Numerical simulation of a viscoelastic pipeline vibration under pulsating fluid flow

Abstract

PurposeThe purpose of this study is to create a mathematical model, a numerical algorithm and a computer program for studying the vibration of composite pipelines based on the theory of beams used in the oil and gas industry, agriculture and water management, housing and communal services and other areas.Design/methodology/approachA mathematical model of vibration of a viscoelastic pipeline based on the theory of beams with a pulsating fluid flowing through it was developed. Using the Bubnov-Galerkin method, based on the polynomial approximation of deflections, the problem is reduced to the study of systems of ordinary integro-differential equations, the solution of which is found by a numerical method. A computational algorithm was developed for solving problems of vibrations of composite pipelines conveying pulsating liquid.FindingsThe stability and amplitude-time characteristics of vibration of composite pipelines with a pulsating fluid flowing in it are studied for wide range of changes in the parameters of deformable systems and fluid flow. The critical velocities of fluid flow at which the viscoelastic pipe loses its rectilinear equilibrium shape are found. The effect of singularity in the kernels of heredity on the vibrations of structures with viscoelastic properties was numerically studied. It is shown that with an increase in the viscosity parameter of the pipeline material, the critical flow velocity decreases. It was determined that an increase in the value of the fluid pulsation frequency and the excitation coefficient leads to a decrease in the critical velocity of the fluid flow. It was established that an increase in the parameters of the Winkler foundation and the rigidity parameter of the continuous layer leads to an increase in the critical flow velocity.Originality/valueThe study of the vibration of pipelines made of composite materials is of great theoretical and applied interest. The solution to this problem is an effective application of the theory of viscoelasticity to real processes. Therefore, the methods and problems of pipeline vibrations attract much attention from researchers. This study is devoted to solving the above problems and therefore its subject is relevant. The paper considers the results of numerical simulation of the processes of vibration of a composite pipeline based on the theory of shells during the flow of a pulsating liquid through it. A mathematical model of vibration of a composite pipeline was developed. A computational algorithm was developed for solving problems of vibrations of composite pipelines conveying pulsating liquid.

About one boundary-value problem arising in modeling dynamics of groundwater

“…The study of equation (16) shows that it is an integral Fredholm equation of the second kind with a weak singularity. Its unique solvability follows from the uniqueness of the solution to the problem.…”

Research on vibration characteristics of rocket engine flow pipeline

“…In addition, the fluid–solid coupling method was used to investigate the vibrations of fluid-conveying pipelines (Matta and Szasz, 2018; Chen et al , 2021b; Lin and Wang, 2019). Khudayarov and Turaev (2022) established a mathematical model of composite pipe vibration and investigated the vibration problem of a composite pipe under the action of a pulsating fluid through the established model. The results indicated that increases in material viscosity decrease the critical flow velocity that can cause pipeline vibration.…”

Analysis of Vibration Characteristics of Cross-Type Hydraulic Pipeline Based on Finite Element Method

“…The causes of vibration in the piping of the main line pumps and the influence of frequency regulation on the level of vibration of the main line pump are analyzed. B Khudayarov [8] developed a computational algorithm for solving problems of vibrations in composite pipelines conveying pulsating liquid. The stability and amplitude-time characteristics of vibration in composite pipelines with pulsating fluid flowing in them are studied for a wide range of changes in the parameters of deformable systems and fluid flow.…”