One-dimensional Steady-state Radial Swirling Gas Flow

Abstract

It is well known that in the case of one-dimensional ideal isentropic flows, Hugoniot's equation enables to analyze the effect of the nozzle geometry on the flow regime. In such flows it is essential that the velocity vector coincides with the longitudinal channel axis.A class of one-dimensional flows, namely axisymmetric swirling radial flows, that are typical for radial turbines and compressors, is described. A generalized Hugoniot equation was developed. Some limiting cases are analyzed and the influence of the channel configuration on the flow characteristics is examined. Four particular cases were considered: (I) flow with constant radial velocity, (2) flow with constant absolute velocity, (3) flow in a channel with parallel walls, and (4) flow with radial Mach number equal to 1.It was established that in the first case the required channel width depends only on a single parameter -the tangential Mach number Μ φ and in the second -only on the swirling angle a a (swirling parameter κ 0 ). Regarding the third case, it was found that there are limiting values of the swirling parameter κ, corresponding to M r * 0 that in turn depend on their initial values κ 0 . It was also found that increase of κ enhances the dependence of M r = M r (r). If radial Mach number equal to 1, (case 4), channel cross section area grows smaller as the channel radius increases.A set of equations relating the channel radius and its width with the gas flow parameters is derived. This set can serve as basis for determination of the channel profile.