Dynamic and Stability Response of a Cylindrical Shell Subjected to Viscous Annular Flow and Thermal Load

This paper presents an analytical approach for investigating the dynamics and stability of an outer cylindrical shell conveying viscous fluid (i.e. water) in the annulus between the inner shell-type body and the outer shell with thermal load. The steady viscous forces that induce prestress on the shells are determined based on the time–mean Navier–Stokes equations. The shell motions are described by Flügge’s shell equations incorporating the prestress arising from the viscous effect. The shell-vibration-induced fluid forces are described by means of the potential flow theory, and the thermal loads are determined by the thermoelastic theory. The analytical model is conducted by the zero-level contour method with the aid of the weighted residual technology. The present study shows that the effect of viscosity in the annular flow renders the system more unstable. Moreover, the thermal load tends to reduce the critical flow velocity pronouncedly, for which there exists a critical temperature rise.