Accounting for entropy production in the system of Navier-Stokes equations when describing the turbulent flow of a viscous compressible heat-conducting liquid

DOI: 10.34759/trd-2023-131-10

Аuthors

Khatuntseva O. N.

e-mail: olga.khatuntseva@rsce.ru

Abstract

To describe both laminar and turbulent flow regimes of a viscous incompressible non—heat-conducting fluid based on the same equations, the references [1-3] proposed to account for what distinguishes these two regimes from each other, namely the entropy production due to the random stochastic perturbations excitation. For this purpose, the Navier-Stokes equations (NSE) were written in a phase space expanded by introduction of an additional stochastic variable. As the result, in the left part of the equations, namely in expressions for the total time derivative, additional terms, characterized by the entropy production due to the excitation of stochastic perturbations, appeared. For laminar flow modes, entropy production adopts a zero value, additional terms vanish, and transition to the NSE in their standard form, of which solutions describe only laminar flow modes, is accomplished.

Inclusion of an extra summand in the expression for the total time derivative, characterized by entropy production (which is always non-negative), allows, in particular, accounting for the irreversibility of physical processes in time in cases where this production is non-zero. The above said applies, among other things, to the case when large values of the Reynolds number are realized and, accordingly, the value of the viscous term in the NSE tends to zero. In this case, the only term of the equation «responsible» for its irreversibility becomes an additional term in the full time derivative.

Solutions corresponding to laminar and turbulent flow regimes have been obtained analytically for Hagen-Poiseuille problems, planar Poiseuille flow and planar Couette flow. Experimental. Comparison of experimental and analytical solutions for different values of the Reynolds number was performed.

The presented article considers a more general case, using a similar approach, namely analyses how the equation of continuity; Navier-Stokes equations; the equations of total conservation of energy, and heat transfer should change, when describing the flow of a viscous compressible heat-conducting fluid, in which stochastic disturbances may occur in a wide range of scales at large values of the Reynolds number.

Keywords:

turbulent flow, viscous compressible heat-conducting liquid, laminar-turbulent transition

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