NDLI: Cooling Optimisation Theory: Part 1 — Optimum Wall Temperature, Coolant Exit Temperature and the Effect of Wall/Film Properties on Performance

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Kirollos, Benjamin Povey, Thomas
Copyright Year	2015
Abstract	Gas turbine cooling system design is constrained by a maximum allowable wall temperature (dictated by the material and the life requirements of the component), minimum coolant mass flow rate (the requirement to minimise cycle-efficiency cost) and uniform wall temperature (to reduce thermal stresses). 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 this paper, we consider the optimum cooling system for parts with both internal and film cooling. 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. Thus, we show that achieving uniform wall temperature achieves minimum coolant flow rate, and vice versa. The purpose is to clarify the interplay between two design requirements that are often discussed separately in the literature. The penalty (in terms of coolant mass flow) associated with cooling non-isothermal components is quantified. We show that a typical high pressure nozzle guide vane (HPNGV) operating isothermally at the maximum allowable wall temperature requires two-thirds the coolant of a typical non-isothermal vane. The optimum coolant exit temperature is also considered. It is shown analytically that the optimum coolant exit temperature depends on the balance between the mean adiabatic film cooling effectiveness, the non-dimensional mass flow rate and the Biot number of the thermal barrier coating (TBC). For the large majority of gas turbine cooling systems (e.g., a typical HPNGV) it is shown that the optimum coolant exit temperature is equal to the local wall temperature at the point of injection. For a small minority of systems (e.g., long effusion cooling systems operating at low mass flow rates) it is shown that the coolant exit temperature should be minimised. An approximation relating the wall/film properties, the non-dimensional mass flow, and the overall cooling effectiveness is derived. It is used to estimate the effect of Biot number (TBC and metal), HTC ratio and film properties on the performance of a typical HPNGV and effusion cooling system. In the companion paper, we show that designs which achieve uniform wall temperature have a particular corresponding internal heat transfer coefficient (HTC) distribution.
Sponsorship	International Gas Turbine Institute
File Format	PDF
ISBN	9780791856710
DOI	10.1115/GT2015-43668
Volume Number	Volume 5A: Heat Transfer
Conference Proceedings	ASME Turbo Expo 2015: Turbine Technical Conference and Exposition
Language	English
Publisher Date	2015-06-15
Publisher Place	Montreal, Quebec, Canada
Access Restriction	Subscribed
Subject Keyword	Cycles Temperature Cooling Approximation Metals Cooling systems Flow (dynamics) Optimization Wall temperature Design High pressure (physics) Gas turbines Thermal barrier coatings Coolants Nozzle guide vanes Film cooling Heat transfer coefficients Thermal stresses
Content Type	Text
Resource Type	Article

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