On the thermodynamic derivation of differential equations for turbulent flow transfer in a compressible heat-conducting fluid |
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Authors: | A V Kolesnichenko |
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Institution: | 1.Keldysh Institute of Applied Mathematics,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | This paper considers the modern approach to the thermodynamic modeling of developed turbulent flows of a compressible fluid
based on the systematic application of the formalism of extended irreversible thermodynamics (EIT) that goes beyond the local
equilibrium hypothesis, which is an inseparable attribute of classical nonequilibrium thermodynamics (CNT). In addition to
the classical thermodynamic variables, EIT introduces new state parameters—dissipative flows and the means to obtain the respective
evolutionary equations consistent with the second law of thermodynamics. The paper presents a detailed discussion of a number
of physical and mathematical postulates and assumptions used to build a thermodynamic model of turbulence. A turbulized liquid
is treated as an indiscrete continuum consisting of two thermodynamic sub-systems: an averaged motion subsystem and a turbulent
chaos subsystem, where turbulent chaos is understood as a conglomerate of small-scale vortex bodies. Under the above formalism,
this representation enables the construction of new models of continual mechanics to derive cause-and-effect differential
equations for turbulent heat and impulse transfer, which describe, together with the averaged conservations laws, turbulent
flows with transverse shear. Unlike gradient (noncausal) relationships for turbulent flows, these differential equations can
be used to investigate both hereditary phenomena, i.e., phenomena with history or memory, and nonlocal and nonlinear effects.
Thus, within EIT, the second-order turbulence models underlying the so-called invariant modeling of developed turbulence get
a thermodynamic explanation. Since shear turbulent flows are widespread in nature, one can expect the given modification of
the earlier developed thermodynamic approach to developed turbulence modeling (see Kolesnichenko, 1980; 1998; 2002–2004; Kolesnichenko
and Marov, 1985; Kolesnichenko and Marov, 2009) to be used in research on a broad class of dissipative phenomena in various
astro- and geophysical applications. In particular, a major application of the proposed approach is the reconstruction of
the processes in the preplanetary circumsolar disk, which might help solve the fundamental problems of stellar-planetary cosmogony. |
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