Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)

Department / School

Mechanical Engineering


A theoretical investigation of the shock wave stability applicable to "sonic" and supersonic inlets is presented. It is assumed that the boundary layer remains attached and that the principal sources of instability are the acoustic wave reflections from the shock wave and the face. The analysis is based on linearized one-dimensional flow theory and involves the solution of the wave equation with variable coefficients. The solution is obtained by series expansion. The results suggest that shock stability is mainly dependent on the shock strength and to a certain extent on the area distribution. For a given geometry, increasing the shock strength increases the shock stability. For strong shocks parabolic diffusers are found to be generally more stable than bell-shaped diffusers, whereas bell-shaped diffusers are more stable for weak shocks. The present solution was found to compare favorably with existing information in this field and reduces to the known solution of a constant area duct. The present method of solution can also be adapted to the case of a supersonic inlet and the same method of approach can be applied to certain two-dimensional supersonic flow problems, since the governing differential equations are of the same form.

Library of Congress Subject Headings

Shock waves



Number of Pages



South Dakota State University