Mathematical modelling of a cryogenic engine

Cryogenic propulsion systems using liquid hydrogen and liquid oxygen propellant combination are used in satellite launch vehicles in view of the higher specific impulse (ISP). Due to extreme low temperature of cryogenic propellant and low density and explosive nature of LH2, the development of cryogenic propulsion system is very complex and time consuming. In ISRO an indigenous cryogenic upper stage powered by an engine developing a nominal thrust of 73.5 kN in vacuum with a propellant loading of 12.8 tonnes is developed and successfully flight tested for the first time in GSLV D5 flight on 5th January 2014. A mathematical model is developed for finalizing the engine start and shut off sequence, ensuring smooth and safe ignition, predicting performance of subsystems under transient phase, nominal and off nominal conditions, control systems parameter settings and for the performance estimation of engine in sea level and flight. This paper highlights the configuration and working of a cryogenic engine, mathematical modelling of the engine, applications of the model in the cryogenic engine development and comparison of predicted values with the test results.