Gas Turbine Model Scaling

Abstract

A dimensional analysis, of both the equations governing boundary-layer flow with heat transfer and of the steady and unsteady boundary conditions, demonstrates that twelve non-geometric, dimensionless parameters are required for the complete similarity of a three-dimensional, compressible, viscous flow with a freestream pressure gradient. The analysis shows that non-dimensional groups describing the machine can be reduced to a function of metal angles and twelve fundamentally derived, dimensionless scaling parameters. The equation describing the rate of local entropy generation caused by fluid friction and heat transfer is also non-dimensionalised. This leads to an estimate of the relative magnitude of entropy generation due to fluid friction and heat transfer. A comparison of the principle operating parameters for a number of existing gas turbine test facilities, designed to model the aerodynamic and heat transfer conditions in real engines, suggests that full modelling of engine boundary-layer phenomena has not been achieved. A semi-empirical, boundary-layer analysis suggests that measured velocity boundary-layer profiles from adiabatic test facilities differ significantly with those from a gas turbine operating at engine gas to wall temperature ratios. Similarly, the analysis established the shape of the velocity boundary-layer to be dependent upon the specific-heat ratio.