Isentropic Swirling Flow Through Supersonic Nozzles - Part I (free Vortex Flow)

Abstract

An analytical model has been developed and an approximate solution for the free vortex swirling supersonic flow through nozzles. Earlier work by Mager, is potential flow based. In the present model swirl number has been redefined to confine the flow properties within the valid range. Flow properties are always determined by the total conditions (P0 and a0), nozzle profile and swirl intensity as in the case of one-dimensional flow. Integral form of the continuity equation has been used in order to satisfy the boundary conditions, since radial velocity component is ignored. For free vortex case, it has been shown that there exists a minimum radius along the length of the nozzle at which the density is zero and flow seems to be void causing reasonable blockage to the flow at throat. In defining the non-dimensional swirl number (β), axial velocity at each section was employed for non-dimensionalization as compared to Mager’s definition of using a global constant to find swirl number (α). The variations of performance parameters of the nozzle such as co-efficient of discharge (Cd) thrust efficiency (ηs) and impulse efficiency (ηI) and flow field parameters such as density, pressure, velocity etc. are presented as a function of swirl numbers (α, β) and compared with the available experimental data. The swirl numbers (α, β) are also correlated.