On using the shell theory in stability analysis of fluid flows in compliant pipes

The linear stability of the Poiseuille flow in a compliant pipe of circular cross-section is numerically analyzed using two different wall models based on the theory of thin shells. Small vibrations of the pipe wall are described by general Love’s equations in one model and by simplified Love’s equations derived using the well-known Donnell–Mushtari–Vlasov approximation in the other model. It is shown that the replacement of the general equations by the simplified ones does not qualitatively change the dependence of the basic flow stability characteristics on the wall stiffness and damping. Nevertheless, for some parameter values of the problem under consideration, this replacement can lead to the emergence of weakly growing disturbances, which are not observed in the case of general Love’s equations and are suppressed significantly by increasing wall the stiffness or damping.