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Session 1633

GAS TURBINE ENGINE SIMULATION USING MATHCAD: A STUDENT PROJECT Michael R. Sexton Mechanical Engineering Department Virginia Military Institute Lexington, VA 24450

Abstract

This paper describes an energy system simulation project assigned to mechanical engineering students at the Virginia Military Institute. This project is part of a required, senior level, course in energy conversion design. The class exposes the student to methods of energy system design based on system simulation and optimization. This gas turbine engine simulation is one of several simulation projects assigned in recent years. This project is particularly relevant in that it requires the use of several modeling and simulation techniques. The project statement provides the student with the design point operating characteristics like engine inlet conditions, pressure ratios, and shaft power developed, which are necessary to develop a design point thermodynamic model. Characteristic curves for the various engine components (compressor and turbine) used are also provided. The student must develop the system of equations necessary to model the engine system and use this model to predict the off-design performance (speed, power, efficiency, etc.) of the engine. Off-design conditions may result from changes in throttle setting, changes in applied load, or changes in environmental conditions. The required equations, including the first and second laws of thermodynamics necessary to describe the various components and processes and curve fits of the graphic component characteristics and working fluid properties data, are developed. The graphic data, representing components like compressor ratio, as a function of compressor speed and compressor flow rate, is curve fitted using multiple regression methods. Depending on how the student approaches the problem the system usually involves thirteen to twenty linear/nonlinear equations that must be solved simultaneously. For this project the solution of these equations is accomplished by using Mathcad; although other software capable of solving this system of equations is available. Mathcad was selected because of the ease of programming and the capability to handle systems of nonlinear equations. As it is with the solution of any system involving nonlinear equations, care must be taken in the selection of initial trial values of the unknown variables. For simulations near the engine’s design operating point, these initial trial values are simply chosen to be the values at the design point. For simulations that are farther from the design operating conditions, the student must use some judgement in selecting these initial trial values. Physical understanding of the engine’s operation is necessary in the selection of these values.

Symbols Cp ≡ specific heat, Btu/(lbm R) To ≡ total temperature, R m ≡ mass flow rate, lbm /sec w ≡ work per unit mass, Btu/lbm N ≡ engine speed, rpm γ ≡ specific heat ratio Po ≡ total pressure, psia η ≡ isentropic efficiency Q ≡ heat rate added to combustor, Btu/sec Subscript d represents design properties

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Sexton, M. (1999, June), Gas Turbine Engine Simulation Using Mathcad: A Student Project Paper presented at 1999 Annual Conference, Charlotte, North Carolina. 10.18260/1-2--7690