Predictions of Store-Induced Limit-Cylce Oscillations Using Euler and Navier-Stokes Fluid Dynamics

Abstract

Store-induced limit cycle oscillation of a rectangular wing with a tip store in transonic flow is simulated. Stability boundaries for this wing are computed for both clean and tip store configurations and behavior beyond the critical freestream velocity is examined at a Mach number of 0.92. The Euler equations are used to model the fluid dynamics and a modal approach is used to model the structural response. Solutions obtained with the Euler equations are compared with results obtained using linear and transonic small disturbance theories. All methods are shown to give similar predictions of the stability boundary in the lower transonic regime but differences develop as the Mach number approaches unity. The linear method fails to capture the rise in flutter speed beyond the flutter dip and is, of course, unable to capture limit cycle behavior. The Euler and transonic small disturbance theories show reasonable qualitative agreement in predicting both unbounded and bounded behavior across a wide range of Mach numbers. There are, however, notable quantitative differences between the Euler and transonic small disturbance theories in the limit cycle onset velocities and response amplitudes and frequencies. The results suggest that the transonic small disturbance theory is a practical alternative to the Euler and Navier-Stokes theories for predicting store-induced limit cycle behavior so long as the small disturbance assumption is valid.