Turbulent Flow and Heat Transfer in Stationary and Rotating Cooling Passages With Inclined Ribs on Opposite Walls

Abstract

This paper discusses the results of a numerical study of water flow through a straight, orthogonally rotating duct, with ribs along the leading and trailing walls, in a staggered arrangement and at an angle of 45° to the main flow direction. The rib spacing to duct height ratio (P/H) is 1, the rib height to duct height ratio (h/H) is 0.1 and the ribs are of square cross-section (h/w = 1). The two ribbed walls are heated, while the two smooth walls are thermally insulated. Flow computations have been produced using a three-dimensional, non-orthogonal flow solver, with two 2-layer models of turbulence (an effective-viscosity model and a second-moment closure), in which across the near-wall regions the dissipation rate of turbulence is obtained from the wall distance. The numerical predictions are first validated through comparisons with available flow and thermal measurements for stationary and rotating passages and are then used to explain how the inclined ribs and the orthogonal rotation influence the flow and thermal development. Flow comparisons have been carried out for a Reynolds number of 100,000 and for rotation numbers of 0 (stationary) and 0.1. Temperature comparisons have been obtained for a Reynolds number of 36,000, a Prandl number of 5.9 (water) and rotation numbers of 0 and 0.2. For the stationary case additional computations using air as the working fluid (Pr = 0.7), help to assess the effect of the molecular Prandtl number on the thermal characteristics. As we have also found in a recent study of flow through a stationary passage with inclined ribs, both 2-layer models returned similar flow and thermal predictions. The former are in close agreement with available LDA data and the latter are also consistent with available liquid crystal measurements. The flow and thermal developments are found to be dominated by the rib-induced secondary motion, which leads to strong spanwise variations in the mean flow and the local Nusselt number and to a uniform distribution of turbulence intensities across the duct. A reduction in the value of the Prandtl number, to that of air, leads to less rapid changes in the local Nusselt number, but does not change the overall thermal characteristics. Rotation causes the development of stronger secondary motion along the pressure side of the duct and also the transfer of the faster fluid to this side. As a result, along the pressure side the Nusselt number after each rib remains high across the ribbed side, while along suction side, the Nusselt number exhibits stronger reduction in the lateral direction. The flow predictions of both models are in close agreement with the rotating flow measurements. The thermal predictions, especially those of the second-moment closure, reproduce the levels and most of the local features of the measured Nusselt number, but over the second half of the rib interval over-predict the local Nusselt number.