Aerodynamic Nonlinearity of Piston Theory in Surface Vibration

Piston theory is widely used in modeling unsteady aerodynamic force caused by surface vibration. The nonlinearity of piston theory is determined by its high-order terms, which are significantly influenced by different working conditions. However, theoretical studies of the nonlinearity of high-order terms receive little attention. Based on previous works, this study discussed the physical meaning of high-order terms in piston theory and conducted a detailed theoretical analysis of the nonlinear behavior of high-order terms. Results demonstrated that the physical meaning of high-order terms denotes the nonlinearity of weak shocks (nonisentropic) and expansions, which can be approximated by isentropic theory in small vibrations. However, when the vibration amplitude and Mach number are large, shocks become stronger (the hypersonic similarity parameter exceeds 0.6) and the nonisentropic effect of shocks becomes significant, leading to the invalidation of piston theory. A spectral analysis concluded that the nonlinearity of piston theory is determined by the superposition of and counteraction between high-order terms.