A Study On The Interaction Between Flow And 3D Large Deformation Incompressible Hyperelastic Tube

Tubular tissues widely exist in various systems of the human body,which are prone to typical mechanical responses such as structural collapse,bulge and vibration under the joint effects of external physiological pressure and internal flow,and these mechanical responses are related to many physiological phenomena(korotkoff sound,jugular humming,respiratory noise,etc.)and medical applications(auxiliary voice devices,sphygmomanometers,etc.)In order to explain these physiological phenomena from mechanical perspectives and provide guidance for the development of medical equipment,the fluid-structure interaction system between the large deformation tube and internal flow is studied in this thesis.A reliable mechanical model is established and an efficient numerical method is proposed for solving the problem of imperfect model,long time-consuming numerical method and lacking method to determine the stability of steady solution in current research about the fluid-structure interaction problem in a large deformation tube.And the contribution of this work includes the following aspects.A three-dimensional model of the interaction between the incompressible hyperelastic large deformation whole tube and the internal flow is established which includes the geometry model,governing equations and boundary conditions of the system.The three-dimensional geometric model of the whole tube is given as three parts,i.e.,the upstream rigid segment,the middle deformable segment and the downstream rigid segment.The tube wall of the middle deformable segment is described by the incompressible hyper-elastic material model and the solid governing equations are established by the Lagrangian description method.Combined with the assumption that the fluid in the tube is Newtonian fluid and the flow state is laminar,the governing equations of the internal flow are determined by the Euler description method.The no slip boundary condition is assumed on the interface between the fluid and inner wall of the tube.Flow driven boundary condition or pressure driven boundary condition is given at the inlet and outlet of the tube.The unprecedented fluid-tube model for flow in a three-dimensional large deformation tube established in this thesis can analyze axisymmetric and non-axisymmetric deformation of the tube,which opens an avenue for simulating various types of buckling mode in tube.An efficient numerical method for the three-dimensional model of the coupling problem of large deformation tube and internal flow is proposed and the corresponding finite element program is developed.Two progresses have been made in the numerical method.The first is that an automatic mesh generation method of high-quality finite element mesh is established to make the mesh which closes to the tube wall denser in the fluid region and construct the adaptive mesh which follows wall deformation by adopting the rotating spine method.The finite element discrete equations of fluidstructure interaction system are established by combining Arbitrary Lagrange-Euler method and Galerkin method.The second is that the large amount of simultaneous equations are solved parallelly by combining the frontal method,substructure method together with the open multi-processing method to reduce the computational time.Then,the experimental platform of the interaction system between large deformation tube and internal flow is built and the three-dimensional tube deformation is measured by the optical method.The numerical results of this thesis are compared with the experimental datas and the existing research results,and the correctness of the theoretical model,numerical method and finite element program are verified.The flow field and wall deformation characteristics of some typical steady solutions of fluid-tube system for flow in large deformation tube are analyzed.First of all,the influences of different material models of tube wall on the response of fluidtube system for flow in large deformation tube are analyzed.It is found that if the strain is large,the responses of the system with different material models are obviously different,which proves the necessity of describing the tube wall by nonlinear model.Secondly,the flow field when the tube is in mode-3 buckling or mixed mode buckling of mode-2 and mode-3 is analyzed and compared with that when the tube is in mode-2buckling.It is found that the characteristics of flow field are as follows: when mode-2buckling and mode-3 buckling occurs separately,the pressure distribution along the axis of the tube is similar and greatly different from that in mixed mode buckling;most of the viscous energy dissipation sites are in the boundary layers of tube buckling region under the three types of buckling;the characteristics of jet along the axial direction of the tube of mode-3 buckling,mode-2 buckling and mixed mode buckling are one jet,two jets and no jet respectively.Then the distribution characteristics of the number of steady solution and tube deformation characteristics in mode-2 or mode-3 buckling are analyzed.In the case of flow driven boundary,with the increase of Reynold number,the tube deformation may increase or decrease and the system may have an axisymmetric solution with a buckling solution,an axisymmetric solution with two buckling solutions,and an axisymmetric solution.In the case of pressure driven boundary,as the Reynold number increases,the tube deformation increases and the system has an axisymmetric solution or an axisymmetric solution with a buckling solution.Two methods for determining the stability of steady solution of the fluid-tube system for flow in a three-dimensional large deformation tube are proposed.Firstly,the eigenvalue equation of the stability problem of the steady solution of the system is established by perturbing the steady solution of the system which is a generalized eigenvalue equation of large-scale asymmetric matrix.The frontal method is adopted to avoid large-scale matrix inversion and the generalized eigenvalue problem is transformed into the standard eigenvalue problem.The ARPACK software package is redeveloped to obtain the eigenvalue with the maximum real part and the stability of the steady solution is determined by the negative or positive of the real part of the eigenvalue with the maximum real part.Secondly,a program is developed to solve the transient problem of the system and the transient solution is obtained based on perturbing the steady solution of the system.The stability of the steady solution is determined according to the variation characteristics of the response's amplitude with time.Then the stability of steady solution in mode-2 buckling is determined by solving the eigenvalue equation and the transient solution respectively.It is found that the two methods give the same conclusion on the stability of the steady solution.The two methods are checked with each other,which shows the availability of the two methods to determine the stability of the steady solution.The mechanical model with the corresponding numerical method and program established in this thesis can be used to solve the steady problem,determine the stability of the steady solution and solve the transient problem of the interaction system of large deformation tube and internal flow.The deformation behaviors and internal flow characteristics of the biological vessels in the actual physiological state can be further investigated by changing the geometric shape of the wall,the material model and parameters,and the inlet and outlet boundary conditions,which provides support for the study of the pathogenesis and pathological process of cardiovascular diseases.