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when I establish the density in Boussinesq hypothesis?

Abstract—Different variants for buoyancy-affected terms in k-ε turbulence model have been utilized to predict the flow parameters more accurately, and investigate applicability of alternative k-ε turbulence buoyant closures in numerical simulation of a horizontal gravity current. The additional non-isotropic turbulent stress due to buoyancy has been considered in production term, based on Algebraic Stress Model (ASM). In order to account for turbulent scalar fluxes, general gradient diffusion hypothesis has been used along with Boussinesq gradient diffusion hypothesis with a variable turbulent Schmidt number and additional empirical constant c3ε.To simulate buoyant flow domain a 2D vertical numerical model (WISE, Width Integrated Stratified Environments), based on Reynolds-Averaged Navier-Stokes (RANS) equations, has been deployed and the model has been further developed for different k-ε turbulence closures. Results are compared against measured laboratory values of a saline gravity current to explore the efficient turbulence model. Keywords—Buoyant flows, Buoyant k-ε turbulence model, Saline gravity current. I.

Abstract—Different variants for buoyancy-affected terms in k-ε turbulence model have been utilized to predict the flow parameters more accurately, and investigate applicability of alternative k-ε turbulence buoyant closures in numerical simulation of a horizontal gravity current. The additional non-isotropic turbulent stress due to buoyancy has been considered in production term, based on Algebraic Stress Model (ASM). In order to account for turbulent scalar fluxes, general gradient diffusion hypothesis has been used along with Boussinesq gradient diffusion hypothesis with a variable turbulent Schmidt number and additional empirical constant c3ε.To simulate buoyant flow domain a 2D vertical numerical model (WISE, Width Integrated Stratified Environments), based on Reynolds-Averaged Navier-Stokes (RANS) equations, has been deployed and the model has been further developed for different k-ε turbulence closures. Results are compared against measured laboratory values of a saline gravity current to explore the efficient turbulence model. Keywords—Buoyant flows, Buoyant k-ε turbulence model, Saline gravity current. I.

How to estimate a turbulent viscosity by the Boussinesq's hypothesis if the tensors are not ..

The Boussinesq hypothesis for ..

Dec 15, 2016 · you can safely use the Boussinesq approximation for the ..

In mixed convection simulations, the Boussinesq approximation [1903] considers the variation of the density only in the buoyancy term as: ( ) The question of the choice of the reference temperature has been already studied by Wang et al. [2003] for the Poiseuille-Rayleigh-Benard problem: an horizontal channel flow heated from below. They compare the solution obtained by numerical simulation using different choices of with the non Boussinesq solution. In their study they consider particulars Rayleigh and Reynolds numbers for which the flow consists of steady 3D longitudinal rolls. In the present study we consider the case where the Rayleigh and Reynolds numbers are such that the flow exhibits transverse unsteady 2D travelling wave. The numerical code "Aquilon" solves the coupled Navier Stokes and Energy equations by an unsteady, 2D finite volume method. We have considered different choices for and we have compared the heat flux at the walls obtained with the Boussinesq and non Boussinesq cases. The local results are not satisfactory in the whole domain. Globally speaking, it seems better to chose as the bottom wall temperature or the average temperature in view to compute the bottom heat flux. Otherwise better results are obtained using = for both top and bottom heat flux with a variable bottom wall temperature. So we propose a modified Boussinesq approximation in view to have a better simulation of the buoyancy force in the whole domain, writing the buoyancy force as: ( ), where is the global average temperature in the whole domain. With this hypothesis, the Boussinesq simulations are better compared with the non Boussinesq case and would permit to have a better simulation of mixed convection problem particularly when then temperature boundary conditions are not uniform in space and time.

Here, f is the molecular transfer coefficient,and Fγ is a source term for heat or substance release (or absorption). The main problem in solving the Reynolds equations and the averaged equation of scalar substance transfer is deriving the relations for,and, i.e., closing the equations for averaged values. By closure methods, the models may be divided into the models utilizing the mean velocity field and the models employing the field of mean turbulence characteristics. The first group methods (of Prandtl, Kantian, van Driest and Cebeci) were constructed based on the analogy between turbulence and molecular chaos. They involve such notions as mixing length as well as turbulent viscosity, thermal conductivity and diffusion coefficients. They presume a linear relationship between the tensor of turbulent stresses and the tensor of average deformation rates (the ), as well as between the turbulent heat (or passive admixture) flux and the average temperature (admixture concentration) gradient. The Boussinesq hypothesis has the form:

account by Boussinesq hypothesis …

the buoyancy term (Boussinesq ..

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with the Boussinesq hypothesis, ..


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