A finite-time thermodynamics of unsteady fluid flows

作者：Noack Bernd R^*; Schlegel Michael; Ahlborn Boye; Mutschke Gerd; Morzynski Marek; Comte Pierre; Tadmor Gilead

来源：Journal of Non-Equilibrium Thermodynamics, 2008, 33(2): 103-148.

DOI：10.1515/JNETDY.2008.006

Turbulent fluid has often been conceptualized as a transient thermodynamic phase. Here, a finite-time thermodynamics (FTT) formalism is proposed to compute mean flow and fluctuation levels of unsteady incompressible flows. The proposed formalism builds upon the Galerkin model framework, which simplifies a continuum 3D fluid motion into a finite-dimensional phase-space dynamics and, subsequently, into a thermodynamics energy problem. The Galerkin model consists of a velocity field expansion in terms of flow configuration dependent modes and of a dynamical system describing the temporal evolution of the mode coefficients. Each mode is treated as one thermodynamic degree of freedom, characterized by an energy level. The dynamical system approaches local thermal equilibrium (LTE) where each mode has the same energy if it is governed only by internal (triadic) mode interactions. However, in the generic case of unsteady flows, the full system approaches only partial LTE with unequal energy levels due to strongly mode-dependent external interactions. The FTT model isfirst illustrated by a traveling wave governed by a ID Burgers equation. It is then applied to two flow benchmarks: the relatively simple laminar vortex shedding, which is dominated by two eigenmodes, and the homogeneous shear turbulence, which has been modeled with 1459 modes.

• 出版日期2008
• 单位东北大学