gradually fuse to one pair under the high discharge. As the ‘two-pairs’ structure in the confluence-bifurcation unit origins from the upstream confluence, the differences in the secondary current structure between the single bifurcation and the confluence-bifurcation unit under the high discharge can also be owing to the effects of the upstream central bar in excess of those of the downstream central bar.

4.2.2.3. Turbulent kinetic energy

Figure 15 shows the TKE distribution along the flow depth at different cross-sections. Under the low discharge, when the two tributary flows have not achieved sufficient convergence in the confluence-bifurcation unit, the maximum TKE is more concentrated in the single bifurcation (Figure 15(a–c)). As flow convergence achieves a steady state, more concentrated high-TKE zones appear at the channel centre within the confluence-bifurcation unit, confirming the finding that the effects of the upstream central bar reign over those of the downstream central bar in the confluence-bifurcation unit. However, things can be very complicated under the high discharge. For TKE distribution at the channel centreline, two peaks appear in the confluence-bifurcation unit with one close to the free surface and the other near the bed (Figure 15(g–l)). By contrast, only one peak near the bed is present in the single bifurcation. Therefore, a larger TKE can be found in the upper flow of the channel centreline in the confluence-bifurcation unit. For TKE distribution near the side banks, two peaks appear in both the confluence-bifurcation unit and the single bifurcation at CS09∼CS14 (Figure 15(h–l)). The upper peak is larger but the lower peak is smaller within the single bifurcation than those within the confluence-bifurcation unit. These significant discordances in TKE distribution under the high discharge further prove that the effects of the upstream bar on the flow structure in the confluence-bifurcation unit are more prominent than those of the downstream central bar.

Figure 15. Comparison of the distribution of TKE along the flow depth at different cross-sections between the confluence-bifurcation unit and the single bifurcation. (a)∼(f) 1a vs. 1c, (g)∼(l) 2a vs. 2c.

4.2.3. Further discussion of the comparisons

The above subsections have revealed significant differences in flow structure within the confluence-bifurcation unit and the single confluence and bifurcation, which directly result from the distinct channel morphologies and vary with the discharge conditions as well. These differences are summarized and further discussed below.

The distinctive morphology of a confluence-bifurcation unit plays a pivotal role in governing streamwise flow velocity distribution, secondary current structure, and turbulent kinetic energy distribution within the channel. Generally, from the upstream bar tail (CS08) to the entrance of the bifurcation (CS14), the flow structure in the confluence-bifurcation unit is highly similar to that in the single confluence, while it exhibits great differences (as shown in 4.2.2) between the confluence-bifurcation unit and the single bifurcation. This indicates that the upstream central bar greatly influences the flow structure in the confluence-bifurcation unit, with the effects spreading to the entrance of the bifurcation. At the downstream bar head (CS15), the flow structure (e.g. the transverse flow patterns) in the confluence-bifurcation unit exhibits high similarity to that in the single bifurcation. However, these similarities do not spread to upstream cross-sections, suggesting that the influence of the downstream central bar is limited at the bifurcation junction. In a word, the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit are in excess of those of the downstream central bar.

However, despite the influence of channel morphology, discharge may also have some important effects on the streamwise flow velocity distribution. On the one hand, when the central bars are exposed under the low discharge, the high-velocity zone is less concentrated in the confluence-bifurcation unit than in the single confluence, while it is more concentrated in the confluence-bifurcation unit than in the single bifurcation. On the other hand, it is noticed that when the central bars are fully submerged under the high discharge, reduced differences in flow structure between the confluence-bifurcation unit and the single confluence/bifurcation are witnessed, and thus the morphology effect seems to be subdued.

4.3. Implications

The present work unravels the flow structure in a laboratory-scale confluence-bifurcation unit and takes the first step to further investigating morphodynamics in such channel morphology. Based on the comparison with a single confluence/bifurcation, the findings provide insight into the complex 3D interactions between water flow and channel morphology. The distinct flow structure in the laboratory-scale confluence-bifurcation unit may appreciably alter sediment transport and morphological evolution, of which research is underway. As the basic morphological element of braided river planform is confluence-bifurcation units, the present work should have direct implications for flow structure in natural braided rivers. This is pivotal for the sustainable management of braided rivers which deals with water and land resources planning, eco-hydrological well-being, and infrastructure safety such as cross-river bridges and oil pipelines (Redolfi et al., 2019; Ragno et al., 2021).

Notably, braided rivers worldwide (e.g. in the Himalayas, North America, and New Zealand) have undergone increased pressures and will continue to evolve due to forces of global climate change and intensified anthropogenic activities (Caruso et al., 2017; Hicks et al., 2021; Lu et al., 2022). In particular, channel aggradation caused by increased sediment supply as well as exploitation of braidplain compromise space for flood conveyance, making the rivers prone to flooding. In this sense, an enhanced understanding of the flow structure under high discharge when central bars are fully submerged is essential for mitigating flooding hazards.

5. Conclusions


This study has numerically investigated the 3D flow structure in a laboratory-scale confluence-bifurcation unit based on the LES model integrated in the FLOW3D® software platform. Two different discharges are considered with the central bars fully submerged or exposed respectively when the discharge is high or low. Cases of a single confluence/bifurcation are included for comparison. The key findings of this paper are as follows:

  1. Several differences are highlighted in the comparison of the flow structure in the confluence-bifurcation unit between the two discharges. When the central bars are fully submerged under the high discharge, the mixing layer of two tributary flows is less obvious, and two high-velocity cores merge more rapidly as compared with those under the low discharge. Besides, flow separation zones are found neither at the confluence corner nor on both sides of the downstream bar when the central bars are fully submerged. Moreover, SCS seems to be smaller near the side banks under the high discharge than under the low discharge. Therefore, it is suggested that flow convergence/divergence is relatively weak in the confluence-bifurcation unit when central bars are fully submerged under the high discharge.
  2. From the upstream bar tail to the entrance of the bifurcation, the flow structure in the confluence-bifurcation unit is highly similar to that in the single confluence, while it exhibits great differences from that in the single bifurcation. Only at the downstream bar head does the flow structure in the confluence-bifurcation unit exhibit high similarity to that in the single bifurcation. Consequently, the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit reign over those of the downstream central bar.
  3. Despite the influence of channel morphology, discharge may also have significant effects on the distribution of streamwise flow velocity. On the one hand, when the central bars are exposed under the low discharge, the high-velocity zone is less concentrated in the confluence-bifurcation unit than in the single confluence, while it is more concentrated in the confluence-bifurcation unit than in the single bifurcation. On the other hand, when the central bars are fully submerged under the high discharge, reduced differences in flow structure between the confluence-bifurcation unit and the single confluence/bifurcation are witnessed, and thus the morphology effect seems to be subdued.

It is noticed that the effects of other factors (e.g. confluence and bifurcation angles, bed discordance) on the flow structure in the confluence-bifurcation unit are not discussed here. Studies on these issues are warranted and reserved for future work.

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Consumer Products | 소비자 제품의 설계 및 제조

자유 표면 흐름은 가정과 사무실 환경 모두에서 사용되는 소비자 제품의 설계 및 제조에서 일반적입니다. 예를 들어, 병 채우기는 매일 대규모로 이루어지는 프로세스입니다. 생산 속도를 극대화하면서 낭비를 최소화하도록 이러한 프로세스를 설계하면 시간이 지남에 따라 상당한 비용 절감으로 이어질 수 있습니다. FLOW-3D는 또한 스프레이 노즐을 설계하고 다공성 재료 및 기타 소비재 구성 요소의 흡수 기능을 모델링하는 데 사용할 수 있습니다. FLOW-3D 의 공기 유입, 다공성 매체 및 표면 장력을 포함한 고급 다중 물리 모델을 사용하면 소비자 제품 설계를 정확하게 시뮬레이션하고 최적화하는 것이 쉽습니다.

충전재

유입된 공기는 생산 라인에서 용기를 채울 때 액체의 부피를 늘릴 수 있습니다. 아래 왼쪽 이미지는 높이가 약 20cm인 병을 1.2초 동안 채우는 것을 보여줍니다. 색상 음영은 액체에 있는 공기의 부피 분율을 나타냅니다. 병에서 혼합 시간이 짧고 혼합 정도가 높기 때문에 공기가 표면으로 올라가 빠져나갈 시간이 없었습니다. 그러나 오른쪽 이미지에서 볼 수 있듯이 약 1.7초의 추가 시간이 지나면 공기가 표면으로 올라가면서 발생하는 액체 부피 감소가 명확하게 보입니다.  FLOW-3D 의 드리프트 플럭스 모델을 사용하면 액체에 있는 기포와 같은 구성 요소를 분리하여 분리할 수 있습니다.

Tide® 병 충전의 빠른 평가

이 기사에서는  FLOW-3D를  사용하여 새로운 타이드 병 디자인의 충전을 모델링하는 방법을 설명하며,  Procter and Gamble Company의 기술 섹션 책임자인 John McKibben이 기고했습니다 .

지금 오전 9시인데 긴급 이메일을 받았다고 상상해보세요.

 방금 새로운 Tide® 병 디자인 중 하나가 손잡이에 채워지고 충전 장비에 문제가 생길 수 있다는 것을 깨달았습니다. 우리는 프로토타입 병이 없으며 몇 주 동안 없을 것입니다. 디자이너와 소비자는 디자인의 모습을 좋아하지만, 채우는 방식이 생산 시설에 쇼스토퍼가 될 수 있습니다.

이런 상황이 제게 주어졌을 때, 저는 3D 지오메트리(그림 1)의 스테레오 리소그래피(.stl) 파일을 요청하여 응답을 시작했고, 제가 무엇을 할 수 있는지 알아보고자 했습니다. 저는  FLOW-3D가  .stl 파일을 사용하여 지오메트리를 입력하고 충전을 위한 자유 표면 문제를 해결할 수 있을 것이라는 것을 알고 있었습니다. 저는 이것이 잠재적인 문제에 대한 좋은 정성적 이해를 제공할 것으로 기대했지만, 이 애플리케이션에 얼마나 정확할지에 대해 약간 불확실했습니다.

병의 기하학

시뮬레이션 설정 및 실행

오후 1시경에 저는 지오메트리 파일, 유량, 유체 특성을 받았습니다. 몇 시간 이내에 시뮬레이션이 실행되어 예비 결과가 나왔습니다. 저는 제 고객을 초대하여 결과를 잠깐 살펴보게 했고 그는 “사장의 상사”를 데려와서 살펴보게 했습니다. 그래서 저녁 5시경에 예비 결과를 살펴보고 원래 우려했던 것이 문제가 아니라는 것을 확인했습니다.

하지만 결과는 몇 가지 다른 의문을 제기했습니다. 손잡이에 채우면 유입 유체 제트가 많이 깨졌습니다. 이렇게 하면 유입 공기와 거품의 양이 늘어날 것이라는 걸 알았습니다(결국 세탁 세제를 채우고 있으니까요).  FLOW-3D  공기 유입 모델을 테스트하기로 했습니다. 이 모델은 원래 난류 제트용으로 개발되었고, 이 층류 문제를 살펴보면 얼마나 잘 수행될지 확신할 수 없었습니다.

병 채우기 시뮬레이션
그림 2: 채워진 결과
병 채우기 시뮬레이션 및 검증
그림 3: 실험 비교

그림 2는 공기 유입 모델이 있는 경우와 없는 경우 병 충전 모델의 결과를 보여줍니다. 유입 공기가 포함되면 충전 레벨이 상당히 증가한다는 점에 유의하십시오. 유입 공기가 병 상단에서 유체를 강제로 밀어내지는 않지만 공기 유입 정확도를 확인해야 할 만큼 충분히 가깝습니다. 그림 3은 공기 유입 레벨을 몇 주 후에 실행한 실험 이미지와 비교합니다(시제품 병이 출시된 후). 제트 분리 및 충전 레벨의 질적 일치는 우수하며 시뮬레이션이 병 설계를 선별하기에 충분히 정확하다는 것을 확인했습니다.

홍조

변기가 어떻게 작동하는지 궁금한 적이 있나요? 사실 꽤 복잡합니다. 손잡이를 밀면 물이 변기 그릇을 채우기 시작합니다. 변기 그릇의 유체 수위가 트랩 상단(변기 그릇 뒤) 위로 올라가면 웨어 유형의 흐름이 시작됩니다. 흐름이 ​​충분히 빠르면 변기 그릇에 거품이 형성되어 사이펀이 생성됩니다. 그 지점에서 사이펀이 변기 그릇에서 물을 끌어내고 변기가 물을 흘립니다. 많은 지역에서 물 절약은 중요한 문제이며, 저유량 변기는 가정과 상업용 모두에 필요합니다. 하지만 변기가 첫 번째 시도에서 제 역할을 하지 못하면 물 절약 목표는 달성되지 않습니다.  FLOW-3D를  사용하면 다양한 설계를 모델링하여 최적의 결과를 얻을 수 있습니다.

식품 가공

식품 가공 산업은 복잡한 유체, 일반적으로 비뉴턴 유체, 슬러리, 고체와 유체의 혼합물을 관리하여 분배 장비를 최적으로 설계하고 제조하기 위한 다양한 요구 사항이 있습니다. 이는 상업용 장비의 일관성과 내구성 및 품질에 필수적입니다. 또한 포장 디자인의 혁신을 통해 한 제품을 다른 제품과 명확히 구별할 수 있습니다. 예를 들어, 꿀, 케첩 또는 크리머를 깨끗하고 정확하게 분배하는 것은 소비자가 매장에서 내리는 선택일 수 있습니다. 운송 및 보관 요구 사항에는 더 나은 모양 엔지니어링과 더 많은 용기 재료 선택이 필요합니다. 1.5리터 물병이나 세탁 세제를 움직이거나 떨어뜨리는 동안의 유체 하중은 상류 설계의 중요한 부분이 될 수 있습니다.

꿀, 옥수수 시럽, 치약과 같은 점성 유체는 일반적으로 고체 표면에 닿으면 코일을 형성하는 경향이 있습니다. 이 효과는 관찰하기에 흥미롭고 재미있지만, 공기가 제품에 끌려들어 포장이 어려워질 수 있는 포장 공정에서는 환영받지 못할 수 있습니다. 코일링이 발생하는 조건은 유체의 점도, 유체가 떨어지는 거리, 유체의 속도에 따라 달라집니다.  FLOW-3D는  다양한 물리적 공정 매개변수를 연구하여 효율적인 공정을 설계하는 데 도움이 되는 정확한 도구를 제공합니다.

혼입

지난 수십 년 동안 컴퓨터화된 측정 및 시뮬레이션 기술의 발전으로 인해 혼합에 대한 이해가 크게 진전되었습니다. 유동 모델링 기술의 지속적인 발전 덕분에 혼합 장비의 유동 의존적 프로세스에 대한 자세한 통찰력을 CFD 소프트웨어를 사용하여 쉽게 시뮬레이션하고 이해할 수 있습니다. 오늘날 블렌딩에서 고체 현탁액, 재킷 반응기의 열 전달에서 발효에 이르기까지 광범위한 응용 분야가  FLOW-3D 의 혼합 기술을 사용하여 모델링됩니다.  FLOW-3D  시뮬레이션은 임펠러의 모든 구성과 모든 용기 형상의 혼합 조건에서 블렌딩 시간, 순환 및 전력 수와 같은 주요 혼합 매개변수를 평가하는 데 도움이 될 수 있습니다. 이러한 시뮬레이션은 실험적 방법을 사용하여 보완합니다. 이러한 장비의 유동 의존적 프로세스를 예측하고 이해하기 위해 CFD 소프트웨어를 사용하면 제품 품질을 향상시키고 많은 제품의 비용과 출시 시간을 모두 줄일 수 있습니다.

비뉴턴 유체

혈액, 케첩, 치약, 샴푸, 페인트, 로션과 같은 비뉴턴 유체는 다양한 점도를 가진 복잡한 유동학을 가지고 있습니다.  FLOW-3D  는 변형 및/또는 온도에 따라 달라지는 비뉴턴 점도를 가진 이러한 유체를 모델링합니다. 전단 및 온도에 따른 점도는 Carreau, 거듭제곱 법칙 함수 또는 단순히 표 형식의 입력을 통해 설명됩니다. 일부 폴리머, 세라믹 및 반고체 금속의 특징인 시간 종속 또는 틱소트로피 거동도 시뮬레이션할 수 있습니다.

핸드 로션 펌프는 종종 여러 가지 설계 문제와 관련이 있습니다. 펌프가 공기 공극을 가두지 않고 효과적으로 작동하고 로션의 연속적인 흐름을 생성하는 것이 중요합니다. 좋은 설계는 노력이 덜 필요하고 이상적으로는 로션을 원하는 곳으로 향하게 합니다. FLOW-3D 의 이동 객체 모델은 노즐이 아래로 눌리는 것을 시뮬레이션하여 저장소의 로션을 가압하는 데 사용됩니다. 로션의 압력과 로션을 추출하는 데 필요한 힘을 연구할 수 있습니다. 여러 설계 변수는 동일한 고정 구조 메시 내에서 쉽게 분석할 수 있습니다.

다공성 재료

다공성 매체에서 유체의 이동에 대한 수치 모델링은 어려울 수 있지만  FLOW-3D 에는 다공성 재료와 관련된 문제를 해결하는 데 유용한 기능이 많이 포함되어 있습니다. FAVOR™ 기술에는 사용자가 연속적인 다공성 매체를 표현할 수 있도록 하는 데 필요한 다공성 변수가 포함되어 있습니다.  FLOW-3D를 사용하면 사용자가 포화 및 불포화 흐름 조건을 모두 시뮬레이션할 수 있습니다. 거듭제곱 법칙 관계를 사용하면 불포화 흐름 조건에서 모세관 압력 과 포화  사이의 비선형 관계를 모델링  할 수 있습니다. 별도의 충전 및 배수 곡선을 사용하여 히스테리시스 현상을 모델링할 수 있습니다. 서로 직접 접촉하는 경우에도 서로 다른 다공성, 투과성 및 습윤성 속성을 서로 다른 장애물에 할당할 수 있습니다. 투과성은 흐름 방향에 따라 지정할 수 있으므로 사용자가 다공성 매체의 이방성 동작을 모델링할 수 있습니다. 유체와 다공성 매체 간의 열 전달을 고려할 수 있습니다.

분무

소용돌이 분무 노즐은 화학 세정제, 의약품 및 연료에서 액체를 분사하는 일반적인 방법입니다. 액체를 성공적으로 분무하려면 일반적으로 노즐로 침투하는 공기 코어를 형성해야 합니다. CFD는 최적의 분무 콘에 대한 기하학, 소용돌이 속도 및 유체 특성의 영향을 탐색하는 효과적인 방법입니다.

이 예에서 2차원 축대칭 소용돌이 흐름이 시뮬레이션되었습니다. 대칭 축을 따라 공기 코어가 노즐의 전체 길이를 거의 관통했습니다. 왼쪽 플롯은 평면에서 속도 분포를 나타내는 벡터가 있는 압력 분포입니다. 오른쪽 플롯은 속도의 소용돌이 구성 요소로 채색되어 있으며 빨간색은 더 높은 값을 나타냅니다.

분무 콘의 규모와 입자 크기가 너무 광범위하기 때문에 분무의 완전한 분무를 직접 계산하는 것은 불가능합니다. 또한 분무는 외부 교란, 노즐의 미세한 결함 및 기타 영향과 밀접하게 관련된 혼란스러운 프로세스입니다. 그러나 노즐을 떠날 때 분무 콘의 특성(예: 벽 두께, 콘 각도, 축 및 방위 속도)을 예측할 수 있다면 이러한 유형의 흐름 장치를 최적화하는 데 큰 도움이 됩니다.

소용돌이 스프레이 노즐
소용돌이 분무 노즐의 FLOW-3D 시뮬레이션

Products

자유 표면 흐름은 가정과 사무실 환경 모두에서 사용되는 소비자 제품의 설계 및 제조에서 일반적입니다.

예를 들어, 병 채우기는 매일 대규모로 진행되는 프로세스입니다. 생산 속도를 최대화하면서 낭비를 최소화하도록 이러한 프로세스를 설계하면 시간이 지남에 따라 상당한 비용 절감으로 이어질 수 있습니다. FLOW-3D는 또한 스프레이 노즐을 설계하고 다공성 재료 및 기타 소비재 구성 요소의 흡수 기능을 모델링하는 데 사용할 수 있습니다.

공기 혼입, 다공성 매질 및 표면 장력을 포함한 FLOW-3D의 고급 다중 물리 모델을 사용하면 소비자 제품 설계를 정확하게 시뮬레이션하고 최적화 할 수 있습니다.


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Abstract


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References


Gong H, Jiang J, Qiu J, Jiang R and Zhang W 2016 Theoretical and Experimental Study on the Water Curtain Shape and Mechanical Relationship of the Smoke Control System Advances in Engineering Research 500-7
Gong H, Jiang J, Zhang W and Guan Y 2017 Theory and Simulation of the Relationship between Smoke-proof Water Curtain’s Tank Structure and Flow Non-uniformity DEStech Transactions on Environment, Energy and Earth Science iceepe 257-63
ZHENG Li, QIAN Zhongdong, CAO Zhixian and TAN Guangming 2009 Comparison of computed result for dam over-topping flow with two 3D models Engineering Journal of Wuhan University 06 758-63
Hartley DE and Murgatroyd W 1964 Criteria for the break-up of thin liquid layers flowing isothermally over solid surfaces International Journal of Heat and Mass Transfer 9 1003-15
QIN Wei, LIU Jianhua, WENG Zemin and JIANG Zhangyan 1997 Characteristics of Interfacial Surface Wave of Free-Falling Liquid Film JOURNAL OF JIMEI NAVIGATION INSTITUTE 02 3-8
Ye X, Yan W, Jiang Z and Li C 2002 Hydrodynamics of Free-Falling Turbulent Wavy Films and Implications for Enhanced Heat Transfer Heat Transfer Engineering 1 48-60

Coating_image

Template-Free Scalable Fabrication of Linearly Periodic Microstructures by Controlling Ribbing Defects Phenomenon in Forward Roll Coating for Multifunctional Applications

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Md Didarul Islam, Himendra Perera, Benjamin Black, Matthew Phillips,Muh-Jang Chen, Greyson Hodges, Allyce Jackman, Yuxuan Liu, Chang-Jin Kim,Mohammed Zikry, Saad Khan, Yong Zhu, Mark Pankow, and Jong Eun Ryu

Abstract


Periodic micro/nanoscale structures from nature have inspired the scientific community to adopt surface design for various applications, including superhydrophobic drag reduction. One primary concern of practical applications of such periodic microstructures remains the scalability of conventional microfabrication technologies. This study demonstrates a simple template-free scalable manufacturing technique to fabricate periodic microstructures by controlling the ribbing defects in the forward roll coating. Viscoelastic composite coating materials are designed for roll-coating using carbon nanotubes (CNT) and polydimethylsiloxane (PDMS), which helps achieve a controllable ribbing with a periodicity of 114–700 µm. Depending on the process parameters, the patterned microstructures transition from the linear alignment to a random structure. The periodic microstructure enables hydrophobicity as the water contact angles of the samples ranged from 128° to 158°. When towed in a static water pool, a model boat coated with the microstructure film shows 7%–8% faster speed than the boat with a flat PDMS film. The CNT addition shows both mechanical and electrical properties improvement. In a mechanical scratch test, the cohesive failure of the CNT-PDMS film occurs in ≈90% higher force than bare PDMS. Moreover, the nonconductive bare PDMS shows sheet resistance of 747.84–22.66 Ω □−1 with 0.5 to 2.5 wt% CNT inclusion.

 

Keywords


multifunctional surfaces, periodic microtrenches, ribbing instabilities,roll coating, scalable manufacturing

 

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Omega-Liutex Method

Prediction of the Vortex Evolution and Influence Analysis of Rough Bed in a Hydraulic Jump with the Omega-Liutex Method

Omega-Luitex법을 이용한 수력점프 발생시 러프 베드의 와류 진화 예측 및 영향 분석

Cong Trieu Tran, Cong Ty Trinh

Abstract

The dissipation of energy downstream of hydropower projects is a significant issue. The hydraulic jump is exciting and widely applied in practice to dissipate energy. Many hydraulic jump characteristics have been studied, such as length of jump Lj and sequent flow depth y2. However, understanding the evolution of the vortex structure in the hydraulic jump shows a significant challenge. This study uses the RNG k-e turbulence model to simulate hydraulic jumps on the rough bed. The Omega-Liutex method is compared with Q-criterion for capturing vortex structure in the hydraulic jump. The formation, development, and shedding of the vortex structure at the rough bed in the hydraulic jumper are analyzed. The vortex forms and rapidly reduces strength on the rough bed, resulting in fast dissipation of energy. At the rough block rows 2nd and 3rd, the vortex forms a vortex rope that moves downstream and then breaks. The vortex-shedding region represents a significant energy attenuation of the flow. Therefore, the rough bed dissipates kinetic energy well. Adding reliability to the vortex determined by the Liutex method, the vorticity transport equation is used to compare the vorticity distribution with the Liutex distribution. The results show a further comprehension of the hydraulic jump phenomenon and its energy dissipation.

Keywords

flow-3D; hydraulic Jump; omega-liutex method; vortex breakdown

References

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[13] Wang, L., Zheng, Z., Cai, W. et al. (2019). Extension Omega and Omega-Liutex methods applied to identify vortex structures in viscoelastic turbulent flow. Journal of Hydrodynamics, 31(5), 911-921. https://doi.org/10.1007/s42241-019-0045-x
[14] Xu, H., Cai, X., & Liu, C. (2019). Liutex (vortex) core definition and automatic identification for turbulence vortex structures. Journal of Hydrodynamics, 31(5), 857-863. https://doi.org/10.1007/s42241-019-0066-5
[15] Tran, C. T. et al. (2020). Prediction of the precessing vortex core in the Francis-99 draft tube under off-design conditions by using Liutex/Rortex method. Journal of Hydrodynamics, 32, 623-628. https://doi.org/10.1007/s42241-020-0031-3
[16] Liu, C. et al. (2019). A Liutex based definition of vortex axis line. arXiv preprint arXiv:1904.10094. https://doi.org/10.48550/arXiv.1904.10094
[17] Samadi-Boroujeni, H. et al. (2013). Effect of triangular corrugated beds on the hydraulic jump characteristics. Canadian Journal of Civil Engineering, 40(9), 841-847. https://doi.org/10.1139/cjce-2012-0019
[18] Ghaderi, A. et al. (2020). Characteristics of free and submerged hydraulic jumps over different macroroughnesses. Journal of Hydroinformatics, 22(6), 1554-1572. https://doi.org/10.2166/hydro.2020.298
[19] Wu, Z. et al. (2021). Analysis of the influence of transverse groove structure on the flow of a flat-plate surface based on Liutex parameters. Engineering Applications of Computational Fluid Mechanics, 15(1), 1282-1297. https://doi.org/10.1080/19942060.2021.1968955
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[21] Tran, C., Bin, J., & Long, X. (2019). Simulation and Analysis of Cavitating Flow in the Draft Tube of the Francis Turbine with Splitter Blades at Off-Design Condition. Tehnicki vjesnik – Technical Gazette, 26(6). https://doi.org/10.17559/TV-20190316042929
Image_Sacrificial_Pier

Sacrificial Piles as Scour Countermeasures in River Bridges A Numerical Study using FLOW-3D

하천 교량의 파괴 대책으로서 희생파일에 대한 FLOW-3D를 이용한 수치 연구

Mohammad Nazari-Sharabian, Aliasghar Nazari-Sharabian, Moses Karakouzian, Mehrdad Karami

Abstract

Scour is defined as the erosive action of flowing water, as well as the excavating and carrying away materials from beds and banks of streams, and from the vicinity of bridge foundations, which is one of the main causes of river bridge failures. In the present study, implementing a numerical approach, and using the FLOW-3D model that works based on the finite volume method (FVM), the applicability of using sacrificial piles in different configurations in front of a bridge pier as countermeasures against scouring is investigated. In this regard, the numerical model was calibrated based on an experimental study on scouring around an unprotected circular river bridge pier. In simulations, the bridge pier and sacrificial piles were circular, and the riverbed was sandy. In all scenarios, the flow rate was constant and equal to 45 L/s. Furthermore, one to five sacrificial piles were placed in front of the pier in different locations for each scenario. Implementation of the sacrificial piles proved to be effective in substantially reducing the scour depths. The results showed that although scouring occurred in the entire area around the pier, the maximum and minimum scour depths were observed on the sides (using three sacrificial piles located upstream, at three and five times the pier diameter) and in the back (using five sacrificial piles located upstream, at four, six, and eight times the pier diameter) of the pier. Moreover, among scenarios where single piles were installed in front of the pier, installing them at a distance of five times the pier diameter was more effective in reducing scour depths. For other scenarios, in which three piles and five piles were installed, distances of six and four times the pier diameter for the three piles scenario, and four, six, and eight times the pier diameter for the five piles scenario were most effective.

 

Keywords

Scouring; River Bridges; Sacrificial Piles; Finite Volume Method (FVM); FLOW-3D.

 

References


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Karami, Mehrdad, Abdorreza Kabiri-Samani, Mohammad Nazari-Sharabian, and Moses Karakouzian. “Investigating the Effects of Transient Flow in Concrete-Lined Pressure Tunnels, and Developing a New Analytical Formula for Pressure Wave Velocity.” Tunnelling and Underground Space Technology 91 (September 2019): 102992. doi:10.1016/j.tust.2019.102992.

Karakouzian, Moses, Mohammad Nazari-Sharabian, and Mehrdad Karami. “Effect of Overburden Height on Hydraulic Fracturing of Concrete-Lined Pressure Tunnels Excavated in Intact Rock: A Numerical Study.” Fluids 4, no. 2 (June 19, 2019): 112. doi:10.3390/fluids4020112.

Chiew, Yee-Meng. “Scour protection at bridge piers.” Journal of Hydraulic Engineering 118, no. 9 (1992): 1260-1269. doi:10.1061/(ASCE)0733-9429(1992)118:9(1260).

Shen, Hsieh Wen, Verne R. Schneider, and Susumu Karaki. “Local scour around bridge piers.” Journal of the Hydraulics Division (1969): 1919-1940.

Richardson, E.V., and Davis, S.R. “Evaluating Scour at Bridges”. Hydraulic Engineering Circular. (2001), 18 (HEC-18), Report no. FHWA NHI 01–001, U.S. Department of Transportation, Federal Highway Administration, Washington, DC, USA.

Elsaeed, Gamal, Hossam Elsersawy, and Mohammad Ibrahim. “Scour Evaluation for the Nile River Bends on Rosetta Branch.” Advances in Research 5, no. 2 (January 10, 2015): 1–15. doi:10.9734/air/2015/17380.

Chang, Wen-Yi, Jihn-Sung Lai, and Chin-Lien Yen. “Evolution of scour depth at circular bridge piers.” Journal of Hydraulic Engineering 130, no. 9 (2004): 905-913. doi:10.1061/(ASCE)0733-9429(2004)130:9(905).

Unger, Jens, and Willi H. Hager. “Riprap failure at circular bridge piers.” Journal of Hydraulic Engineering 132, no. 4 (2006): 354-362. doi:10.1061/(ASCE)0733-9429(2006)132:4(354).

Abdeldayem, Ahmed W., Gamal H. Elsaeed, and Ahmed A. Ghareeb. “The effect of pile group arrangements on local scour using numerical models.” Advances in Natural and Applied Sciences 5, no. 2 (2011): 141-146.

Sheppard, D. M., B. Melville, and H. Demir. “Evaluation of Existing Equations for Local Scour at Bridge Piers.” Journal of Hydraulic Engineering 140, no. 1 (January 2014): 14–23. doi:10.1061/(asce)hy.1943-7900.0000800.

Melville, Bruce W., and Anna C. Hadfield. “Use of sacrificial piles as pier scour countermeasures.” Journal of Hydraulic Engineering 125, no. 11 (1999): 1221-1224. doi:10.1061/(ASCE)0733-9429(1999)125:11(1221).

Yao, Weidong, Hongwei An, Scott Draper, Liang Cheng, and John M. Harris. “Experimental Investigation of Local Scour Around Submerged Piles in Steady Current.” Coastal Engineering 142 (December 2018): 27–41. doi:10.1016/j.coastaleng.2018.08.015.

Link, Oscar, Marcelo García, Alonso Pizarro, Hernán Alcayaga, and Sebastián Palma. “Local Scour and Sediment Deposition at Bridge Piers During Floods.” Journal of Hydraulic Engineering 146, no. 3 (March 2020): 04020003. doi:10.1061/(asce)hy.1943-7900.0001696.

Khan, Mujahid, Mohammad Tufail, Muhammad Fahad, Hazi Muhammad Azmathullah, Muhammad Sagheer Aslam, Fayaz Ahmad Khan, and Asif Khan. “Experimental analysis of bridge pier scour pattern.” Journal of Engineering and Applied Sciences 36, no. 1 (2017): 1-12.

Yang, Yifan, Bruce W. Melville, D. M. Sheppard, and Asaad Y. Shamseldin. “Clear-Water Local Scour at Skewed Complex Bridge Piers.” Journal of Hydraulic Engineering 144, no. 6 (June 2018): 04018019. doi:10.1061/(asce)hy.1943-7900.0001458.

Moussa, Yasser Abdallah Mohamed, Tarek Hemdan Nasr-Allah, and Amera Abd-Elhasseb. “Studying the Effect of Partial Blockage on Multi-Vents Bridge Pier Scour Experimentally and Numerically.” Ain Shams Engineering Journal 9, no. 4 (December 2018): 1439–1450. doi:10.1016/j.asej.2016.09.010.

Guan, Dawei, Yee-Meng Chiew, Maoxing Wei, and Shih-Chun Hsieh. “Characterization of Horseshoe Vortex in a Developing Scour Hole at a Cylindrical Bridge Pier.” International Journal of Sediment Research 34, no. 2 (April 2019): 118–124. doi:10.1016/j.ijsrc.2018.07.001.

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Vijayasree, B. A., T. I. Eldho, B. S. Mazumder, and N. Ahmad. “Influence of Bridge Pier Shape on Flow Field and Scour Geometry.” International Journal of River Basin Management 17, no. 1 (November 10, 2017): 109–129. doi:10.1080/15715124.2017.1394315.

Farooq, Rashid, and Abdul Razzaq Ghumman. “Impact Assessment of Pier Shape and Modifications on Scouring Around Bridge Pier.” Water 11, no. 9 (August 23, 2019): 1761. doi:10.3390/w11091761.

Link, Oscar, Cristian Castillo, Alonso Pizarro, Alejandro Rojas, Bernd Ettmer, Cristián Escauriaza, and Salvatore Manfreda. “A Model of Bridge Pier Scour During Flood Waves.” Journal of Hydraulic Research 55, no. 3 (November 18, 2016): 310–323. doi:10.1080/00221686.2016.1252802.

Karakouzian, Moses, Mehrdad Karami, Mohammad Nazari-Sharabian, and Sajjad Ahmad. “Flow-Induced Stresses and Displacements in Jointed Concrete Pipes Installed by Pipe Jacking Method.” Fluids 4, no. 1 (February 21, 2019): 34. doi:10.3390/fluids4010034.

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DOI: 10.28991/cej-2020-03091531

Computational Fluid Dynamics Study of Perforated Monopiles

Computational Fluid Dynamics Study of Perforated Monopiles

Mary Kathryn Walker
Florida Institute of Technology, mwalker2022@my.fit.edu

Robert J. Weaver, Ph.D.
Associate Professor
Ocean Engineering and Marine Sciences
Major Advisor


Chungkuk Jin, Ph.D.
Assistant Professor
Ocean Engineering and Marine Sciences


Kelli Z. Hunsucker, Ph.D.
Assistant Professor
Ocean Engineering and Marine Sciences


Richard B. Aronson, Ph.D.
Professor and Department Head
Ocean Engineering and Marine Sciences

Abstract

모노파일은 해상 풍력 터빈 건설에 사용되며 일반적으로 설계 수명은 25~50년입니다. 모노파일은 수명 주기 동안 부식성 염수 환경에 노출되어 구조물을 빠르게 분해하는 전기화학적 산화 공정을 용이하게 합니다. 이 공정은 모노파일을 보호 장벽으로 코팅하고 음극 보호 기술을 구현하여 완화할 수 있습니다.

역사적으로 모노파일 설계자는 파일 내부가 완전히 밀봉되고 전기화학적 부식 공정이 결국 사용 가능한 모든 산소를 소모하여 반응을 중단시킬 것이라고 가정했습니다. 그러나 도관을 위해 파일 벽에 만든 관통부는 종종 누출되어 신선하고 산소화된 물이 내부 공간으로 유입되었습니다.

표준 부식 방지 기술을 보다 효과적으로 적용할 수 있는 산소화된 환경으로 내부 공간을 재고하는 새로운 모노파일 설계가 연구되고 있습니다. 이러한 새로운 모노파일은 간조대 또는 조간대 수준에서 벽에 천공이 있어 신선하고 산소화된 물이 구조물을 통해 흐를 수 있습니다.

이러한 천공은 또한 구조물의 파도 하중을 줄일 수 있습니다. 유체 역학적 하중 감소의 크기는 천공의 크기와 방향에 따라 달라집니다. 이 연구에서는 천공의 크기에 따른 모노파일의 힘 감소 분석에서 전산 유체 역학(CFD)의 적용 가능성을 연구하고 주어진 파도의 접근 각도 변화의 효과를 분석했습니다.

모노파일의 힘 감소를 결정하기 위해 이론적 3D 모델을 제작하여 FLOW-3D® HYDRO를 사용하여 테스트했으며, 천공되지 않은 모노파일을 제어로 사용했습니다. 이론적 데이터를 수집한 후, 동일한 종류의 천공이 있는 물리적 스케일 모델을 파도 탱크를 사용하여 테스트하여 이론적 모델의 타당성을 확인했습니다.

CFD 시뮬레이션은 물리적 모델의 10% 이내, 이전 연구의 5% 이내에 있는 것으로 나타났습니다. 물리적 모델과 시뮬레이션 모델을 검증한 후, 천공의 크기가 파도 하중 감소에 뚜렷한 영향을 미치고 주어진 파도의 접근 각도에 대한 테스트를 수행할 수 있음을 발견했습니다.

접근 각도의 변화는 모노파일을 15°씩 회전하여 시뮬레이션했습니다. 이 논문에 제시된 데이터는 모노파일의 방향이 통계적으로 유의하지 않으며 천공 모노파일의 설계 고려 사항이 되어서는 안 된다는 것을 시사합니다.

또한 파도 하중 감소와 구조적 안정성 사이의 균형을 찾기 위해 천공의 크기와 모양에 대한 연구를 계속하는 것이 좋습니다.

Monopiles are used in the construction of offshore wind turbines and typically have a design life of 25 to 50 years. Over their lifecycle, monopiles are exposed to a corrosive saltwater environment, facilitating a galvanic oxidation process that quickly degrades the structure. This process can be mitigated by coating the monopile in a protective barrier and implementing cathodic protection techniques. Historically, monopile designers assumed the interior of the pile would be completely sealed and the galvanic corrosion process would eventually consume all the available oxygen, halting the reaction. However, penetrations made in the pile wall for conduit often leaked and allowed fresh, oxygenated water to enter the interior space. New monopile designs are being researched that reconsider the interior space as an oxygenated environment where standard corrosion protection techniques can be more effectively applied. These new monopiles have perforations through the wall at intertidal or subtidal levels to allow fresh, oxygenated water to flow through the structure. These perforations can also reduce wave loads on the structure. The magnitude of the hydrodynamic load reduction depends on the size and orientation of the perforations. This research studied the applicability of computational fluid dynamics (CFD) in analysis of force reduction on monopiles in relation to size of a perforation and to analyze the effect of variation in approach angle of a given wave. To determine the force reduction on the monopile, theoretical 3D models were produced and tested using FLOW-3D® HYDRO with an unperforated monopile used as the control. After the theoretical data was collected, physical scale models with the same variety of perforations were tested using a wave tank to determine the validity of the theoretical models. The CFD simulations were found to be within 10% of the physical models and within 5% of previous research. After the physical and simulated models were validated, it was found that the size of the perforations has a distinct impact on the wave load reduction and testing for differing approach angles of a given wave could be conducted. The variation in approach angle was simulated by rotating the monopile in 15° increments. The data presented in this paper suggests that the orientation of the monopile is not statistically significant and should not be a design consideration for perforated monopiles. It is also suggested to continue the study on the size and shape of the perforations to find the balance between wave load reduction and structural stability.

Figure 1: Overview sketch of typical monopile (MP) foundation and transition piece (TP) design with an internal j-tube (Hilbert et al., 2011)
Figure 1: Overview sketch of typical monopile (MP) foundation and transition
piece (TP) design with an internal j-tube (Hilbert et al., 2011)

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Numerical Investigation of the Local Scour for Tripod Pile Foundation

Numerical Investigation of the Local Scour for Tripod Pile Foundation

Waqed H. Hassan Zahraa Mohammad Fadhe* Rifqa F. Thiab Karrar Mahdi
Civil Engineering Department, Faculty of Engineering, University of Warith Al-Anbiyaa, Kerbala 56001, Iraq
Civil Engineering Department, Faculty of Engineering, University of Kerbala, Kerbala 56001, Iraq
Corresponding Author Email: Waqed.hammed@uowa.edu.iq

OPEN ACCESS

Abstract: 

This work investigates numerically a local scour moves in irregular waves around tripods. It is constructed and proven to use the numerical model of the seabed-tripod-fluid with an RNG k turbulence model. The present numerical model then examines the flow velocity distribution and scour characteristics. After that, the suggested computational model Flow-3D is a useful tool for analyzing and forecasting the maximum scour development and the flow field in random waves around tripods. The scour values affecting the foundations of the tripod must be studied and calculated, as this phenomenon directly and negatively affects the structure of the structure and its design life. The lower diagonal braces and the main column act as blockages, increasing the flow accelerations underneath them.  This increases the number of particles that are moved, which in turn creates strong scouring in the area. The numerical model has a good agreement with the experimental model, with a maximum percentage of error of 10% between the experimental and numerical models. In addition, Based on dimensional analysis parameters, an empirical equation has been devised to forecast scour depth with flow depth, median size ratio, Keulegan-Carpenter (Kc), Froud number flow, and wave velocity that the results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50) and the scour depth attains its steady-current value for Vw < 0.75. As the Froude number rises, the maximum scour depth will be large.

Keywords: 

local scour, tripod foundation, Flow-3D​, waves

1. Introduction

New energy sources have been used by mankind since they become industrialized. The main energy sources have traditionally been timber, coal, oil, and gas, but advances in the science of new energies, such as nuclear energy, have emerged [1, 2]. Clean and renewable energy such as offshore wind has grown significantly during the past few decades. There are numerous different types of foundations regarding offshore wind turbines (OWTs), comprising the tripod, jacket, gravity foundation, suction anchor (or bucket), and monopile [3, 4]. When the water depth is less than 30 meters, Offshore wind farms usually employ the monopile type [4]. Engineers must deal with the wind’s scouring phenomenon turbine foundations when planning and designing wind turbines for an offshore environment [5]. Waves and currents generate scour, this is the erosion of soil near a submerged foundation and at its location [6]. To predict the regional scour depth at a bridge pier, Jalal et al. [7-10] developed an original gene expression algorithm using artificial neural networks. Three monopiles, one main column, and several diagonal braces connecting the monopiles to the main column make up the tripod foundation, which has more complicated shapes than a single pile. The design of the foundation may have an impact on scour depth and scour development since the foundation’s form affects the flow field [11, 12]. Stahlmann [4] conducted several field investigations. He discovered that the main column is where the greatest scour depth occurred. Under the main column is where the maximum scour depth occurs in all experiments. The estimated findings show that higher wave heights correspond to higher flow velocities, indicating that a deeper scour depth is correlated with finer silt granularity [13] recommends as the design value for a single pile. These findings support the assertion that a tripod may cause the seabed to scour more severely than a single pile. The geography of the scour is significantly more influenced by the KC value (Keulegan–Carpenter number)

The capability of computer hardware and software has made computational fluid dynamics (CFD) quite popular to predict the behavior of fluid flow in industrial and environmental applications has increased significantly in recent years [14].

Finding an acceptable piece of land for the turbine’s construction and designing the turbine pile precisely for the local conditions are the biggest challenges. Another concern related to working in a marine environment is the effect of sea waves and currents on turbine piles and foundations. The earth surrounding the turbine’s pile is scoured by the waves, which also render the pile unstable.

In this research, the main objective is to investigate numerically a local scour around tripods in random waves. It is constructed and proven to use the tripod numerical model. The present numerical model is then used to examine the flow velocity distribution and scour characteristics.

2. Numerical Model

To simulate the scouring process around the tripod foundation, the CFD code Flow-3D was employed. By using the fractional area/volume method, it may highlight the intricate boundaries of the solution domain (FAVOR).

This model was tested and validated utilizing data derived experimentally from Schendel et al. [15] and Sumer and Fredsøe [6]. 200 runs were performed at different values of parameters.

2.1 Momentum equations

The incompressible viscous fluid motion is described by the three RANS equations listed below [16]:

(1)

\frac{\partial u}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial u}{\partial x}+v{{A}_{y}}\frac{\partial u}{\partial y}+w{{A}_{z}}\frac{\partial u}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial x}+{{G}_{x}}+fx

(2)

\frac{\partial v}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial v}{\partial x}+v{{A}_{y}}\frac{\partial v}{\partial y}+w{{A}_{z}}\frac{\partial v}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial y}+{{G}_{y}}+\text{f}y

 (3)

\frac{\partial w}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial w}{\partial x}+v{{A}_{y}}\frac{\partial w}{\partial y}+w{{A}_{z}}\frac{\partial w}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial z}+{{G}_{z}}+\text{fz}

where, respectively, uv, and w represent the xy, and z flow velocity components; volume fraction (VF), area fraction (AiI=xyz), water density (f), viscous force (fi), and body force (Gi) are all used in the formula.

2.2 Model of turbulence

Several turbulence models would be combined to solve the momentum equations. A two-equation model of turbulence is the RNG k-model, which has a high efficiency and accuracy in computing the near-wall flow field. Therefore, the flow field surrounding tripods was captured using the RNG k-model.

2.3 Model of sediment scour

2.3.1 Induction and deposition

Eq. (4) can be used to determine the particle entrainment lift velocity [17].

(4)

{{u}_{lift,i}}={{\alpha }_{i}}{{n}_{s}}d_{*}^{0.3}{{\left( \theta -{{\theta }_{cr}} \right)}^{1.5}}\sqrt{\frac{\parallel g\parallel {{d}_{i}}\left( {{\rho }_{i}}-{{\rho }_{f}} \right)}{{{\rho }_{f}}}}

α𝛼  is the Induction parameter, ns the normal vector is parallel to the seafloor, and for the present numerical model, ns=(0,0,1), θ𝜃cr is the essential Shields variable, g is the accelerated by gravity, di is the size of the particles, ρi is species density in beds, and d The diameter of particles without dimensions; these values can be obtained in Eq. (5).

(5)

{{d}_{*}}={{d}_{i}}{{\left( \frac{\parallel g\parallel {{\rho }_{f}}\left( {{\rho }_{i}}-{{\rho }_{f}} \right)}{\mu _{f}^{2}} \right)}^{1/3}}

μ𝜇f is this equation a dynamic viscosity of the fluid. cr was determined from an equation based on Soulsby [18].

(6)

{{\theta }_{cr}}=\frac{0.3}{1+1.2{{d}_{*}}}+0.055\left[ 1-\text{exp}\left( -0.02{{d}_{*}} \right) \right]

The equation was used to determine how quickly sand particles set Eq. (7):

(7)

{{\mathbf{u}}_{\text{nsettling},i}}=\frac{{{v}_{f}}}{{{d}_{i}}}\left[ {{\left( {{10.36}^{2}}+1.049d_{*}^{3} \right)}^{0.5}}-10.36 \right]

vf  stands for fluid kinematic viscosity.

2.3.2 Transportation for bed loads

Van Rijn [19] states that the speed of bed load conveyance was determined as:

(8)

{{~}_{\text{bedload},i}}=\frac{{{q}_{b,i}}}{{{\delta }_{i}}{{c}_{b,i}}{{f}_{b}}}

fb  is the essential particle packing percentage, qbi is the bed load transportation rate, and cb, I the percentage of sand by volume i. These variables can be found in Eq. (9), Eq. (10), fbδ𝛿i the bed load thickness.

(9)

{{q}_{b,i}}=8{{\left[ \parallel g\parallel \left( \frac{{{\rho }_{i}}-{{\rho }_{f}}}{{{\rho }_{f}}} \right)d_{i}^{3} \right]}^{\frac{1}{2}}}

(10)

{{\delta }_{i}}=0.3d_{*}^{0.7}{{\left( \frac{\theta }{{{\theta }_{cr}}}-1 \right)}^{0.5}}{{d}_{i}}

In this paper, after the calibration of numerous trials, the selection of parameters for sediment scour is crucial. Maximum packing fraction is 0.64 with a shields number of 0.05, entrainment coefficient of 0.018, the mass density of 2650, bed load coefficient of 12, and entrainment coefficient of 0.01.

3. Model Setup

To investigate the scour characteristics near tripods in random waves, the seabed-tripod-fluid numerical model was created as shown in Figure 1. The tripod basis, a seabed, and fluid and porous medium were all components of the model. The seabed was 240 meters long, 40 meters wide, and three meters high. It had a median diameter of d50 and was composed of uniformly fine sand. The 2.5-meter main column diameter D. The base of the main column was three dimensions above the original seabed. The center of the seafloor was where the tripod was, 130 meters from the offshore and 110 meters from the onshore. To prevent wave reflection, the porous media were positioned above the seabed on the onshore side.

image013.png

Figure 1. An illustration of the numerical model for the seabed-tripod-fluid

3.1 Generation of meshes

Figure 2 displays the model’s mesh for the Flow-3D software grid. The current model made use of two different mesh types: global mesh grid and nested mesh grid. A mesh grid with the following measurements was created by the global hexahedra mesh grid: 240m length, 40m width, and 32m height. Around the tripod, a finer nested mesh grid was made, with dimensions of 0 to 32m on the z-axis, 10 to 30 m on the x-axis, and 25 to 15 m on the y-axis. This improved the calculation’s precision and mesh quality.

image014.png

Figure 2. The mesh block sketch

3.2 Conditional boundaries

To increase calculation efficiency, the top side, The model’s two x-z plane sides, as well as the symmetry boundaries, were all specified. For u, v, w=0, the bottom boundary wall was picked. The offshore end of the wave boundary was put upstream. For the wave border, random waves were generated using the wave spectrum from the Joint North Sea Wave Project (JONSWAP). Boundary conditions are shown in Figure 3.

image015.png

Figure 3. Boundary conditions of the typical problem

The wave spectrum peak enhancement factor (=3.3 for this work) and can be used to express the unidirectional JONSWAP frequency spectrum.

3.3 Mesh sensitivity

Before doing additional research into scour traits and scour depth forecasting, mesh sensitivity analysis is essential. Three different mesh grid sizes were selected for this section: Mesh 1 has a 0.45 by 0.45 nested fine mesh and a 0.6 by 0.6 global mesh size. Mesh 2 has a 0.4 global mesh size and a 0.35 nested fine mesh size, while Mesh 3 has a 0.25 global mesh size and a nested fine mesh size of 0.15. Comparing the relative fine mesh size (such as Mesh 2 or Mesh 3) to the relatively coarse mesh size (such as Mesh 1), a larger scour depth was seen; this shows that a finer mesh size can more precisely represent the scouring and flow field action around a tripod. Significantly, a lower mesh size necessitates a time commitment and a more difficult computer configuration. Depending on the sensitivity of the mesh guideline utilized by Pang et al., when Mesh 2 is applied, the findings converge and the mesh size is independent [20]. In the next sections, scouring the area surrounding the tripod was calculated using Mesh 2 to ensure accuracy and reduce computation time. The working segment generates a total of 14, 800,324 cells.

3.4 Model validation

Comparisons between the predicted outcomes from the current model and to confirm that the current numerical model is accurate and suitably modified, experimental data from Sumer and Fredsøe [6] and Schendel et al. [15] were used. For the experimental results of Run 05, Run 15, and Run 22 from Sumer and Fredsøe [6], the experimental A9, A13, A17, A25, A26, and A27 results from Schendel et al. [15], and the numerical results from the current model are shown in Figure 4. The present model had d50=0.051cm, the height of the water wave(h)=10m, and wave velocity=0.854 m.s-1.

image016.png

Figure 4. Cell size effect

image017.png

Figure 5. Comparison of the present study’s maximum scour depth with that authored by Sumer and Fredsøe [6] and Schendel et al. [15]

According to Figure 5, the highest discrepancy between the numerical results and experimental data is about 10%, showing that overall, there is good agreement between them. The ability of the current numerical model to accurately depict the scour process and forecast the maximum scour depth (S) near foundations is demonstrated by this. Errors in the simulation were reduced by using the calibrated values of the parameter. Considering these results, a suggested simulated scouring utilizing a Flow-3D numerical model is confirmed as a superior way for precisely forecasting the maximum scour depth near a tripod foundation in random waves.

3.5 Dimensional analysis

The variables found in this study as having the greatest impacts, variables related to flow, fluid, bed sediment, flume shape, and duration all had an impact on local scouring depth (t). Hence, scour depth (S) can be seen as a function of these factors, shown as:

(11)

S=f\left(\rho, v, V, h, g, \rho s, d_{50}, \sigma g, V_w, D, d, T_v, t\right)

With the aid of dimensional analysis, the 14-dimensional parameters in Eq. (11) were reduced to 6 dimensionless variables using Buckingham’s -theorem. D, V, and were therefore set as repetition parameters and others as constants, allowing for the ignoring of their influence. Eq. (12) thus illustrates the relationship between the effect of the non-dimensional components on the depth of scour surrounding a tripod base.

(12)

\frac{S}{D}=f\left(\frac{h}{D}, \frac{d 50}{D}, \frac{V}{V W}, F r, K c\right)

where, SD𝑆𝐷 are scoured depth ratio, VVw𝑉𝑉𝑤 is flow wave velocity, d50D𝑑50𝐷 median size ratio, $Fr representstheFroudnumber,and𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠𝑡ℎ𝑒𝐹𝑟𝑜𝑢𝑑𝑛𝑢𝑚𝑏𝑒𝑟,𝑎𝑛𝑑Kc$ is the Keulegan-Carpenter.

4. Result and Discussion

4.1 Development of scour

Similar to how the physical model was used, this numerical model was also used. The numerical model’s boundary conditions and other crucial variables that directly influence the outcomes were applied (flow depth, median particle size (d50), and wave velocity). After the initial 0-300 s, the scour rate reduced as the scour holes grew quickly. The scour depths steadied for about 1800 seconds before reaching an asymptotic value. The findings of scour depth with time are displayed in Figure 6.

4.2 Features of scour

Early on (t=400s), the scour hole began to appear beneath the main column and then began to extend along the diagonal bracing connecting to the wall-facing pile. Gradually, the geography of the scour; of these results is similar to the experimental observations of Stahlmann [4] and Aminoroayaie Yamini et al. [1]. As the waves reached the tripod, there was an enhanced flow acceleration underneath the main column and the lower diagonal braces as a result of the obstructing effects of the structural elements. More particles are mobilized and transported due to the enhanced near-bed flow velocity, it also increases bed shear stress, turbulence, and scour at the site. In comparison to a single pile, the main column and structural components of the tripod have a significant impact on the flow velocity distribution and, consequently, the scour process and morphology. The main column and seabed are separated by a gap, therefore the flow across the gap may aid in scouring. The scour hole first emerged beneath the main column and subsequently expanded along the lower structural components, both Aminoroayaie Yamini et al. [1] and Stahlmann [4] made this claim. Around the tripod, there are several different scour morphologies and the flow velocity distribution as shown in Figures 7 and 8.

image023.png

Figure 6. Results of scour depth with time

image024.png

image025.png

image026.png

image027.png

Figure 7. The sequence results of scour depth around tripod development (reached to steady state) simulation time

image028.png

image029.png

image030.png

image031.png

Figure 8. Random waves of flow velocity distribution around a tripod

4.3 Wave velocity’s (Vw) impact on scour depth

In this study’s section, we looked at how variations in wave current velocity affected the scouring depth. Bed scour pattern modification could result from an increase or decrease in waves. As a result, the backflow area produced within the pile would become stronger, which would increase the depth of the sediment scour. The quantity of current turbulence is the primary cause of the relationship between wave height and bed scour value. The current velocity has increased the extent to which the turbulence energy has changed and increased in strength now present. It should be mentioned that in this instance, the Jon swap spectrum random waves are chosen. The scour depth attains its steady-current value for Vw<0.75, Figure 9 (a) shows that effect. When (V) represents the mean velocity=0.5 m.s-1.

image032.png

(a)

image033.png

(b)

image034.png

(c)

image035.png

(d)

Figure 9Main effects on maximum scour depth (Smax) as a function of column diameter (D)

4.4 Impact of a median particle (d50) on scour depth

In this section of the study, we looked into how variations in particle size affected how the bed profile changed. The values of various particle diameters are defined in the numerical model for each run numerical modeling, and the conditions under which changes in particle diameter have an impact on the bed scour profile are derived. Based on Figure 9 (b), the findings of the numerical modeling show that as particle diameter increases the maximum scour depth caused by wave contact decreases. When (d50) is the diameter of Sediment (d50). The Shatt Al-Arab soil near Basra, Iraq, was used to produce a variety of varied diameters.

4.5 Impact of wave height and flow depth (h) on scour depth

One of the main elements affecting the scour profile brought on by the interaction of the wave and current with the piles of the wind turbines is the height of the wave surrounding the turbine pile causing more turbulence to develop there. The velocity towards the bottom and the bed both vary as the turbulence around the pile is increased, modifying the scour profile close to the pile. According to the results of the numerical modeling, the depth of scour will increase as water depth and wave height in random waves increase as shown in Figure 9 (c).

4.6 Froude number’s (Fr) impact on scour depth

No matter what the spacing ratio, the Figure 9 shows that the Froude number rises, and the maximum scour depth often rises as well increases in Figure 9 (d). Additionally, it is crucial to keep in mind that only a small portion of the findings regarding the spacing ratios with the smallest values. Due to the velocity acceleration in the presence of a larger Froude number, the range of edge scour downstream is greater than that of upstream. Moreover, the scouring phenomena occur in the region farthest from the tripod, perhaps as a result of the turbulence brought on by the collision of the tripod’s pile. Generally, as the Froude number rises, so does the deposition height and scour depth.

4.7 Keulegan-Carpenter (KC) number

The geography of the scour is significantly more influenced by the KC value. Greater KC causes a deeper equilibrium scour because an increase in KC lengthens the horseshoe vortex’s duration and intensifies it as shown in Figure 10.

The result can be attributed to the fact that wave superposition reduced the crucial KC for the initiation of the scour, particularly under small KC conditions. The primary variable in the equation used to calculate This is the depth of the scouring hole at the bed. The following expression is used to calculate the Keulegan-Carpenter number:

Kc=Vw∗TpD𝐾𝑐=𝑉𝑤∗𝑇𝑝𝐷                          (13)

where, the wave period is Tp and the wave velocity is shown by Vw.

image037.png

Figure 10. Relationship between the relative maximum scour depth and KC

5. Conclusion

(1) The existing seabed-tripod-fluid numerical model is capable of faithfully reproducing the scour process and the flow field around tripods, suggesting that it may be used to predict the scour around tripods in random waves.

(2) Their results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50).

(3) A diagonal brace and the main column act as blockages, increasing the flow accelerations underneath them. This raises the magnitude of the disturbance and the shear stress on the seafloor, which in turn causes a greater number of particles to be mobilized and conveyed, as a result, causes more severe scour at the location.

(4) The Froude number and the scouring process are closely related. In general, as the Froude number rises, so does the maximum scour depth and scour range. The highest maximum scour depth always coincides with the bigger Froude number with the shortest spacing ratio.

Since the issue is that there aren’t many experiments or studies that are relevant to this subject, therefore we had to rely on the monopile criteria. Therefore, to gain a deeper knowledge of the scouring effect surrounding the tripod in random waves, further numerical research exploring numerous soil, foundation, and construction elements as well as upcoming physical model tests will be beneficial.

Nomenclature

CFDComputational fluid dynamics
FAVORFractional Area/Volume Obstacle Representation
VOFVolume of Fluid
RNGRenormalized Group
OWTsOffshore wind turbines
Greek Symbols
ε, ωDissipation rate of the turbulent kinetic energy, m2s-3
Subscripts
d50Median particle size
VfVolume fraction
GTTurbulent energy of buoyancy
KTTurbulent velocity
PTKinetic energy of the turbulence
ΑiInduction parameter
nsInduction parameter
ΘΘcrThe essential Shields variable
DiDiameter of sediment
dThe diameter of particles without dimensions
µfDynamic viscosity of the fluid
qb,iThe bed load transportation rate
Cs,iSand particle’s concentration of mass
DDiameter of pile
DfDiffusivity
DDiameter of main column
FrFroud number
KcKeulegan–Carpenter number
GAcceleration of gravity g
HFlow depth
VwWave Velocity
VMean Velocity
TpWave Period
SScour depth

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[3] Fazeres-Ferradosa, T., Rosa-Santos, P., Taveira-Pinto, F., Pavlou, D., Gao, F.P., Carvalho, H., Oliveira-Pinto, S. (2020). Preface: Advanced research on offshore structures and foundation design part 2. In Proceedings of the Institution of Civil Engineers-Maritime Engineering. Thomas Telford Ltd, 173(4): 96-99. https://doi.org/10.1680/jmaen.2020.173.4.96

[4] Stahlmann, A. (2013). Numerical and experimental modeling of scour at foundation structures for offshore wind turbines. In ISOPE International Ocean and Polar Engineering Conference. ISOPE, pp. ISOPE-I.

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[9] Jalal, H.K., Hassan, W.H. (2020). Three-dimensional numerical simulation of local scour around circular bridge pier using Flow-3D software. In IOP Conference Series: Materials Science and Engineering. IOP Publishing, 745(1): 012150. https://doi.org/10.1088/1757-899X/745/1/012150

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Investigating effects of lateral inflow characteristics on main flow using numerical modeling

Investigating effects of lateral inflow characteristics on main flow using numerical modeling

수치모델링을 이용한 측면 유입특성이 본류에 미치는 영향 조사

Mohammad Raze Raeisi Dehkordi1*, Amir Hossein Yeganeh Mazhar1
, Farzaneh Kheradzare2
1– PhD. Student in the Department of Construction and Water Management, Science and Research Unit, Islamic Azad
University, Tehran, Iran
2– M.Sc. Graduate Water resource management, Department of Civil Engineering and Mechanics, Ghiaseddin Jamshid
Kashani University, Qazvin, Iran

  • Corresponding author: mohamadreza.raeisi.d@gmail.com

Keywords

Channel Confluence, Channel cross, sectional area, Cross channel angles, Modelling, Flow-3D

Abstract

Introduction

One of the key issues in river engineering is analyzing the flow properties at the intersection of natural rivers and canals. The flow of the side channel moves away from the intersection of the two channels as a result of the exchange of input force from the side channel with the main flow after coming into contact with it. One of the most evident properties of the flow in these sections is the development of a revolving region with low pressure and even negative pressure close to the inner wall of the side channel. One advantage of the whirling flow in this low-pressure region is that it gives the flow enough space to sediment, but it also increases flow speed near the channel’s bottom and outside wall by lowering the intersectional area of the flow. One of the most crucial considerations in the design of these intersections is minimizing sedimentation in the rotating region and scouring in the area above the shear plane.

Materials and methods:

The channel (flume) created in the laboratory based on Weber et al., (2001) model, was employed in the current investigation to confirm the validity and examine other study objectives. The main channel is 21. 95 meters long, while the side channel, which is at a 90-degree angle to the main channel, is 3. 66 meters long. The total downstream discharge is approximately 0. 17 m3/s, with the upstream velocities of the main channel being 0. 166 m/s and the side channel being 0. 5 m/s. In both channels, the flow depth and width are 0. 91 meters and 0. 296 meters, respectively. In this study, 6 various models’ angles of intersection between the main and side channels, inlet flow velocity, intersectional area, and side channel length have been examined. Models 2 and 3 have intersection angles of 60 and 30 degrees, respectively, and share the rest of their attributes with the fundamental model, or model number 1. Model 1 is the same as Weber’s experimental model. The length of the side channel in model 4 is different from model 1. The only difference between model 6 and the basic model is the side channel intake speed.

Results and Discussion

Analyzing the intersection angle The angle between the main channel and the side channel is investigated in this section of the findings. Models 1, 2, and 3 are assessed using the intersection angles of 90, 60, and 30 degrees, respectively. In some studies, the impact of the intersection angle has been examined, but in this study, three-dimensional investigation in transverse and longitudinal sections as well as the plan of the intersection is discussed, as can be observed from the literature review. Considering three models with intersection angles of 90, 60, and 30 degrees, the kinetic energy contours at the channel’s middle height can be obtained for each model. The channel with a 30-degree intersection angle (model 3) has the maximum kinetic energy in the flow. The channel with a 60-degree intersection has the minimum kinetic energy. As a result of the maximum deviation of the flow in the main channel caused by the flow of the side channel, the channel with a 90-degree intersection also has the maximum kinetic energy near the wall in front of the side channel.

Examining the side channel length In model 1, the side channel is 3. 66 meters long, whereas in model 4, it is 5. 52 meters long. This study aims to determine how changing the side channel’s length affects the flow pattern where two channels intersect. The kinetic energy contours were obtained for two states of the channel length, which are known to extend the lateral channel, increase the energy of the flow after the intersection, and shorten the length of the high-kinetic energy zone. When compared to model 1 with a shorter length of the side channel, the width of the flow separation zone is reduced by approximately 20%, which results in less flow sedimentation. Figure 12 illustrates the rotating zones in the flow separation area. The flow separation region’s length is essentially unchanged. Studying the intersection of the lateral channel After determining the lateral channel’s length, its width and, consequently, its intersectional area should be evaluated.

This section compares model 1 width of 0. 91 meters to model 5 width of 1. 40 meters. One of the most recent topics related to the intersection of the main and side channels is examining the intersection of the side channel. In model 5, the side channel’s flow rate has also increased due to an increase in the width or intersection of the channel. The flow rate through the intersection and the momentum of the flow from the side channel and the main channel increase when the side channel flow rate rises. The findings indicate that when flow width and side channel flow rise, energy increases after the inlet.

Investigating the value of inlet speed in the side channel Unlike the preceding sections, which were all concerned with the channel geometry, the inlet velocity in the side channel is one of the hydraulic parameters of the flow. In this section, models 1 and 6 with inlet velocities of the side channel of 0. 5 and 0. 75 m/s are evaluated. According to the modeling, the flow is somewhat horst before and immediately on the intersection of the flow level, but it undergoes a substantial prolapse just after the intersection. Model 6 has a larger volume and height of flow, but a smaller and softer prolapse after the intersection.

Conclusion

Some hydraulic and geometric properties of the intersection of channels have been examined using Flow-3D software. The RNG turbulence model was used for three-dimensional modeling. Some of the results are listed below. The flow is uniform upstream of the main and minor channels and only slightly becomes horst at the intersection. The analysis of the lengthening of the side channel revealed a 20% reduction in the separation zone’s width and a considerable reduction in the kinetic energy at the intersection. The input flow rate of this channel to the intersection increases with the speed and width of the side channel, which accounts for the local drop in the width of the main channel flow.

References

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Difference Analysis of Wave Disaster Characteristics Induced by Landslides of Different Water Entry Scales

다양한 크기의 산사태로 인한 물 침입으로 인한 해일 위험 특성의 차이 분석.

Difference Analysis of Wave Disaster Characteristics Induced by Landslides of Different Water Entry Scales

王雷,  解明礼,  黄会宝,  柯虎,  高强人民珠江   2024年45卷第2期DOI:10.3969/j.issn.1001-9235.2024.02.003

纸质出版日期:2024

Abstract

This paper conducts a three-dimensional numerical analysis on the surges generated by landslides of different water entry scales, and analyzes the characteristics of surge disasters induced by landslides of different water entry scales, such as surge height, surge speed, and bank climbing height. Meanwhile, the impact of surges caused by landslides of different water entry scales on the dam is explored.

The FLOW-3D numerical simulation method is employed to simulate and analyze the entire process of landslide instability, surge formation and propagation, surge climbing, and surge backflow. The results show that the maximum climbing height of the surge generated by the 3. 1 million m~3 landslide of water entry is 54. 5 m on the opposite bank, and the surge height in front of the dam is 6. 69 m.

The surge has a small area of overflow at the right bank dam shoulder. The surge generated by the 0. 8 million m~3 landslide of water entry has a maximum climbing height of 26. 00 m on the opposite bank, and the surge height in front of the dam is 5. 38 m, without influence exerted by the surge on the dam safety. The results indicate that the induced surge caused by 3. 1×10~6 m~3 landslide of water entry is more catastrophic than that brought by 0. 8×10~6 m~3 landslide of water entry.

Difference Analysis of Wave Disaster Characteristics Induced by Landslides of Different Water Entry Scales
Difference Analysis of Wave Disaster Characteristics Induced by Landslides of Different Water Entry Scales

출판물

Pearl River, 2024, Vol 45, Issue 2, p18

ISSN

1001-9235

간행물 유형

Academic Journal

DOI

10.3969/j.issn.1001-9235.2024.02.003

Local Scour Depth Around Bridge Piers: Performance Evaluation of Dimensional Analysis-based Empirical Equations and AI Techniques

Local Scour Depth Around Bridge Piers: Performance Evaluation of Dimensional Analysis-based Empirical Equations and AI Techniques

Abstract

Artificial Intelligence (AI) techniques, such as Artificial Neural Networks (ANN) and Adaptive Neuro-Fuzzy Inference Systems (ANFIS), and dimensional analysis-based empirical equations (DAEEs), can estimate scour depth around bridge piers. AI’s accuracy depends on various architectures, while DAEEs’ performance depends on experimental data. This study evaluated the performance of AI and DAEEs for scour depth estimation using flow velocity, depth, size of bed sediment, critical approach velocity, and pier width. The data from a smooth rectangular (20 m × 1 m) flume and a high-precision particle image velocimetry to study the flow structure around the pier – width: 1.5 – 91.5 cm evaluated DAEEs. Various ANNs (5, 10, and 15 neurons), double layer (DL) and triple layers (TL), and different ANFIS settings were trained, tested, and verified. The Generalized Reduced Gradient optimization identified the parameters of DAEEs, and Nash–Sutcliffe efficiency (NSE) and Mean Square Error (MSE) evaluated the performance of different models. The study revealed that DL ANN-3 with 10 neurons (NSE = 0.986) outperformed ANFIS, other ANN (ANN1, ANN2, ANN4 & ANN5) models, and empirical equations with NSE values between 0.76 and 0.983. The study found pier dimensions to be the most influential parameter for pier scour.

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Abdul Razzaq GhummanHusnain HaiderIbrahim Saleh Al SalamahMd. ShafiquzzamanAbdullah AlodahMohammad AlresheediRashid FarooqAfzal Ahmed & Ghufran Ahmed Pasha

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References

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Acknowledgments

Authors also thank “The US Department of the Interior,” US Geol. Surv. Reston, VA, USA” for providing access to scour data. The Researchers would like to thank the Deanship of Graduate Studies and Scientific Research at Qassim University for financial support (QU-APC-2024-9/1).

Author information

Authors and Affiliations

  1. Dept. of Civil Engineering, College of Engineering, Qassim University, Buraydah, 51452, Saudi ArabiaAbdul Razzaq Ghumman, Husnain Haider, Ibrahim Saleh Al Salamah, Md. Shafiquzzaman, Abdullah Alodah & Mohammad Alresheedi
  2. Dept. of Civil Engineering, International Islamic University, Islamabad, 44000, PakistanRashid Farooq
  3. Dept. of Civil Engineering, University of Engineering and Technology, Taxila, 47050, PakistanAfzal Ahmed & Ghufran Ahmed Pasha

  • DOIhttps://doi.org/10.1007/s12205-024-1161-x


Keywords

An investigation of the effect of the pulse width and amplitude on sand bed scouring by a vertical submerged pulsed jet

An investigation of the effect of the pulse width and amplitude on sand bed scouring by a vertical submerged pulsed jet

수직 수중 펄스 제트에 의한 모래층 정련에 대한 펄스 폭과 진폭의 영향 조사

Chuan Wang abc, Hao Yu b, Yang Yang b, Zhenjun Gao c, Bin Xi b, Hui Wang b, Yulong Yao b

aInternational Shipping Research Institute, GongQing Institute of Science and Technology, Jiujiang, 332020, ChinabCollege of Hydraulic Science and Engineering, Yangzhou University, Yangzhou, 225009, ChinacCollege of Mechanical and Power Engineering, China Three Gorges University, Yichang, 443002, China

https://doi.org/10.1016/j.oceaneng.2024.117324

Highlights

  • Numerical simulations and experiments were combined to investigate pulsed jet scour.
  • The effect mechanism of pulse amplitude on the variation of scour hole depth was analyzed.
  • Models for the prediction of relative low pulse width with the inlet pulse amplitude have been developed.

Abstract

This paper investigates the effects of the pulse width and amplitude on the scouring of sand beds by vertical submerged pulsed jets using a combination of experimental and numerical calculations. The reliability of the numerical calculations is verified through a comparison between the numerical simulations with the sedimentation scour model and the experimental data at a low pulse width T2 of 0, with the result that the various errors are within 5%. The results show that the scour hole depth |hmin| grows with the relative low pulse width T3 throughout three intervals: a slowly increasing zone I, a rapidly increasing zone II, and a decreasing zone III, producing a unique extreme value of |hmin|. The optimal scouring effect equation was obtained by analytically fitting the relationship curve between the pulse amplitude V and the relatively low pulse width T3. Including the optimal T3 and optimal duty cycle ƞ. The difference in the scour hole depth |hmin| under different pulse amplitudes is reflected in the initial period F of the jet. With an increasing pulse amplitude, |hmin| goes through three intervals: an increasing zone M, decreasing zone N, and rebound zone R. It is found that the scouring effect in the pulse jet is not necessarily always stronger with a larger amplitude. The results of the research in this paper can provide guidance for optimizing low-frequency pulsed jets for related engineering practices, such as dredging and rock-breaking projects.

Introduction

Submerged jet scouring technology is widely used in marine engineering and dredging projects due to its high efficiency and low cost, and a wide range of research exists on the topic (Zhang et al., 2017; Thaha et al., 2018; Lourenço et al., 2020). Numerous scholars studied the scouring caused by different forms of jets, such as propeller jets (Curulli et al., 2023; Wei et al., 2020), plane jets (Sharafati et al., 2020; Mostaani and Azimi, 2022), free-fall jets (Salmasi and Abraham, 2022; Salmasi et al., 2023), and moving jets (Wang et al., 2021). Among them, vertical jets were more popular than inclined jets due to theirs simple equipment and good silt-scouring performance (Chen et al., 2023; Wang et al., 2017). So, a large number of scholars have proposed relevant static and dynamic empirical equations for the scour depth of submerged jets. Among them, Chen et al. (2022) and Mao et al. (2023) investigated the influence of jet diameters, jet angles, exit velocities, and impinging distances on scouring effects. Finally, based on a large amount of experimental data and theoretical analysis, a semi-empirical equation for the dynamic scour depth in equilibrium was established. Amin et al. (2021) developed semi-empirical prediction equations for asymptotic lengths and empirical equations for the temporal development of lengths. Shakya et al. (2021, 2022) found that the ANN model in dimensionless form performs better than the ANN model in dimensioned form and proposed an equation for predicting the depth of static scour under submerged vertical jets using MNLR. Kartal and Emiroglu (2021) proposed an empirical equation for predicting the maximum dynamic scour depth for a submerged vertical jet with a plate at the nozzle. The effect of soil properties on jet scour has also been studied by numerous scholars. Among them, Nguyen et al. (2017) investigated the effects of compaction dry density and water content on the scour volume, critical shear stress, linear scour coefficient, and volumetric scour coefficient using a new jet-scour test device. Dong et al. (2020) investigated the effect of water content on scour hole size through experiments with a vertical submerged jet scouring a cohesive sediment bed. It was found that the depth and width of the scour holes increased with the increasing water content of the cohesive sediments, and equations for the scour depth and width in the initial stage of scouring and the calculation of the scouring rate were proposed. Kartal and Emiroglu (2023) studied the scouring characteristics of different nozzle types produced in non-cohesive sands. The results of the study found that the air entrainment rate of venturi nozzles was 2–6.5 times higher than that of circular nozzles. Cihan et al. (2022) investigated the effect of different proportions of clay and sand on propeller water jet scouring. And finally, he proposed an estimation equation for the maximum depth and length of the scour hole under equilibrium conditions. From the above summary, it is clear that a great deal of research has been carried out on submerged jet scouring under continuous jet flows.

Pulsed jets have advantages such as higher erosion rates and entrainment rates compared to continuous jets and have therefore received more attention in the development of engineering fields such as cleaning and rock breaking (Raj et al., 2019; Zhu et al., 2019; Kang et al., 2022; Y. Zhang et al., 2023). In the study of jet structure, Li et al. (2018, 2019a, 2019b, 2023) investigated the effects of the jet hole diameter, the number of jet holes, the jet distance, and the tank pressure on pulse jet cleaning. It was found that the transient pressure below the injection hole gradually increased along the airflow direction of the injection pipe, and the peak positive pressure at the inner surface of the injection pipe also increased. Liu and Shen (2019) investigated the effect of a new venturi structure on the performance of pulse jet dust removal. It was found that the longer the length of the venturi or the shorter the throat diameter of the venturi, the greater the energy loss. Zhang et al. (2023b) studied jet scouring at different angles based on FLOW-3D. It was found that counter flow scouring is better than down flow scouring. In the study of pulsed structure, Li et al. (2020) investigated the effects of different pulse amplitudes, pulse frequencies, and circumferential pressures on the rock-breaking performance. It was found that the rock-breaking performance of the jet increased with increasing pulse amplitude. However, due to the variation in pulse frequency, the rock-breaking performance does not show a clear pattern. The effect of Reynolds number on pulsating jets impinging on a plane was systematically investigated by H. H Medina et al. (2013) It was found that pulsation leads to a shorter core region of the jet, a faster decrease in the centerline axial velocity component, and a wider axial velocity distribution. Bi and Zhu (2021) investigated the effect of nozzle geometry on jet performance at low Reynolds numbers, while Luo et al. (2020) studied pulse jet propulsion at high Reynolds numbers and finally found that higher Reynolds numbers accelerate the formation of irregular vortices and symmetry-breaking instabilities. Cao et al. (2019) investigated the effect of four different pulse flushing methods on diamond core drilling efficiency. It was found that the use of intermittent rinsing methods not only increases penetration rates but also reduces rinse fluid flow and saves power.

Previous research on vertical submerged jet scouring has primarily focused on the effect of jet structure on scouring under continuous jet conditions. However, there have been fewer studies conducted on scouring under pulsed jet conditions. We found that the pulsed jet has a high erosion rate and entrainment rate, which can significantly enhance the scouring effect of the jet. Therefore, to address the research gap, this paper utilizes a combination of numerical calculations and experiments to investigate the effects of high pulse width, low pulse width, and amplitude on the scouring of vertically submerged jets. The study includes analyzing the structure of the pulsed jet flow field, studying the evolution of the scouring effect over time, and examining the relationship between the optimal pulse width, duty cycle, and amplitude. The study’s conclusions of the study can provide a reference for optimizing the performance of pulse jets in the fields of jet scouring applications, such as dredger dredging and pulse rock breaking, as well as a theoretical basis for the development of submerged pulse jets.

Section snippets

Model and calculation settings

Fig. 1 shows the geometric model of the submerged vertical jet impinging on the sand bed, which was built in Flow-3D on a 1:1 dimensional scale corresponding to the experiment. The jet scour simulation was set up between four baffles, where the top baffle was used to ensure that the jet entered only from the brass tube, and the remaining three tank baffles were used to fix the sediment and water body. The computational domain consisted of only solid and liquid components, with the specific

The effects of the pulse width on submerged jet scouring

The blocking pulsed jet, indicated as A and C in Fig. 8(a)–is discontinuous and divided into a water section and a pulse interval section. The water section in region A is not a regular shape, due to part of the water section near the side wall being affected by the wall friction and the falling speed being lower, but this also shows that the wall plays a certain buffer role. Region B of Fig. 8(a) shows the symmetrical vortex generation that occurs below the nozzle as the water section is

conclusions

In this paper, the effects of the pulse width and pulse amplitude on jet scour under submerged low-frequency pulse conditions are discussed and investigated, and the following conclusions have been reached.

  • (1)The errors of between the Flow-3D simulation and the experimental measurements were within 5%, which proves that the sedimentation scouring model of Flow-3D can reliably perform numerical calculation of the type considered in this paper.
  • (2)The change in the high pulse width T1 in the pulse cycle 

CRediT authorship contribution statement

Chuan Wang: Data curation, Conceptualization. Hao Yu: Writing – original draft. Yang Yang: Writing – review & editing, Supervision. Zhenjun Gao: Supervision, Writing – review & editing. Bin Xi: Resources, Project administration. Hui Wang: Software, Data curation. Yulong Yao: Validation, Software.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (44)

Estimating maximum initial wave amplitude of subaerial landslide tsunamis: A three-dimensional modelling approach

Estimating maximum initial wave amplitude of subaerial landslide tsunamis: A three-dimensional modelling approach

해저 산사태 쓰나미의 최대 초기 파동 진폭 추정: 3차원 모델링 접근법

Ramtin Sabeti a, Mohammad Heidarzadeh ab

aDepartment of Architecture and Civil Engineering, University of Bath, Bath BA27AY, UK
bHydroCoast Consulting Engineers Ltd, Bath, UK

https://doi.org/10.1016/j.ocemod.2024.102360

Highlights

  • •Landslide travel distance is considered for the first time in a predictive equation.
  • •Predictive equation derived from databases using 3D physical and numerical modeling.
  • •The equation was successfully tested on the 2018 Anak Krakatau tsunami event.
  • •The developed equation using three-dimensional data exhibits a 91 % fitting quality.

Abstract

Landslide tsunamis, responsible for thousands of deaths and significant damage in recent years, necessitate the allocation of sufficient time and resources for studying these extreme natural hazards. This study offers a step change in the field by conducting a large number of three-dimensional numerical experiments, validated by physical tests, to develop a predictive equation for the maximum initial amplitude of tsunamis generated by subaerial landslides. We first conducted a few 3D physical experiments in a wave basin which were then applied for the validation of a 3D numerical model based on the Flow3D-HYDRO package. Consequently, we delivered 100 simulations using the validated model by varying parameters such as landslide volume, water depth, slope angle and travel distance. This large database was subsequently employed to develop a predictive equation for the maximum initial tsunami amplitude. For the first time, we considered travel distance as an independent parameter for developing the predictive equation, which can significantly improve the predication accuracy. The predictive equation was tested for the case of the 2018 Anak Krakatau subaerial landslide tsunami and produced satisfactory results.

Keywords

Tsunami, Subaerial landslide, Physical modelling, Numerical simulation, FLOW-3D HYDRO

1. Introduction and literature review

The Anak Krakatau landslide tsunami on 22nd December 2018 was a stark reminder of the dangers posed by subaerial landslide tsunamis (Ren et al., 2020Mulia et al. 2020a; Borrero et al., 2020Heidarzadeh et al., 2020Grilli et al., 2021). The collapse of the volcano’s southwest side into the ocean triggered a tsunami that struck the Sunda Strait, leading to approximately 450 fatalities (Syamsidik et al., 2020Mulia et al., 2020b) (Fig. 1). As shown in Fig. 1, landslide tsunamis (both submarine and subaerial) have been responsible for thousands of deaths and significant damage to coastal communities worldwide. These incidents underscored the critical need for advanced research into landslide-generated waves to aid in hazard prediction and mitigation. This is further emphasized by recent events such as the 28th of November 2020 landslide tsunami in the southern coast mountains of British Columbia (Canada), where an 18 million m3 rockslide generated a massive tsunami, with over 100 m wave run-up, causing significant environmental and infrastructural damage (Geertsema et al., 2022).

Fig 1

Physical modelling and numerical simulation are crucial tools in the study of landslide-induced waves due to their ability to replicate and analyse the complex dynamics of landslide events (Kim et al., 2020). In two-dimensional (2D) modelling, the discrepancy between dimensions can lead to an artificial overestimation of wave amplification (e.g., Heller and Spinneken, 2015). This limitation is overcome with 3D modelling, which enables the scaled-down representation of landslide-generated waves while avoiding the simplifications inherent in 2D approaches (Erosi et al., 2019). Another advantage of 3D modelling in studying landslide-generated waves is its ability to accurately depict the complex dynamics of wave propagation, including lateral and radial spreading from the slide impact zone, a feature unattainable with 2D models (Heller and Spinneken, 2015).

Physical experiments in tsunami research, as presented by authors such as Romano et al. (2020), McFall and Fritz (2016), and Heller and Spinneken (2015), have supported 3D modelling works through validation and calibration of the numerical models to capture the complexities of wave generation and propagation. Numerical modelling has increasingly complemented experimental approach in tsunami research due to the latter’s time and resource-intensive nature, particularly for 3D models (Li et al., 2019; Kim et al., 2021). Various numerical approaches have been employed, from Eulerian and Lagrangian frameworks to depth-averaged and Navier–Stokes models, enhancing our understanding of tsunami dynamics (Si et al., 2018Grilli et al., 2019Heidarzadeh et al., 20172020Iorio et al., 2021Zhang et al., 2021Kirby et al., 2022Wang et al., 20212022Hu et al., 2022). The sophisticated numerical techniques, including the Particle Finite Element Method and the Immersed Boundary Method, have also shown promising results in modelling highly dynamic landslide scenarios (Mulligan et al., 2020Chen et al., 2020). Among these methods and techniques, FLOW-3D HYDRO stands out in simulating landslide-generated tsunami waves due to its sophisticated technical features such as offering Tru Volume of Fluid (VOF) method for precise free surface tracking (e.g., Sabeti and Heidarzadeh 2022a). TruVOF distinguishes itself through a split Lagrangian approach, adeptly reducing cumulative volume errors in wave simulations by dynamically updating cell volume fractions and areas with each time step. Its intelligent adaptation of time step size ensures precise capture of evolving free surfaces, offering unparalleled accuracy in modelling complex fluid interfaces and behaviour (Flow Science, 2023).

Predictive equations play a crucial role in assessing the potential hazards associated with landslide-generated tsunami waves due to their ability to provide risk assessment and warnings. These equations can offer swift and reasonable evaluations of potential tsunami impacts in the absence of detailed numerical simulations, which can be time-consuming and expensive to produce. Among multiple factors and parameters within a landslide tsunami generation, the initial maximum wave amplitude (Fig. 1) stands out due to its critical role. While it is most likely that the initial wave generated by a landslide will have the highest amplitude, it is crucial to clarify that the term “initial maximum wave amplitude” refers to the highest amplitude within the first set of impulse waves. This parameter is essential in determining the tsunami’s impact severity, with higher amplitudes signalling a greater destructive potential (Sabeti and Heidarzadeh 2022a). Additionally, it plays a significant role in tsunami modelling, aiding in the prediction of wave propagation and the assessment of potential impacts.

In this study, we initially validate the FLOW-3D HYDRO model through a series of physical experiments conducted in a 3D wave tank at University of Bath (UK). Upon confirmation of the model’s accuracy, we use it to systematically vary parameters namely landslide volume, water depth, slope angle, and travel distance, creating an extensive database. Alongside this, we perform a sensitivity analysis on these variables to discern their impacts on the initial maximum wave amplitude. The generated database was consequently applied to derive a non-dimensional predictive equation aimed at estimating the initial maximum wave amplitude in real-world landslide tsunami events.

Two innovations of this study are: (i) The predictive equation of this study is based on a large number of 3D experiments whereas most of the previous equations were based on 2D results, and (ii) For the first time, the travel distance is included in the predictive equation as an independent parameter. To evaluate the performance of our predictive equation, we applied it to a previous real-world subaerial landslide tsunami, i.e., the Anak Krakatau 2018 event. Furthermore, we compare the performance of our predictive equation with other existing equations.

2. Data and methods

The methodology applied in this research is a combination of physical and numerical modelling. Limited physical modelling was performed in a 3D wave basin at the University of Bath (UK) to provide data for calibration and validation of the numerical model. After calibration and validation, the numerical model was employed to model a large number of landslide tsunami scenarios which allowed us to develop a database for deriving a predictive equation.

2.1. Physical experiments

To validate our numerical model, we conducted a series of physical experiments including two sets in a 3D wave basin at University of Bath, measuring 2.50 m in length (WL), 2.60 m in width (WW), and 0.60 m in height (WH) (Fig. 2a). Conducting two distinct sets of experiments (Table 1), each with different setups (travel distance, location, and water depth), provided a robust framework for validation of the numerical model. For wave measurement, we employed a twin wire wave gauge from HR Wallingford (https://equipit.hrwallingford.com). In these experiments, we used a concrete prism solid block, the dimensions of which are outlined in Table 2. In our experiments, we employed a concrete prism solid block with a density of 2600 kg/m3, chosen for its similarity to the natural density of landslides, akin to those observed with the 2018 Anak Krakatau tsunami, where the landslide composition is predominantly solid rather than granular. The block’s form has also been endorsed in prior studies (Watts, 1998Najafi-Jilani and Ataie-Ashtiani, 2008) as a suitable surrogate for modelling landslide-induced waves. A key aspect of our methodology was addressing scale effects, following the guidelines proposed by Heller et al. (2008) as it is described in Table 1. To enhance the reliability and accuracy of our experimental data, we conducted each physical experiment three times which revealed all three experimental waveforms were identical. This repetition was aimed at minimizing potential errors and inconsistencies in laboratory measurements.

Fig 2

Table 1. The locations and other information of the laboratory setups for making landslide-generated waves in the physical wave basin. This table details the specific parameters for each setup, including slope range (α), slide volume (V), kinematic viscosity (ν), water depth (h), travel distance (D), surface tension coefficient of water (σ), Reynolds number (R), Weber number (W), and the precise coordinates of the wave gauges (WG).

Labα(°)V (m³)h (m)D (m)WG’s Location(ν) (m²/s)(σ) (N/m)Acceptable range for avoiding scale effects*Observed values of W and R ⁎⁎
Lab 1452.60 × 10−30.2470.070X1=1.090 m1.01 × 10−60.073R > 3.0 × 105R1 = 3.80 × 105
Y1=1.210 m
W1 = 8.19 × 105
Z1=0.050mW >5.0 × 103
Lab 2452.60 × 10−30.2460.045X2=1.030 m1.01 × 10−60.073R2 = 3.78 × 105
Y2=1.210 mW2 = 8.13 × 105
Z2=0.050 m

The acceptable ranges for avoiding scale effects are based on the study by Heller et al. (2008).⁎⁎

The Reynolds number (R) is given by g0.5h1.5/ν, with ν denoting the kinematic viscosity. The Weber number (W) is W = ρgh2/σ, where σ represents surface tension coefficient and ρ = 1000kg/m3 is the density of water. In our experiments, conducted at a water temperature of approximately 20 °C, the kinematic viscosity (ν) and the surface tension coefficient of water (σ) are 1.01 × 10−6 m²/s and 0.073 N/m, respectively (Kestin et al., 1978).

Table 2. Specifications of the solid block used in physical experiments for generating subaerial landslides in the laboratory.

Solid-block attributesProperty metricsGeometric shape
Slide width (bs)0.26 mImage, table 2
Slide length (ls)0.20 m
Slide thickness (s)0.10 m
Slide volume (V)2.60 × 10−3 m3
Specific gravity, (γs)2.60
Slide weight (ms)6.86 kg

2.2. Numerical simulations applying FLOW-3D hydro

The detailed theoretical framework encompassing the governing equations, the computational methodologies employed, and the specific techniques used for tracking the water surface in these simulations are thoroughly detailed in the study by Sabeti et al. (2024). Here, we briefly explain some of the numerical details. We defined a uniform mesh for our flow domain, carefully crafted with a fine spatial resolution of 0.005 m (i.e., grid size). The dimensions of the numerical model directly matched those of our wave basin used in the physical experiment, being 2.60 m wide, 0.60 m deep, and 2.50 m long (Fig. 2). This design ensures comprehensive coverage of the study area. The output intervals of the numerical model are set at 0.02 s. This timing is consistent with the sampling rates of wave gauges used in laboratory settings. The friction coefficient in the FLOW-3D HYDRO is designated as 0.45. This value corresponds to the Coulombic friction measurements obtained in the laboratory, ensuring that the simulation accurately reflects real-world physical interactions.

In order to simulate the landslide motion, we applied coupled motion objects in FLOW-3D-HYDRO where the dynamics are predominantly driven by gravity and surface friction. This methodology stands in contrast to other models that necessitate explicit inputs of force and torque. This approach ensures that the simulation more accurately reflects the natural movement of landslides, which is heavily reliant on gravitational force and the interaction between sliding surfaces. The stability of the numerical simulations is governed by the Courant Number criterion (Courant et al., 1928), which dictates the maximum time step (Δt) for a given mesh size (Δx) and flow speed (U). According to Courant et al. (1928), this number is required to stay below one to ensure stability of numerical simulations. In our simulations, the Courant number is always maintained below one.

In alignment with the parameters of physical experiments, we set the fluid within the mesh to water, characterized by a density of 1000 kg/m³ at a temperature of 20 °C. Furthermore, we defined the top, front, and back surfaces of the mesh as symmetry planes. The remaining surfaces are designated as wall types, incorporating no-slip conditions to accurately simulate the interaction between the fluid and the boundaries. In terms of selection of an appropriate turbulence model, we selected the k–ω model that showed a better performance than other turbulence methods (e.g., Renormalization-Group) in a previous study (Sabeti et al., 2024). The simulations are conducted using a PC Intel® Core™ i7-10510U CPU with a frequency of 1.80 GHz, and a 16 GB RAM. On this PC, completion of a 3-s simulation required approximately 12.5 h.

2.3. Validation

The FLOW-3D HYDRO numerical model was validated using the two physical experiments (Fig. 3) outlined in Table 1. The level of agreement between observations (Oi) and simulations (Si) is examined using the following equation:(1)�=|��−����|×100where ε represents the mismatch error, Oi denotes the observed laboratory values, and Si represents the simulated values from the FLOW-3D HYDRO model. The results of this validation process revealed that our model could replicate the waves generated in the physical experiments with a reasonable degree of mismatch (ε): 14 % for Lab 1 and 8 % for Lab 2 experiments, respectively (Fig. 3). These values indicate that while the model is not perfect, it provides a sufficiently close approximation of the real-world phenomena.

Fig 3

In terms of mesh efficiency, we varied the mesh size to study sensitivity of the numerical results to mesh size. First, by halving the mesh size and then by doubling it, we repeated the modelling by keeping other parameters unchanged. This analysis guided that a mesh size of ∆x = 0.005 m is the most effective for the setup of this study. The total number of computational cells applying mesh size of 0.005 m is 9.269 × 106.

2.4. The dataset

The validated numerical model was employed to conduct 100 simulations, incorporating variations in four key landslide parameters namely water depth, slope angle, slide volume, and travel distance. This methodical approach was essential for a thorough sensitivity analysis of these variables, and for the creation of a detailed database to develop a predictive equation for maximum initial tsunami amplitude. Within the model, 15 distinct slide volumes were established, ranging from 0.10 × 10−3 m3 to 6.25 × 10−3 m3 (Table 3). The slope angle varied between 35° and 55°, and water depth ranged from 0.24 m to 0.27 m. The travel distance of the landslides was varied, spanning from 0.04 m to 0.07 m. Detailed configurations of each simulation, along with the maximum initial wave amplitudes and dominant wave periods are provided in Table 4.

Table 3. Geometrical information of the 15 solid blocks used in numerical modelling for generating landslide tsunamis. Parameters are: ls, slide length; bs, slide width; s, slide thickness; γs, specific gravity; and V, slide volume.

Solid blockls (m)bs (m)s (m)V (m3)γs
Block-10.3100.2600.1556.25 × 10−32.60
Block-20.3000.2600.1505.85 × 10−32.60
Block-30.2800.2600.1405.10 × 10−32.60
Block-40.2600.2600.1304.39 × 10−32.60
Block-50.2400.2600.1203.74 × 10−32.60
Block-60.2200.2600.1103.15 × 10−32.60
Block-70.2000.2600.1002.60 × 10−32.60
Block-80.1800.2600.0902.11 × 10−32.60
Block-90.1600.2600.0801.66 × 10−32.60
Block-100.1400.2600.0701.27 × 10−32.60
Block-110.1200.2600.0600.93 × 10−32.60
Block-120.1000.2600.0500.65 × 10−32.60
Block-130.0800.2600.0400.41 × 10−32.60
Block-140.0600.2600.0300.23 × 10−32.60
Block-150.0400.2600.0200.10 × 10−32.60

Table 4. The numerical simulation for the 100 tests performed in this study for subaerial solid-block landslide-generated waves. Parameters are aM, maximum wave amplitude; α, slope angle; h, water depth; D, travel distance; and T, dominant wave period. The location of the wave gauge is X=1.030 m, Y=1.210 m, and Z=0.050 m. The properties of various solid blocks are presented in Table 3.

Test-Block Noα (°)h (m)D (m)T(s)aM (m)
1Block-7450.2460.0290.5100.0153
2Block-7450.2460.0300.5050.0154
3Block-7450.2460.0310.5050.0156
4Block-7450.2460.0320.5050.0158
5Block-7450.2460.0330.5050.0159
6Block-7450.2460.0340.5050.0160
7Block-7450.2460.0350.5050.0162
8Block-7450.2460.0360.5050.0166
9Block-7450.2460.0370.5050.0167
10Block-7450.2460.0380.5050.0172
11Block-7450.2460.0390.5050.0178
12Block-7450.2460.0400.5050.0179
13Block-7450.2460.0410.5050.0181
14Block-7450.2460.0420.5050.0183
15Block-7450.2460.0430.5050.0190
16Block-7450.2460.0440.5050.0197
17Block-7450.2460.0450.5050.0199
18Block-7450.2460.0460.5050.0201
19Block-7450.2460.0470.5050.0191
20Block-7450.2460.0480.5050.0217
21Block-7450.2460.0490.5050.0220
22Block-7450.2460.0500.5050.0226
23Block-7450.2460.0510.5050.0236
24Block-7450.2460.0520.5050.0239
25Block-7450.2460.0530.5100.0240
26Block-7450.2460.0540.5050.0241
27Block-7450.2460.0550.5050.0246
28Block-7450.2460.0560.5050.0247
29Block-7450.2460.0570.5050.0248
30Block-7450.2460.0580.5050.0249
31Block-7450.2460.0590.5050.0251
32Block-7450.2460.0600.5050.0257
33Block-1450.2460.0450.5050.0319
34Block-2450.2460.0450.5050.0294
35Block-3450.2460.0450.5050.0282
36Block-4450.2460.0450.5050.0262
37Block-5450.2460.0450.5050.0243
38Block-6450.2460.0450.5050.0223
39Block-7450.2460.0450.5050.0196
40Block-8450.2460.0450.5050.0197
41Block-9450.2460.0450.5050.0198
42Block-10450.2460.0450.5050.0184
43Block-11450.2460.0450.5050.0173
44Block-12450.2460.0450.5050.0165
45Block-13450.2460.0450.4040.0153
46Block-14450.2460.0450.4040.0124
47Block-15450.2460.0450.5050.0066
48Block-7450.2020.0450.4040.0220
49Block-7450.2040.0450.4040.0219
50Block-7450.2060.0450.4040.0218
51Block-7450.2080.0450.4040.0217
52Block-7450.2100.0450.4040.0216
53Block-7450.2120.0450.4040.0215
54Block-7450.2140.0450.5050.0214
55Block-7450.2160.0450.5050.0214
56Block-7450.2180.0450.5050.0213
57Block-7450.2200.0450.5050.0212
58Block-7450.2220.0450.5050.0211
59Block-7450.2240.0450.5050.0208
60Block-7450.2260.0450.5050.0203
61Block-7450.2280.0450.5050.0202
62Block-7450.2300.0450.5050.0201
63Block-7450.2320.0450.5050.0201
64Block-7450.2340.0450.5050.0200
65Block-7450.2360.0450.5050.0199
66Block-7450.2380.0450.4040.0196
67Block-7450.2400.0450.4040.0194
68Block-7450.2420.0450.4040.0193
69Block-7450.2440.0450.4040.0192
70Block-7450.2460.0450.5050.0190
71Block-7450.2480.0450.5050.0189
72Block-7450.2500.0450.5050.0187
73Block-7450.2520.0450.5050.0187
74Block-7450.2540.0450.5050.0186
75Block-7450.2560.0450.5050.0184
76Block-7450.2580.0450.5050.0182
77Block-7450.2590.0450.5050.0183
78Block-7450.2600.0450.5050.0191
79Block-7450.2610.0450.5050.0192
80Block-7450.2620.0450.5050.0194
81Block-7450.2630.0450.5050.0195
82Block-7450.2640.0450.5050.0195
83Block-7450.2650.0450.5050.0197
84Block-7450.2660.0450.5050.0197
85Block-7450.2670.0450.5050.0198
86Block-7450.2700.0450.5050.0199
87Block-7300.2460.0450.5050.0101
88Block-7350.2460.0450.5050.0107
89Block-7360.2460.0450.5050.0111
90Block-7370.2460.0450.5050.0116
91Block-7380.2460.0450.5050.0117
92Block-7390.2460.0450.5050.0119
93Block-7400.2460.0450.5050.0121
94Block-7410.2460.0450.5050.0127
95Block-7420.2460.0450.4040.0154
96Block-7430.2460.0450.4040.0157
97Block-7440.2460.0450.4040.0162
98Block-7450.2460.0450.5050.0197
99Block-7500.2460.0450.5050.0221
100Block-7550.2460.0450.5050.0233

In all these 100 simulations, the wave gauge was consistently positioned at coordinates X=1.09 m, Y=1.21 m, and Z=0.05 m. The dominant wave period for each simulation was determined using the Fast Fourier Transform (FFT) function in MATLAB (MathWorks, 2023). Furthermore, the classification of wave types was carried out using a wave categorization graph according to Sorensen (2010), as shown in Fig. 4a. The results indicate that the majority of the simulated waves are on the border between intermediate and deep-water waves, and they are categorized as Stokes waves (Fig. 4a). Four sample waveforms from our 100 numerical experiments are provided in Fig. 4b.

Fig 4

The dataset in Table 4 was used to derive a new predictive equation that incorporates travel distance for the first time to estimate the initial maximum tsunami amplitude. In developing this equation, a genetic algorithm optimization technique was implemented using MATLAB (MathWorks 2023). This advanced approach entailed the use of genetic algorithms (GAs), an evolutionary algorithm type inspired by natural selection processes (MathWorks, 2023). This technique is iterative, involving selection, crossover, and mutation processes to evolve solutions over several generations. The goal was to identify the optimal coefficients and powers for each landslide parameter in the predictive equation, ensuring a robust and reliable model for estimating maximum wave amplitudes. Genetic Algorithms excel at optimizing complex models by navigating through extensive combinations of coefficients and exponents. GAs effectively identify highly suitable solutions for the non-linear and complex relationships between inputs (e.g., slide volume, slope angle, travel distance, water depth) and the output (i.e., maximum initial wave amplitude, aM). MATLAB’s computational environment enhances this process, providing robust tools for GA to adapt and evolve solutions iteratively, ensuring the precision of the predictive model (Onnen et al., 1997). This approach leverages MATLAB’s capabilities to fine-tune parameters dynamically, achieving an optimal equation that accurately estimates aM. It is important to highlight that the nondimensionalized version of this dataset is employed to develop a predictive equation which enables the equation to reproduce the maximum initial wave amplitude (aM) for various subaerial landslide cases, independent of their dimensional differences (e.g., Heler and Hager 2014Heller and Spinneken 2015Sabeti and Heidarzadeh 2022b). For this nondimensionalization, we employed the water depth (h) to nondimensionalize the slide volume (V/h3) and travel distance (D/h). The slide thickness (s) was applied to nondimensionalize the water depth (h/s).

2.5. Landslide velocity

In discussing the critical role of landslide velocity for simulating landslide-generated waves, we focus on the mechanisms of landslide motion and the techniques used to record landslide velocity in our simulations (Fig. 5). Also, we examine how these methods were applied in two distinct scenarios: Lab 1 and Lab 2 (see Table 1 for their details). Regarding the process of landslide movement, a slide starts from a stationary state, gaining momentum under the influence of gravity and this acceleration continues until the landslide collides with water, leading to a significant reduction in its speed before eventually coming to a stop (Fig. 5) (e.g., Panizzo et al. 2005).

Fig 5

To measure the landslide’s velocity in our simulations, we attached a probe at the centre of the slide, which supplied a time series of the velocity data. The slide’s velocity (vs) peaks at the moment it enters the water (Fig. 5), a point referred to as the impact time (tImp). Following this initial impact, the slides continue their underwater movement, eventually coming to a complete halt (tStop). Given the results in Fig. 5, it can be seen that Lab 1, with its longer travel distance (0.070 m), exhibits a higher peak velocity of 1.89 m/s. This increase in velocity is attributed to the extended travel distance allowing more time for the slide to accelerate under gravity. Whereas Lab 2, featuring a shorter travel distance (0.045 m), records a lower peak velocity of 1.78 m/s. This difference underscores how travel distance significantly influences the dynamics of landslide motion. After reaching the peak, both profiles show a sharp decrease in velocity, marking the transition to submarine motion until the slides come to a complete stop (tStop). There are noticeable differences observable in Fig. 5 between the Lab-1 and Lab-2 simulations, including the peaks at 0.3 s . These variations might stem from the placement of the wave gauge, which differs slightly in each scenario, as well as the water depth’s minor discrepancies and, the travel distance.

2.6. Effect of air entrainment

In this section we examine whether it is required to consider air entrainment for our modelling or not as the FLOW-3D HYDRO package is capable of modelling air entrainment. The process of air entrainment in water during a landslide tsunami and its subsequent transport involve two key components: the quantification of air entrainment at the water surface, and the simulation of the air’s transport within the fluid (Hirt, 2003). FLOW-3D HYDRO employs the air entrainment model to compute the volume of air entrained at the water’s surface utilizing three approaches: a constant density model, a variable density model accounting for bulking, and a buoyancy model that adds the Drift-FLUX mechanism to variable density conditions (Flow Science, 2023). The calculation of the entrainment rate is based on the following equation:(2)�������=������[2(��−�����−2�/���)]1/2where parameters are: Vair, volume of air; Cair, entrainment rate coefficient; As, surface area of fluid; ρ, fluid density; k, turbulent kinetic energy; gn, gravity normal to surface; Lt, turbulent length scale; and σ, surface tension coefficient. The value of k is directly computed from the Reynolds-averaged Navier-Stokes (RANS) (kw) calculations in our model.

In this study, we selected the variable density + Drift-FLUX model, which effectively captures the dynamics of phase separation and automatically activates the constant density and variable density models. This method simplifies the air-water mixture, treating it as a single, homogeneous fluid within each computational cell. For the phase volume fractions f1and f2​, the velocities are expressed in terms of the mixture and relative velocities, denoted as u and ur, respectively, as follows:(3)��1��+�.(�1�)=��1��+�.(�1�)−�.(�1�2��)=0(4)��2��+�.(�2�)=��2��+�.(�2�)−�.(�1�2��)=0

The outcomes from this simulation are displayed in Fig. 6, which indicates that the influence of air entrainment on the generated wave amplitude is approximately 2 %. A value of 0.02 for the entrained air volume fraction means that, in the simulated fluid, approximately 2 % of the volume is composed of entrained air. In other words, for every unit volume of the fluid-air mixture at that location, 2 % is air and the remaining 98 % is water. The configuration of Test-17 (Table 4) was employed for this simulation. While the effect of air entrainment is anticipated to be more significant in models of granular landslide-generated waves (Fritz, 2002), in our simulations we opted not to incorporate this module due to its negligible impact on the results.

Fig 6

3. Results

In this section, we begin by presenting a sequence of our 3D simulations capturing different time steps to illustrate the generation process of landslide-generated waves. Subsequently, we derive a new predictive equation to estimate the maximum initial wave amplitude of landslide-generated waves and assess its performance.

3.1. Wave generation and propagation

To demonstrate the wave generation process in our simulation, we reference Test-17 from Table 4, where we employed Block-7 (Tables 34). In this configuration, the slope angle was set to 45°, with a water depth of 0.246 m and a travel distance at 0.045 m (Fig. 7). At 0.220 s, the initial impact of the moving slide on the water is depicted, marking the onset of the wave generation process (Fig. 7a). Disturbances are localized to the immediate area of impact, with the rest of the water surface remaining undisturbed. At this time, a maximum water particle velocity of 1.0 m/s – 1.2 m/s is seen around the impact zone (Fig. 7d). Moving to 0.320 s, the development of the wave becomes apparent as energy transfer from the landslide to the water creates outwardly radiating waves with maximum water particle velocity of up to around 1.6 m/s – 1.8 m/s (Fig. 7b, e). By the time 0.670 s, the wave has fully developed and is propagating away from the impact point exhibiting maximum water particle velocity of up to 2.0 m/s – 2.1 m/s. Concentric wave fronts are visible, moving outwards in all directions, with a colour gradient signifying the highest wave amplitude near the point of landslide entry, diminishing with distance (Fig. 7c, f).

Fig 7

3.2. Influence of landslide parameters on tsunami amplitude

In this section, we investigate the effects of various landslide parameters namely slide volume (V), water depth (h), slipe angle (α) and travel distance (D) on the maximum initial wave amplitude (aM). Fig. 8 presents the outcome of these analyses. According to Fig. 8, the slide volume, slope angle, and travel distance exhibit a direct relationship with the wave amplitude, meaning that as these parameters increase, so does the amplitude. Conversely, water depth is inversely related to the maximum initial wave amplitude, suggesting that the deeper the water depth, the smaller the maximum wave amplitude will be (Fig. 8b).

Fig 8

Fig. 8a highlights the pronounced impact of slide volume on the aM, demonstrating a direct correlation between the two variables. For instance, in the range of slide volumes we modelled (Fig. 8a), The smallest slide volume tested, measuring 0.10 × 10−3 m3, generated a low initial wave amplitude (aM= 0.0066 m) (Table 4). In contrast, the largest volume tested, 6.25 × 10−3 m3, resulted in a significantly higher initial wave amplitude (aM= 0.0319 m) (Table 4). The extremities of these results emphasize the slide volume’s paramount impact on wave amplitude, further elucidated by their positions as the smallest and largest aM values across all conducted tests (Table 4). This is corroborated by findings from the literature (e.g., Murty, 2003), which align with the observed trend in our simulations.

The slope angle’s influence on aM was smooth. A steady increase of wave amplitude was observed as the slope angle increased (Fig. 8c). In examining travel distance, an anomaly was identified. At a travel distance of 0.047 m, there was an unexpected dip in aM, which deviates from the general increasing trend associated with longer travel distances. This singular instance could potentially be attributed to a numerical error. Beyond this point, the expected pattern of increasing aM with longer travel distances resumes, suggesting that the anomaly at 0.047 m is an outlier in an otherwise consistent trend, and thus this single data point was overlooked while deriving the predictive equation. Regarding the inverse relationship between water depth and wave amplitude, our result (Fig. 8b) is consistent with previous reports by Fritz et al. (2003), (2004), and Watts et al. (2005).

The insights from Fig. 8 informed the architecture of the predictive equation in the next Section, with slide volume, travel distance, and slope angle being multiplicatively linked to wave amplitude underscoring their direct correlations with wave amplitude. Conversely, water depth is incorporated as a divisor, representing its inverse relationship with wave amplitude. This structure encapsulates the dynamics between the landslide parameters and their influence on the maximum initial wave amplitude as discussed in more detail in the next Section.

3.3. Predictive equation

Building on our sensitivity analysis of landslide parameters, as detailed in Section 3.2, and utilizing our nondimensional dataset, we have derived a new predictive equation as follows:(5)��/ℎ=0.015(tan�)0.10(�ℎ3)0.90(�ℎ)0.10(ℎ�)−0.11where, V is sliding volume, h is water depth, α is slope angle, and s is landslide thickness. It is important to note that this equation is valid only for subaerial solid-block landslide tsunamis as all our experiments were for this type of waves. The performance of this equation in predicting simulation data is demonstrated by the satisfactory alignment of data points around a 45° line, indicating its accuracy and reliability with regard to the experimental dataset (Fig. 9). The quality of fit between the dataset and Eq. (5) is 91 % indicating that Eq. (5) represents the dataset very well. Table 5 presents Eq. (5) alongside four other similar equations previously published. Two significant distinctions between our Eq. (5) and these others are: (i) Eq. (5) is derived from 3D experiments, whereas the other four equations are based on 2D experiments. (ii) Unlike the other equations, our Eq. (5) incorporates travel distance as an independent parameter.

Fig 9

Table 5. Performance comparison among our newly-developed equation and existing equations for estimating the maximum initial amplitude (aM) of the 2018 Anak Krakatau subaerial landslide tsunami. Parameters: aM, initial maximum wave amplitude; h, water depth; vs, landslide velocity; V, slide volume; bs, slide width; ls, slide length; s, slide thickness; α, slope angle; and ����, volume of the final immersed landslide. We considered ����= V as the slide volume.

EventPredictive equationsAuthor (year)Observed aM (m) ⁎⁎Calculated aM (m)Error, ε (%) ⁎⁎⁎⁎
2018 Anak Krakatau tsunami (Subaerial landslide) *��/ℎ=1.32���ℎNoda (1970)1341340
��/ℎ=0.667(0.5(���ℎ)2)0.334(���)0.754(���)0.506(�ℎ)1.631Bolin et al. (2014) ⁎⁎⁎13459424334
��/ℎ=0.25(������ℎ2)0.8Robbe-Saule et al. (2021)1343177
��/ℎ=0.4545(tan�)0.062(�ℎ3)0.296(ℎ�)−0.235Sabeti and Heidarzadeh (2022b)1341266
��/ℎ=0.015(tan�)0.10(�ℎ3)0.911(�ℎ)0.10(ℎ�)−0.11This study1341302.9

Geometrical and kinematic parameters of the 2018 Anak Krakatau subaerial landslide based on Heidarzadeh et al. (2020)Grilli et al. (2019) and Grilli et al. (2021)V=2.11 × 107 m3h= 50 m; s= 114 m; α= 45°; ls=1250 m; bs= 2700 m; vs=44.9 m/s; D= 2500 m; aM= 100 m −150 m.⁎⁎

aM= An average value of aM = 134 m is considered in this study.⁎⁎⁎

The equation of Bolin et al. (2014) is based on the reformatted one reported by Lindstrøm (2016).⁎⁎⁎⁎

Error is calculated using Eq. (1), where the calculated aM is assumed as the simulated value.

Additionally, we evaluated the performance of this equation using the real-world data from the 2018 Anak Krakatau subaerial landslide tsunami. Based on previous studies (Heidarzadeh et al., 2020Grilli et al., 20192021), we were able to provide a list of parameters for the subaerial landslide and associated tsunami for the 2018 Anak Krakatau event (see footnote of Table 5). We note that the data of the 2018 Anak Krakatau event was not used while deriving Eq. (5). The results indicate that Eq. (5) predicts the initial amplitude of the 2018 Anak Krakatau tsunami as being 130 m indicating an error of 2.9 % compared to the reported average amplitude of 134 m for this event. This performance indicates an improvement compared to the previous equation reported by Sabeti and Heidarzadeh (2022a) (Table 5). In contrast, the equations from Robbe-Saule et al. (2021) and Bolin et al. (2014) demonstrate higher discrepancies of 4200 % and 77 %, respectively (Table 5). Although Noda’s (1970) equation reproduces the tsunami amplitude of 134 m accurately (Table 5), it is crucial to consider its limitations, notably not accounting for parameters such as slope angle and travel distance.

It is essential to recognize that both travel distance and slope angle significantly affect wave amplitude. In our model, captured in Eq. (5), we integrate the slope angle (α) through the tangent function, i.e., tan α. This choice diverges from traditional physical interpretations that often employ the cosine or sine function (e.g., Heller and Hager, 2014Watts et al., 2003). We opted for the tangent function because it more effectively reflects the direct impact of slope steepness on wave generation, yielding superior estimations compared to conventional methods.

The significance of this study lies in its application of both physical and numerical 3D experiments and the derivation of a predictive equation based on 3D results. Prior research, e.g. Heller et al. (2016), has reported notable discrepancies between 2D and 3D wave amplitudes, highlighting the important role of 3D experiments. It is worth noting that the suitability of applying an equation derived from either 2D or 3D data depends on the specific geometry and characteristics inherent in the problem being addressed. For instance, in the case of a long, narrow dam reservoir, an equation derived from 2D data would likely be more suitable. In such contexts, the primary dynamics of interest such as flow patterns and potential wave propagation are predominantly two-dimensional, occurring along the length and depth of the reservoir. This simplification to 2D for narrow dam reservoirs allows for more accurate modelling of these dynamics.

This study specifically investigates waves initiated by landslides, focusing on those characterized as solid blocks instead of granular flows, with slope angles confined to a range of 25° to 60°. We acknowledge the additional complexities encountered in real-world scenarios, such as dynamic density and velocity of landslides, which could affect the estimations. The developed equation in this study is specifically designed to predict the maximum initial amplitude of tsunamis for the aforementioned specified ranges and types of landslides.

4. Conclusions

Both physical and numerical experiments were undertaken in a 3D wave basin to study solid-block landslide-generated waves and to formulate a predictive equation for their maximum initial wave amplitude. At the beginning, two physical experiments were performed to validate and calibrate a 3D numerical model, which was subsequently utilized to generate 100 experiments by varying different landslide parameters. The generated database was then used to derive a predictive equation for the maximum initial wave amplitude of landslide tsunamis. The main features and outcomes are:

  • •The predictive equation of this study is exclusively derived from 3D data and exhibits a fitting quality of 91 % when applied to the database.
  • •For the first time, landslide travel distance was considered in the predictive equation. This inclusion provides more accuracy and flexibility for applying the equation.
  • •To further evaluate the performance of the predictive equation, it was applied to a real-world subaerial landslide tsunami (i.e., the 2018 Anak Krakatau event) and delivered satisfactory performance.

CRediT authorship contribution statement

Ramtin Sabeti: Conceptualization, Methodology, Validation, Software, Visualization, Writing – review & editing. Mohammad Heidarzadeh: Methodology, Data curation, Software, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Funding

RS is supported by the Leverhulme Trust Grant No. RPG-2022-306. MH is funded by open funding of State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, grant number SKHL2101. We acknowledge University of Bath Institutional Open Access Fund. MH is also funded by the Great Britain Sasakawa Foundation grant no. 6217 (awarded in 2023).

Acknowledgements

Authors are sincerely grateful to the laboratory technician team, particularly Mr William Bazeley, at the Faculty of Engineering, University of Bath for their support during the laboratory physical modelling of this research. We appreciate the valuable insights provided by Mr. Brian Fox (Senior CFD Engineer at Flow Science, Inc.) regarding air entrainment modelling in FLOW-3D HYDRO. We acknowledge University of Bath Institutional Open Access Fund.

Data availability

  • All data used in this study are given in the body of the article.

References

Fig. 1. Protection matt over the scour pit.

Numerical study of the flow at a vertical pile with net-like scourprotection matt

그물형 세굴방지 매트를 사용한 수직말뚝의 유동에 대한 수치적 연구

Minxi Zhanga,b, Hanyan Zhaoc, Dongliang Zhao d, Shaolin Yuee, Huan Zhoue,Xudong Zhaoa
, Carlo Gualtierif, Guoliang Yua,b,∗
a SKLOE, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
b KLMIES, MOE, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
c Guangdong Research Institute of Water Resources and Hydropower, Guangzhou 510610, China
d CCCC Second Harbor Engineering Co., Ltd., Wuhan 430040, China
e CCCC Road & Bridge Special Engineering Co., Ltd, Wuhan 430071, China
f Department of Structures for Engineering and Architecture, University of Naples Federico II, Italy

Abstract

Local scour at a pile or pier in current or wave environments threats the safety of the upper structure all over the world. The application of a net-like matt as a scour protection cover at the pile or pier was proposed. The matt weakens and diffuses the flow in the local scour pit and thus reduces local scour while enhances sediment deposition. Numerical simulations were carried out to investigate the flow at the pile covered by the matt. The simulation results were used to optimize the thickness dt (2.6d95 ∼ 17.9d95) and opening size dn (7.7d95 ∼ 28.2d95) of the matt. It was found that the matt significantly reduced the local velocity and dissipated the vortex at the pile, substantially reduced the extent of local scour. The smaller the opening size of the matt, the more effective was the flow diffusion at the bed, and smaller bed shear stress was observed at the pile. For the flow conditions considered in this study, a matt with a relative thickness of T = 7.7 and relative opening size of S = 7.7 could be effective in scour protection.

조류 또는 파도 환경에서 파일이나 부두의 국지적인 세굴은 전 세계적으로 상부 구조물의 안전을 위협합니다. 파일이나 교각의 세굴 방지 덮개로 그물 모양의 매트를 적용하는 것이 제안되었습니다.

매트는 국부 세굴 구덩이의 흐름을 약화시키고 확산시켜 국부 세굴을 감소시키는 동시에 퇴적물 퇴적을 향상시킵니다. 매트로 덮인 파일의 흐름을 조사하기 위해 수치 시뮬레이션이 수행되었습니다.

시뮬레이션 결과는 매트의 두께 dt(2.6d95 ∼ 17.9d95)와 개구부 크기 dn(7.7d95 ∼ 28.2d95)을 최적화하는 데 사용되었습니다. 매트는 국부 속도를 크게 감소시키고 말뚝의 와류를 소멸시켜 국부 세굴 정도를 크게 감소시키는 것으로 나타났습니다.

매트의 개구부 크기가 작을수록 층에서의 흐름 확산이 더 효과적이었으며 파일에서 더 작은 층 전단 응력이 관찰되었습니다.

본 연구에서 고려한 유동 조건의 경우 상대 두께 T = 7.7, 상대 개구부 크기 S = 7.7을 갖는 매트가 세굴 방지에 효과적일 수 있습니다.

Keywords

Numerical simulation, Pile foundation, Local scour, Protective measure, Net-like matt

Fig. 1. Protection matt over the scour pit.
Fig. 1. Protection matt over the scour pit.
Fig. 2. Local scour pit of pile below the protection matt.
Fig. 2. Local scour pit of pile below the protection matt.

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Fig 1. (a) The Location of the Bahman Shir dam (upstream), (b) Bahman Shir dam (downstream dam) and (c) Mared Dam. Note: The borders of the countries are not exact.

Initial Maintenance Notes about the First River Ship Lock in Iran

M.T. Mansouri Kia1,2, H.R. Sheibani 3, A. Hoback 4
1 Manager of Dam and Power Plant Construction, Khuzestan Water and Power Authority (KWPA), Ahwaz, Iran.
2 Ph.D., Department of Civil Engineering, Payame Noor University, Tehran, Iran.
3 Associate Professor of PNU University, Tehran, Iran.
4 Professor of Civil, Architectural & Environmental Engineering, University of Detroit Mercy Civil, Rome, Italy.

Abstract

Mared Dam in northern Abadan is under construction on the Karun River and it is the first ship lock in Iran. In this study, the ship’s lock was examined. Every vessel must pass through this lock in order to transport water from Arvand River to Karun and vice versa. The interior dimensions of the Mared Shipping Lock are 160 meters long, 25 meters wide and 8 meters deep. Several important times are calculated for lock operation. 𝑇is the first time the gates open, 𝑇15 the time the initial gates remain open until the height difference between the two sides reaches 150 mm, 𝑇filled is the duration between the start of the opening the gates till the difference between the two ends becomes zero after 𝑇15. Finally, T is the total time required for opening or closing the gates completely. The rotational speeds of the gates range from 5 to 35 radians per minute. Numerical modeling has been used to study fluid behavior and interaction between fluid and gates in flow 3D software. Different lock maintenance scenarios have been analyzed. Important parameters such as inlet and outlet flow rate changes from gates, water depth changes at different times, stress and strain fields, hydrodynamic forces acting on different points of the lock have been calculated. Based on this, the forces acting on hydraulic jacks and gates have been calculated. The minimum time required for the safe passage of the ship through the lock is calculated.

북부 아바단의 마레드 댐은 카룬 강에 건설 중이며 이란 최초의 선박 잠금 장치입니다. 본 연구에서는 선박의 자물쇠를 조사하였습니다. Arvand 강에서 Karun으로 또는 그 반대로 물을 운송하려면 모든 선박이 이 수문을 통과해야 합니다.

Mared Shipping Lock의 내부 치수는 길이 160m, 너비 25m, 깊이 8m입니다. 잠금 작동을 위해 몇 가지 중요한 시간이 계산됩니다. 𝑇은 게이트가 처음 열릴 때, 𝑇15는 양쪽의 높이 차이가 150mm에 도달할 때까지 초기 게이트가 열린 상태로 유지되는 시간, 𝑇filled는 게이트가 열리는 시작부터 이후 두 끝의 차이가 0이 될 때까지의 시간입니다.

𝑇15. 마지막으로 T는 게이트를 완전히 열거나 닫는 데 필요한 총 시간입니다. 게이트의 회전 속도는 분당 5~35라디안입니다. 수치 모델링은 유동 3D 소프트웨어에서 유체 거동과 유체와 게이트 사이의 상호 작용을 연구하는 데 사용되었습니다. 다양한 잠금 유지 관리 시나리오가 분석되었습니다.

게이트의 입구 및 출구 유속 변화, 다양한 시간에 따른 수심 변화, 응력 및 변형 필드, 수문의 다양한 지점에 작용하는 유체역학적 힘과 같은 중요한 매개변수가 계산되었습니다.

이를 바탕으로 유압잭과 게이트에 작용하는 힘을 계산하였습니다. 선박이 자물쇠를 안전하게 통과하는 데 필요한 최소 시간이 계산됩니다.

Fig 1. (a) The Location of the Bahman Shir dam (upstream), (b) Bahman Shir dam (downstream dam) and (c) Mared Dam. Note: The borders of the countries are not exact.
Fig 1. (a) The Location of the Bahman Shir dam (upstream), (b) Bahman Shir dam (downstream dam) and (c) Mared Dam. Note: The borders of the countries are not exact.

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Figure 3 – Free surface views. Bottom left: k-ε RNG model. Bottom right: LES.

Physical Modeling and CFD Comparison: Case Study of a HydroCombined Power Station in Spillway Mode

물리적 모델링 및 CFD 비교: 방수로 모드의 HydroCombined 발전소 사례 연구

Gonzalo Duró, Mariano De Dios, Alfredo López, Sergio O. Liscia

ABSTRACT

This study presents comparisons between the results of a commercial CFD code and physical model measurements. The case study is a hydro-combined power station operating in spillway mode for a given scenario. Two turbulence models and two scales are implemented to identify the capabilities and limitations of each approach and to determine the selection criteria for CFD modeling for this kind of structure. The main flow characteristics are considered for analysis, but the focus is on a fluctuating frequency phenomenon for accurate quantitative comparisons. Acceptable representations of the general hydraulic functioning are found in all approaches, according to physical modeling. The k-ε RNG, and LES models give good representation of the discharge flow, mean water depths, and mean pressures for engineering purposes. The k-ε RNG is not able to characterize fluctuating phenomena at a model scale but does at a prototype scale. The LES is capable of identifying the dominant frequency at both prototype and model scales. A prototype-scale approach is recommended for the numerical modeling to obtain a better representation of fluctuating pressures for both turbulence models, with the complement of physical modeling for the ultimate design of the hydraulic structures.

본 연구에서는 상용 CFD 코드 결과와 물리적 모델 측정 결과를 비교합니다. 사례 연구는 주어진 시나리오에 대해 배수로 모드에서 작동하는 수력 복합 발전소입니다.

각 접근 방식의 기능과 한계를 식별하고 이러한 종류의 구조에 대한 CFD 모델링의 선택 기준을 결정하기 위해 두 개의 난류 모델과 두 개의 스케일이 구현되었습니다. 주요 흐름 특성을 고려하여 분석하지만 정확한 정량적 비교를 위해 변동하는 주파수 현상에 중점을 둡니다.

일반적인 수리학적 기능에 대한 허용 가능한 표현은 물리적 모델링에 따라 모든 접근 방식에서 발견됩니다. k-ε RNG 및 LES 모델은 엔지니어링 목적을 위한 배출 유량, 평균 수심 및 평균 압력을 잘 표현합니다.

k-ε RNG는 모델 규모에서는 변동 현상을 특성화할 수 없지만 프로토타입 규모에서는 특성을 파악합니다. LES는 프로토타입과 모델 규모 모두에서 주요 주파수를 식별할 수 있습니다.

수력학적 구조의 궁극적인 설계를 위한 물리적 모델링을 보완하여 두 난류 모델에 대한 변동하는 압력을 더 잘 표현하기 위해 수치 모델링에 프로토타입 규모 접근 방식이 권장됩니다.

Figure 1 – Physical scale model (left). Upstream flume and point gauge (right)
Figure 1 – Physical scale model (left). Upstream flume and point gauge (right)
Figure 3 – Free surface views. Bottom left: k-ε RNG model. Bottom right: LES.
Figure 3 – Free surface views. Bottom left: k-ε RNG model. Bottom right: LES.
Figure 4 – Water levels: physical model (maximum values) and CFD results (mean values)
Figure 4 – Water levels: physical model (maximum values) and CFD results (mean values)
Figure 5 – Instantaneous pressures [Pa] and velocities [m/s] at model scale (bay center)
Figure 5 – Instantaneous pressures [Pa] and velocities [m/s] at model scale (bay center)

Keywords

CFD validation, hydro-combined, k-ε RNG, LES, pressure spectrum

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