Large Eddy Simulation of Flow Separation and Flow Control on E387
Airfoil using Code_Saturne
Andrew P. Heffron, John J. Williams, Eldad J. Avital
Queen Mary, University of London, Mile End Road, London, E1 4NS, United Kingdom
Introduction
UAVs, wind turbines, and many other applications depend on airfoils operating at low to
moderate Reynolds numbers and that are optimize to minimize drag and maximize lift. Flow
separation on airfoils increase drag and degrades lift generation. Airfoils operating at high angle of
attacks suffer from turbulent flow separation which is caused by adverse pressure gradient and
changes in geometry. At low to moderate Reynolds numbers, a laminar separation bubble commonly
forms on the leading edge of the airfoil owing to laminar flows being less resistant to adverse pressure
gradients before the flow transitions to a turbulent flow and reattaches. Much research has been
conducted on controlling flow separation, and a common method has been microvortex generators
(MVG). MVG function by transferring momentum from the outer to the inner boundary layer.
Although there is a large volume of literature on MVG, limited literature has been published on
modeling MVG on airfoils and how they behave. This study intends to model the separation on the
e387 airfoil at a high angle of attack and then use different MVG configurations to study the effect the
MVGs have on the flow separation.
Numerical Method and Setup
Code_Saturne 4.0.1 is an open sourced CFD code developed by Électricité de France (EDF).
Code_Saturne is based on an unstructured, collocated Finite Volument method. The pressure-velocity
coupling is based upon the fractional step method. Time is advanced with an implicit second order
Crank-Nicholson scheme and spatially discretized with a second order centered scheme. The large
eddy simulation was tested with the DSM (Dynamic Smagorinky Model) and the WALE (WallAdapting Local Eddy-viscosity) subgrid models.
The Eppler e387 airfoil was placed at an angle of attack of 12 degrees relative to the flow
direction with Re = 2x105. A velocity inlet was imposed 3 chords lengths upstream and a pressure
outlet was placed 5 chord lengths downstream of the airfoil. Periodic boundary conditions were
enforced 0.15 chords lengths in the spanwise direction. The wall of the airfoil uses a no-slip wall
boundary condition. The generated mesh contains 24.2 million cells with a C-type grid topology. The
mean y+ is less than 0.4, and x+ and z+ are both less than 20.
Results
Presented below are the preliminary results that have been obtained with Code_Saturne. To
initialize the flow field and allow the flow field to reach a converged state for LES, the simulation was
allowed to run for approximately two downwash periods. The data shown in the four figures below
for DSM has been time averaged over two downwash. Instantaneous results for WALE subgrid model
at t=0.9427 s, approx. 0.44 downwash periods, are shown in Fig. 4 along with the time averaged
results for DSM and experimental published results. The current results for DSM overpredict and
underpredict the lift coefficient and drag coefficient, respectively. Preliminary work has found that the
turbulent viscosity for the DSM is overpredicted which would decrease the degree of separation and
would explain the differences observe between the present and published experimental results.
α
Cl
Selig et al. [1]
12.17°
1.215
McGhee et al. [2]
12.09°
1.174
Code_Saturne – LES DSM
12°
1.309
Code_Saturne – LES WALE
12°
Table 1: Comparison of lift and drag coefficient
Cd
0.0733
0.0510
Laminar Separation Reattachment
Turbulent Separation
McGranahan et al. [3]
0
0.05
0.45
Code_Saturne – LES DSM
0.002
0.0182
0.600
Code_Saturne – LES WALE
Table 2: Comparison of laminar sepration, reattachment, and turbulent separation points, values are nondimensionalised by the chord length
Figure 1: Streamlines of the time averaged flow field and
the time averaged pressure field
Figure 2: Iso-surfaces of Lambda-2 criterion illustrating the
vortical structures
Figure 3: Streamlines of the time averaged flow field and the
time averaged pressure field at the leading edge
Figure 4: Pressure coefficient
References
[1] Selig, M. S., and McGranahan, B. D., “Wind Tunnel Aerodynamic Tests of Six Airfoils for Use on Small Wind
Turbines,” NREL/SR-500-34515, Oct. 2004.
[2] McGhee, R. J., Walker, B. S., and Millibard, B. F., “Experimental Results for the Eppler 387 Airfoil at Low
Reynolds Numbers in the Langley Low-Turbulence Pressure Tunnel,” NASA TM-4062, 1988.
[3] McGranahan, B. D., and Selig, M. S., “Surface Oil Flow Measurements on Several Airfoils at Low Reynolds
Numbers,” AIAA Applied Aerodynamics Conference, AIAA, Orlando, FL, 2003, pp. 1-18.
[4] “Code_Saturne 4.0.0 Theory Guide,” EDF R&D, April 2015.