Detached Eddy Simulations of an Airfoil in Turbulent Inflow

Lasse Gilling, Aalborg University, DenmarkNiels N. Sørensen, Nat. Lab. Sustainable Energy, Risø/DTU, DenmarkLars Davidson, Chalmers University of Technology, Sweden

lg@civil.aau.dk

Agenda

• Introduction• Computational Setup• Numerical Methods• Inflow Boundary Condition• Results and Discussion• Conclusions

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

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

3Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

Computational Setup

• 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

4

Inlet

Periodicity

Symmetry

Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

O-mesh Close to the Airfoil

5

384×64 cells in O-mesh - 128 cells in spanwise direction

Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

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

6Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

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

7Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

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

8Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

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

9Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

Spatial Decay of Homogenous Turbulence

10

Spatial decay is studied• Test numerical

method • Test synthetic

turbulence

Spatial Decay of Isotropic Turbulence

11

The three curves should have the same slope as the emperical line

Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

Results and Discussion: Lift and Drag

• 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

12

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

Angle of attack [deg]

CL

2D RANS

DES, TI=0.0%

DES, TI=0.5%

DES, TI=2.0%

Measurements

0 2 4 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

0.25

0.3

Angle of attack [deg]

CD

2D RANS

DES, TI=0.0%

DES, TI=0.5%

DES, TI=2.0%

Measurements

Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

Surface Pressure

13

AOA=16° AOA=18°

AOA=14°

• Good agreement• Low TI best for low AOA• High TI best for high AOA• Flow very sensitive at 16° AOA

Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

Skin Friction

14

For low AOA:• Increased TI moves separation

point upstreamFor high AOA:• Increased TI moves separation

point downstream

AOA=16° AOA=18°

AOA=14°

Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

Force History

15

• AOA is 16° – close to stall• Required simulation time

depends on the TI

Low TI • Long flow development time• Shows large, slow oscillationsHigh TI • Short flow development time• Only small, fast oscilations

Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

Flow Visualization – Low Turbulence

16

• 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 requiredIntroduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion –

Conclusions

Flow Visualization – High Turbulence

17

• 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

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)

18Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

Eddy Viscosity

19

• 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

Subgrid Kinetic Energy

20

• 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

Resolved Kinetic Energy

21

• 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

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

22Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

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

23Introduction – Computational Setup – Numerical Methods – Inflow Boundary Condition – Results and Discussion – Conclusions

Detached Eddy Simulations of an Airfoil in Turbulent Inflow

Lasse Gilling, Aalborg University, DenmarkNiels N. Sørensen, Nat. Lab. Sustainable Energy, Risø/DTU, DenmarkLars Davidson, Chalmers University of Technology, Sweden

lg@civil.aau.dk