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Walter Frei | September 16, 2013

Which Turbulence Model Should IChoose for my CFD Application?

COMSOL Multiphysics offers several differentformulations for solving turbulent flow problems: the L-VEL, yPlus, Spalart-Allmaras, k-epsilon, k-omega, Low

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Reynolds number k-epsilon, and SST models. All of theseformulations are available in the CFD Module, and the k-epsilon and Low Reynolds number k-epsilon are availablein the Heat Transfer Module. This posting outlines thereasons why we want to use these various turbulencemodels, how to choose between them, and how to usethem effectively. Throughout the post, youll find links torelevant models that highlight the features discussed.

Introduction to Turbulence Modeling

Lets start by considering the flow of a fluid over a flatplate, as shown in the figure below. The uniform velocityfluid hits the leading edge of the flat plate, and a laminarboundary layer begins to develop. The flow in this regionis very predictable. After some distance, small chaoticoscillations begin to develop in the fluid field, and theflow begins to transition to turbulence, eventuallybecoming fully turbulent.

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The transition between these three regions can bedefined in terms of the Reynolds number,

, where is the fluid density, is the velocity, is thecharacteristic length (in this case, the distance from theleading edge), and is the fluid dynamic viscosity. Wewill assume that the fluid is Newtonian, meaning that theviscosity is constant with respect to shear rate. This istrue, or very nearly so, for a wide range of fluids ofengineering importance, such as air or water. Density canvary with respect to pressure, although it is assumed thatthe fluid is only weakly compressible, meaning that theMach number is less than about 0.3.

In the laminar regime, the flow of the fluid can becompletely predicted by solving the steady-state Navier-Stokes equations, which predict the velocity and the

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pressure fields. We can assume that the velocity fielddoes not vary with time, and get an accurate predictionof the flow behavior. An example of this is outlined in themodel The Blasius Boundary Layer. As the flow begins totransition to turbulence, chaotic oscillations appear in theflow, and it is no longer possible to assume that the flowis invariant with time. In this case, it is necessary to solvethe problem in the time domain, and the mesh usedmust be fine enough to resolve the size of the smallesteddies in the flow. Such a situation is demonstrated inthe example model Flow Past a Cylinder. Steady-stateand transient laminar problems can be solved both withCOMSOL Multiphysics alone, as well as along with theMicrofluidics Module, which has additional boundaryconditions applicable for flow in very small channels.

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As the Reynolds number increases, the flow field exhibitssmall eddies, and the timescales of the oscillationsbecome so short that it is computationally unfeasible tosolve the Navier-Stokes equations. In this flow regime, wecan use a Reynolds-Averaged Navier-Stokes (RANS)formulation, which is based on the observation that theflow field (u) over time contains small, local oscillations(u) that can be treated in a time-averaged sense (U). As aconsequence, we add additional unknowns to the systemof equations and introduce approximations for the flowfield at the walls.

Wall Functions

The turbulent flow near a flat wall can be divided up intofour regimes. At the wall, the fluid velocity is zero, and fora thin layer above this, the flow velocity is linear withdistance from the wall. This region is called the viscoussublayer, or laminar sublayer. Further away from the wallis a region called the buffer layer. In the buffer region, theflow begins to transition to turbulent, and it eventuallytransitions to a region where the flow is fully turbulentand the average flow velocity is related to the log of thedistance to the wall. This is known as the log-law region.

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NanangCallouteddies became very small as well as the time fluctuation -> when solving NS using numerical simulation, dx,dy,dz must be very small, as well as dt

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Even further away from the wall, the flow transitions tothe free-stream region. The viscous and buffer layers arevery thin, and if the distance to the end of the bufferlayer is , then the log-law region will extend about

away from the wall.

It is possible to use a RANS model to compute the flowfield in all four of these regimes. However, since thethickness of the buffer layer is so small, it can beadvantageous to use an approximation in this region.Wall functions ignore the flow field in the buffer region,and analytically compute a non-zero fluid velocity at thewall. By using a wall function formulation, you assume ananalytic solution for the flow in the viscous layer, and the

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resultant models will have significantly lowercomputational requirements. This is a very usefulapproach for many practical engineering applications.

If you need a level of accuracy beyond what the wallfunction formulations provide, then you will want toconsider a turbulence model that solves the entire flowregime. For example, you may want to compute lift anddrag on an object, or compute the heat transfer betweenthe fluid and the wall.

If you are solving any kind of problem where the flow isnot fully turbulent, such as a free convection problem,you will need to resolve the flow to the wall, and should

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not use wall functions.

About the Various Turbulence Models

The seven RANS turbulence models differ in their usageof wall functions, the number of additional variablessolved for, and what these variables represent. All ofthese models augment the Navier-Stokes equations withan additional turbulent viscosity term, but they differ inhow it is computed.

Editors note: This blog post has been updatedto include information on the L-VEL and yPlusmodels that were added in COMSOLMultiphysics version 5.0, released on10/31/2014.

L-VEL and yPlus

The L-VEL and yPlus algebraic turbulence modelscompute the turbulent viscosity, based only on the localfluid velocity and the distance to the closest wall; they donot solve for additional variables. These models solve theflow everywhere and are the most robust and least

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computationally intensive of the seven turbulencemodels. While they are generally the least accuratemodels, they do provide good approximations forinternal flow, especially in electronic cooling applications.

Spalart-Allmaras

The Spalart-Allmaras model adds a single additionalvariable for a Spalart-Allmaras viscosity and does not useany wall functions; it solves the entire flow field. Themodel was originally developed for aerodynamicsapplications and is advantageous in that it solves for onlya single additional variable. This makes it less memory-intensive than the other models that solve the flow fieldin the buffer layer. Experience shows that this modeldoes not accurately compute fields that exhibit shearflow, separated flow, or decaying turbulence. Itsadvantage is that it is quite stable and shows goodconvergence.

k-epsilon

The k-epsilon model solves for two variables: k; theturbulent kinetic energy, and epsilon; the rate of

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dissipation of kinetic energy. Wall functions are used inthis model, so the flow in the buffer region is notsimulated. The k-epsilon model is very popular forindustrial applications due to its good convergence rateand relatively low memory requirements. It does not veryaccurately compute flow fields that exhibit adversepressure gradients, strong curvature to the flow, or jetflow. It does perform well for external flow problemsaround complex geometries. For example, the k-epsilonmodel can be used to solve for the airflow around a bluffbody.

k-omega

The k-omega model is similar to k-epsilon, insteadhowever, it solves for omega the specific rate ofdissipation of kinetic energy. It also uses wall functionsand therefore has comparable memory requirements. Ithas more difficulty converging and is quite sensitive tothe initial guess at the solution. Hence, the k-epsilonmodel is often used first to find an initial condition forsolving the k-omega model. The k-omega model is usefulin many cases where the k-epsilon model is not accurate,such as internal flows, flows that exhibit strong curvature,

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separated flows, and jets. A good example of internalflow is flow through a pipe bend.

Low Reynolds Number k-epsilon

The Low Reynolds number k-epsilon is similar to the k-epsilon model but does not use wall functions; it solvesthe flow everywhere. It is a logical extension to k-epsilonand shares many of its advantages, but uses morememory. It is often advisable to use the k-epsilon modelto first compute a good initial condition for solving theLow Reynolds number k-epsilon model. Since it does notuse wall functions, lift and drag forces and heat flux canbe modeled with higher accuracy.

SST

Finally, the SST model is a combination of the k-epsilon inthe free stream and the k-omega models near the walls.It does not use wall functions and tends to be mostaccurate when solving the flow near the wall. The SSTmodel does not always converge to the solution quickly,so the k-epsilon or k-omega models are often solved firstto give good initial conditions. In an example model, the

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SST model solves for flow over a NACA 0012 Airfoil, andthe results are shown to compare well with experimentaldata.

Meshing Considerations

Solving for any kind of fluid flow problem laminar orturbulent is computationally intensive. Relatively finemeshes are required and there are many variables tosolve for. Ideally, you would have a very fast computerwith many gigabytes of RAM to solve such problems, butsimulations can still take hours or days for larger 3Dmodels. Therefore, we want to use as simple of a mesh aspossible, while still capturing all of the details of the flow.

Referring back to the figure at the top, we can observethat for the flat plate (and for most flow problems), thevelocity field changes quite slowly in the directiontangential to the wall, but quite rapidly in the normaldirection, especially if we consider the buffer layerregion. This observation motivates the use of a boundarylayer mesh. Boundary layer meshes (which are the defaultmesh type on walls when using our physics-basedmeshing) insert thin rectangles in 2D, or triangular prisms

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in 3D, at the walls. These high aspect ratio elements willdo a good job of resolving the variations in the flowspeed normal to the boundary, while reducing thenumber of calculation points in the direction tangentialto the boundary.

The boundary layer mesh (magenta) around an airfoil andthe surrounding triangular mesh (cyan) for a 2D mesh.

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The boundary layer mesh (magenta) around a bluff bodyand the surrounding tetrahedral mesh (cyan) for a 3Dvolumetric mesh.

Evaluating the Results of Your TurbulenceModel

Once youve used one of these turbulence models tosolve your flow simulation, you will want to verify that the


solution is accurate. Of course, as you do with any finiteelement model, you can simply run it with finer and finermeshes and observe how the solution changes withincreasing mesh refinement. Once the solution does notchange to within a value you find acceptable, yoursimulation can be considered converged with respect tothe mesh. However, there are additional values you needto check when modeling turbulence.

When using wall function formulations, you will want tocheck the wall lift-off in viscous units (this plot isgenerated by default). This value tells you if your mesh atthe wall is fine enough, and should be 11.06 everywhere.If the mesh resolution in the direction normal to the wallis too coarse, then this value will be greater than 11.06and you should use a finer boundary layer mesh in theseregions. The second variable that you should check whenusing wall functions is the wall resolution in length units.This variable is related to the assumed thickness of theviscous layer, and should be small relative to thesurrounding dimensions of the geometry. If it is not, thenyou should refine the mesh in these regions as well.

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The regions where the wall lift-off is greater than 11.06require a finer mesh.

When solving in the viscous and buffer layer, check thedimensionless distance to cell center (also generated bydefault). This value should be of order unity everywhere,and less than 0.5 for the Low Reynolds number k-epsilonmodel. If it is not, then refine the mesh in these regions.


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Concluding Thoughts

This post has discussed the various turbulence modelsavailable in COMSOL Multiphysics, and when and whyyou should use each of them. The real strength of thesoftware is when you want to combine your fluid flowsimulations with other physics, such as finding stresseson a solar panel in high winds, forced convectionmodeling in a heat exchanger, or mass transfer in amixer, among other possibilities.

If you are interested in using COMSOL software for yourcomputational fluid dynamics (CFD) and multiphysicssimulations, or have a question that isnt addressed here,please contact us.

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Comments

Nagi Elabbasi September 18, 2013 at 9:44 am

That was very informative, thank you. Modelingturbulence accurately is not easy, so its good to see theCOMSOL features and capabilities available for thatpurpose.

Franco Cerna October 5, 2013 at 11:48 am

Someone could hang a video tutorial on turbulentflows?

Mustafa Abd El-Mageed November 9, 2013 at 7:11 am

Can we use turbulent model type in FSI Physics incomsol 4.2a ? as the turbulent model consider the soliddomain belong to the fluid and makes error message


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Failed to evaluate variable.- Variable: mod1.epx- Geometry: 1- Domain: 2 3 4 5

and all domains 2 3 4 5 are solids ?

Zaid B. Jildeh December 2, 2014 at 8:40 am

Thank you, this post helped me a lot to understand thenature of my system.Thank to Comsol for updating the turbulent models, thenew models in v.5.0 are very stable and fast to solvetime-dependent response.

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