Second-moment and scalar flux representations in engineering and geophysical flows

Abstract

Tensor and vector representations of velocity second-moments and the scalar fluxes have long been used in the closure of the transport equations describing the motion of turbulent flows. These representations are the turbulent models or parameterizations that have been the basis for extensive research in the Reynolds-averaged Navier-Stokes approach as well as other formulations resulting in transport equations for averaged flow variables. They have led to the development of improved nonlinear eddy viscosity, algebraic Reynolds stress models and algebraic scalar flux models. Over the last two decades, the process used in developing such closures has been formalized, and this has led to models and parameterizations capable of replicating more complex flow dynamics. The intent here is to provide the reader with a summary description of a procedure that can be followed to rationally construct such explicit representations from the full transport equations for both tensor and vector quantities in general, and the velocity second-moments and the heat fluxes in particular, applicable to both engineering and geophysical flows.

Investigation of the Wall Scalar Fluctuations Effect on Passive Scalar Turbulent Fields at Several Prandtl Numbers by Means of Direct Numerical Simulations

“…This is the case for instance when the fluid density is not dependent upon temperature, when the scalar field is a mere marker of the fluid particles without mechanical action on them, or when variations of the scalar field are small enough to have negligible action on the fluid motion. Direct numerical simulation (DNS) solving all the turbulence and thermal scales of the problem is the best tool to investigate turbulent scalar fields and it allows also to validate closure models with heat transfer used in Reynolds averaged Navier-Stokes (RANS) modeling [1][2][3][4] and large eddy simulation (LES) [5].…”

Extension of the partially integrated transport modeling method to the simulation of passive scalar turbulent fluctuations at various Prandtl numbers

“…In the last step, we finally return to the physical space from partial integration of the spectrum in the wave number ranges [κ c , κ d ] to get the corresponding transport equation for the correlation of the fluctuating variable φ > φ > in the physical space. This mathematical physics formalism will be followed in the present work to derive equations for the subfilter scale of the passive scalar variance, as already performed for the dynamics of the flow field (Schiestel, 1987;Schiestel and Dejoan, 2005;Chaouat and Schiestel, 2005, 2007, 2009) by using the shape of spectra as studied by Batchelor (1959) and reinterpreted recently by Warhaft (2000).…”

“…Since the past two-decade, hybrid RANS-LES have been proposed to take benefit of both RANS and LES methods (Fröhlich andVon Terzi, 2008, Chaouat, 2017). Among these numerous hybrid RANS/LES methods, the partially integrated transport modeling (PITM) is an advanced method that has been developed in previous publications (Schiestel and Dejoan, 2005;Chaouat and Schiestel, 2005, 2009, 2012, 2013Chaouat, 2010Chaouat, , 2012Chaouat, , 2017b for simulating large eddy scale of turbulent flows out of spectral equilibrium performed on coarse grids with a mesh step corresponding to a spectral 2 cutoff wave number that may be located before the inertial zone of the Kolmogorov range. This type of approach allows continuous hybrid non-zonal simulations between near RANS regions and LES regions with seamless coupling.…”

“…After briefly recalling the basics of the PITM method, we will extend it to the study of scalar contaminant fluctuations. In the present case according to previous works of the authors Chaouat and Schiestel (2005, 2009, 2012, 2013 and Chaouat (2010Chaouat ( , 2012Chaouat ( , 2017, we will retain the second moment closure for modeling the subfilter scale stresses considering that this is the appropriate level of closure to get accurate results of complex turbulent flow fields. However a first order closure based on diffusivity models will be sufficient in a first step for modeling the scalar fluxes involved in the production of variance equation for the subfilter passive scalar (Schiestel, 2007;Hanjalic and Launder, 2011).…”

High accuracy flow simulations: Advances and challenges for future needs in aeronautics

“…The turbulence modelling is ranging from the Reynolds Averaged Navier-Stokes equations (RANS [6]) to the Direct Numerical Simulations (DNS [7,8]), pass-through Large-Eddy Simulations (LES) approaches, which reviews are done in the reference [9][10][11]. In order to extend LES to high Reynolds number flows new methods have recently been developed.…”