THE COMPUTATION OF FLOW AND HEAT TRANSFER THROUGH SQUARE-ENDED U-BENDS, USING LOW-REYNOLDS-NUMBER MODELS

Abstract

This study is concerned with the computation of turbulent flow and heat transfer in U-bends of strong curvature. Following the earlier studies within the authors’ group on flows through round-ended U-bends, here attention is turned to flows through square-ended U-bends. Flows at two Reynolds numbers have been computed, one at 100,000 and the other at 36,000. In the heat transfer analysis, the Prandtl number was either 0.72 (air) or, in a further departure from our earlier studies, 5.9 (water). The turbulence modelling approaches examined, include a two-layer and a low-Re k-1 model, a two-layer and a low-Re version of the basic differential stress model (DSM) and a more recently developed, realisable version of the differential stress model that is free of wall-parameters. For the low-Re effective viscosity model (EVM) and DSMs, an alternative, recently proposed length-scale correction term, independent of wall distance has also been tested. Even the simplest model employed – two-layer EVM – reproduces the mean flow development with reasonable accuracy, suggesting that the mean flow development is mainly influenced by mean pressure rather than the turbulence field. The heat transfer parameters, on the other hand, show that only the low-Re DSMs produce reliable Nusselt number predictions for both Prandtl numbers examined. The Emerald Research Register for this journal is available at The current issue and full text archive of this journal is available at www.emeraldinsight.com/researchregister www.emeraldinsight.com/0961-5539.htm Nomenclature c1, c2, c w 1 ; c w 2 ; c1, c 0 1, c2, c 0 2 1⁄4 turbulence modelling constants ct, cm 1⁄4 coefficients f1, f2, fm, fH, fJ 1⁄4 damping functions fw1, fw2, fw3, f 0 w1, fRt, f 0 Rt, f 00 Rt, fA 1⁄4 coefficients in the Craft/NYap model k 1⁄4 turbulent kinetic energy NYap 1⁄4 new, differential, Yap correction term P 1⁄4 pressure Pij 1⁄4 production rate of the Reynolds stress Pr 1⁄4 Prandtl number T, t 1⁄4 mean, fluctuating temperature Ui, i 1⁄4 1; 2; 3 1⁄4 contravariant velocity components uiuj 1⁄4 Reynolds stress tensor uit 1⁄4 turbulent heat flux xi,i i 1⁄4 1; 2; 3 1⁄4 Cartesian coordinates Computation of flow and heat transfer