Problem C3.3. Transitional Flow over a SD7003 Wing

Overview

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.

Governing Equations

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.

Geometry

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 (Re_c ~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.

Flow Conditions

Mach number M=0.1

Reynolds number based on wing chord, Re_c = 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

Boundary Conditions

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 T_wall/T_inf = 1.002

Requirements

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