Prediction of Turbulent Heat Transfer in Rotating and Nonrotating Channels With Wall Suction and Blowing

Abstract

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.

Heat transfer enhancement in a ribbed channel: Development of turbulence closures

“…The model is that of [11]. It is one of several that have been proposed as alternatives to Fourier's law but it is the only one which has been extensively tested in multi-dimensional inhomogeneous shear flows [12][13][14][15]. The present study extends this model's assessment to the more difficult case of non-equilibrium separated flows.…”

“…The processes of diffusion and dissipation were modeled in the conventional way (e.g. [12,15]), the former via a gradient-transport model and the latter by the assumption of isotropic dissipation at high turbulence Reynolds numbers. The focus here is on the modeling of the fluctuating pressure-strain correlations U ij .…”

Simulation of Rotating Channel Flow With Heat Transfer: Evaluation of Closure Models

“…The explicit expressions for the Reynolds stresses from the SG and GI models are shown in Eqs. (8) and (9), respectively. In both models, the terms g 1 and g 2 are equivalent to invariants of the normalized strain-rate and rotation tensors, or S ij S ij and W ij W ij , respectively.…”

“…The following two heat flux models that we consider in this work are used frequently in engineering calculations [26]. The YWL heat flux model proposed by Younis et al [9] is an EAHFM. For EAHFM, the transport equation for u 0 i h 0 may be written as…”

“…In this work, we employ DNS to integrate the Navier-Stokes and energy equations and utilize this database to assess four RANS models proposed by (a) Reif et al [5], (b) Speziale and Gatski [6], (c) Girimaji [7], and (d) Grundestam et al [8]. We also evaluate two algebraic heat flux models proposed by (e) Younis et al [9] and (f) Abe and Suga [10]. In addition, the pressure-strain functions proposed in Refs.…”