Modeling Swirl Evolution Inside Annular Nozzles Under Compressible Effect

Abstract

Swirling flows are widely used to increase fuel mixing in air propulsion systems, and the swirl intensity affects combustion efficiency significantly. We propose a novel one-dimensional model to predict the swirl number and directional Mach numbers for compressible swirling flows inside annular nozzles. Limitations of previous models are addressed via asymmetric wall shear stress, compressible friction factor for boundary-layer thickening, turbulent viscosity, wall heat transfer model, and so on. The proposed model is validated for turbulent flows inside convergent–divergent (CD) and straight annular nozzles. Compared to inviscid modeling, significantly improved predictions are observed. While the effects of compressible friction factor and wall heat transfer model are significant, the effect of turbulent viscosity decreases as inlet Mach number increases. The present model is applied to parametric studies to examine physical effects. For CD annular nozzles, the viscous effects on discharge coefficient and thrust efficiency are examined, and consistent results with previous studies are observed. For straight annular nozzles, the effects of primary parameters are examined. In both subsonic and supersonic cases, the axial changes of azimuthal Mach number depends mainly on the wall shear stress. In a subsonic case, the swirl number decreases to the downstream, and an optimal ratio of inner and outer radii () minimizing the swirl decay rate exists. In a supersonic case, however, the swirl number keeps increasing, and the slope increases monotonically over Gamma.