A finite-time thermodynamics of unsteady flows - from the onset of vortex shedding to developed homogeneous turbulence


A finite-time thermodynamics of unsteady flows - from the onset of vortex shedding to developed homogeneous turbulence

Noack, B. R.; Schlegel, M.; Ahlborn, B.; Mutschke, G.; Morzynski, M.; Comte, P.

Turbulent fluid has often been conceptualized as transient thermodynamic phase. Here, a finite-time thermodynamics (FTT) formalism [1] is proposed to compute mean flow and fluctuation levels of unsteady incompressible flows. That formalism builds upon a traditional Galerkin model which simplifies a continuum 3D fluid motion into a finite-dimensional phase-space dynamics and subsequently, into a thermodynamics energy problem. This model consists of a velocity field expansion in terms of flow configuration dependent eigenmodes and of a dynamical system describing the temporal evolution of the mode coefficients. Each mode may be considered as a wave, parameterized by a wave number and frequency. In our FTT framework, the mode is treated as one thermodynamic degree of freedom, characterized by an energy level. The dynamical system approaches local thermal equilibrium where each mode has the same energy if it is governed only by internal (triadic) mode interactions. However, the full system approaches only partial thermal equilibrium by strongly mode-dependent external interactions. In these interactions, large-scale modes typically gain energy from the mean flow while small-scale modes loose energy to the heat bath. The energy flow cascade from large to small scales is thus a finite-time transition phenomenon. The FTT model has been successfully applied to predict the cascade for flows with simple to complex dynamics. Examples include laminar vortex shedding which is dominated by 2 eigenmodes and homogeneous shear turbulence which has been modeled with 1459 modes. In addition, the onset of vortex shedding is described in the Galerkin and vortex picture as a finite time scale phenomenon.

[1] B. Andresen, P. Salamon & R.S. Berry, J. Chem. Phys. 66 (1977) 1571-1577.

Keywords: finite-time thermodynamics; vortex shedding; turbulence

  • Lecture (Conference)
    Joint European Thermodynamics Conference IX, 12.-15.06.2007, Saint Entienne, France
  • Contribution to proceedings
    Joint European Thermodynamics Conference IX, 12.-15.06.2007, Saint Entienne, France
    Proceedings, 129-132

Permalink: https://www.hzdr.de/publications/Publ-10179
Publ.-Id: 10179