A Simple Parametric Model for the Analysis of Cooled Gas Turbines

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.