Problem C3.3. Transitional Flow over a SD7003 Wing
This test case is aimed at characterizing the accuracy and performance of high-order solvers for the prediction of complex unsteady transitional flows over a wing section under low Reynolds number conditions. Of particular interest is the evaluation of so-called Implicit Large-Eddy Simulation (or ILES) approaches for handling, in a seamless fashion, the mixed laminar, transitional and turbulent flow regions encountered in these low-Re applications. The unsteady flow is characterized by laminar separation, the formation of a transitional shear layer followed by turbulent reattachment. In a time-averaged sense, a laminar separation bubble (LSB) is formed over the airfoil.
The governing equations are the full 3D compressible Navier-Stokes equations with a constant ratio of specific heats of 1.4 and Prandtl number of 0.72. Solutions obtained employing the fully incompressible Navier-Stokes equations are also desired. Given the low value of Reynolds number being considered, emphasis is placed on ILES approaches; however, methodologies which incorporate dynamic sub-grid-scale (SGS) models are also of interest.
The wing section is based on the Selig SD7003 airfoil profile shown in Fig. 1. This airfoil which was originally designed for low-Reynolds number operation (Rec ~105), has a maximum thickness of 8.5% and a maximum camber of 1.45% at x/c = 0.35. The original sharp trailing edge has been rounded with a very small circular arc of radius r/c ~ 0.0004 in order to facilitate the use on an O-mesh topology. The precise profile geometry will be provided to all participants. The flow is considered to be homogeneous in the spanwise direction with periodic boundary conditions being imposed over a width s/c = 0.2.
Mach number M=0.1
Reynolds number based on wing chord, Rec = 60,000.
Angle of attack:
Case 1. a = 4 deg., which corresponds to a relatively long LSB
Case 2. a = 8 deg., which corresponds to a shorter LSB
Far field boundary: subsonic inflow and outflow. This boundary should be located very far from the wing at a distance of ~ 100 chords
Airfoil surface: no slip isothermal wall conditions with Twall/Tinf = 1.002
1. Time-averaged and spanwise-averaged flow variables and turbulent statics need to be provided in the vicinity of the airfoil. A given length of time will be specified to gather these statistics following a certain period of time to guarantee evacuation of transient effects
2. Comparison of mean u-velocity and Reynolds stresses (u’u’, u’v’, v’v’) at prescribed chordwise stations
3. Mean aerodynamic coefficients (Cl, Cd and Cm)
4. Mean surface Cp
5. Frequency spectra for velocity a selected points
6. Computational requirements