Abstract
This paper presents explicit analytical solutions of the pressure coefficient and the pressure ratio across the oblique shock and expansion waves in function of the flow deflection angle. These new explicit pressure-deflection solutions can be efficiently used in solving applied aerodynamic problems in supersonic flows, such as the aerodynamics of airfoils and wings in supersonic-hypersonic flows and the shock and expansion waves interactions, and can be also used to increase the computational efficiency of the numerical methods based on the Riemann problem solution requiring the pressure-deflection solution of the oblique shock and expansion waves, such as the Godunov method.
Highlights
The solution of many applied aerodynamic problems in supersonic flows often requires explicit solutions of the pressure ratio, or the pressure coefficient, in function of the flow deflection angle for the oblique shock and expansion waves
Several numerical methods based on the solution of the Riemann problem, such as the Godunov method, require the pressure-deflection solution of the oblique shock and expansion waves, which are usually obtained by an iterative procedure
Found in perfect agreement with the classical indirect solutions and with the numerical solutions obtained by solving iteratively the implicit equations (6a or b) and (5a), which are given in diagram and table form in References [3,4,5,6,7]
Summary
The solution of many applied aerodynamic problems in supersonic flows often requires explicit solutions of the pressure ratio, or the pressure coefficient, in function of the flow deflection angle for the oblique shock and expansion waves. Several numerical methods based on the solution of the Riemann problem, such as the Godunov method, require the pressure-deflection solution of the oblique shock and expansion waves, which are usually obtained by an iterative procedure (see for example Mateescu [1] and Loh & Hui [2] ). The aim of this paper is to obtain rigorous analytical solutions of the pressure coefficient and pressure ratio across the oblique shock waves in explicit form in function of the flow deflection angle. As a by-product, unitary third-order accurate solutions in explicit pressure-deflection form are derived for both the oblique shocks and expansion waves
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