A Dynamic Model for Two-Dimensional Thrust-Vectoring Nozzles

The frequency response of a two -dimensional thrust -vectoring nozzle designed for the Jet Cat P -80 micro turbojet engine was studied . The model describes the tangential thrust with an overshoot in the low frequency region and rapid decay at the high frequency region. The response of the flow field through the nozzle exhibits maximum amplification at the reduced frequency of 0.00 25 . The leakage flow from the deflectors dominates the bandwidth of thrust -vectoring engine. The transfer function of the thrust -vectoring engine was examined by balancing a horizontal pendulum. A PID controller was used to st abilize the horizontal pendulum. The numerical prediction of the oscillation angle and the oscillation frequency of the horizontal pendulum agree very well with the measurement . Nomenclature c = length of nozzle deflector D = distance between the thrust -vectoring react ion and the pendulum support G0 = transfer function of the th rottle command G1 = transfer function of the thrust -vectoring command G2 = transfer function of the horizontal pendulum Ga = transfer functio n of the actuator Gy = transfer function of the tangential momentum through the nozzle � f = reduced frequency of the deflector oscillation = U c � � = frequency of the deflector oscillation � = maximum set angle of the deflector U = velocity at nozzle exit I. Introduction HE flying wings were developed in 1930s to increase their lift to drag ratio. The small polar inertia and small pitching moment of the f lying wing are such that the stability of the aircraft is poorer than that of a conventional airplane. However, thrust vectoring can stabilize the flying wing. A trade off exists between the lift to drag ratio and the associated with vectoring. In this arr angement, the engine becomes a main controller of the aircraft in flight. The time delay caused by the engine inertia and flow mechanism dominates the stability of the aircraft. Also, the fluctuation of the engine thrust may become a major source of distur bance on the aircraft. An ejector can be used as part of the wing configuration to alleviate the airplane oscillation due to the engine thrust fluctuation. The increase in thrust by the ejector may also reduce the thrust loss caused by thrust vectoring. Th e thrust -vectoring dynamic must be investigated in detail to determine the feasibility and characteristics of thrust vectoring in flight. In this work, a micro turbojet engine is employed. The exhaust pipe is modified to incorporate a square ejector and a two dimensional vectoring nozzle (Ref. 1). The throttle command and thrust -vectoring command were examined. The stability of a horizontal pendulum was used to demonstrate the thrust -vectoring engine control. The minimal vectoring angle was used to stabiliz e the pendulum and explain the accuracy of the current model. Engine thrust vectoring has been emphasized in relation to military aircraft. The steady -state deflection of jet streams on the engine/aircraft has been examined extensively (Ref. 2). The vectoring angle is limited to 25 degree typically in order to avoid large thrust losses (Ref. 3). The deflector requires double curvature on the vectoring