CN109558672A - The determination method and system of large deformation pipeline running system oscillatory hollow - Google Patents

Abstract

The invention discloses a method for determining the oscillation space of a large deformation pipeline flow system. The method for determining the oscillation space includes: obtaining parameters of the large deformation pipeline flow system; determining the control equation and boundary conditions of the large deformation pipeline flow system according to the large deformation pipeline flow system parameters; using the finite element method, according to the control equation The equation and the boundary conditions determine the steady state solution of the large deformation pipeline flow system; determine the eigenvalues according to the steady state solution; determine the oscillation space of the large deformation pipeline flow system according to the eigenvalues. The determination method and system provided by the present invention can accurately determine the oscillation space of the large deformation pipeline flow system.

Description

Method and System for Determining Oscillation Space of Large Deformation Pipeline Flow System

technical field

The invention relates to the field of human body pipe wall simulation, in particular to a method and system for determining the oscillation space of a large deformation pipeline flow system.

Background technique

Large deformation collapsible duct flow occurs in many physiological phenomena in the human body. For example, vascular collapse caused by blood flow plays an important role in the blood circulation that automatically supplies blood to various internal organs; actively compressing lower extremity venous vessels to collapse can be an effective treatment method to prevent the formation of deep vein thrombosis; The sphygmomanometer uses the Korotkoff sound produced by the collapse of blood vessels to measure human blood pressure; in forced breathing, the contraction of the expiratory muscle will increase the pressure of the pleura, and when the pressure exceeds a certain value, it will also make the near The end of the trachea collapsed. The so-called flow limit phenomenon often occurs after the pipeline collapses. With the occurrence of the flow limit phenomenon, self-excited oscillation often occurs, which is physiologically manifested as snoring, asthma and other pathological phenomena. Therefore, the study of these phenomena is of great importance to human life and health. significance.

Because the large deformation pipeline flow system is a strong nonlinear system, the theoretical solution is basically impossible, and the numerical method is mainly used to solve it at this stage. In the current solution model, the linear elastic model is used for the description of the tube wall, and the materials are all compressible, which cannot describe the actual biological materials well.

In the prior art of using numerical methods to solve the large deformation pipeline flow system, some people use a two-dimensional model to simulate the human body pipe wall, and use the eigenvalue method to study the vibration characteristics of the large deformation pipeline flow system, although some good results have been obtained, but two There is still a big gap between the 3D model and the actual 3D entity; when the 3D model is used to simulate the human body wall, the vibration characteristics of the system are studied by calculating the transient solution of the system. However, it takes a lot of time to solve the transient solution of the system one by one. , it is more difficult to map out the oscillation space of the system. It can be seen from this that the two-dimensional model is inconsistent with the actual situation, and the method used in the three-dimensional model to obtain the transient solution cannot be applied to each point in the parameter space due to the large amount of calculation, and the existing methods cannot accurately determine the large Oscillation space for deformed pipe flow systems.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method and system for determining the oscillation space of a large deformation pipeline flow system, so as to solve the problem of low efficiency in determining the oscillation state of a three-dimensional large deformation pipeline flow system.

For achieving the above object, the present invention provides the following scheme:

A method for determining the oscillation space of a large deformation pipeline flow system, using incompressible hyperelastic materials to simulate the large deformation pipeline flow system; the method for determining the oscillation space of the large deformation pipeline flow system includes:

Acquire the parameters of the large deformation pipeline flow system; the large deformation pipeline flow system parameters include pipeline geometric parameters, fluid parameters and pipe wall material parameters; the pipeline geometric parameters include the total length of the pipeline, the inner radius of the pipeline, the diameter of the pipeline, the thickness of the pipeline, the upstream length, pipe midstream length, and pipe downstream length; the fluid parameters include density and coefficient of viscosity; the pipe wall material parameters include shear modulus and density;

Determine the control equation of the large deformation pipeline flow system and obtain boundary conditions according to the large deformation pipeline flow system parameters; the boundary conditions include the inlet boundary conditions, rigid wall boundary conditions, elastic segment boundary conditions, elastic end boundary conditions and Boundary conditions at the exit;

Using the finite element method, determine the steady state solution of the large deformation pipeline flow system according to the control equation and the boundary conditions;

determining eigenvalues according to the steady state solution;

The oscillation space of the large deformation pipeline flow system is determined according to the eigenvalues.

Optionally, determining the control equation and boundary conditions of the large deformation pipeline flow system according to the large deformation pipeline flow system parameters, specifically including:

According to the formula and detF=1 to determine the control equation of the large deformation pipeline flow system; the control equation is the control equation after dimensionless processing; where Re is the Reynolds number, u _i , u _j are the directional fluid speeds, where i =1, ui is the fluid velocity in the x-axis direction, when _{i=2, u i is} the fluid velocity in the y-axis direction, when i=3, _ui is the fluid velocity in the z-axis direction, j=1 , u _j is the fluid velocity in the x-axis direction, when j=2, u _j is the fluid velocity in the y-axis direction, when j=3, u _j is the fluid velocity in the z-axis direction, t is time, x _j is the current configuration coordinate, p is the fluid pressure, is the shear modulus, F _iA,A is the derivative of the deformation gradient tensor with respect to the initial configuration coordinates, is the solid equivalent pressure, is the derivative of the inverse of the deformation gradient tensor with respect to the initial configuration coordinates, is the wall density, is the wall acceleration, detF is the determinant of the deformation gradient tensor;

According to the formula u=v=0 and Determine the boundary conditions at the inlet; where u is the velocity of the fluid in the x direction, v is the velocity in the y direction of the fluid, w is the velocity in the z direction of the fluid, x ₁ is the x coordinate, and x ₂ is the y coordinate;

Determine the rigid wall boundary condition according to the formula u=v=w=0;

According to the formula as well as Determine the boundary conditions of the elastic segment; where u is the velocity of the fluid in the x-direction, is the x-direction velocity of the pipe wall, v is the fluid y-direction velocity, is the velocity in the y direction of the pipe wall, w is the velocity in the z direction of the fluid, is the z-direction velocity of the pipe wall;

According to the formula as well as Determine the elastic end boundary conditions; where, is the displacement of the pipe wall in the x direction, is the displacement of the pipe wall in the y direction, is the displacement of the pipe wall in the z direction;

The boundary conditions at the outlet are determined according to the formulas σ _t =0 and σ _n =-P _d , where σ _t is the outlet interface shear stress, σ _n is the outlet interface normal stress, and P _d is the outlet external pressure.

Optionally, the determining the eigenvalue according to the steady state solution specifically includes:

Determine the mass matrix and the nonlinear matrix of the large deformation pipeline flow system according to the steady state solution;

Eigenvalues are determined from the quality matrix and the nonlinear matrix.

Optionally, the determining the oscillation space of the large deformation pipeline flow system according to the characteristic value specifically includes:

Determine whether the real part of the eigenvalue is equal to 0, and obtain the first judgment result;

If the first judgment result is expressed as the real part of the eigenvalue equal to 0, determine the oscillation space curve;

The oscillation space of the large deformation pipeline flow system is determined according to the oscillation space curve.

A system for determining the oscillation space of a large deformation pipeline flow system adopts incompressible hyperelastic materials to simulate the large deformation pipeline flow system; the system for determining the oscillation space of the large deformation pipeline flow system includes:

A parameter acquisition module is used to acquire parameters of the large deformation pipeline flow system; the large deformation pipeline flow system parameters include pipeline geometric parameters, fluid parameters and pipe wall material parameters; the pipeline geometric parameters include the total length of the pipeline, the inner radius of the pipeline, the pipeline diameter, pipe thickness, pipe upstream length, pipe midstream length, and pipe downstream length; the fluid parameters include density and coefficient of viscosity; the pipe wall material parameters include shear modulus and density;

A control equation and boundary condition determination module, used for determining the control equation and boundary conditions of the large deformation pipeline flow system according to the parameters of the large deformation pipeline flow system; the boundary conditions include inlet boundary conditions, rigid wall boundary conditions, elastic Segment boundary conditions, elastic end boundary conditions, and exit boundary conditions;

a steady-state solution determination module, using the finite element method to determine the steady-state solution of the large deformation pipeline flow system according to the control equation and the boundary conditions;

an eigenvalue determination module, which determines an eigenvalue according to the steady state solution;

The oscillation space determination module is used for determining the oscillation space of the large deformation pipeline flow system according to the characteristic value.

Optionally, the control equation and the boundary condition determination module specifically include:

Governing equation determination unit for formulating and detF=1 to determine the control equation of the large deformation pipeline flow system; the control equation is the control equation after dimensionless processing; where Re is the Reynolds number, u _i , u _j are the directional fluid speeds, where i =1, ui is the fluid velocity in the x-axis direction, when _{i=2, u i is} the fluid velocity in the y-axis direction, when i=3, _ui is the fluid velocity in the z-axis direction, j=1 , u _j is the fluid velocity in the x-axis direction, when j=2, u _j is the fluid velocity in the y-axis direction, when j=3, u _j is the fluid velocity in the z-axis direction, t is time, x _j is the current configuration coordinate, p is the fluid pressure, is the shear modulus, F _iA,A is the derivative of the deformation gradient tensor with respect to the initial configuration coordinates, is the solid equivalent pressure, is the derivative of the inverse of the deformation gradient tensor with respect to the initial configuration coordinates, is the wall density, is the wall acceleration, detF is the determinant of the deformation gradient tensor;

The boundary conditions at the entrance determine the element for u=v=0 according to the formula and Determine the boundary conditions at the inlet; where u is the velocity of the fluid in the x direction, v is the velocity in the y direction of the fluid, w is the velocity in the z direction of the fluid, x ₁ is the x coordinate, and x ₂ is the y coordinate;

The rigid wall boundary condition determination element is used to determine the rigid wall boundary condition according to the formula u=v=w=0;

The elastic segment boundary condition determines the element for use according to the formula as well as Determine the boundary conditions of the elastic segment; where u is the velocity of the fluid in the x-direction, is the x-direction velocity of the pipe wall, v is the fluid y-direction velocity, is the velocity in the y direction of the pipe wall, w is the velocity in the z direction of the fluid, is the z-direction velocity of the pipe wall;

The elastic end boundary condition determines the element for use according to the formula as well as Determine the elastic end boundary conditions; where, is the displacement of the pipe wall in the x direction, is the displacement of the pipe wall in the y direction, is the displacement of the pipe wall in the z direction;

The element for determining the boundary conditions at the outlet is used to determine the boundary conditions at the outlet according to the formulas σ _t = 0 and σ _n = -P _d , where σ _t is the outlet interface shear stress, σ _n is the outlet interface normal stress, and P _d is the outlet interface external pressure.

Optionally, the feature value determination module specifically includes:

a matrix determination unit, configured to determine a mass matrix and a nonlinear matrix of the large deformation pipeline flow system according to the steady state solution;

An eigenvalue determining unit, configured to determine an eigenvalue according to the quality matrix and the nonlinear matrix.

Optionally, the oscillation space determination module specifically includes:

a first judgment unit, configured to judge whether the real part of the eigenvalue is equal to 0, and obtain a first judgment result;

an oscillation space curve determination unit, configured to determine an oscillation space curve if the first judgment result is expressed as the real part of the eigenvalue being equal to 0;

The oscillation space determination unit is configured to determine the oscillation space of the large deformation pipeline flow system according to the oscillation space curve.

According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: the present invention provides a method and system for determining the oscillation space of a large deformation pipeline flow system, by solving the characteristic values of the large deformation pipeline flow system, and According to the eigenvalue, the dynamic state of the large deformation pipeline flow system is determined, so as to avoid the problem that the existing three-dimensional model solves the problem of too much calculation for the transient solution, and accurately determine the oscillation space of the large deformation pipeline flow system.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings required in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some of the present invention. In the embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative labor.

Fig. 1 is the flow chart of the method for determining the oscillation space of the large deformation pipeline flow system provided by the present invention;

2 is a schematic diagram of a geometric model provided by the present invention;

3 is a schematic diagram of a rotating line provided by the present invention;

4 is a schematic diagram of a meshed geometric model provided by the present invention;

FIG. 5 is a structural diagram of the system for determining the oscillation space of the large deformation pipeline flow system provided by the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

The purpose of the present invention is to provide a method and system for determining the oscillation space of the large deformation pipeline flow system, which can accurately determine the oscillation space of the large deformation pipeline flow system.

In order to make the above objects, features and advantages of the present invention more clearly understood, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

Fig. 1 is a flow chart of a method for determining the oscillation space of a large deformation pipeline flow system provided by the present invention. As shown in Fig. 1, a method for determining the oscillation space of a large deformation pipeline flow system adopts an incompressible hyperelastic material to simulate large deformation A pipeline flow system; the method for determining the oscillation space of the large deformation pipeline flow system includes:

Step 101: Obtain the parameters of the large deformation pipeline flow system; the large deformation pipeline flow system parameters include pipeline geometric parameters, fluid parameters and pipe wall material parameters; the pipeline parameters include the total length of the pipeline, the inner radius of the pipeline, the diameter of the pipeline, and the thickness of the pipeline , pipe upstream length, pipe midstream length, and pipe downstream length; the fluid parameters include density and coefficient of viscosity; the pipe wall material parameters include shear modulus and density.

As shown in Figure 2, consider the fluid flowing through a cylindrical pipe of length L, inner radius R, and diameter D. The pipeline is divided into 3 sections, the upstream and downstream are non-deformed sections, the middle is the deformed section, its thickness is d, and it is subjected to an external pressure of size _Pw . The lengths of the upper, middle, and downstream sections are Lu, _Lm , and _Ld , _respectively . A fluid is an incompressible Newtonian fluid with a density ρ and a coefficient of viscosity μ. The flow is assumed to be laminar. The tube wall is made of an incompressible Neo-hookean hyperelastic material with a shear modulus of The density is During the interaction between the fluid and the pipe wall, the pipe wall is the boundary of the flow field and is subject to the force of the flow field on it.

Step 102: Determine the control equation and boundary conditions of the large deformation pipeline flow system according to the parameters of the large deformation pipeline flow system; the boundary conditions include inlet boundary conditions, rigid wall boundary conditions, elastic segment boundary conditions, and elastic end boundaries conditions and boundary conditions at the exit.

First consider the governing equations of the pipe wall. In the initial configuration, the equation of motion without considering the body force is:

where t represents time, represents the displacement of the pipe wall, represents the acceleration of the tube wall, π _iA,A is the derivative of the first Piora Kirchhoff stress with respect to the initial configuration coordinates, and the first Piora Kirchhoff stress can be expressed as:

where W is the strain energy density function, a function of the first, second, and third invariants of the left (right) Cauchy Green strain tensor, is a Lagrange multiplier introduced by the incompressible constraint, which can be understood as the solid equivalent pressure. F _iA is the deformation gradient tensor, is the inverse of the deformed gradient tensor, which can be expressed as

_xi represents the position vector in the current configuration, and X _A represents the position vector in the initial configuration. In order to ensure the incompressibility of the material, the determinant of the deformation gradient tensor needs to be kept as 1, namely:

detF=1 (4)

The tube wall adopts the Neo-hookean material model, and the strain energy density function is:

in is the shear modulus and I is the first invariant of the left (right) Cauchy Green strain tensor. The relationship between it and the deformation gradient tensor F _iA is:

Using equations (2), (3) and (5), equation (1) becomes:

in, is the wall shear modulus; F _iA is the deformation gradient tensor; F _iA,A is the derivative of the deformation gradient tensor to the initial configuration coordinates; is the inverse of the deformation gradient tensor; is the derivative of the inverse of the deformation gradient tensor with respect to the initial configuration coordinates; is the wall density; is the displacement of the pipe wall in three directions, when i=1, is the wall displacement in the x-axis direction, when i=2, is the wall displacement in the y-axis direction, when i=3, is the wall displacement in the z-axis direction; is the acceleration of the tube wall in three directions, when i=1, is the wall acceleration in the x-axis direction, when i=2, is the wall acceleration in the y-axis direction, when i=3, is the wall acceleration in the z-axis direction.

The fluid motion is described by the Navier Stokes equation and the continuity equation. For convenience, dimensionless parameters are introduced, and the quantities with an asterisk are dimensionless quantities. (ie: with and without asterisks mean the same thing, except that no asterisks are dimensional, and those with asterisks are dimensionless).

Where: Re is the Reynolds number, U ₀ is the average velocity of the pipeline flow in the non-deformed section, x _i is the coordinate in three directions, where, when i=1, x _i is the coordinate on the x-axis direction, and when i=2, x _i is the coordinate in the y-axis direction, when i=3, _xi is the coordinate in the z-axis direction; _ui is the fluid velocity in three directions, where, when i=1, _ui is the fluid velocity in the x-axis direction, When i=2, _ui is the fluid velocity in the y-axis direction, and when i=3, _ui is the fluid velocity in the z-axis direction; p is the fluid pressure; is the wall displacement in three directions, where, when i=1, is the wall displacement in the x-axis direction, when i=2, is the wall displacement in the y-axis direction, when i=3, is the wall displacement in the z-axis direction; t is time.

After dimensionless according to the above aspects, in order to simply remove the asterisk indicating dimensionless, the control equation of the coupled system after dimensionless can be obtained as:

detF=1 (12)

Among them, u _j is the fluid velocity in three directions, where, when i=1, u _j is the fluid velocity in the x-axis direction, when i=2, u _j is the fluid velocity in the y-axis direction, and when i=3, u _j is the fluid velocity in the z-axis direction.

The boundary conditions are as follows:

At the entrance (z=0): u=v=0, z is the axis along the pipe;

Rigid wall (0≤z≤L _u , r=R; L _u +L _m ≤z≤L, r=R): u=v=w=0;

Elastic segment (L _u ≤z≤L _u +L _m , R≤r≤R+d):

Elastic end (z=L _u , Lu +L _m , _R≤r≤R +d):

At exit (z=L): σ _t = 0; σ _n = -P _d ; where P _d is the downstream pressure and is a given constant.

Step 103: Using the finite element method, determine a steady state solution of the large deformation pipeline flow system according to the control equation and the boundary conditions.

During the finite element solution process, the boundary of the fluid region of the elastic segment will change. In order to avoid the deformity of the fluid grid when the boundary moves, the self-adaptive grid of the fluid is constructed by the rotating line method, as shown in Figure 3. In an elastic pipe, the mesh remains unchanged in the concentric circles, and there are many connected rotation lines between the concentric circles and the pipe wall. A little inner concentric dots with pipe wall point on the connected rotation line K. The points on the inner concentric circles are fixed. When the pipe wall moves, the rotation line K remains as a straight line segment rotating around a fixed point, and the nodes on the line expand and contract proportionally according to the movement of the pipe wall. After deformation, the pipe wall point movement to the point online node movement to the point point and point The relationship between is:

in,

The coordinates of points not on the rotation line are obtained from the points on the rotation line by linear difference.

As shown in Figure 4, after constructing the mesh by using the rotating line method on a pipe section, and then dividing it along the direction of the pipe, the mesh of the entire model can be obtained.

The partial derivative of velocity with respect to time in the Navier-Stokes equations due to grid movement is referenced to a fixed space. We define the time derivative δ/δt with reference to the grid movement space. Using the chain rule, δ/δt and The relationship between the Navier Stokes equations under the moving grid is obtained as:

Among them, w is the moving speed of the grid when the pipe wall is deformed, _ui is the fluid velocity, p is the fluid pressure, and Re is the Reynolds number.

In the finite element analysis, a 15-node triangular prism isoparametric element is used for fluids, and a 20-node hexahedral isoparametric element is used for solids. In order to ensure the convergence of the solution, the velocity and displacement use quadratic shape functions ψ ^(F) and ψ ^(S) to interpolate, respectively, and the fluid pressure and solid pressure use linear shape functions φ ^(P) , respectively. To interpolate:

In the formula, L ₁ , L ₂ , and L ₃ represent the area coordinates in the triangular prism isoparametric unit, and ξ, η, ζ represent the local coordinates in the three directions of x, y, and z in the isoparametric unit.

Therefore, there are fluid velocity degrees of freedom u, v, w at all 15 nodes of the fluid element, and only 6 vertices have fluid pressure degrees of freedom p. The solid element has displacement degrees of freedom at all 20 nodes Only 8 vertices have pressure degrees of freedom On the common node of fluid element and solid element, there are both fluid degrees of freedom and solid degrees of freedom.

The governing equations of the system are discretized by the Galerkin method, and the finite element equations are obtained. The weight function and the interpolation function are the same function. In the fluid governing equation, the viscous gradient term and the pressure gradient term are integrated by parts to obtain the equation:

where n is the outer normal unit vector of the boundary surface.

First get the finite element form of the solid governing equations in the current configuration:

where σ _ij is the Cauchy stress, σ _ij,j is the derivative of the Cauchy stress with respect to the coordinates of the current configuration, m _j is the external normal unit vector of the lower boundary surface of the current configuration, δ _ij is the delta operator, is the force tensor of the fluid on the pipe wall, which can be expressed as:

The initial configuration has the following relationship with the variables in the current configuration:

N _A is the outer normal unit vector of the lower boundary surface of the initial configuration. Combining equations (7), (18), (19) and (21), the finite element form of the solid governing equations under the initial configuration is obtained:

Since there is only the first-order derivative of time in the fluid equation, and the second-order derivative to time exists in the solid equation, in order to make the order consistent, the solid velocity degree of freedom ε _i (i=1,2,3 ), which represents the solid velocity in the three directions of x, y, and z. Due to the introduction of a new unknown ε _i , a new nodal equation needs to be added:

Express all equations in matrix form:

where U is the overall unknown vector u, v, w are the fluid velocities in the x, y, z directions, P is the fluid pressure, is the displacement of the solid pipe wall in the three directions of x, y, and z, The solid equivalent pressure, ε ₁ , ε ₂ , and ε ₃ are the solid wall velocities in the three directions of x, y, and z, M is the mass matrix, and K(U) represents the nonlinear stiffness matrix. F is the force vector and R is the residual vector, which should be zero when the calculation converges.

Step 104: Determine eigenvalues according to the steady state solution.

Step 105: Determine the oscillation space of the large deformation pipeline flow system according to the characteristic value.

The step 105 specifically includes: judging whether the real part of the characteristic value is equal to 0, and if so, determining an oscillation space curve; and determining an oscillation space of the large deformation pipeline flow system according to the oscillation space curve.

Among them, when the real part of the eigenvalue is equal to 0, it means that the eigenvalue is a point on the oscillation space curve; adjust the pipe wall parameters and fluid parameters, find other points on the oscillation space curve, and connect them as an oscillation space curve .

The eigenvalues of the system are based on the steady-state solution of the system, so the steady-state solution of the system needs to be solved first. When solving the steady-state solution, remove the time term in equation (24), and the steady-state equation to be solved for:

K(U)U-F=R=0

This is a nonlinear system of equations, solved iteratively using Newton-Raphson's method.

get the steady state solution The specific method for solving the modified Orr-Sommerfeld eigenvalue problem is roughly as follows. Let the steady state solution Make a perturbation ΔU, then solution for the system. make where ω and are the corresponding complex eigenvalues and eigenvectors, respectively. Bringing into equation (24), the characteristic equation is obtained as:

Determine the matrix in the formula A steady state solution is required value of .

The stability of the system is determined by the value of the eigenvalue ω. The number of valid eigenvalues that can be obtained from equation (25) is the same as that of the matrix M rank. When the real part of any one of the effective eigenvalues ω is greater than zero, the system is unstable; when all the real parts of the effective eigenvalues ω are less than zero, the system is stable; the critical neutrality between stability and instability of the system The point corresponds to the case where the largest real part of the effective eigenvalues ω is zero.

The characteristic equation solved in ARPACK is of the form Ax=λx, which is different from equation (25) in form. So Equation (25) is transformed into:

get the matrix to be solved The desired eigenvalue

Fig. 5 is the structure diagram of the current state determination system of the oscillation space of the large deformation pipeline flow system provided by the present invention. As shown in Fig. 5, a system for determining the current state of the oscillation space of the large deformation pipeline flow system adopts the incompressible superelasticity material to simulate the large deformation pipeline flow system; the current state determination system of the oscillation space of the large deformation pipeline flow system includes:

The parameter acquisition module 501 is used to acquire the parameters of the large deformation pipeline flow system; the large deformation pipeline flow system parameters include pipeline parameters, fluid parameters and pipe wall parameters when the fluid flows through the pipeline; the pipeline parameters include the total length of the pipeline, the Inner radius, pipe diameter, pipe thickness, pipe external pressure, pipe upstream length, pipe midstream length and pipe downstream length; the fluid parameters include density and viscosity coefficient; the pipe wall parameters include shear modulus and density.

A control equation and boundary condition determination module 502 is used to determine the control equation and boundary conditions of the large deformation pipeline flow system according to the large deformation pipeline flow system parameters; the boundary conditions include inlet boundary conditions, rigid wall boundary conditions, Elastic segment boundary conditions, elastic end boundary conditions, and outlet boundary conditions.

The control equation and boundary condition determination module 502 specifically includes:

Governing equation determination unit for formulating and detF=1 to determine the control equation of the large deformation pipeline flow system; the control equation is the control equation after dimensionless processing; where Re is the Reynolds number, u _i , u _j are the directional fluid speeds, where i =1, ui is the fluid velocity in the x-axis direction, when _{i=2, u i is} the fluid velocity in the y-axis direction, when i=3, _ui is the fluid velocity in the z-axis direction, j=1 , u _j is the fluid velocity in the x-axis direction, when j=2, u _j is the fluid velocity in the y-axis direction, when j=3, u _j is the fluid velocity in the z-axis direction, t is time, x _j is the current configuration coordinate, p is the fluid pressure, is the shear modulus, F _iA,A is the derivative of the deformation gradient tensor with respect to the initial configuration coordinates, is the solid equivalent pressure, is the derivative of the inverse of the deformation gradient tensor with respect to the initial configuration coordinates, is the wall density, is the wall acceleration, detF is the determinant of the deformation gradient tensor;

The boundary conditions at the entrance determine the element for u=v=0 according to the formula and Determine the boundary conditions at the inlet; where u is the velocity of the fluid in the x direction, v is the velocity in the y direction of the fluid, w is the velocity in the z direction of the fluid, x ₁ is the x coordinate, and x ₂ is the y coordinate;

The rigid wall boundary condition determination element is used to determine the rigid wall boundary condition according to the formula u=v=w=0;

The elastic segment boundary condition determines the element for use according to the formula as well as Determine the boundary conditions of the elastic segment; where u(t) is the velocity of the fluid in the x direction, is the x-direction velocity of the tube wall, v(t) is the fluid y-direction velocity, is the velocity in the y direction of the pipe wall, w(t) is the velocity in the z direction of the fluid, is the z-direction velocity of the pipe wall;

The elastic end boundary condition determines the element for use according to the formula as well as Determine the elastic end boundary conditions; where, is the displacement of the pipe wall in the x direction, is the displacement of the pipe wall in the y direction, is the displacement of the pipe wall in the z direction;

The element for determining the boundary conditions at the outlet is used to determine the boundary conditions at the outlet according to the formulas σ _t = 0 and σ _n = -P _d , where σ _t is the outlet interface shear stress, σ _n is the outlet interface normal stress, and P _d is the outlet interface external pressure.

The steady-state solution determination module 503 is configured to use the finite element method to determine the steady-state solution of the large deformation pipeline flow system according to the control equation and the boundary conditions.

The eigenvalue determining module 504 is configured to determine the eigenvalue according to the steady state solution.

The feature value determination module 504 specifically includes:

a matrix determination unit, configured to determine a mass matrix and a nonlinear matrix of the large deformation pipeline flow system according to the steady state solution;

An eigenvalue determining unit, configured to determine an eigenvalue according to the quality matrix and the nonlinear matrix.

The oscillation space determination module 505 is configured to determine the current state of the oscillation space of the large deformation pipeline flow system according to the characteristic value.

The oscillation space determination module 505 specifically includes:

a first judgment unit, configured to judge whether the characteristic value is greater than 0, and obtain a first judgment result;

A divergence space determination unit, configured to be a divergent space if the first judgment result indicates that the characteristic value is greater than 0, and the current state of the oscillation space of the large deformation pipeline flow system is a divergence space;

A stable space determination unit, configured to indicate that the current state of the oscillation space of the large deformation pipeline flow system is a stable space if the first judgment result indicates that the characteristic value is not greater than 0.

The material model for simulating the deformed part of the tube wall in the present invention is an incompressible hyperelastic model. Compared with the linear elastic model adopted by the existing model, the three-dimensional model provided by the present invention is closer to the human body tube wall, and the current state of the oscillation space is description is more accurate.

The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments, and the same and similar parts between the various embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant part can be referred to the description of the method.

In this paper, specific examples are used to illustrate the principles and implementations of the present invention. The descriptions of the above embodiments are only used to help understand the methods and core ideas of the present invention; meanwhile, for those skilled in the art, according to the present invention There will be changes in the specific implementation and application scope. In conclusion, the contents of this specification should not be construed as limiting the present invention.

Claims (8)

1. A method for determining the oscillation space of a flow system of a large-deformation pipeline is characterized in that an incompressible superelastic material is adopted to simulate the flow system of the large-deformation pipeline; the method for determining the oscillation space of the large deformation pipeline flow system comprises the following steps:

acquiring parameters of a flow system of the large-deformation pipeline; the parameters of the large-deformation pipeline flow system comprise pipeline geometric parameters, fluid parameters and pipe wall material parameters; the pipeline geometric parameters comprise the total length of the pipeline, the inner radius of the pipeline, the diameter of the pipeline, the thickness of the pipeline, the upstream length of the pipeline, the midstream length of the pipeline and the downstream length of the pipeline; the fluid parameters include density and viscosity coefficient; the pipe wall material parameters comprise shear modulus and density;

determining a control equation of the large deformation pipeline flow system according to the large deformation pipeline flow system parameters and acquiring boundary conditions; the boundary conditions include an entrance boundary condition, a rigid wall boundary condition, an elastic segment boundary condition, an elastic end boundary condition, and an exit boundary condition;

determining a steady state solution of the large deformation pipeline flow system according to the control equation and the boundary condition by using a finite element method;

determining a characteristic value according to the steady state solution;

and determining the oscillation space of the large deformation pipeline flow system according to the characteristic value.

2. The method for determining the oscillation space of the flow system of the large deformation pipe as claimed in claim 1, wherein the determining the control equation and the boundary condition of the flow system of the large deformation pipe according to the parameters of the flow system of the large deformation pipe specifically comprises:

according to the formulaAnd detF is 1, determining a control equation of the large deformation pipeline flow system; the control equation is subjected to non-dimensionalization processing; wherein Re is Reynolds number, u_i，u_jThe fluid velocity is in three directions, wherein when i is 1, u_iWhen the fluid velocity in the x-axis direction is 2, u_iWhen the fluid velocity in the y-axis direction is 3, u_iWhen j is 1, u is the fluid velocity in the z-axis direction_jWhen j is 2, u is the fluid velocity in the x-axis direction_jWhen j is 3, u is the fluid velocity in the y-axis direction_jIs the fluid velocity in the z-axis direction, t is the time, x_jFor the current configuration coordinate, p is the fluid pressure,as shear modulus, F_iA,AThe derivative of the deformation gradient tensor to the initial configuration coordinates,the equivalent pressure of the solid is the pressure,the derivative of the inverse of the deformation gradient tensor to the initial configuration coordinates,is the density of the tube wall and is,let detF be the determinant of deformation gradient tensor;

according to the formula u-v-0 anddetermining boundary conditions at an entrance; wherein u is the fluid x-direction velocity, v is the fluid y-direction velocity, w is the fluid z-direction velocity, x₁Is the x coordinate, x₂Is a y coordinate;

determining a rigid wall boundary condition according to the formula u-v-w-0;

according to the formulaAnddetermining elastic segment boundary conditions; wherein u is the velocity of the fluid in the x direction,is the x-direction velocity of the pipe wall, v is the y-direction velocity of the fluid,is the tube wall y-direction velocity, w is the fluid z-direction velocity,is the z-direction velocity of the tube wall;

according to the formulaAnddetermining an elastic end boundary condition; wherein,for the displacement of the tube wall in the x-direction,for the y-direction displacement of the tube wall,is the z-direction displacement of the tube wall;

according to the formula σ_t0 and σ_n＝-P_dDetermining boundary conditions at the outlet, where_tShear stress at outlet interface, σ_nIs the outlet interface normal stress, P_dIs the outlet external pressure.

3. The method for determining the oscillation space of the flow system of the large deformation pipeline according to claim 1, wherein the determining the characteristic value according to the steady state solution specifically comprises:

determining a mass matrix and a nonlinear matrix of the large deformation pipeline flow system according to the steady state solution;

and determining a characteristic value according to the quality matrix and the nonlinear matrix.

4. The method for determining the oscillation space of the flow system of the large deformation pipe as claimed in claim 1, wherein the determining the oscillation space of the flow system of the large deformation pipe according to the characteristic value specifically comprises:

judging whether the real part of the characteristic value is equal to 0 or not to obtain a first judgment result;

if the first judgment result shows that the real part of the characteristic value is equal to 0, determining an oscillation space curve;

and determining the oscillation space of the large deformation pipeline flow system according to the oscillation space curve.

5. A system for determining the oscillation space of a flow system of a large-deformation pipeline is characterized in that an incompressible superelastic material is adopted to simulate the flow system of the large-deformation pipeline; the system for determining the oscillation space of the large deformation pipeline flow system comprises:

the parameter acquisition module is used for acquiring the parameters of the flow system of the large deformation pipeline; the parameters of the large-deformation pipeline flow system comprise pipeline geometric parameters, fluid parameters and pipe wall material parameters; the pipeline geometric parameters comprise the total length of the pipeline, the inner radius of the pipeline, the diameter of the pipeline, the thickness of the pipeline, the upstream length of the pipeline, the midstream length of the pipeline and the downstream length of the pipeline; the fluid parameters include density and viscosity coefficient; the pipe wall material parameters comprise shear modulus and density;

the control equation and boundary condition determining module is used for determining the control equation and the boundary condition of the large deformation pipeline flow system according to the large deformation pipeline flow system parameters; the boundary conditions include an entrance boundary condition, a rigid wall boundary condition, an elastic segment boundary condition, an elastic end boundary condition, and an exit boundary condition;

the steady state solution determining module is used for determining a steady state solution of the large deformation pipeline flow system according to the control equation and the boundary condition by using a finite element method;

the characteristic value determining module is used for determining a characteristic value according to the steady-state solution;

and the oscillation space determining module is used for determining the oscillation space of the large deformation pipeline flow system according to the characteristic value.

6. The system for determining the oscillation space of the flow system of the large-deformation pipeline according to claim 5, wherein the control equation and boundary condition determining module specifically comprises:

a control equation determination unit for determining a control equation based on the formula And detF is 1, determining a control equation of the large deformation pipeline flow system; the control equation is subjected to non-dimensionalization processing; wherein Re is Reynolds number, u_i，u_jThe fluid velocity is in three directions, wherein when i is 1, u_iWhen the fluid velocity in the x-axis direction is 2, u_iWhen the fluid velocity in the y-axis direction is 3, u_iWhen j is 1, u is the fluid velocity in the z-axis direction_jWhen j is 2, u is the fluid velocity in the x-axis direction_jWhen j is 3, u is the fluid velocity in the y-axis direction_jIs the fluid velocity in the z-axis direction, t is the time, x_jFor the current configuration coordinate, p is the fluid pressure,as shear modulus, F_iA,AThe derivative of the deformation gradient tensor to the initial configuration coordinates,the equivalent pressure of the solid is the pressure,the derivative of the inverse of the deformation gradient tensor to the initial configuration coordinates,is the density of the tube wall and is,let detF be the determinant of deformation gradient tensor;

an entry boundary condition determining unit for determining a boundary condition according to the formula u-v-0 anddetermining boundary conditions at an entrance; wherein u is the fluid x-direction velocity, v is the fluid y-direction velocity, w is the fluid z-direction velocity, x₁Is the x coordinate, x₂Is a y coordinate;

a rigid wall boundary condition determining unit for determining a rigid wall boundary condition according to the formula u-v-w-0;

an elastic segment boundary condition determining unit for determining the boundary condition of the elastic segment according to the formulaAnddetermining elastic segment boundary conditions; wherein u is the velocity of the fluid in the x direction,is the x-direction velocity of the pipe wall, v is the y-direction velocity of the fluid,is the tube wall y-direction velocity, w is the fluid z-direction velocity,is the z-direction velocity of the tube wall;

an elastic end boundary condition determining unit for determining the elastic end boundary condition according to the formulaAnddetermining an elastic end boundary condition; wherein,for the displacement of the tube wall in the x-direction,for the y-direction displacement of the tube wall,is the z-direction displacement of the tube wall;

an outlet boundary condition determining unit for determining the boundary condition of the outlet according to the formula_t0 and σ_n＝-P_dDetermining boundary conditions at the outlet, where_tShear stress at outlet interface, σ_nIs the outlet interface normal stress, P_dIs the outlet external pressure.

7. The system for determining the oscillation space of the flow system of the large deformation pipeline according to claim 5, wherein the characteristic value determining module specifically comprises:

the matrix determination unit is used for determining a mass matrix and a nonlinear matrix of the large deformation pipeline flow system according to the steady state solution;

and the characteristic value determining unit is used for determining the characteristic value according to the quality matrix and the nonlinear matrix.

8. The system for determining the oscillation space of the flow system of the large deformation pipeline according to claim 5, wherein the oscillation space determining module specifically comprises:

the first judgment unit is used for judging whether the real part of the characteristic value is equal to 0 or not to obtain a first judgment result;

an oscillatory space curve determining unit, configured to determine an oscillatory space curve if the first determination result indicates that the real part of the characteristic value is equal to 0;

and the oscillation space determining unit is used for determining the oscillation space of the large deformation pipeline flow system according to the oscillation space curve.