Numerical study of the influence of surface defects on the stability of a cylindrical pipe containing fluid

This paper is concerned with the dynamic behavior of an elastic cylindrical pipe with surface defects interacting with the internal flow of a compressible fluid. A defect in the form of a ring of rectangular cross-section is located on the inner or outer surface of an elastic body and characterized by its own set of physico-mechanical parameters. The behavior of an ideal compressible fluid is described using the potential theory, and the behavior of the pipe is considered in the framework of the linear theory of elasticity. The hydrodynamic pressure exerted by the fluid on the inner surface of the pipe (defect) is determined with the use of the Bernoulli equation. A mathematical formulation of the problem of the elastic body dynamics is based on the variational principle of virtual displacements, and the system of equations for a liquid medium is developed using the Bubnov-Galerkin method. For the numerical implementation of the algorithm, a semi-analytic version of the finite element method is used. The stability of the system is estimated based on the results of computation and analysis of complex eigenvalues for a coupled system of equations. Verification of the model is carried out for the case of an ideal pipe by comparing the obtained results with the known experimental and numerical data. The effect of the geometric and physico-mechanical parameters of the defect on the critical fluid velocity responsible for the loss of stability is studied for a cylindrical pipe clamped at both ends. It is shown that defects reduce the boundary of hydroelastic stability. It has been found that the defect located on the outer surface of the pipe exerts a greater impact on the system stability than it does when located on the wetted surface of the pipe.