, 44:130 | Cite as

Aerodynamic shape optimization of airfoils at ultra-low Reynolds numbers

  • Meedhu Geogy Ukken
  • M SivapragasamEmail author


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 Cl,α = 2π. 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, Cd, (ii) maximization of lift coefficient, Cl, and (iii) maximization of lift-to-drag ratio, (Cl/Cd). Significant improvement in each of the objective functions is obtained.


Ultra-low Reynolds number flow NACA 0008 airfoil aerodynamic shape optimization adjoint method 



reference area (m2)


airfoil chord length (m)


coefficient of drag


coefficient of lift


objective function


length of the separated region


pressure (Pa)


governing equation


Reynolds number


time (s)


thickness-to-chord ratio


velocity vector (m/s)

x, y

Cartesian coordinates


reattachment location


separation location

Greek symbols


angle of attack (deg.)


density (kg/m3)


kinematic viscosity (m2/s)


flow field variables


physical location of the boundary


Lagrange multiplier


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Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Automotive and Aeronautical Engineering, Faculty of Engineering and TechnologyM S Ramaiah University of Applied SciencesBangaloreIndia

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