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Invariants and asymptotics of axisymmetric swirling submerged jets. (English. Russian original) Zbl 1451.76042

J. Appl. Mech. Tech. Phys. 61, No. 2, 235-249 (2020); translation from Prikl. Mekh. Tekh. Fiz. 61, No. 2, 92-108 (2020).
Summary: An axisymmetric laminar swirling jet of a viscous incompressible fluid flowing from a rotating semi-infinite tube in space filled with the same fluid is explored. The inner surface of the tube rotates with a constant angular velocity, and the outer surface is stationary or rotates with the same angular velocity. It is shown that in the first case, the flow field far from the tube orifice is described by the Loitsyansky asymptotic solution, and in the second case (with weak coflow), it is described by the Long-Gol’dshtik-Zubtsov self-similar solution. The Gol’dshtik hidden invariant is generalized to arbitrary axisymmetric swirling jets, and its influence on the jet asymptotics is studied. Strongly swirling jets are calculated, and the dependence of the parameters of the recirculation zone (vortex breakdown in a swirling jet) on the swirl number and the Reynolds number is examined.

MSC:

76D25 Wakes and jets
76U05 General theory of rotating fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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