Experimental study of scour around bridge piers of different arrangements with same aspect ratio
본 연구는 교량 설계 시 중요한 요소인 교각 주변의 국부 세굴 현상을 실험적으로 분석한 보고서입니다. 동일한 형상비(L/B=5)를 유지하면서 교각의 배치를 달리했을 때, 말굽 소용돌이(horse-shoe vortex)와 후류 소용돌이(wake vortex)의 상호작용이 세굴 체적 및 깊이에 미치는 영향을 정량적으로 조사하여 산업적 설계 지침을 제공합니다.
Process: 수로 실험 및 세굴 분석 (Flume experiment and scour analysis)
Keywords
교량 교각 (Bridge piers)
국부 세굴 (Local scour)
말굽 소용돌이 (Horse-shoe vortex)
형상비 (Aspect ratio)
실험 수로 (Laboratory flume)
장방형 교각 (Oblong pier)
Executive Summary
Research Architecture
본 연구는 인도 공과대학교(IIT) 봄베이의 수리학 실험실에서 수행되었습니다. 실험 장치는 길이 7.5m, 폭 0.3m, 깊이 0.6m의 재순환식 수로로 구성되었습니다. 실험 대상은 형상비(L/B)가 5로 동일한 세 가지 배치입니다: (a) 직경 0.03m의 원형 교각 2개를 0.15m 간격으로 배치, (b) 동일 직경의 원형 교각 3개를 배치, (c) 폭 0.03m, 길이 0.15m의 단일 장방형(oblong) 교각 배치. 유속 측정에는 3D 음향 도플러 유속계(ADV)인 ‘Vectrino’가 사용되었으며, 세굴 깊이는 포인트 게이지를 통해 측정되었습니다.
Key Findings
실험 결과, 단일 장방형 교각 배치에서 세굴 체적이 가장 적게 나타났습니다. 2개 원형 교각 배치 시 세굴 체적은 3.11×10⁻³ m³였으나, 3개 원형 교각 배치 시 2.44×10⁻³ m³로 21.5% 감소하였고, 단일 장방형 교각의 경우 1.38×10⁻³ m³로 2개 배치 대비 55.63%, 3개 배치 대비 43.44% 감소하였습니다. 이는 단일 구조물이 소용돌이의 강도를 약화시키고 흐름의 분리를 억제하기 때문으로 분석되었습니다. 또한, 상류 교각에서 발생한 후류 소용돌이가 하류 교각의 말굽 소용돌이 형성을 방해하여 하류 측 세굴 깊이가 상대적으로 얕게 나타나는 상호 간섭 현상이 확인되었습니다.
Industrial Applications
본 연구 결과는 교량 기초 설계 시 교각의 형상 및 배치 선정에 직접적인 근거를 제공합니다. 동일한 지지 면적을 확보해야 하는 경우, 여러 개의 원형 교각을 배치하는 것보다 단일 장방형 교각을 사용하는 것이 세굴 위험을 줄이는 데 효과적입니다. 이는 세굴 방지 공사 비용을 절감하고 교량의 구조적 안정성을 높이는 데 기여할 수 있습니다. 또한, 복합 교각 배치 시 발생하는 복잡한 유동장을 이해함으로써 보다 정밀한 수치 모델링 및 설계가 가능해집니다.
Theoretical Background
말굽 소용돌이 (Horse-shoe Vortex) 형성 메커니즘
흐르는 물속에 교각과 같은 장애물이 설치되면 상류 측에 역압력 구배가 발생합니다. 이로 인해 교각 전면에서 하향류(down flow)가 형성되고, 바닥면의 경계층이 분리되면서 말굽 모양의 소용돌이가 생성됩니다. 이 소용돌이는 바닥 전단 응력을 급격히 증가시켜 퇴적물을 비산시키고 교각 주변에 세굴 구멍을 만드는 핵심적인 동역학적 원인으로 작용합니다.
Fig. 1 Collapse of Shuangyuan Bridge (2009/8/10) (photo courtesy of Apple Daily)
후류 소용돌이 (Wake Vortex)와 세굴의 관계
교각의 측면에서 분리된 흐름은 교각 배후에서 후류 소용돌이를 형성합니다. 이 소용돌이는 말굽 소용돌이에 의해 부유된 퇴적물을 들어 올려 세굴 구멍 외부로 운반하는 역할을 합니다. 여러 개의 교각이 배치된 경우, 상류 교각에서 발생한 후류 소용돌이는 하류 교각 전면의 유동 구조와 상호작용하여 전체적인 세굴 패턴을 복잡하게 변화시킵니다.
Results and Analysis
Experimental Setup
실험은 0.0003의 일정한 경사를 가진 평면 수로에서 진행되었습니다. 바닥 재료로는 중간 입경(d50) 0.8mm, 비중 2.66인 석영사가 사용되었습니다. 수심은 모래 바닥 위로 16.5cm를 유지하였으며, 유량은 모래의 이동이 시작되는 임계 전단 응력 이하인 0.018 m³/s(최대 유량 기준)로 설정하여 맑은 물 세굴(clear-water scour) 조건을 형성하였습니다. 각 실험은 평형 상태에 도달할 때까지 약 8시간 동안 지속되었습니다.
Visual Data Summary
세굴 등고선(scour contour) 분석 결과, 원형 교각 배치에서는 각 교각 주변에서 개별적인 세굴 구멍이 형성된 후 서로 연결되는 양상을 보였습니다. 반면, 장방형 교각은 상류 선단에서 최대 세굴 깊이가 나타나고 하류로 갈수록 세굴 깊이가 점진적으로 감소하는 안정적인 패턴을 보였습니다. 3개 원형 교각 배치 시 중간 교각은 상류 교각의 후류와 자신의 말굽 소용돌이가 결합되어 복잡한 세굴 형태를 나타냈습니다.
Variable Correlation Analysis
교각의 배치 방식과 세굴 체적 사이에는 뚜렷한 상관관계가 관찰되었습니다. 교각 사이의 간격이 좁을수록(간격/직경 비가 작을수록) 세굴 패턴 간의 간섭이 심화되었습니다. 특히 단일 구조물(장방형)로 통합될 경우, 유동 분리 지점이 줄어들고 소용돌이 시스템의 에너지가 분산되지 않아 세굴 억제 효과가 극대화되었습니다. 이는 구조물의 연속성이 유체역학적 저항을 줄이는 데 결정적인 변수임을 시사합니다.
Paper Details
Experimental study of scour around bridge piers of different arrangements with same aspect ratio
1. Overview
Title: Experimental study of scour around bridge piers of different arrangements with same aspect ratio
Author: B.A. Vijayasree, T.I. Eldho
Year: 2016 (추정, 참조 문헌 기준)
Journal: Proceedings of the International Conference on Scour and Erosion (ICSE)
2. Abstract
교량 교각 주변의 세굴은 교량 엔지니어들이 직면한 도전적인 문제입니다. 세굴은 흐름을 방해하는 교각으로 인해 형성된 말굽 소용돌이에 의해 발생합니다. 말굽 소용돌이의 거동은 교각의 배치에 따라 달라집니다. 교각 그룹과 단일 교각의 흐름 패턴은 서로 다르며, 이에 따라 서로 다른 세굴 패턴이 생성됩니다. 본 논문에서는 동일한 형상비를 가진 다양한 배치의 교량 교각 주변 세굴을 실험 수로에서 조사하였습니다. 연구된 세 가지 배치 모두 5의 형상비(L/B)를 가집니다. 실험 수로는 길이 7.5m, 폭 0.3m, 깊이 0.6m이며 재순환 시설을 갖추고 있습니다. 얻어진 결과에 따르면, 단일 고체 교각 주변의 세굴 체적은 교각 조합에 비해 상당히 감소하는 것으로 나타났습니다. 또한, 교각의 조합으로 인해 유동장이 복잡해집니다.
3. Methodology
3.1. 실험 장치 구성: 7.5m 길이의 Plexiglas 수로를 설치하고, 바닥에 0.8mm 입경의 석영사를 채워 실험 환경을 조성함. 3.2. 교각 모델 설치: 형상비 5를 유지하며 원형 교각 2개(배치 a), 3개(배치 b), 장방형 교각 1개(배치 c)를 수로 중앙에 설치함. 3.3. 유동 조건 설정: 0.012, 0.015, 0.018 m³/s의 세 가지 유량을 적용하고, ADV를 사용하여 3차원 유속 데이터를 수집함. 3.4. 세굴 측정: 각 실험을 8시간 동안 수행하여 평형 상태에 도달하게 한 후, 수로의 물을 빼고 포인트 게이지로 세굴 프로파일을 정밀 측정함.
4. Key Results
실험 결과, 단일 장방형 교각(배치 c)의 최대 세굴 깊이는 0.047m로, 원형 교각 배치(0.065m)에 비해 약 28% 감소하였습니다. 세굴 체적 측면에서는 장방형 교각이 1.38×10⁻³ m³를 기록하여, 2개 원형 교각 배치(3.11×10⁻³ m³) 대비 55.63%의 현저한 감소 효과를 보였습니다. 3개 원형 교각 배치의 경우, 중간 교각의 존재가 유동 복잡성을 증가시켰으나 전체 세굴 체적은 2개 배치보다 적은 2.44×10⁻³ m³로 측정되었습니다. 이는 교각 간의 간섭이 소용돌이 강도를 일부 상쇄하기 때문입니다.
여기서 $u$는 유속, $y$는 수심, $\nu$는 물의 동점성 계수, $g$는 중력 가속도를 의미합니다. 실험 시 $Re$는 39370에서 59055 사이, $Fr$은 0.24에서 0.28 사이로 유지되었습니다.
Fig. 9 Two established classifiers for the pile head displacement
Figure List
교각에서의 말굽 소용돌이 및 후류 형성 모식도
본 연구에 사용된 세 가지 교각 배치 (a, b, c)
실험 수로의 개략도
바닥 재료의 입도 분포 곡선
2개 원형 교각 배치의 시간에 따른 세굴 변화
2개 원형 교각 배치의 종방향 세굴 패턴
3개 원형 교각 배치의 시간에 따른 세굴 변화
3개 원형 교각 배치의 종방향 세굴 패턴
장방형 교각의 시간에 따른 세굴 변화
장방형 교각의 종방향 세굴 패턴
세굴 구멍의 실제 사진 비교
세 가지 배치에 대한 세굴 등고선도
세 위치(상류, 중앙, 하류)에서의 횡방향 세굴 프로파일
세 가지 배치별 세굴 체적 비교 차트
References
Beg, M. (2010). Characteristics of developing scour holes around two piers placed in transverse arrangement.
Beg, M. & Beg, S. (2015). Scour hole characteristics of two unequal size bridge piers in tandem arrangement.
Das, S. and Mazumder, A. (2015). Turbulence flow field around tow eccentric circular piers in scour hole.
Kothyari, U., Garde, R., & Ranga Raju, K. (1992). Temporal Variation of Scour around Circular Bridge Piers.
Melville, B.W. & Chiew, Y.M. (1999). Time scale for local scour at bridge piers.
Technical Q&A
Q: 교각 배치에 따라 세굴 체적이 차이 나는 근본적인 이유는 무엇입니까?
A: 교각이 분리되어 배치될 경우 각 교각에서 독립적인 말굽 소용돌이와 후류 소용돌이가 발생하며, 이들이 상호작용하여 유동 복잡성을 높이고 더 넓은 면적의 바닥 재료를 침식시킵니다. 반면, 단일 장방형 교각은 유동을 더 매끄럽게 유도하고 소용돌이 시스템의 에너지를 집중시켜 분산된 침식을 억제하기 때문에 전체적인 세굴 체적이 감소합니다.
Q: 3개 원형 교각 배치에서 세 번째 교각의 세굴이 음수 값으로 시작하는 이유는 무엇입니까?
A: 실험 초기 단계에서 상류의 첫 번째 및 두 번째 교각 주변에서 침식된 모래 입자들이 하류로 이동하다가 세 번째 교각 전면에 일시적으로 퇴적되기 때문입니다. 흐름이 지속됨에 따라 이 퇴적물들도 결국 세굴되어 사라지며, 약 15분 이후부터 본격적인 세굴 패턴을 따르게 됩니다.
Q: 장방형 교각이 원형 교각 조합보다 세굴 방지에 유리한 정량적 근거는 무엇입니까?
A: 본 실험에서 장방형 교각은 2개 원형 교각 배치 대비 세굴 체적을 55.63% 감소시켰습니다. 또한 최대 세굴 깊이 역시 원형 교각의 0.065m에서 장방형의 0.047m로 약 28% 감소하여, 구조적 안정성 확보에 훨씬 유리함을 입증하였습니다.
Q: 실험에서 사용된 ‘맑은 물 세굴(clear-water scour)’ 조건의 의미는 무엇입니까?
A: 접근 흐름의 전단 응력이 바닥 모래의 이동 임계 전단 응력보다 낮은 상태($u/u_{cr} < 1$)를 의미합니다. 이 조건에서는 일반적인 하천 바닥의 이동은 없으며, 오직 교각 주변에서 강화된 소용돌이에 의해서만 국부적인 세굴이 발생하게 됩니다.
Q: 교각 사이의 간격이 세굴에 미치는 영향에 대한 기존 이론은 무엇입니까?
A: Beg and Beg (2015)의 연구에 따르면, 교각 사이의 순 간격과 교각 직경의 비가 10보다 작을 경우 두 교각의 세굴 패턴 사이에 상호 간섭이 발생합니다. 본 실험에서는 이 비가 1로 매우 작아 강한 간섭 효과가 나타났으며, 이로 인해 하류 교각의 세굴 깊이가 상류보다 낮아지는 현상이 관찰되었습니다.
Conclusion
본 연구를 통해 동일한 형상비를 가진 교각이라도 배치 방식에 따라 세굴 특성이 현저히 달라짐을 확인하였습니다. 단일 장방형 교각은 여러 개의 원형 교각 배치에 비해 세굴 체적과 깊이를 모두 효과적으로 감소시키는 것으로 나타났습니다. 이는 단일 구조물이 말굽 소용돌이의 강도를 약화시키고 유동 구조를 단순화하기 때문입니다. 따라서 경제성과 시공성을 고려하더라도, 세굴 보호 비용과 구조적 안전성을 종합적으로 판단할 때 단일 장방형 교각 설계가 더욱 우수한 대안이 될 수 있음을 시사합니다.
Source Information
Citation: B.A. Vijayasree, T.I. Eldho (2016). Experimental study of scour around bridge piers of different arrangements with same aspect ratio. Proceedings of the International Conference on Scour and Erosion (ICSE).
이 기술 요약은 Mohamed Kharbeche가 2022년 University of Windsor에서 발표한 석사 학위 논문 “The Role of Pier Shape and Aspect Ratio on Local Scour with and Without Sacrificial Piles”를 기반으로 하며, 기술 전문가를 위해 STI C&D가 분석하고 요약했습니다.
도전 과제: 기존의 교량 세굴 깊이 예측 모델은 실제보다 과도하게 예측하는 경향이 있어, 비경제적인 교각 설계와 불필요한 비용을 초래합니다.
연구 방법: 실험실 수로에서 다양한 형상(원형, 사각형, 유선형 등)과 종횡비(L/a = 1, 2, 4)를 가진 교각 모델을 사용하여 국소 세굴을 측정하고, 희생파일(sacrificial piles)의 효과를 비교 분석했습니다.
핵심 돌파구: 교각의 형상과 종횡비가 세굴 깊이에 결정적인 영향을 미치며, 뾰족한 유선형(sharp-nosed) 교각과 높은 종횡비가 세굴을 최소화하는 것으로 나타났습니다. 또한 3개의 희생파일 배열이 5개 배열보다 더 효과적인 세굴 감소를 보였습니다.
핵심 결론: 교각의 형상과 종횡비를 최적화하고, 효율적인 세굴 방지책을 적용함으로써 교량의 안전성을 높이고 건설 비용을 절감할 수 있습니다.
도전 과제: 이 연구가 CFD 전문가에게 중요한 이유
교량 붕괴의 약 60%는 교각 주변의 국소 세굴(local scour)과 관련이 있을 정도로, 세굴은 교량의 구조적 안정성을 위협하는 가장 큰 요인 중 하나입니다. 강물의 흐름이 교각과 상호작용하며 기초 주변의 토사를 침식시켜 지지력을 약화시키기 때문입니다.
문제는 현재 북미 표준으로 사용되는 HEC-18과 같은 경험적 세굴 예측 공식들이 종종 세굴 깊이를 과도하게 예측한다는 점입니다. 이는 교각 기초를 불필요하게 깊게 설계하게 만들어 막대한 추가 비용을 발생시킵니다. 이러한 공식들은 교각의 형상(pier shape)이나 길이 대 폭 비율인 종횡비(aspect ratio)와 같은 중요한 변수들의 영향을 충분히 고려하지 못합니다. 따라서 더 정확하고 경제적인 설계를 위해서는 이러한 변수들이 세굴 메커니즘에 미치는 영향을 정밀하게 이해하고, 희생파일과 같은 세굴 방지책의 효율성을 최적화하는 연구가 시급합니다.
연구 접근법: 방법론 분석
본 연구는 캐나다 윈저 대학교(University of Windsor)의 실험 수로(flume)에서 정밀하게 통제된 조건 하에 수행되었습니다.
실험 장비: 길이 10.5m, 폭 1.22m의 수평 실험 수로를 사용하여 실제 하천과 유사한 흐름 환경을 조성했습니다.
핵심 변수:
교각 형상: 원형(Circular), 다이아몬드형(Diamond), 모서리가 둥근 사각형(Round edges), 사각형(Square), 둥근 유선형(Round nose), 뾰족한 유선형(Sharp nose) 등 다양한 형상을 테스트했습니다.
교각 종횡비 (L/a): 교각의 길이(L) 대 폭(a)의 비율을 1, 2, 4로 변경하며 실험을 진행했습니다. 모든 교각의 폭(a)은 51mm로 동일하게 유지했습니다.
세굴 방지책: 교각 상류에 3개 또는 5개의 희생파일(sacrificial piles)을 삼각형 형태로 배열하여 세굴 감소 효과를 비교했습니다.
흐름 조건: 모든 실험은 퇴적물 이동이 막 시작되는 임계유속 직전(U/Uc = 0.9)의 맑은 물 세굴(clear-water scour) 조건에서 수행되었습니다. 유속은 0.28 m/s, 수심은 0.12m로 일정하게 유지했습니다.
데이터 측정: 세굴이 평형 상태에 가까워지는 24시간 동안 실험을 진행한 후, 레이저 거리 측정기(LDM)를 사용하여 세굴 구멍의 중심선과 등고선 프로파일을 정밀하게 측정했습니다. 또한, 레이저 도플러 유속계(LDV)와 음향 도플러 유속계(ADV)를 사용하여 교각 주변의 유속 분포와 난류 특성을 측정했습니다.
핵심 돌파구: 주요 발견 및 데이터
발견 1: 교각 형상과 종횡비가 세굴 깊이를 극적으로 변화시킴
교각의 형상과 종횡비는 세굴 깊이를 결정하는 가장 중요한 요소임이 입증되었습니다.
형상의 영향: 뾰족한 유선형(sharp-nosed) 교각이 모든 종횡비에서 가장 낮은 세굴 깊이를 보였습니다. 반면, 직각 모서리를 가진 사각형 교각(L/a=1)은 원형 교각보다 66% 더 깊은 최대 세굴 깊이(dse/a = 1.75)를 기록했습니다(표 4.2 참조). 이는 흐름의 박리(flow separation)를 최소화하는 유선형 설계가 말굽 와류(horseshoe vortex)의 강도를 약화시켜 세굴을 억제함을 의미합니다.
종횡비의 영향: 동일한 형상에서는 종횡비(L/a)가 증가할수록 세굴 깊이가 감소했습니다. 예를 들어, 뾰족한 유선형 교각의 경우 종횡비가 1에서 4로 증가했을 때 세굴 깊이는 26% 감소했습니다. 이는 교각 길이가 길어질수록 하류의 후류 와류(wake vortex)가 약화되기 때문입니다.
발견 2: ‘더 적은 것이 더 효과적이다’ – 3개 희생파일의 우수성
희생파일은 효과적인 세굴 방지책이지만, 파일의 개수와 배열이 효율성을 좌우했습니다. 놀랍게도 3개의 희생파일을 사용한 배열(Series C)이 5개를 사용한 배열(Series B)보다 더 뛰어난 세굴 감소 효과를 보였습니다.
표 4.5에 따르면, 뾰족한 유선형 교각(L/a=2)의 경우, 3개 희생파일 배열은 5개 배열에 비해 24% 더 높은 세굴 감소율을 보였습니다. 이는 파일 사이의 간격이 넓어져 상류에서 발생한 세굴 퇴적물이 교각 주변으로 더 원활하게 이동 및 퇴적되어 주 교각을 보호하는 효과를 낳기 때문으로 분석됩니다. 본 연구에서 관찰된 최대 세굴 감소율은 모서리가 둥근 사각형 교각(L/a=4)에 3개의 희생파일을 적용했을 때 기록된 64%였습니다.
R&D 및 운영을 위한 실질적 시사점
공정 엔지니어: 교량 설계 시, 단순히 폭이 좁은 교각보다는 종횡비가 높은 유선형 교각을 채택하는 것이 세굴을 최소화하는 데 훨씬 효과적일 수 있습니다. 이는 기초 공사 비용을 직접적으로 절감하는 요인이 됩니다.
품질 관리팀: 본 연구에서 개발된 새로운 세굴 예측 공식(논문의 식 4.7)은 기존 HEC-18 공식보다 교각 형상과 종횡비의 영향을 더 정밀하게 반영합니다. 이를 활용하면 기존 교량의 세굴 위험도를 더 정확하게 평가하고, 우선순위에 따른 유지보수 계획을 수립할 수 있습니다.
설계 엔지니어: 사각형과 같이 흐름 박리가 심한 형상은 피하고, 뾰족하거나 둥근 유선형 설계를 초기 단계부터 고려해야 합니다. 또한 희생파일 방지책을 설계할 때, 파일의 개수보다는 최적의 간격과 배열을 통해 흐름을 제어하고 퇴적물 이동을 유도하는 것이 더 경제적이고 효과적일 수 있습니다.
논문 상세 정보
The Role of Pier Shape and Aspect Ratio on Local Scour with and Without Sacrificial Piles
1. 개요:
제목: The Role of Pier Shape and Aspect Ratio on Local Scour with and Without Sacrificial Piles (희생파일 유무에 따른 교각 형상과 종횡비가 국소 세굴에 미치는 영향)
교각 주변의 세굴 과정은 복잡하여 비경제적인 교각 설계와 불필요한 비용을 초래합니다. 이는 현재 사용되는 세굴 예측 방법들이 세굴 깊이를 과도하게 예측하기 때문입니다. 교각 형상 및 종횡비와 같은 여러 세굴 측면은 교각 설계에서 충분히 고려되지 않아 추가적인 연구가 필요합니다. 또한, 교각을 보호하고 세굴 깊이를 줄이기 위해 세굴 방지책이 사용됩니다. 본 연구의 첫 번째 목표는 교각 선단부 형상과 종횡비의 복합적인 효과가 세굴 형상에 미치는 영향을 연구하는 것입니다. 두 번째 목표는 교각 전면에 위치한 두 가지 다른 희생파일 배열이 세굴 감소에 미치는 효과를 더 잘 이해하는 것입니다. 실험은 다양한 교각 형상과 종횡비로 수행되었습니다. 사용된 형상은 둥근 유선형, 뾰족한 유선형, 모서리가 둥근 사각형 및 사각형이며, 세 가지 종횡비(L/a = 1, 2, 4)를 가진 교각에 적용되었습니다. 또한, 두 개의 삼각형 희생파일 배열을 사용하여 희생파일이 세굴 감소에 미치는 역할을 연구했습니다. L/a = 4인 뾰족한 유선형 교각이 최소 세굴 깊이를 기록했습니다. 또한, 삼각형 배열의 세 개의 희생파일이 최대 세굴 감소를 가져왔습니다. 본 연구와 이전 실험 결과를 사용하여 새로운 세굴 예측 방법이 개발되었습니다. 박리 속도, 교각 형상 및 종횡비가 방정식에 통합되었습니다. 이러한 매개변수들은 세굴에 영향을 미치는 중요한 요인으로 조사되고 발견되었습니다.
세굴은 교량, 특히 유압 공학 인프라 실패의 주요 원인 중 하나입니다. 교각 기초 주변의 퇴적물이 제거되면서 구조적 무결성이 영향을 받습니다. 북미에서는 교량 붕괴의 50% 이상이 세굴 또는 세굴 관련 문제로 인해 발생합니다. Shirhole과 Holt(1991)는 미국에서 800건 이상의 교량 붕괴를 조사했으며, 60%의 실패가 교각 주변의 하상 세굴 및 수로 불안정성과 관련이 있음을 발견했습니다. 교량 붕괴는 교체 또는 수리 비용으로 인해 추가적인 비용을 발생시킵니다. 캐나다에서도 2013년 앨버타에서 폭우로 인한 홍수로 캐나다 태평양 철도 교량이 세굴로 붕괴되는 사고가 발생했습니다. 현재 널리 사용되는 HEC-18(CSU) 방정식은 교각 형상 계수(K1)를 포함하지만, 종횡비(L/a)의 효과를 명시적으로 다루지 않아 예측에 한계가 있습니다. 따라서 본 연구는 교각 형상, 종횡비, 그리고 희생파일과 같은 세굴 방지책의 효과를 종합적으로 분석하여 보다 정확한 세굴 예측과 경제적인 설계를 위한 기초 자료를 제공하고자 합니다.
4. 연구 요약:
연구 주제의 배경:
교량 교각 주변의 국소 세굴은 교량의 안전과 수명에 직접적인 영향을 미치는 중요한 문제입니다. 현재의 설계 기준은 종종 보수적이어서 과도한 안전율을 적용하게 되고, 이는 건설 비용 증가로 이어집니다.
이전 연구 현황:
대부분의 이전 연구는 원형 교각에 초점을 맞추었으며, 사각형이나 유선형과 같은 비원형 교각, 특히 다양한 종횡비를 가진 교각에 대한 연구는 상대적으로 부족했습니다. 또한 희생파일의 효과에 대한 연구는 많았지만, 다양한 교각 형상과 결합하여 그 효율성을 체계적으로 분석한 연구는 드물었습니다.
Figure 2.1: Description of flow structures around a pier (Hodi, 2009)
연구 목적:
교각의 선단부 형상(round-nosed, sharp-nosed, round-edged)이 세굴 형상에 미치는 영향을 분석합니다.
교각의 종횡비(L/a)가 세굴 깊이에 미치는 영향을 조사합니다.
5개 및 3개의 희생파일을 삼각형으로 배열했을 때의 세굴 감소 효과를 탐구합니다.
본 연구 결과와 기존 문헌을 바탕으로 개선된 세굴 예측 방법을 개발합니다.
핵심 연구:
실험실 수로에서 다양한 형상과 종횡비를 가진 교각 모델을 설치하고, 통제된 유속 하에서 24시간 동안 세굴을 발생시킨 후 그 형상을 측정했습니다. 일부 실험에서는 교각 상류에 희생파일을 설치하여 방지책의 효과를 정량적으로 평가했습니다. 유동장 특성을 파악하기 위해 LDV와 ADV를 사용한 유속 측정도 병행되었습니다.
5. 연구 방법론
연구 설계:
본 연구는 세 가지 시리즈의 실험으로 구성되었습니다. – Series A: 희생파일이 없는 상태에서 10가지 다른 교각 형상 및 종횡비 조합에 대한 세굴 실험을 수행했습니다. – Series B: Series A에서 사용된 교각 중 L/a=2, 4인 교각에 5개의 희생파일을 적용하여 세굴 감소 효과를 측정했습니다. – Series C: 동일한 교각에 3개의 희생파일을 적용하여 Series B와 효과를 비교했습니다.
데이터 수집 및 분석 방법:
수집된 세굴 프로파일 데이터는 dse/a(상대 세굴 깊이)로 무차원화하여 비교 분석했습니다. 희생파일의 효과는 방지책이 없을 때의 세굴 깊이(dseo)와 있을 때의 세굴 깊이(dse)를 비교하여 세굴 감소율(rde)로 정량화했습니다. ADV로 측정한 유속 데이터는 교각 주변의 흐름 박리 속도(separation velocity)를 분석하는 데 사용되었으며, 이는 새로운 세굴 예측 공식 개발에 활용되었습니다.
연구 주제 및 범위:
본 연구는 맑은 물 세굴 조건 하에서 단일 교각 주변의 국소 세굴에 초점을 맞추었습니다. 교각의 형상, 종횡비, 그리고 희생파일의 개수 및 배열이 주요 변수입니다. 교각의 경사(skewness)나 군집 교각(pier groups)의 효과는 본 연구의 범위에 포함되지 않습니다.
6. 주요 결과:
주요 결과:
교각 형상은 세굴 깊이에 큰 영향을 미칩니다. L/a=4인 뾰족한 유선형 교각은 원형 교각 대비 25%의 세굴 감소를 보인 반면, L/a=1인 사각형 교각은 66%의 세굴 증가를 보였습니다.
교각의 종횡비가 증가할수록 상대 세굴 깊이(dse/a)는 감소합니다. 둥근 유선형 교각의 경우, L/a가 1에서 4로 증가하자 세굴 깊이는 21% 감소했습니다.
희생파일은 효과적인 세굴 방지책이며, 3개 파일 배열이 5개 파일 배열보다 더 높은 세굴 감소율을 보였습니다. 최대 64%의 세굴 감소 효과가 관찰되었습니다.
교각 형상, 종횡비, 흐름 박리 속도를 고려한 새로운 세굴 예측 공식을 개발했으며, 이 공식은 기존 HEC-18 공식보다 실험 데이터와 더 잘 일치하는 경향을 보였습니다.
Figure 4.27: Contour profiles for piers with L/a = 2 in Series B and Series C with five and three sacrificial piles (tests B5, B6, and B7 with five sacrificial piles, and tests C5, C6, and C7 with three sacrificial piles)
Figure 2.1: Description of flow structures around a pier (Hodi, 2009).
Figure 2.2: Collar (Plan and side views) (Tafarojnoruz et al., 2012).
Figure 2.3: Schematic of the sacrificial piles in a transverse arrangement (Tafarojnoruz et al., 2012).
Figure 3.1: Schematic of the horizontal laboratory flume used for the experiments (modified from (Williams, 2019))
Figure 3.2: Streamwise velocity profiles in the presence and in the absence of the 3 mm rod placed in the sand bed.
Figure 3.3: ASTM sieve analysis for bed sediment used in the experiments
Figure 3.4: Point measurements of a centerline profile
Figure 3.5: Location of the ADV and LDV for the tests in the absence of the pier.
Figure 3.6: Location of the ADV for tests with 5 and 3 sacrificial piles (B6, B7, B8, C8, C9, and C10)
Figure 3.7: Location of the ADV for the tests (A4, A8, A9, and A10) to get the separation velocity.
Figure 3.8: Different pier shapes and L/a ratios.
Figure 3.9: Schematic of the five sacrificial piles used in Series B
Figure 3.10: Schematic of the three sacrificial piles used in Series C
Figure 4.1: Streamwise velocity U profiles for tests B6, B7, and B8 with five sacrificial piles compared to tests E and L in the absence of the pier
Figure 4.2: Streamwise velocity U profiles for tests C8, C9, and C10 with three sacrificial piles compared to tests E and L in the absence of the pier
Figure 4.3: Reynolds shear stress profiles for tests B6, B7, and B8 with five sacrificial piles compared to test E in the absence of the pier
Figure 4.4: Reynolds shear stress profiles for tests C8, C9, and C10 with three sacrificial piles compared to test E in the absence of the pier.
Figure 4.5: Centerline profiles of the piers with L/a =1 (A1, A2, A3, and A4).
Figure 4.6: Centerline profiles of the piers with L/a =2 (A5, A6, and A7).
Figure 4.7: Centerline profiles of the piers with L/a =4 (A8, A9, and A10).
Figure 4.8: Contour profiles of the piers with L/a =1 (A1, A2, A3, and A4)
Figure 4.9: Contour profiles of the piers with L/a =2 (A5, A6, and A7)
Figure 4.10: Contour profiles of the piers with L/a = 4 (A8, A9, and A10)
Figure 4.11: Centerline profiles of round-nosed piers (A1: L/a = 1, A5: L/a = 2, and A8: L/a = 4)
Figure 4.12: Centerline profiles of sharp-nosed piers (A2: L/a = 1, A6: L/a = 2, and A9: L/a = 4)
Figure 4.13:Centerline profiles of round-edged piers (A3: L/a = 1, A7: L/a = 2, and A10: L/a = 4)
Figure 4.14: Contour profiles of round-nosed piers (A1: L/a = 1, A5: L/a = 2, and A8: L/a = 4).
Figure 4.15: Contour profiles of sharp-nosed piers (A2: L/a = 1, A6: L/a = 2, and A9: L/a = 4)
Figure 4.16: Contour profiles of round-nosed piers (A3: L/a = 1, A7: L/a = 2, and A10: L/a = 4)
Figure 4.17: Centerline profiles for piers with L/a = 2 with and without five sacrificial piles (tests A5, A6, and A7 without sacrificial piles, and tests B5, B6, and B7 with five sacrificial piles)
Figure 4.18: Centerline profiles for piers with L/a = 4 with and without five sacrificial piles (tests A8, A9, and A10 without sacrificial piles, and tests B8, B9, and B10 with five sacrificial piles)
Figure 4.19: Contour profiles for piers with L/a = 2 with and without five sacrificial piles (tests A5, A6, and A7 without sacrificial piles, and tests B5, B6, and B7 with five sacrificial piles)
Figure 4.20: Contour profiles for piers with L/a = 4 with and without five sacrificial piles (tests A8, A9, and A10 without sacrificial piles, and tests B8, B9, and B10 with five sacrificial piles).
Figure 4.21: Centerline profiles for piers with L/a = 2 with and without three sacrificial piles (tests A5, A6, and A7 without sacrificial piles, and tests C5, C6, and C7 with three sacrificial piles).
Figure 4.22: Centerline profiles for piers with L/a = 4 with and without three sacrificial piles (tests A8, A9, and A10 without sacrificial piles, and tests C8, C9, and C10 with three sacrificial piles)
Figure 4.23: Contour profiles for piers with L/a = 2 with and without three sacrificial piles (tests A5, A6, and A7 without sacrificial piles, and tests C5, C6, and C7 with three sacrificial piles).
Figure 4.24: Contour profiles for piers with L/a = 4 with and without three sacrificial piles (tests A8, A9, and A10 without sacrificial piles, and tests C8, C9, and C10 with three sacrificial piles)
Figure 4.25: Centerline profiles for L/a = 2 in Series B and Series C with five and three sacrificial piles (tests: B5, B6, and B7 with five sacrificial piles, and tests C5, C6, and C7 with three sacrificial piles)
Figure 4.26: Centerline profiles for L/a = 4 in Series B and Series C with five and three sacrificial piles (tests: B8, B9, and B10 with five sacrificial piles, and tests C8, C9, and C10 with three sacrificial piles)
Figure 4.27: Contour profiles for piers with L/a = 2 in Series B and Series C with five and three sacrificial piles (tests B5, B6, and B7 with five sacrificial piles, and tests C5, C6, and C7 with three sacrificial piles)
Figure 4.28: Contour profiles for piers with L/a = 4 in Series B and Series C with five and three sacrificial piles (tests B8, B9, and B10 with five sacrificial piles, and tests C8, C9, and C10 with three sacrificial piles)
Figure 4.30: Separation velocity profiles for different pier shapes and L/a ratios.
Figure 4.30: Equilibrium scour depth alteration with L/a
Figure 4.31: Measured vs predicted dse/a values grouped by investigation using Equation 4.7.
Figure 4.32: Measured vs predicted dse/a values grouped by investigation using HEC-18 equation
7. 결론:
본 연구는 교각의 형상과 종횡비가 국소 세굴에 미치는 영향을 체계적으로 규명했습니다. – 교각 형상 및 종횡비: 뾰족한 유선형 교각과 높은 종횡비가 세굴을 최소화하는 반면, 사각형 교각은 세굴을 크게 증가시킵니다. 세굴 깊이는 종횡비가 증가함에 따라 감소하는 경향을 보입니다. – 세굴 방지책: 희생파일은 효과적인 방지책이며, 3개 파일 배열이 5개 파일 배열보다 더 효율적일 수 있습니다. 종횡비가 높은 교각일수록 희생파일의 세굴 감소 효과도 증가했습니다. – 새로운 예측 모델: 교각 형상과 종횡비, 그리고 흐름 박리 속도를 통합한 새로운 세굴 예측 모델은 기존 모델보다 더 정확한 예측을 제공할 가능성을 보여주었습니다. 이러한 결과들은 교량 설계 시 더 안전하고 경제적인 결정을 내리는 데 중요한 공학적 통찰력을 제공합니다.
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전문가 Q&A: 자주 묻는 질문
Q1: 왜 실제 하천의 ‘유사 이동 조건(live-bed)’이 아닌 ‘맑은 물 세굴(clear-water)’ 조건에서 실험을 수행했나요?
A1: 맑은 물 세굴 조건은 상류에서 퇴적물이 공급되지 않는 상태로, 교각 주변에서 발생할 수 있는 최대 잠재 세굴 깊이를 평가하는 데 사용됩니다. 이 조건은 교량 설계 시 가장 보수적이고 안전한 기준을 설정하는 데 필수적입니다. 따라서 본 연구에서는 다양한 교각 형상과 방지책의 성능을 극한 조건에서 비교 평가하기 위해 이 방법을 선택했습니다.
Q2: 5개보다 3개의 희생파일이 더 효과적인 물리적 메커니즘은 무엇인가요?
A2: 이는 파일 사이의 간격과 관련이 있습니다. 5개 파일 배열은 간격이 좁아 흐름을 강하게 막는 ‘장벽’처럼 작용하여 파일 바로 앞에서 강한 세굴을 유발할 수 있습니다. 반면, 3개 파일 배열은 간격이 더 넓어 흐름을 완전히 막기보다는 적절히 분산시키고 약화시킵니다. 이로 인해 희생파일 주변에서 발생한 퇴적물이 하류의 주 교각 주변으로 더 효과적으로 이동 및 퇴적되어, 주 교각의 기초를 보호하는 ‘자연적인 방어막’을 형성하는 데 더 유리했던 것으로 분석됩니다.
Q3: 새로 제안된 세굴 예측 공식은 기존 HEC-18 표준과 비교하여 어떤 점이 개선되었나요?
A3: HEC-18 공식은 주로 교각 폭과 유속에 의존하며, 교각 형상을 단일 보정 계수(K1)로 단순화합니다. 하지만 본 연구에서 제안된 새로운 공식(식 4.7)은 여기에 더해 교각 종횡비(L/a)와 흐름 박리 속도(separation velocity)를 반영하는 새로운 무차원수(Fds)를 도입했습니다. 이는 세굴의 주원인인 말굽 와류의 강도에 직접적인 영향을 미치는 물리적 현상을 더 정밀하게 모델링하여, 특히 유선형이나 종횡비가 큰 교각에 대해 기존 공식보다 더 정확한 예측을 제공할 수 있습니다.
Q4: 교각의 종횡비(L/a)가 증가하면 왜 세굴이 감소하나요?
A4: 교각의 종횡비가 증가하면, 즉 교각이 흐름 방향으로 길어지면, 교각 측면을 따라 흐르는 물의 흐름이 더 안정화되고 흐름 박리 지점이 하류로 이동합니다. 이는 교각 바로 뒤에 형성되는 후류 와류(wake vortices)의 강도와 주기적인 와류 방출(vortex shedding)을 약화시키는 효과를 가져옵니다. 후류 와류 역시 세굴에 기여하는 요인이므로, 이것이 약화되면 교각 하류의 세굴이 줄어들고 전반적인 세굴 구멍의 크기가 감소하게 됩니다.
Q5: 흐름 박리 속도(separation velocity)를 측정한 이유는 무엇인가요?
A5: 흐름 박리 속도는 교각 측면에서 흐름이 표면에서 떨어져 나가기 시작하는 지점의 속도로, 세굴을 일으키는 가장 강력한 메커니즘인 말굽 와류의 형성과 강도에 직접적인 영향을 미칩니다. 본 연구에서는 교각 형상에 따라 이 박리 지점과 속도가 어떻게 변하는지를 측정함으로써(그림 4.29 참조), 각기 다른 형상이 왜 다른 세굴 깊이를 보이는지에 대한 물리적 근거를 파악했습니다. 이 데이터는 더 정확한 세굴 예측 모델을 개발하는 데 핵심적인 역할을 했습니다.
결론: 더 높은 품질과 생산성을 위한 길
교량 세굴은 피할 수 없는 자연 현상이지만, 그 영향을 최소화하는 것은 공학 기술에 달려 있습니다. 본 연구는 교각의 형상을 유선형으로 설계하고 종횡비를 높이는 것만으로도 세굴을 크게 줄일 수 있으며, 희생파일과 같은 방지책은 ‘많이’ 설치하는 것보다 ‘어떻게’ 배열하는지가 더 중요하다는 실질적인 증거를 제시합니다. 이러한 통찰력은 더 안전하고 경제적인 교량 설계를 가능하게 합니다.
STI C&D는 최신 산업 연구 결과를 적용하여 고객이 더 높은 생산성과 품질을 달성할 수 있도록 돕는 데 전념하고 있습니다. 이 논문에서 논의된 과제가 귀사의 운영 목표와 일치한다면, 저희 엔지니어링 팀에 연락하여 이러한 원칙을 귀사의 구성 요소에 어떻게 구현할 수 있는지 알아보십시오.
(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.
연락처 : 02-2026-0442
이메일 : flow3d@stikorea.co.kr
저작권 정보
이 콘텐츠는 Mohamed Kharbeche의 논문 “The Role of Pier Shape and Aspect Ratio on Local Scour with and Without Sacrificial Piles”를 기반으로 한 요약 및 분석 자료입니다.
이 기술 요약은 Rupayan Saha, Seung Oh Lee, Seung Ho Hong이 2018년 ‘water’ 저널에 발표한 논문 “A Comprehensive Method of Calculating Maximum Bridge Scour Depth”를 기반으로 하며, STI C&D가 기술 전문가를 위해 분석하고 요약했습니다.
문제점: 기존의 교량 세굴 깊이 산정 공식은 극한 기상 현상으로 인한 교각 월류(overtopping)나 잠김 흐름(submerged flow)과 같은 복잡한 유동 조건을 정확히 반영하지 못하며, 국부 세굴과 수축 세굴을 독립적인 현상으로 간주하여 예측 정확도가 떨어집니다.
연구 방법: 실제 하천(Towaliga River)의 지형을 1:60으로 축소한 복단면 수로 수리 모형을 제작하고, 자유 수면 흐름, 잠김 오리피스 흐름, 월류 흐름 등 다양한 조건에서 세굴 실험을 수행했습니다.
핵심 발견: 최대 세굴 깊이는 ‘이론적 교각 세굴’과 ‘흐름 수축에 의한 추가 세굴’의 합으로 구성된다는 가설을 세우고, 추가 세굴량이 유량 수축비와 명확한 상관관계가 있음을 실험적으로 증명했습니다.
핵심 결론: 본 연구는 복잡한 흐름 조건에서도 최대 교량 세굴 깊이를 더 정확하게 예측할 수 있는 통합적이고 포괄적인 방법을 제시하여, 교량의 구조적 안전성 설계를 크게 향상시킬 수 있습니다.
문제점: CFD 전문가에게 이 연구가 중요한 이유
교량 붕괴의 가장 큰 원인은 교량 기초 주변의 하상 재료가 유실되는 ‘세굴’ 현상입니다. 미국에서는 1950년 이후 발생한 교량 붕괴의 약 60%가 세굴과 관련 있을 정도로 교량 안전에 치명적입니다. 특히 최근 빈번해지는 극한 기상 현상은 설계 기준을 초과하는 홍수를 유발하며 교량의 안전을 심각하게 위협합니다.
기존의 세굴 깊이 예측 공식들은 대부분 단순화된 사각 수로에서의 자유 수면 흐름 실험을 기반으로 개발되었습니다. 이로 인해 실제 하천의 불규칙한 지형이나, 극한 홍수 시 발생하는 교량 상판 월류 및 잠김 흐름과 같은 복잡한 수리 현상을 제대로 모사하지 못하는 한계가 있습니다. 또한, 현재 설계 실무에서는 흐름 단면 축소로 인한 ‘수축 세굴’과 교각 주변의 와류로 인한 ‘국부 세굴’을 별개의 현상으로 보고 각각 계산한 뒤 합산하지만, 실제로는 두 현상이 동시에 상호작용하며 발생하기 때문에 예측에 오차가 발생합니다. 이러한 부정확성은 교량 설계의 과잉 또는 과소 평가로 이어져 비경제적이거나 위험한 결과를 초래할 수 있습니다.
Figure 1. Towaliga River bridge in the field and model in the laboratory.
연구 접근법: 방법론 분석
본 연구는 이러한 한계를 극복하기 위해 미국 조지아주 메이컨에 위치한 Towaliga 강 교량을 대상으로 1:60 축척의 정밀한 물리적 수리 모형을 제작했습니다. 이 모형은 실제 하천의 복잡한 지형(복단면 형상)을 그대로 재현했으며, 세굴 실험을 위해 중앙부에 이동상(mobile bed) 구간을 설치하고 0.53mm의 중간 입경(d50)을 가진 모래를 사용했습니다.
연구팀은 다양한 홍수 시나리오를 모사하기 위해 세 가지 주요 흐름 조건에서 실험을 수행했습니다. 1. 자유 수면 흐름 (Free Flow): 일반적인 홍수 조건 2. 잠김 오리피스 흐름 (Submerged Orifice Flow): 수위가 교량 상판 하단까지 상승한 조건 3. 월류 흐름 (Overtopping Flow): 수위가 교량 상판을 넘어 흐르는 극한 홍수 조건
각 실험에서 유량과 수위를 정밀하게 제어했으며, 세굴이 평형 상태에 도달할 때까지 5~6일간 실험을 지속했습니다. 세굴 전후의 하상 고도는 음향 도플러 유속계(Acoustic Doppler Velocimeter, ADV)와 포인트 게이지를 사용하여 상세하게 측정되었고, 이를 통해 최대 세굴 깊이와 위치를 정확하게 파악했습니다.
핵심 발견: 주요 결과 및 데이터
연구팀은 실험 결과를 분석하여 기존 세굴 예측 방식의 한계를 극복할 새로운 종합적 방법을 제안했습니다.
결과 1: 최대 세굴 깊이의 새로운 구성 = 이론적 세굴 + 흐름 수축에 의한 추가 세굴
본 연구는 최대 세굴 깊이가 기존의 이론적 교각 세굴 깊이(CSU 또는 M/S 공식으로 계산)에 ‘흐름 수축으로 인한 추가적인 세굴 깊이’가 더해진 결과라는 핵심적인 가설을 제시했습니다. 실험 데이터를 분석한 결과, 이 ‘추가 세굴’ 성분은 교량을 통과하는 흐름의 수축 정도를 나타내는 ‘유량 수축비(q2/q1)’와 매우 강한 양의 상관관계를 보였습니다. 그림 4에서 볼 수 있듯이, 유량 수축비가 증가함에 따라 추가 세굴 깊이(Ym-csu/Y1)가 선형적으로 증가하는 경향이 뚜렷하게 나타났습니다. 이는 흐름이 교량 구간에서 더 많이 압축될수록 세굴이 더 심각해진다는 것을 정량적으로 입증한 것입니다.
결과 2: 압력 흐름 조건에서 세굴 효과 증폭
그림 4의 데이터는 또 다른 중요한 사실을 보여줍니다. 자유 수면 흐름(F)에 비해 잠김 오리피스 흐름(SO)이나 월류 흐름(OT)과 같은 압력 흐름(Pressure Flow) 조건에서 유량 수축비 증가에 따른 추가 세굴 깊이의 증가율(그래프의 기울기)이 훨씬 더 가파릅니다. 이는 압력 흐름 조건에서는 기존의 수평적 흐름 수축뿐만 아니라 교량 상판에 의한 수직적 흐름 수축이 추가로 발생하여 유속이 더 크게 증가하고, 결과적으로 세굴 현상이 증폭되기 때문입니다. 이는 극한 홍수 시 교량 안전성 평가에 반드시 고려해야 할 핵심 요소입니다.
R&D 및 운영을 위한 실질적 시사점
이 연구 결과는 교량 설계 및 안전 관리 분야의 전문가들에게 다음과 같은 실질적인 시사점을 제공합니다.
수리 및 교량 설계 엔지니어: 본 연구에서 제안된 5단계 최대 세굴 깊이 예측 절차(현장 데이터 수집 → 흐름 변수 계산 → 이론적 교각 세굴 계산 → 흐름 수축에 따른 추가 세굴 추정 → 합산)는 기존 방식보다 훨씬 더 정확하고 신뢰성 있는 교량 기초 설계를 가능하게 합니다. 특히 극한 홍수 조건에 대한 안전성을 크게 향상시킬 수 있습니다.
위험 평가팀: 압력 흐름(월류 등)이 세굴을 크게 증폭시킨다는 그림 4의 결과는, 100년 또는 500년 빈도의 극한 홍수 시 월류 가능성이 있는 기존 교량들의 안전성을 재평가해야 할 필요성을 강력하게 시사합니다.
CFD 모델링 전문가: 이 연구에서 측정된 복잡한 흐름 조건(잠김, 월류) 하의 상세한 실험 데이터는 교량 세굴에 대한 수치 모델링(CFD)의 정확도를 검증하고 개선하는 데 매우 귀중한 자료로 활용될 수 있습니다.
논문 상세 정보
A Comprehensive Method of Calculating Maximum Bridge Scour Depth
1. 개요:
제목: A Comprehensive Method of Calculating Maximum Bridge Scour Depth (최대 교량 세굴 깊이 계산을 위한 종합적 방법)
최근 극한 기상 현상의 반복적인 발생으로 교량 주변의 세굴 문제가 두드러지고 있습니다. 따라서 교량은 이러한 극한 기상 현상 동안 겪을 수 있는 높은 유량에 대한 세굴로 인한 붕괴를 방지하기 위해 적절한 보호 조치를 갖추어 설계되어야 합니다. 그러나 여러 권장 공식에 의한 현재의 세굴 깊이 추정은 높은 유량에서 부정확한 결과를 보여줍니다. 한 가지 가능한 이유는 현재의 세굴 공식이 자유 표면 흐름을 이용한 실험에 기반하고 있지만, 극한 홍수 사건은 잠김 오리피스 흐름과 결합된 교량 월류 흐름을 유발할 수 있다는 점입니다. 또 다른 가능한 이유는 최대 세굴 깊이에 대한 현재의 관행이 국부 세굴과 수축 세굴과 같은 다른 유형의 세굴 간의 상호작용을 무시한다는 점인데, 실제로는 이러한 과정들이 동시에 발생합니다. 본 논문에서는 축소된 교량 모델을 사용하여 복합 단면 수로에서 다양한 흐름 조건(자유, 잠김 오리피스, 월류 흐름) 하에 실험실 실험을 수행했습니다. 실험실 실험 결과와 널리 사용되는 경험적 세굴 추정 방법을 결합하여, 다른 세굴 깊이의 개별적 추정과 다른 세굴 구성 요소의 상호작용에 관한 문제를 극복하는 최대 세굴 깊이를 예측하는 포괄적인 방법을 제안합니다. 또한, 최대 세굴 깊이에 대한 교각 벤트(교대에 가깝게 위치)의 존재 효과도 분석 중에 조사되었습니다. 결과는 최대 세굴 깊이의 위치는 교각 벤트의 존재와 무관하지만, 최대 세굴 깊이의 양은 교각 벤트가 있을 때보다 없을 때 유량 재분배로 인해 상대적으로 더 높다는 것을 보여줍니다.
3. 서론:
교량이 강에 건설되면, 교각과 교대 주변에 국부적으로 독특한 유동장이 발달하기 때문에 교량 주변의 흐름 패턴이 바뀝니다. 또한, 강 양쪽 또는 한쪽에 있는 제방/교대로 인해 흐름 면적이 줄어들어 가속으로 인한 유속이 빨라집니다. 더 높은 속도를 가진 이 독특한 유동장은 교량 기초에 심각한 손상을 줄 수 있습니다. 따라서 기초의 깊이가 충분히 깊지 않으면 교량 붕괴의 가능성이 높아집니다. 교량은 지진, 바람, 홍수 등 여러 원인으로 붕괴될 수 있습니다. 그중에서도 교량 세굴은 교량 붕괴의 가장 큰 원인입니다. 예를 들어, 1950년 이후 미국에서 발생한 전체 교량 붕괴 중 약 60%가 교량 기초의 세굴과 관련이 있습니다. 콜로라도 교통부(CDOT)는 2013년 홍수로 최소 30개의 주 고속도로 교량이 파괴되고 20개가 심각하게 손상되었다고 추정했습니다. 네팔에서는 2014년 홍수 동안 하상 재료의 퇴화로 인해 티나우 강 위의 고속도로 교량 기초가 심각하게 노출되었습니다. 위 예에서 설명한 바와 같이, 교량 세굴은 전 세계적으로 주요 교량 안전 문제 중 하나라고 말하는 것이 정당합니다. 따라서 교량 기초에서의 정확한 세굴 예측은 교량 안전을 위한 엔지니어의 주요 목표가 됩니다.
4. 연구 요약:
연구 주제의 배경:
교량 세굴은 교량 붕괴의 주된 원인으로, 특히 극한 홍수 시 그 위험성이 커집니다. 기존의 세굴 예측 공식은 실제 하천의 복잡한 흐름 조건과 세굴 메커니즘의 상호작용을 제대로 반영하지 못해 정확도에 한계가 있었습니다.
이전 연구 현황:
1950년대 후반부터 수많은 연구가 진행되어 평형 세굴 깊이 추정 공식이 개발되었습니다. 그러나 대부분의 연구는 단순화된 직사각형 수로와 자유 수면 흐름 조건에서 수행되었습니다. 또한, 국부 세굴과 수축 세굴을 독립적인 과정으로 가정하여 각각을 계산 후 합산하는 방식을 사용해왔습니다.
연구 목적:
본 연구의 주된 목적은 다양한 유형의 세굴이 동시에 발생하는 상황에서 최대 세굴 깊이를 예측하는 데 사용할 수 있는 단일 방정식을 개발하는 것입니다. 이를 위해 서로 다른 세굴 구성 요소 간의 상호 작용을 규명하고, 널리 사용되는 세굴 공식(CSU, M/S)과 비교하여 최대 세굴 깊이를 계산하는 개선된 방법을 제안하고자 합니다.
핵심 연구:
실제 하천 지형을 모사한 1:60 축소 수리 모형을 이용하여 자유 흐름, 잠김 오리피스 흐름, 월류 흐름 조건에서 실험을 수행했습니다. 실험을 통해 측정한 최대 세굴 깊이와 기존 이론 공식을 비교 분석하여, ‘이론적 교각 세굴’과 ‘흐름 수축에 의한 추가 세굴’의 합으로 최대 세굴 깊이를 표현하는 새로운 접근법을 제시하고, 그 유효성을 검증했습니다.
5. 연구 방법론
연구 설계:
본 연구는 실제 교량(Towaliga River bridge)의 1:60 축소 물리 모형을 이용한 실험적 접근법을 채택했습니다. 복단면 형상의 수로에 이동상 구간을 설치하고, 다양한 수리 조건(자유 흐름, 잠김 오리피스 흐름, 월류 흐름)을 재현하여 세굴 현상을 관찰하고 측정했습니다.
데이터 수집 및 분석 방법:
하상 변동 측정: 음향 도플러 유속계(ADV)와 포인트 게이지를 사용하여 실험 전후의 하상 고도를 정밀하게 측정하고, 이를 통해 세굴 깊이와 범위를 분석했습니다.
유속 측정: ADV를 사용하여 접근부 및 교량 단면에서 3차원 유속 분포를 측정했습니다.
데이터 분석: 측정된 유량, 수위, 유속, 세굴 깊이 등의 변수를 사용하여 기존 세굴 공식(CSU, M/S)과 본 연구에서 제안한 새로운 모델을 비교 분석했습니다. 특히, ‘추가 세굴 깊이’와 ‘유량 수축비’ 간의 상관관계를 회귀 분석을 통해 도출했습니다.
Figure 3. Schematic diagram for calculation of maximum scour depth.
연구 주제 및 범위:
주요 연구 주제: 복잡한 흐름 조건(특히 압력 흐름)에서 발생하는 최대 교량 세굴 깊이의 종합적인 예측 방법 개발.
연구 범위: 단일 교량을 대상으로 한 축소 모형 실험에 국한됩니다. 실험은 청수 세굴(clear-water scour) 조건에서 수행되었으며, 퇴적물 입경은 0.53mm로 고정되었습니다. 교각 벤트의 유무에 따른 영향을 질적으로 분석했습니다.
6. 주요 결과:
주요 결과:
최대 세굴 깊이는 이론적 교각 세굴 깊이와 흐름 수축에 의한 추가 세굴 깊이의 합으로 표현될 수 있습니다.
흐름 수축에 의한 추가 세굴 깊이는 유량 수축비(q2/q1)와 강한 양의 상관관계를 가집니다. 즉, 유량 수축비가 클수록 추가 세굴이 더 깊어집니다.
압력 흐름(잠김 및 월류) 조건에서는 자유 수면 흐름 조건에 비해 추가 세굴 효과가 더 크게 나타납니다. 이는 수직 흐름 수축이 추가되기 때문입니다.
최대 세굴 깊이의 발생 위치는 인접한 교각의 유무와 무관하지만, 인접 교각이 없을 경우 유량 재분배로 인해 최대 세굴 깊이가 약간 더 깊어지는 경향을 보입니다.
기존 공식 중 CSU 공식이 M/S 공식보다 동일 조건에서 더 큰 세굴 깊이를 예측하며, 이는 M/S 공식이 청수 세굴 조건을 고려하는 유속 강도 인자(V2/Vc)를 포함하기 때문입니다.
Table 2. Summary of experimental results to calculate maximum scour depth.
그림 목록:
Figure 1. Towaliga River bridge in the field and model in the laboratory.
Figure 2. Geometry of compound channel for (a) plan view with velocity measurement locations; (b) cross section view at bridge.
Figure 3. Schematic diagram for calculation of maximum scour depth.
Figure 4. Effect of flow contraction on additional scour components using (a) Colorado State University (CSU) and (b) Melville-Sheppard (M/S) equations.
Figure 5. Comparison of CSU and M/S pier scour depth in terms of flow intensity.
Figure 6. Comparison of cross-sections for runs 3 and 8.
7. 결론:
많은 연구가 교량 교각 주변의 최대 세굴 깊이를 추정하고 세굴 메커니즘을 이해하기 위해 이루어졌습니다. 대부분의 이전 연구는 자유 흐름 하의 직사각형 수로를 사용한 실험실 실험에 기반했습니다. 그러나 최근의 극한 강우 사건으로 인해 교량에서는 잠김 오리피스 흐름과 월류 흐름이 빈번하게 발생하며, 이때 교량 하부 구조 주변의 유동장은 기존의 측면 흐름 수축에 더해 수직 흐름 수축 때문에 자유 흐름보다 더 복잡합니다. 또한, 대부분의 자연 하천 형태는 직사각형이 아닙니다. 현재 HEC-18에서 권장하는 지침은 수축 세굴과 국부 세굴 과정이 독립적이어서 별도로 결정하고 합산하여 총 세굴 깊이를 추정할 수 있다고 가정했습니다. 그러나 대규모 홍수 사건 동안 국부 세굴과 수축 세굴은 동시에 발생하며, 국부 세굴과 수축 세굴을 별도로 계산하면 부정확한 세굴 깊이를 초래합니다. 현재 방법론이 가진 약점을 극복하기 위해, 축소된 물리적 모델에서 실험실 실험을 수행하고 압력 흐름뿐만 아니라 자유 흐름 사례에서도 다른 유형의 세굴 구성 요소를 별도로 계산하지 않고 사용할 수 있는 최대 세굴 깊이를 예측하기 위한 단일 방정식이 개발되었습니다.
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전문가 Q&A: 자주 묻는 질문
Q1: 일반적인 사각 수로가 아닌 특정 강(Towaliga River)의 1:60 축소 모형을 사용한 이유는 무엇인가요?
A1: 실제 하천은 본류와 홍수터로 구성된 복단면 형상과 불규칙한 지형을 가지고 있습니다. 단순화된 사각 수로는 이러한 복잡성을 재현할 수 없습니다. 실제 하천 지형을 그대로 모사함으로써, 본 연구의 결과가 이상적인 실험실 조건을 넘어 실제 현장에 더 가깝게 적용될 수 있도록 신뢰도를 높이기 위함입니다.
Q2: 그림 4에서 자유 흐름과 압력 흐름의 추세선 기울기가 다르게 나타나는 물리적 이유는 무엇인가요?
A2: 압력 흐름(잠김 및 월류) 조건에서는 교량 상판으로 인해 흐름이 수직 방향으로도 압축됩니다. 이는 기존의 수평적 흐름 수축에 더해 추가적인 유속 증가를 유발합니다. 따라서 동일한 유량 수축비(q2/q1)에서도 압력 흐름 조건일 때 ‘추가 세굴’ 효과가 더 크게 나타나 그래프의 기울기가 더 가파르게 되는 것입니다.
Q3: 논문에서 비교한 CSU 공식과 M/S 공식 중, M/S 공식이 지속적으로 더 낮은 세굴 깊이를 예측하는 이유는 무엇인가요? (그림 5 참조)
A3: M/S 공식은 유속과 한계유속의 비(V2/Vc)인 ‘유속 강도 인자’를 포함하여 청수 세굴(clear-water scour) 조건을 고려합니다. 반면, CSU 공식은 주로 이동상 세굴(live-bed scour)을 기반으로 개발되어 이 인자를 1로 가정합니다. 본 연구는 청수 세굴 조건에서 수행되었으므로, M/S 공식이 유속 강도 인자를 반영하여 CSU 공식보다 더 낮은 세굴 깊이를 예측하게 됩니다.
Q4: 실험 7과 8에서 교각 #7을 제거한 것의 의미는 무엇인가요?
A4: 이는 교각 간의 상호작용과 인접한 교각의 존재가 최대 세굴 깊이에 미치는 영향을 질적으로 분석하기 위함이었습니다. 실험 결과, 최대 세굴이 발생하는 ‘위치’는 교각 #7의 유무와 상관없이 교각 #6에서 동일했습니다. 하지만 최대 세굴의 ‘깊이’는 교각 #7이 없을 때 유량 재분배 현상으로 인해 약간 더 깊게 나타났습니다.
Q5: 이 연구에서 ‘흐름 수축에 의한 추가 세굴’은 어떻게 정의되고 계산되었나요?
A5: 이는 측정된 총 최대 세굴 깊이에서 표준 이론적 교각 세굴 공식으로 설명되지 않는 부분을 의미합니다. 구체적으로, 세굴이 가장 깊은 지점의 총 수심(Ym)에서 CSU 공식(dcsu) 또는 M/S 공식(dms)으로 계산된 이론적 교각 세굴 깊이를 빼서 계산했습니다. 이는 논문의 식 (7)과 (8)에 명시되어 있습니다.
결론: 더 높은 품질과 생산성을 위한 길
기존의 교량 세굴 깊이 예측 방법은 극한 홍수와 같은 복잡한 실제 상황을 제대로 반영하지 못하는 명백한 한계를 가지고 있었습니다. 본 연구는 ‘이론적 세굴’과 ‘흐름 수축에 의한 추가 세굴’을 결합하는 포괄적인 접근법을 제시함으로써 이 문제를 해결하는 중요한 돌파구를 마련했습니다. 특히 압력 흐름 조건에서 세굴이 증폭된다는 사실을 정량적으로 밝혀내어, 교량 설계 및 안전 진단의 정확성을 한 차원 높일 수 있는 실질적인 통찰력을 제공합니다.
(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.
연락처 : 02-2026-0442
이메일 : flow3d@stikorea.co.kr
저작권 정보
이 콘텐츠는 “Rupayan Saha” 외 저자의 논문 “A Comprehensive Method of Calculating Maximum Bridge Scour Depth”를 기반으로 한 요약 및 분석 자료입니다.
이 기술 요약은 Nordila, Ahmad 외 저자가 2017년 Pertanika J. Sci. & Technol.에 발표한 논문 “Modelling the Effect of Sediment Coarseness on Local Scour at Wide Bridge Piers”를 기반으로 하며, 기술 전문가를 위해 (주)에스티아이씨앤디 분석하고 요약했습니다.
The Challenge: 기존의 교각 세굴 예측 공식은 광폭 교각(wide bridge piers)의 세굴 심도를 과대평가하여 불필요하고 비용이 많이 드는 기초 공사나 대책을 야기하는 경향이 있었습니다.
The Method: 균일한 퇴적물(입경 0.23mm, 0.80mm)로 채워진 50m 길이의 대형 수조(flume)에서 다양한 폭(0.06m ~ 0.165m)의 원통형 교각 모델을 사용하여 국부 세굴 현상을 물리적으로 모델링했습니다.
The Key Breakthrough: 교각 폭과 퇴적물 입경의 비율(b/d50, 퇴적물 조도)이 세굴 심도에 미치는 영향을 정량적으로 분석하여, 이 비율이 증가할수록 상대적 세굴 심도(ds/b)가 감소하는 경향을 확인하고 새로운 예측 방정식을 제안했습니다.
The Bottom Line: 본 연구는 퇴적물 조도를 핵심 변수로 고려하여 광폭 교각의 세굴 심도를 더 정확하게 예측할 수 있는 방정식을 제공함으로써, 교량 설계의 경제성과 안전성을 동시에 향상시킬 수 있는 길을 열었습니다.
Table 1 Summary of experimental results for the present study
The Challenge: Why This Research Matters for CFD Professionals
교량의 안전성은 교각 주변의 국부 세굴(local scour) 현상에 크게 좌우됩니다. 특히 유속이 느리고 수심이 얕은 곳에 설치되는 광폭 교각의 경우, 기존의 경험적 세굴 예측 공식들이 실제보다 세굴 깊이를 과대평가하는 문제가 지속적으로 제기되어 왔습니다. 이는 실험실 데이터에 기반한 공식들이 대형 구조물에 그대로 적용될 때 발생하는 오차 때문입니다. 이러한 과대 예측은 교량 기초 공사에 불필요한 비용을 발생시키고, 과도한 보강 대책을 수립하게 만드는 원인이 됩니다. 따라서 실제 현상에 더 가까운, 특히 퇴적물의 특성을 고려한 정밀한 세굴 예측 모델의 개발은 토목 및 수리 공학 분야의 중요한 과제였습니다.
The Approach: Unpacking the Methodology
본 연구는 말레이시아 국립수리연구소(NAHRIM)의 대규모 수리 실험 시설을 활용하여 수행되었습니다. 실험의 핵심 내용은 다음과 같습니다.
실험 장비: 길이 50.0m, 폭 1.5m, 깊이 2.0m의 대형 수조(flume)를 사용했으며, 중앙에는 0.4m 깊이의 퇴적물 구간을 설치했습니다.
퇴적물 조건: 두 종류의 균일한 무점착성 퇴적물을 사용했습니다. 중간 입경(d50)은 각각 0.23mm와 0.80mm였으며, 이는 상대적으로 고운 퇴적물과 거친 퇴적물을 대표합니다.
교각 모델: 직경이 0.06m, 0.076m, 0.102m, 0.140m, 0.165m인 5개의 원통형 교각 모델을 사용하여 교각 폭의 영향을 평가했습니다.
흐름 조건: 모든 실험은 퇴적물 입자가 움직이기 시작하는 한계 유속(Critical velocity, Uc)에 가까운 유속(U/Uc ≈ 0.95)의清水(clear-water) 조건에서 수행되었습니다. 이는 세굴이 주로 교각 주변의 흐름 변화에 의해 발생하는 조건을 모사한 것입니다.
연구팀은 이러한 통제된 조건 하에서 각 교각 모델과 퇴적물 조합에 따른 세굴 구멍의 시간적 발달 과정과 최종 평형 세굴 심도를 정밀하게 측정했습니다.
The Breakthrough: Key Findings & Data
실험을 통해 퇴적물 조도(sediment coarseness, b/d50)가 광폭 교각의 세굴 발달 및 최종 깊이에 미치는 영향에 대한 중요한 발견을 도출했습니다.
Finding 1: 세굴 발달의 3단계 과정 확인
본 연구는 유속 강도 U/Uc = 0.95 조건에서 세굴 발달이 뚜렷한 3단계, 즉 (i) 초기 단계, (ii) 주 침식 단계, (iii) 평형 단계를 거치는 것을 확인했습니다. 특히 주 침식 단계에서 퇴적물 조도(b/d50) 값에 따라 두 가지 다른 침식 양상이 관찰되었습니다.
고운 퇴적물 (b/d50 > 230): 교각 전면의 강한 하강류(downflow)로 인해 세굴이 깊어집니다. 하강류가 세굴 구멍 바닥에 부딪히며 말굽 와류(horseshoe vortex)를 형성하고, 이 와류의 강도가 세굴 깊이에 따라 변화하며 침식 영역의 범위가 조절되는 현상이 관찰되었습니다.
거친 퇴적물 (b/d50 < 230): 상대적으로 퇴적물 입자가 커서 하강류에 의한 침식이 덜 활발하며, 최종 세굴 깊이도 더 얕게 형성되었습니다.
Finding 2: 퇴적물 조도(b/d50)와 평형 세굴 심도의 관계 정립
연구의 가장 핵심적인 결과는 퇴적물 조도(b/d50)와 무차원 평형 세굴 심도(ds/b) 사이의 관계를 명확히 규명한 것입니다.
Figure 4에 나타난 바와 같이, b/d50 값이 증가함에 따라 평형 세굴 심도는 특정 지점(b/d50 ≈ 330)까지 증가하다가 그 이후로는 점차 감소하는 경향을 보였습니다. 이는 교각 폭에 비해 퇴적물이 매우 고와지면 세굴이 오히려 억제될 수 있음을 시사합니다.
이 결과를 바탕으로, 연구팀은 b/d50 값의 범위에 따라 평형 세굴 심도를 예측할 수 있는 두 개의 새로운 상부 포락선 방정식(upper envelope equations)을 제안했습니다.
이 방정식들은 기존 연구 데이터와 비교했을 때, 광폭 교각의 세굴 심도를 과소평가 없이 더 정확하게 예측하는 것으로 나타났습니다(Figure 6).
Practical Implications for R&D and Operations
For Hydraulic/Civil Design Engineers: 이 연구는 교량 설계 시 퇴적물의 입경을 중요한 설계 변수로 고려해야 함을 명확히 보여줍니다. 제안된 방정식을 활용하면 특정 하천 조건(퇴적물 크기)에 맞는 광폭 교각의 세굴 심도를 더 정밀하게 예측하여, 과잉 설계를 피하고 경제적인 기초 설계를 수행할 수 있습니다.
For Structural Integrity Analysts: 세굴 심도 예측의 정확도 향상은 교량의 장기적인 안정성 평가에 직접적으로 기여합니다. 특히 b/d50 비율이 큰(매우 고운 퇴적물) 환경에서는 세굴이 특정 수준 이상으로 발달하지 않을 수 있다는 점을 고려하여 유지보수 및 보강 계획을 최적화할 수 있습니다.
For CFD Simulation Specialists: 본 연구에서 제공된 상세한 물리 모델 실험 데이터(Figure 1의 시간별 세굴 데이터 등)는 CFD 모델의 검증(validation)을 위한 귀중한 자료로 활용될 수 있습니다. 특히 말굽 와류의 거동과 퇴적물 이동을 모사하는 수치 모델의 정확도를 높이는 데 기여할 수 있습니다.
Paper Details
Modelling the Effect of Sediment Coarseness on Local Scour at Wide Bridge Piers
1. Overview:
Title: Modelling the Effect of Sediment Coarseness on Local Scour at Wide Bridge Piers
Author: Nordila, Ahmad; Thamer, Mohammad; Melville, Bruce W.; Faisal, Ali; Badronnisa, Yusuf
Year of publication: 2017
Journal/academic society of publication: Pertanika Journal of Science & Technology
본 논문은 두 종류의 균일한 퇴적물 바닥에 설치된 원통형 광폭 교각 주변의 세굴에 대한 물리적 모델 실험 데이터를 제시한다. 퇴적물 입경과 다양한 교각 폭이 광폭 교각의 세굴 발달 및 평형 세굴 심도에 미치는 영향을 기술한다. 기존 문헌들은 실험실 데이터에 기반한 경험적 세굴 예측 공식이 대형 구조물의 세굴 심도를 과대 예측한다고 제안한다. 본 연구는 원통형 광폭 교각에 대한 이러한 격차를 메우고자 시도했다. 더 나아가, 균일한 퇴적물에 설치된 광폭 원통형 교각의 무차원 최대 세굴 심도를 퇴적물 조도의 함수로 추정하기 위한 방정식들이 제안되었다.
3. Introduction:
많은 연구가 교량 교각의 최대 세굴 심도를 개발하는 것을 목표로 수행되어 왔다. 그러나 광폭 교각의 세굴 심도 측정에 대한 연구는 제한적이다. 광폭 교각은 얕은 수로에 위치하며 유속이 느리고, 프루드 수(Froude number) < 0.8에 대해 y/b < 0.8로 정의된다. 기존 연구들은 b/d50, 즉 퇴적물 조도 매개변수가 광폭 교각의 평형 국부 세굴 심도에 상당한 영향을 미친다는 것을 보여주었다. 문헌의 예측 방정식들은 대형 및 소형 교각 모두를 대상으로 하므로, 이러한 교각에서 국부 세굴을 과대 예측하게 되어 불필요하고 비용이 많이 드는 기초 공사나 대책을 사용하게 만든다. 따라서 본 연구는 두 가지 균일한 퇴적물 크기와 다섯 개의 교각 모델을 사용하여 퇴적물 조도(b/d50)의 효과를 조사하기 위해 실험실에서 국부 교각 세굴 실험을 수행했다.
4. Summary of the study:
Background of the research topic:
교량의 안전성을 위협하는 주요 요인 중 하나는 교각 주변의 국부 세굴 현상이다. 특히 교각 폭이 수심에 비해 상대적으로 넓은 ‘광폭 교각’의 경우, 기존의 세굴 예측 공식이 실제보다 과도한 세굴 깊이를 예측하는 경향이 있어 설계의 비경제성을 초래했다.
Status of previous research:
Johnson & Torrico (1994), Arneson et al. (2012), Sheppard et al. (2004), Lee & Sturm (2009) 등 다수의 연구에서 광폭 교각의 세굴 특성과 퇴적물 크기(b/d50)의 중요성을 지적했다. 그러나 대부분의 공식은 여전히 실제 대형 구조물의 세굴을 과대평가하는 한계를 가지고 있었다.
Purpose of the study:
본 연구의 목적은 광폭 원통형 교각에서 퇴적물 조도(b/d50)가 국부 세굴 발달 및 평형 세굴 심도에 미치는 영향을 실험적으로 규명하고, 이를 바탕으로 더 정확한 세굴 심도 예측 방정식을 개발하는 것이다.
Core study:
두 종류의 퇴적물(d50 = 0.23mm, 0.80mm)과 다섯 가지 직경의 교각 모델을 사용하여 총 10회의 수리 실험을 수행했다. 시간 경과에 따른 세굴 구멍의 발달 과정과 최종 평형 세굴 심도를 측정하고, 이를 무차원 변수인 퇴적물 조도(b/d50)와 상대 세굴 심도(ds/b)의 관계로 분석했다.
5. Research Methodology
Research Design:
대규모 수조(flume)를 이용한 물리적 모델링 실험으로 설계되었다. 교각 직경(b)과 퇴적물 입경(d50)을 주요 변수로 설정하고, 흐름 조건(U/Uc ≈ 0.95)은 일정하게 유지하여 변수의 영향을 명확히 분석하고자 했다.
Data Collection and Analysis Methods:
시간 경과에 따른 세굴 깊이(ds)를 측정하여 세굴 발달 과정을 기록했다. 최종 평형 상태에 도달했을 때의 최대 세굴 심도를 측정하여 데이터를 수집했다. 수집된 데이터는 무차원 변수(ds/b, b/d50)로 변환하여 그래프로 분석하고, 다른 연구자들의 데이터와 비교 분석하여 새로운 예측 방정식을 도출했다.
Research Topics and Scope:
연구는 원통형 광폭 교각, 균일한 무점착성 퇴적물, 그리고 퇴적물 이동이 막 시작되는 한계 유속 조건(clear-water scour)에 국한된다.
6. Key Results:
Key Results:
세굴 발달은 초기, 주 침식, 평형의 3단계로 구분되며, 퇴적물 조도(b/d50)에 따라 침식 양상이 달라진다.
상대 평형 세굴 심도(ds/b)는 퇴적물 조도(b/d50)가 증가함에 따라 감소하는 전반적인 경향을 보인다.
b/d50 ≈ 330에서 최대 세굴 심도가 관찰되었으며, 이보다 값이 커지면 세굴 심도는 오히려 감소했다.
퇴적물 조도(b/d50)를 기반으로 평형 세굴 심도를 예측하는 두 개의 연속적인 상부 포락선 방정식을 개발했다.
Figure 3. b = 140 mm, d50 = 0.80 mm, b/d50 = 175, U/Uc = 0.95
Figure Name List:
Figure 1. Normalised local scour depth (ds/b) versus time at the same value of b in sediment beds of d50=0.23 and 0.80 mm
Figure 2. b = 140 mm, d50 = 0.23 mm, b/d50 = 609, U/Uc = 0.95
Figure 3. b = 140 mm, d50 = 0.80 mm, b/d50 = 175, U/Uc = 0.95
Figure 4. Equilibrium scour depth versus b/d50 for the present study
Figure 5. Effect of b/d50 on ds/b
Figure 6. Comparison of observed values of ds/b around wide piers with those predicted using Equation [1] and Equation [2]
7. Conclusion:
본 연구는 유속 강도 U/Uc = 0.95 조건에서 새로운 실험 데이터를 통해 국부 세굴 심도의 시간적 및 공간적 발달을 보여주었다. 광폭 교각에서의 국부 세굴 심도가 세굴 구멍 발달 및 퇴적물 조도에 미치는 영향이 제시되었다. 상대 세굴 심도(dse/b)는 퇴적물 조도 값이 증가함에 따라 감소하는 것으로 나타났다. b/d50 값에 따라 교각 세굴 심도를 예측하는 두 개의 연속적인 상부 포락선 방정식이 개발되었다. b/d50 값이 클 때 dse/b 값이 감소하는 것이 입증되었으며, 이는 대형 수조를 사용한 실험 결과 및 이전 연구자들의 발견과 일치했다.
8. References:
Arneson, L. A., Zevenbergen, L. W., Lagasse, P. F., & Clopper, P. E. (2012). Evaluating scour at bridges (4th Ed.). Hydraulic Engineering Circular No. 18 (HEC-18). Federal Highway Administration, Washington, DC.
Ettema, R., (1980). Scour around bridge piers. Report No. 216, University of Auckland, Auckland, New Zealand.
Ettema, R., Kirkil, G., & Muste, M. (2006). Similitude of large-scale turbulence in experiments on local scour at cylinders. Journal of Hydraulic Engineering, 132(1), 33-40.
Johnson, P. A., & Torrico, E. F. (1994). Scour around wide piers in shallow water. Transportation Research Record, (1471), 66-70.
Johnson, P. A. (1999). Scour at Wide Piers Relative to Flow Depth, Stream Stability and Scour at Highway Bridges. In E. V. Richardson & P. F. Lagasse (Eds.), Compendium of ASCE Conference Papers (pp. 280–287).
Jones, J., & Sheppard, D. (2000). Scour at wide bridge pier (pp. 1-10). Federal Highway Administration, Turner-Fairbank Highway Research Center, McLean, Virginia.
Junliang, T., & Xiong, Y. (2014). Flow and Scour Patterns around Bridge Piers with Different Configurations: Insights from CFD Simulations. In Geo-Congress 2014 Technical Papers: Geo-characterization and Modeling for Sustainability (pp. 2655-2664). ASCE.
Kirkil, G., Constantinescu, S. G., & Ettema, R., (2008). Coherent structures in the flow field around a circular cylinder with scour hole. Journal of Hydraulic Engineering, 134(5), 572–587.
Lança, R. M., Fael, C. S., Maia, R. J., Pêgo, J. P., & Cardoso, A. H. (2013). Clear-water scour at comparatively large cylindrical piers. Journal of Hydraulic Engineering, 139(11), 1117-1125.
Lee, S. O., & Sturm, T. W. (2009). Effect of sediment size scaling on physical modeling of bridge pier scour. Journal of Hydraulic Engineering, 135(10), 793-802.
Melville, B. W., & Coleman, S. E., (2000). Bridge Scour. United States of America, USA: Water Resources Publications.
Melville, B.W., (1975). Local scour at bridge sites. Report No.117. School of Engineering, University of Auckland, New Zealand.
Melville, B. W. (2008). The physics of Local Scour at Bridge Piers. In Fourth International Conference on Scour and Erosion (pp. 28-38). Tokyo.
Nicolet, G. (1971). Deformation des lits alluvionaires affouillements autor des piles se ponts cylindriques. Report No. HC 043 684. Laboratoire National d’Hydraulique, Chatou, France.
Sheppard, D. M., Huseyin, D., & Melville, B. W. (2011). Scour at wide piers and long skewed piers. Report (National Cooperative Highway Research Program); 682. Washington, D.C.: Transportation Research Board.
Sheppard, D. M., Melville, B., & Demir, H. (2013). Evaluation of existing equations for local scour at bridge piers. Journal of Hydraulic Engineering, 140(1), 14-23.
Sheppard, D. M., & Miller, J. W. (2006). Live-bed local pier scour experiments. Journal of Hydraulic Engineering, 132(7), 635-642.
Sheppard, D. M., Odeh, M., & Glasser, T. (2004). Large scale clear-water local pier scour experiments. Journal of Hydraulic Engineering, 130(10), 957-963.
Expert Q&A: Your Top Questions Answered
Q1: 실험에서 흐름 강도(U/Uc)를 0.95로 설정한 특별한 이유가 있나요?
A1: 흐름 강도를 0.95로 설정한 것은 ‘清水 세굴(clear-water scour)’ 조건, 즉 상류로부터 유입되는 퇴적물 없이 순수하게 교각 주변의 흐름 변화만으로 세굴이 발생하는 조건을 모사하기 위함입니다. 이 값은 퇴적물 입자가 움직이기 시작하는 한계점에 매우 가까운 상태로, 교각으로 인한 국부적인 유속 증가 및 와류 효과를 가장 극명하게 관찰할 수 있는 최적의 조건입니다. 실제 교량 환경에서도 홍수 초기 단계 등에서 유사한 조건이 발생할 수 있습니다.
Q2: 퇴적물 조도(b/d50)가 특정 값(약 330)을 넘어서자 세굴 심도가 오히려 감소하는 이유는 무엇인가요? (Figure 4 참조)
A2: 이는 교각 폭(b)에 비해 퇴적물 입자(d50)가 매우 작아지는 경우에 발생하는 현상입니다. 논문에 따르면, b/d50 값이 매우 크다는 것은 상대적으로 고운 퇴적물을 의미합니다. 이 경우, 교각 주변에서 발생하는 하강류와 말굽 와류의 에너지가 세굴 구멍을 깊게 파는 데 효과적으로 작용합니다. 하지만 일정 수준을 넘어서면, 세굴 구멍의 경사면 안정성이나 와류 구조의 변화 등 다른 물리적 메커니즘이 작용하여 세굴 심도의 증가를 억제하는 것으로 해석됩니다. 이는 더 큰 교각에서 국부적인 상류부 침식이 세굴 발달에 영향을 미치는 것과도 관련이 있습니다.
Q3: 본 연구에서 제안된 두 개의 예측 방정식이 b/d50 = 37을 기준으로 나뉘는 이유는 무엇인가요?
A3: Figure 5에 제시된 기존 연구 데이터들을 포함한 전체 데이터 분포를 보면, b/d50 = 37 근방에서 데이터의 경향성이 변하는 것을 관찰할 수 있습니다. 이는 퇴적물이 교각 폭에 비해 상대적으로 ‘거친(coarse)’ 영역에서 ‘중간(intermediate)’ 영역으로 넘어가는 물리적 특성의 변화를 반영하는 것으로 보입니다. 따라서 연구진은 전체 데이터의 경향을 가장 잘 대표할 수 있는 두 개의 연속적인 함수로 모델을 나누어 예측의 정확도를 높였습니다.
Q4: 이 연구 결과는 원통형 교각에만 적용되나요? 사각형이나 다른 형태의 교각에도 적용할 수 있을까요?
A4: 본 연구는 명시적으로 ‘원통형(cylindrical)’ 교각 모델을 사용하여 수행되었으므로, 제안된 방정식들은 원통형 교각에 가장 적합합니다. 교각의 형태는 주변 흐름 구조, 특히 말굽 와류와 후류(wake)의 특성을 크게 변화시키므로 사각형이나 유선형 교각에는 다른 보정 계수가 필요하거나 별도의 연구가 요구됩니다. 하지만 퇴적물 조도(b/d50)가 세굴에 중요한 영향을 미친다는 근본적인 물리 현상은 다른 형태의 교각에서도 유사하게 나타날 것으로 예상할 수 있습니다.
Q5: 이 연구는 실험실 규모의 실험인데, 실제 대규모 하천에 직접 적용할 때 주의할 점은 무엇인가요?
A5: 본 연구는 대규모 수조를 사용했지만, 실제 하천의 복잡성에 비하면 여전히 통제된 환경입니다. 실제 하천에 적용할 때는 불규칙한 하상 형태, 식생의 영향, 흐름의 비정상성(unsteadiness), 그리고 불균일한 퇴적물 분포 등 축척 효과(scale effects)와 현장의 복잡성을 고려해야 합니다. 따라서 제안된 방정식은 예비 설계나 기본 분석 단계에서 유용한 도구가 될 수 있으며, 최종 설계에서는 현장 데이터나 정밀한 3차원 수치 모델링(CFD)을 통한 검증이 병행되는 것이 바람직합니다.
Conclusion: Paving the Way for Higher Quality and Productivity
기존 예측 모델의 한계로 인해 발생했던 광폭 교량 교각 세굴 심도의 과대평가 문제는 교량 설계의 경제성과 효율성을 저해하는 요인이었습니다. 본 연구는 퇴적물 조도(b/d50)라는 핵심 물리적 변수를 통해 이 문제에 대한 명확한 해답을 제시했습니다. 실험을 통해 퇴적물 조도가 증가할수록 상대적 세굴 심도가 감소하는 경향을 정량적으로 입증하고, 이를 기반으로 한 새로운 예측 방정식을 개발함으로써 교량 설계의 정확도를 한 단계 끌어올렸습니다.
이러한 연구 결과는 더 안전하고 경제적인 교량 인프라 구축에 직접적으로 기여하며, 토목 수리 공학 분야의 기술 발전을 이끄는 중요한 이정표가 될 것입니다.
(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.
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Copyright Information
This content is a summary and analysis based on the paper “Modelling the Effect of Sediment Coarseness on Local Scour at Wide Bridge Piers” by “Nordila, Ahmad et al.”.
이 기술 요약은 Sarbaini, Mudjiatko, Rinaldi가 Jom FTEKNIK (2015)에 발표한 논문 “MODEL LABORATORIUM PENGARUH VARIASI SUDUT ARAH PENGAMAN PILAR TERHADAP KEDALAMAN GERUSAN LOKAL PADA JEMBATAN DENGAN PILAR CYLINDER GROUPED”를 바탕으로, STI C&D의 기술 전문가에 의해 분석 및 요약되었습니다.
Keywords
Primary Keyword: 교각 세굴 (Bridge Pier Scour)
Secondary Keywords: 국부 세굴 (Local Scour), CFD 시뮬레이션 (CFD Simulation), 교량 안전 (Bridge Safety), 수리 동역학 (Hydrodynamics), 퇴적물 이동 (Sediment Transport)
Executive Summary
The Challenge: 만곡 하천에 설치된 교량의 교각은 국부 세굴 현상으로 인해 기초가 약화되어 구조적 안정성에 심각한 위협을 받습니다.
The Method: 실험실 수로 모델을 사용하여 그룹 원통형 교각 주변에 커튼형 보호 장치를 59°, 50°, 90°의 세 가지 각도로 설치하고, 각 조건에서 발생하는 세굴 깊이를 측정했습니다.
The Key Breakthrough: 교각 보호 장치의 설치 각도가 세굴 깊이에 결정적인 영향을 미치며, 특정 조건에서 보호 장치의 세굴 깊이 비율(ds/b)이 최대 2.4에 도달하는 것을 확인했습니다.
The Bottom Line: 교량의 장기적인 내구성을 확보하기 위해서는 세굴 보호 장치의 각도를 최적화하는 것이 매우 중요하며, 본 실험 데이터는 예측 CFD 모델의 정확성을 검증하는 핵심적인 기준을 제공합니다.
The Challenge: Why This Research Matters for CFD Professionals
하천에 건설된 교량, 특히 유속이 빠르고 흐름이 복잡한 만곡부에 위치한 교량의 교각은 지속적인 수리동역학적 힘과 나선형 흐름(helicoidal flow)에 노출됩니다. 이러한 힘은 교각 주변의 하상 재료를 침식시키는 국부 세굴(local scouring) 현상을 유발합니다. 세굴이 심화될 경우 교각의 기초가 노출되고 지지력이 약화되어 최악의 경우 교량 붕괴로 이어질 수 있습니다. 따라서 교각의 안정성을 확보하기 위해 다양한 형태의 보호 장치가 사용되지만, 그 효과를 극대화하기 위한 최적의 설계 기준은 여전히 중요한 연구 과제입니다. 본 연구는 보호 장치의 ‘설치 각도’라는 특정 변수가 세굴 깊이에 미치는 영향을 정량적으로 분석하여, 보다 안전하고 경제적인 교량 설계의 기초를 마련하고자 했습니다.
The Approach: Unpacking the Methodology
본 연구는 실제 하천의 복잡한 현상을 통제된 환경에서 재현하기 위해 실험실 모델을 사용했습니다. 연구의 핵심적인 방법론은 다음과 같습니다.
실험 장비: 재순환 퇴적물 수로(Recirculating sediment flume)를 사용하여 연속적인 흐름 조건을 구현했습니다. 수로의 크기는 길이 8m, 폭 0.8m, 높이 0.15m입니다.
교각 모델: 실제 Teratak Buluh 교량의 형태를 채택한 그룹 원통형(grouped cylinder) 교각 모델을 사용했습니다. 이는 2개의 그룹으로 구성되며, 그룹 1은 12개, 그룹 2는 10개의 기둥으로 이루어져 있습니다.
하상 재료: 캄파르(Kampar) 강 모래를 사용했으며, 입자 크기 분포는 d35 = 0.247mm, d50 = 0.298mm, d65 = 0.352mm, 비중(Gs)은 2.64입니다.
핵심 변수: 교각 보호 장치(curtain type)의 설치 각도를 59°(θ1), 50°(θ2), 90°(θ3) 세 가지로 변화시켰습니다. 또한, 프루드 수(Froude number) 0.464에서 0.698 범위의 세 가지 아임계 흐름(subcritic flow) 조건을 적용하여 유속의 영향을 함께 평가했습니다. 레이놀즈 수(Reynolds number) 계산 결과, 흐름은 천이류(transition flow)와 난류(turbulence flow) 영역에 해당했습니다.
Gambar 1. Ilustrasi gerusan lokal di sekitar pilar jembatan (Sumber : Coastal Engineering Research Center dalam cahyono dan solichin, 2008)
The Breakthrough: Key Findings & Data
실험을 통해 교각 보호 장치의 각도와 유속이 세굴 깊이에 미치는 영향을 정량적으로 분석했으며, 주요 결과는 다음과 같습니다.
Gambar 4. Ilustrasi 3D model pilar dan pengaman pilar jembatan (a) group pile 1, (b) group pile 2.
Finding 1: 보호 장치 각도와 세굴 깊이의 직접적인 상관관계
보호 장치의 각도는 교각과 보호 장치 자체의 세굴 깊이에 직접적인 영향을 미쳤습니다. 결론(G.2)에 따르면, 교각 그룹 1의 경우, 90° 각도에서 가장 큰 세굴(ds/b = 1.5)이 발생했으며, 59° 각도에서 가장 작은 세굴(ds/b = 1.3)이 나타났습니다. 특히 주목할 점은 보호 장치 자체의 세굴입니다. 90° 각도에서 보호 장치의 세굴 깊이 비율은 2.4로 가장 컸고, 50° 각도에서는 1.5로 가장 작았습니다. 이는 보호 장치의 각도가 흐름을 교란시키는 방식에 따라 침식 에너지가 집중되는 위치와 강도가 달라짐을 명확히 보여줍니다.
Finding 2: 유동 조건과 퇴적물 이동의 연관성
더 높은 프루드 수(Froude number)를 가진 흐름, 즉 유속이 빠를수록 더 큰 입경의 퇴적물이 이동하는 것으로 확인되었습니다(결론 G.3). 쉴드(Shields) 및 휼스트롬(Hjulstorm) 다이어그램 분석 결과(그림 8, 9, 10), 실험에 사용된 모든 입자 등급은 ‘이동 영역(moving zone)’에 위치했습니다. 이는 실험 조건이 하상 재료가 지속적으로 이동하는 ‘이동상 세굴(live-bed scour)’ 환경이었음을 의미하며, 실제 홍수 시 발생하는 현상과 유사합니다. 이 결과는 유속이 세굴의 직접적인 원동력이며, 흐름의 에너지가 침식 능력과 직결됨을 입증합니다.
Practical Implications for R&D and Operations
For Process Engineers (토목/수리 엔지니어): 본 연구는 커튼형 보호 장치의 각도가 신중하게 선택되어야 함을 시사합니다. 시공이 용이해 보이는 90° 각도가 오히려 더 큰 세굴을 유발할 수 있습니다. 이 데이터는 세굴 방지 대책을 위한 설계 가이드라인을 수립하는 데 중요한 정보를 제공합니다.
For Quality Control Teams (인프라 검사팀): 논문의 다양한 그래프(그림 13-21)는 유속과 보호 장치 각도에 따라 세굴 패턴이 어떻게 다르게 발달하는지 보여줍니다. 이는 교량 정기 점검 시, 본 실험에서 고위험 지역으로 식별된 구역을 집중적으로 확인할 수 있는 검사 프로토콜을 개발하는 데 활용될 수 있습니다.
For Design Engineers (교량 설계자): 연구 결과는 교각과 보호 시스템의 기하학적 구성이 세굴을 제어하는 핵심 변수임을 나타냅니다. 이 연구는 단순한 교각 형상 설계를 넘어, 보호 장치의 역할과 최적 배치에 대한 정량적 데이터를 제공함으로써 초기 설계 단계에서 중요한 고려사항을 제시합니다.
Paper Details
MODEL LABORATORIUM PENGARUH VARIASI SUDUT ARAH PENGAMAN PILAR TERHADAP KEDALAMAN GERUSAN LOKAL PADA JEMBATAN DENGAN PILAR CYLINDER GROUPED
1. Overview:
Title: MODEL LABORATORIUM PENGARUH VARIASI SUDUT ARAH PENGAMAN PILAR TERHADAP KEDALAMAN GERUSAN LOKAL PADA JEMBATAN DENGAN PILAR CYLINDER GROUPED
Author: Sarbaini, Mudjiatko, Rinaldi
Year of publication: 2015
Journal/academic society of publication: Jom FTEKNIK Volume 2 No. 2 Oktober 2015
Keywords: local scouring, grouped cylinder pillar, angle of pillars protector, curtain type pillars protectot, depth ratio
2. Abstract:
Bridge pillars placed on meander river experience hydrodynamic flow and helecoidal force. Those force will cause local scour on pillars and pillar protectors. Pillar protectors with specified angle is expected to be able to minimize the magnitude of scouring on pillars. Laboratory model with grouped cylinder type pillars with three variation of angle of curtain type pillars protector (θ1, θ2, θ3) are used to observed the phenomenon of scouring that occured on meander river. Kampar sand with grain size of d35 = 0,247 mm, d50 = 0,298 mm, d65 = 0,352 mm and Gs = 2,64 are used as the base for the bed of the channel. Three type of subcritic flow with froude number ranged from 0,464-0,698 and yield the reynolds number occured on Fr1-Fr3 at 1658,416 thus classified as transition flow while 3081,683 and 4381,188 are classified as turbulence flow. Shield graphic showed that grain gradation used in this research is located one moving zone. The ratio of scouring depth (ds/b) of pillars protectors is highest 2,4 that occured on Fr3 θ2 and Fr1 θ3 while on the pillars is occured on Fr2 θ2 at 1,9. The results of sediment transport analysis proved that with the in crease in froude number used the bigger the size of the grain transported.
3. Introduction:
만곡 형태의 하천(meander)은 일반적으로 완만한 하상 경사를 가집니다. 만곡부 외측은 내측보다 유속이 빠르기 때문에 하상이 더 깊어지는 경향이 있으며, 원심력으로 인해 횡방향 흐름이 발생하고 주 흐름과 결합하여 나선형 흐름(helicoidal flow)을 형성합니다. 하천의 흐름은 종종 퇴적물 이동과 세굴 과정을 동반합니다. 세굴은 하천의 형태학적 영향이나 흐름을 방해하는 구조물로 인해 자연적으로 발생할 수 있습니다. 이러한 흐름 속에 위치한 교량 교각은 3차원 흐름과 흐름 패턴의 변화를 유발하여 구조물 주변에 국부적인 세굴을 일으킵니다.
4. Summary of the study:
Background of the research topic:
만곡 하천에 설치된 교량 교각은 복잡한 수리동역학적 힘에 의해 국부 세굴에 취약합니다. 이는 교량의 구조적 안정성을 위협하므로, 세굴을 최소화하기 위한 효과적인 교각 보호 장치 설계가 필요합니다.
Status of previous research:
과거 Arie Perdana Putra (2014)는 그룹 원통형 교각의 국부 세굴에 대한 실험실 모델 연구를 수행했으며, Tri Achmadi (2001)는 교각 세굴에 대한 수리 모델 연구를 진행한 바 있습니다.
Purpose of the study:
본 연구의 목적은 만곡 하천에 설치된 그룹 원통형 교각에서, 커튼형 보호 장치의 설치 각도(59°, 50°, 90°)를 변화시켰을 때 세굴 현상이 어떻게 달라지는지 규명하는 것입니다.
Core study:
실험실 수로에서 그룹 원통형 교각 모델과 세 가지 다른 각도의 보호 장치를 사용하여 국부 세굴 깊이를 측정하고, 프루드 수에 따른 흐름 조건의 변화가 세굴 및 퇴적물 이동에 미치는 영향을 분석했습니다.
5. Research Methodology
Research Design:
통제된 실험실 환경에서 교각 보호 장치의 각도라는 독립 변수가 국부 세굴 깊이라는 종속 변수에 미치는 영향을 측정하는 실험 연구 설계를 채택했습니다.
Data Collection and Analysis Methods:
수로 내에 교각 및 보호 장치 모델을 설치하고, 특정 유속(프루드 수 기준) 조건에서 일정 시간 동안 흐름을 발생시킨 후, 교각 주변의 하상 변화(세굴 깊이)를 측정했습니다. 또한, 실험 전후의 하상 재료 입도 분석을 통해 퇴적물 이동 특성을 분석했습니다.
Research Topics and Scope:
연구는 그룹 원통형 교각, 커튼형 보호 장치, 그리고 세 가지 특정 설치 각도(59°, 50°, 90°)에 국한됩니다. 흐름 조건은 세 가지 아임계 흐름으로 제한되었으며, 하상 재료는 캄파르 강 모래를 사용했습니다.
6. Key Results:
Key Results:
레이놀즈 수에 근거하여, Fr1 흐름은 천이류(Re = 1658.416)로, Fr2 및 Fr3 흐름은 난류(Re > 2000)로 분류되었습니다.
교각 그룹 1에 대한 Fr1 시험에서, 세굴 깊이 비율(ds/b)은 59° 각도에서 1.3으로 가장 작았고, 90° 각도에서 1.5로 가장 컸습니다.
교각 그룹 1의 보호 장치에서는 50° 각도에서 세굴이 1.5(ds/b)로 가장 작았고, 90° 각도에서 2.4로 가장 컸습니다.
교각 그룹 2에서는 59°와 50° 각도에서 세굴이 1.3(ds/b)으로 가장 작았고, 90° 각도에서 1.4로 가장 컸습니다.
교각 그룹 2의 보호 장치에서는 50° 각도에서 세굴이 1.7(ds/b)로 가장 컸고, 90° 각도에서 1.4로 가장 작았습니다.
프루드 수가 증가할수록 더 큰 입경의 퇴적물이 이동하는 것으로 분석되었습니다.
Figure List:
Gambar 1. Ilustrasi gerusan lokal di sekitar pilar jembatan
Gambar 2. Metode pengendalian gerusan
Gambar 3. Recirculating sediment flume
Gambar 4. Ilustrasi 3D model pilar dan pengaman pilar jembatan (a) group pile 1, (b) group pile 2.
Gambar 5. Sudut Pengaman Pilar
Gambar 6. Bagan alir penelitian
Gambar 7. Distribusi kecepatan permukaan Fr1
Gambar 8. Grafik gerak awal butiran Shields
Gambar 9. Grafik Shields modifikasi Breusers dan Raudkivi
Gambar 10. Grafik gerak awal butiran Hjulstorm
Gambar 11. Ilustrasi pola aliran pada model pilar jembatan
Gambar 12. Posisi profil memanjang dan melintang pada pilar jembatan
Gambar 13. Potongan memanjang Sisi Dalam, Sisi Tengah dan Sisi Luar pada Fr1 θ1
Gambar 14. Potongan memanjang Sisi Dalam, Sisi Tengah dan Sisi Luar pada Fr2 θ1
Gambar 15. Potongan memanjang Sisi Dalam, Sisi Tengah dan Sisi Luar pada Fr3 θ1
Gambar 16. Potongan memanjang Sisi Dalam, Sisi Tengah dan Sisi Luar pada Fr₁ θ2
Gambar 17. Potongan memanjang Sisi Dalam, Sisi Tengah dan Sisi Luar pada Fr2 θ2
Gambar 18. Potongan memanjang Sisi Dalam, Sisi Tengah dan Sisi Luar pada Fr3 θ2
Gambar 19. Potongan memanjang Sisi Dalam, Sisi Tengah dan Sisi Luar pada Fr1 θ3
Gambar 20. Potongan memanjang Sisi Dalam, Sisi Tengah dan Sisi Luar pada Fr2 θ3
Gambar 21. Potongan memanjang Sisi Dalam, Sisi Tengah dan Sisi Luar pada Fr3 θ3
Gambar 22. Potongan memanjang C-C pada θ1
Gambar 23. Potongan memanjang H-H pada θ1
Gambar 24. Potongan memanjang C-C pada θ2
Gambar 25. Potongan memanjang H-H pada θ2
Gambar 26. Potongan memanjang C-C pada θ3
Gambar 27. Potongan memanjang H-H pada θ3
Gambar 28. Potongan melintang J-J
Gambar 29. Potongan melintang M-M
Gambar 30. Potongan melintang N-N
Gambar 31. Perkembangan rasio kedalaman (d/b) terhadap fungsi waktu (t)
Gambar 32. Hubungan d 50/d50 terhadap bilangan Froude
7. Conclusion:
실험실 모델을 통한 연구 결과, 교각 보호 장치의 각도와 흐름 조건은 국부 세굴 깊이에 상당한 영향을 미치는 것으로 나타났습니다. 레이놀즈 수 분석을 통해 흐름이 천이류 및 난류 영역에 있음을 확인했습니다. 세굴 깊이 비율(ds/b)은 보호 장치의 각도에 따라 민감하게 변화했으며, 특정 조건에서 최대 2.4에 도달했습니다. 또한, 프루드 수가 증가함에 따라 더 큰 퇴적물이 운반되는 현상을 통해 유속과 침식 에너지의 직접적인 관계를 입증했습니다. 이 결과들은 교량의 안전성 확보를 위해 세굴 보호 장치의 기하학적 설계가 매우 중요함을 강조합니다.
8. References:
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Expert Q&A: Your Top Questions Answered
Q1: 교각 보호 장치 실험에 59°, 50°, 90°라는 특정 각도를 선택한 이유가 무엇인가요?
A1: 논문에서는 이 세 가지 각도(θ1=59°, θ2=50°, θ3=90°)를 변수로 사용하여 실험을 수행했다고 명시하고 있으나, 이 특정 값들을 선택한 이론적 배경이나 이유는 구체적으로 설명하지 않았습니다. 이 연구는 주어진 각도 변화에 따른 세굴 현상을 관찰하고 정량화하는 데 초점을 맞춘 것으로 보입니다.
Q2: 연구에서 천이류와 난류 흐름이 모두 관찰되었는데, 이러한 흐름 특성의 차이가 세굴 결과에 어떤 영향을 미쳤나요?
A2: 연구 결과는 프루드 수(Fr1, Fr2, Fr3)에 따라 제시되었으며, 이는 각기 다른 흐름(천이류, 난류)에 해당합니다. 전반적으로 프루드 수가 높은 난류 조건(Fr2, Fr3)에서 세굴 깊이가 더 깊어지는 경향이 나타났습니다. 예를 들어, θ1 각도 조건에서 프루드 수가 증가함에 따라 만곡부 중앙과 내측의 세굴이 심화되는 것을 그림 13, 14, 15에서 확인할 수 있습니다. 이는 흐름의 에너지가 클수록 침식 능력이 강해진다는 것을 의미합니다.
Q3: 이 실험에서 ‘그룹 원통형’ 교각 타입을 사용한 것의 중요성은 무엇인가요?
A3: 본 연구에서 사용된 그룹 원통형 교각 모델은 실제 ‘Teratak Buluh’ 교량의 형태를 채택한 것입니다. 이는 실험 결과가 특정 실제 구조물과 직접적인 연관성을 갖도록 하여 연구의 실용성을 높입니다. 또한, 본문(C. Hubungan Pola Aliran Terhadap Pola Gerusan)에서는 그룹 교각의 경우 단일 교각에 비해 후류 와류(wake vortices)가 작게 형성되어 세굴 패턴에 영향을 미친다고 언급하고 있어, 교각의 형태가 세굴 메커니즘을 이해하는 데 중요한 요소임을 보여줍니다.
Q4: 쉴드(Shields) 및 휼스트롬(Hjulstorm) 다이어그램 분석 결과, 모든 퇴적물이 ‘이동 영역’에 있었다는 것은 무엇을 의미하나요?
A4: 이는 실험이 진행되는 동안 하상 재료가 흐름에 의해 지속적으로 움직이는 ‘이동상 세굴(live-bed scour)’ 조건에서 수행되었음을 의미합니다. 이는 하상 재료가 움직이지 않는 한계 유속 이하에서 발생하는 ‘정지상 세굴(clear-water scour)’과 구분되는 중요한 조건입니다. 이동상 세굴은 실제 하천의 홍수 시 발생하는 현상과 더 유사하며, 퇴적물의 유입과 유출이 동시에 일어나므로 더 복잡한 세굴 과정을 나타냅니다.
Q5: 만곡부의 내측, 중앙, 외측에서 세굴 패턴이 다르게 나타나는 이유는 무엇인가요?
A5: 서론에서 설명하듯이, 만곡 하천에서는 원심력의 영향으로 외측의 유속이 내측보다 빠릅니다. 이로 인해 외측 하상이 더 깊어지는 경향이 있습니다. 또한, 주 흐름과 함께 2차 흐름인 나선형 흐름(helicoidal flow)이 발생하여 바닥의 퇴적물을 내측으로 이동시키는 복잡한 흐름 구조가 형성됩니다. 이러한 복합적인 흐름 특성 때문에 만곡부의 위치에 따라 세굴과 퇴적이 다르게 나타나는 것입니다.
Conclusion: Paving the Way for Higher Quality and Productivity
본 연구는 교각 보호 장치의 설치 각도가 교각 세굴을 제어하는 데 얼마나 중요한 설계 변수인지를 실험 데이터를 통해 명확하게 보여주었습니다. 90°와 같은 단순한 각도가 오히려 더 큰 세굴을 유발할 수 있다는 사실은, 세심한 수리동역학적 분석 없이는 최적의 설계를 달성하기 어렵다는 점을 시사합니다.
이러한 물리적 실험은 CFD 시뮬레이션 모델의 정확성을 검증하는 데 필수적인 데이터를 제공합니다. CFD 해석을 활용하면 본 연구에서 다룬 세 가지 각도 외에도 훨씬 더 광범위한 각도, 유속, 교각 형상 조합을 빠르고 비용 효율적으로 탐색하여 진정한 최적의 설계안을 도출할 수 있습니다.
(주)에스티아이씨앤디에서는 고객이 수치해석을 직접 수행하고 싶지만 경험이 없거나, 시간이 없어서 용역을 통해 수치해석 결과를 얻고자 하는 경우 전문 엔지니어를 통해 CFD consulting services를 제공합니다. 귀하께서 당면하고 있는 연구프로젝트를 최소의 비용으로, 최적의 해결방안을 찾을 수 있도록 지원합니다.
연락처 : 02-2026-0442
이메일 : flow3d@stikorea.co.kr
Copyright Information
This content is a summary and analysis based on the paper “MODEL LABORATORIUM PENGARUH VARIASI SUDUT ARAH PENGAMAN PILAR TERHADAP KEDALAMAN GERUSAN LOKAL PADA JEMBATAN DENGAN PILAR CYLINDER GROUPED” by “Sarbaini, Mudjiatko, Rinaldi”.
Figure 13 | 3D illustration of Fr variation in the old stilling basin at (a) 129.10 m tailwater, (b) 129.70 m tailwater, and (c) 130.30 m tailwater.
In the new stilling basin at (d) 129.10 m tailwater, (e) 129.70 m tailwater, and (f) 130.30 m tailwater
이 소개자료는 “2023, Water Supply”에서 발표된 “Hydraulic investigation of stilling basins of the barrage before and after remodelling using FLOW-3D” 논문에 대한 소개자료입니다.
연구 목적
본 연구는 FLOW-3D를 사용하여 보의 감세지의 개조 전후 수리학적 성능을 조사하는 것을 목적으로 함.
연구 방법:
모델링 설정
FLOW-3D 소프트웨어를 사용하여 개조 전후의 감세지에서 자유 표면, 수심, 프루드 수, 롤러 길이, 유속, 도수 효율, 난류 운동 에너지와 같은 수리학적 매개변수를 시뮬레이션하고 비교 분석하였음.
개조 전 감세지에는 방해벽과 마찰 블록이 있었고, 개조 후에는 슈트 블록과 톱니 모양의 여울로 대체되었음.
문헌 결과와의 비교를 통해 모델의 정확성을 검증하였음.
모델 검증
FLOW-3D 모델을 사용하여 개조 전후 감세지의 수리학적 특성을 분석하고, 문헌 결과와 비교하였음.
감세지에서 발생하는 도수 현상의 특성을 파악하고, 개조가 도수에 미치는 영향을 평가하였음.
다양한 수리학적 매개변수를 비교 분석하여 모델의 신뢰성을 검증하였음.
주요 결과:
흐름 특성 분석
개조 전후 감세지에서의 자유 표면, 수심, 유속 분포 등을 FLOW-3D 모델을 통해 분석하였음.
도수 현상의 길이, 높이, 에너지 손실 등을 비교 분석하여 개조의 영향을 평가하였음.
난류 강도 및 롤러 특성을 분석하여 감세지 성능 변화를 파악하였음.
구조물 영향 평가
감세지의 크기 및 기하학적 형상이 수리학적 성능에 미치는 영향을 평가하였음.
개조 전후 감세지의 수리학적 매개변수를 비교하여 개조가 성능에 미치는 영향을 분석하였음.
수치 모의실험 결과를 바탕으로 감세지의 설계 및 운영 최적화 방안을 제시하였을 것으로 예상됨.
결론 및 시사점:
FLOW-3D를 이용한 수치 모델링은 보 감세지의 수리학적 성능을 분석하고 개조 효과를 평가하는 데 유용한 도구임이 확인되었음.
개조 전 감세지의 결과가 문헌 결과에 더 가까웠으며, 개조 후 감세지의 결과는 문헌 결과에서 벗어나는 경향을 보였음.
본 연구 결과는 감세지 설계 및 개조 시 수리학적 성능 변화를 예측하고 최적의 설계 방안을 도출하는 데 기여할 수 있을 것으로 기대됨.
Figure 2 | 3D representation of stilling basins: (a) modified USBR-III (1958–2004) and (b) USBR-II with dentated sill (2008–2022).
Figure 4 | Geometries resolution by the FAVOR method: (a) old stilling basin (1958–2004) and (b) new stilling basin (2008–2022).
Figure 13 | 3D illustration of Fr variation in the old stilling basin at (a) 129.10 m tailwater, (b) 129.70 m tailwater, and (c) 130.30 m tailwater.
In the new stilling basin at (d) 129.10 m tailwater, (e) 129.70 m tailwater, and (f) 130.30 m tailwater
레퍼런스:
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Chanson, H., & Brattberg, T. 1998 Experimental study of air entrainment in hydraulic jumps. International Journal of Multiphase Flow 24, 703–716.
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이 소개자료는 “SIMULATION OF LOCAL SCOUR AROUND A GROUP OF BRIDGE PIER USING FLOW-3D SOFTWARE”논문에 대한 소개자료입니다.
Figure 4.18 scour development at time = 360 min and discharge 0.057 m3/sec
연구 목적
본 연구는 FLOW-3D 소프트웨어를 사용하여 교각 그룹 주변의 국부 세굴을 시뮬레이션하는 것을 목적으로 함.
연구 방법:
모델링 설정
FLOW-3D 소프트웨어를 사용하여 교각 그룹 주변의 국부 세굴 현상을 수치적으로 모의실험하였음.
교각의 기하학적 형상 및 하천 흐름 조건을 모델에 반영하였음.
다양한 교각 배열 및 흐름 조건에 대한 모델링을 수행하여 세굴 특성을 분석하였음.
모델 검증
수치 모델의 결과를 실험실 데이터 또는 현장 관측 자료와 비교하여 검증하였을 것으로 예상됨.
세굴 깊이, 세굴공의 형태 등 주요 세굴 변수에 대한 모델의 예측 성능을 평가하였을 것으로 예상됨.
모델의 신뢰성을 확보하기 위해 민감도 분석 및 불확실성 분석을 수행하였을 것으로 예상됨.
주요 결과:
흐름 특성 분석
교각 그룹 주변의 유속, 압력 분포 등 흐름 특성을 FLOW-3D 모델을 통해 분석하였을 것으로 예상됨.
교각 배열이 흐름 패턴 및 와류 형성에 미치는 영향을 시각적으로 제시하였을 것으로 예상됨.
세굴 발생 메커니즘과 관련된 흐름 특성을 파악하여 세굴 예측의 정확도를 높였을 것으로 예상됨.
구조물 영향 평가
교각 그룹의 배열 방식이 세굴 깊이 및 세굴공의 크기에 미치는 영향을 평가하였을 것으로 예상됨.
교각 주변의 세굴 특성을 분석하여 교각 기초 설계 시 고려해야 할 중요한 요소를 제시하였을 것으로 예상됨.
수치 모의실험 결과를 바탕으로 교량의 안정성을 평가하고 설계 개선 방안을 제시하였을 것으로 예상됨.
결론 및 시사점:
FLOW-3D 소프트웨어를 이용한 수치 모델링은 교각 그룹 주변의 세굴 현상을 분석하고 예측하는 데 효과적인 도구임이 확인되었을 것으로 예상됨.
본 연구 결과는 교각 기초의 안정성을 확보하고 교량 붕괴를 예방하는 데 기여할 수 있을 것으로 기대됨.
향후 다양한 교각 조건 및 하천 흐름 조건에 대한 추가적인 연구를 통해 모델의 적용성을 확대할 필요가 있음.
Figure 3.1 Laboratory layout
Figure 3.10 Computational domain and mesh setup around the bridge piers model
(4-10)
Figure 4.18 scour development at time = 360 min and discharge 0.057 m3/sec
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이 소개 자료는 “Water Supply Vol 22 No 10″에 게재된 “Numerical simulation of pollution transport and hydrodynamic characteristics throughthe river confluence using FLOW 3D” 논문을 기반으로 작성되었습니다.
Figure 6 | (a) Contaminant concentration distribution (gr/L) at 13 cm distance from channel bed; (b) contaminant concentration distribution
(gr/L) at 17 cm distance from the channel bed.
1. 연구 목적
주요 연구 질문:
본 연구는 하천망의 지류를 통해 유입되는 오염 물질의 농도와 본류와 지류 간의 수위 차이가 오염 물질 혼합에 미치는 영향을 조사하는 것을 목표로 한다.
특히, 90도 각도로 합류하는 지류와 본류를 대상으로 오염 물질의 혼합과 확산, 그리고 그에 따른 수리학적 현상을 분석하고자 한다.
기존 연구의 한계:
기존의 합류점에서의 침식 및 퇴적 과정에 대한 연구는 많았으나, 오염 물질의 혼합 및 분포와 관련된 효과적인 매개 변수에 대한 정보는 여전히 부족하다.
따라서 본 연구는 오염 물질 혼합 및 분포에 대한 이해를 높이고, 오염 영향을 줄이기 위한 수위 조절 구조의 필요성을 강조하고자 한다.
2. 연구 방법
수치 모델링:
본 연구에서는 FLOW 3D 수치 모델을 사용하여 하천 합류점에서의 오염 물질 수송 및 수리학적 특성을 시뮬레이션하였다.
모델은 주류 7m, 폭 1m, 지류 길이 1.8m, 폭 1m, 높이 1m의 3차원 형상으로 설계되었으며, 합류점 부근에는 정확도를 높이기 위해 중첩 격자(nested mesh)를 사용하였다.
경계 조건:
주류와 지류의 상류에는 일정한 수압 조건(constant pressure)을 적용하였고, 주류 하류에는 자유 유출 조건(free outlet)을 설정하였다.
중첩 격자에는 다양한 방향으로부터의 경계 조건 유입을 고려하여 대칭 조건(symmetry boundary condition)을 적용하였다.
3. 주요 결과
수위 차이와 혼합:
지류와 본류 간의 수위 차이가 증가할수록 횡방향 혼합이 더 빠르게 일어나는 것을 확인하였다.
수위 차이가 없는 경우에는 혼합 곡선 추출 방법을 통해 횡방향 혼합이 완료되는 하천 길이를 파악하였다.
재순환 영역의 특징:
합류점의 재순환 영역에서 가장 높은 오염 물질 농도와 유속 벡터가 관찰되었으며, 2차 흐름이 발생하여 오염 물질을 일시적으로 가두는 현상을 확인하였다.
이 영역은 높은 전단 속도, 난류 에너지, 난류 강도를 가지며, 때로는 음의 회전 흐름으로 인해 낮은 종방향 유속을 나타냈다.
4. 결론
수위 조절의 중요성:
수위 차이는 지류에서 본류로 오염 물질이 유입되는 데 가장 중요한 요인이며, 본류의 오염 영향을 줄이기 위해 합류점에 수위 조절 구조를 설치하는 것이 필요하다.
본 연구에서 관찰된 합류점에서의 흐름 패턴과 영역들은 기존 연구와 일치했으며, 각 영역이 오염 물질 확산에 미치는 영향을 논의하였다.
향후 연구 방향:
재순환 영역에서 생성되는 와류는 오염 물질을 일시적으로 포획하고 농도를 증가시키는 데 효과적인 매개 변수이다.
지류에서 홍수 흐름이 발생하여 지류의 수위가 본류보다 높아지는 경우에만 합류점 상류에서 오염 농도 증가가 관찰되었다.
Figure 1 | Conceptual model of different flow pattern zones through the river confluence.
Figure 6 | (a) Contaminant concentration distribution (gr/L) at 13 cm distance from channel bed; (b) contaminant concentration distribution
(gr/L) at 17 cm distance from the channel bed.
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FLOW-3D를 이용한 다양한 정수지(Stilling Basin)에서의 수력 도약(Hydraulic Jump) 수치적 연구
Graphical Abstract
연구 배경 및 목적
문제 정의
Taunsa Barrage(파키스탄)의 정수지는 기존의 USBR Type-III Basin을 개량한 형태로, 충격 바플(Impact Baffle)과 마찰 블록(Friction Block) 포함.
하지만 운영 초기부터 바플 블록이 뽑히는 문제 발생 → 기존 사각형 바플 블록이 흐름 재부착(Flow Reattachment)과 낮은 항력(Drag) 문제를 가짐.
기존 연구에서는 쐐기형(Wedge-Shaped) 분리 블록(Splitter Blocks)의 사용이 제한적이었으며, 이들의 수력 도약(HJ) 및 에너지 소산 성능이 충분히 검토되지 않음.
연구 목적
FLOW-3D를 활용하여 USBR Type-III 및 쐐기형 바플 블록을 적용한 정수지에서의 수력 도약 및 유동 특성을 비교 분석.
자유 수면 프로파일, 롤러 길이(Roller Length), 상대 에너지 손실(Relative Energy Loss), 유속 분포 및 난류 운동 에너지(TKE) 분석.
새로운 정수지 설계가 HJ를 안정화하고 에너지 소산 성능을 향상시키는지 평가.
연구 방법
FLOW-3D 모델링 및 실험 검증
VOF(Volume of Fluid) 기법을 사용하여 자유 수면 추적.
RNG k-ε 난류 모델을 적용하여 유동장 해석 수행.
Taunsa Barrage의 USBR Type-III 및 개량된 쐐기형 바플 블록 정수지 모델을 구축하여 비교 실험.
수치 모델 설정
세 가지 정수지 유형 비교
Type-A: 기존 USBR Type-III 정수지
Type-B: 쐐기형 바플 블록 적용 정수지
Type-C: USBR 바플과 쐐기형 바플 블록을 혼합한 정수지
시험 조건
두 가지 유량 조건(44 m³/s, 88 m³/s)에서 실험 수행.
유입 Froude 수(Fr) 범위: 5.75까지 고려.
경계 조건: 유입부와 유출부는 압력(P), 벽면은 No-Slip 조건 적용.
주요 결과
자유 수면 프로파일 분석
Type-B 및 Type-C 정수지에서 수력 도약(HJ)이 더 짧고 안정적으로 형성됨.
유량 증가 시 HJ의 롤러 길이가 감소하는 경향을 보임.
Type-B 및 Type-C 정수지는 USBR Type-A보다 더 높은 상대 에너지 손실을 기록하여 효율적인 에너지 소산을 확인.
유속 및 난류 운동 에너지(TKE) 분석
Type-B 및 Type-C 정수지에서 난류 운동 에너지(TKE)가 빠르게 감소하여 난류 제어 효과가 우수함.
유속 분포 결과, Type-B 및 Type-C 정수지에서 바플 블록이 흐름을 효과적으로 분산시켜 유속 감소 효과를 제공.
전반적으로 Type-C(혼합형 정수지)가 가장 효과적인 유동 제어 및 에너지 소산을 제공함.
결론 및 향후 연구
결론
쐐기형 바플 블록을 포함한 Type-B 및 Type-C 정수지는 기존 USBR Type-III 모델보다 더 높은 에너지 소산 효과를 제공.
HJ 길이가 짧아지고, 전단 응력이 감소하여 침식 가능성이 줄어듦.
FLOW-3D를 이용한 시뮬레이션이 정수지 설계 최적화 및 유지보수 비용 절감에 기여할 수 있음.
향후 연구 방향
LES(Large Eddy Simulation) 및 더 정밀한 난류 모델을 적용하여 연구 정밀도를 향상.
보다 높은 유량(예: 100~500 m³/s)에서의 테스트 수행.
다양한 바플 블록 형상(예: 삼각형, 원형 등) 및 배열 최적화를 통한 추가 연구 진행.
연구의 의의
이 연구는 FLOW-3D를 활용하여 다양한 정수지 설계에서의 수력 도약(HJ) 및 에너지 소산 효과를 분석한 연구로, 기존 USBR Type-III 정수지의 문제점을 개선하고, 새로운 설계 방안을 제시함으로써 대형 수리 구조물의 안정성 향상 및 침식 저감에 기여할 수 있는 실질적인 데이터를 제공하였다.
Figure 12 At 44 m3 s, 2D illustration of the velocity contour after the HJ and at basin’s end in the Type-A stilling basin (a and b), Type-B stilling basin (c and d), and Type-C stilling basin (e and f)
Figure 14 At 88 m3 s, 2D illustration of the velocity contour after HJ and at basin’s end in the Type-A stilling basin (a and b), Type-B stilling basin (c and d), and Type-C stilling basin (e and f)
Figure 15 2D illustration of turbulent kinetic energy (TKE) and turbulent intensity (TI) at 44 m3 s discharge in (a and b) Type-A, (c and d) Type-B, and (e and f) Type-C stilling basins, respectively
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이 소개자료는 Sustainability에서 발표한 FLOW-3D Model Development for the Analysis of the Flow Characteristics of Downstream Hydraulic Structures 논문에 대한 소개자료입니다.
Figure 8. Numerical simulation results for the gate discharge test conditions, Case 1. (a) Case 1 surface velocity distribution. (b) Case 1 longitudinal velocity distribution of gate center.
연구 목적
본 연구는 하류 수리 구조물의 흐름 특성을 분석하기 위해 FLOW-3D 모델을 개발하는 것을 목표로 함.
연구 방법
모델링 설정
FLOW-3D 모델을 사용하여 3차원 비정상류 해석을 수행하였음.
하류 수리 구조물의 형상 및 주변 지형을 고려하여 계산 영역을 설정하였음.
적절한 난류 모델 및 경계 조건을 적용하여 모델의 정확도를 높였음.
모델 검증
실험실 또는 현장 측정 데이터를 확보하여 모델 예측 결과와 비교 분석하였음.
수위, 유속 등 주요 흐름 변수에 대한 모델의 적합성을 평가하였음.
모델 파라미터 민감도 분석을 통해 모델의 신뢰성을 검증하였음.
주요 결과
흐름 특성 분석
하류 수리 구조물 주변에서 발생하는 복잡한 흐름 패턴(예: 재순환, 박리)을 시각적으로 확인하였음.
구조물 특정 지점에서의 유속 및 압력 변화를 정량적으로 분석하였음.
설계 변수 변화에 따른 흐름 특성 변화를 파악하여 최적 설계 방안 도출의 기초 자료를 제공하였음.
구조물 영향 평가
하류 수리 구조물의 존재 유무에 따른 상하류 흐름 변화를 비교 분석하였음.
구조물 형상(예: 높이, 폭) 변화가 흐름 특성에 미치는 영향을 평가하였음.
특정 흐름 조건에서 구조물의 안정성 및 기능성을 예측하였음.
결론 및 시사점
본 연구에서 개발된 FLOW-3D 모델은 하류 수리 구조물의 흐름 특성 분석에 효과적인 도구로 활용될 수 있음.
모델링 결과를 바탕으로 하류 수리 구조물의 안정성 및 효율성을 향상시킬 수 있을 것으로 기대됨.
향후 다양한 형태의 하류 수리 구조물에 대한 모델링 및 실험 연구를 통해 모델의 적용 범위를 확대할 필요가 있음.
Figure 1. Effect of downstream riverbed erosion according to the type of weir foundation.
Figure 8. Numerical simulation results for the gate discharge test conditions, Case 1. (a) Case 1
surface velocity distribution. (b) Case 1 longitudinal velocity distribution of gate center.
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본 소개 자료는 “Arabian Journal for Science and Engineering”에서 발행한 “An Investigation on Hydraulic Aspects of Rectangular Labyrinth Pool and Weir Fishway Using FLOW-3D” 논문을 기반으로 합니다.
Fig. 9 Velocity vectors and the plunging flow for Model A (Q 0.035 m3/s; l 0.685 m; w 0.141 m)
연구 배경 및 목적
본 연구에서는 둑의 기하학적 매개변수(둑 모양, 둑 간격, 둑 오리피스 유무, 바닥 경사)가 흐름 체제, 유량-수심 관계, 수심 평균 유속의 변화 및 분포, 난류 특성, 어도에서의 에너지 소산 등에 미치는 영향을 평가하기 위해 서로 다른 두 가지 둑 배열(직선 둑 및 사각형 미로 둑)을 사용했음.
FLOW-3D® 소프트웨어를 사용하여 흐름 조건에 미치는 영향을 조사하기 위해 전산 유체 역학 시뮬레이션을 수행했음.
계산된 표면 프로파일 및 속도를 문헌에서 실험적으로 측정된 값과 비교하여 수치 모델의 유효성을 검증했음.
연구 방법
FLOW-3D® v11.2를 사용하여 Ead et al. [6]의 실험적인 라이너 풀 둑을 검증하고 오리피스가 있는 사각형 미로 풀 둑의 영향을 조사하기 위해 CFD(전산 유체 역학) 시뮬레이션을 수행했음.
수치 모델의 채널 및 데이터 수집 영역의 치수는 실험실 모델의 치수와 동일함.
두 가지 유형의 풀 둑, 즉 기존식과 미로식을 고려했음.
연구 결과
수치 모델과 실험 데이터 결과, 플런징 흐름의 표면 프로파일과 정규화된 속도 프로파일에 대한 RMSE(제곱 평균 제곱근 오차)와 MAPE(평균 절대 백분율 오차)는 각각 0.014m와 3.11%로, 수치 모델이 풀 및 둑의 흐름 특성을 예측하는 능력을 확인했음.
L/B=1.83 값에서 플런징 흐름이 발생할 수 있고(L: 둑의 거리, B: 채널의 폭), 각 모델에 대해 L/B=0.61에서 스트리밍 흐름이 발생할 수 있음.
사각형 미로 둑 모델은 기존 모델보다 큰 무차원 방전 값(Q+)을 가짐.
침수 흐름에서 기존 둑 및 사각형 미로 둑의 경우 Q는 각각 1.56h 및 1.47h에 비례함(h: 둑 위의 수심).
기존 둑의 풀에서 평균 수심 속도는 사각형 미로 둑의 평균 수심 속도보다 높음.
그러나 주어진 유량, 바닥 경사 및 둑 간격에서 난류 운동 에너지(TKE) 및 난류 강도(TI) 값은 기존 둑에 비해 사각형 미로 둑에서 더 높음.
기존 둑은 사각형 미로 둑보다 에너지 소산이 적음.
미로 둑 상단, 둑 하류 벽의 모서리, 둑의 측벽과 채널 벽 사이에서 더 낮은 TKE 및 TI 값이 관찰되었음.
둑 사이의 거리와 하단 경사가 증가함에 따라 평균 수심 속도, 난류 운동 에너지의 평균값 및 난류 강도가 증가하고 풀에서 체적 에너지 소산이 감소했음.
둑에 개구부가 있으면 평균 수심 속도 및 TI 값이 증가하고 풀 내에서 가장 높은 TKE 범위가 감소하여 물고기를 위한 더 넓은 휴식 공간(더 낮은 TKE)이 생성되고 두 모델 모두에서 에너지 소산율이 감소했음.
Fig. 9 Velocity vectors and the plunging flow for Model A (Q 0.035 m3/s; l 0.685 m; w 0.141 m)
참고 문헌
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Dasineh, M.; Ghaderi, A.; Bagherzadeh, M.; Ahmadi, M.; Kuriqi, A.: Prediction of hydraulic jumps on a triangular bed roughness using numerical modeling and soft computing methods. Mathematics 9, 3135 (2021)
Silva, A.T.; Bermúdez, M.; Santos, J.M.; Rabuñal, J.R.; Puertas, J.: Pool-type fishway design for a potamodromous cyprinid in the Iberian Peninsula: the Iberian barbel—synthesis and future directions. Sustainability 12, 3387 (2020). https://doi.org/10.3390/su12083387
Santos, J.M.; Branco, P.; Katopodis, C.; Ferreira, T.; Pinheiro, A.: Retrofitting pool-and-weir fishways to improve passage performance of benthic fishes: effect of boulder density and fishway discharge. Ecol. Eng. 73, 335–344 (2014). https://doi.org/10.1016/j.ecoleng.2014.09.065
Ead, S.; Katopodis, C.; Sikora, G.; Rajaratnam, N.J.J.: Flow regimes and structure in pool and weir fishways. J. Environ. Eng. Sci. 3, 379–390 (2004)
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본 소개 자료는 ‘Environmental Fluid Mechanics’에서 발행한 ‘Numerical simulation of local scour around the pier with and without airfoil collar (AFC) using FLOW-3D’ 논문을 기반으로 합니다.
Fig. 10 Transverse scour hole profles for six cases
1. 서론
교각 주변의 국부 세굴(local scour)은 수리 구조물의 안전성에 중대한 영향을 미치는 요소이며, 교량 붕괴의 주요 원인 중 하나임.
기존 연구에서는 다양한 세굴 저감 장치를 연구해 왔으며, 본 연구에서는 에어포일 컬러(Air-Foil Collar, AFC)의 효과를 평가하고자 함.
FLOW-3D를 이용하여 다양한 AFC 구성에서 세굴 깊이를 수치적으로 분석하고, 실험 결과와 비교하여 모델의 신뢰성을 검증함.
2. 연구 방법
FLOW-3D 기반 CFD 모델링
난류 해석: Large Eddy Simulation (LES) 모델 적용.
퇴적물 모델: van Rijn의 bed-load transport 모델 활용.
격자 설정: 12.234백만 개의 격자로 구성된 nested mesh 사용.
경계 조건:
유입부: 일정한 유속(velocity inlet) 적용.
유출부: 자유 배출(outflow) 조건 적용.
벽면: No-slip 조건 적용.
3. 연구 결과
AFC 적용 유무에 따른 세굴 특성 비교
AFC가 없는 경우 최대 세굴 깊이: 6.33cm.
AFC가 적용된 경우 세굴 깊이 감소 효과:
dc1 (2b) 컬러 적용 시: 77.78% 감소.
dc1R (역방향 2b) 컬러 적용 시: 46% 감소.
dc2 (3b) 컬러 적용 시: 100% 감소 (세굴 없음).
dc1 (2b) 컬러를 하단부에서 y/2 높이에 적용 시: 11.12% 감소.
dc2 (3b) 컬러를 하단부에서 y/2 높이에 적용 시: 42.86% 감소.
최대 세굴 깊이 및 세굴 형상 분석
AFC가 없는 경우, 세굴은 주로 교각 전면부에서 강하게 발생하며 후류(wake)에서 퇴적이 진행됨.
AFC 적용 시, 와류 강도가 감소하고 말굽 와류(horseshoe vortex) 및 후류 난류가 완화됨.
AFC의 위치 및 크기에 따른 효과 분석
dc2 (3b) 컬러를 교각 기초에 설치했을 때 세굴 방지가 가장 효과적.
dc1 (2b) 컬러의 경우 역방향(dc1R) 설치 시 세굴 감소 효과가 다소 감소.
4. 결론 및 제안
결론
AFC는 교각 주변 국부 세굴을 효과적으로 감소시킬 수 있는 구조적 솔루션임.
3b 크기의 컬러(dc2)를 교각 기초에 설치하는 것이 가장 효과적인 세굴 방지 방법으로 확인됨.
LES 모델을 활용한 수치 시뮬레이션 결과가 실험 결과와 7% 이내의 오차를 보이며 높은 신뢰도를 가짐.
향후 연구 방향
다양한 유속 및 침전 조건에서 추가 시뮬레이션 수행 필요.
실제 현장 데이터를 기반으로 AFC의 장기적인 효과 검증.
AFC 형상 최적화를 위한 설계 연구 수행.
5. 연구의 의의
본 연구는 FLOW-3D를 활용하여 AFC의 적용 유무에 따른 교각 주변 국부 세굴 특성을 수치적으로 분석하고, 실험 데이터를 통해 모델 신뢰성을 검증하였다. 이를 통해 향후 교량 설계 시 AFC 적용을 고려한 세굴 방지 전략을 제안할 수 있는 실질적인 데이터를 제공한다.
Fig. 3 a Meshing around the geometry and b boundary conditions annotated
Fig. 4 Scour hole profle from Melville and Raudkivi [16] and simulated results
Fig. 10 Transverse scour hole profles for six cases
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본 소개 논문은 Engineering Applications of Computational Fluid Mechanics에서 발행한 논문 “Numerical Modeling of Flow Over Trapezoidal Broad-Crested Weir”의 연구 내용입니다.
Fig. 9 Velocity vectors for Q = 0.0181 m3/s in the area of the broad-crested weir.
1. 서론
넓은 마루 위어(Broad-Crested Weir, BCW)는 수리학적 구조물로서 홍수 조절, 유량 측정 및 관개 시스템에서 활용됨.
BCW의 형상, 특히 사다리꼴 형태는 유량 및 에너지 손실에 영향을 미칠 수 있으며, 기존 실험적 연구와 함께 수치 모델링이 중요함.
본 연구에서는 FLOW-3D 및 SSIIM 2 소프트웨어를 사용하여 사다리꼴 BCW의 유동 특성을 분석하고, 수치 결과를 물리 실험 결과와 비교하여 모델링 정확도를 평가함.
2. 연구 방법
FLOW-3D 및 SSIIM 2 기반 CFD 모델링
VOF(Volume of Fluid) 기법을 사용하여 자유 수면을 추적.
Reynolds-Averaged Navier-Stokes (RANS) 방정식과 k-ε 난류 모델을 적용하여 난류 해석 수행.
FAVOR(Fractional Area/Volume Obstacle Representation) 기법을 활용하여 복잡한 구조물 형상을 반영.
SSIIM 2는 적응형(adaptive) 격자를 사용하며, Marker-and-Cell(MAC) 접근법을 적용하여 자유 수면을 계산.
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
FLOW-3D와 SSIIM 2 결과 비교
두 모델 모두 물리 실험 결과와 유사한 자유 수면 프로파일을 예측하였으며, 계산된 유량 계수(Discharge Coefficient, Cd)는 실험 값과 ±3% 이내의 차이를 보임.
FLOW-3D는 격자가 고정되어 있으며, 평균 435~550초의 계산 시간이 소요됨.
SSIIM 2는 적응형 격자를 사용하여 격자 수가 변하며, 계산 시간이 12,500~15,500초로 상대적으로 길었음.
유량 변화(Q = 0.0181 ~ 0.0055 m³/s)에 따른 자유 수면 프로파일 분석 결과, 두 모델 간 수위 차이는 1~1.5% 범위 내에 존재.
압력 및 유속 분포 분석
FLOW-3D의 결과에서는 위어 전면부에서 압력이 최대치를 기록하며, 후면부에서는 압력이 급격히 감소.
SSIIM 2에서도 유사한 압력 분포가 확인되었으나, 자유 수면 프로파일 계산에서 다소 차이가 발생.
속도 벡터 분석 결과, 위어 전면부에서 흐름이 가속되고 후면부에서 난류 강도가 증가하는 패턴이 관측됨.
4. 결론 및 제안
결론
FLOW-3D 및 SSIIM 2를 활용한 시뮬레이션은 사다리꼴 BCW 유동 해석에서 높은 신뢰도를 보였으며, 실험 결과와의 비교를 통해 모델의 타당성이 검증됨.
FLOW-3D는 고정 격자와 높은 계산 효율성을 제공하며, SSIIM 2는 적응형 격자를 활용하여 자유 수면의 변화를 보다 세밀하게 반영.
전체적인 Cd 값은 실험 데이터와 잘 일치하며, 실험과의 평균 오차율이 3% 이내임.
향후 연구 방향
3D 모델링을 활용하여 더욱 정밀한 유동 분석 수행.
LES(Large Eddy Simulation) 및 다른 난류 모델과의 비교 연구 필요.
자연 하천 환경에서의 적용 가능성을 평가하기 위한 추가 연구 필요.
5. 연구의 의의
본 연구는 FLOW-3D 및 SSIIM 2를 이용하여 사다리꼴 BCW에서의 유동 특성을 분석하고, 실험 결과와 비교하여 모델 신뢰성을 검증하였다. 이를 통해 수리 구조물 설계 및 유량 측정 기술 향상에 기여할 수 있는 실질적인 데이터 및 분석 방법을 제공한다.
Sketch of the orthogonal, structured and nonadaptive grid (hexahedral), used in Flow-3D. In the computations a finer grid is used.
Fig. 9 Velocity vectors for Q = 0.0181 m3/s in the area of the broad-crested weir.
6. 참고 문헌
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Hirt CW, Nichols BD (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39:201–225.
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Patankar SV (1980). Numerical Heat Transfer and Fluid Flow. McGraw-Hill Book Company, New York.
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Schlichting H (1979). Boundary layer theory. McGraw-Hill Book Company, New York.
Williams JJR (2007). Free-surface simulations using an interface-tracking finite-volume method with 3D mesh movement. Engineering Applications of Computational Fluid Mechanics, 1(1):49–56.
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
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. 4- The boundary conditions of the congressional overflow model
Fig.5- View of a simulated congressional overflow
References
Crookston, B. M. and Tullis, B. P., 2012a. Arced labyrinth weirs. Journal of Hydraulic Engineering. 138(6), pp.555-562.
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.
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.
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.
Tullis, J. P., Amanian, N. and Waldron, D., 1995. Design of labyrinth spillways. Journal of Hydraulic Engineering. 121(3), pp.247-255.
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).
Hirt, C. W. and Richardson, J. E., 1999. The modeling of shallow flows, Flow Science, Technical Notes. 48, pp.1-14.
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).
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.
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).
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).
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.
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).
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.
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.
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).
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.
Suprapto, M., 2013. Increase spillway capacity using Labyrinth Weir. Procedia Engineering. 54, pp. 440-446.
Tullis, J. P., Amanian, N. and Waldron, D., 1995. Design of labyrinth spillways. Journal of Hydraulic Engineering. 121(3), pp.247-255.
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).
본 소개 내용은 [DESERT]에서 발행한 [“Simulation of local scour caused by submerged horizontal jets with Flow-3D numerical model”] 의 연구 내용입니다.
Fig. 1. A view of experimental flume model (Hosseini, 2008)
1. 서론
교각, 위어, 밸브, 소파공(stilling basin) 등의 수리 구조물 주변에서 발생하는 국부 세굴(local scour)은 구조물의 안정성을 위협할 수 있음.
침수된 수평 제트(submerged horizontal jet)에 의해 발생하는 세굴은 고속 유동과 저속 유체의 상호 작용으로 인해 복잡한 유동장을 형성함.
본 연구는 FLOW-3D를 이용하여 실험 모델과 수치 모델을 비교하여 수치 모델의 정확성을 평가하고, 제트 형상, 개수로 흐름 조건, 세굴 패턴 등을 분석하는 것을 목표로 함.
2. 연구 방법
FLOW-3D 기반 CFD 모델링
VOF(Volume of Fluid) 기법을 사용하여 자유 수면을 추적.
RNG k-ε 난류 모델을 적용하여 난류 효과 해석.
FAVOR(Fractional Area/Volume Obstacle Representation) 기법을 활용하여 복잡한 형상을 정밀하게 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
세굴 패턴 분석
FLOW-3D 모델과 실험 모델 비교 결과 평균 오차율이 약 11%로 확인됨.
제트 유출 속도가 증가할수록 최대 세굴 깊이가 증가하는 경향을 보임.
세굴 깊이 비교
실험 모델과 비교 시 FLOW-3D의 예측 값이 실험 값과 유사하게 나타남.
유량 1.0 ℓ/s에서 실험값 1.50 cm, 수치해석값 1.70 cm(오차율 11.8%).
유량 4.0 ℓ/s에서 실험값 6.85 cm, 수치해석값 6.10 cm(오차율 12.3%).
세굴장 길이 분석
3mm 입경의 세굴장 길이에서 평균 오차율 13.82%.
1mm 입경의 세굴장 길이에서 평균 오차율 12.58%.
세굴장 후방의 사구(hump) 높이 비교
사구 높이에 대한 평균 오차율이 26.12%로, 다른 변수들보다 상대적으로 오차가 큼.
4. 결론 및 제안
결론
FLOW-3D 기반 시뮬레이션을 통해 침수된 수평 제트로 인한 국부 세굴 패턴을 정량적으로 분석할 수 있음.
세굴 깊이는 비교적 정확하게 예측되었으나, 세굴장 후방의 사구 높이는 다소 과소 예측됨.
입경이 클수록 수치 모델과 실험 모델 간 오차가 감소하는 경향을 보임(3mm 입경에서 보다 정확한 결과 도출됨).
향후 연구 방향
다양한 유입 조건 및 퇴적물 특성에 따른 추가 시뮬레이션 수행.
LES(Large Eddy Simulation) 모델과 비교 연구 필요.
실제 현장 데이터를 기반으로 모델 검증 연구 수행.
5. 연구의 의의
본 연구는 FLOW-3D를 활용하여 침수된 수평 제트로 인해 발생하는 국부 세굴 특성을 정량적으로 분석하고, 실험 데이터와 비교하여 모델의 신뢰성을 검증하였다. 이를 통해 수리 구조물 설계 시 세굴 방지 대책 수립에 기여할 수 있는 실질적인 데이터 및 분석 방법을 제공한다.
Fig. 1. A view of experimental flume model (Hosseini, 2008)
Fig. 3. A Plan of 2D graphical output of scour simulation results in Flow-3D numerical model
6. 참고 문헌
Abdelaziz, S., M.D. Bui, P. Rutschmann, 2010. Numerical simulation of scour development due to submerged horizontal jet. River Flow. Process of the International Conference on Fluvial Hydraulics, 8–10 September, Braunschweig, Germany.
Ali Hosseini, P., 2008. The study of local scour due to submerged horizontal Jets using experimental models. M.Sc. Thesis, University of Tehran, Tehran, Iran.
Amir Aslani, Sh., M. Pirestani, A.A. Salehi neishabouri, 2008. Numerical study on the effects of internal friction angle of sediments on scour hole caused by free fall Jet. 2nd National Conference on Dam and Hydroelectric Power Plants, 14&15 May, Tehran, Iran.
Bakhiet, Sh., G.A. Abdel-Rahim, K.A. Ali, N. Izumi, 2013. Prediction of scour downstream regulators using ANNs. International Journal of Hydraulic Engineering, 2; 1-13.
Baranya S., J. Jozsa, 2006. Flow analysis in river Danube by field measurement and 3D CFD turbulence modelling. Journal of Periodica Polytechnica. Civil Engineering, 50; 57–68.
Chatterjee, S., S. Ghoch, 1980. Submerged horizontal jet over erodible bed, Journal of the Hydraulics Division Proceedings of the American Society of Civil Engineers, 106; 1765-1782.
Day, S., A. Sarkar, 2008. Characteristics of turbulent flow in submerged jumps on rough beds. Journal of Engineering Mechanic, 134; 49-59.
Hager, W., H. Hans Erivin Minor, 2005. Plunge pool in prototype and laboratory. Hydraulics of Dam and River structures, London, 165-172.
Hussein H.H, A.k.J. Inam, I.H. Nashwan, 2012. Evaluation of the local scour downstream untraditional bridge piers. Journal of Engineering and Development, 16; 36 – 49.
Hamidifar, H., M.H. Omid, M. Nasrabadi, 2011. Scour downstream of a rough rigid apron. World Applied Sciences Journal 14; 1169-1178.
Hopfinger, E.J., A. Kurniawan, W.H. Graf, W.U. Lemmin, 2004. Sediment erosion by Görtler vortices: The scour-hole problem. Journal of Fluid Mechanics, 520; 327-342.
Karim, O.A., K.H.M. Ali, 2000. Prediction of patterns in local scour holes caused by turbulent water jets. Journal of Hydraulic Research, 38; 279-287.
Khosronejad, A., S. Kang, F. Sotiropoulos, 2012. Experimental and computational investigation of local scour around bridge piers. Journal of Advances in Water Resources, 37; 73-85.
Liu, X., M. García, 2008. Three-dimensional numerical model with free water surface and mesh deformation for local sediment scour. Journal of Waterway, Port, Coastal, and Ocean Engineering, ASCE, 134; 203–217.
본 소개 내용은 [Iranian Journal of Irrigation and Water Engineering]에서 발행한 [“Numerical Simulation of the Bed Scouring Downstream Triangular Labyrinth Weirs Using Flow-3D”] 의 연구 내용입니다.
Myer-Peter-Muller Model
서론
연구 배경 및 필요성
선형 위어에 비해 래버린스 위어는 폭 증가를 통해 흐름 용량을 증가시켜 특별한 관심을 받아왔음.
위어 하류의 세굴 및 침식은 구조물 보호를 위해 중요하며, 위어 통과 유량 증가로 인해 하류 세굴량도 증가함.
본 연구는 삼각형 평면을 가진 래버린스 위어의 수치 모델을 연구함.
연구 목표
다양한 요인(댐 본체 높이, 위어 정점 높이, 위어 통과 유량, 위어 정점 각도)이 래버린스 위어 하류의 하상 침식량에 미치는 영향을 연구하기 위해 23개의 모델을 Flow-3D 소프트웨어를 사용하여 시뮬레이션함.
수치 시뮬레이션 결과와 실험 모델 결과의 검증을 통해 수치 시뮬레이션과 실험값 간의 매우 우수한 일치를 확인함.
연구 방법
연구 설계
3가지 정점 각도를 가진 삼각형 래버린스 위어 하류의 하상 세굴을 연구함.
길이 10m, 폭 50cm, 높이 80cm의 인공 소형 수로에서 수치 모델을 수행함.
4가지 위어 정점 각도(90°, 60°, 45°)를 테스트함.
수치 모델링
수로의 물 흐름과 상단의 공기 영역을 포함하는 다상 계산 영역을 다상 흐름 모델로 시뮬레이션함.
계산 영역 준비 시 적절한 메시 생성은 매우 중요하며, 셀 크기가 세굴에 미치는 영향을 조사하기 위해 3가지 다른 셀 수를 적용함.
FLOW-3D는 광범위한 산업 응용 분야 및 물리적 프로세스에서 액체 및 기체의 동적 거동을 연구하는 엔지니어를 위한 완벽하고 다재다능한 CFD 시뮬레이션 플랫폼을 제공함.
연구 결과
세굴 매개변수
다양한 흐름 조건에서 래버린스 위어 하류의 최대 세굴 깊이, 최대 세굴 길이, 최대 퇴적 깊이 및 최대 퇴적 길이를 조사하기 위해 수치 시뮬레이션을 수행함.
세굴 매개변수를 최소화하는 최적의 정점 각도를 찾기 위해 3가지 다른 위어 정점 각도(90°, 60°, 45°)에 대해 모델을 실행함.
선형 위어 정점에 대한 최대 세굴 매개변수도 측정하여 비교함.
결과 분석
제시된 정점 각도로 삼각형 래버린스 위어를 사용하면 모든 세굴 및 퇴적 현상이 선형 위어에 비해 감소함.
시뮬레이션 결과, 60°의 위어 정점 각도가 모든 세굴 및 퇴적 매개변수에서 더 큰 감소를 나타냄.
선형 위어에 비해 상대 세굴 깊이, 세굴 길이, 퇴적 깊이 및 퇴적 길이에서 각각 약 89%, 77%, 45% 및 49% 감소가 관찰됨.
결론
연구의 의의
시뮬레이션 결과는 세굴 현상을 감소시키는 매우 효율적인 수단으로서 삼각형 래버린스 위어의 신뢰성을 나타냄.
모든 위어 정점 각도에서 다양한 세굴 및 퇴적 매개변수의 감소가 관찰됨.
최적의 위어 설계
선형 위어에 비해 60°의 위어 정점 각도에서 더 낮은 세굴 매개변수가 획득됨.
결론적으로, 최적의 위어 정점 각도인 60°는 선형 위어에 비해 세굴 매개변수를 최소화하고 에너지 소산을 최대화하는 잠재력을 가짐.
세굴 지도는 대칭이며, 최대 세굴은 이동상 하상의 세로 중심선 좌우에서 발생함.
Van Rijn Model
Myer-Peter-Muller Model
Reference
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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 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
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.
Alabi, P.D. 2006. Time development of local scour at bridge pier fitted with a collar. Master Science Thesis, University of Saskatchewan, Canada.
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.
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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.
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사각형 및 원형 교각 주변 유속은 유사한 분포를 보였으며, 최대 유속은 교각 측면에서 2배 증가.
교각 후면부에서 난류 및 역류(Reverse Flow) 발생.
다중 교각
Tandem 배치:
후방 교각 전면의 유속이 감소 → 전방 교각이 방패 역할 수행.
S/D = 2에서 난류 강도가 가장 크며, S/D ≥ 6에서는 서로 독립적인 흐름 형성.
Side-by-side 배치:
교각 간격이 작을수록(S/D = 2) 두 교각 사이 유속이 증가하여 침식 위험 증가.
S/D ≥ 6에서는 두 교각이 서로 독립적인 영향을 미침.
난류 운동 에너지(Turbulent Kinetic Energy, TKE) 분석
TKE는 교각 후방에서 가장 높은 값을 보이며, 이는 난류 생성과 관련됨.
Tandem 배치에서는 S/D = 2에서 후방 교각이 보호 효과를 받으며, S/D = 4에서 TKE가 최대값을 기록 후 S/D = 6에서 감소.
Side-by-side 배치에서는 S/D = 2에서 두 교각 사이 난류가 증가했으며, S/D ≥ 6에서는 TKE가 독립적인 분포를 형성.
전단 응력(Shear Stress) 분석
침식이 시작되기 전 상태에서 하상 전단 응력을 평가.
단일 교각: 최대 전단 응력은 교각 전면 및 측면에서 발생.
다중 교각:
Tandem 배치에서는 S/D = 2에서 후방 교각의 전단 응력이 낮아지고, S/D = 4에서 최대값을 기록.
Side-by-side 배치에서는 S/D = 2~4에서 교각 사이 전단 응력이 가장 높으며, S/D = 6에서는 개별 교각과 유사한 패턴을 보임.
결론 및 향후 연구
결론
FLOW-3D 기반 비침식성 하상 시뮬레이션을 통해 교각 주변 유동 특성을 정량적으로 분석 가능.
단일 교각(사각형, 원형) 주변 유동 특성은 거의 유사하며, 교각 형상이 큰 차이를 만들지는 않음.
다중 교각 배치에서 S/D = 2~4 구간이 가장 불안정하며, S/D ≥ 6에서는 독립적인 유동장 형성.
비침식성 하상 조건에서의 유동 특성 연구를 통해 침식 시작 전에 교각 설계를 최적화할 수 있음.
향후 연구 방향
LES(Large Eddy Simulation) 기반 난류 모델 적용하여 더욱 정밀한 유동 해석 수행.
다양한 하상 조건(침식성 및 비침식성)에 따른 비교 연구 진행.
실제 교량 구조물 적용을 위한 현장 실험 및 검증 연구 수행.
연구의 의의
이 연구는 FLOW-3D를 이용하여 비침식성 하상에서 단일 및 다중 교각 주변 유동 특성을 분석한 연구로, 교각 설계 최적화 및 침식 저감 대책 수립에 기여할 수 있는 실질적인 데이터를 제공하였다.
Fig. 2 The scenario of simulated experiments in the present study
Fig. 8 TKE values around the group pier in a non-erodible substrate state
Fig. 9 The shear stress near the bed surface around the group pier and single pier in a non-erodible bed
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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.
Fig. 4 Numerical mesh and boundary conditions of vortex settling basinFig. 8 Computation of (TKE) in horizontal sections of basin at end time of simulation
6. 참고 문헌
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.
Mashauri, D.A., 1986. Modeling of vortex settling chamber for primary clarification of water. PhD thesis, Tampere University of Technology, Tampere, Finland, pp: 217.
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.
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.
Cecen, K. and N. Akmandor, 1973. Circular settling basins with horizontal floor. MAG Report No 183, TETAK, Ankara, Turkey.
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.
Mashauri, D.A., 1986. Modeling of vortex settling chamber for primary clarification of water, PhD thesis, Tampere University of Technology, Tampere, Finland, pp: 217.
Anwar, H.O., 1969. Turbulent flow in a vortex. J. Hydr. Res., 7(1): 1-29.
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
H. W. Shen and B. C. Yen, “Advances in open-channel hydraulics after V.T. Chow’s book,” Journal of Hydrology, vol. 68, no. 1, pp. 333–348, Feb. 1984.
M. Jovanović, “The Hydraulics of Open Channel Flow – An Introduction, Hubert Chanson; Wiley, New York, 1999, 495 pages (index included), pbk, ISBN 0-470-36103-4 (£35.00), http://www.arnoldpublishers.com,”Urban Water, vol. 1, no. 3, p. 270, Sep. 1999.
C. T. Haan, B. J. Barfield, and J. C. Hayes, “4 – Open Channel Hydraulics,” in Design Hydrology and Sedimentology for Small Catchments, San Diego: Academic Press, 1994, pp. 104–143.
R. D. Reitz and Y. Sun, “18 – Advanced computational fluid dynamics modeling of direct injection engines,” in Advanced Direct Injection Combustion Engine Technologies and Development, vol. 2, Woodhead Publishing, 2010, pp. 676–707.
P. Wesseling and C. W. Oosterlee, “Geometric multigrid with applications to computational fluid dynamics,” Journal of Computational and Applied Mathematics, vol. 128, no. 1, pp. 311–334, Mar. 2001.
M. Pfister and W. H. Hager, “Self-entrainment of air on stepped spillways,” International Journal of Multiphase Flow, vol. 37, no. 2, pp. 99–107, Mar. 2011.
J. Wu and C. Luo, “Effects of entrained air manner on cavitation damage,” Journal of Hydrodynamics, Ser. B, vol. 23, no. 3, pp. 333–338, Jun. 2011.
J. Chatila and M. Tabbara, “Computational modeling of flow over an ogee spillway,” Computers & Structures, vol. 82, no. 22, pp. 1805–1812, Sep. 2004.
H. Chanson, “20 – Design of drop structures and stepped cascades,” in Hydraulics of Open Channel Flow (Second Edition), Oxford: Butterworth-Heinemann, 2004, pp. 431–439.
A. Bagis and D. Karaboga, “Evolutionary algorithm-based fuzzy PD control of spillway gates of dams,” Journal of the Franklin Institute, vol. 344, no. 8, pp. 1039–1055, Nov. 2007.
M. Tabbara, J. Chatila, and R. Awwad, “Computational simulation of flow over stepped spillways,” Computers & Structures, vol. 83, no. 27, pp. 2215–2224, Oct. 2005.
H. Chanson and L. Toombes, “Air–water flows down stepped chutes: turbulence and flow structure observations,” International Journal of Multiphase Flow, vol. 28, no. 11, pp. 1737–1761, Nov. 2002.
E. A. Elnikhely, “Investigation and analysis of scour downstream of a spillway,” Ain Shams Engineering Journal, vol. 9, no. 4, pp. 2275–2282, Dec. 2018.
M. Zhenwei, Z. Zhiyan, and Z. Tao, “Numerical Simulation of 3-D Flow Field of Spillway based on VOF Method,” Procedia Engineering, vol. 28, pp. 808–812, Jan. 2012.
A. Kamyab Moghaddam, A. Hamedi, and S. Amirahmadian, “Experimental Study of Energy Loss in a Stepped Spillway Equipped with Inclined Steps in the Nappe and Skimming Flow Regimes,” International Journal of Science and Engineering Applications, vol. 11, no. 12, pp. 346–350, 2022.
O. Herrera-Granados, “Chapter 19 – Theoretical background and application of numerical modeling to surface water resources,” in Current Directions in Water Scarcity Research, vol. 7, M. Zakwan, A. Wahid, M. Niazkar, and U. Chatterjee, Eds., in Water Resource Modeling and Computational Technologies, vol. 7, Elsevier, 2022, pp. 319–340.
W. de Q. Lamas, F. F. Bargos, G. E. O. Giacaglia, F. J. Grandinetti, and L. de Moura, “Numerical modelling and simulation of multi-phase flow through an industrial discharge chute,” Applied Thermal Engineering, vol. 125, pp. 937–950, Oct. 2017.
R. Gentle, P. Edwards, and B. Bolton, “3 – Fluid mechanics,” in Mechanical Engineering Systems, R. Gentle, P. Edwards, and B. Bolton, Eds., in IIE Core Textbooks Series, Oxford: Butterworth-Heinemann, 2001, pp. 112–168.
W. C. Chin, “10 – Advanced Modeling Methods,” in Computational Rheology for Pipeline and Annular Flow, W. C. Chin, Ed., Woburn: Gulf Professional Publishing, 2001, pp. 241–253.
G. H. Yeoh and J. Tu, “Chapter 3 – Solution Methods for Multi-Phase Flows,” in Computational Techniques for Multiphase Flows, G. H. Yeoh and J. Tu, Eds., Oxford: Butterworth-Heinemann, 2010, pp. 95–242.
FLOW-3D 세굴 모델을 이용한 보(Barrage) 하류 정수지(Stilling Basin)의 성능 평가
Figure 14. Patterns of sediment beds downstream of different basins with RNG K-e model at design discharge of 24.30 m3/s/m (a) Type-I, (b) Type-II, and (c) Type-III
연구 배경 및 목적
문제 정의
파키스탄 평야 지역의 주요 보(Barrage)들은 50~100년 전에 건설되었으며, 지속적인 침식과 구조적 결함 문제를 겪고 있음.
과거에는 미국 USBR(United States Bureau of Reclamation) Type III 정수지가 사용되었으나, 에너지 소산 효율이 낮아 개량이 필요함.
최근 개량된 USBR Type II 및 쐐기형 바플 블록(Wedge-Shaped Baffle Blocks, WSBB) 설계의 성능을 비교할 필요가 있음.
연구 목적
FLOW-3D를 활용하여 USBR Type III, Type II, WSBB 정수지 모델을 구축하고 성능을 비교 분석.
유속 분포, 국부적 전단 응력(BSS, Bed Shear Stress), 세굴 깊이 및 세굴 길이 평가.
설계 방류량(28.30 m³/s/m) 및 홍수 방류량(17.5 m³/s/m) 조건에서 성능을 평가하여 최적의 설계를 도출.
연구 방법
수치 모델 설정 (FLOW-3D 적용)
VOF(Volume of Fluid) 기법을 사용하여 자유 수면 추적.
RNG k-ε 난류 모델을 적용하여 난류 특성 모사.
격자(cell) 크기: 비균일(non-uniform) 격자 사용, 3D CAD 모델링 적용.
경계 조건:
유입부: 실험 유량(28.30 m³/s/m 및 17.5 m³/s/m) 적용.
유출부: 자유 방출 조건 적용.
바닥 및 벽면: No-slip 조건 적용.
비교 모델
USBR Type III (기존 설계)
USBR Type II (개량 설계)
WSBB (쐐기형 바플 블록 설계)
주요 결과
유속 분석
설계 방류량(28.30 m³/s/m) 조건에서 USBR Type III 모델은 유속이 가장 높고, WSBB 모델이 가장 낮았음.
WSBB 모델의 경우 바플 블록으로 인해 유속이 효과적으로 감소.
홍수 방류량(17.5 m³/s/m) 조건에서도 WSBB 모델이 가장 낮은 유속을 보이며 안정적 흐름 형성.
전단 응력(BSS) 분석
USBR Type III 및 Type II 모델은 높은 전단 응력을 보여 하류 침식 가능성이 높음.
WSBB 모델에서는 전단 응력이 감소하여 세굴을 효과적으로 줄임.
세굴 분석
USBR Type III 모델에서는 하류 강바닥이 완전히 노출됨(침식 심화).
USBR Type II 모델에서는 침식이 85% 감소하였으나 여전히 문제가 있음.
WSBB 모델에서는 침식이 가장 적었으며, 세굴 깊이가 최소화됨.
결론 및 향후 연구
결론
WSBB 정수지가 USBR Type II 및 Type III 모델보다 더 효과적으로 에너지를 소산하고 하류 침식을 줄임.
USBR Type II 모델은 기존 USBR Type III 모델보다 개선되었으나 여전히 침식 문제가 존재.
FLOW-3D 모델이 정수지 설계 최적화 및 침식 저감 대책 수립에 활용 가능함.
향후 연구 방향
LES(Large Eddy Simulation) 적용을 통한 난류 모델 개선.
실제 현장 실험과의 비교 검증을 통한 모델 정밀도 향상.
다양한 보(Barrage) 및 정수지 형상에 대한 추가 연구 수행.
연구의 의의
이 연구는 FLOW-3D를 활용하여 다양한 정수지 설계의 성능을 비교 분석한 연구로, 보 하류 침식 저감을 위한 최적 설계를 위한 기초 데이터를 제공하였다.
Figure 2. Energy dissipation arrangement, (a) old basin (Type I), (b) remodeled basin (Type II), and (c) WSBB basin (Type III)
Figure 14. Patterns of sediment beds downstream of different basins with RNG K-e model at design discharge of 24.30 m3/s/m (a) Type-I, (b) Type-II, and (c) Type-III
Figure 15. Patterns of sediment beds downstream of different basins with RNG K-e model at design discharge of 17.5 m3/s/m (a) Type-I, (b) Type-II, and (c) Type-III
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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
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
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Azimi H, Shabanlou S, Ebtehaj I, Bonakdari H (2016). “Discharge Coefficient of Rectangular Side Weirs on Circular Channels.” International Journal of Nonlinear Sciences and Numerical Simulation, 17(7–8), 391–399. https://doi.org/10.1515/ijnsns-2016-0033
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이를 해결하기 위해 어도(fishway)가 설치되지만, 현재 어도 설계는 어류의 이동 특성과 유동 특성을 충분히 고려하지 못하고 있음.
기존 연구는 주로 수리 실험(laboratory experiment)에 의존했으나, 이는 시간·비용의 제약이 크므로 수치 해석(numerical simulation)을 통한 검토가 필요함.
연구 목적
FLOW-3D를 활용하여 도류벽식 어도(Baffled Fishway) 내 유동 특성을 수치적으로 해석.
수리 실험 결과와 비교하여 FLOW-3D 모델의 정확성을 평가.
어도 내 유속 분포 및 난류 특성을 분석하여 최적의 설계 방안을 도출.
연구 방법
수리 실험(Laboratory Experiment)
길이 25m × 폭 0.8m × 높이 0.8m의 개수로(rectangular flume)에서 실험 수행.
0.45m × 0.007m × 0.4m 크기의 도류벽(baffles) 5개 배치.
유량 조건: 46 L/s
유속 측정 위치: 도류벽 중앙 및 하류 3개 지점
수치 모델(FLOW-3D) 설정
VOF(Volume of Fluid) 기법을 사용하여 자유 수면 추적.
RNG k-ε 난류 모델 적용.
격자(cell) 크기 0.015m, 비균일(non-uniform) 격자 적용.
경계 조건:
유입부: 실험 유량(46 L/s) 적용.
유출부: 자유 방출 조건 적용.
바닥 및 벽면: No-slip 조건 적용.
주요 결과
유속 분포 분석
수리 실험과 FLOW-3D 결과 비교 시, 최대 오차율 13% 이내로 나타남.
도류벽과 도류벽 사이에서는 유속 변화가 크며, 도류벽 중앙부에서 난류 강도가 증가.
FLOW-3D 결과가 실험 결과와 유사한 경향을 보이며, 신뢰성이 높음.
최대 유속 발생 지점 비교
최대 유속 발생 위치는 실험과 수치 모델에서 유사하게 나타남(오차율 6%).
도류벽 시작 지점에서 유속이 가장 높았으며, 도류벽 하류에서는 난류로 인해 유속이 감소.
결론 및 향후 연구
결론
FLOW-3D를 이용한 도류벽식 어도 해석이 실험 결과와 높은 일치도를 보이며, 신뢰성 확보 가능.
어도 내 유동 특성을 정확히 예측하여 최적 설계를 위한 기초 자료로 활용 가능.
도류벽 간격 및 형상을 조정하면 어류 이동을 돕는 유속을 형성할 수 있음.
향후 연구 방향
다양한 어도 형상(슬롯형, 계단식)과 비교 연구 수행.
어종별 이동 특성을 반영한 최적 유속 범위 검토.
LES(Large Eddy Simulation) 모델을 활용한 난류 해석 수행.
연구의 의의
이 연구는 FLOW-3D를 활용하여 도류벽식 어도의 유동 특성을 분석한 연구로, 향후 어도 설계 및 최적화를 위한 수치 모델 활용 가능성을 제시하였다.
그림 1. 개수로 실험 장치 및 어도 설치 (b) 어도 설치 후
그림 4. 수리실험과 수치모의 유속 분포 비교
그림 5. 수리실험과 수치모의 유속 분포 비교
References
백경오, 안성식. (2008). “효율적인 어도설치를 위한 흐름해석 – 왕숙천을 대상으로.” 한국수자원학회 학술발표대회 논문집, pp. 2100-2104.
한국수자원학회. (2005). “하천설계기준.”
L. Cea, L. Pena, J. Puertas, M.E. Vazquez-Cendon, E. Pens. (2007). “Application of Several Depth-Averaged Turbulence Models to Simulate Flow in Vertical Slot Fishways.” J. of Hydraulic, ASCE, pp.160-172.
Minnan Liu, Nallamuthu Rajaratnam, David Z. Zhu. (2006). “Mean Flow and Turbulence Structure in Vertical Slot Fishways.” J. of Hydraulic, ASCE, pp.765-777.
S. Wu, N. Rajaratnam, C. Katopodis. (1999). “Structure of Flow in Vertical Slot Fishway.” J. of Hydraulic, ASCE, pp.351-360.
Figure 5 Top view of velocity distribution of tailings mortar at 40s
연구 배경 및 목적
문제 정의
폐광석 저수지(tailings pond)는 광산 채굴 후 배출되는 폐기물을 저장하는 인공 저수지로, 붕괴 시 하류 지역에 심각한 환경적·경제적 피해를 초래할 수 있음.
폐광석 모르타르(tailings mortar)는 중금속(Pb, Cu, Mn 등)을 포함하며, 붕괴 시 고속 동적 에너지 모래 흐름(high-speed dynamic energy sand flow)으로 변환되어 하류 지역에 영향을 미침.
기존 연구는 폐광석 모르타르의 확산 범위 및 중금속 이동 경로 분석에 초점을 맞췄으며, 배출 속도 및 유동 특성에 대한 연구가 부족함.
연구 목적
FLOW-3D를 이용하여 댐 붕괴 시 폐광석 모르타르의 유동 특성을 수치적으로 분석.
폐광석 모르타르의 밀도, 점도, 하류 거칠기(roughness height)가 배출 속도 및 이동 거리에 미치는 영향을 연구.
기존 경험식과 비교하여 FLOW-3D 모델의 신뢰성을 검증.
연구 방법
FLOW-3D 모델링
VOF(Volume of Fluid) 기법을 사용하여 유체-고체 경계를 추적.
RNG k-ε 난류 모델을 적용하여 난류 특성 해석.
3D CAD 모델링을 통해 폐광석 저수지 및 하류 1000m × 400m × 30m 영역을 설정.
격자(cell) 수: 48,592개, 격자 크기: 3m.
경계 조건:
유입부: 폐광석 저수지에서 배출되는 유체 설정.
유출부: 하류 개방 경계 조건 적용.
바닥면: 다양한 거칠기(0.25m, 0.5m, 1.0m) 적용.
실험 데이터 및 경험식 비교
기존 Kang(1960), Fu(2007) 등의 경험식을 사용하여 FLOW-3D 결과 검증.
폐광석 모르타르의 밀도(1800, 2500, 3200 kg/m³), 점도(0.5, 5, 15 kg/m/s) 변화에 따른 배출 속도 비교.
주요 결과
배출 속도 변화
FLOW-3D 결과와 기존 경험식 비교 시 최대 오차율 3% 이내로 확인.
폐광석 모르타르의 배출 속도는 초기 급격히 증가한 후 점진적으로 감소하며 안정화됨.
밀도가 높을수록 초기 속도가 빠르지만, 일정 거리 이후 속도 차이 감소.
점도가 클수록 유동 저항 증가 → 유속 감소 및 이동 거리 단축.
거칠기(roughness height)가 클수록 배출 속도 감소 (450m에서 속도 감소율: 19.6~43.7%).
결론 및 향후 연구
결론
FLOW-3D를 활용한 폐광석 모르타르 유동 해석이 기존 경험식과 높은 일치도를 보이며, 신뢰성 검증됨.
밀도 및 점도 변화가 배출 속도에 영향을 미치며, 하류 지역의 거칠기 증가가 유동 속도를 효과적으로 저감할 수 있음.
폐광석 저수지 붕괴 시 피해 최소화를 위해 하류에 식생 및 수리 구조물 설치 필요.
향후 연구 방향
LES(Large Eddy Simulation) 모델을 활용한 추가 난류 분석.
하류 지역의 실제 데이터와 비교 검증 수행.
다양한 저수지 형상 및 붕괴 시나리오 적용 연구 진행.
연구의 의의
이 연구는 FLOW-3D를 이용하여 댐 붕괴 시 폐광석 모르타르의 배출 속도 및 유동 특성을 수치적으로 분석한 연구로, 향후 광산 안전 관리 및 재난 예방 시스템 구축에 기여할 수 있는 데이터를 제공하였다.
Figure 2 Top view of velocity distribution of tailings mortar at 10s
Figure 3 Top view of velocity distribution of tailings mortar at 20s
Figure 4 Top view of velocity distribution of tailings mortar at 30s
Figure 5 Top view of velocity distribution of tailings mortar at 40s
References
Chopra, M., Rohit, R., Kumar, A.V., Sunny F., Nair R.N. (2013). Response Surface Method Coupled with First-Order Reliability Method Based Methodology for Groundwater Flow and Contaminant Transport Model for the Uranium Tailings Pond Site. Environmental Modeling & Assessment, 18(4), 439-150.
Christina, C.S., Sunny, C., Hashisho, Z., Ulrich, A.C. (2015). Emissions from oil sands tailings ponds: Review of tailings pond parameters and emission estimates. Journal of Petroleum Science and Engineering, 127.
Dimache, L.B., Iancu, I., Pante, G., Omer, I. (2016). Numerical Modelling of Exfiltrations from Leaching Tailing Ponds. Energy Procedia, 85, 193-200.
Dibike, Y.B., Shakibaeinia, A., Droppo, I.G., Caron, E. (2018). Modelling the potential effects of Oil-Sands tailings pond breach on the water and sediment quality of the Lower Athabasca River. Science of the Total Environment, 642, 1263-1281.
Willis, C.E., Louis, V., Kirk, J.L., Pierre, K.A., Dodge, C. (2019). Tailings ponds of the Athabasca Oil Sands Region, Alberta, Canada, are likely not significant sources of total mercury and methylmercury to nearby ground and surface waters. Science of the Total Environment, 647.
Taylor, C., Hughes, T.G., Morgan, K. (1973). Analysis of turbulent flow in pipes. Compute Fluids, 1(1), 73-100.
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스키점프형 여수로는 유속이 20m/s를 초과할 때 사용되는 중요한 구조물이며, 에너지 소산을 위한 핵심 설계 요소임.
기존의 물리 실험은 비용이 높고 시간이 많이 소요되므로 컴퓨터 기반 CFD(전산유체역학) 시뮬레이션을 통한 연구가 필요함.
연구 목적
FLOW-3D를 이용하여 스키점프형 여수로의 유동 특성을 수치적으로 분석.
실험 데이터와 비교하여 FLOW-3D 모델의 정확성을 검증.
여수로의 제트 궤적(jet trajectory), 압력 분포 및 에너지 소산 특성 분석.
연구 방법
실험 및 수치 모델 개요
연구 대상: IS 7365 (2010) 표준을 따른 전통적인 스키점프형 여수로.
실험 조건:
수로 크기: 폭 0.30m, 깊이 0.30m, 길이 6m의 유리제 수리 실험 수로.
연속된 곡면 립(lip) 각도 35°, 반경 0.0915m.
유량(Q): 0.00431 ~ 0.00962 m³/s 범위.
FLOW-3D 기반 CFD 시뮬레이션 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 장애물 영역 설정.
경계 조건:
유입: 지정 속도 조건.
유출: 지정 압력 조건.
벽면: No-slip 조건 적용.
주요 결과
유동 및 에너지 소산 특성 분석
스키점프형 여수로에서 유동이 곡면을 따라 흐르면서 에너지가 점진적으로 소산됨.
FLOW-3D 결과와 실험 데이터의 에너지 소산율 비교
최대 오차율 15.69%로 나타났으며, 실험과 높은 일치도를 보임.
유량이 증가할수록 에너지 소산율이 감소하는 경향 확인.
제트 궤적 및 압력 분포 분석
시뮬레이션 결과와 실험값이 3D 유동장 및 압력 분포에서 일치함을 확인.
결론 및 향후 연구
결론
FLOW-3D 기반 시뮬레이션이 실험 결과와 높은 일치도를 보이며, 스키점프형 여수로의 유동 및 에너지 소산 특성을 효과적으로 예측 가능.
유량 변화에 따른 에너지 소산율 감소 경향을 확인하였으며, 추가적인 최적화 연구 필요.
향후 연구 방향
LES(Large Eddy Simulation) 난류 모델과 비교 분석 수행.
다양한 여수로 형상 및 유량 조건에서 추가적인 검증 수행.
실제 댐 적용 사례와 비교 연구 수행.
연구의 의의
이 연구는 FLOW-3D를 활용하여 스키점프형 여수로의 유동 및 에너지 소산 현상을 정량적으로 분석하고, 수치 모델의 정확성을 실험적으로 검증하였다. 댐 설계 및 홍수 방지 인프라 구축에 중요한 데이터와 분석 방법을 제공한다.
References
High Overflow Dams, Hydraulic Design Criteria, U.S. Army Corps of Engineers, Waterways Experiment Station, 1970.
R. Maitre, S. Obolensky, Etude de Quelques Caractéristiques de l’Ecoulement dans la Partie Aval des Evacuateurs de Surface, La Houille Blanche 4 (1954) 481–511.
T.J. Rhone, A. J. Peterka, Improved tunnel spillway flip buckets, Journal of Hydraulic Engineering, ASCE 126 (1959) 1270–1291.
A.C. WATERS, Terraces and coulees along the Columbia River near lake Chelan, Washington. Geological Society of America Bulletin 44 (1933) 783–820.
R. Joun, W.H. Hager, Flip bucket without and with deflectors, Journal of Hydraulic Engineering, ASCE 126 (2000) 837–845.
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O. A. Yamini, M. R. Kavianpour, Experimental study of static and dynamic pressures over simple flip bucket, 5th symposium on advances in science and technology, Khavaran Highereducation Institute, Mashhad, Iran. May 12-14 (2011).
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F.A. Bombardelli, I. Meireles, J. Matos, Laboratory measurements and multi-block numerical simulation of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped spillways, Environ Fluid Mech, Springer 11 (2011) 263–288.
P.G. Chanel, J.C. Doering, An evaluation of computational fluid dynamics for spillway modelling, 16th Australian Fluid Mechanics Conference, Crown Plaza, Gold Coast, Australia, (2007).
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FLOW-3D 소프트웨어를 사용한 다양한 모양의 교각 주변의 국부적인 세굴에 대한 수치적 연구
Figure 22 scouring depth at equillibrium condition in 3D geometry
연구 배경 및 목적
문제 정의
세굴은 흐르는 물의 침식 작용으로 인해 하천의 바닥과 제방에서 발생하는 자연적인 현상이다.
본 연구에서는 FLOW-3D를 사용하여 교각 주변의 세굴 지형, 깊이 및 퇴적을 정확하게 예측할 수 있는지 조사하고자 한다.
비점착성 하상 퇴적물의 세굴을 시뮬레이션하고 정성적 및 정량적 분석을 제시한다.
RANS(Reynolds Average Navier Stokes) 방정식과 k-ε 모델 및 2차 정확도의 난류 방법을 사용한다.
연구 목적
다양한 모양(원형, 사각형, 다이아몬드형, 육각형, 에어포일형)의 교각에 대한 세굴 깊이를 비교 분석한다.
시간 변화에 따른 세굴 깊이의 변화를 검증한다.
교각 주변의 속도 분포를 분석한다.
세굴 깊이를 줄이기 위한 대책(collar 설치)의 효과를 평가한다.
연구 방법
수치 모델(FLOW-3D) 설정
RANS(Reynolds Average Navier Stokes) 방정식과 k-ε 모델을 사용하여 난류를 모델링한다.
VOF(Volume of Fluid) 방법을 사용하여 자유 표면 흐름을 추적한다.
비점착성 모래의 세굴을 시뮬레이션하기 위해 적절한 경계 조건과 물리적 모델을 설정한다.
다양한 모양의 교각(원형, 사각형, 다이아몬드형, 육각형, 에어포일형)에 대한 3D 모델을 생성한다.
격자 독립성 테스트를 수행하여 적절한 격자 크기를 결정한다.
주요 결과
원형 교각의 경우 다른 모양에 비해 세굴 깊이가 만족스러운 결과를 보였다.
에어포일 모양의 경우 예상보다 세굴이 훨씬 크게 발생했다.
교각의 업스트림에서 다운스트림보다 세굴이 더 크게 발생했다.
FLOW-3D 소프트웨어는 세굴 깊이를 예측하는 데 몇 가지 제한사항이 있는 것으로 나타났다.
collar를 설치하면 세굴 깊이가 감소하는 것을 확인했다.
결론 및 향후 연구
결론
FLOW-3D는 교각 주변의 세굴 현상을 시뮬레이션하는 데 유용한 도구임을 확인했다.
교각 모양은 세굴 깊이에 큰 영향을 미치며, 원형 교각이 가장 안정적인 것으로 나타났다.
collar 설치는 세굴 깊이를 줄이는 효과적인 방법이다.
향후 연구 방향
다양한 흐름 조건과 토사 조건에 대한 추가 연구가 필요하다.
FLOW-3D의 세굴 예측 정확도를 향상시키기 위한 모델 개선이 필요하다.
실제 교량에 대한 적용 가능성을 평가하기 위한 현장 연구가 필요하다.
연구의 의의
본 연구는 FLOW-3D를 사용하여 교각 주변의 세굴 현상을 분석하고, 다양한 교각 모양과 collar 설치 효과를 비교 평가했다.
연구 결과는 교량 설계 및 유지 관리에 유용한 정보를 제공하며, 향후 교량 안전성 향상에 기여할 수 있다.
Figure 5~6 Horse shoe and wake vortex around a cylinderical element
Figure 22 scouring depth at equillibrium condition in 3D geometry (a) circular pier (b) square pier and (c) diamond pier
Figure 23 scouring depth at equilibrium condition in 3D geometry (d) hexagonal pier and (e) airfoil pier
Reference
J. Briaud, F. Ting, H. Chen, R. Gudavalli, S. Perugu and G. Wei, “SRICOS: Prediction of Scour Rate in Cohesive Soils at Bridge Piers”, Journal of Geotechnical and Geoenvironmental Engineering, vol. 125, no. 4, pp. 237-246, 1999. Available: 10.1061/(asce)1090-0241(1999)125:4(237)
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Figure 3 The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model
연구 배경 및 목적
문제 정의
댐 구조물의 필수적인 요소 중 하나인 여수로(spillway)는 홍수 방류 시 댐을 보호하는 중요한 역할을 수행함.
기존의 오지(ogee)형 여수로와 달리, 계단형 여수로(stepped spillway)는 유체의 에너지 소산을 증가시켜 캐비테이션(cavitation) 위험을 감소시키는 장점이 있음.
계단형 여수로에서 유동 형태(nappe flow, transition flow, skimming flow)가 다르게 나타나며, 유속, 압력, 공기 유입 등의 변화가 발생함.
연구 목적
Flow-3D를 활용하여 계단형 여수로에서의 난류 유동을 수치적으로 해석하고 실험 결과와 비교.
여수로 경사의 변화가 공기 유입(air entrainment), 유속 분포(velocity distribution), 동압(dynamic pressure)에 미치는 영향을 분석.
다양한 유량 조건에서 수치 해석 결과와 기존 실험 결과를 비교하여 모델의 신뢰성을 검증.
연구 방법
수치 해석 설정
CFD(전산유체역학) 모델: Flow-3D 사용
난류 모델: RNG k-ε 모델 적용
자유 수면 추적: VOF(Volume of Fluid) 기법 활용
격자 설정: 직교 격자(orthogonal mesh) 사용, 셀 크기 0.015m
모델 실험 조건:
경사 변화: 50° → 30° 및 50° → 18.6°
단수(step height): 0.06m
유량 조건: 0.1 m³/s 및 0.235 m³/s
주요 결과
공기 유입(air entrainment) 및 유속 분포 분석
경사 변화 후 공기 유입 증가 → 동일 유량에서 계단 경사가 낮을수록 공기 함유량 상승.
실험 결과와 비교 시 모델의 공기 유입 예측이 높은 신뢰도를 가짐.
유속 분포 분석 결과, 계단 경사 감소 시 유속이 더 균일하게 분포하며 난류 발생이 감소.
동압(dynamic pressure) 분석
실험 데이터와 비교 시 경사 변화 전후 압력 분포가 유사한 경향을 보임.
경사 변화 후, 계단면의 압력 변동이 증가하나, 전체적인 패턴은 실험 결과와 잘 일치.
실험 데이터 대비 압력 차이는 10% 이내로 나타남.
결론 및 향후 연구
결론
Flow-3D를 활용한 계단형 여수로의 수치 해석이 실험 결과와 높은 일치도를 보이며, 신뢰성이 검증됨.
경사 변화가 공기 유입과 유속 분포에 큰 영향을 미치며, 유량 조건에 따라 최적 설계가 필요.
계단형 여수로 설계 시, 경사와 유량 조건을 고려하여 최적의 유동 상태를 확보하는 것이 중요함.
향후 연구 방향
LES(Large Eddy Simulation) 난류 모델 적용을 통한 세밀한 유동 해석.
다양한 계단 형상 및 유량 조건에서 추가적인 검증 수행.
실제 댐 및 홍수 방류 시스템 적용을 위한 현장 실험 데이터와 비교 연구.
연구의 의의
이 연구는 Flow-3D를 활용하여 계단형 여수로의 유동 특성을 정량적으로 분석하고, 수치 모델의 신뢰성을 검증하였다. 여수로 설계 최적화 및 댐 안전성 향상을 위한 기초 데이터를 제공하였다.
Figure 1 Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016)
Figure 3 The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model
Figure 5 Experimental and simulated air concentration distribution for steps number
References
Boes, R. M. & Hager, W. H. 2003a Hydraulic design of stepped spillways. Journal of Hydraulic Engineering 129 (9), 671–679.
Boes, R. M. & Hager, W. H. 2003b Two-Phase flow characteristics of stepped spillways. Journal of Hydraulic Engineering 129 (9), 661–670.
Chanson, H. 1994 Hydraulics of skimming flows over stepped channels and spillways. Journal of Hydraulic Research 32 (3), 445–460.
Chanson, H. 1997 Air Bubble Entrainment in Free Surface Turbulent Shear Flows. Academic Press, London.
Chanson, H. 2002 The Hydraulics of Stepped Chutes and Spillways. Balkema, Lisse, The Netherlands.
Felder, S. & Chanson, H. 2011 Energy dissipation down a stepped spillway with nonuniform step heights. Journal of Hydraulic Engineering 137 (11), 1543–1548.
Flow Science, Inc. 2012 FLOW-3D v10-1 User Manual. Flow Science, Inc., Santa Fe, CA.
Ghaderi, A., Daneshfaraz, R., Torabi, M., Abraham, J. & Azamathulla, H. M. 2020a Experimental investigation on effective scouring parameters downstream from stepped spillways. Water Supply 20 (5), 1988–1998.
Ghaderi, A., Abbasi, S., Abraham, J. & Azamathulla, H. M. 2020b Efficiency of trapezoidal labyrinth shaped stepped spillways. Flow Measurement and Instrumentation 72, 101711.
Gonzalez, C. A. & Chanson, H. 2008 Turbulence and cavity recirculation in air-water skimming flows on a stepped spillway. Journal of Hydraulic Research 46 (1), 65–72.
Gunal, M. 1996 Numerical and Experimental Investigation of Hydraulic Jumps. PhD Thesis, University of Manchester, Institute of Science and Technology, Manchester, UK.
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39 (1), 201–225.
Matos, J. 2000 Hydraulic design of stepped spillways over RCC dams. In: Intl Workshop on Hydraulics of Stepped Spillways (H.-E. Minor & W. Hager, eds). Balkema Publ, Zurich, pp. 187–194.
Mohammad Rezapour Tabari, M. & Tavakoli, S. 2016 Effects of stepped spillway geometry on flow pattern and energy dissipation. Arabian Journal for Science & Engineering (Springer Science & Business Media BV) 41 (4), 1215–1224.
Ostad Mirza, M. J. 2016 Experimental Study on the Influence of Abrupt Slope Changes on Flow Characteristics Over Stepped Spillways. Communications du Laboratoire de Constructions Hydrauliques, No. 64 (A. J. Schleiss, ed.). Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
Roshan, R., Azamathulla, H. M., Marosi, M., Sarkardeh, H., Pahlavan, H. & Ab Ghani, A. 2010 Hydraulics of stepped spillways with different numbers of steps. Dams and Reservoirs 20 (3), 131–136.
Shahheydari, H., Nodoshan, E. J., Barati, R. & Moghadam, M. A. 2015 Discharge coefficient and energy dissipation over stepped spillway under skimming flow regime. KSCE Journal of Civil Engineering 19 (4), 1174–1182.
Takahashi, M. & Ohtsu, I. 2012 Aerated flow characteristics of skimming flow over stepped chutes. Journal of Hydraulic Research 50 (4), 427–434.
Versteeg, H. K. & Malalasekera, W. 2007 An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Pearson Education, Harlow.
FLOW-3D 수치 모델의 검증: 소형 수력 발전소(SHPP) 터빈 취수구 구조의 물리적 유압 모델과의 비교 및 실용적 활용
Fig. 8. Proposed form of the intake bottom
연구 배경 및 목적
문제 정의:
드라바 강(Drava River) 유역의 Zlatoličje 수력 발전소(HPP)에서 Melje 소형 수력 발전소(SHPP)의 터빈 취수구 구조물을 건설할 계획이 진행됨.
소형 수력 발전소는 생태 유량(Biological Minimum Discharge)을 활용하여 전력을 생산하므로 효율적인 취수구 설계가 필수적.
물리적 유압 모델은 비용이 높아 대신 FLOW-3D 기반의 3D 수치 모델을 활용하여 취수구 구조 검증 수행.
물리적 모델과 수치 모델을 병행 검증하여 최적 설계 도출.
연구 방법
물리적 유압 모델 구축
모형 제작:
Zlatoličje HPP의 도수로(Headrace Channel) 및 SHPP Melje의 취수구 구조를 1:20 축척으로 제작.
도수로 구간(길이 120m) 중 상류 39m, 하류 54m 포함하여 취수구와 자유 표면 흐름에서 압력 흐름으로 전환되는 구간까지 재현.
경계 조건 설정:
Zlatoličje HPP 총 유량(QZLAT) = 530 m³/s.
SHPP Melje 최소 유량(QSHPP) = 20 m³/s (해수면 기준 고도 252.90m).
SHPP Melje 최대 유량(QSHPP) = 20 m³/s (고도 253.30m).
실험은 2003년 현장 유량 측정 데이터 및 2D 수치 모델(SMS-RMA2) 결과를 반영하여 수행.
연구 목표:
취수구 설계 형태의 유압 효율성 검증 및 최적화 수행.
취수구 각 요소(상류 모서리, 하류 모서리, 피어 배치, 취수구 하부 형상)의 수리적 성능 분석.
유량 측정, 속도 측정, 수두 분포 측정을 통한 최적 설계 도출.
FLOW-3D 기반 수치 모델 구축
3D 지오메트리 생성:
ACAD에서 모델링 후 STL 파일로 변환, FLOW-3D 내 유한체적 격자(Finite Volume Mesh) 생성.
모델 영역을 3개 블록으로 구분하여 격자 최적화:
블록 1: 15,000개 셀 (Δx = 1m, Δy = 1m, Δz = 0.2m).
블록 2: 480,000개 셀 (Δx = 0.5m, Δy = 0.5m, Δz = 0.2m).
블록 3: 719,200개 셀 (Δx = 0.25m, Δy = 0.25m, Δz = 0.1m).
경계 조건 설정:
블록 1: 유량 조건 (Vz 유량).
블록 2: 실험 모델의 수위 측정값 반영.
블록 3: 유량 조건 적용하여 최종 배출 경계 설정.
수치 해석 방법:
RANS (Reynolds-Averaged Navier-Stokes) 방정식 적용.
FAVOR (Fractional Area/Volume Obstacle Representation) 방법을 이용하여 취수구 형상 정밀 재현.
VOF (Volume-of-Fluid) 기법을 활용하여 자유 표면 흐름 해석.
주요 결과
물리적 모델 분석 결과
상류 모서리(Upstream Corner)
초기 설계에서는 소규모 역류(Return Flow) 발생 확인됨.
모서리를 둥글게 수정(Rounding-Off)하면 역류가 감소하고 흐름이 원활해짐.
피어 배치(Orientation of Piers)
초기 설계에서는 중앙 및 하류 피어의 방향이 불규칙하여 난류(Turbulence Zone) 발생.
피어 방향을 조정하면 유동 저항 감소 및 수두 손실 최소화 가능.
하류 모서리(Downstream Corner)
기존 설계에서는 흐름이 분기되면서 정체 영역(Dead Zone) 형성.
하류 벽 기하 구조를 조정하여 유동 저항을 줄이고 정체 영역 제거 가능.
취수구 하부(Intake Bottom)
기존 설계에서는 트래시 랙(Trashrack) 이후 수평 소용돌이(Vortex) 발생.
하부를 완만한 기울기로 변경하면 흐름이 원활해지고 압력 손실 감소.
FLOW-3D 수치 모델 분석 결과
수치 모델 결과가 물리적 모델과 유사한 패턴을 보이며 신뢰성 검증됨.
취수구 하부 유동을 비교한 결과:
기존 설계에서는 트래시 랙 이후 역류 발생.
최적화 설계에서는 유선(Streamline)이 원활하게 진행되며 역류 제거됨.
속도 분포 비교:
3D ADV(Acoustic Doppler Velocimeter) 측정 결과와 FLOW-3D 시뮬레이션 결과 비교 시 평균 오차 5% 이내.
특정 지점에서는 수치 모델이 실측 데이터보다 속도를 과소평가하는 경향 확인됨.
결론 및 향후 연구
결론:
FLOW-3D 수치 모델이 취수구 설계 최적화에 유용하게 활용 가능함을 입증.
피어 방향 최적화, 하류 벽 기하 수정, 취수구 하부 형상 변경을 통해 수두 손실 최소화 가능.
물리적 모델을 병행 활용하면 정밀한 취수구 설계 검증이 가능.
FLOW-3D는 최적화 도구로 유용하지만, 정밀한 조정에는 물리적 모델 병행 필요.
향후 연구 방향:
곡선 좌표 시스템 적용이 가능한 CFD 모델 개발 필요.
더 정밀한 유량 조건 설정을 위한 추가 데이터 확보 필요.
실제 발전소 운영 데이터와의 비교 연구 수행 필요.
연구의 의의
본 연구는 FLOW-3D 기반 수치 모델을 활용하여 소형 수력 발전소의 취수구 설계를 최적화할 수 있음을 입증하였으며, 물리적 모델과의 비교를 통해 수치 모델의 신뢰성을 검증하였다. 이는 수력 발전소 설계 최적화 및 효율 향상을 위한 실질적인 데이터와 설계 기준을 제공할 수 있다.
Fig. 3. Proposed intake form
Fig. 5. Proposed form of the intake bottom
Fig. 8. Proposed form of the intake bottom
Reference
Mlačnik, J., Vošnjak, S., “Mathematical model of the intake of the SHPP Melje”, Final research report, 2007,
Vošnjak, S., “Verification of the Flow-3D mathematical model by a physical hydraulic model of a small hydropower plant”, presentation, European FLOW-3D User Meeting 2006, CFD Consultants, Tübingen
Mlačnik, J., Vošnjak, S., “Optimisation of the intake into the headrace channel of the HPP Soteska by means of the mathematical model”, Final research report 2007,
Savage, M., Johnson C., “Flow over ogee spillway: Physical and numerical model case study”, Journal of hydraulic engineering, Vol. 127, No. 8, 2001,
Savage, M., Johnson C., “Physical and Numerical Comparison of Flow over Ogee Spillway in the Presence of Tailwater”, Journal of hydraulic engineering, Vol. 132, No. 12, 2006
Versteeg, H.K., Malalasekera W., “An introduction to computational fluid dynamics”, Longman Scientific and Technical, 1995
Figure 5. Flow field, eddies and dead zones in S1 and S2 simulations
Groynes 주변의 지형 및 수리학적 수치 시뮬레이션
연구 배경 및 목적
문제 정의
하천 및 하구에서 발생하는 침식 문제를 해결하기 위해 Groynes(제방 구조물)이 널리 사용됨.
Groynes 주변의 흐름과 침식 현상을 정확히 이해하는 것은 수로 보호 및 유지관리에 필수적임.
실험적 연구는 시간과 비용이 많이 소요되므로 컴퓨터 기반 CFD(전산유체역학) 시뮬레이션을 활용하여 수리학적 특성을 분석하는 연구가 필요함.
연구 목적
FLOW-3D를 이용하여 Groynes 주변의 유동 및 세굴(scour) 현상을 수치적으로 분석.
실험 결과와 비교하여 FLOW-3D 모델의 정확성을 검증.
SSIIM 2.0 소프트웨어와의 비교 분석을 통해 다양한 모델의 예측 정확도 평가.
연구 방법
FLOW-3D 모델링 및 시뮬레이션 설정
VOF(Volume of Fluid) 기법을 사용하여 자유 수면을 추적.
RNG k-ε 난류 모델을 적용하여 난류 흐름을 해석.
지형 모델링: Soulsby-Whitehouse 방정식을 이용하여 세굴 예측.
경계 조건:
유입: Froude 수 기반의 흐름 조건 적용.
유출: 자연 배출 경계 조건 설정.
바닥: 이동 가능한 퇴적층으로 설정.
주요 결과
유동 및 세굴 특성 분석
Groynes 주변에서 강한 와류(vortex) 발생 → 세굴 형성에 주요 원인.
Froude 수가 낮을수록 모델 예측 정확도 향상.
SSIIM 2.0 대비 FLOW-3D가 보다 정확한 흐름 및 세굴 패턴 예측.
실험 결과와 비교 시 최대 세굴 깊이 차이가 10% 이내로 나타남.
결론 및 향후 연구
결론
FLOW-3D를 활용한 수치 시뮬레이션이 실험 결과와 높은 일치도를 보이며, Groynes 주변의 유동 및 세굴 현상을 효과적으로 예측 가능.
Froude 수와 유속 비(Uavg/Ucr)에 따라 모델 정확도가 달라지며, 추가적인 실험 검증이 필요.
향후 연구 방향
LES(Large Eddy Simulation)와 같은 고급 난류 모델 적용을 통한 예측 정확도 향상.
다양한 하천 형상 및 유량 조건에서 추가적인 검증 수행.
실제 하천 데이터와의 비교를 통한 모델 보정.
연구의 의의
이 연구는 FLOW-3D를 활용하여 Groynes 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.
Figure 5. Flow field, eddies and dead zones in S1 and S2 simulations
Figure 6. Morphology bed changes in S1 (a) laboratory experiments and (b) FLOW-3D simulation
Figure 7. Morphology bed changes in S2 (a) laboratory experiments and (b) FLOW-3D simulation
References
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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 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
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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 조건은 대칭(Symmetry), 연속(Continuative), 체적 유량(Volume Flow Rate), 벽(Wall) 경계로 설정.
시뮬레이션 시나리오 및 변수 설정
강우 강도 시나리오:
낮은 강우(5 mm/h) 및 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 수는 유속과 관성력의 비율을 나타내며, 유동 상태(서브크리티컬 또는 슈퍼크리티컬) 평가에 사용.
주요 결과
속도(X-, Y-, Z-방향) 분석
시뮬레이션 결과:
x, y 속도는 z 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.
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 이루어정상 상태(Steady State) 도달.
포장 구조의 투수성 덕분에 강우 강도가 증가해도 표면 유출(Surface Runoff)이 발생하지 않음.
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 수는 낮은 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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교각 주변 최대 세굴 깊이에 대한 부유물(Debris)의 영향 분석: FLOW-3D 시뮬레이션
연구 배경 및 목적
문제 정의: 교각(Bridge Pier) 주변의 국부 세굴(Local Scour)은 하천 바닥의 침식을 유발하여 교량의 구조적 안전성을 위협하는 주요 요인 중 하나이다.
홍수 시에는 유량 증가와 부유물 증가로 인해 세굴 현상이 더욱 심화된다.
부유물은 교각 주변에 쌓여 흐름을 방해하고, 난류(Turbulence) 증가 및 전단응력(Shear Stress) 증대로 이어져 세굴을 악화시킨다.
연구 목적:
FLOW-3D CFD 모델을 사용하여 부유물 형태 및 위치가 원형 교각 주변의 최대 세굴 깊이에 미치는 영향을 평가.
삼각형 및 직사각형 부유물을 수면에 떠있는 경우(floating)와 하상(sand bed)에 놓인 경우로 구분하여 비교.
실험 결과와의 비교 검증을 통해 모델의 신뢰성을 평가.
연구 방법
수치 모델링 및 시뮬레이션 설정
FLOW-3D 소프트웨어를 활용한 3차원 CFD 해석 수행.
RNG k-ε 난류 모델을 사용하여 난류 흐름을 모델링.
VOF(Volume of Fluid) 기법을 통해 자유 수면(free surface)을 추적.
모델 검증:
Robalo (2014)의 실험 데이터를 사용하여 평균 속도 및 세굴 깊이 비교.
실험 채널은 길이 12.0m, 폭 0.83m, 높이 1.0m의 직사각형 콘크리트 플룸(fluvial hydraulic channel) 사용.
부유물(Debris) 유형 및 조건
부유물 형태: 삼각형(Triangular) 및 직사각형(Rectangular).
부유물 위치:
수면(floating debris): 부유물이 흐름을 막아 세굴을 증대시킴.
하상(sand bed debris): 세굴 억제(countermeasure) 역할을 하여 세굴 깊이를 줄이는 효과.
하상 재료:
천연 석영 모래(Quartz Sand) 사용, D50 = 0.86 mm, 밀도 2666 kg/m³.
평균 접근 유속(U) = 0.317 m/s, 수심 0.15 m 설정.
모델 검증 및 비교 분석
FLOW-3D 결과와 실험 결과 비교:
평균 속도 프로파일 비교 시, 실험과 유사한 흐름 발달을 보여 모델의 신뢰성 확보.
그러나 이동 가능한 하상(movable bed)을 적용했을 때, 평균 30%의 편차가 발생.
Shields (1936) 기준과의 비교:
실험에서는 Neil (1967) 및 Garde (1970) 공식을 사용하여 한계 유속(Uc) 0.314 m/s를 평가.
FLOW-3D에서는 Shields 기준(Uc 0.403 m/s)을 사용하여 20% 높은 값을 적용.
이는 세굴 깊이 과소 예측의 주요 원인으로 분석.
주요 결과
세굴 깊이 및 부유물 영향 비교
부유물 없는 경우:
세굴 깊이 0.06 m.
부유물 유형에 따른 세굴 깊이:
직사각형 부유물(수면): 세굴 깊이 0.07 m (가장 큰 세굴).
삼각형 부유물(수면): 세굴 깊이 0.05 m.
삼각형 부유물(하상): 세굴 깊이 0.04 m, 세굴 감소 효과 ≈ 40%.
FLOW-3D 모델의 신뢰성 평가
고정된 하상(fixed bed) 시뮬레이션에서는 실험과 높은 일치도를 보임.
그러나 이동 가능한 하상(movable bed) 적용 시, 실험 결과와 평균 30% 편차 발생.
Shields 기준의 한계:
Uc 평가 방법의 차이가 주요 원인으로 분석.
Shields 기준은 한계 전단응력(Threshold Shear Stress)을 과대 평가하여 세굴 깊이를 과소 예측.
결론 및 향후 연구
결론:
FLOW-3D 모델은 부유물 유형 및 위치에 따른 세굴 깊이 변화를 예측할 수 있음.
수면에 떠 있는 직사각형 부유물이 세굴을 가장 크게 증가시키며, 삼각형 부유물(하상)은 세굴을 줄이는 효과가 있음.
Shields 기준의 적용이 세굴 깊이 과소 예측의 원인으로, 국내 하천 조건에 맞는 보정 필요.
향후 연구 방향:
다양한 난류 모델(예: LES, k-ω 모델) 적용 및 비교.
다양한 하상 조건 및 교각 형상에 대해 추가 검증.
AI 및 머신러닝을 활용한 세굴 예측 모델 개발.
부유물의 재질, 크기 및 배열에 따른 세굴 영향 연구.
연구의 의의
이 연구는 FLOW-3D를 활용한 교각 주변 부유물의 세굴 영향 분석을 통해 교량 설계 및 유지보수 전략 수립에 중요한 기초 데이터를 제공하며, 홍수 시 구조물 안전성을 높이는 데 기여할 수 있다.
Reference
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문제 정의: 교각(Bridge Pier) 주변의 국부 세굴(Local Scour)은 하천 바닥의 침식으로 인해 구조물의 안전성을 위협하는 주요 요인 중 하나이다.
연구 목적: FLOW-3D를 활용하여 교각 주변의 국부 세굴 형상을 3D 시뮬레이션하고, 실험 데이터를 비교하여 모델의 신뢰성을 검증하는 것이다.
핵심 기여:
FLOW-3D를 활용한 CFD 모델 개발: 유체 흐름과 퇴적물 이동을 고려한 세굴 시뮬레이션.
실험 결과와 비교 검증: Melville 실험 데이터를 바탕으로 모델 검증 및 정확도 평가.
세굴 깊이 예측 및 설계 최적화: 교각 설계 및 유지관리 전략에 적용 가능.
연구 방법
수치 모델링 및 난류 모델 적용
Navier-Stokes 방정식 기반 CFD 해석 수행.
VOF(Volume of Fluid) 기법을 활용하여 자유 수면 추적.
RNG k-ε 난류 모델을 사용하여 교각 주변 난류 구조를 해석.
세굴 모델링
Meyer-Peter & Müller 공식을 사용하여 침식 및 퇴적 거동 해석.
Shields Parameter를 적용하여 세굴 발생 임계값 예측.
Melville 실험 모델과 동일한 유속(0.25 m/s) 및 입자 크기(0.385 mm) 설정.
메쉬 설정 및 경계 조건
격자 독립성 검토: 1~30 mm의 다양한 격자 크기를 적용하여 최적의 메쉬 크기(5 mm) 선정.
경계 조건:
입구: 일정한 유속(0.25 m/s) 설정.
출구: 자유 유출 조건 적용.
하천 바닥: 이동 가능 침전층(Sediment Bed)으로 설정.
주요 결과
세굴 깊이 비교
실험 값: 4.00 cm
Flow-3D 예측값: 3.6 cm (실험 대비 오차 10%)
시뮬레이션 결과와 실험 데이터 간 높은 상관관계 확인.
유동장 및 세굴 형상 분석
세굴 패턴: 교각 전면부에서 강한 와류(Horseshoe Vortex) 발생 → 침식 심화.
교각 후류(Downstream) 영역: 유속이 급격히 감소하며 침전 형성.
RNG k-ε 모델 적용 효과: 세굴 깊이 및 와류 구조를 효과적으로 예측.
메쉬 크기의 영향
5mm 이하의 세밀한 격자에서 최적의 결과 도출.
30mm 이상의 거친 격자에서는 세굴 깊이가 과소 예측됨.
결론 및 향후 연구
FLOW-3D 기반 세굴 시뮬레이션이 실험 결과와 높은 정확도로 일치함을 확인.
RNG k-ε 난류 모델이 교각 주변의 난류 구조 및 세굴 깊이 예측에 적합함을 입증.
향후 연구에서는 LES(Large Eddy Simulation) 모델과 비교, 다양한 교각 형상 및 유량 조건에서 추가 검증이 필요.
연구의 의의
이 연구는 FLOW-3D를 활용하여 교각 주변 국부 세굴을 정량적으로 분석하는 방법론을 제시하며, 교량 설계 및 유지보수 전략 수립에 활용될 수 있는 중요한 기초 데이터를 제공한다.
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문제 정의: 교각 주변에서 발생하는 국부 세굴(Local Scour)은 하천 바닥 침식을 유발하여 교량의 구조적 안정성을 위협하는 주요 요인 중 하나이다.
연구 목적:
FLOW-3D를 활용한 세굴 모델 개발: CFD(Computational Fluid Dynamics) 기반 수치 모델을 사용하여 교각 주변의 세굴 형상을 예측.
실험 데이터와의 비교: 실험실 실험과 수치 모델의 결과를 비교하여 모델의 신뢰성을 평가.
세굴 깊이 및 유속 패턴 분석: 교각 앞쪽 및 후류에서 형성되는 유동 구조와 세굴의 관계를 분석.
연구 방법
실험 데이터 수집 및 모델링
실험실 실험:
터키 가지안테프 대학교의 수리 실험실에서 수행.
0.8m × 0.9m 크기의 직사각형 수로에서 직경 10cm의 원형 교각을 배치.
유량 0.048 m³/s, 유속 0.48 m/s, 수심 11cm 설정.
세굴층은 비응집성(non-cohesive) 모래(d₅₀ = 1.45mm)로 구성.
FLOW-3D 기반 CFD 모델링:
VOF(Volume of Fluid) 기법을 사용하여 자유 수면 모델링.
RNG k-ε 난류 모델을 적용하여 난류 흐름 분석.
침식 및 퇴적 모델을 적용하여 하상 변화 예측.
격자 설정 및 경계 조건
메쉬 독립성 검토: 64,000개 이상의 격자를 사용하여 최적화 수행.
경계 조건:
입구: 일정한 유속(0.48 m/s) 설정.
출구: 자유 유출 조건 적용.
하천 바닥: 이동 가능 침전층(Sediment Bed)으로 설정.
주요 결과
세굴 깊이 비교
실험 값: 6.9 cm
FLOW-3D 예측값: 6.5 cm (실험 대비 오차 10%)
실험과 수치 모델의 결과가 높은 상관관계를 보임.
유동 및 세굴 패턴 분석
유속 분포:
교각 전면부에서 강한 와류(Horseshoe Vortex) 발생 → 침식 심화.
후류 영역에서는 유속이 감소하며 퇴적 형성.
세굴 형상:
최대 세굴 깊이는 교각 전면부 및 측면에서 발생.
FLOW-3D 모델은 세굴 발생 위치 및 심도를 효과적으로 예측.
시간에 따른 세굴 발전
실험 및 CFD 모델 모두에서 1시간 후 세굴 깊이가 안정화됨.
세굴 속도는 초기 30분 동안 급격히 증가한 후 점진적으로 감소.
결론 및 향후 연구
결론:
FLOW-3D 기반 CFD 모델은 교각 주변의 세굴 깊이를 실험 결과와 높은 정확도로 예측할 수 있음.
RNG k-ε 난류 모델이 국부 세굴 해석에 적합함을 확인.
세굴 깊이 예측에서 실험 대비 오차는 약 10%로 양호한 결과를 보임.
향후 연구 방향:
더 정교한 난류 모델(예: LES) 적용 및 비교.
다양한 교각 형상 및 유량 조건에서 추가 검증.
인공지능(AI) 및 머신러닝을 활용한 세굴 예측 모델 개발.
연구의 의의
이 연구는 FLOW-3D를 이용한 국부 세굴 예측의 신뢰성을 검증하고, 교량 설계 및 유지보수 전략 수립에 활용될 수 있는 중요한 기초 데이터를 제공한다.
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문제 정의: 교각이나 말뚝(pile) 주위에서 발생하는 국부적인 세굴(scour)은 구조물의 안정성에 중요한 영향을 미친다.
연구 목적: FLOW-3D 소프트웨어를 이용하여 두 개의 말뚝(쌍둥이 말뚝) 주위의 유동 패턴과 세굴 메커니즘을 수치적으로 시뮬레이션하고, 실험 데이터를 활용하여 검증하는 것이다.
연구 방법
수치 모델링 및 난류 모델
FLOW-3D 소프트웨어를 사용하여 RNG k-ε 난류 모델을 기반으로 유동 해석 수행.
말뚝의 배치: 병렬(side-by-side) 배치 및 직렬(tandem) 배치 두 가지를 고려.
실험 데이터와 비교하여 모델의 신뢰성을 검증.
계산 영역 및 격자(Grid) 설정
비균일(non-uniform) 격자 분포를 사용하여 말뚝 주변의 유동을 정밀하게 모델링.
최소 격자 크기: 0.009 m, 최대 격자 크기: 0.039 m.
메쉬 개수: x 방향 400개, y 방향 110개, z 방향 40개.
경계 조건
유입 속도 및 압력을 각각 입출력 경계 조건으로 설정.
상류에서 개발된 유동을 프로파일로 생성하여 말뚝이 존재하는 구역의 유입 경계 조건으로 적용.
주요 결과
유동 패턴 분석
병렬 배치(Side-by-side):
말뚝 사이에서 제트(Jet) 유동이 발생하며 비대칭적인 흐름 형성.
배치 간격이 증가할수록 후류(Vortex shedding) 현상이 뚜렷해짐.
직렬 배치(Tandem):
앞쪽 말뚝이 후방 말뚝을 보호하는 Sheltering 효과 발생.
Reynolds 수와 배치 간격(S/d)에 따라 와류 형성 패턴이 변화.
후류에서 강한 난류 구조가 나타나며, Wake Vortex가 형성됨.
실험과의 비교
실험 데이터와 시뮬레이션 결과를 비교한 결과, 전반적으로 유동 패턴이 잘 일치함.
그러나 말뚝 사이의 복잡한 유동장에서는 일부 차이가 발생하여 추가적인 모델 보정이 필요함.
Reynolds 수와 배치 간격의 영향
말뚝 간 간격(S/d)이 증가할수록 앞쪽 말뚝의 보호 효과가 감소하고, 후방 말뚝 주변에서 강한 와류가 형성됨.
낮은 Reynolds 수에서는 단일 말뚝과 유사한 흐름 패턴을 보이나, 높은 Reynolds 수에서는 와류가 더욱 강하게 나타남.
결론 및 향후 연구
FLOW-3D를 활용한 3D 유동 시뮬레이션은 말뚝 주변 유동 패턴과 세굴 메커니즘을 효과적으로 분석할 수 있음을 확인함.
실험 데이터와 전반적으로 높은 일치도를 보였으나, 말뚝 사이의 복잡한 유동장에서 추가적인 모델 개선이 필요함.
향후 연구에서는 더 다양한 Reynolds 수와 배치 조건을 고려한 추가 실험 및 난류 모델 비교 분석이 필요함.
연구의 의의
이 연구는 교량 기초 및 해양 구조물 설계에서 말뚝 주변의 유동과 세굴 예측을 정밀하게 분석할 수 있는 CFD 기반 접근법을 제시하였으며, 향후 말뚝 배치 최적화 및 구조물 안전성 향상에 기여할 수 있음을 시사한다.
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해상풍력 발전 기초는 파랑 조건에 의해 주변 유동이 크게 교란되어 세굴(Scour) 현상이 발생할 수 있다.
기초의 안정성 확보를 위해 세굴 현상을 정확하게 예측하는 것이 필수적이다.
본 연구는 Flow-3D를 활용하여 해상풍력기초(모노파일 및 삼각대 파일) 주변의 세굴현상을 수치해석하였다.
연구 방법
모형 설정 및 입력 조건
해상풍력기초 형상: 직경이 다른 모노파일(예: D = 5.0 m, d = 1.69 m)과 동일한 직경의 모노파일, 그리고 삼각대 파일 형식을 대상으로 분석.
경계조건: 상류경계에 관측 유속(약 1.066 m/s) 및 극치파랑 조건을 적용하여 세굴현상을 평가.
난류 모형: LES 모형과 RNG 모형을 각각 적용하여 세굴 깊이 및 분포에 미치는 영향을 비교.
수치 해석 기법
Flow-3D 모형을 이용하여 3차원 유동해석을 수행.
FAVOR 기법과 VOF(Volume of Fluid) 방법을 사용해 복잡한 경계와 자유 표면을 정확히 재현.
메쉬 독립성 및 민감도 분석을 통해 계산의 신뢰성을 확보함.
주요 결과
모노파일 분석:
서로 다른 직경의 모노파일에서는 최대 세굴심이 약 4.13 m로 나타났으며, 동일한 직경의 모노파일에서는 하강류가 증가하여 최대 세굴심이 약 7.13 m로 증가함.
이는 동일 직경 모노파일에서 유속이 더욱 빨라지며, 세굴 현상이 심화됨을 시사함.
삼각대 파일 분석:
상류 경계조건으로 관측 유속과 극치파랑 조건을 각각 적용한 결과, 극치파랑 조건에서는 최대 세굴심이 약 1.3배 정도 더 깊게 발생함.
난류 모형 비교:
LES 모형을 적용한 경우, 세굴심이 일정 시간이 경과하면 평형상태에 도달함.
반면, RNG 모형은 전체 해석 영역에서 계속해서 세굴현상이 발생하여 평형상태에 도달하지 않음.
따라서 해상풍력기초 세굴 해석에는 LES 모형과 극치파랑 조건의 적용이 타당함.
결론 및 향후 연구
해상풍력기초에 대한 세굴현상 분석에서는 동일 직경 모노파일보다 서로 다른 직경의 파일 형식이 기초 안정성 측면에서 유리할 수 있음.
LES 난류 모형과 극치파랑 조건을 적용하는 것이 실제 세굴현상을 더 정확하게 예측할 수 있음을 확인함.
향후 연구에서는 다양한 해양 파랑 조건 및 추가 난류 모형 비교를 통해 보다 정밀한 세굴예측 모델을 개발할 필요가 있음.
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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
삼각형 허들(Weir) 개요
위어(Weir)는 개수로에서 유량 조절과 방류 역할을 수행하는 중요한 수리 구조물.
본 연구에서는 크기가 50 cm × 30 cm × 7 cm인 Sharp-Crested Triangular Hump 모델을 사용.
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.
총 1,920,000개의 격자 셀을 사용하여 시뮬레이션 수행.
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
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.
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.
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.
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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/m3; t is time, s; ui, uj are average flow velocities, u1, u2, u3 represent average flow velocity components in Cartesian coordinates x, y, and z, respectively, m/s; μ is dynamic viscosity of fluid, N·s/m2; p 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 k–ε 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/s2; μeff 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*, C2ε 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/cm
Section Position
b = 20 cm
b = 30 cm
b = 40 cm
b = 47 cm
hm/cm
hs/cm
R/%
hm/cm
hs/cm
R/%
hm/cm
hs/cm
R/%
hm/cm
hs/cm
R/%
7
④
21.49
19.4
9.73
17.74
16.9
4.74
16.07
14.51
9.71
13.79
12.50
9.35
④′
20.48
19.05
6.98
17.78
16.14
9.22
15.69
14.31
8.80
⑥
20.71
19.02
8.16
17.82
16.31
8.47
15.92
14.53
8.73
15.23
13.80
9.39
⑧′
22.00
20.22
8.09
18.27
16.74
8.37
16.59
14.96
9.83
⑧
22.37
20.17
9.83
17.73
16.80
5.25
16.27
15.08
7.31
15.36
14.36
6.51
10
④
24.15
22.6
6.42
19.96
18.84
5.61
19.03
18.58
2.36
16.83
15.85
5.82
④′
24.21
22.05
8.92
19.49
18.19
6.67
18.75
18.35
2.13
⑥
24.01
21.78
9.29
19.65
18.34
6.67
18.95
18.63
1.69
17.52
16.09
8.16
⑧′
24.88
22.4
9.97
20.65
19.21
6.97
20.12
19.29
4.13
⑧
24.03
22.96
4.45
21.16
19.34
8.60
19.71
19.43
1.42
18.39
17.36
5.60
15
④
28.85
27.56
4.47
25.86
24.09
6.84
24.05
21.89
8.98
22.73
20.80
8.49
④′
28.49
26.97
5.34
25.19
23.84
5.36
23.42
21.46
8.37
⑥
28.85
26.98
6.48
25.72
23.99
6.73
23.23
21.82
6.07
23.10
21.05
8.87
⑧′
28.96
27.30
5.73
26.38
24.19
8.30
24.18
22.27
7.90
⑧
29.18
27.96
4.18
26.57
24.54
7.64
24.57
22.33
9.12
23.20
21.10
9.05
20
④
33.29
32.34
2.85
30.63
29.02
5.26
28.49
26.87
5.69
26.99
25.81
4.37
④′
33.14
31.95
3.59
29.75
28.62
3.80
28.11
26.79
4.70
⑥
33.32
31.79
4.59
30.04
28.45
5.29
28.99
26.86
7.35
27.42
26.72
2.55
⑧′
34.02
32.39
4.79
30.69
28.95
5.67
29.59
27.25
7.91
⑧
34.62
32.84
5.14
31.44
29.29
6.84
29.51
27.31
7.46
28.21
27.00
4.29
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. (a) P = 20 cm, b = 20 cm; (b) P = 20 cm, b = 30 cm; (c) P = 20 cm, b = 40 cm; (d) P = 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. (a) P = 7 cm, b = 20 cm; (b) P = 10 cm, b = 20 cm; (c) P = 15 cm, b = 20 cm; (d) P = 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 Fr1, b/h1, and P/h1, discharge coefficient values were plotted against Fr1, b/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 Fr1, b/h1, and P/h1 was conducted using data analysis software (IBM SPSS Statistics 19). The various coefficients obtained are shown in Table 3.
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig
B
Std. Error
Beta (β)
Constant
−1.294
0.155
−8.369
0.000
Fr1
3.430
0.286
3.401
12.013
0.000
b/h1
−0.004
0.004
−0.045
−0.944
0.348
P/h1
2.401
0.167
4.064
14.394
0.000
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.
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
0.913 a
0.833
0.829
0.03232
Table 4. Model Summary b. Note: a. Predictors:(Constant), Fr1, P/h1; b. Discharge coefficient.
Model
Sum of Squares
df
Mean Square
F
Sig
1
Regression
0.402
2
0.201
192.545
0.000 a
Residual
0.080
77
0.001
Total
0.483
79
Table 5. ANOVA b. Note: a. Predictors:(Constant), Fr1, P/h1; b. Discharge coefficient.
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig
B
Std. Error
Beta (β)
Constant
−1.326
0.151
−8.796
0.000
Fr1
3.479
0.281
3.449
12.396
0.000
P/h1
2.427
0.164
4.108
14.765
0.000
Table 6. Coefficient a. Note: a. Predictors:(Constant), Fr1, P/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/cm
Height of Side Weir/cm
Number of Formula
10~14
10~20
6~12
(24)
35–100
20~75
1~19
(26), (27)
6~30
20~47
7~20
(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:
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.
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.
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.
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.
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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Hongliang Wang, Xuanwen Jia,Chuan Wang, Bo Hu, Weidong Cao, Shanshan Li, Hui Wang
Abstract
Water-jet-scouring technology finds extensive applications in various fields, including marine engineering. In this study, the pulse characteristics are introduced on the basis of jet-scouring research, and the sand-scouring characteristics of a pulsed jet under different Reynolds numbers and the impact distances are deeply investigated using Flow-3D v11.2. The primary emphasis is on the comprehensive analysis of the unsteady flow structure within the scouring process, the impulse characteristics, and the geometric properties of the resulting scouring pit. The results show that both the radius and depth of the scour pit show a good linear correlation with the jet-flow rate. The concentration of suspended sediment showed an increasing and then decreasing trend with impinging distance. The study not only helps to enrich the traditional theory of jet scouring, but also provides useful guidance for engineering applications, which have certain theoretical and practical significance.
Water-jet-scouring technology is widely used in marine engineering and its related ancillary fields, such as in the maintenance and repair of marine structures, extraction of deep-sea resources, dredging works, seabed geological research, and cleaning and maintenance of ships. The jet flow establishes a velocity shear layer at its boundary, leading to the destabilization and subsequent generation of vortices. These vortices undergo continuous deformation, rupture, merging, and evolution into turbulence during their movement. Consequently, they entrain surrounding fluid into the jet region, facilitating the transfer of momentum, heat, and mass between the jet and its ambient environment [1,2,3]. Therefore, numerous scholars have carried out detailed studies on the scouring characteristics associated with jets. Chatterjee et al. [4] investigated the local scouring and sediment-transport phenomena due to the formation of horizontal jets during the opening of sluice gates based on experiments, and successfully established empirical expressions for the correlation between the time of reaching the equilibrium stage, the maximum depth of scouring, and the peak of the dune. The important role of jet-diffusion properties in the scouring process was also emphasized. Hoffmans [5] calculated the equilibrium scour process induced using a horizontal jet in the absence of a streambed and used experiments to verify the accuracy of the equations for jet-scour depths in the relevant literature. Luo et al. [6] investigated the induction mechanism of scour in planar jets through particle-image velocimetry (PIV). It was found that the initial stage of scour was dominated by wall shear, while the later stages of the scour process were mainly influenced by the turbulent vortex. Canepa et al. [7] investigated the scour characteristics of gas-doped water jets and found that gas-doped jets significantly reduce the scour depth if the velocity of the mixture is used as a reference. Pulsed jets introduce pulsation, resulting in a water-hammer effect, as well as increased diffusion and coil suction rates. These factors contribute to a more intricate interaction between the pulsed jet and the adjacent wall. The process of generation, development and evolution of its internal vortex structure as well as the interaction between the vortex structure and the surrounding ambient fluid and solid wall have changed significantly [8,9]. At this juncture, researchers in this domain have undertaken investigations centered on the utilization of pulsed jets. Coussement et al. [10] investigated the flow characteristics of a pulsed jet in a cross-flow environment based on Large Eddy Simulation (LES). A new approach to characterize mixing was introduced, which successfully explains and quantifies the complex mixing process between the pulsating jet and the ambient fluid. Bi et al. [11] investigated the thrust of a deformable body generated through a pulsed jet based on an axisymmetric immersed-boundary model. The numerical results show that in addition to the momentum flux of the jet, the jet acceleration is also an important source of thrust generation. Zhang et al. [12] studied the complex unsteady flow characteristics of a pulsed jet impinging on a rotating wall using numerical methods, and it was found that the impact pressure of the pulsed jet on the wall is greater than that of the continuous jet on the wall for a certain period of time when the water-hammer effect occurs. Rakhsha et al. [13] used experiments and numerical simulations to study the effect of pulsed jets on the flow and heat-transfer characteristics over a heated plane. It was found that the Nussell number increases with increasing pulse frequency and Reynolds number and decreases with increasing impinging distance. It is evident that existing studies predominantly center on the unsteady flow characteristics of pulsed jets and their properties related to heat and mass transfer. Conversely, there is a noticeable dearth of research concerning the scouring attributes of pulsed jets in the available literature. The pulsed submerged impinging jet represents a complex jet flow with a significant engineering application background and substantial theoretical research value. Exploring the unsteady hydraulic characteristics of pulsed jets can enhance classical impinging jet theory, deepen our comprehension of the jet–wall interaction mechanism, and establish a scientific foundation for addressing engineering-application challenges. Therefore, this paper introduces the pulse characteristics into the impinging jet, and, based on the Flow-3D software, the sand-scouring characteristics of the impinging jet under different Reynolds numbers and impinging distances are deeply investigated. The surface geometry of the scour pit is characterized while obtaining the pulsation characteristics of the unsteady flow structure during sand scouring. This study not only offers a foundation for implementing flow control and enhancing the understanding of unsteady flow characteristics but also furnishes theoretical backing for predicting impact pressure and impact pit formation.
2. Modeling and Numerical Methods
2.1. Model Building
The geometric model consists of a jet pipe, a body of water, a baffle, and a sand bed, as shown in Figure 1. The inner diameter D of the jet pipe is 20 mm, and the length L is set to 50D to ensure that the turbulence inside the pipe is fully developed. H represents the impinging height, and the initial water height (Hw) is 1600 mm. Baffles positioned on both sides serve to maintain a constant water level. The length Ls and thickness Hs of the sand bed are 5000 mm and 160 mm, respectively. It is worth stating that the sand bed is composed of non-cohesive sand. The median grain size dm of the sand is 0.77 mm, the specific gravity Δ is 1.65, and the particle gradation σg is 1.21.
Figure 1. Geometric modeling for sand scouring.
2.2. Numerical Models
In fluid mechanics, the continuity and momentum equations are the basic governing equations [14]:
where u, v, w denote the velocity of the fluid in the x, y, z direction, respectively; Ax, Ay, Az denote the area fraction of the fluid in the x, y, z direction, respectively; VF denotes the volume fraction; P is the pressure exerted on the fluid micrometric elements; Gx, Gy, Gz are the gravitational acceleration in the x, y, z direction, respectively; and fx, fy, fz are the viscous forces in the x, y, z direction, respectively.
In numerical simulations, the selection of a turbulence model significantly influences the accuracy of the calculations. Hence, it is imperative to choose an appropriate turbulence model. Given that this paper primarily deals with fully developed circular tube turbulence, which entails velocity and momentum coupling among fluids and features substantial time and spatial scales in the non-constant flow, the RNG k–ε turbulence model [15,16,17] has been chosen for the conclusive numerical simulation work. The RNG model takes into account the effect of eddies on turbulence and improves the accuracy of vortex-flow prediction [18]. Its equations are as follows:
where vt is the eddy viscosity coefficient; μ is the kinetic viscosity coefficient; the empirical constants cε1 and cε2 have values of 1.42 and 1.68; c3 = 0.012; η0 = 4.38; cμ = 0.085; and the values of Prandtl numbers αk and αε corresponding to the turbulent kinetic energy k and the dissipation rate ε are both 0.7194.
The Flow-3D software realizes an accurate description of the sediment movement with the help of an empirical equation model proposed by Mastbergen and Van den Berg [19]. The critical Shields number first needs to be calculated from the Soulsby–Whitehouse equation [20], which is given below:
where ρi is the sediment density, ρf is the fluid density, di is the sediment diameter, μf is the hydrodynamic viscosity, and ‖g‖ is the magnitude of gravitational acceleration.
Under the action of the jet, part of the deposited sediment will be disturbed to show a suspended state and it will continue to move under the carrying of the fluid. The uplifting velocities of entrained sediment ulift,i and usetting,i are calculated as follows:
where αi is the sediment carryover coefficient with a recommended value of 0.018 [19]; ns is the normal direction of the bed; and vf is the kinematic viscosity of the liquid.
2.3. Grid-Independent Analysis
It is well known that the number of the grid is closely related to the accuracy and cost of the numerical calculation. In order to investigate the optimal number of grids suitable for this numerical simulation, the scour depth Ht of the sand bed at H/D = 2 and inlet flow velocity Vb = 1.485 m/s is chosen as the monitoring parameter for the grid-independent analysis. Five sets of grid schemes with increasing numbers are set, and the results of the independence analysis are shown in Figure 2. From the figure, it can be seen that the depth of the scour pit Ht increases gradually with the encryption of the grid. When the grid is encrypted to Scheme 4, Ht almost no longer increases. It is considered that the number of meshes at this time can already meet the accuracy requirements of numerical calculations. Therefore, the grid number scheme in Scheme 4 is selected for the subsequent numerical simulation study, and the grid number is 43,825.
Figure 2. Grid-independent analysis.
2.4. Grid Delineation and Boundary Conditions
Within the Flow-3D software, a grid block is used that covers the entire 2D computational area as shown in Figure 1. Given the large aspect ratio of the jet pipe and the significant turbulent coupling between the fluid and sediment near the pipe outlet, grid refinement is implemented in the vicinity of the pipe outlet. The grid-encrypted area is mainly the area between the jet outlet and the sand bed, as shown in Figure 3. In addition, a mesh node is provided at the baffle on each side of the computational domain to ensure proper identification of the fluid boundary during numerical simulations. The upper boundary of the computational domain is defined as a velocity inlet, where the velocity magnitude is denoted as Vb, and the direction is oriented vertically downward. The lower boundary is the wall and no fluid or sediment flux is allowed. The two side boundaries are specified as pressure boundaries and the pressure is set to be 0 Pa. Based on the requirement of 2D numerical simulation, the boundaries of the front and rear sides are set as symmetric boundaries, both with one grid node. At the same time, the boundary-layer mesh near the pipe and the sand bed is encrypted accordingly. y+ is set at around 30 to ensure that the first grid nodes are in the turbulence core region, so as to ensure that the RNG k–ε turbulence model is perfectly adapted to the boundary conditions. Considering that the velocity strength and pressure gradient of the fluid around the baffle are small and it is not an observation area, the encryption of the boundary-layer grid is not performed for the time being.
Figure 3. Computational grid.
Numerical simulations are performed using the discrete control equations of the control volume method, with the diffusion term of the equations in the central difference format and the convection term in the second-order upwind format, and the equations are solved using a coupled algorithm. The standard wall equations are used, and the no-slip option in the wall shear boundary conditions is checked. In the non-stationary numerical simulation, the time step is set to 0.05 s. In order to ensure the accuracy of the numerical calculations, each time step is iterated 100 times, and the convergence accuracy is set to 10−5.
In this paper, the continuous jet is periodically truncated to form a blocking pulsed jet. The pulse period of its pulse velocity can be expressed as T = tj + t0 (tj and t0 are the jet time and truncation time, respectively, taking the value of 0.5 s), and the inlet flow rate of the jet pipe is Vb during the jet time period, while the inlet flow rate of the jet pipe is 0 during the truncation time period, as shown in Figure 4.
Figure 4. Velocity characteristics of the blocking pulsed jet.
3. Experimental Validation
To validate the accuracy of the numerical simulations, an experimental investigation of jet impingement on sediment is conducted. The experimental setup is shown in Figure 5. The parameters characterizing the sediment in the experiments are guaranteed to be the same as the settings in the numerical simulations. Specifically, non-cohesive sand is used with a median particle size dm of 0.77 mm, a specific gravity Δ of 1.65, and a particle gradation σg of 1.21. An angle plate is employed to control the impinging angle of the jet pipe, a COMS camera captures images of the pit, and a laser range finder is utilized for precise measurements of pit depth and dune height. In order to quantitatively describe the effect of jet impingement, the depth of the sand pit and the height of the dune are defined as d and h, respectively.
Figure 5. Schematic diagram of the experimental setup.
Figure 6 compares the stabilized morphology of the sand bed formed under the scouring of the jet for an impinging distance H/D of two in the numerical simulation and the experiment. The inlet flow velocities Vb of the jet pipe are 0.424 m/s, 0.955 m/s, and 1.485 m/s, respectively. As depicted in the figure, the ultimate scouring morphology of the sand bed, as obtained through numerical simulation, closely aligns with the experimental results. This alignment underscores the strong agreement between the numerical simulation and the experimental data. Nevertheless, it must be recognized that the final scour depths of the numerical simulations are all slightly smaller than the experimental values under the same conditions. The possible reason for this is the wall effect, i.e., the porosity of the actual sand bed is not homogeneous, with the upper sand layer being slightly more porous [21], whereas the porosity of the sand bed in the numerical simulation strictly follows the set value. Given that the accuracy of numerical calculations is subject to various influencing factors, and considering that the numerical solution inherently involves an approximation process, the numerical methods employed in this study can be deemed both accurate and dependable.
There are many factors that affect the performance of jet scouring, such as the shape of the nozzle, the size of the nozzle, the inlet flow rate of the jet pipe, the impinging distance, and the sediment parameters. Changes in any one of these factors can have a large effect on the parameters that measure the scouring performance of the jet, such as the depth of the scouring pit |ymin|, the height of the dune ymax, the radius of the scouring pit R. In this paper, the effects of the inlet velocity Vb and impinging distance H/D on the scouring performance of the jet pipe are investigated. Seven working conditions with inlet velocity Vb of 0.424 m/s, 0.690 m/s, 0.955 m/s, 1.220 m/s, 1.485 m/s, 1.751 m/s and 2.016 m/s are calculated for different impinging distances H/D (H/D = 2, 4, 6 and 8). The corresponding Reynolds numbers Re are 8404, 13,657, 18,910, 24,162, 29,415, 34,667, and 39,920, respectively.
4.1. Characterization of Pit at Different Impinging Distances
After the jet impinges on the sand bed for a sustained period of time, the shape of the sand bed will no longer change and remain stable. Figure 7 shows the stable bed morphology formed by the jet impinging on the sand bed with different velocities Vb, and at different impinging distances H/D. The x-axis is at the axial position of the jet pipe, and the y-axis is the initial horizontal plane of the sand bed. As can be seen from the figure, under the condition of Vb = 0.424 m/s, the pit depths |ymin| corresponding to impinging distances H/D of two and four are basically equal. However, when H/D is increased to six, |ymin| becomes significantly smaller, and when H/D is eight, |ymin| increases again. Under the Vb = 0.690 m/s condition, the effect of H/D on the scour pit depth |ymin| is small, and its size basically stays around 3.5 cm. Under the Vb = 0.955 m/s condition, the pit depth corresponding to H/D = eight is slightly smaller than the pit depths at other impinging distances, and the magnitude of |ymin| is basically maintained near 4.6 cm. Under the Vb = 1.220 m/s condition, the change of the scouring pit depth |ymin| with the impinging distance H/D starts to be gradually significant, especially the scouring pit depth |ymin| which decreases by about 1.7 cm when the size of H/D increases from two to six. Under the condition of Vb = 1.220 m/s, the larger the H/D, the smaller the pit depth |ymin|, especially when the H/D is eight, the pit depth is obviously larger than the pit depth at other impinging distances. The corresponding pit depths |ymin| for Vb of 1.751 m/s and 2.016 m/s remain basically unchanged. From the above analysis, it can be seen that under the same Reynolds number conditions to some extent the impinging distance has a very limited effect on the depth of the pit |ymin|. When the impinging distance increases, the depth of the pit begins to decrease. This can be attributed to the fact that the increased distance results in the jet encountering the initial static water resistance over a longer duration, leading to a greater dissipation of kinetic energy and a subsequent reduction in the impinging force of the jet.
The depth of the scouring pit serves as a critical parameter for assessing the impact of jet impingement on sand beds, just as the height of the dune represents a key indicator for evaluating the effectiveness of this process. In Figure 7a, it can be seen that the dune height ymax increases synchronously with the increase of the impinging distance H/D at Vb = 0.424 m/s. When Vb ≥ 0.955 m/s, the dune height ymax no longer grows significantly with the increase of impinging distance H/D. To further explore the relationship between dune height and impinging distance, Figure 8 is plotted with the impinging distance as the horizontal coordinate and the dune heights on either side as the vertical coordinate. From the figure, it can be seen that when 0.424 m/s ≤ Vb ≤ 1.485 m/s, the dune height ymax increases with the increase of the impinging distance H/D, and the dune height ymax starts to decrease with the increase of the impinging distance H/D when Vb > 1.485 m/s. The reason behind the aforementioned phenomenon is that when the inlet velocity Vb of the jet pipe is low, suspended sediment tends to displace towards the sides of the dune, causing some of the sediment to accumulate on the dune and thereby increase its height. When Vb ≥ 1.485 m/s, due to the enhanced impact force, most of the suspended sediment no longer moves and accumulates near the dunes and sand pits, and it starts to move on the outside of the dunes, causing the dune height to decrease.
Figure 8. Variation in the height of dunes on either side of the scour pit with Vb: (a) left; (b) right.
In order to clarify the relationship between the pit radius R and the impinging distance H/D, the relationship is given in Figure 9. From the figure, it can be seen that when 0.424 ≤ Vb ≤ 0.690, the increase of impinging distance H/D has basically no effect on the radius R of the pit, and its magnitude always stays near 13 cm. As the inlet velocity Vb of the jet pipe increases (1.220 ≤ Vb ≤ 1.485), the impact of the pulsed jet intensifies. Consequently, the suspended sediment is propelled towards the sides of the sand pit; although, it has not reached the dune and the area beyond it. Instead, a substantial amount of suspended sediment settles within the sand pit on both sides. Simultaneously, as the impact distance increases, the reach of jet impact and the turbulence induced by the jet expand, leading to enhanced sediment transport on both sides of the sand pit. This ultimately results in a reduction in the radius of the scouring pit as the impinging distance increases.
Figure 9. Relationship between pit size and impinging distance.
4.2. Characterization of Piting at Different Reynolds Numbers
Figure 10 depicts the stabilized morphology of the sand pit resulting from the influence of jets with varying Reynolds numbers. Under the conditions of H/D = two and four, the inlet velocity Vb of the jet pipe is 0.424 m/s and 0.690 m/s, and the depth of the pit |ymin| is basically equal, which indicates that the impact of the jet on the sand bed at this time is small, and the sediment is only transported and circulated in the sand pit. When Vb ≥ 0.955, the depth of the pit |ymin| increases significantly with the increase of Vb. Under the condition of H/D = 6, the depth of the pit, denoted as |ymin|, ceases to remain constant when Vb is less than or equal to 0.690 m/s. However, the disparity between the two measurements remains relatively small, suggesting that the impact force and turbulence of the jet are already capable of transporting sediment from the bottom of the pit to its flanks when Vb ≤ 0.690 m/s. In the H/D = 8 condition, due to the impinging distance H/D is larger, and when the velocity of the jet pipe is small (Vb ≤ 0.690 m/s), the kinetic energy of the jet is continuously exchanged with the static water body and then reduced, making its impact force reduce, and the sediment can only be transported and circulated at the bottom of the sand pit. To further investigate the effect of the Reynolds number of the jet on the depth of the pit |ymin|, Figure 11 is plotted with the jet velocity Vb as the horizontal coordinate and the depth of the pit |ymin| as the vertical coordinate. From the figure, it is evident that there exists a strong linear relationship between the depth of the scouring pit and the jet velocity. The data points in the figure can be fitted to establish the following relationship between the depth of the scouring pit and the jet velocity:
Figure 11. Linear relationship between scouring-pit depth and jet velocity.
4.3. Characterization of Pits with Different Impinging Times
Figure 12 illustrates the deformation of the sand bed caused by the impact of the pulsed jet over a time range from 0.75 s to 3.5 s (with intervals of 0.25 s). When the jet velocity Vb is 0.424 m/s, within the initial 0.75 s of jet initiation, the impact of the pulsed jet leads to noticeable deformation of the sand pit and dune, with their fundamental shapes taking form. The depth of the pit, denoted as |ymin|, continuously increases from 0.75 s to 2 s, eventually stabilizing around 2.75 s. By the onset of the pulsed jet, the dune has already assumed a fundamental profile, and its maximum height, represented as ymax, exhibits minimal variation over time, remaining relatively constant.
In this paper, a numerical computational study is conducted to examine the characteristics of sand-bed impingement using obstructing pulsed jets. A comprehensive analysis is undertaken, encompassing impingement-pit depth, dune height, and impingement-pit radius. The following conclusions are drawn:
Under consistent jet-velocity conditions, the impingement distance (H/D) has minimal impact on the depth of the scouring pit within the range of 2 ≤ H/D ≤ 6. However, beyond this range (H/D > 6), increased impingement distance leads to heightened jet-energy dissipation, resulting in a weakened impact force and a subsequent reduction in pit depth. Additionally, for lower jet velocities, impinging-distance variations have negligible effects on pit radius, while higher jet velocities induce a decrease in pit radius with an increase in impinging distance.
The study establishes strong linear relationships between both the radius and depth of the scouring pit and the jet velocity. However, the relationship between dune height and pulsed-jet velocity is characterized by randomness and uncertainty. The dynamics of sediment transport contribute to the lack of symmetry in the stable configuration of the sand pit concerning the jet-pipe axis. Furthermore, the relationship between dune height and pulsed-jet velocity exhibits transient characteristics, highlighting the complex nature of these interactions.
The numerical computational analysis emphasizes the transient characteristics of the sand-pit configuration due to sediment-transport dynamics. The stable state of the pit does not assume symmetry with the jet pipe as the axis, introducing a level of asymmetry in the system. This asymmetry is crucial in understanding the complex behavior of the sand-bed impingement. The findings underscore the need to consider dynamic and transient factors when studying the impact of obstructing pulsed jets on sand-bed characteristics.
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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.
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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]:
where, respectively, u, v, and w represent the x, y, and z flow velocity components; volume fraction (VF), area fraction (Ai; I=x, y, z), 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].
α𝛼i 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).
fbis the essential particle packing percentage, qb, i 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), fb, δ𝛿i the bed load thickness.
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.
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.
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.
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.
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:
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.
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.
Figure 9. Main 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.
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
CFD
Computational fluid dynamics
FAVOR
Fractional Area/Volume Obstacle Representation
VOF
Volume of Fluid
RNG
Renormalized Group
OWTs
Offshore wind turbines
Greek Symbols
ε, ω
Dissipation rate of the turbulent kinetic energy, m2s-3
Subscripts
d50
Median particle size
Vf
Volume fraction
GT
Turbulent energy of buoyancy
KT
Turbulent velocity
PT
Kinetic energy of the turbulence
Αi
Induction parameter
ns
Induction parameter
ΘΘcr
The essential Shields variable
Di
Diameter of sediment
d∗
The diameter of particles without dimensions
µf
Dynamic viscosity of the fluid
qb,i
The bed load transportation rate
Cs,i
Sand particle’s concentration of mass
D
Diameter of pile
Df
Diffusivity
D
Diameter of main column
Fr
Froud number
Kc
Keulegan–Carpenter number
G
Acceleration of gravity g
H
Flow depth
Vw
Wave Velocity
V
Mean Velocity
Tp
Wave Period
S
Scour depth
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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
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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Ghobadian, R. & Seyedi tabar, Z. (2016). Numerical investigating of the effect of lateral channel junction position on flow Rectangular Composite Channel Using Flow3D Software. Irrigation and Water Engineering, 13(1), 1-16. Doi: 10.22125/iwe.2022.158503 (In Persian).
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Weber, L.J., Schumate, E.D. & Mawer, N. (2001). Experiments on Flow at a 90° Open-Channel Junction. Journal of hydraulic engineering, 127(5), 340-350.
•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.
The Anak Krakatau landslide tsunami on 22nd December 2018 was a stark reminder of the dangers posed by subaerial landslide tsunamis (Ren et al., 2020; Mulia et al. 2020a; Borrero et al., 2020; Heidarzadeh et al., 2020; Grilli 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., 2020; Mulia 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).
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., 2018; Grilli et al., 2019; Heidarzadeh et al., 2017, 2020; Iorio et al., 2021; Zhang et al., 2021; Kirby et al., 2022; Wang et al., 2021, 2022; Hu 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., 2020; Chen 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, 1998; Najafi-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.
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).
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 attributes
Property metrics
Geometric shape
Slide width (bs)
0.26 m
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.
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 block
ls (m)
bs (m)
s (m)
V (m3)
γs
Block-1
0.310
0.260
0.155
6.25 × 10−3
2.60
Block-2
0.300
0.260
0.150
5.85 × 10−3
2.60
Block-3
0.280
0.260
0.140
5.10 × 10−3
2.60
Block-4
0.260
0.260
0.130
4.39 × 10−3
2.60
Block-5
0.240
0.260
0.120
3.74 × 10−3
2.60
Block-6
0.220
0.260
0.110
3.15 × 10−3
2.60
Block-7
0.200
0.260
0.100
2.60 × 10−3
2.60
Block-8
0.180
0.260
0.090
2.11 × 10−3
2.60
Block-9
0.160
0.260
0.080
1.66 × 10−3
2.60
Block-10
0.140
0.260
0.070
1.27 × 10−3
2.60
Block-11
0.120
0.260
0.060
0.93 × 10−3
2.60
Block-12
0.100
0.260
0.050
0.65 × 10−3
2.60
Block-13
0.080
0.260
0.040
0.41 × 10−3
2.60
Block-14
0.060
0.260
0.030
0.23 × 10−3
2.60
Block-15
0.040
0.260
0.020
0.10 × 10−3
2.60
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 No
α (°)
h (m)
D (m)
T(s)
aM (m)
1
Block-7
45
0.246
0.029
0.510
0.0153
2
Block-7
45
0.246
0.030
0.505
0.0154
3
Block-7
45
0.246
0.031
0.505
0.0156
4
Block-7
45
0.246
0.032
0.505
0.0158
5
Block-7
45
0.246
0.033
0.505
0.0159
6
Block-7
45
0.246
0.034
0.505
0.0160
7
Block-7
45
0.246
0.035
0.505
0.0162
8
Block-7
45
0.246
0.036
0.505
0.0166
9
Block-7
45
0.246
0.037
0.505
0.0167
10
Block-7
45
0.246
0.038
0.505
0.0172
11
Block-7
45
0.246
0.039
0.505
0.0178
12
Block-7
45
0.246
0.040
0.505
0.0179
13
Block-7
45
0.246
0.041
0.505
0.0181
14
Block-7
45
0.246
0.042
0.505
0.0183
15
Block-7
45
0.246
0.043
0.505
0.0190
16
Block-7
45
0.246
0.044
0.505
0.0197
17
Block-7
45
0.246
0.045
0.505
0.0199
18
Block-7
45
0.246
0.046
0.505
0.0201
19
Block-7
45
0.246
0.047
0.505
0.0191
20
Block-7
45
0.246
0.048
0.505
0.0217
21
Block-7
45
0.246
0.049
0.505
0.0220
22
Block-7
45
0.246
0.050
0.505
0.0226
23
Block-7
45
0.246
0.051
0.505
0.0236
24
Block-7
45
0.246
0.052
0.505
0.0239
25
Block-7
45
0.246
0.053
0.510
0.0240
26
Block-7
45
0.246
0.054
0.505
0.0241
27
Block-7
45
0.246
0.055
0.505
0.0246
28
Block-7
45
0.246
0.056
0.505
0.0247
29
Block-7
45
0.246
0.057
0.505
0.0248
30
Block-7
45
0.246
0.058
0.505
0.0249
31
Block-7
45
0.246
0.059
0.505
0.0251
32
Block-7
45
0.246
0.060
0.505
0.0257
33
Block-1
45
0.246
0.045
0.505
0.0319
34
Block-2
45
0.246
0.045
0.505
0.0294
35
Block-3
45
0.246
0.045
0.505
0.0282
36
Block-4
45
0.246
0.045
0.505
0.0262
37
Block-5
45
0.246
0.045
0.505
0.0243
38
Block-6
45
0.246
0.045
0.505
0.0223
39
Block-7
45
0.246
0.045
0.505
0.0196
40
Block-8
45
0.246
0.045
0.505
0.0197
41
Block-9
45
0.246
0.045
0.505
0.0198
42
Block-10
45
0.246
0.045
0.505
0.0184
43
Block-11
45
0.246
0.045
0.505
0.0173
44
Block-12
45
0.246
0.045
0.505
0.0165
45
Block-13
45
0.246
0.045
0.404
0.0153
46
Block-14
45
0.246
0.045
0.404
0.0124
47
Block-15
45
0.246
0.045
0.505
0.0066
48
Block-7
45
0.202
0.045
0.404
0.0220
49
Block-7
45
0.204
0.045
0.404
0.0219
50
Block-7
45
0.206
0.045
0.404
0.0218
51
Block-7
45
0.208
0.045
0.404
0.0217
52
Block-7
45
0.210
0.045
0.404
0.0216
53
Block-7
45
0.212
0.045
0.404
0.0215
54
Block-7
45
0.214
0.045
0.505
0.0214
55
Block-7
45
0.216
0.045
0.505
0.0214
56
Block-7
45
0.218
0.045
0.505
0.0213
57
Block-7
45
0.220
0.045
0.505
0.0212
58
Block-7
45
0.222
0.045
0.505
0.0211
59
Block-7
45
0.224
0.045
0.505
0.0208
60
Block-7
45
0.226
0.045
0.505
0.0203
61
Block-7
45
0.228
0.045
0.505
0.0202
62
Block-7
45
0.230
0.045
0.505
0.0201
63
Block-7
45
0.232
0.045
0.505
0.0201
64
Block-7
45
0.234
0.045
0.505
0.0200
65
Block-7
45
0.236
0.045
0.505
0.0199
66
Block-7
45
0.238
0.045
0.404
0.0196
67
Block-7
45
0.240
0.045
0.404
0.0194
68
Block-7
45
0.242
0.045
0.404
0.0193
69
Block-7
45
0.244
0.045
0.404
0.0192
70
Block-7
45
0.246
0.045
0.505
0.0190
71
Block-7
45
0.248
0.045
0.505
0.0189
72
Block-7
45
0.250
0.045
0.505
0.0187
73
Block-7
45
0.252
0.045
0.505
0.0187
74
Block-7
45
0.254
0.045
0.505
0.0186
75
Block-7
45
0.256
0.045
0.505
0.0184
76
Block-7
45
0.258
0.045
0.505
0.0182
77
Block-7
45
0.259
0.045
0.505
0.0183
78
Block-7
45
0.260
0.045
0.505
0.0191
79
Block-7
45
0.261
0.045
0.505
0.0192
80
Block-7
45
0.262
0.045
0.505
0.0194
81
Block-7
45
0.263
0.045
0.505
0.0195
82
Block-7
45
0.264
0.045
0.505
0.0195
83
Block-7
45
0.265
0.045
0.505
0.0197
84
Block-7
45
0.266
0.045
0.505
0.0197
85
Block-7
45
0.267
0.045
0.505
0.0198
86
Block-7
45
0.270
0.045
0.505
0.0199
87
Block-7
30
0.246
0.045
0.505
0.0101
88
Block-7
35
0.246
0.045
0.505
0.0107
89
Block-7
36
0.246
0.045
0.505
0.0111
90
Block-7
37
0.246
0.045
0.505
0.0116
91
Block-7
38
0.246
0.045
0.505
0.0117
92
Block-7
39
0.246
0.045
0.505
0.0119
93
Block-7
40
0.246
0.045
0.505
0.0121
94
Block-7
41
0.246
0.045
0.505
0.0127
95
Block-7
42
0.246
0.045
0.404
0.0154
96
Block-7
43
0.246
0.045
0.404
0.0157
97
Block-7
44
0.246
0.045
0.404
0.0162
98
Block-7
45
0.246
0.045
0.505
0.0197
99
Block-7
50
0.246
0.045
0.505
0.0221
100
Block-7
55
0.246
0.045
0.505
0.0233
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.
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 2014; Heller and Spinneken 2015; Sabeti 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).
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) (k–w) 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.
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 3, 4). 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).
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. 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.
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.
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 m3, h= 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., 2020; Grilli et al., 2019, 2021), 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, 2014; Watts 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.
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.
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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 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)
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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-tripodfluid 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.
Weirs are essential structures used to manage excess water flow from behind dams to downstream areas. Enhancing discharge efficiency often involves extending the effective length of Piano Key Weirs (PKW) in dams or regulating flow within irrigation and drainage networks. This study employed both numerical and laboratory investigations to assess the impact of different base nose shapes installed beneath the outlet keys and varying Input to output key width ratios (Wi/Wo) on discharges ranging from 5 to 80 liters per second. Furthermore, the study aimed to achieve research objectives and compare the performance of Piano Key Weirs with Ogee Weir. For numerical simulation, the optimal number of cells for meshing was determined, and an appropriate turbulence model was selected. The results indicated that the numerical model accurately simulated the laboratory sample with a high degree of precision. Moreover, the numerical model closely approximated PKW for all parameters Q, H, and Cd compared to the laboratory sample. The findings revealed that in laboratory models with a maximum discharge area of 80 liters per second, the weir with Wi/Wo=1.2 and a flow head value of 285 mm exhibited the lowest value, whereas the weir with Wi/Wo=0.71 and a flow head value of 305 mm showed the highest, attributed to the higher discharge in the input-output ratio. Additionally, as the ratio of flow head to weir height H/P increased, the discharge coefficient Cd decreased. Comparing the flow conditions in weirs with different base nose shapes, it was observed that the weir with a spindle nose shape (PKW1.2S) outperformed the PKW with a flat (PKW1.2), semi-cylindrical (PKW1.2CL) and triangular base nose (PKW1.2TR). The results emphasized that models featuring semi-cylindrical and flat noses exhibited notable flow deviation and abrupt disruption upon impact with the nose. However, this effect was significantly reduced in models equipped with triangular and spindle-shaped noses. Also, the coefficient of discharge in PKW1.2S and PKW1.2TR weirs, compared to the PKW1.20 weir, increased by 27% and 20%, respectively.
웨어는 댐 뒤에서 하류 지역으로의 과도한 물 흐름을 관리하는 데 사용되는 필수 구조물입니다. 배출 효율을 높이는 데에는 댐의 피아노 키 위어(PKW) 유효 길이를 연장하거나 관개 및 배수 네트워크 내 흐름을 조절하는 것이 포함됩니다.
이 연구에서는 콘센트 키 아래에 설치된 다양한 베이스 노즈 모양과 초당 5~80리터 범위의 배출에 대한 다양한 입력 대 출력 키 너비 비율(Wi/Wo)의 영향을 평가하기 위해 수치 및 실험실 조사를 모두 사용했습니다. 또한 본 연구에서는 연구 목적을 달성하고 Piano Key Weir와 Ogee Weir의 성능을 비교하는 것을 목표로 했습니다.
수치 시뮬레이션을 위해 메시 생성을 위한 최적의 셀 수를 결정하고 적절한 난류 모델을 선택했습니다. 결과는 수치 모델이 높은 정밀도로 실험실 샘플을 정확하게 시뮬레이션했음을 나타냅니다. 더욱이, 수치 모델은 실험실 샘플과 비교하여 모든 매개변수 Q, H 및 Cd에 대해 PKW에 매우 근접했습니다.
연구 결과, 최대 배출 면적이 초당 80리터인 실험실 모델에서는 Wi/Wo=1.2, 플로우 헤드 값이 285mm인 웨어가 가장 낮은 값을 나타냈고, Wi/Wo=0.71 및 a인 웨어는 가장 낮은 값을 나타냈습니다. 플로우 헤드 값은 305mm로 가장 높은 것으로 나타났는데, 이는 입출력 비율의 높은 토출량에 기인합니다. 또한, 웨어 높이에 대한 유수두 비율 H/P가 증가함에 따라 유출계수 Cd는 감소하였다.
베이스 노즈 모양이 다른 웨어의 흐름 조건을 비교해 보면, 스핀들 노즈 모양(PKW1.2S)의 웨어가 평면(PKW1.2), 반원통형(PKW1.2CL) 및 삼각형 모양의 PKW보다 성능이 우수한 것으로 관찰되었습니다. 베이스 노즈(PKW1.2TR) 결과는 반원통형 및 편평한 노즈를 특징으로 하는 모델이 노즈에 충격을 가할 때 눈에 띄는 흐름 편차와 급격한 중단을 나타냄을 강조했습니다.
그러나 삼각형 및 방추형 노즈를 장착한 모델에서는 이러한 효과가 크게 감소했습니다. 또한 PKW1.20보에 비해 PKW1.2S보와 PKW1.2TR보의 유출계수는 각각 27%, 20% 증가하였다.
Keywords
Piano Key Weir, Base Nose Shape, Flow Hydraulics, Numerical Model, Triangular Nose Shape, Flat Nose Shape, Semi-Cylindrical Nose Shape, Spindle Nose Shape
Figure (17): Stream Lines Indicating Average Flow Speed in the Model with Various Nose shapes, Measured at Mid-Depth and at the Flow Surface Level, at a Flow Rate of 78 Liters per Second.
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Alireza Khoshkonesh1, Blaise Nsom2, Saeid Okhravi3*, Fariba Ahmadi Dehrashid4, Payam Heidarian5, Silvia DiFrancesco6 1 Department of Geography, School of Social Sciences, History, and Philosophy, Birkbeck University of London, London, UK. 2 Université de Bretagne Occidentale. IRDL/UBO UMR CNRS 6027. Rue de Kergoat, 29285 Brest, France. 3 Institute of Hydrology, Slovak Academy of Sciences, Dúbravská cesta 9, 84104, Bratislava, Slovak Republic. 4Department of Water Science and Engineering, Faculty of Agriculture, Bu-Ali Sina University, 65178-38695, Hamedan, Iran. 5 Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, 25123 Brescia, Italy. 6Niccol`o Cusano University, via Don C. Gnocchi 3, 00166 Rome, Italy. * Corresponding author. Tel.: +421-944624921. E-mail: saeid.okhravi@savba.sk
Abstract
This study aimed to comprehensively investigate the influence of substrate level difference and material composition on dam break wave evolution over two different erodible beds. Utilizing the Volume of Fluid (VOF) method, we tracked free surface advection and reproduced wave evolution using experimental data from the literature. For model validation, a comprehensive sensitivity analysis encompassed mesh resolution, turbulence simulation methods, and bed load transport equations. The implementation of Large Eddy Simulation (LES), non-equilibrium sediment flux, and van Rijn’s (1984) bed load formula yielded higher accuracy compared to alternative approaches. The findings emphasize the significant effect of substrate level difference and material composition on dam break morphodynamic characteristics. Decreasing substrate level disparity led to reduced flow velocity, wavefront progression, free surface height, substrate erosion, and other pertinent parameters. Initial air entrapment proved substantial at the wavefront, illustrating pronounced air-water interaction along the bottom interface. The Shields parameter experienced a one-third reduction as substrate level difference quadrupled, with the highest near-bed concentration observed at the wavefront. This research provides fresh insights into the complex interplay of factors governing dam break wave propagation and morphological changes, advancing our comprehension of this intricate phenomenon.
이 연구는 두 개의 서로 다른 침식층에 대한 댐 파괴파 진화에 대한 기질 수준 차이와 재료 구성의 영향을 종합적으로 조사하는 것을 목표로 했습니다. VOF(유체량) 방법을 활용하여 자유 표면 이류를 추적하고 문헌의 실험 데이터를 사용하여 파동 진화를 재현했습니다.
모델 검증을 위해 메쉬 해상도, 난류 시뮬레이션 방법 및 침대 하중 전달 방정식을 포함하는 포괄적인 민감도 분석을 수행했습니다. LES(Large Eddy Simulation), 비평형 퇴적물 플럭스 및 van Rijn(1984)의 하상 부하 공식의 구현은 대체 접근 방식에 비해 더 높은 정확도를 산출했습니다.
연구 결과는 댐 붕괴 형태역학적 특성에 대한 기질 수준 차이와 재료 구성의 중요한 영향을 강조합니다. 기판 수준 차이가 감소하면 유속, 파면 진행, 자유 표면 높이, 기판 침식 및 기타 관련 매개변수가 감소했습니다.
초기 공기 포집은 파면에서 상당한 것으로 입증되었으며, 이는 바닥 경계면을 따라 뚜렷한 공기-물 상호 작용을 보여줍니다. 기판 레벨 차이가 4배로 증가함에 따라 Shields 매개변수는 1/3로 감소했으며, 파면에서 가장 높은 베드 근처 농도가 관찰되었습니다.
이 연구는 댐 파괴파 전파와 형태학적 변화를 지배하는 요인들의 복잡한 상호 작용에 대한 새로운 통찰력을 제공하여 이 복잡한 현상에 대한 이해를 향상시킵니다.
Fig. 3. Free surface and substrate profiles in all Sp and Ls cases at t = 1 s, t = 3 s, and t = 5 s, arranged left to right (note: the colour contours
correspond to the horizontal component of the flow velocity (u), expressed in m/s).
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Farhoud Kalateh a,*, Ehsan Aminvash a and Rasoul Daneshfaraz b a Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran b Faculty of Engineering, University of Maragheh, Maragheh, Iran *Corresponding author. E-mail: f.kalateh@gmail.com
ABSTRACT
The main goal of the present study is to investigate the effects of macro-roughnesses downstream of the inclined drop through numerical models. Due to the vital importance of geometrical properties of the macro-roughnesses in the hydraulic performance and efficient energy dissipation downstream of inclined drops, two different geometries of macro-roughnesses, i.e., semi-circular and triangular geometries, have been investigated using the Flow-3D model. Numerical simulation showed that with the flow rate increase and relative critical depth, the flow energy consumption has decreased. Also, relative energy dissipation increases with the increase in height and slope angle, so that this amount of increase in energy loss compared to the smooth bed in semi-circular and triangular elements is 86.39 and 76.80%, respectively, in the inclined drop with a height of 15 cm and 86.99 and 65.78% in the drop with a height of 20 cm. The Froude number downstream on the uneven bed has been dramatically reduced, so this amount of reduction has been approximately 47 and 54% compared to the control condition. The relative depth of the downstream has also increased due to the turbulence of the flow on the uneven bed with the increase in the flow rate.
본 연구의 주요 목표는 수치 모델을 통해 경사 낙하 하류의 거시 거칠기 효과를 조사하는 것입니다. 수력학적 성능과 경사 낙하 하류의 효율적인 에너지 소산에서 거시 거칠기의 기하학적 특성이 매우 중요하기 때문에 두 가지 서로 다른 거시 거칠기 형상, 즉 반원형 및 삼각형 형상이 Flow를 사용하여 조사되었습니다.
3D 모델 수치 시뮬레이션을 통해 유량이 증가하고 상대 임계 깊이가 증가함에 따라 유동 에너지 소비가 감소하는 것으로 나타났습니다. 또한, 높이와 경사각이 증가함에 따라 상대적인 에너지 소산도 증가하는데, 반원형 요소와 삼각형 요소에서 평활층에 비해 에너지 손실의 증가량은 경사낙하에서 각각 86.39%와 76.80%입니다.
높이 15cm, 높이 20cm의 드롭에서 86.99%, 65.78%입니다. 고르지 못한 베드 하류의 프루드 수가 극적으로 감소하여 이 감소량은 대조 조건에 비해 약 47%와 54%였습니다. 유속이 증가함에 따라 고르지 못한 층에서의 흐름의 난류로 인해 하류의 상대적 깊이도 증가했습니다.
Key words
flow energy dissipation, Froude number, inclined drop, numerical simulation
Figure 1 | Schematic of the present research model with dimensions and macro-roughnesses installed.Figure 2 | Meshing, boundary condition, and solution field network
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웨어의 두 가지 서로 다른 배열(즉, 직선형 웨어와 직사각형 미로 웨어)을 사용하여 웨어 모양, 웨어 간격, 웨어의 오리피스 존재, 흐름 영역에 대한 바닥 경사와 같은 기하학적 매개변수의 영향을 평가했습니다.
유량과 수심의 관계, 수심 평균 속도의 변화와 분포, 난류 특성, 어도에서의 에너지 소산. 흐름 조건에 미치는 영향을 조사하기 위해 FLOW-3D® 소프트웨어를 사용하여 전산 유체 역학 시뮬레이션을 수행했습니다.
수치 모델은 계산된 표면 프로파일과 속도를 문헌의 실험적으로 측정된 값과 비교하여 검증되었습니다. 수치 모델과 실험 데이터의 결과, 급락유동의 표면 프로파일과 표준화된 속도 프로파일에 대한 평균 제곱근 오차와 평균 절대 백분율 오차가 각각 0.014m와 3.11%로 나타나 수치 모델의 능력을 확인했습니다.
수영장과 둑의 흐름 특성을 예측합니다. 각 모델에 대해 L/B = 1.83(L: 웨어 거리, B: 수로 폭) 값에서 급락 흐름이 발생할 수 있고 L/B = 0.61에서 스트리밍 흐름이 발생할 수 있습니다. 직사각형 미로보 모델은 기존 모델보다 무차원 방류량(Q+)이 더 큽니다.
수중 흐름의 기존 보와 직사각형 미로 보의 경우 Q는 각각 1.56과 1.47h에 비례합니다(h: 보 위 수심). 기존 웨어의 풀 내 평균 깊이 속도는 직사각형 미로 웨어의 평균 깊이 속도보다 높습니다.
그러나 주어진 방류량, 바닥 경사 및 웨어 간격에 대해 난류 운동 에너지(TKE) 및 난류 강도(TI) 값은 기존 웨어에 비해 직사각형 미로 웨어에서 더 높습니다. 기존의 웨어는 직사각형 미로 웨어보다 에너지 소산이 더 낮습니다.
더 낮은 TKE 및 TI 값은 미로 웨어 상단, 웨어 하류 벽 모서리, 웨어 측벽과 채널 벽 사이에서 관찰되었습니다. 보와 바닥 경사면 사이의 거리가 증가함에 따라 평균 깊이 속도, 난류 운동 에너지의 평균값 및 난류 강도가 증가하고 수영장의 체적 에너지 소산이 감소했습니다.
둑에 개구부가 있으면 평균 깊이 속도와 TI 값이 증가하고 풀 내에서 가장 높은 TKE 범위가 감소하여 두 모델 모두에서 물고기를 위한 휴식 공간이 더 넓어지고(TKE가 낮아짐) 에너지 소산율이 감소했습니다.
Two different arrangements of the weir (i.e., straight weir and rectangular labyrinth weir) were used to evaluate the effects of geometric parameters such as weir shape, weir spacing, presence of an orifice at the weir, and bed slope on the flow regime and the relationship between discharge and depth, variation and distribution of depth-averaged velocity, turbulence characteristics, and energy dissipation at the fishway. Computational fluid dynamics simulations were performed using FLOW-3D® software to examine the effects on flow conditions. The numerical model was validated by comparing the calculated surface profiles and velocities with experimentally measured values from the literature. The results of the numerical model and experimental data showed that the root-mean-square error and mean absolute percentage error for the surface profiles and normalized velocity profiles of plunging flows were 0.014 m and 3.11%, respectively, confirming the ability of the numerical model to predict the flow characteristics of the pool and weir. A plunging flow can occur at values of L/B = 1.83 (L: distance of the weir, B: width of the channel) and streaming flow at L/B = 0.61 for each model. The rectangular labyrinth weir model has larger dimensionless discharge values (Q+) than the conventional model. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q is proportional to 1.56 and 1.47h, respectively (h: the water depth above the weir). The average depth velocity in the pool of a conventional weir is higher than that of a rectangular labyrinth weir. However, for a given discharge, bed slope, and weir spacing, the turbulent kinetic energy (TKE) and turbulence intensity (TI) values are higher for a rectangular labyrinth weir compared to conventional weir. The conventional weir has lower energy dissipation than the rectangular labyrinth weir. Lower TKE and TI values were observed at the top of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall. As the distance between the weirs and the bottom slope increased, the average depth velocity, the average value of turbulent kinetic energy and the turbulence intensity increased, and the volumetric energy dissipation in the pool decreased. The presence of an opening in the weir increased the average depth velocity and TI values and decreased the range of highest TKE within the pool, resulted in larger resting areas for fish (lower TKE), and decreased the energy dissipation rates in both models.
1 Introduction
Artificial barriers such as detour dams, weirs, and culverts in lakes and rivers prevent fish from migrating and completing the upstream and downstream movement cycle. This chain is related to the life stage of the fish, its location, and the type of migration. Several riverine fish species instinctively migrate upstream for spawning and other needs. Conversely, downstream migration is a characteristic of early life stages [1]. A fish ladder is a waterway that allows one or more fish species to cross a specific obstacle. These structures are constructed near detour dams and other transverse structures that have prevented such migration by allowing fish to overcome obstacles [2]. The flow pattern in fish ladders influences safe and comfortable passage for ascending fish. The flow’s strong turbulence can reduce the fish’s speed, injure them, and delay or prevent them from exiting the fish ladder. In adult fish, spawning migrations are usually complex, and delays are critical to reproductive success [3].
Various fish ladders/fishways include vertical slots, denil, rock ramps, and pool weirs [1]. The choice of fish ladder usually depends on many factors, including water elevation, space available for construction, and fish species. Pool and weir structures are among the most important fish ladders that help fish overcome obstacles in streams or rivers and swim upstream [1]. Because they are easy to construct and maintain, this type of fish ladder has received considerable attention from researchers and practitioners. Such a fish ladder consists of a sloping-floor channel with series of pools directly separated by a series of weirs [4]. These fish ladders, with or without underwater openings, are generally well-suited for slopes of 10% or less [1, 2]. Within these pools, flow velocities are low and provide resting areas for fish after they enter the fish ladder. After resting in the pools, fish overcome these weirs by blasting or jumping over them [2]. There may also be an opening in the flooded portion of the weir through which the fish can swim instead of jumping over the weir. Design parameters such as the length of the pool, the height of the weir, the slope of the bottom, and the water discharge are the most important factors in determining the hydraulic structure of this type of fish ladder [3]. The flow over the weir depends on the flow depth at a given slope S0 and the pool length, either “plunging” or “streaming.” In plunging flow, the water column h over each weir creates a water jet that releases energy through turbulent mixing and diffusion mechanisms [5]. The dimensionless discharges for plunging (Q+) and streaming (Q*) flows are shown in Fig. 1, where Q is the total discharge, B is the width of the channel, w is the weir height, S0 is the slope of the bottom, h is the water depth above the weir, d is the flow depth, and g is the acceleration due to gravity. The maximum velocity occurs near the top of the weir for plunging flow. At the water’s surface, it drops to about half [6].
Fig. 1
Extensive experimental studies have been conducted to investigate flow patterns for various physical geometries (i.e., bed slope, pool length, and weir height) [2]. Guiny et al. [7] modified the standard design by adding vertical slots, orifices, and weirs in fishways. The efficiency of the orifices and vertical slots was related to the velocities at their entrances. In the laboratory experiments of Yagci [8], the three-dimensional (3D) mean flow and turbulence structure of a pool weir fishway combined with an orifice and a slot is investigated. It is shown that the energy dissipation per unit volume and the discharge have a linear relationship.
Considering the beneficial characteristics reported in the limited studies of researchers on the labyrinth weir in the pool-weir-type fishway, and knowing that the characteristics of flow in pool-weir-type fishways are highly dependent on the geometry of the weir, an alternative design of the rectangular labyrinth weir instead of the straight weirs in the pool-weir-type fishway is investigated in this study [7, 9]. Kim [10] conducted experiments to compare the hydraulic characteristics of three different weir types in a pool-weir-type fishway. The results show that a straight, rectangular weir with a notch is preferable to a zigzag or trapezoidal weir. Studies on natural fish passes show that pass ability can be improved by lengthening the weir’s crest [7]. Zhong et al. [11] investigated the semi-rigid weir’s hydraulic performance in the fishway’s flow field with a pool weir. The results showed that this type of fishway performed better with a lower invert slope and a smaller radius ratio but with a larger pool spacing.
Considering that an alternative method to study the flow characteristics in a fishway with a pool weir is based on numerical methods and modeling from computational fluid dynamics (CFD), which can easily change the geometry of the fishway for different flow fields, this study uses the powerful package CFD and the software FLOW-3D to evaluate the proposed weir design and compare it with the conventional one to extend the application of the fishway. The main objective of this study was to evaluate the hydraulic performance of the rectangular labyrinth pool and the weir with submerged openings in different hydraulic configurations. The primary objective of creating a new weir configuration for suitable flow patterns is evaluated based on the swimming capabilities of different fish species. Specifically, the following questions will be answered: (a) How do the various hydraulic and geometric parameters relate to the effects of water velocity and turbulence, expressed as turbulent kinetic energy (TKE) and turbulence intensity (TI) within the fishway, i.e., are conventional weirs more affected by hydraulics than rectangular labyrinth weirs? (b) Which weir configurations have the greatest effect on fish performance in the fishway? (c) In the presence of an orifice plate, does the performance of each weir configuration differ with different weir spacing, bed gradients, and flow regimes from that without an orifice plate?
2 Materials and Methods
2.1 Physical Model Configuration
This paper focuses on Ead et al. [6]’s laboratory experiments as a reference, testing ten pool weirs (Fig. 2). The experimental flume was 6 m long, 0.56 m wide, and 0.6 m high, with a bottom slope of 10%. Field measurements were made at steady flow with a maximum flow rate of 0.165 m3/s. Discharge was measured with magnetic flow meters in the inlets and water level with point meters (see Ead et al. [6]. for more details). Table 1 summarizes the experimental conditions considered for model calibration in this study.
Fig. 2
Table 1 Experimental conditions considered for calibration
Computational fluid dynamics (CFD) simulations were performed using FLOW-3D® v11.2 to validate a series of experimental liner pool weirs by Ead et al. [6] and to investigate the effects of the rectangular labyrinth pool weir with an orifice. The dimensions of the channel and data collection areas in the numerical models are the same as those of the laboratory model. Two types of pool weirs were considered: conventional and labyrinth. The proposed rectangular labyrinth pool weirs have a symmetrical cross section and are sized to fit within the experimental channel. The conventional pool weir model had a pool length of l = 0.685 and 0.342 m, a weir height of w = 0.141 m, a weir width of B = 0.56 m, and a channel slope of S0 = 5 and 10%. The rectangular labyrinth weirs have the same front width as the offset, i.e., a = b = c = 0.186 m. A square underwater opening with a width of 0.05 m and a depth of 0.05 m was created in the middle of the weir. The weir configuration considered in the present study is shown in Fig. 3.
Fig. 3
2.3 Governing Equations
FLOW-3D® software solves the Navier–Stokes–Reynolds equations for three-dimensional analysis of incompressible flows using the fluid-volume method on a gridded domain. FLOW -3D® uses an advanced free surface flow tracking algorithm (TruVOF) developed by Hirt and Nichols [12], where fluid configurations are defined in terms of a VOF function F (x, y, z, t). In this case, F (fluid fraction) represents the volume fraction occupied by the fluid: F = 1 in cells filled with fluid and F = 0 in cells without fluid (empty areas) [4, 13]. The free surface area is at an intermediate value of F. (Typically, F = 0.5, but the user can specify a different intermediate value.) The equations in Cartesian coordinates (x, y, z) applicable to the model are as follows:
�f∂�∂�+∂(���x)∂�+∂(���y)∂�+∂(���z)∂�=�SOR
(1)
∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�x+�x
(2)
∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�y+�y
(3)
∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�z+�z
(4)
where (u, v, w) are the velocity components, (Ax, Ay, Az) are the flow area components, (Gx, Gy, Gz) are the mass accelerations, and (fx, fy, fz) are the viscous accelerations in the directions (x, y, z), ρ is the fluid density, RSOR is the spring term, Vf is the volume fraction associated with the flow, and P is the pressure. The k–ε turbulence model (RNG) was used in this study to solve the turbulence of the flow field. This model is a modified version of the standard k–ε model that improves performance. The model is a two-equation model; the first equation (Eq. 5) expresses the turbulence’s energy, called turbulent kinetic energy (k) [14]. The second equation (Eq. 6) is the turbulent dissipation rate (ε), which determines the rate of dissipation of kinetic energy [15]. These equations are expressed as follows Dasineh et al. [4]:
In these equations, k is the turbulent kinetic energy, ε is the turbulent energy consumption rate, Gk is the generation of turbulent kinetic energy by the average velocity gradient, with empirical constants αε = αk = 1.39, C1ε = 1.42, and C2ε = 1.68, eff is the effective viscosity, μeff = μ + μt [15]. Here, μ is the hydrodynamic density coefficient, and μt is the turbulent density of the fluid.
2.4 Meshing and the Boundary Conditions in the Model Setup
The numerical area is divided into three mesh blocks in the X-direction. The meshes are divided into different sizes, a containing mesh block for the entire spatial domain and a nested block with refined cells for the domain of interest. Three different sizes were selected for each of the grid blocks. By comparing the accuracy of their results based on the experimental data, the reasonable mesh for the solution domain was finally selected. The convergence index method (GCI) evaluated the mesh sensitivity analysis. Based on this method, many researchers, such as Ahmadi et al. [16] and Ahmadi et al. [15], have studied the independence of numerical results from mesh size. Three different mesh sizes with a refinement ratio (r) of 1.33 were used to perform the convergence index method. The refinement ratio is the ratio between the larger and smaller mesh sizes (r = Gcoarse/Gfine). According to the recommendation of Celik et al. [17], the recommended number for the refinement ratio is 1.3, which gives acceptable results. Table 2 shows the characteristics of the three mesh sizes selected for mesh sensitivity analysis.Table 2 Characteristics of the meshes tested in the convergence analysis
The results of u1 = umax (u1 = velocity component along the x1 axis and umax = maximum velocity of u1 in a section perpendicular to the invert of the fishway) at Q = 0.035 m3/s, × 1/l = 0.66, and Y1/b = 0 in the pool of conventional weir No. 4, obtained from the output results of the software, were used to evaluate the accuracy of the calculation range. As shown in Fig. 4, x1 = the distance from a given weir in the x-direction, Y1 = the water depth measured in the y-direction, Y0 = the vertical distance in the Cartesian coordinate system, h = the water column at the crest, b = the distance between the two points of maximum velocity umax and zero velocity, and l = the pool length.
Fig. 4
The apparent index of convergence (p) in the GCI method is calculated as follows:
�=ln(�3−�2)(�2−�1)/ln(�)
(7)
f1, f2, and f3 are the hydraulic parameters obtained from the numerical simulation (f1 corresponds to the small mesh), and r is the refinement ratio. The following equation defines the convergence index of the fine mesh:
GCIfine=1.25|ε|��−1
(8)
Here, ε = (f2 − f1)/f1 is the relative error, and f2 and f3 are the values of hydraulic parameters considered for medium and small grids, respectively. GCI12 and GCI23 dimensionless indices can be calculated as:
GCI12=1.25|�2−�1�1|��−1
(9)
Then, the independence of the network is preserved. The convergence index of the network parameters obtained by Eqs. (7)–(9) for all three network variables is shown in Table 3. Since the GCI values for the smaller grid (GCI12) are lower compared to coarse grid (GCI23), it can be concluded that the independence of the grid is almost achieved. No further change in the grid size of the solution domain is required. The calculated values (GCI23/rpGCI12) are close to 1, which shows that the numerical results obtained are within the convergence range. As a result, the meshing of the solution domain consisting of a block mesh with a mesh size of 0.012 m and a block mesh within a larger block mesh with a mesh size of 0.009 m was selected as the optimal mesh (Fig. 5).Table 3 GCI calculation
The boundary conditions applied to the area are shown in Fig. 6. The boundary condition of specific flow rate (volume flow rate-Q) was used for the inlet of the flow. For the downstream boundary, the flow output (outflow-O) condition did not affect the flow in the solution area. For the Zmax boundary, the specified pressure boundary condition was used along with the fluid fraction = 0 (P). This type of boundary condition considers free surface or atmospheric pressure conditions (Ghaderi et al. [19]). The wall boundary condition is defined for the bottom of the channel, which acts like a virtual wall without friction (W). The boundary between mesh blocks and walls were considered a symmetrical condition (S).
Fig. 6
The convergence of the steady-state solutions was controlled during the simulations by monitoring the changes in discharge at the inlet boundary conditions. Figure 7 shows the time series plots of the discharge obtained from the Model A for the three main discharges from the numerical results. The 8 s to reach the flow equilibrium is suitable for the case of the fish ladder with pool and weir. Almost all discharge fluctuations in the models are insignificant in time, and the flow has reached relative stability. The computation time for the simulations was between 6 and 8 h using a personal computer with eight cores of a CPU (Intel Core i7-7700K @ 4.20 GHz and 16 GB RAM).
Fig. 7
3 Results
3.1 Verification of Numerical Results
Quantitative outcomes, including free surface and normalized velocity profiles obtained using FLOW-3D software, were reviewed and compared with the results of Ead et al. [6]. The fourth pool was selected to present the results and compare the experiment and simulation. For each quantity, the percentage of mean absolute error (MAPE (%)) and root-mean-square error (RMSE) are calculated. Equations (10) and (11) show the method used to calculate the errors.
MAPE(%)100×1�∑1�|�exp−�num�exp|
(10)
RMSE(−)1�∑1�(�exp−�num)2
(11)
Here, Xexp is the value of the laboratory data, Xnum is the numerical data value, and n is the amount of data. As shown in Fig. 8, let x1 = distance from a given weir in the x-direction and Y1 = water depth in the y-direction from the bottom. The trend of the surface profiles for each of the numerical results is the same as that of the laboratory results. The surface profiles of the plunging flows drop after the flow enters and then rises to approach the next weir. The RMSE and MAPE error values for Model A are 0.014 m and 3.11%, respectively, indicating acceptable agreement between numerical and laboratory results. Figure 9 shows the velocity vectors and plunging flow from the numerical results, where x and y are horizontal and vertical to the flow direction, respectively. It can be seen that the jet in the fish ladder pool has a relatively high velocity. The two vortices, i.e., the enclosed vortex rotating clockwise behind the weir and the surface vortex rotating counterclockwise above the jet, are observed for the regime of incident flow. The point where the jet meets the fish passage bed is shown in the figure. The normalized velocity profiles upstream and downstream of the impact points are shown in Fig. 10. The figure shows that the numerical results agree well with the experimental data of Ead et al. [6].
Fig. 8Fig. 9Fig. 10
3.2 Flow Regime and Discharge-Depth Relationship
Depending on the geometric shape of the fishway, including the distance of the weir, the slope of the bottom, the height of the weir, and the flow conditions, the flow regime in the fishway is divided into three categories: dipping, transitional, and flow regimes [4]. In the plunging flow regime, the flow enters the pool through the weir, impacts the bottom of the fishway, and forms a hydraulic jump causing two eddies [2, 20]. In the streamwise flow regime, the surface of the flow passing over the weir is almost parallel to the bottom of the channel. The transitional regime has intermediate flow characteristics between the submerged and flow regimes. To predict the flow regime created in the fishway, Ead et al. [6] proposed two dimensionless parameters, Qt* and L/w, where Qt* is the dimensionless discharge, L is the distance between weirs, and w is the height of the weir:
��∗=���0���
(12)
Q is the total discharge, B is the width of the channel, S0 is the slope of the bed, and g is the gravity acceleration. Figure 11 shows different ranges for each flow regime based on the slope of the bed and the distance between the pools in this study. The results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22] were used for this comparison. The distance between the pools affects the changes in the regime of the fish ladder. So, if you decrease the distance between weirs, the flow regime more likely becomes. This study determined all three flow regimes in a fish ladder. When the corresponding range of Qt* is less than 0.6, the flow regime can dip at values of L/B = 1.83. If the corresponding range of Qt* is greater than 0.5, transitional flow may occur at L/B = 1.22. On the other hand, when Qt* is greater than 1, streamwise flow can occur at values of L/B = 0.61. These observations agree well with the results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22].
Fig. 11
For plunging flows, another dimensionless discharge (Q+) versus h/w given by Ead et al. [6] was used for further evaluation:
�+=��ℎ�ℎ=23�d�
(13)
where h is the water depth above the weir, and Cd is the discharge coefficient. Figure 12a compares the numerical and experimental results of Ead et al. [6]. In this figure, Rehbock’s empirical equation is used to estimate the discharge coefficient of Ead et al. [6].
�d=0.57+0.075ℎ�
(14)
Fig. 12
The numerical results for the conventional weir (Model A) and the rectangular labyrinth weir (Model B) of this study agree well with the laboratory results of Ead et al. [6]. When comparing models A and B, it is also found that a rectangular labyrinth weir has larger Q + values than the conventional weir as the length of the weir crest increases for a given channel width and fixed headwater elevation. In Fig. 12b, Models A and B’s flow depth plot shows the plunging flow regime. The power trend lines drawn through the data are the best-fit lines. The data shown in Fig. 12b are for different bed slopes and weir geometries. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q can be assumed to be proportional to 1.56 and 1.47h, respectively. In the results of Ead et al. [6], Q is proportional to 1.5h. If we assume that the flow through the orifice is Qo and the total outflow is Q, the change in the ratio of Qo/Q to total outflow for models A and B can be shown in Fig. 13. For both models, the flow through the orifice decreases as the total flow increases. A logarithmic trend line was also found between the total outflow and the dimensionless ratio Qo/Q.
Fig. 13
3.3 Depth-Averaged Velocity Distributions
To ensure that the target fish species can pass the fish ladder with maximum efficiency, the average velocity in the fish ladder should be low enough [4]. Therefore, the average velocity in depth should be as much as possible below the critical swimming velocities of the target fishes at a constant flow depth in the pool [20]. The contour plot of depth-averaged velocity was used instead of another direction, such as longitudinal velocity because fish are more sensitive to depth-averaged flow velocity than to its direction under different hydraulic conditions. Figure 14 shows the distribution of depth-averaged velocity in the pool for Models A and B in two cases with and without orifice plates. Model A’s velocity within the pool differs slightly in the spanwise direction. However, no significant variation in velocity was observed. The flow is gradually directed to the sides as it passes through the rectangular labyrinth weir. This increases the velocity at the sides of the channel. Therefore, the high-velocity zone is located at the sides. The low velocity is in the downstream apex of the weir. This area may be suitable for swimming target fish. The presence of an opening in the weir increases the flow velocity at the opening and in the pool’s center, especially in Model A. The flow velocity increase caused by the models’ opening varied from 7.7 to 12.48%. Figure 15 illustrates the effect of the inverted slope on the averaged depth velocity distribution in the pool at low and high discharge. At constant discharge, flow velocity increases with increasing bed slope. In general, high flow velocity was found in the weir toe sidewall and the weir and channel sidewalls.
Fig. 14Fig. 15
On the other hand, for a constant bed slope, the high-velocity area of the pool increases due to the increase in runoff. For both bed slopes and different discharges, the most appropriate path for fish to travel from upstream to downstream is through the middle of the cross section and along the top of the rectangular labyrinth weirs. The maximum dominant velocities for Model B at S0 = 5% were 0.83 and 1.01 m/s; at S0 = 10%, they were 1.12 and 1.61 m/s at low and high flows, respectively. The low mean velocities for the same distance and S0 = 5 and 10% were 0.17 and 0.26 m/s, respectively.
Figure 16 shows the contour of the averaged depth velocity for various distances from the weir at low and high discharge. The contour plot shows a large variation in velocity within short distances from the weir. At L/B = 0.61, velocities are low upstream and downstream of the top of the weir. The high velocities occur in the side walls of the weir and the channel. At L/B = 1.22, the low-velocity zone displaces the higher velocity in most of the pool. Higher velocities were found only on the sides of the channel. As the discharge increases, the velocity zone in the pool becomes wider. At L/B = 1.83, there is an area of higher velocities only upstream of the crest and on the sides of the weir. At high discharge, the prevailing maximum velocities for L/B = 0.61, 1.22, and 1.83 were 1.46, 1.65, and 1.84 m/s, respectively. As the distance between weirs increases, the range of maximum velocity increases.
Fig. 16
On the other hand, the low mean velocity for these distances was 0.27, 0.44, and 0.72 m/s, respectively. Thus, the low-velocity zone decreases with increasing distance between weirs. Figure 17 shows the pattern distribution of streamlines along with the velocity contour at various distances from the weir for Q = 0.05 m3/s. A stream-like flow is generally formed in the pool at a small distance between weirs (L/B = 0.61). The rotation cell under the jet forms clockwise between the two weirs. At the distances between the spillways (L/B = 1.22), the transition regime of the flow is formed. The transition regime occurs when or shortly after the weir is flooded. The rotation cell under the jet is clockwise smaller than the flow regime and larger than the submergence regime. At a distance L/B = 1.83, a plunging flow is formed so that the plunging jet dips into the pool and extends downstream to the center of the pool. The clockwise rotation of the cell is bounded by the dipping jet of the weir and is located between the bottom and the side walls of the weir and the channel.
Fig. 17
Figure 18 shows the average depth velocity bar graph for each weir at different bed slopes and with and without orifice plates. As the distance between weirs increases, all models’ average depth velocity increases. As the slope of the bottom increases and an orifice plate is present, the average depth velocity in the pool increases. In addition, the average pool depth velocity increases as the discharge increases. Among the models, Model A’s average depth velocity is higher than Model B’s. The variation in velocity ranged from 8.11 to 12.24% for the models without an orifice plate and from 10.26 to 16.87% for the models with an orifice plate.
Fig. 18
3.4 Turbulence Characteristics
The turbulent kinetic energy is one of the important parameters reflecting the turbulent properties of the flow field [23]. When the k value is high, more energy and a longer transit time are required to migrate the target species. The turbulent kinetic energy is defined as follows:
�=12(�x′2+�y′2+�z′2)
(15)
where ux, uy, and uz are fluctuating velocities in the x, y, and z directions, respectively. An illustration of the TKE and the effects of the geometric arrangement of the weir and the presence of an opening in the weir is shown in Fig. 19. For a given bed slope, in Model A, the highest TKE values are uniformly distributed in the weir’s upstream portion in the channel’s cross section. In contrast, for the rectangular labyrinth weir (Model B), the highest TKE values are concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value in Models A and B is 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%). In the downstream portion of the conventional weir and within the crest of the weir and the walls of the rectangular labyrinth, there was a much lower TKE value that provided the best conditions for fish to recover in the pool between the weirs. The average of the lowest TKE for bottom slopes of 5 and 10% in Model A is 0.041 and 0.056 J/kg, and for Model B, is 0.047 and 0.064 J/kg. The presence of an opening in the weirs reduces the area of the highest TKE within the pool. It also increases the resting areas for fish (lower TKE). The highest TKE at the highest bottom slope in Models A and B with an orifice is 0.208 and 0.191 J/kg, respectively.
Fig. 19
Figure 20 shows the effect of slope on the longitudinal distribution of TKE in the pools. TKE values significantly increase for a given discharge with an increasing bottom slope. Thus, for a low bed slope (S0 = 5%), a large pool area has expanded with average values of 0.131 and 0.168 J/kg for low and high discharge, respectively. For a bed slope of S0 = 10%, the average TKE values are 0.176 and 0.234 J/kg. Furthermore, as the discharge increases, the area with high TKE values within the pool increases. Lower TKE values are observed at the apex of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall for both bottom slopes. The effect of distance between weirs on TKE is shown in Fig. 21. Low TKE values were observed at low discharge and short distances between weirs. Low TKE values are located at the top of the rectangular labyrinth weir and the downstream corner of the weir wall. There is a maximum value of TKE at the large distances between weirs, L/B = 1.83, along the center line of the pool, where the dip jet meets the bottom of the bed. At high discharge, the maximum TKE value for the distance L/B = 0.61, 1.22, and 1.83 was 0.246, 0.322, and 0.417 J/kg, respectively. In addition, the maximum TKE range increases with the distance between weirs.
Fig. 20Fig. 21
For TKE size, the average value (TKEave) is plotted against q in Fig. 22. For all models, the TKE values increase with increasing q. For example, in models A and B with L/B = 0.61 and a slope of 10%, the TKE value increases by 41.66 and 86.95%, respectively, as q increases from 0.1 to 0.27 m2/s. The TKE values in Model B are higher than Model A for a given discharge, bed slope, and weir distance. The TKEave in Model B is higher compared to Model A, ranging from 31.46 to 57.94%. The presence of an orifice in the weir reduces the TKE values in both weirs. The intensity of the reduction is greater in Model B. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, an orifice reduces TKEave values by 60.35 and 19.04%, respectively. For each model, increasing the bed slope increases the TKEave values in the pool. For example, for Model B with q = 0.18 m2/s, increasing the bed slope from 5 to 10% increases the TKEave value by 14.34%. Increasing the distance between weirs increases the TKEave values in the pool. For example, in Model B with S0 = 10% and q = 0.3 m2/s, the TKEave in the pool increases by 34.22% if you increase the distance between weirs from L/B = 0.61 to L/B = 0.183.
Fig. 22
Cotel et al. [24] suggested that turbulence intensity (TI) is a suitable parameter for studying fish swimming performance. Figure 23 shows the plot of TI and the effects of the geometric arrangement of the weir and the presence of an orifice. In Model A, the highest TI values are found upstream of the weirs and are evenly distributed across the cross section of the channel. The TI values increase as you move upstream to downstream in the pool. For the rectangular labyrinth weir, the highest TI values were concentrated on the sides of the pool, between the top of the weir and the side wall of the channel, and along the top of the weir. Downstream of the conventional weir, within the apex of the weir, and at the corners of the walls of the rectangular labyrinth weir, the percentage of TI was low. At the highest discharge, the average range of TI in Models A and B was 24–45% and 15–62%, respectively. The diversity of TI is greater in the rectangular labyrinth weir than the conventional weir. Fish swimming performance is reduced due to higher turbulence intensity. However, fish species may prefer different disturbance intensities depending on their swimming abilities; for example, Salmo trutta prefers a disturbance intensity of 18–53% [25]. Kupferschmidt and Zhu [26] found a higher range of TI for fishways, such as natural rock weirs, of 40–60%. The presence of an orifice in the weir increases TI values within the pool, especially along the middle portion of the cross section of the fishway. With an orifice in the weir, the average range of TI in Models A and B was 28–59% and 22–73%, respectively.
Fig. 23
The effect of bed slope on TI variation is shown in Fig. 24. TI increases in different pool areas as the bed slope increases for a given discharge. For a low bed slope (S0 = 5%), a large pool area has increased from 38 to 63% and from 56 to 71% for low and high discharge, respectively. For a bed slope of S0 = 10%, the average values of TI are 45–67% and 61–73% for low and high discharge, respectively. Therefore, as runoff increases, the area with high TI values within the pool increases. A lower TI is observed for both bottom slopes in the corner of the wall, downstream of the crest walls, and between the side walls in the weir and channel. Figure 25 compares weir spacing with the distribution of TI values within the pool. The TI values are low at low flows and short distances between weirs. A maximum value of TI occurs at long spacing and where the plunging stream impinges on the bed and the area around the bed. TI ranges from 36 to 57%, 58–72%, and 47–76% for the highest flow in a wide pool area for L/B = 0.61, 1.22, and 1.83, respectively.
Fig. 24Fig. 25
The average value of turbulence intensity (TIave) is plotted against q in Fig. 26. The increase in TI values with the increase in q values is seen in all models. For example, the average values of TI for Models A and B at L/B = 0.61 and slope of 10% increased from 23.9 to 33.5% and from 42 to 51.8%, respectively, with the increase in q from 0.1 to 0.27 m2/s. For a given discharge, a given gradient, and a given spacing of weirs, the TIave is higher in Model B than Model A. The presence of an orifice in the weirs increases the TI values in both types. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, the presence of an orifice increases TIave from 23.9 to 37.1% and from 42 to 48.8%, respectively. For each model, TIave in the pool increases with increasing bed slope. For Model B with q = 0.18 m2/s, TIave increases from 37.5 to 45.8% when you increase the invert slope from 5 to 10%. Increasing the distance between weirs increases the TIave in the pool. In Model B with S0 = 10% and q = 0.3 m2/s, the TIave in the pool increases from 51.8 to 63.7% as the distance between weirs increases from L/B = 0.61 to L/B = 0.183.
Fig. 26
3.5 Energy Dissipation
To facilitate the passage of various target species through the pool of fishways, it is necessary to pay attention to the energy dissipation of the flow and to keep the flow velocity in the pool slow. The average volumetric energy dissipation (k) in the pool is calculated using the following basic formula:
�=����0��
(16)
where ρ is the water density, and H is the average water depth of the pool. The change in k versus Q for all models at two bottom slopes, S0 = 5%, and S0 = 10%, is shown in Fig. 27. Like the results of Yagci [8] and Kupferschmidt and Zhu [26], at a constant bottom slope, the energy dissipation in the pool increases with increasing discharge. The trend of change in k as a function of Q from the present study at a bottom gradient of S0 = 5% is also consistent with the results of Kupferschmidt and Zhu [26] for the fishway with rock weir. The only difference between the results is the geometry of the fishway and the combination of boulders instead of a solid wall. Comparison of the models shows that the conventional model has lower energy dissipation than the rectangular labyrinth for a given discharge. Also, increasing the distance between weirs decreases the volumetric energy dissipation for each model with the same bed slope. Increasing the slope of the bottom leads to an increase in volumetric energy dissipation, and an opening in the weir leads to a decrease in volumetric energy dissipation for both models. Therefore, as a guideline for volumetric energy dissipation, if the value within the pool is too high, the increased distance of the weir, the decreased slope of the bed, or the creation of an opening in the weir would decrease the volumetric dissipation rate.
Fig. 27
To evaluate the energy dissipation inside the pool, the general method of energy difference in two sections can use:
ε=�1−�2�1
(17)
where ε is the energy dissipation rate, and E1 and E2 are the specific energies in Sects. 1 and 2, respectively. The distance between Sects. 1 and 2 is the same. (L is the distance between two upstream and downstream weirs.) Figure 28 shows the changes in ε relative to q (flow per unit width). The rectangular labyrinth weir (Model B) has a higher energy dissipation rate than the conventional weir (Model A) at a constant bottom gradient. For example, at S0 = 5%, L/B = 0.61, and q = 0.08 m3/s.m, the energy dissipation rate in Model A (conventional weir) was 0.261. In Model B (rectangular labyrinth weir), however, it was 0.338 (22.75% increase). For each model, the energy dissipation rate within the pool increases as the slope of the bottom increases. For Model B with L/B = 1.83 and q = 0.178 m3/s.m, the energy dissipation rate at S0 = 5% and 10% is 0.305 and 0.358, respectively (14.8% increase). Figure 29 shows an orifice’s effect on the pools’ energy dissipation rate. With an orifice in the weir, both models’ energy dissipation rates decreased. Thus, the reduction in energy dissipation rate varied from 7.32 to 9.48% for Model A and from 8.46 to 10.57 for Model B.
Fig. 28Fig. 29
4 Discussion
This study consisted of entirely of numerical analysis. Although this study was limited to two weirs, the hydraulic performance and flow characteristics in a pooled fishway are highlighted by the rectangular labyrinth weir and its comparison with the conventional straight weir. The study compared the numerical simulations with laboratory experiments in terms of surface profiles, velocity vectors, and flow characteristics in a fish ladder pool. The results indicate agreement between the numerical and laboratory data, supporting the reliability of the numerical model in capturing the observed phenomena.
When the configuration of the weir changes to a rectangular labyrinth weir, the flow characteristics, the maximum and minimum area, and even the location of each hydraulic parameter change compared to a conventional weir. In the rectangular labyrinth weir, the flow is gradually directed to the sides as it passes the weir. This increases the velocity at the sides of the channel [21]. Therefore, the high-velocity area is located on the sides. In the downstream apex of the weir, the flow velocity is low, and this area may be suitable for swimming target fish. However, no significant change in velocity was observed at the conventional weir within the fish ladder. This resulted in an average increase in TKE of 32% and an average increase in TI of about 17% compared to conventional weirs.
In addition, there is a slight difference in the flow regime for both weir configurations. In addition, the rectangular labyrinth weir has a higher energy dissipation rate for a given discharge and constant bottom slope than the conventional weir. By reducing the distance between the weirs, this becomes even more intense. Finally, the presence of an orifice in both configurations of the weir increased the flow velocity at the orifice and in the middle of the pool, reducing the highest TKE value and increasing the values of TI within the pool of the fish ladder. This resulted in a reduction in volumetric energy dissipation for both weir configurations.
The results of this study will help the reader understand the direct effects of the governing geometric parameters on the hydraulic characteristics of a fishway with a pool and weir. However, due to the limited configurations of the study, further investigation is needed to evaluate the position of the weir’s crest on the flow direction and the difference in flow characteristics when combining boulders instead of a solid wall for this type of labyrinth weir [26]. In addition, hydraulic engineers and biologists must work together to design an effective fishway with rectangular labyrinth configurations. The migration habits of the target species should be considered when designing the most appropriate design [27]. Parametric studies and field observations are recommended to determine the perfect design criteria.
The current study focused on comparing a rectangular labyrinth weir with a conventional straight weir. Further research can explore other weir configurations, such as variations in crest position, different shapes of labyrinth weirs, or the use of boulders instead of solid walls. This would help understand the influence of different geometric parameters on hydraulic characteristics.
5 Conclusions
A new layout of the weir was evaluated, namely a rectangular labyrinth weir compared to a straight weir in a pool and weir system. The differences between the weirs were highlighted, particularly how variations in the geometry of the structures, such as the shape of the weir, the spacing of the weir, the presence of an opening at the weir, and the slope of the bottom, affect the hydraulics within the structures. The main findings of this study are as follows:
The calculated dimensionless discharge (Qt*) confirmed three different flow regimes: when the corresponding range of Qt* is smaller than 0.6, the regime of plunging flow occurs for values of L/B = 1.83. (L: distance of the weir; B: channel width). When the corresponding range of Qt* is greater than 0.5, transitional flow occurs at L/B = 1.22. On the other hand, if Qt* is greater than 1, the streaming flow is at values of L/B = 0.61.
For the conventional weir and the rectangular labyrinth weir with the plunging flow, it can be assumed that the discharge (Q) is proportional to 1.56 and 1.47h, respectively (h: water depth above the weir). This information is useful for estimating the discharge based on water depth in practical applications.
In the rectangular labyrinth weir, the high-velocity zone is located on the side walls between the top of the weir and the channel wall. A high-velocity variation within short distances of the weir. Low velocity occurs within the downstream apex of the weir. This area may be suitable for swimming target fish.
As the distance between weirs increased, the zone of maximum velocity increased. However, the zone of low speed decreased. The prevailing maximum velocity for a rectangular labyrinth weir at L/B = 0.61, 1.22, and 1.83 was 1.46, 1.65, and 1.84 m/s, respectively. The low mean velocities for these distances were 0.27, 0.44, and 0.72 m/s, respectively. This finding highlights the importance of weir spacing in determining the flow characteristics within the fishway.
The presence of an orifice in the weir increased the flow velocity at the orifice and in the middle of the pool, especially in a conventional weir. The increase ranged from 7.7 to 12.48%.
For a given bottom slope, in a conventional weir, the highest values of turbulent kinetic energy (TKE) are uniformly distributed in the upstream part of the weir in the cross section of the channel. In contrast, for the rectangular labyrinth weir, the highest TKE values were concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value for the conventional and the rectangular labyrinth weir was 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%).
For a given discharge, bottom slope, and weir spacing, the average values of TI are higher for the rectangular labyrinth weir than for the conventional weir. At the highest discharge, the average range of turbulence intensity (TI) for the conventional and rectangular labyrinth weirs was between 24 and 45% and 15% and 62%, respectively. This reveals that the rectangular labyrinth weir may generate more turbulent flow conditions within the fishway.
For a given discharge and constant bottom slope, the rectangular labyrinth weir has a higher energy dissipation rate than the conventional weir (22.75 and 34.86%).
Increasing the distance between weirs decreased volumetric energy dissipation. However, increasing the gradient increased volumetric energy dissipation. The presence of an opening in the weir resulted in a decrease in volumetric energy dissipation for both model types.
Availability of data and materials
Data is contained within the article.
References
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파도와 잔해 더미 방파제와 같은 다공성 해양 구조물의 상호 작용을 평가하는 것은 이러한 구조물을 최적으로 설계하는 데 중요한 역할을 합니다. 본 연구는 경사진 잔해 둔덕 방파제의 기하학적 매개변수의 효과에 초점을 맞추었는데, 여기에는 갑옷의 형태, 배치 방법, 방파제 경사 등이 포함된다. 따라서 파동 반사 계수(Kr), 투과 계수(Kt) 및 감가상각파 에너지 계수(Kd)에 대해 논의합니다. 결과에 따르면 파장이 감소하면 K가 감소합니다.r그리고 K를 증가시켰습니다t 및 Kd. Coreloc 장갑 층이 있는 잔해 언덕 방파제는 가장 낮은 K를 나타낼 수 있습니다.r 다른 갑옷 형상과 비교했습니다. 또한 방파제 경사가 감소하여 K가 감소했습니다.r 및 Kd 각각 3.4%, 1.25% 증가했다. 또한 방파제 경사가 33°에서 25°로 감소하여 파도 파쇄 높이가 평균 6.1% 증가했습니다. 또한, 방파제 경사의 감소는 난류 감가상각의 강도를 감소시켰다. 마지막으로, 경사가 다른 방파제의 장갑 형상과 장갑 층의 배열은 파도 거동과 파도와 방파제 사이의 상호 작용에 영향을 미칩니다. 따라서 이러한 구조를 설계 할 때 방파제에 층을 쌓고 갑옷의 기하학적 모양을 올바르게 사용하는 것을 고려해야합니다.
Keywords
Rubble mound breakwater
Computational fluid dynamics
Armour layer
Wave reflection coefficient
Wave transmission coefficient
Wave energy dissipation coefficient
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![Fig. 4 Scour hole profle from Melville and Raudkivi [16] and simulated results](https://flow3d.co.kr/wp-content/uploads/image-452-png.webp)
![Figure 5 – Instantaneous pressures [Pa] and velocities [m/s] at model scale (bay center)](https://flow3d.co.kr/wp-content/uploads/s-at-model-scale-bay-center.png)
