The Optimal Distribution of Chordwise Rib Fin Arrays for Blade Tip Cap Underside Cooling

A fundamental question in the design of fin-augmented heat transfer surfaces is how to determine the optimal spacing between the fins. It has already been demonstrated that considerable heat transfer augmentation in the underside of a high-pressure turbine (HPT) blade tip cap can be achieved using arrays of discrete shaped pins (Bunker, 2008, “The Augmentation of Internal Blade Tip-Cap Cooling by Arrays of Shaped Pins,” ASME J. Turbomach., 130(4), p. 041007). However, it is desirable to predict the maximum heat transfer augmentation that can be achieved by installing the array of fins and the geometric arrangement (fin-to-fin spacing) that has to be used to achieve such augmentation. In this paper chordwise parallel ribs installed on the underside of a blade tip cap are studied. The objective is to maximize the overall thermal conductance between the fin array and the surrounding fluid. The optimization is performed numerically in the range 25,000 < Re < 100,000 and Pr = 0.72. The behavior of the optimal spacing data is explained and correlated analytically using the method of intersecting the two asymptotes: small spacing and large spacing heat transfer (Bejan and Morega, 1994, “The Optimal Spacing of a Stack of Plates Cooled by Turbulent Forced Convection,” Int. J. Heat Mass Trans., 37, pp. 1045–1048).