Numerical Study of Reduced Frequency Effect on Longitudinal Stability Derivatives of Airfoil under Pitching and Plunging Oscillations


  • Vahid Nasr Esfahani Amirkabir University of Technology (Tehran Polytechnic)
  • Mahmoud Mani Amirkabir University of Technology (Tehran Polytechnic)


Oscillating airfoil, Pitching oscillation, Plunging oscillation, Stability Derivatives, Co-located method


In this study, incompressible, unsteady and turbulent flow over an airfoil with pitching and plunging oscillations is numerically studied in order to investigate the effect of reduced frequency on stability derivatives of oscillating airfoil. Linear k – ε model called Launder-Sharma and Rhie and Chow model are used for turbulence modeling and overcoming pressure checkerboard problem. This means that a co-located approach is proposed in this paper to study a moving grid problem, and the results demonstrate the high accuracy of the method. Control volume and Crank-Nicholson discretization method are also used for the numerical solution. It is shown that the longitudinal stability derivatives of plunging and pitching motions trend change intensively beyond the stall angle of attack while pitching rate has a completely opposite behavior. The results also show that increasing reduced frequency leads to stability reduction in plunging oscillation but it does not have significant effect on pitching oscillation case in pre-stall, stall and post-stall conditions. Grid convergence is examined to assess the accuracy of the numerical method that shows the high accuracy of it and this is a prominent achievement of the present study. The results of the proposed method in forces and moment show a good agreement with the experimental data.

Author Biographies

Vahid Nasr Esfahani, Amirkabir University of Technology (Tehran Polytechnic)

Aerospace Engineering Department 


Mahmoud Mani, Amirkabir University of Technology (Tehran Polytechnic)

Professor, Aerospace Engineering Department






Original Papers