Treatment of turbulent heat fluxes with the elliptic-blending second-moment closure for turbulent natural convection flows

An elliptic blending differential flux model for natural, mixed and forced convection

“…Assuming that L θ = L and, consequently, α θ = α in Eq. (10), as proposed by Shin et al (2008) and Choi and Kim (2008), is thus a questionable hypothesis, that we propose to avoid. Therefore, after Dehoux et al (2012), we solve an elliptic relaxation equation for α θ ,…”

“…The elliptic blending (EB) strategy, proposed by Manceau and Hanjalić (2002) for representing the effects of wall blockage on the Reynolds stresses, can be extended to the modelling of the turbulent heat fluxes, in the framework of differential flux models (DFMs), leading to the EB-DFM. In the present work, modifications of the EB-DFMs proposed by Shin et al (2008) and Choi and Kim (2008) are introduced in order to improve the predictions of the dynamic and thermal fields in forced, mixed and natural convection regimes. It can be shown, following the proposal of Dehoux et al (2012) in the framework of algebraic heat flux models, that the length scale driving the thermal elliptic blending parameter must be different from the length scale of the mechanical elliptic blending parameter.…”

“…Consistent with Manceau (2015), it can be seen that the EB-RSM very accurately reproduces the mean velocity and Reynolds stresses in a channel flow. On the contrary, using the version used by Choi and Kim (2008), in which the coefficients have been modified in order to improve the predictions in natural convection flows, the results are not satisfactory. Two eddy-viscosity models (EVMs), widely used in the industry, the k-ω-SST model of Menter (1994) model, using the stabilized formulation φ -f of Laurence et al (2005), are also used for comparison.…”

“…For mixed and natural convection, elaborate heat flux models are needed in order to account for buoyancy/turbulence interactions (Hanjalić, 2002). Shin et al (2008) and Choi and Kim (2008) proposed extensions of the elliptic blending strategy to full differential flux models (DFMs), in order to account for the influence of the wall on the turbulent heat flux. With the objective of avoiding the resolution of additional transport equations, Dehoux et al (2012) derived an implicit algebraic version of such models, called the elliptic-blending algebraic flux model (EB-AFM), which is merely a near-wall extension of the standard AFM (Dol et al, 1997).…”

“…(9). Shin et al (2008) used γ1 = 1, whereas, in order to satisfy the individual asymptotic behaviour of φ w iθ and ε w iθ , Choi and Kim (2008)…”