VECTOR POLAR METHOD FOR THE EVALUATION OF WAVE INTERACTION PROCESSES
Abstract
Vector polar method is a graphical technique for the solution of wave interaction problems that are concerned with the overall results rather than with the progress of the process. The method is based on the use of wave polars, that is diagrams representing the loci of states attained by a given wave process in a coordinate system of which one component is pressure or velocity of sound and the other is particle velocity. Furthermore, if the ratio of pressures or sound speeds is represented on a logarithmic scale, usually as the ordinate, while the abscissa represented the change in particle velocity across the wave in a linear scale, then such a generalized hodograph plane has the property of a vector field, that is, the change of state brought about by the wave action is expressed in terms of a vector between the origin and any point of the polar. By simple vector addition one can then evaluate rapidly some quite complex wave interaction processes. The utility of the method is illustrated by a variety of shock-tube problems involving interactions between shocks, deflagrations, rarefaction waves, contact discontinuities and area change. Although the analysis of most of such problems is known, the application of the vector polar method led to the discovery of some interesting regimes of solutions that would be difficult to discern by the more laborious conventional techniques.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1964
- Accession Number
- AD0622843
Entities
People
- A. J. Laderman
- A. K. Oppenheim
- P. A. Urtiew
Organizations
- University of California, Berkeley