Solution in one-dimensional approximation of the variational problem of constructing a maximum-thrust nozzle for gas-particle flow

Abstract

In view of the complexity of the exact solution to the variational problem of constructing an optimum nozzle for gas-particle flow (see, for example, [1]) its solution in the one-dimensional approximation is of interest. In certain studies of this sort, by Marble [2] and Sternin [3], in addition to the assumption of one-dimensionality, an important role is also played by additional assumptions of smallness in the differences of the gas and particle velocities (and temperatures), which characterize the dynamic and thermal lag. The resulting linearization, used in [2, 3], not only narrows still further the region of validity of the one-dimensional approximation, but also leads to certain qualitative characteristics which do not correspond to the actual flow. For example, it is found [3] that variation of the contour curvature at only a single point may yield a finite thrust increment.

In the following a solution of this problem is obtained without the additional assumptions as to smallness of the lag and the corresponding linearization.