Numerical Simulation Of Vortex Induced Vibration Of Suspension-span Pipelines Using SPH Method At Low Reynolds Number

When the fluid flows around the cylinder,an alternate vortex occurs on both sides of the cylinder,so the cylinder is subjected to the pulsating pressure of the cross-flow direction and the forward direction.When the pulsating pressure frequency of the cylinder is close to the natural vibration frequency of the structure,the phenomenon of "frequency locking" will occur.In the locking interval,the periodic action of fluid will cause a strong motion response of the structure and thus cause fatigue damage to the structure.In recent years,with the rapid development of submarine cable transmission projects at home and abroad,the cable structure is frequently damaged by vortex-induced vibration,and the research of vortex-induced vibration has been widely concerned in engineering practice.This paper establishes a mathematical model to simulate the vortex-induced vibration problem of a cylinder based on the fluid dynamics method of smooth particles(Smoothed Particle Hydrodynamic,SPH).Fluid motion is described by NS(Navier-Stokes)and solid motion by Newton's rigid body equation of motion.A forced oscillating cylinder and a freely vibrating cylinder undergoing the steady flows are studied based on the open-source Dual SPHysics.By setting the buffer particles at the left and right boundaries of the numerical tank and introducing the open boundary algorithm suitable for the SPH method,the flow generation function of the numerical tank is successfully realized.In order to avoid the cavity in the wake area behind the cylinder and suppress the nonphysical oscillation of the pressure of the fluid particles,the particle shifting algorithm and the particle pressure correction algorithm are introduced in the mathematical model.At the fluid-solid junction,the surface boundary of the cylinder is discretized into two layers of boundary particles.the pressure of the boundary particles is solved according to the equation of state,and their velocities are determined by the equation of motion of the cylinder.Firstly,the mathematical model is verified by an example of the flow around a fixed cylinder.The lift and drag variation of the fixed cylinder at Reynolds number = 100 and 200 and the wake vortex shedding mode are numerically simulated.Secondly,numerical simulations are then performed for flow past a forced oscillating cylinder at Reynolds equal to 100.The lock-in interval is determined and the time series of the fluctuating aerodynamic coefficients and their power spectral densities are analyzed.Thirdly,in the study of vortexinduced vibration,the convergence of computational domain size and particle resolution of the established model is verified.Then,when the Reynolds number is equal to 20 times the reduced velocity and the mass ratio of the cylinder is 10,the vortex-induced vibration process of circular cylinder which is isolated or near the stationary plate are numerically simulated,their lock-in interval are determined,and the variation of the transversely displacement and lift characteristics at different reduced velocities and the wake vortex shedding modes are analyzed,as well as the relationship between the frequency of the transversely displacement,lift coefficients,the natural frequency of the system and the vortex shedding frequency of the fixed cylinder.For the isolated circular cylinder,the phase relationship between the transversely displacement and lift coefficients in the lock-in interval is studied by Hilbert transformation.Numerical results show that the SPH numerical model can well simulate the vibration of pipeline structures under current excitation.