TRANSONIC DECOMPOSITION FOR THE PROBLEM OF FLOW AROUND A THREE-DIMENSIONAL WING
Keywords:
Transonic aerodynamics, small perturbation method, velocity potential, Karman–Guderley equation, asymptotic expansion, transonic similarity parameter, shock wave, Kutta–Zhukovsky conditionAbstract
This article explores the mathematical formalism of the asymptotic expansion of the full velocity potential equation for steady-state transonic gas flows. The authors develop the classical transonic small-perturbation theory (the Karman-Guderley equation) by constructing a hierarchical recurrent system of differential equations up to and including fourth-order approximation. The method is based on simultaneous limiting with respect to the relative airfoil thickness and the Mach number at infinity, as well as on the introduction of scale stretchings of the transverse coordinates. A closed boundary value problem for flow past a three-dimensional wing is formulated, including linearized impermeability boundary conditions, the Kutta-Zhukovsky condition, and dynamic compatibility conditions on shock waves.
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