Detached Eddy Simulations of an Airfoil in Turbulent Inflow

1. Detached Eddy Simulations of an Airfoil in Turbulent Inflow Lasse Gilling, Aalborg University, Denmark Niels N. Sørensen, Nat. Lab. Sustainable Energy, Risø/DTU, Denmark Lars Davidson, Chalmers University of Technology, Sweden lg@civil.aau.dk

2. Agenda • Introduction • Computational Setup • Numerical Methods • Inflow Boundary Condition • Results and Discussion • Conclusions Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

3. Introduction • The most common approach to DES of airfoils is to use a mesh like this • Coarse grid far from the airfoil • Fine grid close the airfoil • Laminar inflow with low eddy viscosity • Wind turbines operate close to the ground and are subjected to high levels of turbulence • This work investigates the importance of resolving the inflow turbulence Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

4. Computational Setup Inlet Periodicity Symmetry • Geometry like the wind tunnel • NACA 0015 airfoil • Re=1.6×106 • 21 million cells • Extruded 2D mesh • O-mesh close to the airfoil • Cartesian cells everwhere else • The cells are stretched prior to the outlet • Here every 8th cell is shown Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

5. O-mesh Close to the Airfoil 384×64 cells in O-mesh - 128 cells in spanwise direction Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

6. Cell Sizes • Close to the wall • Cell size in wall units is shown in the figure • Non-constant friction velocity • In the Cartesian part • Δx ≈ 1.4×10-2 c • Δy ≈ 1.6×10-2 c • Δz ≈ 1.2×10-2 c Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

7. Numerical Methods • EllipSys3D • Developed by J. Michelsen and N. Sørensen from DTU and Risø • Incompressible Navier-Stokes equations • Finite volume (cell-centered) • Structured, multi-block grid • Rhie/Chow interpolation • PISO algorithm • Detached eddy simulations with the k-ω SST subgrid turbulence model • Momentum equations are solved with 4th order central difference scheme • 2nd order accurate dual time stepping algorithm Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

8. Inflow Boundary Condition • Fluctuating velocity field is used for inflow boundary condition • Synthetic inflow turbulence is created by the method of Mann • All three velocity components • Components are correlated • Velocity field is divergence free Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

9. Precursor Simulation • Random phases and incorrect statistical moments of third and higher order • The synthetic turbulence is run through a precursor simulation to • Let the flow solver correct random phases and incorrect higher order moments • Let the turbulence adopt to the grid and the numerical method Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

10. Spatial Decay of Homogenous Turbulence • Spatial decay is studied • Test numerical method • Test synthetic turbulence

11. Spatial Decay of Isotropic Turbulence The three curves should have the same slope as the emperical line Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

12. Results and Discussion: Lift and Drag 1.5 2D RANS DES, TI=0.0% 0.3 DES, TI=0.5% DES, TI=2.0% Measurements 0.25 1 0.2 D L C C 0.15 0.5 0.1 2D RANS DES, TI=0.0% DES, TI=0.5% 0.05 DES, TI=2.0% Measurements 0 0 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Angle of attack [deg] Angle of attack [deg] • Flow is sensitive to turbulence • DES with no inflow turbulence predicts stall too late • DES with 0.5% turbulence intensity (TI) gives good agreement before stall • DES with 2.0% TI gives poor results for low AOA but better after stall • 2D RANS is good for low AOA, but fails to predict stall • Experiment: ~0.1% turbulence intensity Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

13. Surface Pressure • Good agreement • Low TI best for low AOA • High TI best for high AOA • Flow very sensitive at 16° AOA AOA=14° AOA=18° AOA=16° Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

14. Skin Friction AOA=14° AOA=18° AOA=16° • For low AOA: • Increased TI moves separation point upstream • For high AOA: • Increased TI moves separation point downstream Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

15. Force History • AOA is 16° – close to stall • Required simulation time depends on the TI • Low TI • Long flow development time • Shows large, slow oscillations • High TI • Short flow development time • Only small, fast oscilations Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

16. Flow Visualization – Low Turbulence • TI is 0.1% and AOA is 16° • Surface limited streamlines and iso-vorticity • Large separation gives low lift and vice versa • Very unsteady, large spanwise variations • Modeling full width of tunnel is required Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

17. Flow Visualization – High Turbulence • TI is 2.0% and AOA is 16° • Surface limited streamlines and iso-vorticity • Much smaller variations in time and spanwise direction • More steady lift Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

18. Averaged Turbulence Intensity • AOA is 12° and TI is 0.5% • Leading edge is located at x/c=0 • Only little decay upstream of the airfoil • Turbulence is generated in the separation bubble and the first part of the wake • Larger decay in stretched part of the grid (for x/c>6) Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

19. Eddy Viscosity • Eddy viscosity normalized by the molecular viscosity • AOA is 12° and TI is 0.5% • High eddy viscosity in the wake and separated region • Eddy viscosity far from the airfoil is constant Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

20. Subgrid Kinetic Energy • Subgrid kinetic energy normalized by the mean velocity squared • AOA is 12° and TI is 0.5% • High subgrid kinetic energy close to the wall • Far from the airfoil is constant and low • Intermediate values in the wake Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

21. Resolved Kinetic Energy • Resolved kinetic energy normalized by the mean velocity squared • AOA is 12° and TI is 0.5% • High resolved kinetic energy in the wake • Far from the airfoil is is constant with a value corresponding to the intensity of the resolved turbulence Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

22. Conclusions • Computed lift and drag depends on the resolved turbulence intensity • Stall is predicted best with TI similar to the one in the experiment • Low AOA: Increased turbulence moves separation point upstream • High AOA: Increased turbulence moves separation point downstream • Best agreement with measurements is obtained • Low AOA: Low turbulence intensity • High AOA: High turbulence intensity Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

23. Future Plans • Implement an actuator disc approach of imposing the turbulence • Turbulence can be imposed immediately upstream of the airfoil • Save mesh points • Investigate the influence of the turbulence length scale Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

24. Detached Eddy Simulations of an Airfoil in Turbulent Inflow Lasse Gilling, Aalborg University, Denmark Niels N. Sørensen, Nat. Lab. Sustainable Energy, Risø/DTU, Denmark Lars Davidson, Chalmers University of Technology, Sweden lg@civil.aau.dk