A thermodynamic model of turbulent motions in a granular material

I. Luca, Chung Fang, K. Hutter

研究成果: Article

16 引文 (Scopus)

摘要

This paper is devoted to a thermodynamic theory of granular materials subjected to slow frictional as well as rapid flows with strong collisional interactions. The microstructure of the material is taken into account by considering the solid volume fraction as a basic field. This variable is of a kinematic nature and enters the formulation via the balance law of the configurational momentum, including corresponding contributions to the energy balance, as originally proposed by Goodman and Cowin, but modified here. Complemented by constitutive equations, the emerging field equations are postulated to be adequate for motions, be they laminar or turbulent, if the resolved length scales are sufficiently small. On large length scales the sub-grid motion may be interpreted as fluctuations, which manifest themselves in correspondingly filtered equations as correlation products, like in the turbulence theory. We apply an ergodic (Reynolds) filter to these equations and thus deduce averaged equations for the mean motions. The averaged equations comprise balances of mass, linear and configurational momenta, energy, and turbulent kinetic energy as well as turbulent configurational kinetic energy. They are complemented by balance laws for two internal fields, the dissipation rates of the turbulent kinetic energy and of the turbulent configurational kinetic energy. We formulate closure relations for the averages of the laminar constitutive quantities and for the correlation terms by using the rules of material and turbulent objectivity, including equipresence. Many versions of the second law of thermodynamics are known in the literature. We follow the Müller-Liu theory and extend Müller's entropy principle to allow the satisfaction of the second law of thermodynamics for both laminar and turbulent motions. Its exploitation, performed in the spirit of the Müller-Liu theory, delivers restrictions on the dependent constitutive quantities (through the Liu equations) and a residual inequality, from which thermodynamic equilibrium properties are deduced. Finally, linear relationships are proposed for the nonequilibrium closure relations.

原文English
頁(從 - 到)363-390
頁數28
期刊Continuum Mechanics and Thermodynamics
16
發行號4
DOIs
出版狀態Published - 2004 一月 1

指紋

Granular materials
granular materials
Kinetic energy
Thermodynamics
kinetic energy
thermodynamics
Momentum
closures
Energy balance
Constitutive equations
Volume fraction
Kinematics
Turbulence
Entropy
constitutive equations
thermodynamic equilibrium
exploitation
Microstructure
emerging
constrictions

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Mechanics of Materials
  • Physics and Astronomy(all)

引用此文

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A thermodynamic model of turbulent motions in a granular material. / Luca, I.; Fang, Chung; Hutter, K.

於: Continuum Mechanics and Thermodynamics, 卷 16, 編號 4, 01.01.2004, p. 363-390.

研究成果: Article

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