Theoretical solutions and physical significances for minimum ratio of total pressure loss by oblique shock

Theoretical solutions for the minimum ratio of total pressure loss are derived based on the oblique shock relation and a definition of the strength by using normal Mach number for an oblique shock. First, the governing equation for the minimum ratio of total pressure loss is formulated as a linear function of the shock angle and the corresponding deflection angle. Second, based on the analytical formulae, a new oblique shock efficiency diagram regarding the deflection angle, the shock angle and the upstream Mach number is generated. For applications of the total pressure loss, the line for minimum ratio of total pressure loss is mapped on the diagram. Then a three-dimensional contour graph is proposed to study the distribution on ratio of total pressure loss in terms of the deflection angle, the shock angle and the characteristic Mach number. Third, according to the oblique shock efficiency diagram, solutions for the upstream Mach number and the corresponding shock angle are obtained. For the same ratio of total pressure loss, these solutions have symmetrical double values properties in their domain.

Duke Scholars

Author Earl H. Dowell Thomas Lord Department of Mechanical Engineering and Materia ...