Film Cooling Superposition Theory for Multiple Rows of Cooling Holes With Multiple Coolant Temperatures

Abstract

The classical method of superposition has been used for several decades to provide an estimate of the adiabatic effectiveness for multiple sets of already well-characterized film cooling hole rows. In this way, design work is aided by classical superposition theory prior to higher fidelity experiments or simulations that would account for fluid dynamic interaction for which superposition cannot account. In the present work, we consider the additive effects of multiple rows of coolant holes, but now also with coolant issuing at different temperatures. There are a number of ways that coolant may issue from different cooling hole rows at different temperatures, one of which is simply the necessarily different internal channels through which the coolant must pass. The film cooling effectiveness is investigated for double rows of cooling holes wherein the two rows have different coolant temperatures. A double row consisting of an upstream slot and a downstream row of 7–7–7 cooling holes were first evaluated with a single coolant temperature to demonstrate that classical superposition theory applies well to the present configuration. Superposition theory is then extended to the context of multiple coolant temperatures and a new nondimensional parameter is identified, which governs cooling performance. The theory is experimentally evaluated by independently varying the coolant temperatures of the two rows. Circumstances are identified in which the second row of cooling holes may be detrimental to cooling performance.