Grating-equipped ellipsoidal liquid storage device and mechanical property simulation method thereof

Abstract

The application provides a kind of ellipsoidal liquid storage device with grating and its mechanical property simulation method, and the liquid storage structure includes: liquid tank body and the grating for dissipating sloshing energy arranged inside the liquid tank body, the liquid tank body and the grating are all spatial axisymmetric ellipsoids, a plurality of through holes are arranged on the grating and connected with the internal volume of the grating, and the porosity of the through holes is uniform; the upper part of the liquid tank body is provided with a liquid inlet; the lower part of the liquid tank body is provided with a liquid outlet; the mechanical property simulation method adopts three-dimensional axisymmetric liquid sloshing analysis satisfying Laplace equation to be reduced to two-dimensional solution, then the discrete equation of the meridian plane boundary is obtained, and the axisymmetric equal-geometry boundary element method matrix equation of axisymmetric liquid sloshing is obtained, and based on the axisymmetric equal-geometry boundary element method matrix equation, the dynamic water pressure p of the liquid storage device, the liquid surface elevation η, and the x-direction sloshing force are obtained; the liquid storage device has simple structure and good sloshing reduction effect; the stress calculation method has high accuracy and high efficiency.

Description

Technical Field

[0001] This invention relates to the field of liquid storage devices and their mechanical property simulation calculation technology, and in particular to an ellipsoidal liquid storage device with a grid and its mechanical property simulation method. Background Technology

[0002] Liquid sloshing is a widespread phenomenon in engineering fields such as aerospace, shipping, large aqueduct structures, nuclear power, and road transportation. The complex nonlinear motion exhibited by liquid sloshing, as well as the resulting unbalanced sloshing forces and moments, have a significant impact on the stability and safety of liquid tanks and their related structures.

[0003] Traditionally, sloshing reduction measures often employ active and semi-active methods to suppress liquid sloshing within containers. However, these require complex external control systems and consume external energy. Passive sloshing reduction measures, on the other hand, require no external control or energy input; they achieve sloshing reduction by altering the internal structure of the container. Among passive sloshing reduction measures, liquid storage devices with perforated structures possess the characteristics of absorbing and dissipating sloshing energy and are widely used in related research. However, research on liquid sloshing problems in liquid storage devices with perforated structures is currently at the stage of analytical solutions and experimental analysis for simple structures.

[0004] In existing technologies, traditional numerical methods for fluid simulation, such as finite difference, finite element, and finite volume methods, are all domain-specific discretization methods. Considering the special geometry of gridded liquid tanks, these numerical methods often require denser meshes to describe complex computational domains, which increases preprocessing and computational costs. In addition, traditional numerical methods often use interpolation-type basis functions (such as Lagrange basis functions) to approximate the geometry of the computational domain, which cannot achieve absolute accuracy. In other words, CAD modeling and computer-aided engineering (CAE) analysis are carried out at different levels, resulting in a disconnect between CAD and CAE technologies.

[0005] Therefore, there is an urgent need for an ellipsoidal liquid storage device with a grid and a simulation method for its mechanical properties, which can reduce swaying without any external control or energy input, and the force calculation method of the liquid storage device is highly accurate and efficient. Summary of the Invention

[0006] The purpose of this invention is to provide an ellipsoidal liquid storage device with a grid and a simulation method for its mechanical properties, aiming to solve the technical problems of traditional active and semi-active sloshing reduction measures requiring external control and external energy consumption, as well as the low accuracy and low efficiency of force calculation in passive sloshing reduction measures.

[0007] To achieve the above objectives, in a first aspect, the present invention provides an ellipsoidal liquid storage device with a grid, comprising: a liquid tank body and a grid disposed inside the liquid tank body for dissipating sloshing energy, wherein both the liquid tank body and the grid are spatial axisymmetric ellipsoids, and the grid is provided with a plurality of through holes communicating with its internal volume, and the porosity influence coefficient of the through holes is uniform.

[0008] The upper part of the liquid tank body is provided with a liquid inlet for injecting liquid into the liquid tank; the lower part of the liquid tank body is provided with a liquid drain hole for draining the liquid in the liquid tank.

[0009] As a further improvement to the above solution, the grille is installed inside the liquid tank body by a grille fixing bracket, and the grille fixing bracket is installed in the upper part of the liquid tank body.

[0010] As a further improvement to the above solution, a liquid tank fixing support is also provided at the bottom of the outer wall of the liquid tank body for fixing and supporting the liquid tank body.

[0011] Secondly, the present invention also provides a method for simulating the mechanical properties of the above-mentioned ellipsoidal liquid storage device with a grid, the steps of which include:

[0012] S1: Reduce the three-dimensional axisymmetric liquid sloshing analysis that satisfies the Laplace equation to a two-dimensional problem that is only related to the reference section;

[0013] S2: Introduce NURBS basis functions as shape functions to discretize the elements and obtain the discrete equations of the meridional boundary.

[0014] S3: Based on the discrete equation of the meridional boundary in step S2, obtain the axisymmetric isogeometric boundary element method matrix equation for axisymmetric liquid sloshing.

[0015] S4: Based on step S3, obtain the axisymmetric isogeometric boundary element method matrix equation, and obtain the dynamic water pressure p, liquid surface elevation η, and swaying force in the x direction of the liquid storage device.

[0016] As a further improvement to the above scheme, in step S1, the three-dimensional axisymmetric liquid sloshing analysis that satisfies the Laplace equation is reduced to a two-dimensional problem that is only related to the reference section. The specific steps are as follows:

[0017] Let S represent the domain boundary formed by the free liquid surface, the tank body, and the grid. f S r and S b The porosity influence coefficient of the grid is G. The liquid tank contains liquid of depth H. The liquid tank experiences a stress of x = Ae in the x-direction. -iωt The swaying displacement is given by A, where A is the amplitude of the swaying displacement, ω is the swaying frequency, t is the time, and g is the gravitational acceleration.

[0018] S11: The entire watershed is divided into two computational subdomains. The entire fluid domain is Ω. The first computational subdomain is the ellipsoidal domain Ω1 formed by the grid, and the second computational subdomain is the region Ω2Γ between the tank body and the grid. 1,l ,l=1,2,…,N;

[0019] S12: Represent the fluid in each subdomain using the velocity potential function Φ(x,y,z,t):

[0020] Φ(x,y,z,t)=φ(x,y,z)e -iωt (1)

[0021] In the above equation, φ(x,y,z) satisfies the three-dimensional Laplace equation:

[0022]

[0023] The boundary conditions for a liquid free surface are expressed as follows:

[0024]

[0025] The boundary conditions on the rigid sidewalls of the liquid tank body are:

[0026]

[0027] The boundary conditions on both sides of the grid can be expressed as:

[0028]

[0029] The superscripts "+" and "-" indicate the two sides of the grille closest to the axis, one inside and one outside.

[0030] S13: Let P and Q represent the source point and field point respectively, and their perpendicular distances to the central axis z-axis are r. P and r Q Considering the above boundary conditions and the axisymmetric nature of the computational domain, the general axisymmetric boundary integral equation of the governing equations can be expressed as:

[0031]

[0032] Where m = 0, 1, 2, ..., ∞ are integers related to the oscillation mode, and Γ is the generatrix of the axisymmetric three-dimensional surface. It is a constant related to the geometry at point P. and The velocity potentials at the source point and the field point are respectively. and All of them are quantities to be solved in equation (6).

[0033] As a further improvement to the above scheme, its characteristic is that the basic solution and Determined by the following formula:

[0034]

[0035]

[0036] Where, β=β Q -β P Let β be the angle between the projections of point P and point Q onto the o-xy plane. P and β Q Let z be the angle between the projections of two points onto the o-xy plane and the x-axis, respectively. P and z Q Let P and Q be the z-coordinates. b = 2r Q r P , n r and n z Let r be the radial and axial components of the unit normal vector at point Q, respectively. PQ It is the distance from point P to point Q in three-dimensional space. and For the first and second kind of complete elliptic integrals.

[0037] As a further improvement to the above scheme, the characteristic is that r PQ It can be calculated using the following formula:

[0038]

[0039] and They can be represented as:

[0040]

[0041]

[0042] As a further improvement to the above scheme, the feature is that, in step S2, the discrete equation of the meridional boundary is as follows;

[0043]

[0044] Where e′ represents the cell number where source point i is located. Let J represent the local coordinates on element e′, Ne be the total number of elements, and J be the Jacobian determinant of element e. e Let ξ′ be the parametric coordinates of the source point, ξ be the parametric coordinates, and the local coordinates of each element be... Let C be a basis function on unit e. i Let i = 1, 2, ..., n be the control points on the corresponding unit e. and Let be the velocity potential and flux on unit e, respectively, and κ represent the order of the curve.

[0045] As a further improvement to the above scheme, the specific steps for obtaining the axisymmetric isogeometric boundary element method matrix equation for axisymmetric liquid sloshing in step S3 are as follows:

[0046] S31: A set of placement points is introduced to construct the system equations of the isogeometric boundary element method, which can be expressed in parameter space as:

[0047]

[0048] Where n is the number of control points;

[0049] S32: Integrating equation (11) over all boundary elements for each configuration point yields the matrix equation for the axisymmetric liquid sloshing problem:

[0050] Hφ=Gq (13)

[0051] Here, H and G are coefficient matrices, and vectors φ and q contain the velocity potential and flux at all control points, respectively.

[0052] As a further improvement to the above scheme, in step S4, based on the axisymmetric isogeometric boundary element method matrix equation obtained in step S3, the specific steps for obtaining the dynamic water pressure p, liquid surface elevation η, and swaying force in the x-direction of the liquid storage device are as follows:

[0053] S41: Determine the matrix equation for the axisymmetric liquid sloshing problem of the ellipsoidal liquid storage device with grid:

[0054]

[0055]

[0056] Among them, Γ i,j Subfield Ω i and Ω j The boundary between them, φ i,j and q i,j Representing the boundary Γ i,j Above Ω i The velocity potential and flux on one side, and H accordingly i,j and G i,j Represents the coefficient matrices H and G related to φ i,j and q i,j The corresponding block matrix;

[0057] S42: Substituting equations (3) and (4) into equation (14) yields:

[0058]

[0059]

[0060] Solve the system of equations (15) to obtain the velocity potential and flux at all control points;

[0061] S43: The dynamic water pressure p inside the tank is given by p = -ρΦ ,t The liquid level elevation is obtained by formula (16) as follows:

[0062]

[0063] The swaying force in the x-direction is calculated using equation (17) as follows:

[0064]

[0065] Among them, F r and F p These are the swaying forces acting per unit length along the z-direction on the tank body and the grid, respectively:

[0066]

[0067] Among them, R r and R p p represents the distance from a point on the tank body and a point on the grid to the axis of symmetry, respectively. r , and These are the dynamic water pressures acting on the tank body and both sides of the grid, respectively.

[0068] Because the present invention adopts the above technical solutions, the beneficial effects of this application are as follows:

[0069] 1. This invention provides an ellipsoidal liquid storage device with a grid, comprising: a liquid tank body and a grid disposed inside the liquid tank body for dissipating sloshing energy. Both the liquid tank body and the grid are spatially axisymmetric ellipsoids. The grid has a plurality of through holes communicating with its internal volume, and the porosity influence coefficient of the through holes is uniform. The upper part of the liquid tank body is provided with a liquid inlet for injecting liquid into the liquid tank. The lower part of the liquid tank body is provided with a liquid drain hole for discharging liquid from the liquid tank. This invention achieves excellent sloshing reduction effect through the ellipsoidal liquid tank body, the ellipsoidal grid nested inside the liquid tank body, and the through holes uniformly disposed on the ellipsoidal grid communicating with its internal volume. It requires no external control or external energy consumption; the ellipsoidal grid with uniformly disposed through holes effectively absorbs and dissipates sloshing energy. Furthermore, the anti-sloshing structure adopted by this invention is simple and easy to manufacture.

[0070] 2. This invention also provides a simulation method for the mechanical properties of an ellipsoidal liquid storage device with a grid. First, the three-dimensional axisymmetric liquid sloshing analysis satisfying the Laplace equation is reduced to a two-dimensional problem only related to the reference section. Then, NURBS basis functions are introduced as shape functions for element discretization to obtain the discrete equations of the meridional boundary. Next, based on the obtained discrete equations of the meridional boundary, the axisymmetric isogeometric boundary element method matrix equations for axisymmetric liquid sloshing are obtained. Finally, based on the obtained axisymmetric isogeometric boundary element method matrix equations, the dynamic water pressure p, liquid surface elevation η, and sloshing force in the x-direction of the liquid storage device are obtained. This invention proposes for the first time an axisymmetric isogeometric boundary element method for liquid tank mechanical simulation, requiring only the discretization of the meridional boundary. This achieves two order reductions in solving the liquid sloshing problem in a three-dimensional liquid tank, simplifying the preprocessing of the calculation and analysis and accurately describing the geometry, thus significantly improving computational efficiency and accuracy. Numerical results show that the internal grid installation has a significant energy dissipation effect, providing theoretical guidance and technical support for the design of large liquid tanks and promoting the seamless integration of CAD and CAE technologies. Attached Figure Description

[0071] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0072] Figure 1 This is a three-dimensional structural diagram of the liquid storage device;

[0073] Figure 2 This is a simplified diagram of the liquid tank pump body and its Cartesian coordinate system;

[0074] Figure 3 It is the meridional surface of the half-full tank body;

[0075] Figure 4 This is a schematic diagram of the geometric boundary element mesh of the half-full liquid tank body.

[0076] Table 1 compares the convergence of the normalized characteristic frequencies of a half-full tank calculated by different numerical methods when a = b = R and d1 / a = d2 / b = 0.001.

[0077] Figure 5 Given a = 1.6, b = 3.1, d² / b = 0.5, and the excitation frequency is ω / (g / b). 1 / 2 When =1.9, the variation of sloshing force in the liquid tank with the transverse dimension of grid 4 under different porosity influence coefficients is shown in the figure.

[0078] Figure 6 Given a = 1.6, b = 3.1, d1 / b = 0.5, and the excitation frequency is ω / (g / b). 1 / 2 When =1.9, the variation of sloshing force in the liquid tank with the longitudinal dimension of grid 4 under different porosity influence coefficients is shown in the figure.

[0079] Figure 7 This is a graph showing the variation of the liquid level elevation in the tank with the excitation frequency under different transverse dimensions of the grid 4 when a=1.6, b=3.1, d2 / b=0.5, and G=0.50.

[0080] Figure 8 This is a graph showing the variation of the liquid level elevation in the tank with the excitation frequency under different longitudinal dimensions of the grid 4 when a=1.6, b=3.1, d1 / b=0.5, and G=0.50.

[0081] Figure label:

[0082] 1. Liquid inlet; 2. Grille fixing bracket; 3. Liquid tank body; 4. Grille; 5. Drain hole; 6. Liquid tank base; 7. Liquid;

[0083] The realization of the objective, functional characteristics and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0084] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0085] It should be noted that all directional indicators such as up, down, etc. in the embodiments of the present invention are only used to explain the relative positional relationship and movement of the components in a specific posture as shown in the attached figure. If the specific posture changes, the directional indicator will also change accordingly.

[0086] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0087] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0088] In the above embodiments, those skilled in the art can use existing technology for software control. This invention only protects a liquid storage device with multiple openings and their interconnection relationships.

[0089] Example 1:

[0090] Reference Figure 1-8 The present invention provides an ellipsoidal liquid storage device with a grid, comprising: a liquid tank body 3 and a grid 4 disposed inside the liquid tank body 3 for dissipating sloshing energy. Both the liquid tank body 3 and the grid 4 are spatial axisymmetric ellipsoids. The grid 4 is provided with a plurality of through holes that connect its internal volume, and the porosity influence coefficient of the through holes is uniform.

[0091] The upper part of the liquid tank body 3 is provided with a liquid inlet 1 for injecting liquid 7 into the liquid tank; the lower part of the liquid tank body is provided with a liquid drain hole 5 for draining liquid 7 from the liquid tank; and in this embodiment, the grid 4 is set inside the liquid tank body 3 by a grid fixing bracket 2, and the grid fixing bracket 2 is set in the upper part of the liquid tank body 3; the bottom of the outer wall of the liquid tank body 3 is also provided with a liquid tank fixing support 6 for fixing and supporting the liquid tank body 3.

[0092] This invention achieves excellent sloshing reduction by using an ellipsoidal liquid tank body 3, an ellipsoidal grid 4 nested inside the liquid tank body 3, and through holes uniformly arranged on the ellipsoidal grid 4 that connect its internal volume. This results in a solution that requires no external control or energy consumption; the ellipsoidal grid 4 with its uniformly arranged through holes effectively absorbs and dissipates sloshing energy. Furthermore, the anti-sloshing structure used in this invention is simple and easy to manufacture. Additionally, the use of openings to reduce sloshing reduces material consumption, resulting in a lower manufacturing cost for the liquid storage device provided by this invention.

[0093] Example 2:

[0094] Secondly, referring to Figures 2-8 The present invention also provides a method for simulating the mechanical properties of the above-mentioned ellipsoidal liquid storage device with grid, the steps of which include:

[0095] S1: Reduce the three-dimensional axisymmetric liquid sloshing analysis that satisfies the Laplace equation to a two-dimensional problem that is only related to the reference section;

[0096] S2: Introduce NURBS basis functions as shape functions to discretize the elements and obtain the discrete equations of the meridional boundary.

[0097] S3: Based on the discrete equation of the meridional boundary in step S2, obtain the axisymmetric isogeometric boundary element method matrix equation for axisymmetric liquid sloshing.

[0098] S4: Based on step S3, obtain the axisymmetric isogeometric boundary element method matrix equation, and obtain the dynamic water pressure p, liquid surface elevation η, and swaying force in the x direction of the liquid storage device;

[0099] This invention proposes for the first time an axisymmetric isogeometric boundary element method for mechanical simulation of liquid tanks. It only requires discretization of the meridional boundary, achieving two order reductions in solving the liquid sloshing problem in a three-dimensional liquid tank. On the one hand, it simplifies the preprocessing of computational analysis, and on the other hand, it can accurately describe the geometry, thus significantly improving computational efficiency and accuracy. Numerical results show that the energy dissipation effect of the internal grid is significant, providing theoretical guidance and technical support for the design of large liquid tanks, and promoting the seamless integration of CAD and CAE technologies.

[0100] As a preferred embodiment, in step S1, the three-dimensional axisymmetric liquid sloshing analysis that satisfies the Laplace equation is reduced to a two-dimensional problem that is only related to the reference section. The specific steps are as follows:

[0101] Let S represent the domain boundary formed by the free liquid surface, the tank body, and the grid. f S r and S bThe porosity influence coefficient of the grid is G. The liquid tank contains liquid of depth H. The liquid tank experiences a stress of x = Ae in the x-direction. -iωt The swaying displacement is given by A, where A is the amplitude of the swaying displacement, ω is the swaying frequency, t is the time, and g is the gravitational acceleration.

[0102] S11: The entire watershed is divided into two computational subdomains. The entire fluid domain is Ω. The first computational subdomain is the ellipsoidal domain Ω1 formed by the grid, and the second computational subdomain is the region Ω2Γ between the tank body and the grid. 1,l ,l=1,2,…,N;

[0103] S12: Represent the fluid in each subdomain using the velocity potential function Φ(x,y,z,t):

[0104] Φ(x,y,z,t)=φ(x,y,z)e -iωt (1)

[0105] In the above equation, φ(x,y,z) satisfies the three-dimensional Laplace equation:

[0106]

[0107] The boundary conditions for a liquid free surface are expressed as follows:

[0108]

[0109] The boundary conditions on the rigid sidewalls of the liquid tank body are:

[0110]

[0111] The boundary conditions on both sides of the grid can be expressed as:

[0112]

[0113] The superscripts "+" and "-" indicate the two sides of the grille closest to the axis, one inside and one outside.

[0114] S13: Let P and Q represent the source point and field point respectively, and their perpendicular distances to the central axis z-axis are r. P and r Q Considering the above boundary conditions and the axisymmetric nature of the computational domain, the general axisymmetric boundary integral equation of the governing equations can be expressed as:

[0115]

[0116] Where m = 0, 1, 2, ..., ∞ are integers related to the oscillation mode, and Γ is the generatrix of the axisymmetric three-dimensional surface. χ is a constant related to the geometry at point P, and χ is the internal spatial angle at point P. If P is inside or outside the computational domain, χ is equal to 4π or 0, respectively. For a smooth boundary, χ = 2π. and The velocity potentials at the source point and the field point are respectively. and All of these are quantities to be solved in equation (6). Basic solution and Determined by equation (7):

[0117]

[0118]

[0119] Where, β=β Q -β P Let β be the angle between the projections of point P and point Q onto the o-xy plane. P and β Q Let z be the angle between the projections of two points onto the o-xy plane and the x-axis, respectively. P and z Q Let P and Q be the z-coordinates. b = 2r Q r P , n r and n z Let r be the radial and axial components of the unit normal vector at point Q, respectively. PQ It is the distance from point P to point Q in three-dimensional space. and For the first and second kind of complete elliptic integrals.

[0120] As a preferred embodiment, r PQ It can be calculated using the following formula:

[0121]

[0122] and F They can be represented as:

[0123]

[0124]

[0125] In a preferred embodiment, in step S2, the discrete equation of the meridional boundary is as follows;

[0126]

[0127] Where e′ represents the cell number where source point i is located. Let J represent the local coordinates on element e′, Ne be the total number of elements, and J be the Jacobian determinant of element e. e Let ξ′ be the parametric coordinates of the source point, ξ be the parametric coordinates, and the local coordinates of each element be... Let C be a basis function on unit e. i Let i = 1, 2, ..., n be the control points on the corresponding unit e. and Let be the velocity potential and flux on unit e, respectively, and κ represent the order of the curve.

[0128] Specifically, the process of obtaining the discrete equations of the meridional boundary is as follows:

[0129] We introduce NURBS basis functions as shape functions for element discretization. Assuming the parametric coordinates are represented by ξ, given n NURBS basis functions R... i,κ i = 1, 2, ..., n, and the corresponding control points C i If i = 1, 2, ..., n, then the NURBS curve can be represented as:

[0130]

[0131] The problem of liquid sloshing under external excitation along the x-direction can be regarded as an anti-axisymmetric mode, in which the value of m is equal to 1. At this time, equation (6) can be simplified to:

[0132]

[0133] To ensure consistency in program implementation, Gaussian integration is used for integration operations on NURBS elements. Therefore, a mapping relationship from local coordinates to parametric coordinates is required, namely:

[0134]

[0135] in and Given the coordinate values ​​of the two endpoints of the e-th element, the Jacobian determinant for the transformation from parameter space to physical space can be expressed as:

[0136]

[0137] The transformation relationships from parameter space to physical space and from local space to parameter space are respectively expressed as follows:

[0138]

[0139] In the formula, ξ2 and ξ1 are the parametric coordinates of the two endpoints of the element. According to the isoparametric concept, the element geometry, velocity potential, and flux can be expressed as:

[0140]

[0141] Substituting equation (11-5) into equation (6-1) and considering that ξ is The function can be expressed as equation (11).

[0142] As a preferred embodiment, the specific steps for obtaining the axisymmetric isogeometric boundary element method matrix equation for axisymmetric liquid sloshing in step S3 are as follows:

[0143] S31: A set of placement points is introduced to construct the system equations of the isogeometric boundary element method, which can be expressed in parameter space as:

[0144]

[0145] Where n is the number of control points;

[0146] S32: Integrating equation (11) over all boundary elements for each configuration point yields the matrix equation for the axisymmetric liquid sloshing problem:

[0147] Hφ=Gq (13)

[0148] Here, H and G are coefficient matrices, and vectors φ and q contain the velocity potential and flux at all control points, respectively.

[0149] In a preferred embodiment, the steps in step S4, based on the axisymmetric isogeometric boundary element method matrix equation obtained in step S3, to obtain the dynamic water pressure p, liquid surface elevation η, and swaying force in the x-direction of the liquid storage device, are as follows:

[0150] S41: Determine the matrix equation for the axisymmetric liquid sloshing problem of the ellipsoidal liquid storage device with grid:

[0151]

[0152]

[0153] Among them, Γ i,j Subfield Ω i and Ω j The boundary between them, φ i,j and q i,j Representing the boundary Γ i,j Above Ω i The velocity potential and flux on one side, and H accordingly i,j and G i,j Represents the coefficient matrices H and G related to φ i,j and q i,j The corresponding block matrix;

[0154] S42: Substituting equations (3) and (4) into equation (14) yields:

[0155]

[0156]

[0157] Solve the system of equations (15) to obtain the velocity potential and flux at all control points;

[0158] S43: The dynamic water pressure p inside the tank is given by p = -ρΦ ,t The liquid level elevation is obtained by formula (16) as follows:

[0159]

[0160] The swaying force in the x-direction is calculated using equation (17) as follows:

[0161]

[0162] Among them, F r and F p These are the swaying forces acting per unit length along the z-direction on the tank body and the grid, respectively:

[0163]

[0164] Among them, R r and R p p represents the distance from a point on the tank body and a point on the grid to the axis of symmetry, respectively. r , and These are the dynamic water pressures acting on the tank body and both sides of the grid, respectively.

[0165] It should be noted that, in this invention, the relevant calculations are based on linear potential flow theory.

[0166] See attached document Figure 3 The horizontal and vertical half-axis of the liquid tank body are a and b, respectively, and the horizontal and vertical half-axis of the perforated grid are d1 and d2, respectively.

[0167] See attached document Figure 4 The initial uniform geometric boundary element mesh of the gridded ellipsoidal liquid tank is given. To illustrate the hydrodynamic characteristics of the system, in the relevant examples, a = 1.6 and b = 3.1.

[0168] Referring to Table 1, the first six dimensionless characteristic frequencies (ω) of the semi-full spherical container are listed. 2For comparison, the analytical solutions are also listed in the table. Both the boundary element method and the model proposed in this invention use quadratic elements, containing 25, 33, 41, and 49 nodes (control points), respectively. It can be seen that, compared with the traditional boundary element method, the calculation results of the axisymmetric and other geometric boundary element method proposed in this invention have better consistency with the analytical solutions, and the convergence speed is significantly faster than the boundary element method. Especially for low-order modes, the calculation results of this invention using 25 control points have converged, and the accuracy is much higher than that of the traditional boundary element method.

[0169] Table 1

[0170]

[0171] See attached document Figure 5 The excitation frequency ω / (g / b) is given. 1 / 2 =1.9, with fixed parameters d2 / b = 0.5, the dimensionless swaying force |F x |Based on the variation of the transverse dimension d1 / a of the grille 4, five porosity influence coefficients (G = 0.10, 0.30, 0.50, 0.70, and 0.90) were selected for comparison. It can be seen that as d1 / a increases, |F x The value of | first decreases to a minimum, and as the value of G increases, the position of the minimum value gradually shifts to the right. When the lateral dimension of the grid 4 is close to the transverse half-axis of the tank body, |F x | Gradually increases to a constant value, and the smaller the G value, the more |F x The smaller.

[0172] See attached document Figure 6 The excitation frequency ω / (g / b) is given. 1 / 2 =1.9, with fixed parameters d1 / a = 0.5, the dimensionless swaying force |F x |Based on the variation of the longitudinal dimension d1 / a of the grille 4, five porosity influence coefficients (G = 0.10, 0.30, 0.50, 0.70, and 0.90) were selected for comparison. It can be seen that as the longitudinal dimension of the grille 4 increases, |F x The curvature of the curve gradually decreases, and the curvature changes significantly when d² / b ≤ 0.4.

[0173] See attached document Figure 5-6 Analysis shows that a reasonable lateral dimension and a large longitudinal dimension can enable the grid to more effectively suppress the liquid sloshing phenomenon in the ellipsoidal liquid tank.

[0174] See attached document Figure 7Given fixed parameters d2 / b = 0.5 and porosity influence coefficient G = 0.5, and |η| / A as the dimensionless liquid level elevation at the intersection of the container sidewall and the x-axis, it can be seen that changing d1 / a has a significant impact on the liquid level elevation. Furthermore, as d1 / a increases, the peak value of |η| / A first decreases and then increases. When d1 / a = 0.1 and d1 / a = 0.9, the curves basically overlap. This indicates that grids with excessively small or large lateral dimensions have no significant effect on suppressing liquid sloshing in the ellipsoidal container.

[0175] See attached document Figure 8 Given a fixed parameter d1 / a = 0.5 and a porosity influence coefficient G = 0.5, and |η| / A as the dimensionless liquid level elevation at the intersection of the container sidewall and the x-axis, it can be seen that changing d2 / b has a significant impact on the liquid level elevation. Furthermore, |η| / A initially decreases sharply with the increase of d2 / b, and then the rate of change of |η| / A gradually decreases as d2 / b further increases.

[0176] See attached document Figure 7-8 Analysis shows that liquid sloshing in an ellipsoidal container is more sensitive to changes in the longitudinal dimension of the perforated structure.

[0177] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. All equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A method for simulating mechanical properties of a girded ellipsoidal liquid storage device, characterized in that, The steps include: S1: reducing the three-dimensional axisymmetric liquid sloshing analysis satisfying Laplace equation to a two-dimensional problem only related to a reference section; S2: introducing NURBS basis functions as shape functions for element discretization to obtain discrete equations of meridional plane boundaries, which are as follows: (11) in, Represents the source point The unit number it belongs to. Representative Unit Local coordinates on, The total number of units, units Jacobi determinant express, The coordinates of the source point. For parametric coordinates, the local coordinates of each element. , For unit basis functions on, For the corresponding unit Control points on, and Units The velocity potential and flux on the surface Indicates the order of the curve; S3: obtaining an axisymmetric isogeometric boundary element method matrix equation of axisymmetric liquid sloshing based on the discrete equations of meridional plane boundaries in step S2, and the step is specifically as follows: S31: introducing a set of configuration points for constructing an isogeometric boundary element method system equation, which can be expressed in a parameter space as: (12) wherein is the number of control points; S32: performing integral of formula (11) on all boundary elements for each configuration point to finally obtain a matrix equation of the axisymmetric liquid sloshing problem: (13) wherein, and is a coefficient matrix, the vector and respectively contain the velocity potential and flux at all control points; S4: obtaining the axisymmetric isogeometric boundary element method matrix equation based on step S3 to obtain the hydrodynamic pressure of the liquid storage device , liquid surface elevation , and directional sloshing force; The application also discloses an ellipsoidal liquid storage device with a grid. The liquid tank body and the grid are both spatial axisymmetric ellipsoids, the grid is provided with a plurality of through holes communicating with the internal volume of the grid, and the aperture influence coefficient of the through holes is uniform. The upper portion of the liquid tank body is provided with a liquid inlet for injecting liquid into the liquid tank, and the lower portion of the liquid tank body is provided with a liquid outlet for discharging liquid in the liquid tank.

2. The method according to claim 1, wherein The grid is arranged in the interior of the liquid tank body through a grid fixing support arranged in the upper portion of the interior of the liquid tank body.

3. The method of claim 1 or 2, wherein the method is characterized by, The outer wall of the liquid tank body is further provided with a liquid tank fixing support for fixing and supporting the liquid tank body.

4. The method of claim 1, wherein the method is characterized by, In step S1, the three-dimensional axisymmetric liquid sloshing analysis satisfying Laplace equation is reduced to a two-dimensional problem only related to a reference section, and the specific steps are as follows: Let the domain boundaries formed by the free liquid surface, the tank body, and the grid be represented as follows: , and The porosity influence coefficient of the grid is The liquid tank body contains a depth of The liquid, the tank is Directional bearing The swaying displacement, among which The amplitude of the sway displacement. For the oscillation frequency, For time, gravitational acceleration ; S11: divide the whole flow field into two calculation sub-fields, the whole flow field is , the first calculation sub-field is the ellipsoid field formed by the grid , and the second calculation sub-field is the region between the liquid tank body and the grid ; S12: Adopt a velocity potential function for the fluid in each subdomain Indicates: (1) In the above formula satisfies the three-dimensional Laplace equation: (2) The liquid free surface boundary condition is expressed as: , in the above (3) The boundary condition on the rigid side wall of the liquid tank body is: , in the upper (4) The boundary condition on both sides of the grid can be expressed as: (5) wherein the superscripts "+" and " indicate the two sides of the grid close to the inner and outer of the axis; S13: Use and denote the source point and the field point, respectively, and the vertical distance from the source point and the field point to the central axis of the axisymmetric domain is and and Considering the boundary conditions mentioned above and the axisymmetric property of the computational domain, the general axisymmetric boundary integral equation of the governing equation can be expressed as: (6) wherein is an integer related to the sloshing mode, is a generatrix of an axisymmetric three-dimensional surface, is a constant related to the geometry at the point, is a constant related to the geometry at the point, and are the velocity potentials of the source point and the field point, respectively, and are both to be solved quantities of equation (6).

5. The method of claim 4, wherein the method further comprises: Fundamental solution and is determined by the equation: ，(7) ， where is the point to the point is the angle between the projection of the two points on the plane, and are the angles between the projections of the two points on the plane and the axis, and are the coordinates of the two points, and are the components of the unit normal vector at the point along the radial and axial directions, , are the coordinates of the two points, , , , and are the components of the unit normal vector at the point along the radial and axial directions, is the distance from the point to the point is the distance from the point to the point is the distance from the point to the point and are the first and second complete elliptic integrals.​​ 6. The method of claim 5, wherein the method further comprises: may be calculated from the formula: (8) and may be expressed as: ， (9) (10)。 7. The method according to claim 6, wherein In step S4, based on the step S3, the axisymmetric isogeometric boundary element method matrix equation is obtained to obtain the hydrodynamic pressure of the liquid storage device , liquid surface elevation , and The step of the direction sloshing force is specifically as follows: S41: determining the matrix equation of the axisymmetric liquid sloshing problem of the ellipsoidal liquid storage device with a grid: ， (14) where denotes the boundary between the subdomains and , and denote the velocity potential and flux on the upper side of the boundary and , respectively, and and denote the block matrices in the coefficient matrices and corresponding to and , respectively; S42: substituting formula (3) and formula (4) into formula (14) to obtain: ， (15) Solving the equation group formula (15) to obtain the velocity potential and flux on all control points; S43: Dynamic water pressure inside the tank Depend on The liquid level elevation is obtained by formula (16) as follows: (16) The directional sway force is calculated by equation (17) as follows: ， (17) wherein, and are the sloshing forces acting on the tank body and the grid per unit length in the direction, i.e.: ， ， wherein, and are the distance from a point on the tank body and the grid to the axis of symmetry, respectively, , and are the hydrodynamic pressures acting on the two sides of the tank body and the grid, respectively.

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