Design of Combustor Cooling Slots for High Film Effectiveness: Part I—Film General Development

The metal liners of gas turbine engine combustors usually have to be provided with some form of thermal protection from the high temperatures of the reacting mixture of gases contained therein. For aircraft gas turbines, where weight is a factor, the protective medium is air. The air is most usually introduced by tangential injection as a discrete film at a number of axial stations along the combustor liner so that as the cooling potential of one film is depleted it is periodically renewed by another. Although invariably referred to as film cooling, the most important function of the film air is to act as a relatively cool barrier between the vulnerable liner and the reacting gases. The design margin for error is very small. Failure to design a cooling slot that provides a high film effectiveness can result in thermal damage to the liner. Manufacturing considerations almost always determine how a real slot design is reduced to practice. The resulting liners (inner and outer in the case of an annular combustor) contain no two slots that are exactly alike in aerodynamic behavior and, therefore, in film effectiveness performance. Phenomenological models of the film cooling process are invariably based on considerations of two-dimensional shear mixing. Empirical factors may be introduced to account for the differences in performance existing between two-dimensional film slots and real slots. However, such methods are not of much help in designing a slot configuration that will deliver good performance, for making comparative evaluations of competing designs, or in establishing the performance penalties associated with compromises made for manufacturing reasons. Heuristic arguments are used to derive a dimensionless grouping of internal geometric parameters that describe the lateral aerodynamic uniformity of the films produced by practical slots. It is assumed that the average film effectiveness is uniquely related to the film lateral uniformity. Experimental data from a number of different practical slot designs are examined in terms of this geometric mixing parameter, and film effectiveness is shown to depend on it over a wide range of axial distances and film blowing ratios. It is concluded that the geometric mixing parameter provides a means to differentiate good film cooling slot designs from poor ones.