1 st Automotive Aerodynamics workshop The University of Sydney Mr Liang Yu Dr. Asiful Islam (now JLR) Dr. Sammy Diasinos (Macquarie) A/Prof Ben Thornber The University of Sydney Page 1
Outline 1. Introduction to research group 2. Numerical methods, models and meshes 3. Notchback Results 4. Case 2a 5. Conclusions. The University of Sydney Page 2
1. Introduction to Research Group 1. Develop governing models for compressible turbulent flows 2. Explore novel numerical methods for unsteady turbulent flows. 3. Unsteady applied aerodynamics computations (aero and auto) The University of Sydney Page 3
1. Prior relevant research – 2013-2016 – Developed hybrid RANS-ILES methods with flow-adaptive blending, incorporating wall functions 1 – Targeting Automotive Aeroacoustics (compressible solver) – Smooth transition from Spalart Allmaras to ILES – can use the equation to keep regions RANS or ILES when desired – Utilises an additional scalar transport equation to ‘label’ the boundary layer – simple solution to remove some sensitivity to gridding The University of Sydney Page 4 1 Islam, A. & Thornber, B, Computers and Fluids, 167, 292-312, 2018.
1. Prior relevant research – 2013-2016 – Undertook hybrid RANS-ILES and Powerflow computations of the notchback in ~2015. Flamenco PIV RANS-ILES Powerflow The University of Sydney Page 5
1. Prior relevant research – 2013-2016 Powerflow captured experimental pressure drop at rear of the backlight (y=102). Flamenco captured the base flow better The University of Sydney Page 6
2. Numerical Methods: Fractional step method for low-Mach number 1) Momentum predictor to get intermediate velocity 2) Pressure gradient added – similar to Rhie-Chow interpolation 3) Pressure corrector 4) Final velocity update Transient SIMPLE (PimpleFOAM): (1 -> 2 -> 3 -> 4) -> (1 -> 2 -> 3 - > 4)…(usually 5 -8 iterations) until converged per time step Fractional step method: (1 -> 2 -> 3 -> 4) once only per time step The University of Sydney Page 7
2. Test Case One: linear gas dynamics Pressure (Pa) Distance (m) Propagation of a Gaussian pulse of amplitude 0.09Pa (solid lines) Splitting into two waves at late time (dash-dotted lines) Formal convergence study against analytical solution from characteristics The University of Sydney Page 8
2. Test Case One: linear gas dynamics L2 error norm Solid lines: CFL=4 Dashed lines: CFL=2e-3 Fractional step (circles) rhoPimpleFoam (asterix) dx (m) Computational time (s) On the same grid, L2 errors are equal For the same grid, the fractional step method is ~5x faster than rhoPimpleFoam The University of Sydney Page 9
2. Test Case Two: Isentropic vortex convection Advection of an isentropic vortex with a mean flow: • Aligned with the mesh (0 deg) • Angled to the mesh (45 deg) Run for both the fractional step method (cFSM) and existing rhoPimpleFoam The University of Sydney Page 10
2. Test Case Two: isentropic vortex convection L2 error norm Dashed lines: 0 deg Dotted lines: 45 Deg Fractional step (squares) rhoPimpleFoam (plus) dx (m) Computational time (s) On the same grid, L2 errors are equal For the same error, the fractional step method is ~5x faster than rhoPimpleFoam Benefit does not diminish when the flow direction is not aligned with the grid The University of Sydney Page 11
2. Mesh for Case 1 Refinement zones Stationary ground (non-slip) SAE notchback (non-slip) 𝑽 ∞ The University of Sydney Page 12
2. Mesh for Case 1 Stationary ground Total Cells Size on car Prism layer 𝑽 ∞ 16 layers, 1 st height = 0.0115mm Coarse 6 Million 2.3mm Growth rate 1.313(leg) and 1.360 16 layers, 1 st height = Medium 9 Million 2.05mm 0.01025mm SAE car body Growth rate 1.313(leg) and 1.360 16 layers, 1 st height = Fine 12 Million 1.875mm 0.009375mm Growth rate 1.313(leg) and 1.360 The University of Sydney Page 13
2. Mesh for Case 1 Stationary ground 1) First layer y+ ~ 1 for a low-Re Final layer mesh. 16 layers Adjacent cell 1.36 growth 2) With growth rate of 1.313 and 1.36, the total layer thickness is 16 layers legs more than y+ = 250. 1.313 growth 𝑽 ∞ 3) Final layer thickness is 0.3-0.5 of the adjacent cell size for smooth transition. 16 layers SAE body 1.36 growth The University of Sydney Page 14
2. Mesh for Case 1 1) snappyHexMesh allows mesh distortion to add prism layer 2) Mesh quality needs to be carefully Stationary ground controlled for max prism layer coverage 3) Influence of mesh qualities on flow solution: legs Face pyramids -> discretisation 𝑽 ∞ conservation Non-orthonality -> diffusive term accuracy Skewnesss -> convective term SAE body interpolation accuracy Cell determinate -> gradient term accuracy Tet decomposition -> Affects lagrangian computation The University of Sydney Page 15
2. Mesh for Case 1 1) The distance at which distortion is allows is also controlled so that the distortion does not affect all interior cells. 𝑽 ∞ SAE body 2) The distance is important for prism layer coverage around corners 𝑽 ∞ Distortion distance SAE body The University of Sydney Page 16
2. Mesh for Case 1: y+ Needs much smaller surface mesh here for thicker prism layer coverage. The wall boundary condition of the turbulent viscosity is the continuous nutUSpaldingWallFunction in OpenFOAM. The University of Sydney Page 17
2. Mesh for Case 2a Low-Re, 16 layers on car body Contact patch Rear wheel well High-Re, 4 layers on contact patch High-Re, 4 layers and moving ground on wheels The University of Sydney Page 18
2. Mesh for Case 2a Number of prism layers reduces at some ‘sharp’ locations. Currently under testing: snappyHexMesh addLayer process modified to force generate one layer on all surfaces The University of Sydney Page 19
2. Computation time summary Case 1 Case 2a Number of Cells 80 Million Number of Cells 12 Million Inflow Velocity 16 m/s Inflow Velocity 40 m/s Number of 960 Number of processors 960 processors Time Step 1.0e-05 s Time Step 1.0e-04 s Simulation Time 2.0s Simulation Time 2.0s Clock Time 14.7 h Clock Time 10 h The University of Sydney Page 20
2. Other computational details Turbulence model: compressible SST-DDES in OpenFOAM-v1612+ Discretisation: Temporal terms: Second-order backward differencing Gradient terms: Gauss linear with a limiter (Minmod) Turbulence quantities: Second-order upwind Diffusive term discretisation: Central differencing with full non-orthogonality correction Momentum convective terms: Hybrid convection scheme of Travin et al. for hybrid RANS/LES calculations Central differencing in Second-order upwind elsewhere LES-like region The University of Sydney Page 21
3. Workshop Case 1 Second-order upwind Second-order upwind Iso-surface of Q = 100000 1/s Second-order central differencing The University of Sydney Page 22
3. Workshop Case 1 Cd Cl Cm Coarse mesh 0.197 -0.076 -0.102 Medium mesh 0.194 -0.075 -0.115 Fine mesh 0.195 -0.079 -0.114 Experiment 0.207 0.054 -0.073 Cp-backlight Cp-centreline over the car 0.3 1.5 0.2 1 0.1 0.5 0 0 -0.1 Cp-experiment Cp-experiment Cp [-] Cp [-] -0.2 -0.5 Cp-coarse mesh Cp-coarse mesh -0.3 -1 Cp-medium Cp-medium -0.4 -1.5 Cp-fine Cp-fine -0.5 -2 -0.6 -0.7 -2.5 0 10 20 30 40 50 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Sensor number X [m] The University of Sydney Page 23
3. Workshop Case 1 Time-averaged Cp on the SAE model, left Flamenco (in-house, very high order compressible solver), right OpenFOAM Fractional step. The University of Sydney Page 24
4. Workshop Case 2a Whole car Car no wheels Cd 0.260 0.185 Cl -0.070 -0.073 Clf -0.145 -0.151 Clr 0.075 0.078 The University of Sydney Page 25
4. Workshop Case 2a Iso-surface of Ux = -0.001 m/s The University of Sydney Page 26
4. Aeroacoustics of side mirror Iso-surface of Q = Wall shear stress 100000 1/s magnitude The University of Sydney Page 27
5. Conclusions and Acknowledgements Gave a quick introduction to our recent developments of a compressible fractional step method – No reduction in accuracy compared to current best options – Considerable speed saving in practical configurations – Weakly compressible – may be used for direct aeroacoustics computations Preliminary results gained for Case 1 and Case 2a. Grid convergence and further analysis for Case 2a still underway. The University of Sydney Page 28
Thank-you for listening The University of Sydney Page 29
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