Numerical modelling of momentumless wakes using semiempirical turbulence models of second and third order

Abstract

In this paper we present numerical models of dynamics of a momentumless turbulence wake behind a body of revolution, which are based on improved second-and third-order turbulence models. We compare data of numerical experiments with experimental data.The determination of the limits of applicability of current semiempirical turbulent models, which are instruments for studying complex turbulent 3D flows, is an urgent problem. A rather nontrivial test in these numerical experiments is the classical problem of the dynamics of a momentumless turbulent wake behind a body of revolution, which has been extensively studied in the past few decades.The results of laboratory investigations of momentumless turbulent wakes behind bodies of revolution are given in a great number of papers. The most comprehensive ones are works of Naudashcer [37], Meritt [33], Aleksenko and Kostomakha [1,2] (see also [29]), Higuchi and Kubota [21], Sirviente and Patel [45], and also reviews by Schetz [44] and Pequet [39]. The self-similarity of the flow is observed at short distances from the body. The averaged velocity decreases faster than in turbulent fluctuations, so that at an appreciable distance from a body a nonshear flow regime is observed in a homogeneous medium. The construction of adequate mathematical models of the flow relies on laboratory measurements of the characteristic dimension and certain parameters of the averaged and pulsation motion, such as turbulent energy, dissipation rate, and Reynolds stress tensor components along the axis of the wake and in its cross-section. The papers of Finson [16], Ginevskii [17], Gorodtsov [18], Hassid [19], Kolovandin [24], Korneev [26], Novikov [38], and Sabelnikov [42] are devoted to theoretical analysis of the specified 3D flow. In particular, asymptotic laws of decay of the main characteristics of momentumless wakes, which are consistent with experimental data, have been derived.Numerical models of momentumless turbulent wakes behind bodies of revolution were developed in [4 -8, 13 -15, 20, 25, 29, 31, 32, 46 -49] (additional bibli-