Aerodynamic shape optimization of airfoils at ultra-low Reynolds numbers

The flow over NACA 0008 airfoil is studied computationally in the ultra-low Reynolds number regime Re ∈ [1000, 10000] for various angles of attack α ∈ [0°, 8°]. The laminar flow separation occurs even at low angles of attack in this Reynolds number regime. The lift curve slope is far reduced from the inviscid thin airfoil theory value of C l,α = 2 π . Significant increase in the values of drag coefficient is seen with a decrease in Re . Lift-to-drag ratios are consequently very low. An adjoint-based aerodynamic shape optimization methodology is employed to obtain improved aerodynamic characteristics in the ultra-low Re regime. Three different objective functions are considered, namely, (i) minimization of drag coefficient, C d , (ii) maximization of lift coefficient, C l , and (iii) maximization of lift-to-drag ratio, ( C l / C d ). Significant improvement in each of the objective functions is obtained.