Rib fin effects on the overall equivalent heat transfer coefficient in a rib-roughened cooling channel

摘要

Rib-roughened cooling passages are commonly used in heat exchangers and in turbine airfoils to maintain acceptable metal temperatures in gas turbine high temperature environments. The presence of ribs on the heat exchanger walls and on the airfoil cooling walls introduces two heat transfer enhancing features- an increase in heat transfer area and a significant increase in heat transfer coefficients. Considerable amount of data are reported in open literature for the heat transfer coefficients both on the rib surface and on the floor area between the ribs. These studies cover some important geometric parameters such as the rib cross-sectional area, the rib angle with the flow direction, the rib height relative to the passage hydraulic diameter, the rib pitch-to-height ratio, the rib aspect ratio, etc. Many cooling design software tools, however, require an overall average heat transfer coefficient on a rib-roughened wall. For example, in an airfoil, dealing with a complex axial flow circuit in conjunction with 180° bends, numerous film holes, trailing-edge slots, tip bleeds, cross-over impingement, and a conjugate heat transfer problem, these tools often are not capable of handling the geometric details of the rib-roughened surfaces or local variations in heat transfer coefficient on a rib-roughened wall. On the other hand, assigning an overall area-weighted average heat transfer coefficient based on the rib and floor area and their corresponding heat transfer coefficients will have the inherent error of assuming a 100% "fin" efficiency for the ribs, i.e., assuming that rib surface temperature is the same as the rib base temperature. Depending on the rib geometry, this error could produce an overes-timation of up to 20% in the evaluated rib-roughened wall heat transfer coefficient. In this paper, a correction factor is developed that can be applied to the overall area-weighted average heat transfer coefficient that, when applied to the ribbed wall's projection area, the net heat removal is the same as that of the rib-roughened wall. To develop this correction factor, the experimental results of heat transfer coefficients on the rib and on the surface area between the ribs are combined with about 400 numerical conduction models to determine an overall equivalent heat transfer coefficient that can be used in cooling design software tools. The end result of this investigation is a correlation that encompasses most pertinent parameters including the rib geometry, rib fin efficiency, and the rib and floor heat transfer coefficients.