A Simple Parametric Model for the Analysis of Cooled Gas Turbines S. Can Gülen Principal Engineer GE Energy, 1 River Road, Building 40-412, Schenectady, NY 12345 e-mail: can.gulen@ge.com
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A natural gas fired gas turbine combined cycle power plant is the most efficient option for fossil fuel based electric power generation that is commercially available. Trade publications report that currently available technology is rated near 60% thermal efficiency. Research and development efforts are in place targeting even higher efficiencies in the next two decades. In the face of diminishing natural resources and increasing carbon dioxide emissions, leading to greenhouse gas effect and global warming, these efforts are even more critical today than in the last century. The main performance driver in a combined cycle power plant is the gas turbine. The basic thermodynamics of the gas turbine, described by the well-known Brayton cycle, dictates that the key design parameters that determine the gas turbine performance are the cycle pressure ratio and maximum cycle temperature at the turbine inlet. While performance calculations for an ideal gas turbine are straightforward with compact mathematical formulations, detailed engineering analysis of real machines with turbine hot gas path cooling requires complex models. Such models, requisite for detailed engineering design work, involve highly empirical heat transfer formulations embedded in a complex system of equations that are amenable only to numerical solutions. A cooled turbine modeling system incorporating all pertinent physical phenomena into compact formulations is developed and presented in this paper. The model is fully physics-based and amenable to simple spreadsheet calculations while illustrating the basic principles with sufficient accuracy and extreme qualitative rigor. This model is valuable not only as a teaching and training tool, it is also suitable to preliminary gas turbine combined cycle design calculations in narrowing down the field of feasible design options. 关DOI: 10.1115/1.4001829兴
Introduction
As is well-known from decades worth of theoretical analysis and field experience, the performance of a gas turbine 共GT兲, defined by specific work output and thermal efficiency, is driven by the two key Brayton cycle parameters: maximum cycle temperature and cycle pressure ratio 共PR兲. The ideal air-standard Brayton cycle thermodynamics are readily amenable to simple mathematical formulation and can be found in virtually all textbooks on thermodynamics and, specifically, on gas turbines 关1,2兴. An ideal GT would be constructed of materials that can withstand the highest possible operating temperatures without a need for cooling. In reality, available materials have operating temperature limits well below the temperature of the hot gases expanding in the turbine section of a modern GT, and hence require cooling. Since the early days of GT development, the components exposed to the highest temperature environment, i.e., the turbine hot gas path 共HGP兲 components have been cooled with air drawn from the compressor. The resulting flow network renders simple models describing the uncooled cycle performance of limited value for the investigation of optimal GT design parameters. The best example to illustrate this deficiency is the behavior of the GT cycle thermal efficiency as a function of PR. For the ideal Brayton cycle, thermal efficiency is a function of PR only and increases monotonically with increasing PR as opposed to a real GT with cooling, where the thermal efficiency reaches a maximum and diminishes with a further rise in PR due to increasing cooling flow needed to maintain the turbine HGP metal temperatures within their operational limits. The increase in these so-called “parasitic” Contributed by the International Gas Turbine Institute 共IGTI兲 of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received April 9, 2010; final manuscript received April 19, 2010; published online September 27, 2010. Editor: Dilip R. Ballal.
flows is a direct result of increasing compressor extraction and discharge temperatures commensurate with higher compression ratios. There are myriad ways to expand the ideal Brayton cycle formulas to accommodate turbine HGP cooling requirements. It is relatively straightforward to model the requisite flow network and provide a numerical solution to the resulting system of heat and mass balance equations. But the heart of the problem is an accurate assessment of requisite cooling flows to maintain the HGP metal temperatures. Complex heat transfer models are required to provide a solution to multiple problems associated with stationary and rotating stage components 共i.e., airfoils that are referred to as stators and rotors, respectively兲, and wheel spaces between individual stages and the parts of the turbine shaft exposed to the hot gas flow. An elegant and comprehensive mathematical treatment of these problems that can easily be translated into cycle calculations is not available. The great bulk of the past research efforts can be divided into CFD and experimental studies 共quite frequently a combination of the two兲. A comprehensive theoretical treatment of the gas turbine aerodynamics and heat transfer can be found in Ref. 关3兴. Consulting a recent article on the state-of-the-art 共SOA兲 of gas turbine heat transfer provides more specific details 关4兴. A quick glance at the cited works reveals the difficulty in translating the enormous research and field test data into formulations, let alone readily integrating them into cycle performance calculations. The most widely used approach to tackle this problem is the effectiveness curve method 关5,6兴. A series of papers by El-Masri 关7–9兴 described the application of a more detailed thermodynamic analysis of the cooled turbine stage to GT simple cycle and combined cycle 共CC兲 performance calculations. The theoretical framework for rigorous aerothermodynamic analysis of cooled gas turbine stages, established in cited references, is available in a commercial software tool for engineering calculations 关10兴. Bol-
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JANUARY 2011, Vol. 133 / 011801-1
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