ON THE CALCULATION OF TURBULENT HEAT TRANSPORT DOWNSTREAM FROM AN ABRUPT PIPE EXPANSION

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Abstract
A numerical study is reported of flow and heat transfer in the separated flow region created by an abrupt pipe expansion. Computations have employed an adaptation of the TEACH-2E computer program with the standard k ˜ e model of turbulence. The study has given its main attention to the simulation, from both a physical and a numerical viewpoint, of the region in the immediate vicinity, of the wall where turbulent transport gives way to molecular conduction and diffusion. As in other separated flow studies, wall resistance laws or “wall functions” used to bridge this near-wall region are based on the idea that, beyond the viscous sublayer, the turbulent length scale is universal, increasing linearly with distance from the wall. Attention to detailed modeling, however, has, it appears, produced a more satisfactory set of relations than have formerly been used. Predictions of the experimental data of Zemanick and Dougall for a diameter ratio of 0.54 show generally encouraging agreement with experiment. At a diameter ratio of 0.43 different trends are discernible between measurement and calculation, though this appears to be due to effects unconnected with the wall region studied here. For a single test case computations were made using the low-Reynolds-number form of the k ˜ ϵ model in which fine-grid, numerical computations were carried all the way to the wall. The fine grids led to excessively slow convergence and the predicted rates of heat transfer were too high by up to a factor of 5 as a result of too large predicted levels of near-wall length scale.