Application of Variational Methods to Transonic Flows With Shock Waves
Abstract
Variational methods for the approximate solution of subsonic and transonic flows of a compressible fluid before the occurrence of shock waves have been carried out in previous papers. The methods fail as soon as the shock waves occur as the flow behind the shock waves now becomes rotational and has variable entropy. Since most transonic flows are accompanied by shock waves, a method which allows for shock waves and variable entropy is necessary for the study of such flows. By modifying Bateman's variational principle for irrotational flows, it is shown that a variational principle for flows with rotation and variable entropy can be obtained. By applying this variational principle to the regions of flow behind shock waves and Bateman's original principle to the other regions in the fluid, shock equations can be directly obtained. A procedure for computing numerical solutions for such flows is suggested, and a numerical example is carried out. At high Mach number above a certain limiting value, the results show that irrotational flow fails. However, by inserting shock waves and allowing a part of the flow to be rotational, computation indicates that solution exists again.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1951
- Accession Number
- ADA380491
Entities
People
- Chi-teh Wang
- Pei-chi Chou
Organizations
- National Aeronautics and Space Administration