On the Self-Preservation of Turbulence in Axisymmetric Jets

Abstract

A novel generalized framework of self-preservation for axisymmetric jets with non-constant spreading rates is applied to compressible jets, confined jets, and the intermediate region of classical incompressible jets. The framework describes less restrictive relationships among the jet thickness spreading rate, Reynolds stresses, and higher-turbulence moments via the similarity of the governing equations, providing new insight into the inherent scalings of the energetic transfer of turbulence in self-preserving flows. A particle image velocimetry experiment was designed and constructed to provide high-fidelity jet data at subsonic and supersonic speeds in both free and confined environments. In the free compressible jet, the local jet spreading rate and Reynolds shear stress are found to be attenuated with increasing convective Mach number, as in the compressible mixing layer. The anisotropy in the Reynolds stress components is found to arise from the self-preservation framework, providing an \emph{a priori} description of the effects of compressibility. The reduction in turbulence intensity is accompanied by a corresponding decrease in the pressure-gradient terms, experimentally confirming that the attenuation arises from reduced pressure fluctuations due to limitations imposed by the speed of sound. In the confined environment, compressibility-induced reductions in mixing are reflected in similar trends in the Reynolds shear stress, while the scaling between Reynolds stress components within the framework remains valid, demonstrating the intrinsic effects of compressibility on turbulence despite confinement. In the incompressible jet, the self-preservation framework is found to describe the highly anisotropic structural reorganization in the intermediate region. These results indicate that, from the perspective of the self-preservation equations, the scaling of the moments may be treated similarly across a wide range of jet flows, with the primary distinction being the different physical mechanisms that influence the Reynolds shear stress, thereby demonstrating the generalizability of the less-restrictive framework. Analysis of free jet turbulence stress budgets suggests that certain terms must be considered in groups to achieve self-preservation, with a strong scaling relationship between the pressure-gradient and Reynolds-stress–containing terms, highlighting differences between less-restrictive and classical self-preservation.