Evaluation of wave drag reduction by flow control

An analytical expression is proposed to estimate the wave drag of an aerofoil equipped with shock control. The analysis extends the conventional approach for a single normal shock wave in the absence of control, based on the knowledge that all types of successful shock control on transonic aerofoils cause bifurcated λ-shock structures. The influence of surface curvature on the λ-shock structure has been taken into account. The extended method has been found to produce fairly good agreement with the results obtained by CFD methods while requiring negligible computational effort. This new formulation is expected to be beneficial in the industrial design process of transonic aerofoils and wings where a large number of computational simulations have to be performed.