Computational Fluid Dynamics (CFD) is a numerical approach to modelling fluids in multidimensional space using the Navier-Stokes equations and databases of fluid properties to arrive at a full simulation of a fluid dynamics and heat transfer system.

The turbulence models employed in CFD are a set of equations that determine the turbulence transport terms in the mean flow equations. They are based on hypotheses about the process of turbulence, and as such require empirical input in the form of constants or functions, in order to achieve closure. By introducing a set of empirical constants to a model, that model then becomes valid for certain flow conditions, or for a range of flows.

Of those constants, the turbulent Prandtl number appears in multiple equations; energy, momentum, turbulent kinetic energy, turbulent kinetic energy dissipation rate, etc. and the value it takes in each equation is different and chosen empirically to fit a wide range of flows in the subcritical region. The studies that attempt to find the effect of varying the turbulent Pr number on simulation results, often only mention one number; presumably the one that appears in the energy equation (although it is never explicitly explained). The rest of the constants are treated as universally acceptable for generalized flow and not tested for their effect on flow parameters.

A numerical study on heat transfer to supercritical water flowing in a vertical tube is carried out using the ANSYS FLUENT code and employing the Realizable k-ε (RKE) and the SST k-ε turbulence models. The 3-D mesh consists of a 1/8 slice (45° radially) of a bare tube. The study explored the effects of turbulent Pr numbers, and their variations, in order to understand their significance, and to build on previous knowledge to modify the turbulence models and achieve higher accuracy in simulating experimental conditions.

The numerical results of 3D flow and thermal distributions under normal and deteriorated heat transfer conditions are compared to experimental results. The distributions of temperature and turbulence levels are used to understand the underlying phenomena of the heat transfer deterioration in supercritical water flows.

Reducing the energy turbulent Pr number produced the most accurate prediction of the deterioration in heat transfer, by altering the production term due to buoyancy, which appears in the equations for turbulent kinetic energy as well as its dissipation rate. The buoyancy forces in upward flows act to reduce the turbulent shear stress, resulting in localized increase in wall temperatures.

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