Study On The Dynamic Response Of Viscoelastic Fluid In An Elastic Tube

Fluid-solid interaction(FSI)has been widely used in many engineering fields due to its involvement in interdisciplinary knowledge.As an important branch of FSI,viscoelastic interaction(VEI)has also received the attention of many researchers,especially the dynamic response of fluid flow in elastic tubes.Elastic tubes deform or move under fluid loads,which in turn affect the distribution of the flow field,thereby changing the magnitude of fluid loads and the flow characteristics of the fluid.This paper mainly studies the dynamic response of viscoelastic fluids in an elastic tube,including Maxwell fluid,fractional Maxwell fluid and Jeffrey fluid.In the first part,the dynamic response of Maxwell fluid in an elastic tube is considered.Focusing on the Maxwell fluid through a thin-walled slender elastic tube and neglecting inertia in the liquid and solid,a non-homogeneous linear diffusion equation controlling the viscoelastic coupled system is obtained.Setting different initial and boundary conditions according to different application scenarios,the pressure field of the fluid and the deformation field of the tube are obtained by Laplace transform and numerical Laplace inversion.The results show that with the increase of relaxation time,the pressure propagation speed of Maxwell fluid in the elastic tube increases,and the dynamic deformation response of the elastic tube also increases.In the case of oscillating inlet pressure,the amplitude of the pressure oscillation is positively correlated with the relaxation time,which means that the elasticity of Maxwell fluid enhances the flow oscillation.In addition,the influence of Poisson’s ratio of the tube on the dynamic response of the coupled system is also discussed.Compared with the tube with a larger Poisson’s ratio,the tube with a smaller one has a greater retardation effect on the propagation of the fluid,that is,the softer the tube is,the more conducive to the propagation of the fluid.In the second part,the viscoelastic interaction between fractional Maxwell fluid and a slender elastic tube is studied.Applying the elastic shell approximation and orderof-magnitude analysis,a non-homogeneous linear diffusion equation relating external forces acting on the tube,the inlet pressure,and the pressure distribution within the channel is obtained.Using Laplace transform and numerical Laplace inversion,we obtain the pressure,velocity,and deformation fields of the viscoelastic coupled system in different boundary and initial conditions.The analysis results indicate that the fractional parameter a has a significant but nonlinear effect on the dynamic response of the viscoelastic coupled system.The smaller the fractional parameter a,the slower the response of the fluid to external excitation in the initial stage,but in the later stage,its response speed will become faster.In addition,the influence of fractional parameter a on the pressure contraction region under oscillating inlet pressure is also analyzed.The third part further studies the dynamic response of Jeffrey fluid in an elastic tube.Focusing on the Jeffrey fluid through a thin-walled slender elastic tube and neglecting inertia in the liquid and solid,applying the elastic shell approximation and order-of-magnitude analysis,a non-homogeneous linear diffusion equation controlling the viscoelastic coupled system is obtained.Using Laplace transform and numerical inversion methods,we obtain the pressure,velocity,and deformation fields of the viscoelastic coupled system caused by a sudden change of inlet pressure and oscillating inlet pressure.The analysis results show that contrary to the fact that the increase of relaxation time accelerates the dynamic response of the system,the larger the retardation time,the slower the dynamic response of the coupled system.This is because the larger the retardation time,the more dominant the viscosity of Jeffrey fluid,and viscous damping slows down the dynamic response of the coupled system.In addition,the amplitude of the pressure oscillation and the length of the pressure contraction region also have a negative correlation with the retardation time.