Similarity analysis of the momentum field of a subsonic, plane air jet with varying jet-exit and local Reynolds numbers

Abstract

A similarity analysis is presented of the momentum field of a subsonic, plane air jet over the range of the jet-exit Reynolds number Reh (≡ Ubh/υ where Ub is the area-averaged exit velocity, h the slot height, and υ the kinematic viscosity) = 1500 − 16 500. In accordance with similarity principles, the mass flow rates, shear-layer momentum thicknesses, and integral length scales corresponding to the size of large-scale coherent eddy structures are found to increase linearly with the downstream distance from the nozzle exit (x) for all Reh. The autocorrelation measurements performed in the near jet confirmed reduced scale of the larger coherent eddies for increased Reh. The mean local Reynolds number, measured on the centerline and turbulent local Reynolds number measured in the shear-layer increases non-linearly following x1/2, and so does the Taylor microscale local Reynolds number that scales as x1/4. Consequently, the comparatively larger local Reynolds number for jets produced at higher Reh causes self-preservation of the fluctuating velocity closer to the nozzle exit plane. The near-field region characterized by over-shoots in turbulent kinetic energy spectra confirms the presence of large-scale eddy structures in the energy production zone. However, the faster rate of increase of the local Reynolds number with increasing x for jets measured at larger Reh is found to be associated with a wider inertial sub-range of the compensated energy spectra, where the −5/3 power law is noted. The downstream region corresponding to the production zone persists for longer x/h for jets measured at lower Reh. As Reh is increased, the larger width of the sub-range confirms the narrower dissipative range within the energy spectra. The variations of the dissipation rate (ɛ) of turbulent kinetic energy and the Kolmogorov (η) and Taylor (λ) microscales all obey similarity relationships, $\varepsilon h/U_{\rm b}^3 \sim Re_h^3$ɛh/Ub3∼Reh3, η/h ∼ Reh−3/4, and λ/h ∼ Reh−1/2. Finally, the underlying physical mechanisms related to discernible self-similar states and flow structures due to disparities in Reh and local Reynolds number is discussed.