Computational Study on the Unsteady Shock Wave Dynamics around a Circular Arc Airfoil in Transonic Internal Flow

Abstract

Self-sustained shock wave oscillations on airfoils at transonic flow conditions are associated with the phenomenon of buffeting. The physical mechanisms of the periodic shock motion are not yet fully understood even though experiments performed over fifty years ago have demonstrated the presence of oscillatory shock waves on the airfoil surfaces at high subsonic speeds. The unsteady pressure fluctuations generated by the low-frequency large-amplitude shock motions are highly undesirable from the structural integrity and aircraft maneuverability point of view. Dynamics of unsteady shock wave phenomena around a biconvex circular arc airfoil in transonic internal flow fields are often observed due to complex shock wave boundary layer interaction. Numerical model is developed to predict the self-excited shock oscillation around a biconvex circular arc airfoil in transonic internal flow. A commercial finite volume CFD package has been used for this computation. The computational domain has been discretized into a structured mesh by using a commercial preprocessing tool. The transonic flow around a biconvex airfoil is governed by the unsteady compressible Reynolds-average Navier-Stokes equation together with the energy equation. Two additional equations of κ-ω SST turbulence model have been included to model the turbulence in the flow field. Unsteady shock wave phenomena numerically studied for outlet pressure to inlet pressure ratios of 0.71–0.75. The characteristics of self-excited shock wave dynamics under various flow conditions such as total pressure ratio, free stream Mach number and so on were investigated and then used to classify the types of shock wave. The results obtained from the numerical computation have been validated with the experimental results. The various modes of shock wave motion for different flow conditions are described. The mechanisms of self-sustained shock oscillations are discussed for symmetrical circular-arc airfoils at zero incidence angles. Finally, cavity method has been used to control the shock oscillation and find its effectiveness.