Modeling Turbulent Flows

1. Modeling Turbulent Flows General introduction that Fluent CFD software contains a variety of state-of-the-art turbulence modeling options; however, successful predictions of turbulent flows will only result from turbulence modeling decisions based on sound engineering judgement. In this lecture we will identify the issues which must be considered, discuss the turbulence modeling options available in Fluent CFD software, and describe how an engineer should decide when modeling turbulent flows. The pictures is the iso-surfaces of instantaneous vorticity magnitude of flow over a square cylinder at a Reynolds number of 22000General introduction that Fluent CFD software contains a variety of state-of-the-art turbulence modeling options; however, successful predictions of turbulent flows will only result from turbulence modeling decisions based on sound engineering judgement. In this lecture we will identify the issues which must be considered, discuss the turbulence modeling options available in Fluent CFD software, and describe how an engineer should decide when modeling turbulent flows. The pictures is the iso-surfaces of instantaneous vorticity magnitude of flow over a square cylinder at a Reynolds number of 22000

2. What is Turbulence? Unsteady, irregular (aperiodic) motion in which transported quantities (mass, momentum, scalar species) fluctuate in time and space Identifiable swirling patterns characterize turbulent eddies. Enhanced mixing (matter, momentum, energy, etc.) results Fluid properties and velocity exhibit random variations Statistical averaging results in accountable, turbulence related transport mechanisms. This characteristic allows for Turbulence Modeling. Contains a wide range of turbulent eddy sizes (scales spectrum). The size/velocity of large eddies is on the order of mean flow. Large eddies derive energy from the mean flow Energy is transferred from larger eddies to smaller eddies In the smallest eddies, turbulent energy is converted to internal energy by viscous dissipation. Point out that the governing equations for turbulence are well-known and are the non-linear, unsteady three-dimensional Navier-Stokes equations. Useful to think of the instantaneous velocity in terms of a mean velocity with random fluctuations superimposed. Not only are there fluctuations in velocity but also in pressure, temperature, and scalar variables. The ability to predict the enhanced mixing resulting from turbulence is important in a large number of applications. Point out that the governing equations for turbulence are well-known and are the non-linear, unsteady three-dimensional Navier-Stokes equations. Useful to think of the instantaneous velocity in terms of a mean velocity with random fluctuations superimposed. Not only are there fluctuations in velocity but also in pressure, temperature, and scalar variables. The ability to predict the enhanced mixing resulting from turbulence is important in a large number of applications.

3. Is the Flow Turbulent? That first thing to consider is whether or not you need to consider turbulence modeling at all. Basically, the types of flows can be classified as either external, internal, or natural convection, The criteria for transition to turbulent flow is different depending on the type of flow you are considering. For external/internal flows common criteria are based on Reynolds number where the length scale varies depending on the flow. For flows along a surface, the Reynolds number is based on the distance along the surface. For flows about some object the Reynolds number is based on the diameter of the obstruction. Internal flows have the Reynolds number based on the hydraulic diameter. These criteria are not steadfast and can be affected by the other factors listed. Flows involving natural convection have been observed to transition from laminar to turbulent flow over a range of Rayleigh numbers.That first thing to consider is whether or not you need to consider turbulence modeling at all. Basically, the types of flows can be classified as either external, internal, or natural convection, The criteria for transition to turbulent flow is different depending on the type of flow you are considering. For external/internal flows common criteria are based on Reynolds number where the length scale varies depending on the flow. For flows along a surface, the Reynolds number is based on the distance along the surface. For flows about some object the Reynolds number is based on the diameter of the obstruction. Internal flows have the Reynolds number based on the hydraulic diameter. These criteria are not steadfast and can be affected by the other factors listed. Flows involving natural convection have been observed to transition from laminar to turbulent flow over a range of Rayleigh numbers.

4. Two Examples of Turbulent Flow

5. Overview of Computational Approaches Direct Numerical Simulation (DNS) Theoretically all turbulent flows can be simulated by numerically solving the full Navier-Stokes equations. Resolves the whole spectrum of scales. No modeling is required. But the cost is too prohibitive! Not practical for industrial flows - DNS is not available in Fluent. Large Eddy Simulation (LES) Solves the spatially averaged N-S equations. Large eddies are directly resolved, but eddies smaller than the mesh sizes are modeled. Less expensive than DNS, but the amount of computational resources and efforts are still too large for most practical applications. Reynolds-Averaged Navier-Stokes (RANS) Equations Models Solve ensemble-averaged Navier-Stokes equations All turbulence scales are modeled in RANS. The most widely used approach for calculating industrial flows. There is not yet a single turbulence model that can reliably predict all turbulent flows found in industrial applications with sufficient accuracy. For DNS, you may mention the scaling argument; where R is turbulent Reynolds number Therefore, the minimum number of grid points per integral scale is Including time discretization, the computational work For DNS, you may mention the scaling argument; where R is turbulent Reynolds number Therefore, the minimum number of grid points per integral scale is Including time discretization, the computational work

6. Turbulence Scales and Prediction Methods The notion of scales can be used as an aid, helping us to classify turbulence prediction methods, especially in terms of what to model and what to resolve. Spend a minute to explain the large and small scales and the energy transfer down the hierarchy and what�s responsible for generating smaller eddies (I.e., vortex stretching). Use the analogy of generations. Also mention that the large eddies more intimately interact with the mean flow and more directional bias, and that smaller eddies tend to forget their roots and ancestry, and become more universal andisotrpic. Explain the energy transfer. Mention that this sketch depicts the famous energy cascade according to Kolmogorov�s 1941 theory. Energy is injected mostly at largest scales at a rate (e), is cascading down the hierarchy of eddies at the same rate, and is eventually removed by dissipation at the smallest scales.The notion of scales can be used as an aid, helping us to classify turbulence prediction methods, especially in terms of what to model and what to resolve. Spend a minute to explain the large and small scales and the energy transfer down the hierarchy and what�s responsible for generating smaller eddies (I.e., vortex stretching). Use the analogy of generations. Also mention that the large eddies more intimately interact with the mean flow and more directional bias, and that smaller eddies tend to forget their roots and ancestry, and become more universal andisotrpic. Explain the energy transfer. Mention that this sketch depicts the famous energy cascade according to Kolmogorov�s 1941 theory. Energy is injected mostly at largest scales at a rate (e), is cascading down the hierarchy of eddies at the same rate, and is eventually removed by dissipation at the smallest scales.

7. Turbulence Models in Fluent Over the years, many different types of turbulence models have been developed and this slide tries to show you where the turbulence models available in Fluent CFD software fit in the grand scheme of things. The various types of turbulence models are listed in the center in order of increasing sophistication or increasing inclusion of more physics (more physics is supposed to be good !?). Unfortunately, inclusion of more physics usually increases the computational cost. Engineers must find the turbulence modeling approach that satisfies their technical needs at the lowest cost! Fluent Inc. offers several state-of-the-art turbulence modeling options that provide the accuracy that engineers need at reasonable computational expense. These turbulence models include the two-equation and RSM models. We are also working to expand the number of turbulence modeling options available to take advantage of progress in turbulence modeling field that improve the accuracy of one-equation models, develop a k-e model that is fully realizable, and make LES methods more practical.Over the years, many different types of turbulence models have been developed and this slide tries to show you where the turbulence models available in Fluent CFD software fit in the grand scheme of things. The various types of turbulence models are listed in the center in order of increasing sophistication or increasing inclusion of more physics (more physics is supposed to be good !?). Unfortunately, inclusion of more physics usually increases the computational cost. Engineers must find the turbulence modeling approach that satisfies their technical needs at the lowest cost! Fluent Inc. offers several state-of-the-art turbulence modeling options that provide the accuracy that engineers need at reasonable computational expense. These turbulence models include the two-equation and RSM models. We are also working to expand the number of turbulence modeling options available to take advantage of progress in turbulence modeling field that improve the accuracy of one-equation models, develop a k-e model that is fully realizable, and make LES methods more practical.

8. Large Eddy Simulation (LES) Spectrum of turbulent eddies in the Navier-Stokes equations is filtered: The filter is a function of grid size Eddies smaller than the grid size are removed and modeled by a sub-grid scale (SGS) model Larger eddies are directly solved numerically by the filtered transient N-S equation

9. LES in FLUENT LES has been most successful for high-end applications where the RANS models fail to meet the needs. For example: Combustion Mixing External Aerodynamics (flows around bluff bodies) Implementations in FLUENT: Sub-grid scale (SGS) turbulent models: Smagorinsky-Lilly model WALE model Dynamic Smagorinsky-Lilly model Dynamic kinetic energy transport model Detached eddy simulation (DES) model LES is applicable to all combustion models in FLUENT Basic statistical tools are available: Time averaged and root-mean-square (RMS) values of solution variables, built-in FFT Before running LES, one should consult guidelines in the �Best Practices For LES� (containing advice for mesh, SGS models, numerics, BC�s, and more)

10. Detached Eddy Simulation (DES) Motivation For high-Re wall bounded flows, LES becomes prohibitively expensive to resolve the near-wall region Using RANS in near-wall regions would significantly mitigate the mesh resolution requirement RANS/LES hybrid model based on the Spalart-Allmaras turbulence model: One-equation SGS turbulence model In equilibrium, it reduces to an algebraic model. DES is a practical alternative to LES for high-Reynolds number flows in external aerodynamic applications

11. RANS Modeling: Ensemble-Averaging Ensemble averaging may be used to extract the mean flow properties from the instantaneous ones: The Reynolds-averaged momentum equations are as follows: where is called the Reynolds stresses. The Reynolds stresses are additional unknowns introduced by the averaging procedure, hence they must be modeled (related to the averaged flow quantities) in order to close the equations.

12. The Closure Problem The RANS models can be closed in one of the following ways: (1) Eddy-Viscosity Models (EVM): Boussinesq hypothesis � Reynolds stresses are modeled using an eddy (or turbulent) viscosity mt . (The hypothesis is reasonable for simple turbulent shear flows: boundary layers, round jets, mixing layers, channel flows, etc.) (2) Reynolds-Stress Models (RSM): solving transport equations for the individual Reynolds stresses: Modeling is still required for many terms in the transport equations. RSM is more advantageous in complex 3-D turbulent flows with large streamline curvature and swirl, but the model is more complex, computationally intensive, more difficult to converge than eddy-viscosity models. Boussinesq hypothesis is reasonable for simple turbulent shear flows---see �Turbulent Flows,� S.B. Pope, p. 361-362Boussinesq hypothesis is reasonable for simple turbulent shear flows---see �Turbulent Flows,� S.B. Pope, p. 361-362

13. Calculating mt for the Eddy-Viscosity Models Based on dimensional analysis, mt can be determined from a turbulence time scale (or velocity scale) and a length scale: is the turbulent kinetic energy [L2/T2] is the turbulence dissipation rate [L2/T3] is the specific dissipation rate [1/T] mt is calculated differently under various turbulence models: Spalart-Allmaras: This one-equation model solves only one transport equation for a modified turbulent viscosity. Standard k-e, RNG k-e, Realizable k-e These two-equation models solve transport equations for k and e. Standard k-w, SST k-w These two-equation models solve transportequations for k and w. This is where the term modeling in Turbulence Modeling becomes a reality. There are two approaches in this case for defining the Reynolds stresses.This is where the term modeling in Turbulence Modeling becomes a reality. There are two approaches in this case for defining the Reynolds stresses.

14. RANS Models - Spalart-Allmaras Model A low-cost model solving an equation for the modified eddy viscosity Eddy-viscosity is obtained from The variation of very near the wall is easier to resolve than k and e. Mainly intended for aerodynamic/turbo-machinery applications with mild separation, such as supersonic/transonic flows over airfoils, boundary-layer flows, etc. The RANS modeling based on isotropic eddy viscosity boils down to how the eddy viscosity can be computed. Point out that the S-A model is based on the simple idea of computing the turbulent viscosity directly from a transport equation. That�s it ! No breakdown of turbulent viscosity into turbulent velocity scale and length scale as is done in k-epslion models as you�ll see in a minute. The idea is fairly attractive. However, this poses a problem when turbulence length and velocity scales are needed separately (combustion model). Point out that some others also have pursued a similar line of thought, adopting transport equation model for turbulent viscosity (they can be called more generically �eddy-viscosity transport model�). Mention in passing that actual transport equation is solved for a �modified� (scaled) turbulent viscosity, not the turbulent viscosity.The RANS modeling based on isotropic eddy viscosity boils down to how the eddy viscosity can be computed. Point out that the S-A model is based on the simple idea of computing the turbulent viscosity directly from a transport equation. That�s it ! No breakdown of turbulent viscosity into turbulent velocity scale and length scale as is done in k-epslion models as you�ll see in a minute. The idea is fairly attractive. However, this poses a problem when turbulence length and velocity scales are needed separately (combustion model). Point out that some others also have pursued a similar line of thought, adopting transport equation model for turbulent viscosity (they can be called more generically �eddy-viscosity transport model�). Mention in passing that actual transport equation is solved for a �modified� (scaled) turbulent viscosity, not the turbulent viscosity.

15. RANS Models - Standard k-e (SKE) Model Transport equations for k and e: The most widely-used engineering turbulence model for industrial applications Robust and reasonably accurate; it has many sub-models for compressibility, buoyancy, and combustion, etc. Performs poorly for flows with strong separation, large streamline curvature, and high pressure gradient. Add the �standard� k-e model is basically the Launder and Spalding�s k-e model including enhancements for buoyancy, compressibility, etc. This model has almost become an industrial norm as far as turbulence modeling in CFD is concerned in spite of its well-known limitations. The reason it still enjoys popularity is that - There�s no other model which is clearly superior. - Computational database accumulated over a long period of time - �Security-blanket� syndrome - No one was fired or called stupid because he used standard k-epsilon model.Add the �standard� k-e model is basically the Launder and Spalding�s k-e model including enhancements for buoyancy, compressibility, etc. This model has almost become an industrial norm as far as turbulence modeling in CFD is concerned in spite of its well-known limitations. The reason it still enjoys popularity is that - There�s no other model which is clearly superior. - Computational database accumulated over a long period of time - �Security-blanket� syndrome - No one was fired or called stupid because he used standard k-epsilon model.

16. RANS Models - Realizable k-e (RKE) Model Realizable k-e (RKE) model ensures �realizability� of the k-e model, i.e., Positivity of normal stresses Schwarz� inequality for Reynolds shear-stresses Good performance for flows with axisymmetric jets. Special Note: In the RNG k-e model, there is an additional term in the epsilon equation which is an ad hoc model, not derived from the RNG theory. It is this term which is largely responsible for the difference in performance of the standard and the RNG models. (Pope, p.383)Special Note: In the RNG k-e model, there is an additional term in the epsilon equation which is an ad hoc model, not derived from the RNG theory. It is this term which is largely responsible for the difference in performance of the standard and the RNG models. (Pope, p.383)

17. RANS Models - k-w Models Belongs to the general 2-equation EVM family. Fluent 6 supports the standard k-w model by Wilcox (1998), and Menter�s SST k-w model (1994). k-w models have gained popularity mainly because: Can be integrated to the wall without using any damping functions Accurate and robust for a wide range of boundary layer flows with pressure gradient Most widely adopted in the aerospace and turbo-machinery communities. Several sub-models/options of k-w : compressibility effects, transitional flows and shear-flow corrections.

18. RANS-Models - Reynolds-Stress Model (RSM) Point out that 4 additional transport equations for 2D and axisymmetric flow (w/o swirl) (3 r-s and the dissipation) and 7 additional equations (6 r-s and 1 dissipation) for 3-D. More equations means more computational effort. Solving these equations implies that effects of history and transport of Reynolds-stresses are directly accounted for. Briefly mention that pressure-strain is the toughest one to model. Its role is critically important in the second-moment closure, inasmuch as it�s the mechanism responsible for redistribution of energy among different normal stress components and eventually the anisotropy of normal Reynolds stresses.Point out that 4 additional transport equations for 2D and axisymmetric flow (w/o swirl) (3 r-s and the dissipation) and 7 additional equations (6 r-s and 1 dissipation) for 3-D. More equations means more computational effort. Solving these equations implies that effects of history and transport of Reynolds-stresses are directly accounted for. Briefly mention that pressure-strain is the toughest one to model. Its role is critically important in the second-moment closure, inasmuch as it�s the mechanism responsible for redistribution of energy among different normal stress components and eventually the anisotropy of normal Reynolds stresses.

19. Near-Wall Treatments:The Structure of Near-Wall Flows The structure of turbulent boundary layers in the near-wall region: Point out that near-wall modeling is very important considering that walls are the source of vorticity in the flow (due to the no-slip boundary condition) and high gradients observed in the near wall region have a significant effect on the generation of turbulence and turbulent fluctuations, which are most vigorous in this region, have a very significant roll in the transport of conserved quantities (mass, momentum, energy, etc.) Mention intermittency.Point out that near-wall modeling is very important considering that walls are the source of vorticity in the flow (due to the no-slip boundary condition) and high gradients observed in the near wall region have a significant effect on the generation of turbulence and turbulent fluctuations, which are most vigorous in this region, have a very significant roll in the transport of conserved quantities (mass, momentum, energy, etc.) Mention intermittency.

20. Accurate near-wall modeling is important: Successful prediction of frictional drag, pressure drop, separation, etc., depends on the fidelity of local wall shear predictions. Near-wall modeling is used to supply boundary conditions for turbulent flows. Most k-e and RSM turbulence models are not valid in the near-wall region: Special near-wall treatment is required to provide proper BC�s: Standard wall functions Non-Equilibrium wall functions Enhanced wall treatment S-A, k-w models are capable of resolving the steep near-wall profiles - provided the mesh is sufficiently fine. Wall Boundary Conditions Make sure to identify the various regions in the figure showing the boundary-layer structure because those regions will be discussed later in the near-wall treatment section. Also, point out the the first grid point should lie in the log-law region if wall functions are used, or at y+=1-4 if the enhanced wall treatment (EWT) is used.Make sure to identify the various regions in the figure showing the boundary-layer structure because those regions will be discussed later in the near-wall treatment section. Also, point out the the first grid point should lie in the log-law region if wall functions are used, or at y+=1-4 if the enhanced wall treatment (EWT) is used.

21. In general, wall functions are a collection or set of laws that serve as boundary conditions for momentum, energy, and species as well as for turbulence quantities. Wall Function Options The Standard and Non-equilibrium Wall Functions(SWF and NWF) use the law of the wall to supply boundary conditions for turbulent flows. The near-wall mesh can be relatively coarse. For equilibrium boundary layers and full-developed flows where log-law is valid. Enhanced Wall Treatment Option Combines the use of blended law-of-the wall and a two-layer zonal model. Suitable for low-Re flows or flows with complex near-wall phenomena. Turbulence models are modified for the inner layer. Generally requires a fine near-wall mesh capable of resolving the viscous sub-layer (more than 10 cells within the inner layer) Near-Wall Modeling Options Given the behavior discussed on the previous slide, there are two basic approaches for handling the flow near walls� The picture at the top is for the wall-function approach, and the one at the bottom is the EWT mesh Given the behavior discussed on the previous slide, there are two basic approaches for handling the flow near walls� The picture at the top is for the wall-function approach, and the one at the bottom is the EWT mesh

22. Placement of The First Grid Point For standard or non-equilibrium wall functions, each wall-adjacent cell�s centroid should be located within the log-law layer: For the enhanced wall treatment (EWT), each wall-adjacent cell�s centroid should be located within the viscous sublayer: EWT can automatically accommodate cells placed in the log-law layer. How to estimate the size of wall-adjacent cells before creating the grid: , The skin friction coefficient can be estimated from empirical correlations: Use post-processing (e.g., xy-plot or contour plot) to double check the near-wall grid placement after the flow pattern has been established. Note that y_p is the perpendicular distance between the centroid of the first cell and the wallNote that y_p is the perpendicular distance between the centroid of the first cell and the wall

23. Near-Wall Modeling: Recommended Strategy Use SWF or NWF for most high Re applications (Re > 106) for which you cannot afford to resolve the viscous sub-layer. There is little gain from resolving the viscous sub-layer. The choice of core turbulence model is more important. Use NWF for mildly separating, reattaching, or impinging flows. You may consider using EWT if: The characteristic Re is low or if near wall characteristics need to be resolved. The same or similar cases which ran successfully previously with the two-layer zonal model (in Fluent v5). The physics and near-wall mesh of the case is such that y+ is likely to vary significantly over a wide portion of the wall region. Try to make the mesh either coarse or fine enough to avoid placing the wall-adjacent cells in the buffer layer (y+ = 5 ~ 30).

24. Boundary Conditions at Inlet and Outlet When turbulent flow enters a domain at inlets or outlets (backflow), boundary conditions for k, ?, w and/or must be specified, depending on which turbulence model has been selected Four methods for directly or indirectly specifying turbulence parameters: Explicitly input k, ?, w, or This is the only method that allows for profile definition. See user�s guide for the correct scaling relationships among them. Turbulence intensity and length scale Length scale is related to size of large eddies that contain most of energy. For boundary layer flows: l ? 0.4d99 For flows downstream of grid: l ? opening size Turbulence intensity and hydraulic diameter Ideally suited for internal (duct and pipe) flows Turbulence intensity and turbulent viscosity ratio For external flows: 1 < mt/m < 10 Turbulence intensity depends on upstream conditions: The code will internally calculate k and e based on turbulence intensity and other parameters input. Here is the relationship Fluent uses: Mixing length: Lm=0.07 L; k=1.5*(intensity*U)^2 Epsilon= [C_mu^(3/4) k^1.5] / Lm Non-uniform profiles would be done using user defined functions.The code will internally calculate k and e based on turbulence intensity and other parameters input. Here is the relationship Fluent uses: Mixing length: Lm=0.07 L; k=1.5*(intensity*U)^2 Epsilon= [C_mu^(3/4) k^1.5] / Lm Non-uniform profiles would be done using user defined functions.

25. GUI for Turbulence Models Although model constants for various models may be changed, the need to do this is very rare. (Users should know exactly what they are doing.) Although model constants for various models may be changed, the need to do this is very rare. (Users should know exactly what they are doing.)

26. Expect enhanced heat transfer at separation bubble reattachment (impingement flow). Expect enhanced heat transfer at separation bubble reattachment (impingement flow).

27. Example (1): Turbulent Flow over a Blunt Plate Ske is compared with rke and rng in skin friction figure. Note the peak cf at the leading edge for the ske and the considerably smaller re-circulation region (where cf returns to zero around x/d=2 under ske (experiment is 4.7). Rke appears to be slightly better at predicting this flow than rng.Ske is compared with rke and rng in skin friction figure. Note the peak cf at the leading edge for the ske and the considerably smaller re-circulation region (where cf returns to zero around x/d=2 under ske (experiment is 4.7). Rke appears to be slightly better at predicting this flow than rng.

28. Example (2): Turbulent Flow in a Cyclone 40,000 cell hexahedral mesh High-order upwind scheme was used. Computed using SKE, RNG, RKE and RSM (second moment closure) models with the standard wall functions Represents highly swirling flows (Wmax = 1.8 Uin)

30. Example (3): LES of the Flow Past a Square Cylinder (ReH = 22,000) Here�s an example which has been used as a validation for the two dynamic sub-grid models in 6.2. The flow considered is turbulent flow past a square cylinder measured by Lyn et al. (1992, Univ. Karlshue, Germany). This flow essentially represents bluff-body flows often accompanied by vortex shedding. RANS simulations have not been successful for this simple shape like other bluff-body flows. The Reynolds number based on the free stream and the cylinder width is 22,000. For the present LES with FLUENT, approximately 0.7 million cells are used for a full 3-D domain. The mesh used in this calculation is not sufficiently fine enough to capture some smaller scales. However, the results in terms of mean flow-field, drag, and Strouhal number are quite close to the results published in the literature based on meshes of comparable resolution. You can see that the FLUENT predictions overpredict the mean velocity recovery in the wake. Yet I should point out that LES results in the literature also overpredict the mean velocity in the wake as much as or even more than our results. The first figure is the power spectrum of CL which shows the vortex shedding frequency at St = 0.130Here�s an example which has been used as a validation for the two dynamic sub-grid models in 6.2. The flow considered is turbulent flow past a square cylinder measured by Lyn et al. (1992, Univ. Karlshue, Germany). This flow essentially represents bluff-body flows often accompanied by vortex shedding. RANS simulations have not been successful for this simple shape like other bluff-body flows. The Reynolds number based on the free stream and the cylinder width is 22,000. For the present LES with FLUENT, approximately 0.7 million cells are used for a full 3-D domain. The mesh used in this calculation is not sufficiently fine enough to capture some smaller scales. However, the results in terms of mean flow-field, drag, and Strouhal number are quite close to the results published in the literature based on meshes of comparable resolution. You can see that the FLUENT predictions overpredict the mean velocity recovery in the wake. Yet I should point out that LES results in the literature also overpredict the mean velocity in the wake as much as or even more than our results. The first figure is the power spectrum of CL which shows the vortex shedding frequency at St = 0.130

31. Example (3): LES of the Flow Past a Square Cylinder (ReH = 22,000) Here�s an example which has been used as a validation for the two dynamic sub-grid models in 6.2. The flow considered is turbulent flow past a square cylinder measured by Lyn et al. (1992, Univ. Karlshue, Germany). This flow essentially represents bluff-body flows often accompanied by vortex shedding. RANS simulations have not been successful for this simple shape like other bluff-body flows. The Reynolds number based on the free stream and the cylinder width is 22,000. For the present LES with FLUENT, approximately 0.7 million cells are used for a full 3-D domain. The mesh used in this calculation is not sufficiently fine enough to capture some smaller scales. However, the results in terms of mean flow-field, drag, and Strouhal number are quite close to the results published in the literature based on meshes of comparable resolution. You can see that the FLUENT predictions overpredict the mean velocity recovery in the wake. Yet I should point out that LES results in the literature also overpredict the mean velocity in the wake as much as or even more than our results. The first figure is the power spectrum of CL which shows the vortex shedding frequency at St = 0.130Here�s an example which has been used as a validation for the two dynamic sub-grid models in 6.2. The flow considered is turbulent flow past a square cylinder measured by Lyn et al. (1992, Univ. Karlshue, Germany). This flow essentially represents bluff-body flows often accompanied by vortex shedding. RANS simulations have not been successful for this simple shape like other bluff-body flows. The Reynolds number based on the free stream and the cylinder width is 22,000. For the present LES with FLUENT, approximately 0.7 million cells are used for a full 3-D domain. The mesh used in this calculation is not sufficiently fine enough to capture some smaller scales. However, the results in terms of mean flow-field, drag, and Strouhal number are quite close to the results published in the literature based on meshes of comparable resolution. You can see that the FLUENT predictions overpredict the mean velocity recovery in the wake. Yet I should point out that LES results in the literature also overpredict the mean velocity in the wake as much as or even more than our results. The first figure is the power spectrum of CL which shows the vortex shedding frequency at St = 0.130

32. Summary: Turbulence Modeling Guidelines Successful turbulence modeling requires engineering judgment of: Flow physics Computer resources available Project requirements Accuracy Turnaround time Near-wall treatments Modeling Procedure Calculate characteristic Re and determine whether the flow is turbulent. Estimate wall-adjacent cell centroid y+ before generating the mesh. Begin with SKE (standard k-?) and change to RKE, RNG, SKO, SST or V2F if needed. Check the tables in the appendix as a starting guide. Use RSM for highly swirling, 3-D, rotating flows. Use wall functions for wall boundary conditions except for the low-Re flows and/or flows with complex near-wall physics. We have described the turbulence models and near-wall treatments available in Fluent CFD software and have tried to show how successful modeling of turbulent flows requires engineering judgement. We have described the turbulence models and near-wall treatments available in Fluent CFD software and have tried to show how successful modeling of turbulent flows requires engineering judgement.

33. Appendix Summary of RANS Turbulence Models: Description, Model Behavior and Usage More Details on Near-wall Modeling Turbulent Heat Transfer Modeling Additional Information on Menter�s SST k-w Model V2F Turbulence Model Initial Velocity Field for LES/DES

34. RANS Turbulence Model Descriptions

35. RANS Turbulence Model Behavior and Usage

36. Standard Wall Function Momentum boundary condition based on Launder-Spaulding law-of-the-wall: Similar �wall laws� apply for energy and species. Additional formulas account for k, e, and ruiuj. Less reliable when flow departs from conditions assumed in their derivation. Severe ?p or highly non-equilibrium near-wall flows, high transpiration or body forces, low Re or highly 3D flows Non-Equilibrium Wall Function SWF is modified to account for stronger ?p and non-equilibrium flows. Useful for mildly separating, reattaching, or impinging flows. Less reliable for high transpiration or body forces, low Re or highly 3D flows. The Standard and Non-Equilibrium Wall functions are options for the k-e and RSM turbulence models. Near-wall modeling (1):Standard and Non-Equilibrium Wall Functions The inclusion of k^1/2 as an additional velocity scale in the wall function allows the wall function to be less susceptible to error for slight non-equilibrium boundary layer flows. If k^1/2 over u_tau =1 then the flow is at equilbrium. >1 implies non equilbrium(higher freestream turbulent flows, or wall jets�) and <1 implies developing boundary layer. In solving for tke at the wall adjacent cell, production does not cancel out dissipation explicitly since they are calculated separately. This allows partial non-equilibrium flows. The impact of having the wall adjacent cells to be too near the wall is that excessive tke will be generated, increasing turbulent viscosity, turbulent mixing, etc.The inclusion of k^1/2 as an additional velocity scale in the wall function allows the wall function to be less susceptible to error for slight non-equilibrium boundary layer flows. If k^1/2 over u_tau =1 then the flow is at equilbrium. >1 implies non equilbrium(higher freestream turbulent flows, or wall jets�) and <1 implies developing boundary layer. In solving for tke at the wall adjacent cell, production does not cancel out dissipation explicitly since they are calculated separately. This allows partial non-equilibrium flows. The impact of having the wall adjacent cells to be too near the wall is that excessive tke will be generated, increasing turbulent viscosity, turbulent mixing, etc.

37. Near-wall modeling (2): Enhanced Wall Treatment Enhanced Wall Treatment Enhanced wall functions Momentum boundary condition based on blended law-of-the-wall (Kader). Similar blended �wall laws� apply for energy, species, and w. Kader�s form for blending allows for incorporation of additional physics. Pressure gradient effects Thermal (including compressibility) effects Two-layer zonal model A blended two-layer model is used to determine near-wall e field. Domain is divided into viscosity-affected (near-wall) region and turbulent core region. Based on �wall-distance� turbulent Reynolds number: Zoning is dynamic and solution adaptive. High Re turbulence model used in outer layer. �Simple� turbulence model used in inner layer. Solutions for e and mt in each region are blended, e.g., The Enhanced Wall Treatment option is available for the k-e and RSM turbulence models ( EWT is the sole treatment for Spalart Allmaras and k-w models). Slide is self-explanatory. Slide is self-explanatory.

38. The two regions are demarcated on a cell-by-cell basis: Rey > 200 turbulent core region Rey < 200 viscosity affected region Rey = rk1/2y/m y is shortest distance to nearest wall zoning is dynamic and solution adaptive Near Wall Modeling(3):Two-Layer Zones Slide is self-explanatory. Slide is self-explanatory.