Accuracy of M²-Expansion Solution of the Flow past a Circular Cylinder

Abstract

Theoretical test for the accuracy of the M²-expansion solutions to subsonic flow problems has been made by taking the simplest and basic case of the flow past a circular cylinder without circulation. Imai’s equation of two-dimensional compressible flow is used for this purpose and the velocity q is assumed to bear the characteristics of the M²-expansion solutions of this particular flow problem. It is shown then that, under a certain condition, all q’s satisfying the above equation approximately do not differ much as to their magnitudes. This property which is called the ‘appropriateness’ of the equation is utilized to check the accuracy of the M²-expansion solutions, leading to an error estimate in terms of the free stream Mach number M and the adiabatic index γ.