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International Heat Transfer Conference 9

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

SPECTRAL ELEMENT-RNG SIMULATIONS OF TURBULENT HEAT TRANSFER IN COMPLEX GEOMETRIES

George Em Karniadakis
Division of Applied Mathematics Brown University, 182 George Street Providence, RI 02912, USA

Alexander Yakhot
Mechanical and Aerospace Engineering Princeton University; Department of Mechanical Engineering, Ben-Gurion University, Beersheva 84105, Israel

Steven Alan Orszag
Mechanical and Aerospace Engineering Princeton University, Princeton, NJ 08540, USA

Victor Yakhot
Mechanical and Aerospace Engineering Princeton University; Boston University

DOI: 10.1615/IHTC9.2940
pages 247-252

Abstract

In this paper, we combine RNG modeling techniques with spectral element discretization procedures to formulate algorithms appropriate for simulating turbulent heat transfer for a wide range of parameters in complex geometries. Given a velocity field and the corresponding eddy-viscosity distribution the turbulent Prandtl number is computed from the Yakhot−Orszag formula derived in [1]. The hydronamics of the flow can also be computed entirely using a similar spectral element-RNG methodology using a large-eddy or a k − ε simulation approach. Here we present preliminary heat transfer results for flow in a pipe and flow over a backward-facing step to demonstrate that the proposed formulation is general and that the same RNG model applies for both non-separated as well as separated flows without the need of determining any free constants or prescribing wall functions in the near-wall regions. The implementation of RNG heat transfer models within the framework of spectral element methods is essential, as it provides great flexibility in handling very complex geometries common in heat transfer applications with a high-degree of accuracy.

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