**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} ~10^{5}), 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