Prediction of Turbulent Flow and Heat Transfer in a Ribbed Rectangular Duct With and Without Rotation

Abstract

The present study deals with the numerical prediction of turbulent flow and heat transfer in a 2:1 aspect ratio rectangular duct with ribs on the two shorter sides. The ribs are of square cross–section, staggered and aligned normal (90–deg) to the main flow direction. The ratio of rib height to duct hydraulic diameter equals 0.063, and the ratio of rib spacing to rib height equals 10. The duct may be stationary or rotating. The axis of rotation is normal to the axis of the duct and parallel to the ribbed walls (i.e., the ribbed walls form the leading and the trailing faces). The problem is three–dimensional and fully elliptic; hence, for computational economy, the present analysis deals only with a periodically–fully–developed situation where the calculation domain is limited to the region between two adjacent ribs. Turbulence is modelled with the k–epsilon model in conjunction with wall–functions. However, since the rib height is small, use of wall–functions necessitates that the Reynolds number be kept high. (Attempts to use a two–layer model that permits integration to the wall did not yield satisfactory results and such modelling issues are discussed at length). Computations are made here for Reynolds number in the range (30,000–100,000) and for Rotation number=0 (stationary), 0.06, and 0.12. For the stationary case, the predicted heat transfer agrees well with the experimental correlations. Due to the Coriolis induced secondary flow, rotation is found to enhance heat transfer from the trailing and the side walls, while decreasing heat transfer from the leading face. Relative to the corresponding stationary case, the effect of rotation is found to be less for a ribbed channel as compared to a smooth channel.