پيش بيني جريان و انتقال حرارت در كانال هاي ريب دار سه بعدي توسط مدل هاي K-اپسيلون خطي و غير خطي

Prediction of Three-Dimensional Flow and Heat Transfer through Ribbed Ducts Using a Non-Linear k-e Model

The present paper deals with the prediction of three-dimensional fluid flow and heat transfer in rib-roughened ducts of square cross-section. Such flows are of direct relevance to the internal cooling system of modern gas turbine blades. The main objective is to assess how a recently developed variant of a cubic non-linear k - c model (proposed by Craft et al. (1999)), that has been shown to produce reliable thermal predictions through axi-symmetric and plane two-dimensional ribbed passages (Raisee et al. (2004)), can predict flow and heat transfer characteristics through more complex three-dimensional ribbed ducts. To fulfil this objective, the present paper discusses turbulent air flow and heat transfer through two different configurations, namely: (I) a square duct with "in-line" ribs normal to the flow direction at Re = 5.0 xl04 and (II) a square duct with normal ribs in a "staggered" arrangement at Re = 1.0xl05. In this paper the flow and thermal predictions of the linear k-s model (EVM) are also included, as a set of baseline predictions. Both turbulence models have been used with the form of length-scale correction term to the dissipation rate originally proposed by ʹYapʹ and also a differential version of this term, ʹNYPʹ. The mean flow predictions show that both linear and non-linear k-c models can successfully reproduce most of the measured data for stream-wise and cross-stream velocity components. Moreover, the non-linear model, which is sensitive to turbulence anisotropy, is able to produce better results for the turbulent stresses. As far as heat transfer predictions are concerned, it was found that both EVM and NLEVM2, the more recent variant of the non-lineark-e, with the algebraic length-scale correction term, overestimate the measured Nusselt numbers for both geometries examined. While the EVM with the differential length-scale correction term underestimates heat transfer levels, the Nusselt number predictions with the NLEVM2 and the ʹNYPʹ term are in close agreements with the measured data. Comparisons with our earlier work, Iacovides and Raisee (1999), show that the NLEVM2 thermal predictions are of similar quality to those of a second-moment closure. This modified version of the non-linear k-e model, that in earlier studies was shown to improve thermal predictions in axi-symmetric and plane ribbed passages, is thus now found to also produce reasonable heat transfer predictions in three-dimensional ribbed ducts.