Similarity in the Far Swirling Momentumless TurbulentWake

Abstract

Turbulent swirling wakes are usually generated during flow past around a body. Swirls are inserted into the flow by propulsors and they can be formed in various technological devices. An overview of papers devoted to experimental and numerical investigations of the swirling turbulent wakes is presented in [1, 2]. The similarity laws of the swirling turbulent flow decay are investigated [3]. Asymptotic and numerical analysis of the swirling turbulent wakes was performed [4–6]. The classical k− ε model of turbulence was used in these studies. It was shown that even if the tangential component of the mean velocity is small it significantly affects the flow pattern in the turbulent wake and this influence can be traced at sufficiently large distances behind a body. The streamwise component of the excess momentum J and angular momentum M are important integral characteristics of the swirling turbulent wake. The case J = 0, M = 0 corresponds to the swirling turbulent wake behind a self–propelled body. This configuration can be implemented in a wake behind the self–propelled body of revolution (the thrust of a body propulsor compensates the hydrodynamic drag force) with compensation of the swirl introduced by a propulsor. Numerical modelling of the swirling momentumless turbulent wake (J = 0) with nonzero angular momentum was carried out on the basis of the second–order semi–empirical models of turbulence [7–9]. Furthermore, a comparison with experimental data [7] obtained in a wind tunnel in the wake past an ellipsoid of revolution was performed. The drag was compensated by momentum of a swirling jet exhausted from its trailing part and the swirl introduced by the jet was balanced out by the rotation of the body part in the opposite direction. Experimental results on the swirling turbulent wake for M ̸= 0 were presented [10–14]. It should be noted that there is a discrepancy in the results obtained by different authors.