Dynamics modeling of a nonuniform variable-area jet nozzle using the arbitrary Lagrangian-Eulerian shell formulation

An area-varying jet nozzle structure is studied, which consists of three main segments, a flexible shell, several rigid guides, and a rigid hull, such that the thrust of the nozzle can be controlled by adjusting the area. The major difficulty in studying the area-varying nozzle dynamics is to effectively formulate the sliding motions of the variable-area flexible shells along the rigid guides, and an arbitrary Lagrangian-Eulerian (ALE) approach is proposed to achieve this purpose. Even if the drive forces may be different on different driving motors, the jet nozzle only has mass flowing along its generatrix, and the nonuniform one-dimensional ALE assumptions are proposed to improve the computational efficiency. The mesh and material nodes are adopted to distinguish the mass flow and the spatial motion of the jet nozzle, and the Reynolds transport theorem is applied to simplify the dynamic equations. The governing equations are derived from d'Alembert's Principle on the mesh domain, and the sliding constraints between the rigid hull and the flexible shell are simplified as second-order polynomial constraints and calculated by the differential-algebraic equations (DAEs). The unfolding process of the jet nozzle with different drive forces along different guides is studied to verify the accuracy and effectiveness of this approach, and the results agree well with those calculated by the commercial software ABAQUS using complicated contact mechanics and other techniques. Finally, the feedforward PD control strategy is developed to make the jet nozzle unfold steadily.