Ahmed F. El-Sayed
The matching between the compressor and turbine is a fundamental aspect of gas-turbine engine design and performance, governing the stable and efficient operation of aero-engines, industrial gas turbines, and propulsion systems. Proper matching ensures that the power produced by the turbine balances the power required by the compressor over the entire operating envelope while satisfying constraints on mass flow, pressure ratio, temperature, and rotational speed. This chapter presents the theoretical foundations of compressor–turbine matching, beginning with steady-state power balance and flow compatibility and extending to the use of characteristic maps, corrected parameters, and nondimensional performance variables. Classical matching techniques, including equilibrium point determination, graphical map matching, and iterative numerical solution methods, are discussed for single-spool, two-spool, and three-spool engines. The influence of flight conditions, throttle setting, component efficiencies, cooling and bleed flows, and variable geometry on matching behavior is examined. Additionally, off-design operation, transient matching, surge margin considerations, and the impact of shaft dynamics are addressed. Hybrid–electric propulsion introduces new matching requirements among the thermal engine, electric motors/generators, power electronics, and energy sources.