Accession Number : AD0115007

Title :   ON THE ''TRIPLE POINT'' IN SHOCK-DIFFRACTION PROBLEMS,

Corporate Author : CORNELL UNIV ITHACA N Y GRADUATE SCHOOL OF AEROSPACE ENGINEERING

Personal Author(s) : Sun,Tien-Fun

Report Date : SEP 1956

Pagination or Media Count : 122

Abstract : A study is made to determine (1) the flow inside the diffracted wave that originates when a horizontally advancing plane straight shock encounters an infinitely long wedge, (2) the position and strength the diffracted wave, and (3) the way the diffracted wave reinforces or attenuates the incident or the reflected shock at the triple points were it intersects them. Only weak incident shocks are considered. A nonviscous adiabatic flow is assumed. Consideration is given to the differential equations governing the flow inside the field, the shock position and its strength in 2-dimensional flow, and shocks diffracted by a right-angle wedge. A pole-type sigularity at the triple point is obtained even with a more general expansion of the conical coordinates r and that used by Lighthill (Phil Mag. 40:1202, 1949). A transition function is introduced to remove the pole singularity by connecting the discontinuous boundary values. The pressure and velocity components are then expressed in terms of transition function. The magnitude of the first-order approximations thus obtained is uniformly correct in the triple-point region, although the approximations themselves may not be complete. A set of simultaneous nonlinear integro-differential equations governing the transition function and the shock position is obtained for the tangential and normal shock conditions. A numerical solution based on polynomial approximations is obtained which shows fairly good agreement with experimental data. (Author)

Descriptors :   *SHOCK WAVES, DIFFRACTION, MATHEMATICAL ANALYSIS, REFLECTION, WEDGES

Distribution Statement : APPROVED FOR PUBLIC RELEASE