Cooling Optimisation Theory: Part 2 — Optimum Internal Heat Transfer Coefficient Distribution

Abstract

Gas turbine cooling system design is constrained by a maximum allowable wall temperature (dictated by the material, the life requirements of the component and a given stress distribution), the desire to minimise coolant mass flow rate (requirement to minimise cycle-efficiency cost) and the requirement to achieve as close to uniform wall temperature as possible (to reduce thermal gradients, and stress). These three design requirements form the basis of an iterative design process. The relationship between the requirements has received little discussion in the literature, despite being of interest from both a theoretical and a practical viewpoint. In the companion paper, we show analytically that the coolant mass flow rate is minimised when the wall temperature is uniform and equal to the maximum allowable wall temperature. In this paper, we show that designs optimised for uniform wall temperature have a corresponding optimum internal heat transfer coefficient (HTC) distribution. In this paper, analytical expressions for the optimum internal HTC distribution are derived for a number of cooling systems, with and without thermal barrier coating. Most cooling systems can be modelled as a combination of these representative systems. The optimum internal HTC distribution is evaluated for a number of engine-realistic systems: long plate systems (e.g., combustors, afterburners), the suction-side of a high pressure nozzle guide vane, and a radial serpentine cooling passage. For some systems, a uniform wall temperature is unachievable; the coolant penalty associated with this temperature non-uniformity is estimated. A framework for predicting the optimum internal HTC for systems with any distribution of external HTC, wall properties and film effectiveness is outlined.