Computations of Turbulent Flow over an Aircraft Windshield Wiper Model

Transcription

1 19th AIAA Computational Fluid Dynamics June 2009, San Antonio, Texas AIAA Computations of Turbulent Flow over an Aircraft Windshield Wiper Model Michael P. Urban 1 and Klaus A. Hoffmann 2 Department of Aerospace Engineering Wichita State University, Wichita, KS, Numerical simulations of turbulent flow over a model representing an aircraft windshield wiper were performed. The finite volume code, FLUENT was utilized to solve the governing equations. Three-dimensional Detached-Eddy simulations were computed with the Menter s Shear Stress Transport Turbulence Model. A backward facing step simulation validated the numerical simulations. The backstep validation produced mean hydrodynamic data accurate with experimental data, overpredicted pressure fluctuation magnitudes, and physically correct spectra relative to empirical relations from the literature. Computations on the windshield wiper model produced data as expected from trends observed in the literature. O I. Introduction BSTACLES in a turbulent flow field produce undesirable wall pressure fluctuations which lead to increased structural vibration and generation of noise. In an aircraft flight deck, it is especially difficult to dam pen the vibrations through the structure since the flight deck contains a window and a birdstrike structure. The optimal solution is to passively reduce the source of the turbulent fluctuations by improving the geometric design features of an obstacle. Computational fluid dynamics is a young field that benefits from continual improvement. In past years, three approaches of turbulent flow simulation are typically considered. Direct Numerical Simulation (DNS) solves the governing equations without any filtering or modeling. Therefore, the grid must be fine enough to resolve all scales of turbulence. This essentially translates to generating cells smaller than the Kolmogorov length scale. The result is an extremely large requirement of cell count. Consequently, the cell count requirement grows exponentially based upon the Reynolds number: [1] Ndns ( 3Re ) 9/4 τ Along with the cell count requirements, the timestep must be adequately small to maintain numerical stability: [1] 0.003H Δt Re u With strict requirements for the grid and timestep, the DNS is typically affordable for low Reynolds number flows which are one or two orders below typical cruise conditions for an aircraft. Grids generated for DNS also often require the high quality available through structured grids while minimizing the cell aspect ratio which further limits the complexity of the problem geometry. The second approach, Large-Eddy Simulation (LES), improves the computational affordability of DNS by relieving the grid and timestep requirements. LES operates on the assumption that large eddies in the system are τ ς 1 2 Graduate Research Assistant, AIAA Member Marvin J. Gordon Distinguished Professor, Associate Fellow AIAA. 1 Copyright 2009 by the, Inc. All rights reserved.

2 dependent on the problem geometry whereas small eddies are not. Therefore, small eddies are modeled with a subgrid scale (SGS) model. If the grid is constructed so that the small turbulent length scale eddies are smaller than the grid size, the resulting simulation will appropriately solve the large eddies via DNS and model the small eddies through the SGS. Despite the relief LES provides on grid and timestep requirements, LES can still be far from affordable for simulations in the flow regime of aircraft cruise conditions. The third approach, which averages the Navier-Stokes equations through time, is known as the Reynolds Averaged Navier-Stokes (RANS) equations. Since they are averaged, the grid is designed to capture the gradients of flow rather than numerically solving the fluid movement. Consequently, a RANS type grid permits much larger cell aspect ratios and relaxed skewness requirements. Therefore, the use of an unstructured grid is more likely, which in turn allows greater success with increased geometric complexity of the problem. Stepping the RANS equations through time is known as an unsteady RANS simulation, which is not able to generate accurate aeroacoustic data. To capitalize on the affordability of RANS, hybrid methods were developed. Detached-Eddy Simulation (DES) uses RANS methods to model the flow in a boundary layer and LES to track the regions of flow separation. By combining these two approaches, it is possible to achieve a solution of a turbulent flow field with reasonable computational resources. Experiments of Mohsen [2] and LeClercq [3] both included forward/backward facing steps; however, they vary in length. The obstacle in LeClercq s experiment has a length of 10 step heights which allows a second recirculation region to form on the top before a third individual region. Mohsen s shorter block was not adequately long enough to develop this second recirculation region. The literature survey generally had insufficient information for geometries and flow conditions relevant to the present work. II. Flow Models The present work makes use of three different geometries to validate the numerical simulation and provide comparative data. The final geometry is simulated with two different flow fields to represent wind tunnel test conditions and aircraft cruise conditions. Details of modeling the cruise condition flow were provided by the Boeing Company. A. Backstep Experiment The first simulation replicates the experiment of Driver [4, 5] for validation purposes. The height of the step is H = 1.27cm. The incoming boundary layer of δ = 1.9cm is approaching with a free stream Mach number of This yields a Reynolds number based on step height of Re H = 37,000. The upper wall of the wind tunnel is 9 step heights above the lower wall. The step has a width of 12 step heights. A backstep produces a canonical flow with consistent general flow features. As the boundary layer flows over the step, a shear layer forms. Beneath the shear layer is a recirculation region and a counter-rotating weak corner eddy. The boundary layer begins to reform at a time-dependent reattachment point. The grid was designed based on the work of Dietiker [6]. The present work also uses a structured grid of 1.1 million cells with clustering where appropriate. The grid of the present work also has the same dimensions of the domain. Dietiker found that a grid of approximately 800,000 cells is adequate. The y+ at the wall behind the step was kept below 1. B. Straight Fence at Wind Tunnel Conditions The straight fence allows for direct comparisons to be made with the change in geometry with a fence. The incoming flow field is still the same as the backstep simulation, with the exception of the inlet height, which is now 9 step heights. A new flat plate boundary layer simulation was performed to produce the same boundary layers on the top and bottom of the domain with the new height. Figure 1 shows the domain. Figure 2 shows a portion of the grid. C. Angled Fence at Wind Tunnel Conditions The same incoming flow conditions were used from the straight fence simulation. The same crossection of the straight fence was extruded 30 degrees off the spanwise direction through a distance of 12 step heights. The increased spanwise width is necessary to produce a region in the center of the domain that is relatively unaffected by the walls. The domain is shown in Figure 3. The meshing strategy implemented spanwise clustering in the center of 2

3 the domain. Figure 4 shows a portion of the grid. D. Angled Fence at Cruise Conditions Performing an ideal validation experiment would require a flight test to correctly replicate all conditions. To prepare for a future validation using a wind tunnel, the domain and boundary conditions for the simulation were designed to be compatible. The incoming Mach number is set to 0.5; but, the incoming turbulent boundary layer information was determined by running the flat plate simulation to the wind tunnel test conditions. The remaining atmospheric conditions were derived from the standard atmosphere model at 35,000 feet altitude. III. Governing Equations Simulations were performed by the code FLUENT, which is a finite-volume based commercial code. The governing equations are the conservations of mass, momentum, and energy of a compressible viscous flow described through the Navier-Stokes equations in a Cartesian coordinate system: where: U A B C E F G = 0 t x y z x y z U = ( ρ, ρu, ρv, ρw, e) 2 A = ( ρu, p + ρu, ρuv, ρuw,( e + p) u) 2 B = ( ρv, ρuv, p + ρv, ρvw,( e + p) v) 2 C = ( ρw, ρuw, ρvw, p+ ρw,( e+ p) w) E = (0, τ11, τ12, τ13, uτ11 + vτ12 + wτ13 qx ) F = (0, τ21, τ22, τ23, uτ21 + vτ22 + wτ23 qy ) G = (0, τ, τ, τ, u, τ + vτ + wτ ) where ρ, p, e, u, v, w, are the density, pressure, total energy density, and velocity components. IV. Turbulence Model In FLUENT, several turbulence models are available; however, the present work will exclusively use Menter s Shear Stress Transport (SST) model. Several investigations reported improved results from the SST model over the Spalart-Almaras model [6]. Menter s SST model is a two-equation model which hybridizes the k ε and the k ω turbulence models. The k ω model performs well in the near wall region where it is utilized via a switching function. Outside of the boundary layer, the switching function activates the k ε model. q z V. Boundary Conditions In order to simulate the turbulent flow accurately, precise boundary conditions are required. As Eaton [7] has shown, the height and turbulence level of the incoming boundary layer affects the flow. Experimental results of Farabee [8,9] demonstrated a significant difference in wall pressure fluctuation magnitude between an incoming laminar boundary layer and a turbulent boundary layer. Generation of an accurate boundary layer within the domain may increase the domain size significantly leading to excessive computational cost. Therefore, a separate simulation of a turbulent boundary layer over a flat plate was performed. Profiles of velocity and turbulence quantities were extracted from the locations where the turbulent boundary layer grew to levels which matched experimental conditions. For the cruise condition simulation, profiles were extracted in the same location in the flat plate simulation. These profiles were then applied to the inlet boundary condition. 3

4 The outlet boundary condition was chosen to allow turbulent structures to properly exit the domain [10]. Further more, the outlet is sufficiently downstream of the region of interest to limit the impact of numerical error. For the flow analysis at the center line, periodic boundary conditions were imposed on the sides. These boundary conditions were successfully utilized by Addad [11]. His simulations also verified sufficient spanwise width of the domain while using periodic boundary conditions. When the fence is angled, it is no longer physically correct to model the side walls with a periodic condition. The spanwise domain is sufficiently wide, proven through preliminary simulations, to use slip walls on the sides to minimize their impact on the region of interest in the center of the domain. The tops of all the domains are no-slip walls with adequate near wall resolution to accurately simulate the boundary layers. VI. Numerical Solver The coupled solver was used with the iterative time advancement scheme. 2 nd order implicit methods were used for stepping through time. 3 rd order MUSCL discretized the spatial calculations. The node-based gradient option was used. The PRESTO! method was used for the pressure interpolation. VII. Convergence Criteria Due to the hybrid nature of DES, it is necessary to simultaneously assess the convergence of the both the RANS and LES regions of the grid. To determine the RANS convergence behavior, the grid was first run entirely in RANS mode. As the residuals fell, numerical data was compared to experimental data for the backstep problem. In all cases, proper convergence was obtained when the residuals remained below 1e-5. The default relaxation factors were all adequate with the exception of specific dissipation rate (ω); the default value of 0.8 was reduced to 0.7 to yield desirable residual behavior. In the LES regions, numerical error is avoided by restricting the maximum Courant Friedrichs Lewy (CFL) number. It is generally accepted to limit the maximum CFL number below 1. Since the CFL number is a ratio of spatial resolution with temporal resolution, a theoretical fluid particle would not travel over a distance greater than one cell. Because LES is only run away from the wall, the CFL numbers in the finely meshed regions near the wall do not need consideration. This highlights another advantage of DES: the ability to simulate at larger time steps. However, the time step must also be adequately fine to properly resolve frequencies in the desired spectral range. After proper convergence of each individual timestep is understood, it is now necessary to ensure the solution is converged through time by assessing its ability to achieve a dynamically steady-state. The unsteady simulation was initialized with steady-state data from a RANS solution. Therefore, adequate time advancement in the unsteady simulation is required to form realistic turbulence before statistics can be collected. A. Backstep Experiment VIII. Results Two-dimensional RANS computations produced nearly identical data as Dietiker [6]. The expected features of the backstep flow were resolved. Figure 5 shows the presence of a corner eddy, recirculation region, and reattaching streamline. Figure 6 shows the accurate modeling of the velocity field relative to the experimental data of Driver s. Figure 7 shows turbulence intensity data. Compared to the experimental data, turbulence intensity was overpredicted but also in a similar manner to the results of Dietiker [6]. The pressure coefficient shown in Figure 8 behind the step agrees well with the experimental data. Because FLUENT has the ability to run a two-dimensional DES simulation, a simulation was performed to assess its capabilities. The velocity flow field was not modeled correctly, evident by a significant delay of a predicted reattachment length of 8H rather than 6.1H. Furthermore, the recorded pressure fluctuations produce a tonal signal similar to the results of Hamed [12] which are not indicative of random noise. Figure 9 shows a sample of the pressure fluctuation signal. A three-dimensional DES computation produced results similar to those of Dietiker [6]. The resulting recirculation region is displayed in Figure 10 and the flow field in Figure 11. The qualitative features of the pressure coefficient were in agreement with experimental data, but the magnitudes were slightly overpredicted. 4

5 Figure 12 shows the wall pressure fluctuation magnitude distribution behind the step. Figure 13 shows a portion of the time history at the same point Driver observed [4,5]. The frequency of large events appears consistent with the expected frequency of shear layer flapping calculated from the Strouhal number. The power spectral density (PSD) of the pressure fluctuations displayed in Figure 14 is consistent with the empirical relations of Efimstov [13] and the numerical results of Dietiker [6]. The power spectral density was performed on several segments of pressure signal data to ensure that it is stationary. The data was not averaged due to the possibility that peaks corresponded with Strouhal numbers. A. Straight Fence at Wind Tunnel Conditions The time-averaged velocity flow field of the DES simulation produced results consistent with observations from Mohsen s experiment [2]. The straight fence did not allow the formation of a recirculation region above itself. The reattachment length of 12 step heights is also consistent with Mohsen s findings. The pressure coefficient distribution Figure 15 shows a significant increase over the backstep. Figure 16 shows one iso-surface of the resulting vortical structures. Note the density is higher in the reattachment region, lower in the recirculation region, and lower behind the reattachment region. Figure 17 displays the pressure fluctuation intensity which has a peak intensity approximately 4 times greater than the backstep simulation. B. Angled Fence at Wind Tunnel Conditions Figure 18 shows the recirculation region of the angled fence. The wall effect is apparent in the regions close to the spanwise walls. Figure 19 plots the pressure coefficient at various center planes. The peak pressure coefficient is the same for all planes in front of the fence. Behind the fence, it equals the straight fence in only one plane. The remaining planes show the ability of the angled feature to relax the flow field in the spanwise direction. Figure 20 shows one iso-surface of the resulting vortical structures. Figure 21 shows the root-mean-square (RMS) static pressure. It appears that near the z = 0 wall, wall pressure fluctuation magnitude does not increase much moving in the positive z-direction. Figure 22 plots a PSD of wall pressure at the reattachment point. The empirical relations of Efimstov [13] are still present with the angled fence configuration. The low frequency region contains most of the energy while the high frequency region quickly loses energy as the turbulence is dissipated into shear forces. C. Angled Fence at Cruise Conditions Figure 23 displays the pressure fluctuation magnitude results. Even though the coefficient of pressure is similar to the results from the wind tunnel conditions, the pressure fluctuation magnitude is higher. At the z = 7H plane, the peak value reaches approximately 0.23 compared to the value of 0.12 of the angled fence at wind tunnel conditions and 0.24 from the straight fence at wind tunnel conditions. The PSD of pressure fluctuations of the center plane wall pressure is shown in Figure 24. The first obvious difference between these spectra and the spectra from the angled fence at wind tunnel conditions is the absence of dominant peaks. This is similar to the results of Dietiker [6] when he increased the mach number of his simulations to 0.5. IX. Conclusion DES simulations can provide useful data when an LES simulation or experiment is not affordable. Mean flow quantities are well predicted. There is a tendency to overpredict the pressure fluctuation magnitude which is consistent with literature. The spectral data for the validation case agrees with experimental data, but likely contains more energy in the low-frequency domain than in reality. The straight fence geometry creates a significant increase of pressure fluctuation intensity over the backstep. The angled geometry reduces the pressure fluctuation intensity. There may be a relationship between the fence angle and pressure fluctuation intensity, but the present investigation does not have sufficient data to reduce such a relationship. 5

6 Acknowledgments The authors thank Dr. Jean-François Dietiker of West Virginia University for his advice with DES simulation. The authors appreciate the contributions of Ms. Judith Gallman, Dr. Sang Lee, Ms. Terri Miller, and Dr. Mark Moeller of Spirit AeroSystems, Inc. during the research program. Thanks to Robert Rackl of the Boeing Company for advice on the incoming cruise flow field. Computations were performed at the High Performance Computing Center (HiPeCC) at Wichita State University and Spirit AeroSystems, Inc. References [1] D. C.Wilcox 1998 Turbulence Modeling for CFD" 2nd edition, DCW Industries, Inc. [2] Mohsen,A. M., Experimental Investigation Of The Wall Pressure Fluctuations In Subsonic Separated Flows, Boeing Co Renton Wash Commercial Airplane Div, Jan 26, 1967 [3] D. J. J. Leclercq, M. C. Jacob, A. Louisot and C. Talotte 2001 Forward-Backward Facing Step Pair: Aerodynamic Flow,Wall Pressure And Acoustic Characterization" AIAA paper no [4] Driver, D.M., and Seegmiller, H.L., Features of a Reattaching Turbulent Shear Layer in Divergent Channel Flow, AIAA Journal, Vol. 23, No. 2, pp , February [5] Driver, D.M., Seegmiller, H.L., and Marvin, J.G., Time-Dependent Behavior of a Reattaching Shear Layer, AIAA Journal, Vol. 25, No. 7, pp , July [6] Dietiker, Jean-Francois and Hoffmann, Klaus A., Computations of Turbulent Flow over a Backstep, AIAA Paper , June [7] J.K. Eaton, J.P. Johnston, A Review of Research on Subsonic Turbulent Flow Reattachment, AIAA Journal Vol 19, No 9, Sept 1981 [8] Farabee, T. M., and Casarella, M. J., Effects of Surface Irregularity on Turbulent Boundary Layer Wall Pressure Fluctuations, ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 106, 1984, pp [9] Farabee, T. M., and Casarella, M. J., Measurements of Fluctuating Wall Pressure for Separated/Reattached Boundary Layer Flows, ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 108, 1986, pp [10] J. U. Schlueter, H. Pitsch, and P. Moin 2005 Outflow Conditions for Integrated Large Eddy Simulation/Reynolds-Averaged Navier Stokes Simulations [11] Y. Addad, D. Laurence, C. Talotte, M.C. Jacob 2003 Large eddy simulation of a forward-backward facing step for acoustic source identification [12] Hamed, A., Basu, D., Das, K., Detached Eddy Simulations of Supersonic Flow Over Cavity, AIAA Paper [13] Efimtsov, B.M., Kozlov,N.M., Kravchenko, S.V., and Andersson, A.O., Wall Pressure-Fluctuation Spectra at Small Backward-Facing Steps, AIAA paper , 6th AIAA/CEAS Aeroacoustics Conference and Exhibit, Lahaina, HI, June 12-14,

7 Figure 1: Domain of straight fence flow (units in step heights) Figure 2: Portion of fence grid cross-section 7

8 Figure 3: Domain of angled fence in step height units Figure 4: Top view of angled fence grid Figure 5: Streamlines of 2D RANS 8

9 Figure 6: X-Velocity Profiles of 2D RANS Figure 7: TKE Profiles of 2D RANS 9

10 Coefficient of Pressure D RANS Driver Experiment Position Behind Step (x / h) Figure 8: Pressure Coefficient Distribution of 2D RANS Pressure (Pa) Normalized Time Figure 9: Example of Erroneous Pressure Signal 10

11 Figure 10: Recirculation Region of 3D DES Colored with Z-Coordinate Figure 11: X-Velocity of 3D DES 11

12 P_rms/q Position behind Step (X/H) Dietiker - DES Experiment Urban - DES Figure 12: Static Pressure RMS Velocity (U/U_inf) Characteristic Time [t_c] 6 Figure 13: Time History of Velocity at (6H,1H) 12

13 Figure 14: Pressure PSD of Reattachment Point Coefficient of Pressure Position (X/H) Figure 15: Coefficient of Pressure Distribution at Center Plane 13

14 Figure 16: Vortical Structures 0.25 Pressure Fluctuation Magnitude (P_RMS/q) Position behind step (X/H) Figure 17: RMS Static Pressure Distribution at Center Plane 14

15 Figure 18: Recirculation Region Colored with Z-Coordinate Figure 19: Pressure Coefficient Distribution at Various Spanwise Planes 15

16 Figure 20: Vortical Structures Figure 21: RMS Static Pressure Distribution at Various Planes 16

17 Figure 22: Pressure PSD at Reattachment of Z=4H Figure 23: RMS Static Pressure Distribution 17

18 Figure 24: Pressure PSD at Reattachment of Center Plane 18