CFD++ High Speed Flow Analysis on Turrets

Transcription

1 CFD++ High Speed Flow Analysis on Turrets P. Gratton*, E. Zuppel*, N. Stathopoulos**, O. Trifu *Bombardier Aerospace, Controlled Facilities & Engineering Services (CFES), Montreal, QC, (514) **Bombardier Aerospace, Loads and Dynamics), Montreal, QC TechWise Networks Inc., Montreal, QC Abstract Steady-state RANS analyses of the flow at M = 0.68 over a hemisphere-cylinder turret have been prepared and performed in CFD++, the CFD solver used at CFES. A refined unstructured hybrid mesh was generated and used to conduct a first set of runs, to identify the proper boundary conditions and the turbulence model best suited for being used in such conditions. Then, the mesh-independence threshold was determined, as well as the effects related to the use of a half (symmetric) model and mesh for analyzing this inherently non-symmetric type of flow. Compared with available experimental data, the CFD++ results proved its capability to provide, from steady-state RANS analysis at higher speeds, fairly accurate aero loads on turret-type fairings 1. Introduction Offering the largest possible observation field, the turret is the preferred type of aircraft-installed fairing for housing optical or directed energy systems, thus quite frequently present in the configuration of missionized aircraft. But, its blunt shape (hemisphere on top of a cylinder) produces massive, highly unstable separation (Fig. 1), which makes the accurate prediction of the flow about it particularly challenging. Indeed, steady-state RANS analysis is not quite adequate for flows about blunt bodies that generate viscous effects related unsteadiness 2. Such effects can be properly captured through LES, or at least with a hybrid URANS/LES approach. However, performing LES and even hybrid URANS/LES flow analyses on the complex configuration of a missionized aircraft remains a non-practical option when large number of cases need to be treated. Computation of aerodynamic loads and coefficients/derivatives of missionized aircraft constitutes a major part of CFD team activity at Bombardier Fig.1 Flow on a hemisphere-cylinder turret 1 Aerospace CFES. Given its good accuracy - efficiency balance, steady-state RANS analysis is used in virtually all situations, including the configurations that feature turret-type fairings. This raised a question on the quality of the results obtained on turrets from steady-state RANS analyses. The main objective of this investigation was to assess, against open source test data, the results provided for high speed flows on turrets via steady-state RANS analysis by the solver CFD used at CFES. A set of good geometry data and experimental results on a hemisphere-cylinder tested in a higher speed (M = 0.68) flow 6 was found through a search in the open domain. Based on it, the model of the turret inside the wind-tunnel could be developed and a high resolution, hybrid unstructured mesh was generated within the test section volume. Via a series of test runs, carried out with the k-ω SST turbulence model, the proper boundary conditions at the domain inflow and outflow frontiers were determined. Based on them, similar runs were performed with the SA (Spalart-Allmaras) and the Realizable k-ε closure models, and their results were compared with those obtained with the SST model, to identify which would be best for 1

2 conducting steady-state CFD++ flow analyses on turret-type geometries. Using four additional meshes with uniformly decreasing resolution the mesh-independence threshold was located and it proved to be, in terms of turret surface mesh resolution, close to the values commonly used at CFES in the mesh-generation process. Finally, through CFD++ runs on a half model & mesh, the effects caused by forcing the symmetry upon the flow about the turret were also evaluated. Details on the solver and on all these phases are presented, along with results that demonstrate the capability of CFD++ to provide, from steady-state RANS analysis, fairly accurate aero loads at higher speeds on hemisphere-cylinder shaped turrets. 2. Reference data Aircraft-installed turrets were extensively studied in the 1970 s and early 1980 s, due to their use for housing airborne directed energy systems. Major challenges, associated to separated flow perturbations affecting the quality of the optical field surrounding the turret, focussed that research towards the understanding and control of the phenomena in turret s aero-optical environment. Currently, research in this domain is conducted almost exclusively at low speed, thus avoiding the transonic flow related complications 7-8. Since recent data is available at lower speeds and most of the older high speed data is proprietary, a quite comprehensive search in the open domain was necessary to find good geometry data and experimental results on a hemisphere-cylinder tested in a higher speed flow. Several turrets could be found in papers and reports published by Purohit 9, de Jonckheere 10, Gordeyev 11, Jelic 12, Sherer 6. Some were used to build CFD models and meshes (Turret 1-3 9, Turret 4 10, Turret 5 11 ), but due to uncertainties in their geometry definition, or to insufficient experimental reference data, the CFD++ results obtained on them are regarded with caution, thus not presented here. Fig. 2 Hemisphere-cylinder turret installed in the wind tunnel test section 6 The geometry and test data provided by Sherer 6, proved to be the best available, thus retained and used as reference in this investigation. The turret (referred here as Turret 7), has a simple hemisphere-cylinder configuration. Equipped with pressure taps, it was tested at low and higher speed re-gimes in the indraft (low turbulence) transonic wind tunnel at the University of Notre Dame, Indiana (Fig. 2). The experimental results obtained at M = 0.68 (highest available 6 ) were those used in the present study. 3. The flow solver CFD++ Created and constantly improved by Metacomp Technologies, CFD++ is a commercial Computational Fluid Dynamics software suite employed mainly in aerospace and automotive, but also in other domains 3-5. It uses the finite volume method to analyze steady or unsteady incompressible or compressible nonreacting or reacting flows, by solving the appropriate set of equations in a very flexible and efficient numerical frame-work that combines three unifying approaches: unified grid, unified physics and unified computing. 2

3 Given the conception of its flow solver, and the numerous grid-manipulation tools it incorporates, CFD++ accepts multi-block structured curvilinear as well as unstructured and hybrid grids. The treatment of various cell shapes (hexahedral, triangular prism, pyramid and tetrahedral) is fully unified, making it applicable to all these cell and grid topologies, hence its grid-transparency or unified-grid nature. Along with the 3-D time dependent Reynolds-averaged Navier-Stokes (RANS) equations, CFD++ is able, through its highly modular architecture, to handle equations describing multi-species, multi-phase and reacting flows across all regimes, from low subsonic to hypersonic. As a result of the unified physics approach, specific modules for each of the mentioned physical states were developed and embedded in CFD++. With its versatile GUI, these can be easily interchanged and combined to provide the modeling capability for a quite large variety flows. For capturing the turbulent flow features, a consistent number of turbulence models are available, including the one-equation SA, the two-equation Realizable k-ε, SST, the three-equation Realizable k-ε-rt and the 7-equation Nonlinear Reynolds Stress. Most of them are topography-parameter-free (point-wise), hence do not require knowledge of distance to walls, and can be integrated directly to the solid boundaries or combined with wall functions that account for compressibility, pressure gradient and heat transfer effects. Flows with massive separation regions can be analyzed by using the one equation LES model or the hybrid LES/RANS models, which are also included. The unified computing approach makes CFD++ totally portable from mono-processor desktop to massively parallel systems, under different versions of Windows, Linux and Unix, with binary files compatible across all platforms. For parallel computing, CFD++ provides domain decomposition tools for all grid topologies, in particular the convenient interface to the METIS domain decomposition package. The builtin detection capability automatically turns on the proper message passing routines (native, or MPI) for the platform on which CFD++ was compiled. Because the same cell, node, boundary condition and restart files are used for single-cpu and multi-cpu runs, parallel computations are simple to set and perform. Its numerical framework includes high-order Total Variation Diminishing (TVD) discretization, based on multidimensional interpolation and used to avoid spurious numerical oscillations in the solution, various approximate Riemann solvers to ensure proper signal propagation for the inviscid terms, pre-conditioning, relaxation and multi-grid algorithms for convergence acceleration, implicit time-integration with dual time-stepping, as well as a large number of boundary conditions. 4. Geometry and mesh Turret 7 (T7) has the typical hemisphere-on-cylinder shape, with no optical windows or cuts, thus with full axial symmetry, which made it a good test configuration for assessing CFD++ capability of reliably analyzing flows about blunt bodies of this type. The geometry of the turret and the Notre Dame University wind tunnel test section are defined in figure 3, reproduced here from reference 6. Fig. 3 Turret 7 in the wind tunnel test section 6 (all dimensions in inches) Fig. 4 Static pressure ports position on Turret 7 dome 6 3

4 As shown, the turret is located on the centerline of the test chamber floor, 12 (37.5%) downstream of the inlet section. Given its small overall dimensions, the model was equipped with only 19 static pressure taps, of which 7 uniformly spaced along the left half shoulder line and 12 in the symmetry plane, along the dome s zero azimuth meridian (Fig. 4). The turret caused 5.43% of solid blockage, hence significant wall interference effects on the flow over it 13. Since pressures measured during tests have not been corrected to free air conditions 6, to use them as reference for validating CFD++ results required to analyze the flow within the test chamber solid boundaries. Accordingly, based on the data given in figure 3 the geometry (points, curves, surfaces) of the turret in the wind tunnel test chamber model, consisting of 8 parts (families), was built in ICEM CFD 14, the meshing software used at CFES. In spite of the longitudinal symmetry, a full model was created since the real flow within the test chamber, and especially in turret s wake, lacks symmetry. The lateral faces of the CFD domain far field boundary were placed in the planes of the test section solid walls. Its inflow and outflow faces were taken 2, respectively 4 closer to the turret (Fig. 3), at locations where pressure data was collected during the tests 6. For the initial series of analyses, aiming at identifying the proper set of inflow/outflow boundary conditions and the most suitable turbulence model, a quite refined mesh was considered, so as make sure that the analyses will be performed beyond the mesh convergence threshold, thus preventing any possible mesh-related effects. An unstructured hybrid mesh for viscous (Navier-Stokes) computations was generated in ICEM CFD with the mentioned model, by applying the best practices that are used at CFES in this domain. First, an unstructured mesh of tetra elements was created within the entire CFD domain, its quality inspected and further enhanced through three successive smoothing cycles. Next, the height of the first prism layer on the turret and on the test chamber walls, which ensures y + = 1 in a M = 0.68 test, was calculated and used to determine the necessary number of prism layers on domain s solid boundaries. The prism layers were grown with exponentially increasing height and the resulted hybrid mesh was subjected to another round of smoothing cycles. The final mesh (Fig.5) totalled prism, pyramid, Fig. 5 Mesh Turret7_0 and shell mesh detail tetra and tri elements, with no less than 16 pyramid-free prism layers close to walls, hence good to be used for performing RANS analyses. As shown in the included detail, the turret shell (surface) mesh was quite refined, the size of the tri elements being several times finer than the one commonly used on fairings in the CFD analyses conducted at CFES. Given the mesh higher resolution, and since only steady flow analyses were to be performed at this stage, no increased density region was included behind the turret. 5. Results 5.1. Boundary conditions Choosing the condition to be applied on the solid boundaries of the CFD domain for performing RANS analyses was straightforward, namely viscous (no-slip) wall with solve to wall (y + 1) option. However, there was initially not equally obvious to decide what conditions to use at the inflow and outflow boundaries. Therefore, instead of initiating this numerical investigation the usual way, by determining the mesh- independence threshold, a set of analyses was first conducted to identify the proper inflow/outflow conditions. 4

5 CFD++ includes in its Inflow/Outflow boundary conditions group (BC) a large number of options, from which several combinations were chosen and run, through a trial and error approach. Al runs have been performed assuming a steady, viscous flow, governed by the RANS equations, colosed with a turbulence model, of those mostly used for conducting the CFD analyses at CFES. The following conditions were also common for all runs: - M = 0.68 (highest for which good experimental data was available) - inflow turbulence intensity = (reference data was obtained in an indraft wind tunnel 6 ) - refined mesh (Fig. 5), with METIS domain decomposition in 92 sub-domains As shown in reference 6, at M = 0.68, the flow choked behind the turret (M local 1), 0.68 being the highest reachable M for that turret-test section configuration. Based on this detail, the centroidal extrapolation BC was set for run#1 at domain s outflow, thus imposing there a supersonic outflow boundary, with no conditions prescribed, and flow parameters extrapolated from the domain (nearest centroids) 5. The inflow boundary being relatively close to the turret ( 5D), the characteristics based BC was tentatively set there for run#1. This used the specified free-stream data (M = 0.68, wind tunnel altitude = 750ft) to compute the local interface fluxes from the solution of a Riemann problem solved at that boundary. Run#1, and in fact all that were performed during this study, was conducted on 92 CPUs of the CFES parallel processing system. It was repeated in similar conditions (same BCs) with the Realizable k-ε, SA, respectively SST turbulence models. After dropping to 10-3 in 200 iterations, the residuals stalled and went on oscillating with small amplitude around that level over the remaining 550 steps, thus proving that the analyzed flow is actually unsteady. Quite similar convergence histories were obtained with all three turbulence models. Given the stabilized periodic variation of the residuals over most of the integration steps, the solution of these steady flow analyses was considered converged. The verification of y + values showed that the y + 1 condition, imposed at the generation of the prism layers, was satisfied, hence the mesh adequate for being used with the integration to wall option. The comparison of the pressure coefficient Cp computed along the dome s centerline, respectively its lefthand shoulder line, with the corresponding test data 6, revealed that although the CFD++ results followed a similar trend, the disagreement was significant for all turbulence models. While some differences in the separated flow region were to be expected, those in the attached flow zone (turret s front side) warned on improper inflow and/or outflow boundary conditions. Fig. 6 Convergence history for run#6 Fig. 7 Inflow P st set/resulted in CFD++ runs #5, #6 Thus, a second run was performed, by setting the characteristics-based BC, both at the inflow and the outflow boundaries. Since run#1 showed that the position of the shock wave was better predicted with the SST and the SA turbulence models, run#2 was done only with this two models. But, no improved agreement between test and computed Cp was obtained with this inflow/outflow BC combination. By checking the static pressures computed at the inflow and the outflow boundaries it was found that, indeed, these were about 47% larger than those measured in the wind tunnel during the M = 0.68 run 6. This 5

6 showed that the wind tunnel inflow/outflow static pressure should be used for setting those conditions. However, runs #3 & #4, which were performed with inflow/ outflow BCs based on pressure, temperature, velocity and mass flow rate deduced from the available tunnel data, produced little improvement in the CFD++ results, most probably due to incompatibilities in the BC combinations that were used. Finally, with the inflow/outflow boundary conditions applied for runs #5 (Mass Flow Rate and Temperature/ Simple Back Pressure) and, especially, #6 (Reservoir P 0,T 0 / Simple Back Pressure), the correlation of the test and computed Cp data improved significantly. Although, like for all previous runs performed with this mesh, the residuals stalled at 10-3, the convergence in run#6 (Fig. 6) was somewhat better than in run#5. Moreover, with the boundary conditions used in run#6, the flow parameters (M, P 0, T 0, P st ) at the inflow and outflow boundaries closely matched the corresponding wind tunnel data, whereas the conditions set in run#5 produced variable values, whose average differed from the test data (Fig. 7). Fig. 8 CFD++ runs #5, #6 Cp variation along T7 dome centerline (left) and shoulder line (right) Even if not large, the differences in the Cp obtained from runs#5 and #6 are clearly visible on the graphs of figure 8. A marginally better test CFD++ run#6 data agreement in the attached flow region and a better shock position/intensity prediction from run#6 in the turret dome centerline (Fig.8-left) also pleaded in favour of the Reservoir Simple Back Pressure inflow/outflow BCs. Consequently this combination was retained and used throughout the rest of the study Turbulence model Fig. 9 Turbulence model effect on Cp variation along T7 dome centerline (left) and shoulder line (right) 6

7 Since most of the CFD++ analyses that aimed at identifying the proper set of inflow/outflow BCs have been performed only with the SST turbulence model, run #6 ( 5.1) was repeated with the Realizable k-ε, respectively the SA turbulence models. The use of the Reservoir (inflow) / Simple Back Pressure (outflow) BCs had no significant effects on the evolution of the residuals, which dropped close to 10-3, but stalled earlier than with SST. As expected, the lowest clock time/iteration was attained with the SA model (10.85s), being at 13.54s (+25%) for Rk-ε, and at 13.82s (+27%) for SST. As can be seen on figure 9, over the front side of the turret where the flow is attached (less influenced by viscous effects) all three models produce quasi identical results, matching quite well the test data. On dome s centerline (Fig.9-left), the SST model is best predicting the position/intensity of the shock wave, as well as the Cp variation in the separated flow region on turret s back side. In the shoulder cut (Fig.9-right), both SST and SA models predict reasonably well the shock position and the Cp in the separated flow zone, with SST over-predicting the shock intensity. Fig. 10 Turbulence model effect on predicted flow separation in front, on and behind T7 On, and around the turret, the zones of separated flow (where the x component of the computed shear stress had negative values, τ x < 0) are plotted in red on figure 10, as captured at M = 0.68 with each turbulence model. All predict similar separation regions on the turret, with the shock position, which coincides with the separation line, slightly down-stream for the Rk-ε, compared to SA and SST. These observations and the information provided in the Cp comparative graphs, indicate that the SA and SST turbulence models generate comparable results. However, based on figure 9-left, the SST model appears to perform better, hence preferable for analyzing flows over turrets Mesh convergence The 5.2 million elements mesh (T7_0), used in the runs performed to identify the proper inflow/outflow BCs and the suitable turbulence model, was purposely an over-refined one, to discard any mesh-related effects. Once those objectives attained ( 5.1, 5.2), a mesh-convergence analysis was carried out to confirm the initial assumption and to determine the mesh-independence threshold, hence an appropriate mesh size for conducting this type of analyses. Four additional meshes with lower resolutions (T7_1 to T7_4) have been generated, as shown in Table 1. Like T7_0, these were also of hybrid (tetra + prism) type, computed with the global parameters set to the same values and with the same number of prism layers. To diminish the number of their elements, the ICEM CFD Max Size and Max Deviation parameters used for producing mesh T7_0 have been multiplied for each model family with the Mesh Factor given in Table 1. The surface (shell) mesh resolution, which is usually employed at CFES on turret-type fairings when generating the meshes for CFD++ analyses on missionized configurations, is situated between that of T7_2 and T7_3 (Fig. 11), closer to the latter. The analyses on T7_1 T7_4, have all been performed at M = 0.68, with the SST turbulence model, same inflow turbulence intensity (0.002) and same inflow/outflow BCs (Reservoir / Simple Back Pressure) derived from the available wind tunnel data 6. Continuous and relatively quick decrease in the residuals, to the requested 5.5e -5 level, was obtained with meshes T7_1 and T7_2 (Fig. 12), whereas the convergence history for the runs done with meshes T7_3, T7_4 was similar to that observed for mesh 7

8 T7_0, namely a drop to 10-3 and stall around there, followed by an oscillatory evolution over several hundreds of iterations, revealing the unsteady nature of the flow, not captured by the coarsest meshes. Table 1 Mesh convergence runs Mesh No. Mesh Elements Mesh Factor Iterations T7_ T7_ T7_ T7_ T7_ Fig. 11 Turret surface mesh T7_2 and T7_3 The turret vertical force ( lift ) coefficient, averaged over the last 100 iterations of these analyses, was plotted against the mesh size (Fig.13). The corresponding regression indicates that the mesh-independence threshold is at 2.2 million elements. With the turret meshes commonly used at CFES, which are coarser (near T7-3) the error in CL would be under 0.5%, quite acceptable for many aero loads related purposes. Fig. 12 Convergence of CFD++ run with mesh T7_2 Fig. 13 Mesh resolution effect on T7 lift coefficient 5.4. Symmetric flow The massive, unsteady separation on the turret induces unsteadiness and non-symmetry in the flow within the entire CFD domain. Accordingly, the meshes used so far in this study were created with a full model (see sec-tion 4). However, for efficiency reasons, in the common practice at CFES all symmetric flight cases are com-puted on half-model meshes. Thus, when analyzing a symmetric flight case on a configuration that includes a centerline-located turret, the symmetry of the half model&mesh is enforced on the non-symmetrical flow that the blunt-shaped turret is generating in its vicinity and in its wake. It was, therefore, considered useful to get an idea about the effects produced by the use of a half model& mesh for analyzing turret flows in CFD++. A half model was derived from the existing CFD model (section 4) and used to generate in ICEM CFD an unstructured, hybrid (tetra + prism) mesh - T7_0h - with elements. The meshing parameters were set to the same values as for the full mesh T7_0, giving on the turret the high resolution shown in figure 14. Also, an identical number of prim layers were grown, with y + = 1 at the solid walls. 8

9 Fig. 14 Half turret surface mesh T7_0h Fig. 15 Convergence history for run on mesh T7_0h The analysis performed with the half model & mesh in CFD++, in the same conditions as for the run#6 ( 5.1), followed a quite similar convergence history, with residuals dropping to about 10-3 in the first 200 steps, then oscillating at that level for over 500 iterations (Fig. 15). Fig. 16 Half model effect on Cp variation along T7 dome centerline (left) and shoulder line (right) On the Cp plots (Fig. 16), the values computed with the full and the half models compare well with the wind tunnel data 6 in the attached flow region of the centerline and the shoulder cuts. While the half model predicts equally well as the full model the centerline position/strength of the shock wave, the agreement of its results with the test data is slightly inferior to the full model in the separated flow region (Fig. 16-left). Along turret s shoulder line, the half model captures the shock to early and its Cp values compare less well with the test data in the separated flow zone (Fig. 16-right). These inaccuracies produce a 2.3% error in turret CL, relative to the value obtained with the full model (Fig. 13). For aero loads related purposes, this might still be acceptable, thus justifying the use of a half model for analyzing flows over turrets. 6. Conclusions Steady state RANS analyses have been performed in CFD++, the computational fluid dynamics software used at CFES, on a hemisphere-cylinder turret at high speed (M = 0.68), in the attempt to validate the code s capability of computing with good accuracy the flow over such shapes, included in the configuration of many missionized aircraft As the only set of accurate reference data available in the open domain was on a turret installed in the wind tunnel, a representative CFD model and mesh had to be created and a series of analyses had to be conducted to identify the proper set of boundary conditions. The Reservoir (inflow) / Simple Back 9

10 Pressure (outflow) conditions, based on measured wind tunnel parameters, ensured the closest agreement between the CFD++ results and the test data Among the turbulence models used in this investigation, the best results (in terms of shock position and pressure levels in the separated flow region) were obtained with the SST model. While slightly less accurate, the SA model required about 25 % less time/iteration, thus being a good option in situations when a large number of analyses need to be run and computational efficiency is critical The mesh convergence study indicated that the mesh-independence threshold was not far from the turret surface mesh size commonly used at CFES, which is somewhat coarser. The difference in the mesh density would translate in an error of under 0.5% for turret lift coefficient. For aero loads related applications, this is usually quite acceptable Although with clearly visible differences, the CFD++ results obtained with a half model & mesh, hence by enforcing symmetry on the flow over the turret, were quite close to those obtained with the full model Additional analyses could be conducted, to see the effects of other factors (structured mesh, mesh density box in turret s wake, flow unsteadiness) on the CFD++ capability to accurately simulate the high speed flows over turrets. Yet, the above elements prove that CFD++ can deliver good results for high speed flows on hemisphere-cylinder turrets, when run in conditions that are usually applied in CFES CFD practice. 7. References 1 Morgan, P., Visbal, M., Large Eddy Simulation of Flow Around a Turret, Proceedings of the 38 th fluid dynamics conference and exhibit, Seattle, WA, June 23 26, AIAA Paper Lynch, C.E., Smith, M.J., Extension and Exploration of a Hybrid Turbulence Model on Unstructured Grids, AIAA Journal, vol. 49, no. 11, November 2011, pp Chakravarthy, S., Metacomp Technologies and Its Simulation Software.What, Why, How, October, 2007, AIAA-LA-Las Vegas Enterprise Documents 4 Chakravarthy, S. et al, The CFD++ Computational Fluid Dynamics Software Suite, SAE Paper , CFD++ User Manual, version 11.1; Metacomp Technologies, Argoura Hills, CA, Sherer, S.E., Aero-Optics Code Development. Experimental Databases and AVUS Code Improvements, AFRL-RB-TR , Wright Patterson Air Force Base, March Gordeyev, S., Jumper, E., Fluid dynamics and aero-optics of turrets, Progress in Aerospace Sciences vol. 46 (2010), pp Gordeyev, S., Jumper, E., Fluid Dynamics and Aero-Optical Environment Around Turrets, AIAA Paper Purohit, S.C. et al, Numerical Simulation of Flow Around a Three-Dimensional Turret, AIAA Journal, Nov.1983, pp de Jonckheere, R. et al, High Subsonic Flowfield Measurements and Turbulent Flow Analysis Around a Turret Protuberance, AIAA Paper Gordeyev et al, Aero-Optical Environment Around a Conformal-Window Turret, AIAA Journal, July 2007, pp Jelic, R., Study of Varying Boundary Layer Height on Turret Flow Structures, MSc AE Thesis, Air Force IT, Wright-Patterson AFB, June Maskell, E.C., A Theory of the Blockage Effects on Bluff Bodies and Stalled Wings in a Closed Wind Tunnel, Aeronautical Research Council Reports and Memoranda No. 3400, London, U.K., ANSYS ICEM CFD 12.0 User s Manual, ANSYS Inc., Canonsburg, PA, April