Fluid–structure interaction analysis of a piezoelectric cantilever-driven pneumatic servo pilot valve under different outlet back pressures

A piezoelectric cantilever-driven pneumatic servo pilot valve involves confined slit throttling, compressible jet expansion, shear layer instability, and pressure-induced structural deformation. These coupled mechanisms remain insufficiently understood, especially under different outlet back pressures. In this study, a three-dimensional fluid–structure interaction model was developed to investigate the flow regime, flow losses, and passive structural response of a nozzle–flapper pneumatic pilot valve under six operating conditions, combining three opening conditions and two outlet back pressures. The results show that outlet back pressure governs the flow regime. Under low back pressure, the pressure ratio far exceeds the critical pressure ratio of air, the slit chokes, and supersonic expansion develops with a maximum Mach number of 2.68, whereas under high back pressure the flow remains subsonic and incompressible. A key finding is the supersonic jet-induced negative pressure attraction effect under low back pressure. The choked slit flow forms a high-speed wall-attached jet along the lower surface of the piezoelectric cantilever. The combined effect of local supersonic expansion and wall-jet acceleration reduces the lower surface pressure below the upper surface pressure, causing the free end to bend toward the nozzle. Under high back pressure, this attraction mechanism disappears, and the distributed high pressure on the lower surface pushes the cantilever away from the nozzle. The energy loss analysis shows that the total flow loss under low back pressure is more than 300 times that under high back pressure, with the dominant loss region localized in the wall jet and downstream shear layer. These results reveal the pressure ratio controlled flow regime transition, supersonic jet-induced attraction mechanism, and localized irreversible loss structure in piezoelectric pneumatic pilot valves.