Preliminary Detached Eddy Simulations of a Generic Tractor/Trailer

Transcription

1 24th Applied Aerodynamics Conference 5-8 June 26, San Francisco, California AIAA Preliminary Detached Eddy Simulations of a Generic Tractor/Trailer Harshavardhan A. Ghuge * and Christopher J. Roy 2 Aerospace Engineering Bldg, Auburn University, Auburn, Alabama This paper discusses preliminary results from the Detached Eddy Simulations (DES) of a simplified Generic Tractor/Trailer geometry at a Reynolds number of two million based on the trailer width. The simulations were carried out on two meshes of differing resolution. The results from the simulations are compared with the experimental data. An attempt has been made to analyze the effects of mesh refinement, estimate the time of initial transients, and time required to reach statistical convergence. The medium mesh shows better results than the coarse mesh. The overall lack of agreement of the simulations with the experiment may be due to insufficient mesh refinement or inadequate marching in time to obtain statistically converged results. Nomenclature C DES = DES constant d = distance from the wall in Spalart-Allmaras model G = modified distance = min(d, C DES Ä) y + = normalized turbulence coordinate showing distance from the wall C p = pressure coefficient k = kinetic energy of turbulent fluctuations per unit mass å = dissipation of kinetic energy per unit mass ù = specific dissipation rate v t = kinematic eddy viscosity ì t = dynamic eddy viscosity ñ avg = time averaged density Ä = maximum mesh spacing along the three co-ordinate directions = max(äx, Äy, Äz) Äx = mesh spacing along x-axis Äy = mesh spacing along y-axis Äz = mesh spacing along z-axis C S = Smagorinsky constant 6 = term related to magnitude of stain rate in the Spalart-Allmaras model Kappa = numerical diffusion constant W = width of the trailer Re W = Reynolds number based on trailer width = normalized distance along the x-axis y/w = normalized distance along the y-axis z/w = normalized distance along the z-axis t ref = reference time = W/U inf U inf = freestream velocity in the simulations Ä wall = mesh spacing normal to the wall in the wake Ä wake = maximum grid spacing along the z-axis on the trailer base t = time = dimensionless time = t/ t ref * Graduate Research Assistant, ghugeha@auburn.edu, Student Member AIAA. Assistant Professor, roychri@auburn.edu, Senior Member AIAA. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

2 Äô W = dimensionless time window f v = damping function used in Spalart-Allmaras model C w = closure coefficient in the Spalart-Allmaras model f w = parameter in the Spalart-Allmaras model C b = closure coefficient in the Spalart-Allmaras model Äô S = dimensionless time step used in temporal discretization u = velocity along the x-axis v = velocity along the y-axis w = velocity along the z-axis u rms = root mean square velocity along the x-axis v rms = root mean square velocity along the y-axis w rms = root mean square velocity along the z-axis U ref = reference velocity = dimensionless time where time averaging starts end = dimensionless time where time averaging ends C D-inst = instantaneous drag coefficient C D-mean = mean drag coefficient C D-rms = root mean square drag coefficient C L-mean = mean lift coefficient C S-mean = mean side force coefficient FFT = fast Fourier transformation Nfft = number of points used in each window averaging during fast Fourier transformation P Instantaneous-simulations = instantaneous reference pressure from the simulations P mean-simulations = mean reference pressure from the simulations P mean-experiment = reference pressure given by the experiment Instantaneous = instantaneous value of normalized unsteady pressure signal in trailer base RMS = root mean square of the unsteady pressure signal in the trailer base Mean = mean value of normalized unsteady pressure signal in the trailer base Zero = zero value to which mean should converge I. Introduction N a typical class 8 tractor/trailer, energy losses due to rolling resistance and accessories increase linearly with I vehicle speed, while energy losses due to aerodynamic drag increase as velocity squared. At a typical highway speed of 7 mph, aerodynamic drag accounts for approximately 65% of the energy output of the engine. Due to the large number of tractor/trailers on the US highways even modest reductions in aerodynamic drag can significantly reduce domestic fuel consumption. The most common engineering approach to model turbulence involves solving the Reynolds Averaged Navier- Stokes (RANS) equations. In this approach the inherently three-dimensional phenomenon of turbulence is modeled using the concept of eddy viscosity and eddy conductivity. RANS models are usually developed to solve simple, zero pressure gradient attached flows. These models fail in presence of large pressure gradients and/or large flow separation. The flow over a bluff body like a truck involves massive separation and shedding of three-dimensional turbulent eddies in the wake region. Therefore RANS model may not give accurate prediction of the flow in the base of the trailer. Accurate prediction of the flow in the wake is necessary to calculate the pressure on the trailer base. The pressure on the trailer base plays an important role in calculation of the pressure drag acting on the truck which is the main component of the aerodynamic drag acting on the truck. The Large Eddy Simulation (LES) approach to model flow over a bluff body is becoming popular with advances in computing power. In this technique, the larger eddies are resolved while the smaller, more homogeneous turbulent eddies are modeled using a sub-grid scale models. Smagorinsky s eddy viscosity model and Germano s dynamic one-equation model are two of the widely used sub-grid scale models in LES. This paper is concerned with wall-bounded flows where additional modeling is required near the surface. The modeling technique implemented in this paper is the hybrid RANS/LES model called Detached Eddy Simulation (DES) developed by Spalart and co-workers. 4 The present work is an extension of the previous work by Roy et al. 2 in which the authors performed DES simulations and RANS modeling of the simplified tractor-trailer model (see 2

3 Fig. ) at a Reynolds number of two million and compared the results from the simulations with the experiment. In the current work DES simulations of the simplified truck model have been carried out on a coarse grid of four million grid points and medium grid of thirteen million grid points. II. Simulation Approach A. Simulation Code The computational fluid dynamics code used herein is SACCARA, the Sandia Advanced Code for Compressible Aerodynamics Research and Analysis. The SACCARA code was developed from a parallel distributed memory version of the INCA code, originally written by Amtec Engineering. The SACCARA code is used to solve the Navier-Stokes equations for conservation of mass, momentum, energy, and turbulence transport in either 2D or 3D form. Prior code verification studies with SACCARA include code-to-code comparisons with other Navier-Stokes codes 2,3 and the Direct Simulation Monte Carlo method. 4 The studies provide some confidence that the code is free from coding errors affecting the discretization. B. Discretization The governing equations are discretized using a cell-centered finite-volume approach. The discretization of the convective terms is based on a finite-volume form of Harten and Yee s symmetric TVD 5,6 scheme. Taking advantage of the fact that any upwind scheme can be written in terms of a central scheme plus a dissipative component, the baseline scheme is modified using a characteristic-based filter which globally decreases the numerical dissipation by a constant Kappa. 7 The resulting scheme is still second-order accurate, but with low dissipation, especially in smooth regions. The viscous terms are discretized using central differences. The SACCARA code employs a massively parallel distributed memory architecture based on multi-block structured grids. The solver is a Lower-Upper Symmetric Gauss-Seidel scheme based on the works of Yoon and Jameson 8 and Peery and Imlay, 9 which provides for excellent scalability up to thousands of processors. 9 Second-order accuracy is obtained in the temporal discretization via a sub-iterative procedure. In this approach, time derivative in the governing equations is discretized with second-order backward difference. The three-point backward time derivative is added to the steady-state residual, and the solution at time level n+ is iterated until the right-hand side, which includes both the steady-state residual and the time derivative, are driven below a given tolerance. C. Turbulence Models For simulation results presented herein, the turbulence transport equations are integrated all the way to the vehicle walls, thus no wall functions are employed. In all cases the distance from the wall to the first cell center off the wall is less than unity in normalized turbulence coordinates (i.e., y + < ).. Steady-State RANS The steady-state RANS model examined is Menter s baseline (BSL) hybrid model which switches from a k-å formulation in the outer flow to a k-ù formulation near solid walls. Additional details on RANS solution using the Menter model can be found in Ref Detached Eddy Simulation (DES) The hybrid RANS/LES method developed by Spalart and co-workers 4,6 has been developed the furthest and is called Detached Eddy Simulation, or DES. The DES approach uses the unsteady form of the Spalart-Allmaras oneequation eddy viscosity model to provide the eddy viscosity õ t = ì t /ñ avg for use in the sub-grid scale stress model. The Spalart-Allmaras one-equation eddy viscosity model provides the usual RANS-based eddy viscosity in the boundary layer, but must be modified to the appropriate eddy viscosity for LES outside of the boundary layer. This modification is performed by changing the definition of the distance to the wall d in the destruction term. The distance d is replaced with G, where this new term is defined as Far from the wall, the value of G thus becomes G = min(d, C DES Ä) () 3

4 G = C DES Ä (2) The local grid spacing is defined as Ä and is equal to the maximum mesh spacing in the three coordinate directions. Ä = max(äx, Äy, Äz) (3) As discussed by Spalart et al., 4 when the production term is balanced with the destruction term (at equilibrium), the following is obtained ì t = C f 2 C S ñ avg Ä 2 6, C S = C b v DES (4) Cw f w where 6 is related to the magnitude of the strain rate. In the outer part of the boundary layer, C asymptotes to C S =.29 C DES =.9. The constant C DES is given by Spalart as C DES =.65 (5) The DES model thus asymptotes to a Smagorinsky-type LES model in the bluff-body wake assuming sufficient mesh refinement. S III. Problem Description The flow over the Ground Transportation System (GTS) model has been investigated experimentally at a Reynolds number based on the trailer width W (Re W ) of 2 million by Storms et al. A photograph of the GTS mounted in the NASA Ames 7 wind tunnel is presented in Figure. The experimental data set is unique in that it presents both ensemble-averaged surface pressure data (see Fig. 2) as well as multiple planes of instantaneous and ensemble-averaged velocity data in the wake (see Fig. 3) for this high Reynolds number flow. Unlike the previous DES simulations by Roy et al., 2 the current simulations involve the complete truck body with the four posts and the wind tunnel. The Cartesian coordinate system employed for the simulations is normalized by the trailer width W as shown in the Fig. 3. In the previous DES simulations the front portion of the GTS was truncated along with the tunnel wall at =.2. The two current grids, which include the entire GTS model, were constructed of approximately 4 million and 3 million grid points and were domain decomposed and run on 85 processors of a Linux cluster. A. Boundary Conditions The inflow boundary condition employs stagnation values for pressure (2,653 N/m 2 ) and temperature (282. K) and enforces inflow normal to the boundary. The outflow boundary used a fixed static pressure of 97,7 N/m 2. This back pressure was chosen so that the tunnel wall reference pressure, located at = 4.47, y/w= , z/w= -4.7, matched with the experiment. The reference pressure found from the computation of the coarse mesh was 97,289 N/m 2 (see Fig. 4) which corresponds to a freestream velocity of approximately 93.9 m/s. Slip conditions on velocity are employed on the top and side walls of the wind tunnel, while the lower wind tunnel wall, the GTS surface and the support posts employ no-slip velocity conditions and assume an adiabatic wall. The freestream eddy viscosity is set at -5 N.s/m 2. Solid wall boundary conditions for the turbulence model can be found in Ref. 2. B. Characteristic Scales Time has been normalized by a reference time scale defined as t ref = W/U inf The value if U inf is taken to be 93.9 m/s. A time history of the reference pressure from the coarse grid is given in Fig. 4. Two time steps of Äô s =.2, and Äô s =.24 were used in the simulations. Characteristic-based filtering values of Kappa =.35 and appa =.2 were used to see the effect of numerical diffusion. Some characteristic 4

5 length scales are given in Table. The extremely fine grid spacing near the wall (Ä wall ) is required because the RANS model is integrated to the wall. The maximum grid spacing in the trailer wake (Ä wake ) leads to approximately 26 points across the trailer width for the coarse grid case and 38 points for the medium grid case. Table. Characteristic length scales Mesh Ä wall Ä wake Coarse Medium IV. Numerical Accuracy A. Estimation of Initial Transients Initial transients are generated in the flow because of the sudden exposure of the truck body to initial freestream conditions. Some initial data statistics need to be ignored to overcome the effect of initial transients. The experiment had one unsteady pressure sensor located on the trailer base. Fig. 5 shows the corresponding normalized unsteady pressure plot from the simulations of the coarse grid. From the reference pressure plot (Fig. 4) and the normalized unsteady pressure plot of the coarse grid, the initial transient period appears to be over by a dimensionless time of ô ~ 8; however, Fig. 7 and Fig. 8 (discussed below) suggest otherwise. Power spectral density (PSD) plots for the unsteady base pressure from a) the experiment, b) the coarse mesh, and c) the medium mesh are given in Fig. 6. The experimental PSD suggests a broad range of energy-containing scales, while the simulations results show energy at the lower frequencies only due to the mesh filtering properties of the LES method (note: the medium mesh simulations do show some of the higher-frequency content). The peak power levels are somewhat higher in the simulations (~4 db) than found in the experiment (~3 db). Fig. 7 shows the distribution of the pressure coefficient values at z/w = along the height of the trailer base averaged over a constant time window of Äô W = 7 for five different time values. Although a reduction in the appa value from.35 to.2 changes the pressure coefficient distribution over the trailer surface, the lack of convergence of these distributions as time increases suggests that either the initial transient period is not completely over by the time ô = 65 (which is the starting time of the last time window) or the time window of Äô W = 7 is not long enough to obtain sufficient statistics for convergence. A longer time window could not be used because of limited simulation data availability. A similar plot is shown in Fig. 8 for the u-velocity, v-velocity and u rms -velocity along an axial line through wake showing a mismatch of the time averaged velocity profiles obtained from the five different time windows having the same time span. Fig. 9 shows the unsteady pressure fluctuations obtained from the medium mesh. The aperiodic random fluctuations of the instantaneous pressure values suggest that the data collected for the medium mesh may lie completely in the initial transient period. B. Statistical Convergence The length of time for which flowfield statistics sampling should be done needs to be determined to keep the statistical error to a minimum. Fig. shows the time-averaged pressure coefficient distribution from the coarse grid starting from a time of ô start = 4, with a constant increment in time span by Äô W = 23.5 during each step. The pressure coefficient distribution obtained from a time span of Äô W = 47 and Äô W = 7.5 matches with the one from Äô w = 94, suggesting that averaging over a time span of Äô W = 47 may be sufficient for getting statistical convergence for the coarse grid. But this observation is not supported by Fig., which shows the time-averaged values of u-velocity, v-velocity and u rms -velocity along the axial line through the wake from the coarse grid and averaged over the same time span used in Fig.. The profiles of the u-velocity, v-velocity and u rms -velocity obtained from the largest time span of Äô W = 94 deviate at many locations from the profiles obtained using the smaller time span suggesting that there may be still some initial transients present in the simulation, or that even the largest time window of Äô W = 94 may not be sufficient for obtaining statistical convergence. 5

6 V. Results In this section, preliminary results using the DES simulations of the coarse and medium grid and the results from the steady-state RANS model of Menter are compared with experimental data. These data comparisons include time-averaged streamlines, velocity contour plots, and surface pressure distributions. A. Streamlines and Velocity Contours Time-averaged streamlines are shown in Fig. 3 along with time-averaged contours of the u- (streamwise-) component of velocity for the experiment, the steady-state Menter k-ù RANS model, and the DES model. All the velocity contour plots have been normalized by a reference velocity U ref which is taken as 94 m/s. This value is obtained from the freestream flow region of the vertical streamwise plot of a u-velocity contour from the coarse grid simulations (Fig. 3 c.). The flow is from left to right, and the aft end of the trailer is also shown in the figures. The experiment shows a large, counter- clockwise-rotating vortex centered at y/w =.4 near the trailer base. While the corresponding clockwise-rotating vortex is outside of the experimental PIV window, the streamlines appear to suggest that this vortex is centered near the top-right corner of the window ( = 9, y/w =.2). The results for the Menter k-ù model give a more symmetric pair of counter-rotating vortices than seen in the experiments. An outline of the location of the experimental PIV window is also shown in the computational plots for reference. The time averaged u-velocity contours along with the streamlines from the DES simulations from the medium and coarse meshes are shown at the bottom. The top and bottom vortices from the medium mesh are not exactly symmetric, but are similar to those from the Menter k-ù model. The coarse grid shows the upper vortex much more dominant than the lower vortex when compared with the medium grid. The center of the upper vortex in the medium grid is further away from trailer base than the coarse grid, but this may still change with availability of more simulation data for statistical convergence. The streamlines do not form closed circuits for the lower vortex in the plots of DES simulations, but spiral towards the center of the vortex. Since this location is a right-left symmetry plane where the out-of-plane (w) velocity component should be zero, this spiraling suggests that the simulation results from both the grids are not statistically converged for the lower vortex. Also, it should be noted that the averaging for the medium grid has been done at an earlier period in time and for a smaller span of time when compared to the coarse mesh due to limited simulation data availability. Time-averaged streamlines and v-velocity contours are shown in Fig. 4 for a horizontal, streamwise plane in the wake located at y/w =.5. The streamlines from the Menter k-ù model appear to match the experiment; however, the vertical (out-of-plane) velocity contours differ. The DES results show counter-rotating vortices but the streamlines from the simulations of the two grids suggest that the results from the simulations are not statistically converged. The reason that the vertical velocities are opposite to that shown in the experiment is due to the fact that the flow predicted by the DES model is dominated by the upper, counter-clockwise-rotating vortex seen in the bottom plots of Fig. 3. B. Surface Pressure Distributions on the Trailer Base and Coefficient of Drag, Lift and Side Forces Distributions of the pressure coefficient on the trailer base are presented in Fig. 5 for z/w = (the symmetry plane). The experiment shows an asymmetrical pressure distribution from top to bottom. The minimum pressure occurs near y/w =.4 where the lower vortex is located (Fig. 3 a). The DES simulations on the coarse grid show opposite trends compared to the experiments due to the dominance of the upper vortex as seen in the Fig. 3 c. However when appa is changed from.35 to.2 for the coarse grid, the negative trend of pressure distribution was reduced by a noticeable margin. The DES simulations of the medium mesh with appa =.2 show almost a flat pressure distribution curve because of the nearly equal upper and lower vortices seen in of Fig. 3 d. Fig. 6 and Fig. 7 show the plot of drag coefficient of the truck obtained from the coarse and medium meshes, respectively. The mean force coefficients are summarized below in the table. Table 2. Coefficient of Drag, Lift and Side Forces. C D-mean C S-mean C L-mean Experiment (Ref. ) * Coarse Mesh Medium Mesh * - Coefficient of lift from the experiment is doubtful because of poor reliability of the measuring instrument 6

7 VI. Conclusions Preliminary results were presented for Detached Eddy Simulations (DES) of a generic tractor/trailer geometry on two grids at a Reynolds number of two million based on the trailer width. The DES simulations were compared to both experimental data and to steady-state Reynolds-Averaged Navier-Stokes computations using the Menter k-ù turbulence model. These comparisons included time-averaged wake velocities and base pressure coefficients. The coarse grid DES simulations did not show improved agreement with the experiments when compared with the RANS computations. This lack of improvement may be due to the coarseness of the grid. The medium grid DES simulations showed some encouraging results, such as the reduced dominance of the upper vortex (as seen in the Fig. d) and better surface pressure distributions in the trailer base than the coarse grid DES simulations (see Fig. 5). Both meshes need to be run for a longer time to collect sufficient statistics to ensure that there is no effect of the initial flow transients and to minimize the error due to incomplete statistical convergence. The effect of iterative convergence needs to be investigated for both the grids. The effect of appa needs to be analyzed as it was observed that with a lower Kappa value better surface pressure distributions were achieved (Fig. 2) due to lower numerical dissipation. Also the effect of different Äô S values used for temporal discretization should be analyzed. In addition to the longer runs needed on the coarse and medium meshes, future work includes running the DES simulations on a fine grid of 32 million cells and comparing the results with the experimental data and the coarse and medium grids. VII. Acknowledgements We would like to thank Dr. Matthew Barone of Sandia National Laboratories for his helpful suggestions on this paper. This work was supported by the U.S. Department of Energy FreedomCAR and Vehicle Technologies Program. VIII. References. B. Storms, Ross JC, Heineck JT, Walker SM, Driver DM, Zillac GG, An Experimental Study of the Ground Transportation System (GTS) Model in the NASA Ames 7- by -ft Wind Tunnel, NASA TM , C. J. Roy, J. C. Brown, L. J. DeChant, and M. F. Barone, Unsteady Turbulent Flow Simulations of the Base of a Generic Tractor/Trailer, AIAA Paper , Oregon, June 28-, C. J. Roy, J. L. Payne, M. A. McWherter-Payne and K. Salari, RANS Simulations of a Simplified Tractor/Trailer Geometry, Conference Proceedings of Heavy Vehicles: Trucks, Buses, and Trains, United Engineering Foundation, Monterey-Pacific Grove, CA, Dec. 2-6, 22 (see also C. J. Roy, J. L. Payne, and M. A. McWherter-Payne, RANS Simulations of a Simplified Tractor/Trailer Geometry, to appear in the ASME Journal of Fluids Engineering, September 26). 4. P. R. Spalart, W. H. Jou, M. Strelets, and S.R. Allmaras, Comments on the Feasibility of LES for Wings, and on a Hybrid RANS/LES Approach, in Advances in DNS/LES, Proceedings of the First AFOSR International Conference on DNS/LES, Edited by C. Liu and Z. Liu, Greyden Press, Colombus, OH, C. J. Roy, L. J. DeChant, F. G. Blottner, and J. L. Payne, Bluff-Body Flow Simulations using Hybrid RANS/LES, AIAA Paper , Orlando, FL, June M. Shur, P. R. Spalart, M. Strelets, and A. Travin, Detached-Eddy Simulation of an Airfoil at High Angle of Attack, 4 th International Symposium Engineering Turbulence Modeling and Measurements, May 24-26, Corsica, France P. R. Spalart and S. R. Allmaras, A One-Equation Turbulence Model for Aerodynamic Flows, La Recherche Aeropatiale, No., pp. 5-2, Menter, F. R. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, AIAA Journal, Vol. 32, No. 8, 994, pp Payne, J. L., and Hassan, B., Massively Parallel Computational Fluid Dynamics Calculations for Arodynamics and Aerothermodynamics Applications, Proceedings of the 998 HPCCP/CAS Workshop, NASA/Cp , Jan. 999, pp INCA User s Manual, Version 2., Amtec Engineering, Inc., Bellevue, WA, Wong, C. C., Blottner, F. G., Payne, J. L., and Soetrisno, M., Implementation of Parallel Algorithm for Thermo-Chemical Nonequilibrium Flow Solutions, AIAA Paper 95-52, Jan

8 2. Payne, J. L., and Walker, M.A., Verification of Computational Aerodynamic Predictions for Complex Hypersonic Vehicles using the INCA TM Code, AIAA Paper , January C. J. Roy, M. A., Verification and Validation for Laminar Hypersonic Flowfields Part : Verification, AIAA Journal, Vol 4, No., 23, pp C. J. Roy, M. A. Gallis, T. J. Bartel, and J. L. Payne, Navier-Stokes and DSMC Predictions for Laminar Hypersonic Shock-Induced Seperation, AIAA Journal, Vol. 4, No., 23, pp Harten, A., On a class of High Resolution Total-Variation-Stable Schemes, SIAM Journal of Numerical Analysis, Vol. 2, No., 984, pp Yee, H. C., Implicit and Symmetric Shock Capturing Schemes, NASA-TM-89464, May Yee, H. C., Sadham, N. C., and Djomehri, MJ. Low-Dissipative High-Order Shock-Capturing Methods using Characteristics-Based Filters, Journal of Computational Physics, Vol. 5, No., pp , March Yoon, S., and Jameson, A., An LU-SSOR Scheme for the Euler and Navier-Stokes Equations, AIAA Paper 87-6, Jan Peery, K. M., and Imlay, S. T., An Efficient Implicit Method for Solving Viscous Multi-Stream Nozzle/Afterbody Flow Fields, AIAA Paper 86-38, June C. J. Roy and F. G. Blottner, Methodology for Turbulence Model Validation: Application to Hypersonic Flows, Journal of Spacecraft and Rockets, Vol. 4, No. 3, 23, pp

9 Figure. Photograph of GTS geometry in the NASA Ames wind tunnel. Y Z X.5 y/w W z/ 8-2 Y X Z y/w z /W 8 Figure 2. Locations of experimental surface pressure data. Y Experimental PIV Planes X Z y/w W 3 z/ 2 9 Figure 3. Location of experimental velocity data planes. 9

10 DES, Coarse Grid s =.2 Reference Pressure, N/m Kappa =.35 Kappa =.2 P instantaneous-simulations P mean-simulations P mean-experiment Figure 4. Reference pressure history from coarse mesh : = 4.5, y/w = 2.6, z/w = -4.7.

11 3 DES, Coarse Mesh s =.2 Normalized Pressure, N/m Kappa =.35 Kappa =.2 Instantaneous Mean RMS Zero Figure 5. Unsteady Pressure fluctuations from the coarse mesh. Trailer Base :y/w =.65, z/w =.46.

12 Figure 6 a. Figure 6 b. 2

13 Figure 6 c. Figure 6. Unsteady base pressure power spectra from a) experiment, b) coarse mesh and c) medium mesh. 3

14 y/w DES, Coarse Grid s =.2 Kappa =.35 : - = 24, end = 97 = 47, end = 8 = 69, end = 4 Kappa =.2 : - = 4, end = 22 = 65, end = C p Figure 7. Initial transient period estimation using Pressure coefficient distribution along the height of the trailer base :z/w =. u/u ref, v/u ref, u rms /U ref DES, Coarse Grid Kappa =.35, s =.2 =., end = 47 = 24, end = 68.5 = 47, end = 96 = 68.5, end = 8 = 96, end = 4 u rms /U ref -.2 v/u ref u/u ref Figure 8. Initial transient period estimation using velocity profiles along the axial line of wake. 4

15 Normalized Pressures, N/m Kappa =.35, s =.2 DES, Medium Grid Instantaneous Mean RMS Zero Kappa =.2, s = Figure 9. Unsteady Pressure fluctuations from the medium mesh. Trailer Base: y/w =.65, z/w =.46. 5

16 DES, Coarse Mesh Kappa =.2, s =.2 w = 94 w = 7.5 w = 47 w = 23.5 y/w C p Figure. Estimation of time period required for statistical convergence using pressure coefficient distribution along the height of trailer base :z/w = DES, Coarse Mesh, Kappa =.2, s =.2 u/u ref, v/u ref, u rms /U ref u rms /U ref v/u ref w = 94 w = 7.5 w = 47 w = u/u ref Figure. Estimation of the time period required for statistical convergence using velocity profiles along the axial line through the wake. 6

17 Figure 2. Z-vorticity in the truck wake. 7

18 Experiment, Streamlines and u-velocity Contour Vertical Streamise Cut: z/w = Menter k-, Streamlines and u-velocity Contour Vertical Streamise Cut: z/w = y/w u/u ref y/w u/u ref a b DES, Coarse Mesh, Kappa =.2, s =.2, = 4, end = 235, 2.5 DES, Medium Grid, kappa =.2, s =.24, = 47, end = 94 y/w u/uref y/w u/uref c d Figure 3. Streamlines and u-velocity contours on a vertical streamwise cut :z/w = for experiment (a), Menter k-ù (b) coarse grid DES (c), and medium grid DES (d). 8

19 Experiment, Streamlines and v-velocity Contour Horizontal Streamwise Cut: y/w =.5 Menter k-, Streamlines and v-velocity Contour Horizontal Streamwise Cut: y/w = z/w v/u ref z/w v/u ref a b DES, Coarse Mesh, Kappa =.2, s =.2, = 4, end = 235, DES, Medium Grid, Kappa =.2, s =.23, = 47, end = 94.8 z/w v/uref z/w v/uref c d Figure 4. Streamlines and v-velocity contours on a horizontal streamwise cut :y/w =.5 for experiment (a), Menter k-ù (b), coarse grid DES (c), and medium grid DES (d). 9

20 .6.4 Experiment and DES of the Medium and Coarse Grid.2 y/w Experiment Coarse Grid, = 4, end = 235, Kappa =.2, s =.2 Coarse-Grid, = 23, end = 4, Kappa =.35, s =.2 Medium Grid, = 47, end = 94, Kappa =.2, s = C p Figure 5. Pressure coefficient distribution from the experiment, medium mesh, coarse mesh along the height of the trailer base:z/w =. 2

21 DES, Coarse Mesh, s =.2, Kappa =.2 C D-inst C D-mean C D-rms.4 C D Figure 6. Drag coefficient from the coarse mesh. 2

22 C D Kappa =.35, s =.2 DES, Medium Mesh C D-inst C D-mean C D-rms Kappa =.2, s = Fig 7. Drag coefficient from medium mesh. 22