Fully coupled nonlinear aerothermoelastic computational model of a plate in hypersonic flow

A recent structural model of a plate is extended to include a nonuniform temperature differential that varies in time using a modal expansion. The nonlinear structural plate model with first-order piston theory aerodynamics and cavity dynamics is coupled with the heat equation to form a single system of dynamical equations for the fluid-structural-thermal system. The heat flux from the boundary layer to the plate is modeled using the temperature reference method. A computational scheme is formulated by linearizing the heat flux in terms of two variables: the local aerodynamic downwash due to plate motion and the local wall temperature. The proposed linearization produces a local force equivalent for the pointwise heat flux and substantially simplifies the time-marching scheme of the coupled equations. The model is correlated with results from a recent supersonic wind-tunnel experiment conducted at Air Force Research Laboratory (AFRL). It is found that when a nonlinear response is expected in an experiment (for example, flutter that reaches limit cycle oscillation or a large static buckled deformation), the in-plane boundary stiffness should be measured before the wind-tunnel experiment to fully characterize the experimental model. The heat flux linearization error is quantified, and the modal convergence of the temperature differential is investigated.