FSR_01-12_Air-Entrainment-Report [공기 혼입 모델 분석]

Overview
In free-surface flows the turbulence in the liquid may be sufficient to disturb the surface to the point of entraining air into the flow. This process is important, for example, in water treatment where air is needed to sustain microorganisms for water purification and in rivers and streams for sustaining a healthy fish population. Air entrainment is typically engineered into spillways downstream of hydropower plants to reduce the possibility of cavitation damage at the base of the spillway. Situations where air entrainment is undesirable are in the sprue and runner systems used by metal casters, and in the filling of liquid containers used for consumer products.
The importance of being able to predict the amount and distribution of entrained air at a free liquid surface has led to the development of a unique model in FLOW-3D®. The model has two options. One option, to be used when the volume fraction of entrained air is relatively low, uses a passive scalar variable to record and transport the air volume fraction. This model is passive in that it does not alter the dynamics of the flow.
The second air-entrainment model option is based on a variable density formulation. This model includes the “bulking” of fluid volume by the addition of air and the buoyancy effects associated with entrained air. This dynamically coupled model cannot, however, be used in conjunction with heat transport and natural (thermal) convection.
In addition, when using the variable density formulation, the model can include a relative drifting of air in water, the possible escape of air if it rises to the surface of the water and the removal or addition of air to trapped bubble regions represented as adiabatic bubbles.
The same basic entrainment process is used in both options. It is based on a competition between the stabilizing forces of gravity and surface tension and the destabilizing effects of surface turbulence.
Because turbulence is the main cause of entrainment, a turbulence-transport model must be used in connection with the air-entrainment model. It is recommended that the RNG version of the more traditional k-epsilon turbulence model be employed. All the validation tests reported in this Technical Note were performed using the RNG model.

 

[다운로드]

FSR_01-12_Air-Entrainment-Report

The Sedimentation Scour Model [침전 세굴(쇄굴) 모델]

1. Introduction
The three-dimensional sediment scour model for non-cohesive soils was first introduced to FLOW-3D in Version 8.0 to simulate sediment erosion and deposition (Brethour, 2003). It was coupled with the three-dimensional fluid dynamics and considered entrainment, drifting and settling of sediment grains. In Version 9.4 the model was improved by introducing bedload transport and multiple sediment species (Brethour and Burnham, 2010). Although applications were successfully simulated, a major limitation of the model was the approximate treatment of the interface between the packed and suspended sediments. The packed bed was represented by scalars rather than FAVORTM (Fractional Area Volume Obstacle Representation, the standard treatment for solid components in FLOW-3D). As a result, limited information about the packed bed interface was available. That made accurate calculation of bed shear stress, a critical factor determining the model accuracy, challenging.

In this work, the 3D sediment scour model is mostly redeveloped and rewritten. The model is still fully coupled with fluid flow, allows multiple non-cohesive species and considers entrainment, deposition, bedload transport and suspended load transport. The fundamental difference from the old model is that the packed bed is described by the FAVORTM technique. At each time step, area and volume fractions describing the packed sediments are calculated throughout the domain. In the mesh cells at the bed interface, the location, orientation and area of the interface are calculated and used to determine the bed shear stress, the critical Shields parameter, the erosion rate and the bedload transport rate. Bed shear stress is evaluated using the standard wall function with consideration of bed surface roughness that is related to the median grain size d50. A sub-mesh method is developed and implemented to calculate bedload transport. Computation of erosion considers entrainment and deposition simultaneously in addition to bedload transport.

Furthermore, a shallow-water sediment scour model is developed in this work by adapting the new 3D model. It is coupled with the 2D shallow water flows to calculate depth-averaged properties for both suspended and packed sediments. Its main differences from the 3D model are 1) the settling velocity of grains is calculated using an existing equation instead of the drift-flux approach in the 3D model, and 2) turbulent bed shear stress is calculated using a well-accepted quadratic law rather than the log wall function. The drag coefficient for the bed shear stress is either user-given or locally evaluated using the water depth and the bed surface roughness that is proportional to d50 of the bed material. The following sections present the sediment theory used in the model and application and validation cases.

Comments on a comparison of CFD for microfluidic app

Introduction
A recent effort to compare the performance of four commercial computational fluid dynamics (CFD) software packages for microfluidic applications (T. Glatzel, 2008) was recently brought to the attention of the staff at Flow Science, Inc. The paper reported simulation results from the four CFD packages for a set of flow problems typically encountered in microfluidics. The intent of the paper was to compare the quality of the solvers by removing differentiating features (meshing, special numerical algorithms, etc.) from the analysis. While we acknowledge the worthiness and difficulty of the task, we believe there are some significant limitations to the usefulness of the comparisons made in the paper.
To begin, the modeling restrictions employed prevented the individual software programs from making use of particular options they might have for obtaining better simulations of particular flow problems. A second point, at least in connection with our software product, FLOW-3D®, we have noted numerous inaccuracies in the software’s description, an incorrect use of boundary conditions and several other failures to operate the software properly. This note is intended to correct these deficiencies and omissions as well as to present a repetition of the computational examples, as near as possible, from data given in the original paper. It will be shown that FLOW-3D® performs all the comparison problems as well or better than other software tools included in the original study.

Salt dissolution model [소금 용해 모델]

Introduction
Dissolution of salt in liquid is of interest in several applications – from solution mining to food processing to medical applications. This article describes a new model in FLOW-3D1 version 10.0 for dissolving salt in fluids and tracking the solute in the brine.
The dissolution of salt increases the density of the fluid and thus may affect the flow. In addition, as salt is dissolved, the flow domain increases. It is of interest, therefore, to predict these changes in the flow as well as the transport of the dissolved salt in the fluid.
The model accounts for the basic physical phenomena, such as mass transfer at the interface between salt and fluid, the change of volume and shape of the solid salt, diffusion and convection of dissolved salt in fluid and, finally, the change in fluid density, viscosity and surface tension coefficient.

Steady-State Solver for Free-Surface Flows [자유 표면 유동에 대한 정상 상태 솔버]

Introduction
There is frequently a need to have a faster way to generate a steady free-surface flow than by simply trying to compute the asymptotic state of a transient flow. The situation is similar to solving for incompressible flow by trying to use a compressible flow solver. In the latter case, compression waves can take an extremely long time to decay and leave a resultant “incompressible” flow. Correspondingly, in free-surface flows the fluid is incompressible, but surface waves may require a very long time to damp out to produce a steady surface configuration.

On the implementation of two-equation turbulence models in FLOW-3D

Abstract
Concerns have been raised as to the dependency of the solutions of turbulent flows in FLOW-3D® 1on the maximum ”turbulent mixing length,” 𝑇𝐿𝐸𝑁, which is set by the user when a two-equation turbulence model is used. This parameter acts as a limiter on the turbulent length scale which in turn limits the minimum turbulent dissipation. It has been observed that if the value is not chosen appropriately the results could become physically unrealistic. In order to resolve this issue, modifications have been made to the two-equation turbulence models to construct local bounds on turbulent length and time scales. This technical note shows that these changes effectively eliminate the sensitivity of the solution to the value of 𝑇𝐿𝐸𝑁.
Some valuable discoveries were made along the way which led to more modifications of the turbulence models in FLOW-3D that further improved the results. The test cases discussed here include both simple as well as complex flows. Starting with the simplest flow configurations and obtaining reasonably accurate results permits the consideration of more complex cases. The data and conclusions documented here should be used as a starting point for any other changes to the turbulence models in FLOW-3D.

Binder Gas Generation and Transport in Sand Cores and Molds

Overview
The making of resin-bonded sand castings has made great strides in quality over its long history. Even so, there remain some process-related defects that are not fully understood and can cause quality issues. For instance, chemical binders in the sand can produce gas when heated by the molten metal and if not vented adequately, the gas may flow into the metal resulting in a gas porosity defect. This is most likely with cores that form thin interior features of castings that heat up quickly and have long venting paths.

The core gas model in FLOW-3D1 is designed to predict the possibility of such gas defects and is intended to help design core venting that would evacuate safely all the binder product gas
from the cores.
Two major types of binders are used in core making practice: resin-based organic binders and inorganic binders such as sodium silicate [1]. The organic binders are either thermosetting, or cured at room temperature with an aid of a catalyst. These are favored in many applications due to their complete degradation even at aluminum casting temperatures and for the ease of subsequent sand shake out. The core gas model is developed with these binders in mind, but can be extended to inorganic binders if appropriate data on their decomposition is available.

Drift Model for Two-Component Flows [두 구성 요소 흐름에 대한 표류 모델]

Overview
In fluids composed of multiple components, e.g., fluid/particles, fluid/bubbles, fluid/fluid mixtures, where the components have different densities, it is observed that the components can assume different flow velocities. Velocity differences arise because the density differences result in non-uniform body forces. Often the differences in velocities can be very pronounced, for example, large raindrops falling through air or gravel sinking in water. Under many conditions, however, the relative velocities are small enough to be described as a “drift” of one component through the other. Examples are dust in air and silt in water.
The “drift” distinction has to do with whether or not the inertia of a dispersed component moving in a continuous component is significant. If the inertia of relative motion can be ignored, and the relative velocity reduced to a balance between a driving force (say gravity or a pressure gradient) and an opposing drag force between the components, then we can speak of a “drift-flux” approximation. Drift velocities are primarily responsible for the transport of mass and energy. Some momentum may be transported as well, but this is usually quite small and has been neglected in the FLOW-3D1 drift model. A more complete analysis of when the “drift” assumption is valid can be found in the Flow Science, Inc.

Improved Generalized Minimal Residual (GMRES) Solver in FLOW-3D—How it works and when to use it

Overview
In FLOW-3D1 there are three linear solvers (as of Version 9.2) with which to solve for pressure from the linear system of continuity equations throughout the domain: the successive over-relaxation (SOR) algorithm, the alternating direction implicit (ADI) algorithm and the generalized minimal residual (GMRES) solver. With GMRES, the system of equations is solved simultaneously throughout the domain by an iterative technique. This is quite unlike the approach used in the SOR algorithm, which adjusts the pressure on a cell-by-cell basis to enforce the continuity equation, or the ADI algorithm, which adjusts the pressures along each mesh column, whose direction alternates through the chosen directions. Although the SOR algorithm is very simple and memory efficient—no extra information from each cell needs to be stored—it can require a large number of iterations to converge, especially for problems where nearly uniform pressure adjustments must be made over a large region of the domain. However, it will always eventually converge so long as the relaxation parameter Ω is less than or equal to 1.
With GMRES, the number of iterations required for convergence is typically much smaller (less than 10) than for SOR; however, it does not always converge. Therefore, for many problems the GMRES algorithm is computationally much more efficient because it is able to converge with far fewer iterations than other solver schemes. This is especially true for problems where the pressures over a large region of the domain are intimately coupled; examples are incompressible flow through a piping network, compressing a gas within a storage tank and most confined flow problems. SOR still may be more computationally efficient for fairly shallow free-surface problems where the pressure is more or less controlled by the location of the free surface—the pressure between two points in the liquid are not strongly coupled.

Turbulent Flow Over a Backward-Facing Step Using the RNG Model

Abstract
Turbulent flow over a backward-facing step is one of the classical tests to validate turbulence models in CFD. In the present work, steady-state turbulent flow over a backward-facing step was simulated using FLOW-3D1 with the Renormalization-group (RNG) k-ε model to account for turbulent viscosity. The Reynolds number was computed using the step height h and the inlet free-stream velocity. The test case was run for two different Reynolds numbers: Reh=5100 and Reh=44,000.

The numerical predictions were compared with the experimental results with the same flow configuration. Streamwise velocity profiles at different locations in the flow direction were in good agreement both qualitatively and quantitatively with the experimental results.

One of the main objectives of this work is to study the sensitivity of the results to the turbulent mixing length parameter tlen in the RNG model. The steady-state velocity was used to compute the reattachment length behind the step for different values of tlen and compared with experimental data. A grid refinement study was performed to find the least mesh resolution needed to capture the essential flow physics of the problem.

Simulating the Residue left by Evaporating Drops

Background
The “coffee ring” effect is the name given to a well known observation where the evaporative drying of a drop of coffee leaves behind a ring of dark material at the edge of the original drop. On first thought one would expect that the coffee particles, which are uniformly distributed in the drop, would simply be deposited uniformly over the area wetted by the drop. It has only been in recent years that researchers have uncovered the mechanisms that produce the ring effect (Deegan, R.D., et al).
As currently understood, the edges of drops can become pinned because of roughness or chemical elements on the surface on which they lie. Heat transfer to the drops from the substrate or the air induces evaporation, which is usually greater near the drop edge. Surface tension forces then adjust the curvature of the remaining liquid consistent with the pinned edge, which results in a net flow of liquid toward the edge. This flow replenishes the evaporative loss but also moves solute to the edge where it is concentrated by evaporation. Eventually, this mechanism builds up a ring deposit of solute at the original edge of the drop.
The residue from dried drops has implications for many useful applications, including general coating processes, formation of pixel arrays of organic materials for video displays and for a variety of micro-electro-mechanical (MEMS) devices.
Because many factors control the distribution of dried residue it is desirable to have some means to model the fluid dynamics of the process to aid engineers in making the best choices for each specific application. Such a capability has been incorporated into FLOW-3D1 making it possible to computationally investigate the influence of such parameters as the initial solute concentration, fluid viscosity, volatility of the solvent, evaporation rate, surface tension and initial shape of the drop.
This technical note presents a brief description of the residue formation model and illustrates it with several computations of an evaporating drop subject to different physical conditions.

THE ELASTIC MEMBRANE AND WALL MODEL IN FLOW-3D [FLOW-3D의 탄성 멤브레인과 벽 모델]

1. Introduction
An elastic membrane and wall model has been developed to provide a limited Fluid-Structure Interaction (FSI) capability in FLOW-3D. In the model, deformation of an elastic membrane or an elastic wall impacts the adjacent fluid flow, while fluid pressure, in turn, affects the deformation. These interactions are described in the code in a fully coupled fashion.
The main assumption of the model is that the deformations are small, i.e., the deflections are much smaller than the size of the deforming object (for elastic membranes) or the characteristic lengths of fluid flow and wall thickness (for elastic walls), allowing for a few useful simplifications. The geometries of membranes and elastic walls are assumed to be time-invariant, while the effects of their deformation on fluid flow are described with volume sources and sinks distributed along the fixed fluid-structure interface. With the further assumption that the pressure force is uniformly distributed on the membrane surface, analytical solutions rather than structural analysis algorithms are used to determine the membrane deformation.
There are many potential applications for the model in microfluidic systems, e.g., chemical analysis systems, medical microdosage systems and inkjet devices. The model can be used to simulate flow in piezoelectric valveless pumps which convert membrane vibrations into a pumping action. The model can also be used to simulate droplet formation for piezoelectric inkjet printheads where a membrane or an elastic tube deforms under the force of a piezoelectric actuator to produce a droplet of ink.

The Non-Condensable Gas Model [비 응축 가스 모델]

Overview
The non-condensable gas model is built upon the two-fluid, liquid/vapor phase change model and includes the effects of a non-condensable gas present in the vapor space. The new model is designed to work only with the two-fluid phase change model because the spatial distribution of vapor and gas components is needed to predict the phase change behavior. By contrast, the one-fluid phase change model assumes spatially uniform pressure and temperature throughout the gas phase. The assumption of a uniform gas/vapor concentration in a two-component gas would rarely be valid. This model is the basis of work completed to simulate the ullage space of cryogenic tanks2, but it is applicable to any two-component gas problem.

AN IMPLICIT METHOD TO SOLVE PROBLEMS OF RIGID BODY MOTION COUPLED WITH FLUID FLOW

For general moving object (GMO) problems, when mass density of the moving object(s) under coupled motion is less than that of fluid, the existing explicit GMO method in FLOW-3D® often fails due to stability difficulties. In this work, an implicit GMO method was developed and incorporated into FLOW-3D®. The main difference between the implicit and the explicit GMO methods is that in each computational cycle, or time step, the former calculates the object motion and the fluid flow iteratively while the later calculates them separately. Unlike the explicit method, the implicit approach imposes no limitations on mass density of the moving objects. Tests show it possesses good stability for density of moving objects as low as 0.1% of that of fluid. Close matches between the computational and experimental results were obtained for simulations of a light boat under coupled motion in water stream.

THREE-DIMENSIONAL COLLISION MODELING FOR RIGID BODIES AND ITS COUPLING WITH FLUID FLOW COMPUTATION

A computational algorithm for 3-D rigid-body collision and its coupling with fluid flow was developed and implemented in FLOW-3D® as an addition to the existing General Moving Object (GMO) model. It is assumed that all the bodies have negligible deformation during collision and instantaneously change velocities when they collide. A set of existing equations of motion for collision under six degrees of freedom were adopted. Modifications were made for collisions of bodies with fixed axis, fixed point and prescribed motion. Numerical methods for collision detection and collision integration were developed. Stronge’s energetic coefficient of restitution was employed to determine completion of collision calculation. The model allows for simultaneous collisions of multiple bodies. Collisions can be perfectly elastic, partially plastic or completely plastic. Surfaces of bodies can be smooth or rough, allowing existence of impulse of friction during collision. Continuous contact between moving objects is modeled through a series of micro-collisions. Several applications of the model with and without presence of fluid flow were made. Good agreements of the computational results with analytical and experimental results were obtained and are presented at the end of the report.

Implicit_Advection

A powerful implicit advection technique has been incorporated into FLOW-3D®, Version 9.2. This paper illustrates uses of this technique to show its advantages, but also indicates certain limitations related to the accuracy of implicit methods.
Using the implicit advection scheme requires the selection of an input parameter impadv that activates the scheme according to:

impadv = 0, no implicit advection (i.e., explicit, the default);
1, implicit advection, with limited advection at free surfaces
controlling the time-step size for accuracy;
2, implicit advection, with no advection limit on time-step size.

When using FLOW-3D® to simulate transient problems, especially those involving sharp free surfaces and/or fluid-fluid interfaces the best implicit advection option is impadv=1. In this case, the program will limit time-step size by those fluid velocities at a free surface where the velocity is normal to the surface and the fluid fraction at that location has changed by more than 5% in the preceding cycle. Otherwise, the surface velocities will not impose a limit on time-step size.

A FIXED-MESH METHOD FOR GENERAL MOVING OBJECTS

A fixed-mesh method for general moving objects in fluid flow was developed and implemented into FLOW-3D®. A general moving object (GMO) is a rigid body with any type of six-degrees-of freedom, fixed-point and fixed-axis motion which can be either user-prescribed or dynamically coupled with fluid flow. The method allows for multiple independently general moving objects.

Equations of motion for rigid body are solved for coupled motion. Area and volume fractions are used to represent the objects in the fixed-grid at every time step to describe time-variation of object locations and orientations. Continuity and momentum equations for fluid and scalar transport equations are modified to account for the effects of object motion. Good agreement was achieved between computational and theoretical/experimental results in several application cases.

Electro-Hydrodynamics of Semi-Conductive Fluids With Application to Electro-Spraying

Background
It has long been known that strong electric fields can disrupt liquid surfaces. One particularly useful application of this observation has been the development of electrospray-ionization (ESI) systems.

The basic concept is to eject liquid from a nozzle connected to a voltage source that has a relatively high electric potential compared to its surroundings. When adjusted for certain operating conditions, a thin jet of liquid is ejected from the nozzle that subsequently breaks up into charged droplets having a relatively uniform size. There are many useful industrial applications for a system that produces small droplets of specified size; particularly if the droplets don’t coalesce because of their electrical repulsion.

Having a charge also means that these drops can be electrically deflected toward a target. This technology, for example, has been advantageously applied to paint spraying, atomization of fuels, printing, mass spectroscopy and a variety of spray drying processes.

Modeling of Electroosmosis without Resolving Physics inside the Electric Double Layer

A model for electroosmosis has been developed and released in version 8.2 of FLOW-3Dr. It is a general model in which the zeta potential distribution is solved through the electric double layer (EDL). When the EDL thickness (¸D) is very small, such as ¸D < 0:1¹m or in nanoscale, it is very computationally expensive to resolve the physics inside the EDL. In this note, we describe a simple model that has been developed to simulate electroosmosis without resolving the EDL.

That is, the zeta potential distribution is not solved, instead, a zeta potential on the obstacle surface is used as a boundary condition to calculate a slip velocity. This velocity is imposed on the obstacle surface if a zeta potential exists around that obstacle. It is de¯ned by ³²Ex ¹ and called the Helmholtz-Smoluchowski velocity with ³, Ex, ¹ representing zeta potential, electric ¯eld intensity in x-direction, ² permittivity, and liquid viscosity respectively.

However, if the EDL thickness is large compared to the problem geometry such as channel width, the simpli¯ed model is not accurate, and the original model is recommended. The new model has been validated against the corresponding analytical solution in a channel °ow and its application to complex microchannel °ow is demonstrated. The new simpli¯ed model will be incorporated in a future version of FLOW-3D

Development of New Pressure-Velocity Solvers in FLOW-3D [FLOW-3D의 새로운 압력-속도 해법의 개발]

1 Introduction
The purpose of this note is to document the development of new pressure-velocity solvers in FLOW-3Dr. In the following section, new solvers are described ¯rst followed by a section of sample problems where typical simulations were performed to illustrate the application of these new solvers. Two appendices are added to describe in detail the general minimum residual (GMRES) and generalized conjugate gradient (GCG) algorithms used in the new solvers.

Lost Foam Variable Pattern Density

Overview
Making foam patterns for use in the lost foam casting process is a difficult business. To make a pattern foam beads are blown into a mold containing discrete vent locations for the displaced air and steam. This makes the density of the packed beads difficult to control. Patterns typically show final density variations of ±20%. Much larger variations are not uncommon.
One goal of the Lost Foam Consortium is to evaluate techniques for improving the uniformity of patterns. A related goal is to determine to what extent density variations in patterns are significant with respect to the quality of the parts produced.
Recent real-time X-Ray observations of the metal filling process reported by Dr. Wayne Sun (Advanced Lost Foam Casting Technology-Phase V Meeting, June 20-21, 2001) revealed several interesting facts about the behavior of foam patterns. In particular, when the foam has a low degree of fusion metal is observed to move very fast into the foam (e.g., 4 to 5 times faster than in normal fusion foam). The advancement of the metal is typically in the form of fingers, which subsequently spread sideways causing the meeting of metal fronts that result in many fold defects. Furthermore, the location of the fingering is significantly affected by density variations in the foam pattern.
In contrast, when the foam patterns consisted of normal fusion foam, the metal front moved smoothly (i.e., no fingering) and considerably fewer fold defects occur. Also, the presence of density variations in the foam has little effect on the propagation of the metal fronts.
Based on these findings it was concluded that no attempt should be made to model low fusion foam because this in not likely to be choice for production work. Instead, we report here the development and testing of a model for adding a variable foam density to the FLOW-3D® software package from Flow Science, Inc.

Modeling shrinkage induced microporosity [마이크로 미세기공 발생 예측]

Overview
Cast metal parts are sometimes unusable because they have internal gas pockets, or bubbles, which develop when the metal shrinks during solidification. A general term describing such bubbles or voids is “porosity.” When these bubbles are relatively large and localized the porosity is called macro-porosity. Prediction of macro-porosity in the interior of cast parts is a capability of most software packages currently used for the modeling of metal casting processes.
Another type of porosity, characterized by a more uniform distribution of small bubbles with a total average volume fraction on the order of one percent, is referred to as micro-porosity. This type of porosity is also caused by metal shrinkage during solidification, but its character is different from macro-porosity because it develops at a later stage in the solidification process. This distinction in types of porosity is important because each type requires a different modeling approach.
In this note we propose a new model that has been implemented in FLOW-3D® for predicting the occurrence of micro-porosity. The model is simple, requires only basic material property data, and adds virtually no noticeable CPU time to a solidification simulation. Best of all, the model is complimentary to macro-porosity models and may be used in conjunction with either a complete hydrodynamic shrinkage simulation that includes fluid flow or with simpler heat-transfer and shrinkage simulation having no fluid flow.
The new model has been checked using three sets of experimental test data. A final test, involving only qualitative results for the influence of pressure on micro-porosity formation has also been conducted.

Computational Model for Simulation of Electroosmotic Flow in Microsystems

ABSTRACT
A numerical model has been developed to simulate three-dimensional and transient electroosmotic °ow oc-curring in various microdevices for handling °uid °ow and transport. The model can simulate one °uid °ow, with or without a free surface, and two-°uid °ow, with or without a sharp interface, using a VOF method. The model is validated by comparing numerical predictions against available analytical solution. Capabilities of the model to simulate processes such as sample focusing, mi-cropumping, and micromixing. are demonstrated through examples.
Keywords: Electroosmotic Flow, Micropump, Micromixer, and Sample Injection

Incremental Elastic Stress Model

Introduction
Elastic stress has been incorporated into FLOW-3D® to emulate viscoplastic materials, which are materials which behave as solids up to a yield stress, beyond which they behave like a viscous liquid.

The incremental elastic stress model recently incorporated into FLOW-3D® computes the elastic stress using linear Hookean theory (Equation 2 above). Although this constitutive equation predicts only a linear response to stress, implementation as an incremental model, in which the stress changes in each time step are accumulated, allows the prediction of highly nonlinear responses. This works because the response within each small time step can be well approximated as linear. Pictorially, with this model, FLOW-3D® predicts the total stress as a summation of the viscous stress and the elastic stress, as shown in Figure 1.

Lagrangian VOF Advection Method for FLOW-3D

1. Introduction
A new VOF advection method based on a 3-D reconstruction of the fluid interface has been developed and implemented in FLOW-3D® Version 8.2. The Volume-of-Fluid (VOF) function is moved in one step, without resorting to an operator splitting technique, which gives the present method increased accuracy when the flow is not aligned with a coordinate direction.
The existing VOF advection method in FLOW-3D® (hereinafter called the standard method) is based on the donor-acceptor approach first introduced by Hirt and Nichols [1]. Numerous enhancements have been made to the original algorithm to improve its accuracy and stability in complex one- and two- fluid flows with sharp interfaces1.
The standard method uses operator splitting and old time-level values of the VOF function to compute fluxes in three coordinate directions. The approach creates a possibility of overfilling or over-emptying computational cells when volume fluxes are significant in all three directions and the time step size is close to the local Courant stability limit.
The new advection method has been developed to alleviate these deficiencies of the standard algorithm. The fluid interface is reconstructed in 3D using a piecewise linear representation, where the interface is assumed to be planar in each control volume (or cell) containing the interface. The fluid volume bounded by the interface and cell faces is then moved according to the local velocity vector in a Lagrangian manner. Finally, the advected volume is overlaid back onto the Eulerian grid to obtain the new values of the fraction-of-fluid function. This combination of the Lagrangian and Eulerian methodology gives the new method its name (similar approaches have been used to approximate advection terms, for example, by Colella [2], Puckett et al [3], and Pilliod and Puckett [4]). The new option is activated in the code by setting IFVOF=5.

Sediment Scour [침전 / 세굴(쇄굴)]

Introduction
The sediment scour model predicts the behavior of packed and suspended sediment within the three-dimensional flow capabilities of FLOW-3D®. Potential applications include erosion around bridge piers, weirs, dams and underwater pipelines, and removal and drifting of sand or snow over terrain. The model consists of two basic components: drifting and lifting. Drifting acts on sediment that is suspended in the flow; gravity (along with other body forces) causes the settling of the sediment. This model is based on the drift-flux model already incorporated into FLOW-3D®. Lifting takes place only at the interface between the packed sediment and fluid and occurs where the local shear stress imposed by the liquid on the bed interface exceeds a critical value. The amount of lifting is proportional to the shear stress. In conjunction with the drifting and lifting models, a drag model is used to mimic the solid-like behavior of the sediment in regions where its concentration exceeds a cohesive solid fraction. The viscosity and density are functions of the sediment concentration; they are calculated as a function of the sediment concentration.

Modeling Turbulent Entrainment of Air at a Free Surface

Overview
In free-surface flows the turbulence in the liquid may be sufficient to disturb the surface to the point of entraining air into the flow. This process is important, for example, in water treatment where air is needed to sustain microorganisms for water purification and in rivers and streams for sustaining a healthy fish population. Air entrainment is typically engineered into spillways downstream of hydropower plants to reduce the possibility of cavitation damage at the base of the spillway. Other situations where air entrainment is undesirable are in the sprue and runner systems used by metal casters, and in the filling of liquid containers used for consumer products.
The importance of being able to predict the amount and distribution of entrained air at a free liquid surface has led to the development of a unique model that can be easily inserted into FLOW-3D® as a user customization. The model has two options. One option, to be used when the volume fraction of entrained air is relatively low, uses a scalar variable to record the air volume fraction. This model is passive in that it does not alter the dynamics of the flow.
A second air-entrainment model, option two, is based on a variable density formulation. This model includes the “bulking” of fluid volume by the addition of air and the buoyancy effects associated with entrained air. However, this dynamically coupled model cannot be used in connection with heat transport and natural (thermal) convection.
In both model options the same basic entrainment process is used that is based on a competition between the stabilizing forces of gravity and surface tension and the destabilizing effects of surface turbulence. The model is described in the next section. Because turbulence is the main cause of entrainment, a turbulence-transport model must be used in connection with the air-entrainment model (i.e., ifvis=3 or 4). It is recommended that the RNG version of the more traditional k-epsilon turbulence model be employed. All the validation tests reported in this Technical Note were performed using the RNG turbulence model.

Modeling Roughness Effects in Open Channel Flows

Overview
Flows along rivers, through pipes and irrigation channels encounter resistance that is proportional to the roughness of bounding walls. Roughness can vary considerably from smooth steel, to concrete or sand, pebbles, and even large boulders. In traditional hydraulics the influence of roughness has been cataloged in the form of a roughness coefficient based on data obtained from a wide range of field and laboratory observations.
Roughness coefficients are typically defined in one of two ways: (1) Ch¾zy’s resistance coefficient, or (2) Manning’s n. To understand these terms we must first state the conditions under which they are defined. For this discussion, and much more information about flow resistance caused by roughness, the reader is referred to Open Channel Hydraulics by Ven Te Chow and published by McGraw-Hill, reissued 1988.
Flow losses are defined in terms of a uniform flow state defined as steady flow with a fixed discharge and flow depth. In practice this usually means the flow in a channel of uniform cross section and having a constant slope such that the gravitational acceleration down the slope is balanced by frictional resistance at the boundaries of the channel.

Surface Tension Validation Tests

Modeling surface tension phenomena is computationally difficult because it requires the evaluation of second derivatives.
This is particulary true in the FLOW-3D program where the capability to represent highly complicated and multiple free surfaces difficulties are further compounded in three-dimensional calculations because one is often forced, for reasons of economy, to use marginal numerical resolution.

Multi-Block Gridding Technique for FLOW-3D [FLOW-3D에서 멀티블럭 설정 기법]

1. Introduction
A major new extension of the capabilities of FLOW-3D® — the multi-block grid model — has been incorporated into the code starting with Version 8.0. Multi-block gridding in FLOW-3D® will enable more efficient use of the software’s resources when modeling complex flow phenomena. Each block spans a certain region of the whole flow domain and contains the standard structured rectangular mesh. Two types of mesh blocks can be used: the nested blocks and the linked blocks.
Data transfer between any two mesh blocks is facilitated by special boundary (or ghost) cells. Solution quantities are interpolated from the real cells of a donor block into the boundary cells of the acceptor block. The interpolation technique varies depending on the variable at hand. Conserved quantities, like concentrations and thermal energy, are interpolated using the piecewise constant method. A special variant of this method is used for fluid fraction interpolation, where a reconstruction of the interface is performed to locate the interface within the donor cells before the interpolation.
Pressure and velocities are calculated using linear interpolation to preserve the gradients. A mixture of the Neumann- and Dirichlet-type boundary conditions is used for the solution of the Poisson equation for pressure. A weighing factor defines the contribution of each type of the boundary condition to the final solution, ensuring continuity of both pressure and velocities across the inter-block boundaries, convergence and local conservation of mass.

Modeling Thermal Expansion Effects in FLOW-3D

This note describes the modeling used in FLOW-3D® for thermal expansion processes in onefluid, incompressible flows. Volume changes are modeled in unconfined flows while the limited
compressibility model may be used to compute the change is pressure in flows that are confined and density cannot change.

Initiating Homogeneous Bubbles in Pure Liquid

Initiating Homogeneous Bubbles in Pure Liquid

  1. Barkhudarov and C.W. Hirt

Flow Science, Inc.

The combined Temperature-Dependent-Cavitation and Homogenous Bubble models work together as a way to simulate the formation and growth of vapor bubbles by locally heating a liquid. The Homogeneous Bubble model is only activated when a bubble has a size that encompasses at least one complete grid cell, i.e., can be resolved as a “bubble” or void region.

The Cavitation model contains a mechanism for the initiation of bubbles, which works in the follow way. At the end of each time cycle of a transient computation every grid cell containing liquid is tested to see if its pressure is less than the saturation pressure corresponding to the temperature in the cell. The saturation pressure is computed from the pressure-temperature saturation relation specified by the user (e.g., usually a Clapeyron relation). If the cell pressure is less than its saturation pressure it is assumed that boiling can begin. The essential assumption is that there exist sufficient impurities or nucleation sites for this to happen. A very simple model nucleation has been incorporated into FLOW-3D®.

Once a cell has been identified for possible boiling it is given a time delay before vaporization begins. For vaporization to occur it is necessary to have at least 1% void fraction in the cell. This small void can be thought of as the nucleation process. The time delay is input as variable CAVRT (denoted as Ccav in the following).

Addition of Dielectric Phenomena to FLOW-3D

Overview
There are situations where it would be helpful to account for the interaction of electric fields with liquid and solid materials. For example, electrostatic air cleaners rely on the ability to attract small particles in flowing air to a surface where they can be collected and removed from the air. In this case the primary attractive force arises from dielectric polarization of the particles.
Spraying liquid drops onto a surface, as in spray painting, is often improved by electrifying the drops so that they repel one another and produce a more uniform distribution. Also, electrified drops can be driven to overcome air resistance by suitable electric fields.
In many types of micro-electrical-mechanical-systems (MEMS) fluids are caused to move by the application of electric potentials. Usually this behavior is induced by electric forces acting on dielectric polarization charges generated at free fluid surfaces or at the interfaces between two fluids.

In some situations the effects of both dielectrically induced charges as well as free electric charges in a fluid must be considered. For these cases the fluid has some nonzero conductivity that must be accounted for by tracking charge densities and adding additional body forces to the fluid. The range of possibilities when conduction is present includes bound and free charges, recombination, ionization, currents without net charge densities, etc. As described next, we shall limit the present development to a useful subset of the many possibilities.

In this note we describe a set of program developments that give FLOW-3DÒ the capability to model fluid and particulate flows involving both free and induced charge densities. In the current released version of FLOW-3D® (Ver. 7.7) both particles and fluid can contain a fixed charge density, but there is no provision for dielectric materials.

Here we describe the addition of dielectric properties for particles, fluids, and solids. In addition, linear polarization forces acting on particles and fluids by electrostatic fields are added to the momentum equations for fluid and particles.

Simulating the Wetting and Drying of Shallow Flows [얕은 흐름의 습윤 및 건조 시뮬레이션]

Introduction
Shallow flows, characterized by having a thickness much smaller than their lateral extent, can often be modeled by a depth-averaged (shallow-water or 2.5 dimensional) approximation.
Average fluid velocities are computed in the layer and the top fluid surface is free to move, which leads to a changing fluid-layer thickness. The advantages of this approach are its speed
and simplicity over full three-dimensional simulations.
One complication, however, is how to efficiently account for dynamic contact-line effects at lateral boundaries of the fluid. These boundaries are free to move over the underlying solid
surface. Furthermore, the fluid contact angle at these boundaries depends on the local dynamic flow conditions.
In this paper we present a new shallow-flow computational method based on the Volume-of-Fluid (VOF) technique, which conserves fluid mass, while allowing for general wetting and
drying behavior. Non-uniform surface tension and fluid-substrate interactions, defined by a static contact angle, are included in the model. No special prescriptions are needed to locate
contact line locations or define dynamic contact angles.

Movable Fluid Sources in FLOW-3D [FLOW-3D에서 움직이는 유체]

OVERVIEW


There are many examples of fluid flow simulation where it would be useful to have specified fluid sources located inside the computational grid. By “fluid sources” we mean a source of
fluid mass and momentum. Even more useful would be a capability where the location, flow rate, and flow direction of the fluid sources could be specified.
In this Technical Note, we describe a scheme that meets these goals in the FLOW-3D® program.
In the next section we describe the basic approach that was taken to add this capability and following that there are several examples illustrating the method.
MODELING APPROACH FOR GENERAL FLUID SOURCES
A recent addition to FLOW-3D® is the ability to have full momentum coupling between a continuum fluid and discrete mass particles. This addition is described in the Flow Science
Technical Note FSI-99-TN50, “Particle-Fluid Coupling.” It is this capability that forms the basis of our addition for general fluid sources.
For purposes of discussion, suppose that we want to model fluid exiting the end of a pipe placed somewhere inside a computational grid. Fluid exits the end of the pipe with a specified flow rate
and flow velocity, i.e., both magnitude and direction are specified. In the most general case, the velocity distribution over the cross section of the pipe exit could be non-uniform. The location
of the pipe end should be arbitrary, so that moving the pipe by relocating it every time step in a transient computation would be possible.
To meet these goals, we imagine covering the end of the pipe with a set of particles. Each particle is assigned a mass source rate and a velocity corresponding to the fluid flow direction at
its location. We may think of these particles as representing average values of the flow for small areas surrounding them. In this sense, summing up the particles is equivalent to a numerical
integration of the flow over the cross section of the pipe. The particles simply represent the discrete elements of the integration area.

Self-Consistent Electric Fields and Electric Forces On Charged Particles

SCOPE
A recent addition to the computational fluid dynamics program FLOW-3D® is a capability for modeling discrete mass particles moving through a continuum. This model implicitly couples
the particles and continuum so that they may exchange momentum in a conservative way.
This report addresses how that model has been extended to account for mass particles having an electric charge and moving in an electric field. The extension is self-consistent in the sense that
the particle charges contribute to the electric field. For this reason the field is time dependent and must be recomputed for each time step of a numerical simulation.
In addition to the charged particles, solid objects (obstacles) located within the computational region may be assigned arbitrary, but constant in time, potentials. Each obstacle may have a
fixed potential value consistent with the obstacle being a conductor. A zero potential value is the default value if not otherwise specified. It should be noted that an electric potential can be
computed even when there are no charged particles, although this field will have no effect on flow processes unless the user adds some kind of additional interaction to the model.
Mesh boundaries that are rigid walls may be assigned non-zero potential values. All other boundaries are treated as symmetry boundaries with respect to the potential. Furthermore, no
insulated obstacles are allowed in this model. It is also assumed that if there are free fluid surfaces or fluid-fluid interfaces then the dielectric constants (i.e., ratios of material permittivities
to that of vacuum) of the different materials must be the same, otherwise additional development will be needed to solve for the electric potential. In general, this is not correct because the
dielectric constant does vary with material type; for example, water has a dielectric constant about 81 times that for air.

A Surface Tension Model Update [표면장력 모델 업데이트]

PURPOSE AND BACKGROUND
The modeling of surface tension forces is computationally difficult because it requires the evaluation of surface curvatures, i.e., second derivatives of the surface location. This is
particularly true in FLOW-3D® since it uses a regular rectangular grid that does not conform to surface shapes. Although this simple grid structure makes it more difficult to evaluate surface
slopes and curvatures, it is this feature that also gives the strength needed to simulate coalescence and breakup of fluid blobs.
Evaluation of surface slope and curvature in FLOW-3D® is done by determining which coordinate direction is closest to the outward normal vector to the surface. Then fluid in a 3 by 3
by 3 set of grid cells surrounding a given cell is summed up in the cell columns parallel to the normal. This, in effect, gives a discrete representation of the surface height in nine (3×3)
columns, which can be used to compute slopes and curvatures.
In most cases this procedure works quite well, but when normal directions in the grid are near 45° the surface may be too steep for this procedure to work accurately. A consequence of this
loss of accuracy is the introduction of spurious pressures or perturbations that sometimes generate undesirable capillary waves (i.e., kinetic energy noise). Occasionally, these
perturbations can even destroy a computation.
A summary of the original surface tension model was given in Technical Note TN6, “Surface Tension Validation Tests,” (1987). Since that Note there have been a number of major improvements:

1. Wall adhesion sensitive to slope of wall,
2. Static contact angle as an obstacle property,
3. Two-fluid interfacial surface tension,
4. Thermocapillary (i.e., tangential) surface forces (see TN47).

In this Technical Note we document another improvement that has been made. In particular, we have improved the accuracy of the column summation technique for the computation of surface
curvatures. As the following examples will show, this improvement is quite dramatic in many cases where the earlier model experienced substantial difficulties.

Particle-Fluid Coupling [입자-유체 연동]

There are many important flow situations involving a dispersed liquid or solid material in a continuous gas or liquid. A few everyday examples are fuel injection in a automobile engine,
rain, dust storms and all sorts of atomizers for painting, cleaning and applying medicine. In most cases there are significant interactions between the continuous and dispersed materials
that arise because of the drag experienced by the dispersed particles as they move through the continuous fluid. A secondary interaction effect is the displacement of fluid volume by particle
volume.
Of the two interaction effects, i.e., volume exclusion and momentum exchange, the most important is momentum exchange because this can be significant even when the volume of
particles is small. To see why this is so, consider a typical two-phase system with properties similar to that of water and air. The density ratio between water and air is about 1000. This
means that a liquid fraction of only 10E-4 translates into 10% of the mixture mass. Thus, even when the water volume is a negligible fraction of the whole, it still may account for a significant
portion of the mixture momentum.

Plume Rise in a Stratified Fluid

The evolution of a buoyant plume in a stratified fluid is a flow problem that occurs in many natural and man made situations, for example, volcanoes, industrial smoke stacks, and hot water discharges in thermally stratified ponds.

Sample Problem for Free Surface Hydraulics [자유표면 유압문제 샘플]

The field of open-channel hydraulics is filled with many interesting and complicated fluid dynamics problem. Large scale channel flows can often be adequately treated using simplified shallow water analysis methods, but localized flows around ge\ates, wairs, and other structures generally require more sophisticated methods.

Core gas defects in steel castings

Abstract

Porosity is a common but serious casting defect. One type of porosity is a result of core gas that has evolved and been trapped in the casting during solidification. In order to reduce or eliminate core gas related defects, detailed information regarding the core gas generation, flow, and venting in the core, and the metal flow and solidification behavior in the mold is needed. In this paper, numerical simulations are conducted based on a prototype design, which is a steel casting part from Caterpillar. The core gas in the core and the porosity defects in the casting are analyzed and discussed, and then compared with the real casting results. Using simulations to determine porosity defects can help in optimizing the design.

Keywords: Porosity, Core Gas Defects, Steel Castings, Numerical Simulation, PUCB

No Loss with FAVOR™

본 자료는 국내 사용자들의 편의를 위해 원문 번역을 해서 제공하기 때문에 일부 오역이 있을 수 있어서 원문과 함께 수록합니다. 자료를 이용하실 때 참고하시기 바랍니다.

No Loss with FAVOR™

Mampaey and Xu1 showed how Cartesian grid representations of curved flow channels, using a zigzag approximation for the walls, can result in substantial numerical flow losses. There are two sources for these losses. The first source arises from changes in flow direction at a zigzag in the grid boundary. Each abrupt direction change is accompanied by a small loss in kinetic energy. The second source of flow loss may arise from poor approximations of fluid momentum advection near a zigzag boundary. If the finite-difference algorithm uses velocity data located in solid regions outside the channel, these values generally contribute to a slowing down of the flow, i.e., result in a loss of energy.

FAVOR TM를 사용한 손실 제로

Mampaey 와 Xu (아래 자료 참조)는 벽에 대해 지그재그 근사를 사용하여 곡선 유로를 직교 격자로 나타낸 결과 상당한 수치적 유동 손실이 발생할 수 있음을 보여줍니다.  이 손실에는 두 가지 원인이 있습니다.  첫 번째 원인은 격자 경계의 지그재그 부분에서 흐름의 방향이 변화하는 것입니다.  방향이 급변 할 때마다 운동 에너지는 조금씩 감소합니다.  유동 손실의 두 번째 원인으로 생각되는 것은 지그재그 경계 부근의 유체 운동량 이류(advection)의 근사치가 불충분 한 것입니다.  유로의 외부 고체 영역의 속도 데이터를 유한 차분 알고리즘에서 사용하는 경우 이 값이 유속 저하되는 것은 일반적이며, 그 결과 에너지 손실이 발생합니다.

No loss with FAVOR

Flow Loss Reduction

Since FLOW-3D uses a Cartesian grid, it is reasonable to ask if it too suffers from numerical flow losses. The answer is no, it does not. The Fractional Area-Volume Obstacle Representation, FAVOR™, method used exclusively in FLOW-3D eliminates zigzag direction changes by smoothly blocking out fractional portions of grid cell faces and volumes. FAVOR™ also has a collection of special algorithms for computing interfacial areas, evaluating wall stresses, enhancing numerical stability, and for computing advection along solid boundaries.

유동 손실의 감소

FLOW-3D는 직교 격자를 사용하고 있기 때문에 수치적 유동 손실의 영향에 대한 의문이 나오는 것은 당연합니다.  대답은 ‘노’입니다.  영향은 없습니다.  FLOW-3D에서 독점적으로 사용되는 FAVOR TM (Fractional Area-Volume Obstacle Representation) 법에서는 격자 셀면이나 체적의 세세한 부분을 매끄럽게 블록 분류하여 지그재그 방향 변화를 제거합니다 .  FAVOR TM는 계면 면적 계산, 벽 응력의 평가, 수치 안정성 강화, 고체 경계에 따른 이류의 계산 등을 목적으로 한 일련의 특수한 알고리즘도 포함되어 있습니다.

Energy Conservation Example

A simple demonstration of energy conservation in FLOW-3D is provided by a variation of the Mampaey and Xu experiment. In the figure, we show the lower half of a circular channel with fluid located in the left half. The fluid is initially at rest, but gravity is directed downwards causing the fluid to flow to the right side of the channel. In the absence of flow losses, the fluid should reach the same height on the right side as it started from on the left side.

에너지 보존의 예

FLOW-3D의 에너지 절약에 대한 부분을 Mampaey 와 Xu 의 실험을 응용하여 쉽게 보여줍니다.  그림은 원형 수로의 하단에서 왼쪽에 유체가 배치되어있는 모습을 보여줍니다.  이 유체는 처음에는 정지하고 있습니다 만, 아래로 중력이 걸려 있기 때문에 유체는 수로의 오른쪽으로 흐릅니다.  유동 손실이 없는 경우 이 유체는 오른쪽으로 흐를 때 왼쪽에서 첫 번째 상태와 같은 높이에 도달해야합니다.

FLOW-3D simulations of this problem show a realistic sloshing distortion of the free surface (figure above) and the center of mass of the fluid rises to nearly its initial height on the right side of the channel indicating little flow loss. This result is all the more remarkable considering the coarse gridding.

이 문제를 FLOW-3D로 시뮬레이션하면 자유 표면의 리얼한 슬로싱 왜곡은 있지만 (위 그림 참조) 유체의 질량 중심은 수로의 오른쪽에서 처음과 거의 같은 높이까지 상승하고 유동 손실이 거의없는 것을 보여줍니다.  격자가 거친 것을 고려하면이 결과는 더욱 주목할만 합니다.

Reference

Mampaey, F. and Xu, Zhi-An, Simulation and Experimental Validation of Mould Filling, Proc. Modeling of Casting, Welding and Advanced Solidification Processes VII, London, September 10-12, p.3 (1995).