Robin Langtry, Florian Menter User Manual – CFX 5.7 Transition Model AEA Technology GmbH, ANSYS CFX Staudenfeldweg 12, 83624 Otterfing April 22, 2004 Technical Report ANSYS / TR-04- 05 2 Table of Contents 1 Introduction 3 2 Estimating when the Transition Model Should be Used 4 3 Grid Requirements 5 4 Specifying Inlet Turbulence Levels 11 5 Summary 12 6 References 13 3 1 Introduction The goal of the Bypass project is to develop a transition model that is compatible with modern CFD methods. ANSYS CFX has developed a locally formulated transport equation for intermittency, which can then be used to trigger transition. The model is detailed in reference 1 and is actually based on two transport equations, one for the intermittency and one for the transition onset criteria in terms of momentum thickness Reynolds number. This report is intended to provide new users of the transition model with some basic guidelines for using the transition model successfully. These best practice guidelines are based primarily on the present authors experience, which has been gained largely over the development phase of the transition model. To perform a transitional simulation first the case must be setup in CFX 5.7 Pre (or a latter version) as if the normal SST model was going to be used. Once the .def file has been written, the CCL (CFX Command Language) must be extracted and modified to enable the transition model. The CCL extraction is performed with the following command: cfx5cmds –def name.def –text name.ccl –read where name.def is the .def file name and name.ccl is the CCL text file to be created. The transition model is enabled by adding to the object ‘TURBULENCE MODEL’ the sections ‘TRANSITIONAL TURBULENCE’ and ‘TRANSITION ONSET CORRELATION’. The FLUID MODELS section of the CCL file should now look like this: FLUID MODELS: TURBULENCE MODEL : Option = SST TRANSITIONAL TURBULENCE : Option = Gamma Theta Model TRANSITION ONSET CORRELATION : Option = Langtry Menter END END END END This is the recommend setup for the transition model. Once the CCL file has been modified it must be patched back into the .def file. This is performed using the following command: cfx5cmds –def name.def –text name.ccl –write The last step is to run the solver manager (cfx5solve) and define a run using the standard CFX 5.7 solver. During a run the convergence of the intermittency (Intermit) and transition 4 onset (Rethetat) equations can be monitored in the Transitional Turbulence window of the solver manager. There are actually three different transition models implemented in CFX 5 as follows: Zero equation model (i.e. prescribed intermittency), One equation model, which solves only the intermittency equation using a user specified value of the transition onset Reynolds number (where the transition onset momentum thickness Reynolds number is treated as a constant). Two equation model, where both the intermittency and transition onset Reynolds number equations are solved. For this model different empirical correlations can be selected to drive the transition onset Reynolds number equation as follows: o Langtry and Menter correlation f(Tu, dp/ds), (Recommended) o Abu-Ghannam and Shaw  correlation f(Tu, dp/ds) o Mayle  correlation f(Tu) o User defined correlation, driven by CCL and can be based on any solver variable For the zero equation transition model the best way to specify the intermittency is with a user defined subroutine that is based on the x, y and z co-ordinates. This way, if else statements can be used to defined geometric bounds where the intermittency can be specified as zero (laminar flow) or one (turbulent flow). This method was used to prescribe laminar zones at the leading edges of the wings for the 2 nd AIAA drag prediction workshop . The CCL for enabling the zero equation model is shown below where the user function TRANSITION TRIP(x,y,z) returns either a 0 or a 1 based on the geometric location: FLUIDS MODELS: TURBULENCE MODEL: Option = SST TRANSITIONAL TURBULENCE: Option = Specified Intermittency Intermittency = TRANSITION TRIP(x,y,z) END END END CEL: FUNCTION: TRANSITION TRIP Option = User Function Argument List = [m],[m],[m] Result Units =  END # FUNCTION END 5 USER ROUTINE DEFINITIONS: USER ROUTINE: TRANSITION TRIP Option = User CEL Function Calling Name = transition_trip Library Name = transitiontrip Library Path = /work-rodi/rl/work/CFX5/Flomania/wb/b2b-icem/\ UserSource/ END END For the one-equation transition model the user must enter the transition onset momentum thickness Reynolds number in the CCL and this is used along with the intermittency equation. The advantage to this method is that it avoids the need to solve the second transport equation however the predicted transition onset is entirely dependant on the value selected by the user. As a result, local effects such as turbulence intensity or pressure gradient are not accounted for. The CCL for enabling the one equation model with a transition momentum thickness Reynolds number of 260 is as follows: FLUID MODELS: TURBULENCE MODEL: Option = SST TRANSITIONAL TURBULENCE: Option = Gamma Model Transition Onset Reynolds Number = 260.0 END END END For the two equation transition model the recommended empirical correlation is “Langtry Menter” as all the validations for the BYPASS project have been run using this correlation. The well known Abu-Ghannam and Shaw  and Mayle  correlations have also been included. The CCL for enabling the two equation model is as follows: FLUID MODELS: TURBULENCE MODEL : Option = SST TRANSITIONAL TURBULENCE : Option = Gamma Theta Model TRANSITION ONSET CORRELATION : Option = Langtry Menter END END END END 6 As well, the additional options for the TRANSITION ONSET CORRELATION are “Abu- Ghannam Shaw” and “Mayle”. Finally, a very powerful option has been included to allow the user to enter their own user defined empirical correlation, which can then be used to control the transition onset momentum thickness Reynolds number equation. The method is driven by CCL and as a result any valid CCL expression can be used to define the correlation. A simple example is shown below where the transition Reynolds number was specified as a function of the x-coordinate: FLUID MODELS: TURBULENCE MODEL : Option = SST TRANSITIONAL TURBULENCE : Option = Gamma Theta Model TRANSITION ONSET CORRELATION: Option = User Defined Transition Onset Reynolds Number = 260.0*(1.0 + x/(1.0 [m])) END END END END The computed transition onset Reynolds number equation for a flat plate is shown in Figure 1. Figure 1 User defined transition onset Reynolds number for a flat plate Wall Re t lags from the freestream value in the boundary layer Inlet 7 2 Estimating when the Transition Model Should be Used Because the transition model requires the solution of two extra transport equations there are additional CPU costs associated with using it. A rough estimate is that for the same grid the transition model solution requires approximately 18 percent additional CPU time compared to a fully turbulent solution. As well, the transition model requires somewhat finer grids than are typically used for routine design purposes. This is because the max grid y + must be approximately equal to one (i.e. wall-function grids cannot be used because they cannot properly resolve the laminar boundary layer) and sufficient grid points in the streamwise direction are needed to resolve the transitional region. For this reason it is important to be able to estimate when the additional cost of using the transition model in terms of CPU and grid generation time is justified. The relative percentage of laminar flow on a device can be estimated using the following formula, which is based on the Mayle (1991) empirical correlation for transition onset. Where Re xt is the transition Reynolds number, Re x is the device Reynolds number, L Device is the length of the device, V is a representative velocity, and Tu is the freestream turbulence intensity, which can be calculated as follows. V k Tu 5.0 3/2 where k is the turbulent kinetic energy. The fraction of laminar flow for some representative devices is shown in Table 1. Clearly, there are many cases where the assumption of fully turbulent flow is not correct and a significant amount of laminar flow could be present. Devicex xt LV Tu )/( 100380000 Re Re 4 5 8 Table 1 Fraction of laminar flow for a variety of different devices. 3 Grid Requirements The effect of increasing and decreasing y + for the T3A flat plate test case is shown in Figures 2 and 3. For y + values between 0.001 and 1 there is almost no effect on the solution. Once the maximum y + increases above 8 the transition onset location begins to move upstream. At a maximum y + of 25 the boundary layer is almost completely turbulent. For y + values below 0.001 the transition location appears to move downstream. This is presumably caused by the large surface value of omega, which scales with the first grid point height. Additional simulations on the Zierke compressor  have indicated that at very small y + values the SST blending functions switch to k-e in the boundary layer. For these reasons very small (below 0.001) y + values should be avoided at all costs. 0.86 0.3 2 000 000 F1 Race Car Spoiler 0.57 0.2 5 000 000 Small Aircraft wing 0.38 1.0 1 000 000 Comp ressor blade 0.10 6.0 500 000 HP Turbine blade 0.80 2.5 150 000 LP Turbine blade Fraction Laminar Flow Tu (%) Re X Case 9 Figure 2 Effect of increasing y + for the flat plate T3A test case. Re x C f 0 250000 500000 750000 1E+06 0 0.002 0.004 0.006 0.008 0.01 T3AExperiment Y + =1.0 Y + =0.5 Y + =0.1 Y + =0.01 Y + =0.001 Y + =0.0001 Figure 3 Effect of decreasing y + for the flat plate T3A test case (figure provided by Likki, Suzen and Huang ). 10 The effect of wall normal expansion ratio from a y + value of 1 is shown in Figure 4. For expansion factors of 1.05 and 1.1 there is no effect on the solution. For larger expansion factors of 1.2 and 1.4 there is a small but noticeable upstream shift in the transition location. Figure 4 Effect of wall normal expansion ratio for the flat plate T3A test case. The effect of streamwise grid refinement is shown in Figure 5. Surprisingly the model was not that sensitive to the number of streamwise nodes. The solution differed significantly from the grid independent one only for the case of 25 streamwise nodes where there was only one cell in the transitional region. Nevertheless the grid indepenant solution appears to occur when there is approximately 75 – 100 streamwise grid points. As well, separation induced transition occurs over a very short length and for cases where this is important a fine grid is necessary. Note that the high resolution advection scheme has been used for all equations including the turbulent and transition equations and this is the recommended default setting for transitional computations. In CFX 5.7 when the transition model is active and the high resolution scheme is selected for the hydrodynamic equations the default advection scheme for the turbulence and transition equations is automatically set to high resolution. 11 Figure 5 Effect of streamwise grid density for the flatplate T3A test case. One point to note is that for sharp leading edges often transition can occur at the leading edge due to a small leading edge separation bubble. If the grid is too course, the rapid transition caused by the separation bubble is not captured. A good example of this is the Zierke (PSU) compressor. Contours of velocity (top) and turbulence intensity (Tu, bottom) for the Zierke (PSU) compressor are shown in Figure 6. On the suction side transition occurs at the leading edge due to a small leading edge separation bubble. On the pressure side transition occurs at about mid-chord. The effect of stream-wise grid resolution on resolving the leading edge laminar separation and subsequent transition on the suction side is shown in Figure 7. Clearly, if there are not a large enough number of streamwise nodes, the model cannot resolve the rapid transition and a laminar boundary layer on the suction side is the result. Based on the grid sensitivity study the recommended best practice mesh guidelines are a max y + of 1, a wall normal expansion ratio of 1.1 and about 75 – 100 grid nodes in the streamwise direction. Note that if separation induced transition is present additional grid points in the streamwise direction are most likely needed. For a typical 2-D blade assuming an H-O-H type grid the above guide lines result in an inlet H-grid of 15x30, an O-grid around the blade of 200x80 and an outlet H-grid of 100x140 for a total of approximately 30 000 nodes, which has been found to be grid independent for most turbomachinery cases. It should also be noted that for the surfaces in the out of plane z-direction symmetry planes should always be used, not slip walls. The use of slip walls has been found to result in an incorrect calculation of the wall distance, which is critical for calculating the transition onset location accurately. Another point to note is that all the validations cases for the transition model have been performed on hexahedral meshes. At this point the accuracy of the transition model on tetrahedral meshes has not been investigated. 12 Figure 6 Contours of velocity (top) and turbulence intensity (Tu, bottom) for the Zierke (PSU) compressor. Leading Edge Separation Induced Transition Pressure Side Transition 13 Figure 7 Effect of stream-wise grid resolution (coarse grid, top), (fine grid, bottom), for resolving transition due to a leading edge separation bubble for the Zierke (PSU) compressor. Turbulence Intensity Velocity 14 4 Specifying Inlet Turbulence Levels It has been observed that the turbulence intensity specified at an inlet can decay quit rapidly depending on the inlet viscosity ratio ( t / ) (and hence turbulence eddy frequency). As a result, the local turbulence intensity downstream of the inlet can be much smaller than the inlet value (see Figure 8). Typically, the larger the inlet viscosity ratio the smaller the turbulent decay rate. However, if too large a viscosity ratio is specified (i.e. >100) the skin friction can deviate significantly from the laminar value. There is experimental evidence that suggests that this effect occurs physically, however at this point it is not clear how accurately the transition model reproduces this behavior. For this reason, if possible it is desirable to have a relatively low (i.e 1 - 10) inlet viscosity ratio and to estimate the inlet value of turbulence intensity such that at the leading edge of the blade/airfoil the turbulence intensity has decayed to the desired value. The decay of turbulent kinetic energy can be calculated with the following analytical solution that was derived by Menter. * 1 tkk inletinlet For the SST turbulence model in the freestream the constants are: =0.09 * =0.0828 The time scale can be determined as follows: V x t where x is the streamwise distance downstream of the inlet and V is the mean convective velocity. The eddy viscosity is defined as: k t The decay of turbulent kinetic energy equation can be rewritten in terms of inlet turbulence intensity (Tu inlet ) and eddy viscosity ratio ( t / ) as follows: 5.0 2 2 * /2 3 1 t inlet inlet TuxV TuTu 15 Figure 8 Decay of turbulence intensity (Tu) as a function of streamwise distance (x). 5 Summary This report has summarized the key issues required to successfully apply the new transition model. Proper grid refinement and specification of inlet turbulence levels is crucial for accurate transition prediction. In general there is some additional effort required during the grid generation phase because a low-Re grid with sufficient streamwise resolution is needed to accurately resolve the transition region. As well, in regions where laminar separation occurs, additional grid refinement is necessary in order to properly capture the rapid transition due to the separation bubble. Finally, the decay of turbulence from the inlet to the leading edge of the device should always be estimated before running a solution as this can have a large effect on the predicted transition location. 0 1 2 3 4 5 6 7 00.010.020.030.04 x (m) Tu (%) Inlet Tu = 6.0 t / = 10 16 6 References  Menter, F.R., Langtry, R.B., Likki, S.R., Suzen, Y.B., Huang, P.G., and Völker, S., (2004), "A Correlation based Transition Model using Local Variables Part 1- Model Formulation ASME-GT2004-53452, ASME TURBO EXPO 2004, Vienna, Austria.  Langtry, R.B., Menter, F.R., Likki, S.R., Suzen, Y.B., Huang, P.G., and Völker, S., (2004), "A Correlation based Transition Model using Local Variables Part 2 – Test Cases and Industrial Applications ASME-GT2004-53454, ASME TURBO EXPO 2004, Vienna, Austria.  Mayle, R.E., (1991), “The Role of Laminar-Turbulent Transition in Gas Turbine Engines,” ASME Journal of Turbomachinery, Vol. 113, pp. 509-537.  Zierke, W.C. and Deutsch, S., “The measurement of boundary layers on a compressor blade in cascade – Vols. 1 and 2”, NASA CR 185118, 1989.  Abu-Ghannam, B.J. and Shaw, R., (1980), “Natural Transition of Boundary Layers-The Effects of Turbulence, Pressure Gradient, and Flow History,” Journal of Mechanical Engineering Science, Vol. 22, No. 5, pp. 213 – 228.