Analytical extension of curved shock theory

• Published in: Shock waves Vol. 28; no. 2; pp. 417 - 425
• Main Author: Emanuel, G.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2018; Springer Nature B.V
• Subjects: Acoustics; Condensed Matter Physics; Curvature; Differential geometry; Downstream effects; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Euler-Lagrange equation; Fluid- and Aerodynamics; Heat and Mass Transfer; Mathematical analysis; Original Article; Shock waves; Thermodynamics; Two dimensional flow; Unsteady flow; Upstream; Vorticity; Curved shock theory; Shock jump relations; Imperfect gas; Unsteady flow; Intrinsic coordinate Euler equations; Three-dimensional flow
• ISSN: 0938-1287; 1432-2153
• DOI: 10.1007/s00193-017-0735-7

Curved shock theory (CST) is limited to shock waves in a steady, two-dimensional or axisymmetric (2-Ax) flow of a perfect gas. A unique feature of CST is its use of intrinsic coordinates that result in an elegant and useful formulation for flow properties just downstream of a shock. For instance, the downstream effect of upstream vorticity, shock wave curvature, and the upstream pressure gradient along a streamline is established. There have been several attempts to extend CST, as mentioned in the text. Removal of the steady, 2-Ax, and perfect gas limitations, singly or in combination, requires an appropriate formulation of the shock wave’s jump relations and the intrinsic coordinate Euler equations. Issues discussed include flow plane versus osculating plane, unsteady flow, vorticity, an imperfect gas, etc. The extension of CST utilizes concepts from differential geometry, such as the osculating plane, streamline torsion, and the Serret–Frenet equations.