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Kinetic Approachbased Investigation of TaylorGörtler Instability in Jets
Mathematics and Mathematical Modelling # 01, February 2016
DOI: 10.7463/mathm.0116.0833621
authors: O.I. Rovenskaya^{1,*}, V.V. Aristov^{1}, T.I. Farkhutdinov^{2}
 ^{1} Federal Research Centre "Information and Management" of the Russian Academy of Sciences, Moscow, Russia ^{2} Moscow Institute of Physics and Technology, Moscow, Russia 
The aim of the paper is to study the unstable processes in free supersonic unstable jet flows. The direct method of solving a kinetic equation is used. For numerical solution the finitedifferent schemes are applied. To perform parallel computations a supercomputer MVS100K is used. The maximum number of processors was 480. A mechanism of instability for a supercritical regime for 3D flows is investigated. Solutions of these problems are made for flows in a wide range of Knudsen number Kn with different aspect ratio of the orifice (square and rectangular forms). Mach number M_{a} = 1.4 and a ratio of pressure in the orifice and the background pressure n_{p} = 3.16. Comparison with results of known experiments is made. In calculations we have observed that for a subcritical regime with the large Knudsen numbers (small Reynolds numbers) a vorticity of the flow fields in the cross sections is equal zero. For supercritical regimes a system of streamwise pair vortices is obtained. That corresponds to theoretical and experimental data. The paper studies such a system of the TaylorGörtler vortices in different crosssections in an initial region of a jet. It presents results of numerous computations. When modeling a roughness in the nozzle orifice it has been found that the character of instability with disturbance of the symmetry in the crosssections downstream is complicated. Based on direct method to solve the kinetic equation the paper, for the first time, studies in detail the character of 3D instability. Previously, these problems were solved by continuum methods and also for some variants of flows was used the Direct Simulation Monte Carlo method. A potential field of application of the given results is theoretical and experimental investigations with more detailed, in comparison with previous studies, description of unstable supersonic flows, which show the similar features of the TaylorGörtler instability. Based on conducted study the paper comes to conclusion that the direct methods of the kinetic approach allow us to describe appropriately a mechanism of the transition to the unstable flows in supersonic jets. We believe that a further study will make it possible to show up the characteristics of turbulence in free supersonic jets. References Floryan J.M. On the Görtler instability of boundary layers. Progress in Aerospace Sciences, 1991, vol. 28, pp. 235271.
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