Turbine Map Extension - Theoretical Considerations and Practical Advice

Abstract

Physically sound compressor and turbine maps are the key to accurate aircraft engine performance simulations. Usually, maps only cover the speed range between idle and full power. Simulation of starting, windmilling and re-light requires maps with sub-idle speeds as well as pressure ratios less than unity. Engineers outside industry, universities and research facilities may not have access to the measured rig data or the geometrical data needed for CFD calculations. Whilst research has been made into low speed behavior of turbines, little has been published and no advice is available on how to extrapolate maps. Incompressible theory helps with the extrapolation down to zero flow as in this region the Mach numbers are low. The zero-mass flow limit plays a special role; its shape follows from turbine velocity triangle analysis. Another helpful correlation is how mass flow at a pressure ratio of unity changes with speed. The consideration of velocity triangles together with the enthalpy-entropy diagram leads to the conclusion that in these circumstances flow increases linearly with speed. In the incompressible flow region, a linear relationship exists between torque/flow and flow. The slope is independent of speed and can be found from the speed lines for which data are available. This knowledge helps in extending turbine maps into the regions where pressure ratio is less than unity. The application of the map extension method is demonstrated with an example of a three-stage low pressure turbine designed for a business jet engine.