Comparison of Minimum Length Nozzles

Abstract

A second-order accurate method-of-characteristics algorithm is used to determine the flow field and wall contour for a supersonic, axisymmetric, minimum length nozzle with a straight sonic line. Results are presented for this nozzle and compared with three other minimum length nozzle configurations. It is shown that the one investigated actually possesses the shortest length as well as the smallest initial wall turn angle at the throat. It also has an inflection point on the wall contour, in contrast to the other configurations.

Calculation of supersonic minimum length nozzles for equilibrium flow

“…The unit processes described by Argrow and Emanuel [2] are used to construct the kernel region, the transition region, and the wall contour. The streamline corresponding to the wall contour is determined by integrating the equation, subject to the wall initial condition 19, = O* at x = 0.…”

“…This does not imply that the general method is not applicable to axisymmetric equilibrium flows. As mentioned earlier, Aldo and Argrow [I], Argrow and Emanuel [2], and Zucrow and Hoffman [15] are examples of successful application of the axisymmetric MOC for perfect and imperfect gas flows. The application of the method fails because of the centered expansion located at the MLN throat and the subsequent implementation of the MOC unit processes in a nonsimple wave region for this particular axisymmetric equilibrium flow.…”

“…The Prandtl-Meyer relation is, of course, only valid for planar two-dimensional flow. For the axisymmetric nozzle, the centered expansion at point A is locally planar at the wall, consequently the Prandtl-Meyer relation may be used [2]. The region OAB is the kernel region of the flow, which is a nonsimple wave region for both the planar and axisymmetric cases.…”

“…The method of characteristics (MOC) technique developed by Argrow and Emanuel [2] for designing minimum length nozzle (MLN) contours incorporates frozen ideal gas flow. Here the term frozen *Address for correspondence: Dept.…”

Dense Gas Flow in Minimum Length Nozzles

“…The method of characteristics (MOC) used by Argrow and Emanuel (1988) assumes an isentropic, irrotational flow of a perfect gas. The governing two-dimensional partial differential equation reduces to a set of four equations, two characteristic and two compatibility equations.…”