1. 1 Case 2: URANS Application with CFL3D Christopher L. Rumsey NASA Langley Research Center Hampton, VA CFDVAL2004 Workshop, March 29-31, 2004

2. 2 Outline Numerical method Turbulence models Sample of Results Summary

3. 3 CFL3D code description Finite-volume, upwind-biased solver for compressible N-S Roe Flux-difference splitting for inviscid fluxes, central differences for viscous/heat fluxes Globally second-order spatial accuracy Steady state or time accurate (second-order) Point-match, patched, or overset zonal boundaries Extensive suite of turbulence models (Spalart-Allmaras (SA), Menter shear-stress transport (SST), and nonlinear explicit algebraic stress model (EASM) used in this study) –EASM completed after deadline: not included in compilation

4. 4 Turbulence models Spalart-Allmaras (SA) –one-equation for transport of turbulent viscosity –linear eddy-viscosity model –La Recherche Aerospatiale, No. 1, 1994, pp. 5-21 Menter shear-stress transport (SST) –two-equation k-ω model –blend of k-ω and k-ε form, with Bradshaw correction to eddy viscosity (shear stress in B.L. proportional to k) –linear eddy-viscosity model –AIAA Journal, Vol. 32, No. 8, 1994, pp. 1598-1605

5. 5 Turbulence models Explicit Algebraic Stress Model (EASM) –compromise between full second-moment closure and 2-equation model –nonlinear eddy-viscosity model ( k-ω form) –JFM, Vol. 254, 1993, pp. 59-78 –J Aircraft, Vol. 38, No. 5, 2001, pp. 904-910 –NASA/TM-2003-212431, June 2003

6. 6 Explicit Algebraic Stress Model (EASM) Algebraic relationship between turbulent Reynolds stress and mean velocity field (nonlinear model)  linear part  nonlinear part

7. 7 EASM (cont’d) Derived from the Reynolds stress transport equation, assuming: –anisotropy equilibrium: –particular behavior of turbulent transport and viscous diffusion tensor –tensorially linear pressure-strain correlation

8. 8 EASM (cont’d) Implemented in two-equation framework is variable: function of invariants of mean rate-of-strain tensor and mean vorticity tensor Constants from Speziale-Sarkar-Gatski pressure-strain correlation model used

9. 9 Case-specific details 3-D, full-plane Supplied 3-D structured grid #1 (3.9 million cells) & every-other-point (0.49 million cells) Time-accurate with multi-grid dual-time- stepping subiterations

10. 10 Case-specific details (cont’d) SA (fine) SA (med) SST (med) EASM (med) 720 steps/cycle, 5 subiteration XXX 720 steps/cycle, 10 subiterations X 1440 steps/cycle, 10 subiterations X (late)

11. 11 Boundary conditions

12. 12 Effect of time step & subiterations SST, medium grid, x=57.15mm, z=10mm -SA did not exhibit any instability with 720 steps/cycle and 5 subiterations

13. 13 Effect of grid and turbulence model at the orifice exit

14. 14 CFD does not model large spanwise component of velocity seen in experiment at the orifice exit

15. 15 Contours of U/Uinf at x=76.2mm phase=200 deg. SA, fine gridSA, medium grid

16. 16 Contours of U/Uinf at x=76.2mm phase=200 deg., medium grid SST, 720 steps/cycle SST, 1440 steps/cycle

17. 17 Contours of U/Uinf at x=76.2mm phase=200 deg., medium grid SASSTEASM

18. 18 U/Uinf at x=57.15mm medium grid Phase=0 Phase=120Phase=240

19. 19 u’w’/Uinf 2 at x=57.15mm medium grid Phase=0Phase=120 Phase=240

20. 20 Contours of U/Uinf at x=57.15mm long-time-average, medium grid SASSTEASM

21. 21 Velocity vectors & vorticity contours SA, fine grid, at z = -0.1mm and -5 mm (inside cavity) Phase=0Phase=120

22. 22 Velocity vectors & v-velocity x=57.15, medium grid, phase=120 deg z=10mm

23. 23 Cavity size - cavity in experiment is extremely shallow - volume changes by more than factor of 2 - may amplify inherent asymmetries - CFD’s approximate BC (simulating moving wall with velocity specified) probably not a good approximation in this case

24. 24 Summary V-component of velocity at orifice in experiment not modeled by CFD Instability in SST result goes away with more subiterations & smaller time step –global results do not change much Medium grid and fine grid results are very similar in their global results Three turbulence models differ in their details, but are similar in their global results