# Low Reynolds Number Aerodynamics

Fixed wing, as a miniature of large airplane wing, has deteriorating performance as its operating Reynolds number drops below 10^5. Under such low Reynolds number conditions, the boundary layer at the onset of the pressure rise may still be laminar, and thus it is unable to resist substantial adverse pressure gradients and hence flow separates. Under certain circumstances, the separated flow experiences laminar-to-turbulent transition and reattaches to form a laminar separation bubble (LSB). The laminar separation and the phenomena followed largely determine the MAV's aerodynamic performance. For this reason, fixed wing research focuses on the low Reynolds number aerodynamics, including the laminar separation bubble and the laminar-turbulent transition.

The main features of a laminar separation bubble are illustrated in the Figure below. After separation, the laminar flow forms a free shear layer, which is contained between outer edge S"T" of the viscous region and the mean dividing streamline ST'. Downstream the transition point T, turbulence can entrain significant amount of high momentum fluid through diffusion, which enables the separated flow to reattach to the wall and form a turbulent free shear layer. The turbulent free shear layer is contained between lines T"R" and T'R. The recirculation zone is bounded by the ST'R and STR. Just downstream of the separation point, there is a "dead-fluid" region, where the recirculation velocity is significantly less than the freestream velocity and the flow can be considered almost stationary. Since the free shear layer is laminar and is less effective in mixing, the flow velocity between the separation and transition is virtually constant . This is also reflected in the pressure distribution. The pressure "plateau" is a typical feature of the laminar part of the separated flow.

To gain better understanding of the fluid physics and the associated aerodynamics characteristics, we have coupled (i) a Navier-Stokes solver, (ii) the e^N transition model, and (iii) a Reynolds-averaged two-equation closure to study the low Reynolds number flow characterized with laminar separation bubble and transition. A new intermittency function suitable for low Reynolds number transitional flow incurred by laminar separation is proposed and tested. With the method, we investigate the performance of a rigid airfoil and a flexible airfoil, mounted with flexible membrane structure on the upper surface, using SD7003 as the configuration. Good agreement is obtained between the prediction and experimental measurements regarding the transition location, aerodynamic coefficients, and overall flow structures.

Experiment

CFD results

Streamlines and shear stress contours over a SD7003 airfoil. Left: AoA=4 degrees; Right: AoA=11 degrees.

**References**

- Lian, Y., and Shyy, W., "Laminar-Turbulent Transition of a Low Reynolds Number Rigid or Flexible Airfoil," AIAA Journal, Vol. 47, No. 7, 2007.