A simple model for the estimation of turbofan engine performance in all airborne phases of flight

Abstract

The overall efficiency of a turbofan engine may be expressed as a function of the Mach number, flight level and one other parameter. This may be either the net thrust, the turbine entry temperature or the fuel flow rate. Using basic aero-thermodynamic principles, dimensional analysis, normalisation and curve fitting, five approximate and ‘near universal’ relations have been identified for engines having bypass ratios between 1 and 13. These relations contain five independent characteristic engine parameters. When these parameters are known, the relations form the basis of an estimation method for engine overall efficiency that is simple, fast, open source, completely transparent and, as new information appears, capable of further refinement. Since the empirical relations presented in this analysis are valid for Mach numbers greater than 0.2, the method is applicable to all airborne phases of flight. For a given aircraft, if the flight trajectory is specified in sufficient detail for the variation of net thrust with Mach number and flight level to be determined, only three of the five relations, together with the value of engine overall efficiency at a single reference condition, are needed to estimate the overall efficiency at every point on the trajectory. Comparisons with the data used in this analysis suggest that the accuracy is better than ±5% in most cases. In the completely general case, two additional engine characteristic parameters, one a total temperature ratio and the other a Mach number, are introduced. If these are known, both engine overall efficiency and net thrust can be expressed as functions of Mach number, flight level and turbine entry temperature. This allows the method to be used for the estimation of operating limits in the various phases of flight and in simplified optimisation studies, e.g. finding the environmentally optimum flight trajectory. In previous work, estimates of engine overall efficiency at the design optimum condition have been estimated for 53 aircraft and engine combinations. It is shown that the ‘design optimum’ condition is an appropriate choice for the engine reference condition. Updated and revised values for the relevant parameters for these 53 examples, together with estimates for the two additional engine characteristic parameters, are given in tabular form.