Higher-order axial singularity distributions for potential flow about bodies of revolution

Abstract

The approach of using axial singularity distributions of different orders for representing bodies of revolution in axial flow to solve both the direct and inverse problems has been developed and critically evaluated. A polynomial of arbitrary degree is used to represent the variation of the intensity of the source distribution over each element. The effects of the order of the distribution, the number of elements, the normalization of the body coordinates, the fineness ratio and the geometry of the profile on the performance of the method have been studied in detail by using a number of test cases of known solutions. With appropriate choice of these parameters, this approach for both the direct and inverse axisymmetric problems can be as accurate as the surface singularity approach even for simple bodies with inflection points. However, the present scheme has the advantage of being much simpler and faster. A new technique has been developed for the calculation of the body radius in the authors' iterative inverse problem scheme. This technique proved to be essential for velocity distributions representing bodies with inflection points. Such bodies are of great interest in the design of low drag shapes.