Numerical simulations of the four parameter k-w-kt-et heat transfer turbulence model in single rod and rod bundle geometries with LBE coolant

Abstract: Low Prandtl number fluids, such as heavy liquid metals, may be used as coolant for Generation IV nuclear power plants for their high conductivity and neutronic properties. These fluids show a rather different convective heat transfer behavior compare with that of ordinary fluids, such as water or gas. In such ordinary fluids various turbulence models are available to match the experimental data for flow and temperature fields. In particular it is well known that a two-equation turbulence model, for example k-e or k-w, can be used to simulate many experiments and for fluid with approximately unit Prandtl number the thermal exchange can be reproduced by considering complete similarity between velocity and thermal field. Nowdays the similarity hypothesis is assumed in almost all Computational Fluid Dynamics (CFD) codes where simple eddy diffusivity models (SED) with constant turbulent Prandtl number is implemented. In low Prandtl number fluids, the standard constant turbulent Prandtl number model fails to reproduce standard correlations build from experimental data. Nevertheless these standard correlations are commonly used by engineers to predict heat transfer in generation IV nuclear reactor cores. For this it is important to develop new heat transfer turbulent models that are able to reproduce numerically the desired behavior. The present work addresses a new effort to improve the prediction of turbulent heat flux in vertical annular and rod bundle geometries by applying the four parameter k-w-kt- et model. These numerical cases are investigated by using an in-house finite element code. The k-w turbulence model is employed for simulating the turbulent flow field right up to the wall with no wall functions since they are available only for ordinary fluids. The thermal eddy heat diffusivity can be expressed in a definite manner similar to the viscous eddy diffusivity as a function of the square temperature fluctuation kt and its dissipation rate et . These variables can be computed by solving two new transport equations. Results obtained from the four parameter k-w-kt-et model are compared with standard experimental correlations when available.