Analysis Of Flow-induced Instability Of Coaxial Cylindrical Shell Based On Differential Quadrature Method

Coaxial cylindrical shells are widely used in the structural design of the core barrel of a nuclear power plant reactor.Under working conditions,if the shell structure appears dynamic instability,it will seriously affect the safe operation of the nuclear power plant reactor.Therefore,it is of great significance to study the dynamic stability of the coaxial cylindrical shell structure conveying fluid.In this paper,the flow induced instability of coaxial cylindrical shells in ideal fluids is studied based on the differential quadrature method,and the instability characteristics of coaxial cylindrical shells under different boundary conditions are explored,which can provide theoretical reference for engineering design.Based on the hypothesis of linearized potential flow theory,the fluid forces of internal fluid and annular fluid are derived by means of the Laplace equation,the Bernoulli equation and fluid-structure coupling boundary.Combined with Donnell-Mushtari shell equation,the fluid-structure coupling motion equation of coaxial cylindrical shell under axial flow is established.The fluid force and shell equation in the fluid-structure coupling equations are discretized respectively.The differential quadrature method is used to discretize the shell equation and boundary conditions of cylindrical shells.The pressure distribution of the fluid on the grid is calculated by interpolation function,and the discrete format of the perturbation pressure on the grid is obtained.Modal analysis and fluid-induced instability analysis of coaxial cylindrical shells were carried out by solving the generalized eigenvalue problem.The calculation results show that the fluid force discrete method proposed in this paper is feasible,which can be used for the modal analysis and fluid-induced instability analysis of coaxial cylindrical shells effectively.The natural frequencies and modal shapes of simply supported-simply supported,clamped-simply supported and clamped-clamped coaxial cylindrical shell in stagnant fluid are obtained by modal analysis.Through the analysis of fluid-induced instability,it is found that simply supported-simply supported,clamped-simply supported and clamped-clamped coaxial cylindrical shell lose stability by divergence firstly,and coupled-mode flutter will occur at a higher flow velocity.The losing stability mode is related to the natural frequency in the stagnant fluid,and the lower the frequency,the more likely the mode is to lose stability.By variable parameter analysis,it is found that for coaxial cylindrical shells supported at both ends,the critical flow velocity of system losing stability decreases significantly with the decrease of annular gap width.Increasing the length of the cylindrical shell will decrease the critical flow velocity and corresponding circumferential mode number of system instability.An increasing in the wall thickness of the cylindrical shell stabilizes the system.Fluid in the annular gap is more likely to destabilize the system.