A new k-ϵ eddy viscosity model for high reynolds number turbulent flows

Publisher Summary This chapter presents a discussion on jet impingement heat transfer. The chapter describes the applications and physics of the flow and heat transfer phenomena, available empirical correlations and values they predict, and numerical simulation techniques and results of impinging jet devices for heat transfer. The relative strengths and drawbacks of the Reynolds stress model, algebraic stress models, shear stress transport, and v 2 f turbulence models for impinging jet flow and heat transfer are compared in the chapter. The chapter provides select model equations as well as quantitative assessments of model errors and judgments of model suitability. The review of recent impinging jet research publications identified a series of engineering research tasks that are important for improving the design and resulting performance of impinging jets: (1) clearly resolve the physical mechanisms by which multiple peaks occur in the transfer coefficient profiles, and clarify which mechanism(s) dominate in various geometries and Reynolds number regimes, (2) develop a turbulence model, and associated wall treatment if necessary, that reliably and efficiently provides time-averaged transfer coefficients, (3) develop alternate nozzle and installation geometries that provide higher efficiency, meaning improved Nu profiles at either a set flow or set blower power, and (4) further explore the effects of jet interference in jet array geometries, both experimentally and numerically. This includes improved design of exit pathways for spent flow in array installations.

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Jet Impingement Heat Transfer: Physics, Correlations, and Numerical Modeling

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A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.

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Tsan-Hsing Shih

Papers

A New K-epsilon Eddy Viscosity Model for High Reynolds Number Turbulent Flows: Model Development and Validation