Accession Number : AD0700297

Title :   THE CALCULATION OF GAS FLOWS IN THE SUBSONIC PART OF A LAVAL NOZZLE USING APPROXIMATING POLYNOMIALS,

Corporate Author : FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO

Personal Author(s) : Danilov,Yu. M.

Report Date : 29 SEP 1969

Pagination or Media Count : 14

Abstract : An approximate solution for the flow of an ideal gas in a Laval nozzle is offered. An exact solution of the equation describing such a process is impossible because of nonlinearities. In a subsonic nozzle the basic gas dynamics equation is of the ellipital type and has no real characteristics. In addition, the region of integration is usually open, hence the initial conditions depend on the solution itself, which further complicates the problem. In the majority of cases the problem can be solved, however, by the method of indeterminate coefficients. The only necessary condition is that the contour of the nozzle be analytic and that it can be approximated by a polynomial of the n-th order. The application of this method leads to a system of algebraic equations, some of which can be nonlinear. This system, in general, is not compatible; that is to say, the solution of a number of equations from this system may not satisfy the rest. Hence, an approximate solution is needed which satisfies as closely as possible all equations of the system. Such approximate solutions can be found using the least squares method which produces a closed equation system and therefore makes a solution possible. Use of least squares method is particularly convenient if the equation system is linear. (Author)

Descriptors :   (*LAVAL NOZZLES, *NOZZLE GAS FLOW), SUBSONIC CHARACTERISTICS, APPROXIMATION(MATHEMATICS), POLYNOMIALS, LEAST SQUARES METHOD, USSR

Subject Categories : Aerodynamics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE