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Closure of turbulent fluxes for the transport of momentum, energy, and mass
Author(s) -
Alfradique Marcelo Ferreira,
Telles Affonso Silva
Publication year - 2006
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.10877
Subject(s) - turbulence , moment closure , closure (psychology) , reynolds stress , scalar (mathematics) , momentum (technical analysis) , closure problem , moment (physics) , time derivative , classical mechanics , constitutive equation , mathematics , mechanics , statistical physics , physics , thermodynamics , geometry , finance , economics , market economy , finite element method
Abstract The methods of extended thermodynamics are employed to establish a set of closure equations for the turbulent fields. The main advantage of its use resides in the elimination of all arbitrariness in the selection of the constitutive variables and basic model for the average fields present in the various equations for the turbulent moments. In addition, the method provides a systematic way correcting observed improprieties. Starting with the equations for the fluctuations of the velocity and of passive scalar fields, it is possible to write successive equations for the moments of increasing orders in the form of balances in terms of a time derivative, a convective flux, and a source field. The unknown terms for each order are assumed to be determined by constitutive equations given as functions, exclusively, of the moments of lower order. The only free choice is on the level of description, as determined by the order of the highest moment considered. Equations required for the two first levels, pertaining to the moments of the fluctuations of velocity, and of temperature and concentrations are presented, discussed and compared to previous models and known results. Heat and mass‐transfer effects are considered, and it is shown the existence of interference between these processes in a form analogous to the Dufour and Soret effects, with a marked anisotropy following the Reynolds stress. © 2006 American Institute of Chemcial Engineers AIChE J, 2006