Thermoviscous fluid flow in nonisothermal layer: structures, scales, and correlations
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DOI: 10.1134/S0869864320020079
Thermoviscous fluid flow in nonisothermal layer: structures, scales, and correlations * Yu.M. Kulikov and E.E. Son Joint Institute for High Temperatures RAS, Moscow, Russia E-mail: [email protected]; [email protected] (Received July 2, 2019; revised September 6, 2019; accepted for publication November 6, 2019) The paper studies turbulent mixing in thermoviscous fluid flow in a 3D cubic domain which is extended periodically in two directions (X and Y). The flow turbulization develops under the impact of two-dimensional chaotic disturbances at mass average Reynolds number Re1 = 4704. The vortex field structure is discussed in terms of an isosurface of Q-criterion and local enstrophy ζl. For the advanced stages of flow evolution, the study considers Eulerian correlation coefficients for velocity fluctuations (auto-correlation functions) and the cross-correlations of pressure and temperature. The Eulerian correlation coefficient is split for analysis of correlation characteristics in periodicity and wallnormal directions. The integral scale is evaluated depending on the distance to the walls. The flow analysis is performed in the terms of viscous scale. The mesh resolution is evaluated for the flow regions corresponding to the logarithmic boundary layer and the near-wall thermal layers. Keywords: thermoviscosity, Q-criterion, enstrophy, velocity autocorrelation functions, cross-correlation functions, hairpin vortex, Eulerian correlation coefficient, correlation length, integral scale, friction velocity, Reynolds scaling.
Introduction Developing the turbulence theory in XX century scientists have elaborated several approaches to this problem [1]. The primary approach was statistical one considering the turbulence as a purely random phenomenon to relate the statistical and physical properties of flow (the Boussinesq hypothesis, eddy viscosity turbulence model). The relation between physical and statistical properties of flow relies upon the similarity of transport processes in gas being in local-thermodynamic equilibrium state and the chaotic motion of fluid particles [2]. Further development of experimental techniques originated an approach based on the study of structures in the flow that to identify numerous types of collective motion, different types of vortices, and other coherent structures. The most recent approach is taking turbulence from a viewpoint of dynamic systems. The problem statement for the current study was described in detail in [3]. The results of this paper are based on numerical simulation of instability development for thermoviscous fluid flow in a 3D computational domain, which is periodically replicated in two directions. The free * Research was financially supported by the Russian Foundation for Basic Research (Project # 19-708-00484), State order for JIHT RAS.
Yu.M. Kulikov and E.E. Son, 2020
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Yu.M. Kulikov and E.E. Son
flow is characterized by an inflectional velocity profile. The initial velocity distribution is coherent to the temperature
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