A k–Ω–kθ–

A Logarithmic Turbulent Heat Transfer Model in Applications with Liquid Metals for Pr = 0.01–0.025

“…Table 1. Values for the KLW model constants in Equations ( 8)-( 11) [22]. We define the turbulent Reynolds number R t and the non-dimensional length R δ by using the variables k and ε.…”

“…Two-equation turbulent models can be solved if appropriate boundary conditions are applied. When a near-wall approach with no wall functions is used, the boundary conditions can be computed by a near wall series expansion, as reported in [22]. In Table 2 the expansion is computed for the mean and fluctuating velocity, and for the mean and fluctuating temperature, by considering a small, plane surface area with x-z plane coordinates and y the wall distance.…”

“…The model has been validated against DNS and experimental correlation data, with simulations of Pr = 0.025 fluids for several geometries, involving plane channels, cylindrical ducts and triangle and square bundle lattices [8,19,20]. With the purpose of improving the numerical stability of the model, a change of state variables has been considered in [21], where specific dissipation rates ω and ω θ have been used in place of ε and ε θ , and in [22], where, by following the work of [23], logarithmic values of ω and ω θ , i.e., Ω and Ω θ , have been used. As a consequence of the change of state variables, some model coefficients had to be changed in order to improve the numerical stability, and the resulting models have been validated with simulations of plane channels and cylindrical ducts for Pr = 0.025.…”

A New Anisotropic Four-Parameter Turbulence Model for Low Prandtl Number Fluids

“…In [11], the thermal model has been coupled with a low-Reynolds linear k-ε model, while in [12], the coupling with a second-order Reynolds stress model has shown better results. In [13][14][15][16], an isotropic four-parameter model has been proposed. The model introduces two additional thermal transport equations for the evaluation of the squared temperature fluctuations k θ and its dissipation ε θ .…”

“…Both configurations have been tested with the isotropic four-parameter turbulence model. Plane channel simulations for several Re τ and Pr = 0.01, 0.025 have been successfully performed [13,14,16]. Numerical simulations in forced and mixed convection regimes are very promising for the backward-facing step configuration [15], however the adoption of an anisotropic formulation is required to improve the prediction of turbulent heat flux components.…”