A New Statistical-Based Correlation for the Rib Fin Effects on the Overall Heat Transfer Coefficient in a Rib-Roughened Cooling Channel

摘要

Heat transfer coefficients in the cooling cavities of turbine airfoils are greatly enhanced by the presence of discrete ribs on the cavity walls. These ribs introduce two heat transfer enhancing features: a significant increase in heat transfer coefficient by promoting turbulence and mixing, and an increase in heat transfer area. 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. Many airfoil cooling design software tools, however, require an overall average heat transfer coefficient on a rib-roughened wall. Dealing with a complex flow circuit in conjunction with 180∘ bends, numerous film holes, trailing-edge slots, tip bleeds, crossover impingement, and a conjugate heat transfer problem; these tools are not often able to handle the geometric details of therib-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, that is, assuming that rib surface temperature is the same as the rib base temperature. Depending on the rib geometry, this error could produce an overestimation of up to 10% 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 projected rib-roughened cooling cavity walls, the net heat removal from the airfoil is the same as that of the rib-roughened wall. To develop this correctionfactor, the experimental results of heat transfer coefficients on the rib and on the surface area between the ribs arecombined with about 400 numerical conduction models to determine an overall equivalent heat transfer coefficient that can be used in airfoil cooling design software. A well-known group method of data handling (GMDH) scheme was then utilized to develop a correlation that encompasses most pertinent parameters including the rib geometry, rib fin efficiency, and the rib and floor heat transfer coefficients.