This paper reports on the prediction of heat transfer in a fully developed turbulent flow in a straight rotating channel with blowing and suction through opposite walls. The channel is rotated about its spanwise axis; a mode of rotation that amplifies the turbulent activity on one wall and suppresses it on the opposite wall leading to reverse transition at high rotation rates. The present predictions are based on the solution of the Reynolds-averaged forms of the governing equations using a second-order accurate finite-volume formulation. The effects of turbulence on momentum transport were accounted for by using a differential Reynolds-stress transport closure. A number of alternative formulations for the difficult fluctuating pressure–strain correlations term were assessed. These included a high turbulence Reynolds-number formulation that required a “wall-function” to bridge the near-wall region as well as three alternative low Reynolds-number formulations that permitted integration through the viscous sublayer, directly to the walls. The models were assessed by comparisons with experimental data for flows in channels at Reynolds-numbers spanning the range of laminar, transitional, and turbulent regimes. The turbulent heat fluxes were modeled via two very different approaches: one involved the solution of a modeled differential transport equation for each of the three heat-flux components, while in the other, the heat fluxes were obtained from an explicit algebraic model derived from tensor representation theory. The results for rotating channels with wall suction and blowing show that the algebraic model, when properly extended to incorporate the effects of rotation, yields results that are essentially identically to those obtained with the far more complex and computationally intensive heat-flux transport closure. This outcome argues in favor of incorporation of the algebraic model in industry-standard turbomachinery codes.
This paper is concerned with the prediction of heat transfer rates in fully-developed turbulent flows in straight channels with mass transfer by suction and blowing through opposite walls, and with rotation about the spanwise axis. The predictions are based on the solution of the Reynolds-averaged forms of the governing equations using a second-order accurate finite-volume formulation. The effects of turbulence on momentum transport were accounted for by using turbulence closures based on the solution of modeled differential transport equations for the Reynolds stresses. A number of alternative models were assessed. These included a high turbulence Reynolds-number model in which the computationally-efficient ‘wall-function’ approach was used to bridge the near-wall region. As the effects of stabilizing system rotation can cause flow relaminarization, the wall-function approach becomes unreliable and integration must be carried out through the viscous sub-layer, directly to the walls. The suitability of three alternative low Reynolds-number models was assessed in these flows. Experimental data from flows in stationary channels with Reynolds numbers spanning the range of laminar, transitional and turbulent regimes were also used in this assessment. Excellent predictions of the wall skin-friction coefficient across the entire range were obtained with a low Reynolds-number model in which the effects of a rigid wall on the fluctuating pressure field in its vicinity were accounted for by a method which incorporates the gradients of the turbulence length scale and the invariants of turbulence anisotropy. For the cases of heated flows, two very different models for the turbulent heat fluxes were examined: one involved the solution of a differential transport equation for each component of the heat-flux tensor and another in which the heat fluxes were obtained from an explicit algebraic model derived from tensor representation theory. It was found that the two models yielded results that were essentially similar and in close agreement with results from recent Direct Numerical Simulations.
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