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A New Irreducible Dynamic Nonlinear Tensor-Diffusivity SGS Heat-Flux Model for LES of Convective Flows

DOI: 10.1615/ICHMT.2006.TurbulHeatMassTransf.590
pages 315-318

Bing-Chen Wang
Department of Mechanical & Manufacturing Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada

Jing Yin
Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, SK, S7N5A9, Canada

Eugene Yee
Defence Research & Development Canada − Suffield P.O. Box 4000, Medicine Hat, Alberta, T1A 8K6, Canada

Donald J. Bergstrom
Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, SK, S7N 5A9, Canada


In this paper, two new dynamic linear and nonlinear tensor diffusivity models are proposed for representing the subgrid-scale (SGS) heat flux (HF). The constitutive relation for the first model is based on Noll's formulation, which provides a nonlinear tensor diffusivity and is complete and irreducible. The first model represents a general formulation for SGS HF modelling based on the resolved strain rate tensor and temperature gradient vector. The constitutive relation for the second model is based on the linear subset of the Noll's formulation, which provides a general nonhomogeneous linear tensor diffusivity. Both proposed models are general in terms of the tensor polynomial expression and include the conventional dynamic eddy diffusivity model of Moin et al. [Phys. Fluids A, 3:2746-2757, 1991] and the dynamic homogeneous linear tensor diffusivity model of Peng and Davidson [Int. J. Heat Mass Trans., 45:1393-1405, 2002] as special cases. In contrast to the conventional SGS HF modelling approaches, the proposed models admit nonlinearity in tensor diffusivity, more degrees of freedom in tensor representation and non-alignment between the SGS HF and resolved temperature gradient, and therefore, allow for a more realistic geometrical representation of the SGS heat flux for large eddy simulation of thermal convection.

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