CN114611423A - Three-dimensional multiphase compressible fluid-solid coupling rapid calculation method - Google Patents

Three-dimensional multiphase compressible fluid-solid coupling rapid calculation method Download PDF

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CN114611423A
CN114611423A CN202210208677.9A CN202210208677A CN114611423A CN 114611423 A CN114611423 A CN 114611423A CN 202210208677 A CN202210208677 A CN 202210208677A CN 114611423 A CN114611423 A CN 114611423A
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谢文锋
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Haifang Shanghai Technology Co ltd
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Abstract

The invention particularly relates to a rapid calculation method for three-dimensional multiphase compressible fluid-solid coupling, which comprises the following steps: establishing a three-dimensional model of the impacted material and dividing a Cartesian non-uniform grid; establishing a mass, momentum and energy equation and a state equation of the inviscid compressible fluid under Cartesian coordinates; performing multiphase compressible fluid-solid coupling calculation; providing initial pressure to the structural field through a fluid-solid coupling solver, and simultaneously obtaining the initial node speed provided by the structural field; and simulating the whole underwater impact period and the whole flow by a compressible-incompressible conversion solving algorithm. The three-dimensional multiphase compressible fluid algorithm and the fluid-solid coupling algorithm based on the virtual medium method greatly improve the precision and stability of underwater impact simulation calculation; the algorithm for interconversion between the underwater shock wave stage and the bubble dynamics stage judges the conversion between the two algorithms based on the pressure of a flow field, and greatly improves the efficiency of overall solving the underwater shock problem.

Description

Three-dimensional multiphase compressible fluid-solid coupling rapid calculation method
Technical Field
The invention belongs to the technical field of fluid calculation, and particularly relates to a three-dimensional multiphase compressible fluid-solid coupling rapid calculation method.
Background
As the underwater strong impact is a highly complex interdisciplinary physical and chemical problem with multiple phases, multiple media and multiple physical fields, the technologies adopted for simulating the problems comprise a high-order precision shock wave capture algorithm, a compressible multiphase computational fluid mechanics algorithm, a large-deformation large-displacement structure finite element algorithm and a strong impact multi-media solid-solid coupling algorithm. At present, no efficient and stable algorithm is internationally provided for solving the underwater strong impact. Although researchers have made certain breakthrough in the local field, there are many problems in forming a complete and efficient set of underwater shock simulation algorithms by fully coupling these algorithms, including the problems of multiphase flow interface decoupling, fluid-solid interface cavitation collapse, and huge calculation amount of the integral simulation at the dynamic stage of shock waves and bubbles.
The current main methods applied to underwater shock include any Euler-Lagrange coupling algorithm, a dipping boundary method and a loose fluid-solid coupling algorithm.
The method is a method which is relatively wide in application at present and solves the problems that the underwater impact compressible fluid-solid coupling is complex in fluid-solid interface processing and the calculation efficiency and stability are reduced due to the fact that a grid needs to be reconstructed under the condition that the structure is deformed.
The dipping boundary method has the advantages of simple fluid-solid interface processing and no need of reconstructing a grid. The prior immersion boundary method is mainly applied to solving the problem of coupling of incompressible fluid and a structure, and the application in the field of underwater impact multiphase compressible fluid-solid coupling also has the technical difficulty of solving multiphase flow and compressible flow.
Disclosure of Invention
The invention aims to provide a rapid calculation method for three-dimensional multiphase compressible fluid-solid coupling, which overcomes the defects of the prior art, and greatly improves the precision and stability of underwater impact simulation calculation by developing a three-dimensional multiphase compressible fluid algorithm and a fluid-solid coupling algorithm based on a virtual medium method; an algorithm for mutual conversion between an underwater shock wave stage and a bubble dynamics stage is developed, conversion of the two algorithms is judged based on the pressure of a flow field, and the efficiency of overall solving of the underwater shock problem is greatly improved.
In order to solve the problems, the technical scheme adopted by the invention is as follows:
a three-dimensional multiphase compressible fluid-solid coupling rapid calculation method comprises the following steps:
(1) establishing a three-dimensional model of the impacted material and dividing a Cartesian non-uniform grid;
(2) establishing a mass, momentum and energy equation and a state equation of the inviscid compressible fluid under Cartesian coordinates;
(3) performing multiphase compressible fluid-solid coupling calculation;
(4) providing initial pressure to the structural field through a fluid-solid coupling solver, and simultaneously obtaining the initial node speed provided by the structural field;
(5) simulating the whole underwater impact period and the whole process by a compressible-incompressible conversion solving algorithm, and outputting a calculation result.
Further, the mass, momentum and energy equation of the non-viscous compressible fluid in the step (2) under the cartesian coordinates can be expressed as:
Figure BDA0003532233370000021
wherein the content of the first and second substances,
Figure BDA0003532233370000022
ρ is the fluid density, p is the pressure, u, v, w are the velocities in the x, y, z directions, g acceleration of gravity;
total energy et＝e+0.5(u2+v2+w2) Wherein e is the internal energy.
Further, the equation of state in the step (2) can be expressed as
p＝p(ρ,e),ρ＝ρ(p,e),ore＝e(ρ,p).。
Further, the calculation of the multiphase compressible fluid-solid coupling in the step (3) specifically comprises
Determining the position of the interface through a distance function;
defining virtual fluid states of the virtual nodes and performing approximate Riemann's solution at the interface.
Further, the distance function may be obtained by solving the following transient transport equation:
φt+uφx+vφy+wφz＝0
ψt+uψx+vψy+wψz＝0
wherein u, v, w are the velocities of the fluid in the x, y, z directions; phi is at，φx，φy，φzIs the variation of the distance function of the first two-phase flow interface, Ψ, over time and spacet，Ψx，Ψy，ΨzIs the amount of change in the distance function of the second two-phase flow interface over time and space.
Further, the solution of the approximate Riemann can be expressed as:
Figure BDA0003532233370000031
Figure BDA0003532233370000032
Figure BDA0003532233370000033
Figure BDA0003532233370000034
wherein, subscripts "I", "IL" and "IR" refer to the interface, and the left and right sides of the interface; rhoIL(ρIR) And cIL(cIR) Is the fluid density and sound velocity on the left and right sides of the interface; u. ofI，pIIs the velocity and pressure of the interface; u shapeIL，UIRCan be obtained by interpolation of two nonlinear characteristic lines of the interface, which can be regressed to corresponding media, or set as UIL＝Ui-1，UIR＝Ui+2；ρL(pI)，ρR(pI) Is at the interface pressure pIDensity of fluid flowing in the lower left and right shock waves.
Further, the fluid-solid coupling solver in the step (4) is a solver for coupling the euler function and the lagrangian function.
Further, the flow of the compressible-incompressible conversion solving algorithm in the step (5) includes: during conversion, the compressible algorithm has physical parameters of flow and fluid in all volume grids; calculating the position of an interface by adopting an interface tracking algorithm, wherein the position comprises the positions of bubbles and a free interface; the boundary element method generates an ideal bubble and the position of a free interface according to the calculation result of the compressible fluid; generating a potential flow boundary element grid; interpolating the flow field of the compressible fluid during conversion to obtain a velocity field normal to the boundary element grid; applying the flow to a flow-solid interface; the Green's equation is applied to solve the potential on the BEM grid; and calculating BEM and outputting the result.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, a high-precision decoupling is carried out on a material interface by coupling a virtual medium-based method and a high-order shock wave capturing method, and the structure of a material interface wave is accurately solved; the precision and the stability of the three-phase multiphase compressible fluid-solid coupling algorithm are ensured.
2. According to the method, the conversion of the two algorithms is judged based on the pressure of the flow field through the algorithm of the mutual conversion between the underwater shock wave stage and the bubble dynamics stage, so that the efficiency of the integral solution of the underwater shock problem is greatly improved.
Drawings
FIG. 1 is a schematic view of a multiphase flow interface.
Fig. 2 is a schematic view of a virtual fluid node.
FIG. 3 is a schematic diagram of a boundary approximation method for searching for a fluid grid-to-node distance, a fluid grid-to-line segment distance, and a fluid grid-to-plane shortest distance.
Fig. 4 is a schematic view of a fluid-solid coupling interface.
Fig. 5 is a schematic diagram of fluid grid velocity.
Fig. 6 is a geometric topology of an impacted composite propeller.
FIG. 7 is a computational grid of an impacted composite propeller.
Fig. 8 is a pressure cloud diagram of a flow field at different times in a shock wave stage and deformation of a propeller.
Fig. 9 shows the evolution process of the bubble and the deformation of the propeller at different times during the bubble phase.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention discloses a rapid calculation method of three-dimensional multiphase compressible fluid-solid coupling, which comprises the following steps:
(1) establishing a three-dimensional model of the impacted material and dividing a Cartesian non-uniform grid;
(2) establishing a mass, momentum and energy equation and a state equation of the inviscid compressible fluid under Cartesian coordinates;
(3) performing multiphase compressible fluid-solid coupling calculation;
(4) providing initial pressure to the structural field through a fluid-solid coupling solver, and simultaneously obtaining the initial node speed provided by the structural field;
(5) simulating the whole underwater impact period and the whole process by a compressible-incompressible conversion solving algorithm, and outputting a calculation result.
1. The mass, momentum and energy equations of a non-viscous compressible fluid in cartesian coordinates can be expressed as:
Figure BDA0003532233370000051
wherein the content of the first and second substances,
Figure BDA0003532233370000052
ρ is the fluid density, p is the pressure, u, v, w are the velocities in the x, y, z directions, g acceleration of gravity;
total energy et＝e+0.5(u2+v2+w2) Wherein e is the internal energy.
2. The equation of state can be expressed as:
p＝p(ρ,e),ρ＝ρ(p,e),ore＝e(ρ,p).。
in general, the state equations can be described in the unified format of Mie-Gruneisen, and the state equations for various media can be shown in the following table:
Figure BDA0003532233370000061
3. as shown in fig. 1, the two interfaces divide three media, the first LevelSet function (Φ ═ 0) defines the interface between media 1(Med1) and media 2(Med2), while the second LevelSet function (ψ ═ 0) defines the interface between media 2(Med2) and media 3(Med 3).
The definition of each medium is as follows:
Figure BDA0003532233370000062
the Med2 is generally regarded as the main medium, and the Med1& Med2 constitutes the first two-phase flow, and the Med3& Med2 constitutes the other two-phase flow. Since the calculations of Med1 and Med2 are independent of each other, the combination of these two-phase flow solutions will give the final solution for three-phase flow. For each medium, the distance function can be obtained by solving the following transient transport equation:
φt+uφx+vφy+wφz＝0
ψt+uψx+vψy+wψz＝0
wherein u, v, w are the velocities of the fluid in the x, y, z directionsDegree; phi is at，φx，φy，φzIs the variation of the distance function of the first two-phase flow interface, Ψ, over time and spacet，Ψx，Ψy，ΨzIs the amount of change in the distance function of the second two-phase flow interface over time and space.
This calculation of Med1 is relevant to Med2 if the two interfaces coincide, in which case the calculation of Med1/Med3 requires information from Med3/Med1, so the patented method defines different media by the following equation:
Figure BDA0003532233370000071
4. as shown in fig. 2, assume that the material interface is at time t ═ tnBetween mesh nodes i and i +1, we calculate the next time t ═ tn+1The flow field of (a). The new position of the interface is firstly obtained by using a LevelSet technology of a distance function, and in order to calculate the flow field of Med1, grid nodes i +1, i +2 or more nodes need to be defined as Med1 virtual fluid nodes according to the precision of the algorithm used. The states of the virtual fluid nodes are defined by the same state equations as Med1, and the virtual fluid nodes (i, i-1, i-2.) and virtual fluid nodes (i, i-1, i-2.) of Med2 can be defined by applying the same method.
The virtual fluid state of the virtual node can define and solve a multi-media riemann problem at the interface by two non-linear eigenequations at the two-phase flow interface:
Figure BDA0003532233370000072
along
Figure BDA0003532233370000073
Figure BDA0003532233370000074
along
Figure BDA0003532233370000075
the subscripts "I", "IL" and "IR" refer herein to the interface, and to the left and right sides of the interface; rhoIL(ρIR) And cIL(cIR) Is the fluid density and sound velocity on the left and right sides of the interface; u. ofI，pIIs the velocity and pressure of the interface; u shapeIL，UIRThe interpolation can be carried out by two nonlinear characteristic lines of the interface, which can return to corresponding media, or the interpolation is simply set as UIL＝Ui-1，UIR＝Ui+2. Since u is the shock wave when it impacts the interfaceIL(pIL) And uIR(pIR) Is discontinuous (intermittent) in passing through the interface and therefore must be solved for an approximate riemann at the interface, as follows:
Figure BDA0003532233370000081
Figure BDA0003532233370000082
Figure BDA0003532233370000083
Figure BDA0003532233370000084
ρL(pI)，ρR(pI) Is at the interface pressure pIDensity of fluid flowing in the lower left and right shock waves.
5. In the fluid-solid coupling solver, the first step is to determine the distance function, which is actually the shortest distance from the fluid grid to the structural interface. The distance function of the fluid-solid coupling at each time step is calculated by a boundary approximation method. As shown in fig. 3, the boundary approximation searches for the shortest distance of the fluid mesh to the node, the fluid mesh to the line segment, and the fluid mesh to the plane. To reduce the computational cost, the distance search is only performed in a narrow region of the structure surface.
Using the distance function provided above, the second step is a solver that couples the euler function and the lagrange function. The fluid calculations are performed on a fixed cartesian grid and the structural calculations are performed using structural finite element calculations. The fluid-solid coupling interface is eventually a stepped approximation as shown in fig. 4.
The key to the fluid-solid coupling solver is to define virtual cells inside the structure for fluid computation using virtual node coordinates and velocities. The normal direction of each fluid grid may be based on a distance function
Figure BDA0003532233370000091
And (6) performing calculation. Virtual nodes inside the structure can be projected by the following equation:
Figure BDA0003532233370000092
where q is an array of extrapolated quantities (ρ, p, u, v, w). Calculating tau along normal direction by adopting simple windward format, and when reaching steady state
Figure BDA0003532233370000093
Then, the non-physical extrapolated velocity field at the virtual node can be reconstructed by the following equation:
Figure BDA0003532233370000094
wherein
Figure BDA0003532233370000095
Is the velocity, v, obtained by extrapolation of the actual fluid grid velocitysIs the solid interface velocity, which is the velocity at the crossover point, as shown in fig. 5.
6. Compressible algorithms can simulate the dynamics of including shock waves and bubbles, however the computational cost and CPU time of this approach results in an inability to simulate the full cycle and flow of underwater shock in a reasonable time. The patent develops a combined transformation solution algorithm that uses a compressible fluid algorithm to simulate the initial phase of an explosion, then switches to a boundary element method to simulate bubble dynamics, and switches back to the compressible fluid algorithm when the bubble collapses. The key of the conversion solving algorithm is to construct initial conditions of a flow field during conversion.
The flow of this algorithm is illustrated with compressible flow converted to incompressible flow:
(1) during conversion, the compressible algorithm has physical parameters of flow and fluid in all volume grids;
(2) calculating the position of an interface by adopting an interface tracking algorithm, wherein the position comprises the positions of bubbles and a free interface;
(3) the boundary element method generates an ideal bubble and the position of a free interface according to the calculation result of the compressible fluid;
(4) generating a potential flow boundary element grid;
(5) interpolating the flow field of the compressible fluid during conversion to obtain a velocity field normal to the boundary element grid;
(6) applying the procedures (1) to (5) on a flow-solid interface
(7) The Green's equation is applied to solve the potential on the BEM grid;
(8) and calculating BEM and outputting the result.
The implementation case is as follows:
(1) composite material underwater impact case-case physical schematic model
The geometric topology of an impacted composite propeller is shown in fig. 6, which is the structure that the present example primarily studies to respond under impact.
(2) Composite underwater impact case-computing grid
The computational grid for the case of underwater impact on the composite is shown in fig. 7, which results in a cartesian non-uniform grid. For accurate calculation of the shock phase, a dense structural grid is generated in the impact source physical region.
(3) Composite underwater shock case-shock stage calculation
In the shock wave stage, a multiphase compressible fluid-solid coupling calculation method is mainly applied, and fig. 8 shows a pressure cloud chart of a flow field and deformation of a propeller at different times in the shock wave stage.
(4) Composite underwater impact case-bubble dynamics calculation
In the bubble dynamics stage, a compressible-incompressible conversion algorithm is adopted, mainly a boundary element fluid-solid coupling calculation method is applied, and fig. 9 shows the evolution process of bubbles and the deformation of a propeller at different times in the bubble stage. The conversion algorithm is applied to reduce the calculation time from 30 days to 4 hours, and the efficiency is improved by more than two orders of magnitude.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.

Claims (8)

1. A three-dimensional multiphase compressible fluid-solid coupling rapid calculation method is characterized by comprising the following steps: the method comprises the following steps:
(1) establishing a three-dimensional model of the impacted material and dividing a Cartesian non-uniform grid;
(2) establishing a mass, momentum and energy equation and a state equation of the inviscid compressible fluid under Cartesian coordinates;
(3) performing multiphase compressible fluid-solid coupling calculation;
(4) providing initial pressure to the structural field through a fluid-solid coupling solver, and simultaneously obtaining the initial node speed provided by the structural field;
(5) simulating the whole underwater impact period and the whole process by a compressible-incompressible conversion solving algorithm, and outputting a calculation result.
2. The method for rapidly calculating the three-dimensional multiphase compressible fluid-solid coupling according to claim 1, wherein the method comprises the following steps: the equation of mass, momentum and energy of the non-viscous compressible fluid in the step (2) under the cartesian coordinates can be expressed as:
Figure FDA0003532233360000011
wherein the content of the first and second substances,
Figure FDA0003532233360000012
ρ is the fluid density, p is the pressure, u, v, w are the velocities in the x, y, z directions, g acceleration of gravity;
total energy et＝e+0.5(u2+v2+w2) Wherein e is the internal energy.
3. The method for rapidly calculating the three-dimensional multiphase compressible fluid-solid coupling according to claim 2, wherein the method comprises the following steps: the equation of state in step (2) can be expressed as:
p＝p(ρ,e),ρ＝ρ(p,e),or e＝e(ρ,p).。
4. the method for rapidly calculating the three-dimensional multiphase compressible fluid-solid coupling according to claim 1, wherein the method comprises the following steps: the calculation of the multiphase compressible fluid-solid coupling in the step (3) specifically comprises
Determining the position of the interface through a distance function;
defining virtual fluid states of the virtual nodes and performing approximate Riemann's solution at the interface.
5. The method for rapidly calculating the three-dimensional multiphase compressible fluid-solid coupling according to claim 4, wherein the method comprises the following steps: the distance function may be obtained by solving the following transient transport equation:
φt+uφx+vφy+wφz＝0
ψt+uψx+vψy+wψz＝0
wherein u, v, w are the velocities of the fluid in the x, y, z directions; phi is at,φx,φy,φzIs the variation of the distance function of the first two-phase flow interface, Ψ, over time and spacet,Ψx,Ψy,ΨzIs the amount of change in the distance function of the second two-phase flow interface over time and space.
6. The method for rapidly calculating the three-dimensional multiphase compressible fluid-solid coupling according to claim 4, wherein the method comprises the following steps: the solution to the approximate Riemann can be expressed as:
Figure FDA0003532233360000021
Figure FDA0003532233360000022
Figure FDA0003532233360000023
Figure FDA0003532233360000024
wherein, subscripts "I", "IL" and "IR" refer to the interface, and the left and right sides of the interface; rhoIL(ρIR) And cIL(cIR) Is the fluid density and sound velocity on the left and right sides of the interface; u. ofI，pIIs the velocity and pressure of the interface; u shapeIL，UIRReturnable to the respective medium via two strips of the interfaceThe nonlinear characteristic line is obtained by interpolation or is set as UIL＝Ui-1，UIR＝Ui+2；ρL(pI)，ρR(pI) Is at the interface pressure pIDensity of fluid flowing in the lower left and right shock waves.
7. The method for rapidly calculating the three-dimensional multiphase compressible fluid-solid coupling according to any one of claims 4 to 6, wherein the method comprises the following steps: and (4) the fluid-solid coupling solver in the step (4) is a solver for coupling the Euler function and the Lagrange function.
8. The method for rapidly calculating the three-dimensional multiphase compressible fluid-solid coupling according to claim 7, wherein the method comprises the following steps: the flow of the compressible-incompressible conversion solving algorithm in the step (5) comprises the following steps: during conversion, the compressible algorithm has physical parameters of flow and fluid in all volume grids; calculating the position of an interface by adopting an interface tracking algorithm, wherein the position comprises the positions of bubbles and a free interface; the boundary element method generates an ideal bubble and the position of a free interface according to the calculation result of the compressible fluid; generating a potential flow boundary element grid; interpolating the flow field of the compressible fluid during conversion to obtain a velocity field normal to the boundary element grid; applying the flow to a flow-solid interface; the Green's equation is applied to solve the potential on the BEM grid; and calculating BEM and outputting the result.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116127611A (en) * 2023-04-13 2023-05-16 中国人民解放军国防科技大学 Dynamic simulation method for underwater vehicle

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116127611A (en) * 2023-04-13 2023-05-16 中国人民解放军国防科技大学 Dynamic simulation method for underwater vehicle

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