A Mathematical Model for Windmilling of a Turbojet Engine

The transient windmilling characteristic of a modern turbojet engine under different flight conditions and altitudes is obtained with numerous tests conducted at an Altitude Test Facility (ATF). A simple and practical mathematical model for predicting the transient and steady-state rotational speed of a simple turbojet engine in flight has been developed. The method is derived from Froude’s momentum theory or disk actuator theory and implemented to a turbojet engine. A correction factor is introduced to match with test results of KTJ-3200 being indigenously developed by Kale R&D Inc. The present model’s predictions are compared with the test data of Microturbo TRI 60 engine and KTJ-3200 engine. The estimation of the present windmilling model fits very well with test results of two different engines within an error band of ±1.2% for various atmosphere conditions depending on flight speed, altitudes and temperature. The present model is compared with loss modeling windmilling estimation methods described in literature which requires large amount of inputs as blade angle, blade pitch and component efficiencies. The comparison with the available windmilling model at literature shows that both models capture the terminal speed estimation very well. However, the model in literature is not able to capture the transient engine speed, which is important for missile applications as the missile can be fired before the engine reaches to terminal speed. The difference between the test data and the available model during transients is up to 50%. The present model matches perfectly with test data even at transients. It is more practical and much simpler than the available windmilling model in the literature to estimate the both transient and terminal windmilling speed of the turbojet engines. The agreement between the present model, KTJ 3200 test data, windmilling method available in the literature and test data of Microturbo TRI 60 is very good for most of the ranges investigated.