CN114611423B - Rapid calculation method for three-dimensional multiphase compressible fluid-solid coupling - Google Patents
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Abstract
The invention particularly relates to a three-dimensional multiphase compressible fluid-solid coupling rapid calculation method, which comprises the following steps: establishing a three-dimensional model of the impacted material and dividing a Cartesian non-uniform grid; establishing mass, momentum and energy equations and state equations of the non-viscous compressible fluid under Cartesian coordinates; performing multiphase compressible fluid-solid coupling calculation; providing an initial pressure to the structural field through a fluid-solid coupling solver, and simultaneously obtaining an initial node speed provided by the structural field; the full period and the full flow of the underwater impact are simulated by a compressible-incompressible transformation solving algorithm. The three-dimensional multiphase compressible fluid algorithm and the fluid-solid coupling algorithm based on the virtual medium method greatly improve the accuracy and stability of underwater impact simulation calculation; the conversion algorithm of the underwater shock wave stage and the bubble dynamics stage is used for judging the conversion of the two algorithms based on the pressure of the flow field, so that the overall solving efficiency of the underwater shock problem is greatly improved.
Description
Technical Field
The invention belongs to the technical field of fluid computing, and particularly relates to a three-dimensional multiphase compressible fluid-solid coupling rapid computing method.
Background
As the underwater strong impact is a highly complex interdisciplinary physical and chemical problem of multiple phases, multiple media and multiple physical fields, the technology adopted for simulating the problem comprises a high-order precision shock wave capturing algorithm, a compressible multiphase computational fluid mechanics algorithm, a large deformation large displacement structure finite element algorithm and a strong impact multiple media fluid-solid coupling algorithm. At present, no particularly efficient and stable algorithm is available internationally in solving the problem of underwater strong impact. Although researchers have made a breakthrough in the local field, the complete coupling of the algorithms together to form a complete and efficient underwater impact simulation algorithm has a plurality of problems including multiphase flow interface decoupling, fluid-solid interface cavitation collapse and huge calculation amount of integral simulation of shock wave and bubble dynamics stages.
The main methods currently applied to underwater impact include any Euler-Lagrange coupling algorithm, a boundary immersion method and a loose fluid-solid coupling algorithm.
The method has the advantages that the universality of any Euler-Lagrange coupling algorithm is good, the problem that the computational efficiency and stability are reduced due to the fact that the fluid-solid interface is complex to process and the grid needs to be reconstructed under the condition of structural deformation is solved.
The immersion boundary method has the advantage of simple fluid-solid interface processing and no need to reconstruct the mesh. The current immersed boundary method is mainly applied to solving the problem of coupling of incompressible fluid and a structure, and the technical difficulty of solving multiphase flow and compressible flow exists in the application of the underwater impact multiphase compressible fluid-solid coupling field.
Disclosure of Invention
The invention aims to provide a three-dimensional multiphase compressible fluid-solid coupling rapid calculation method, which overcomes the defects of the prior art and greatly improves the accuracy 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; the algorithm for interconversion between the underwater shock wave stage and the bubble dynamics stage is developed, the conversion of the two algorithms is judged based on the pressure of the flow field, and the overall solving efficiency 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 mass, momentum and energy equations and state equations of the non-viscous compressible fluid under Cartesian coordinates;
(3) Performing multiphase compressible fluid-solid coupling calculation;
(4) Providing an initial pressure to the structural field through a fluid-solid coupling solver, and simultaneously obtaining an initial node speed provided by the structural field;
(5) And simulating the whole period and the whole flow of the underwater impact by using a compressible-incompressible conversion solving algorithm, and outputting a calculation result.
Further, the mass, momentum and energy equations of the non-viscous compressible fluid in the step (2) under cartesian coordinates may be expressed as:
Wherein,
Ρ is the fluid density, p is the pressure, u, v, w is the velocity in the x, y, z direction, g gravitational acceleration;
total energy e t＝e+0.5(u2+v2+w2), where e is the internal energy.
Further, the state equation in the step (2) may be expressed as
p＝p(ρ,e),ρ＝ρ(p,e),ore＝e(ρ,p).。
Further, the multi-phase compressible fluid-solid coupling calculation in the step (3) specifically comprises
Determining the position of the interface through a distance function;
Virtual fluid states of the virtual nodes are defined and an approximate Riemann solution is performed 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
Where u, v, w are the velocity of the fluid in the x, y, z directions; phi t,φx,φy,φz is the time-space variation of the distance function of the first two-phase flow interface, and ψ t,Ψx,Ψy,Ψz is the time-space variation of the distance function of the second two-phase flow interface.
Further, the approximate Riemann solution may be expressed as:
Wherein, subscripts "I", "IL" and "IR" refer to the interface and the left and right sides of the interface; ρ IL(ρIR) and c IL(cIR) are fluid density and sound velocity on the left and right sides of the interface; u I,pI is the speed and pressure of the interface; u IL,UIR can be interpolated from two non-linear characteristic lines of the interface that can be returned to the corresponding medium, or set to U IL＝Ui-1,UIR＝Ui+2;ρL(pI),ρR(pI) is the fluid density of the shock flow at the interface pressure p I.
Further, the fluid-solid coupling solver in the step (4) is a solver coupling the euler function and the lagrangian function.
Further, the flow of the compressible-incompressible transformation solving algorithm in the step (5) includes: at the time of conversion, the compressible algorithm has physical parameters of flow and fluid in all volume meshes; 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 ideal bubbles and the positions of free interfaces according to the calculation result of the compressible fluid; generating a potential flow boundary element grid; interpolation is carried out on the flow field of the compressible fluid during conversion to obtain a normal speed field of the boundary element grid; the flow is applied to a fluid-solid interface; the green's equation is applied to solve for the potentials on the BEM grid; and performing BEM calculation and outputting a result.
Compared with the prior art, the invention has the following beneficial effects:
1. According to the invention, a material interface is decoupled with high precision by coupling based on a virtual medium method and a high-order shock wave capturing method, and the structure of the material interface wave is accurately solved; and the precision and stability of a three-phase multiphase compressible fluid-solid coupling algorithm are ensured.
2. According to the invention, through the mutual conversion algorithm of the underwater shock wave stage and the bubble dynamics stage, the conversion of the two algorithms is judged based on the pressure of the flow field, and the overall solving efficiency of the underwater shock problem is greatly improved.
Drawings
FIG. 1 is a schematic illustration of a multiphase flow interface.
Fig. 2 is a schematic diagram of a virtual fluidic node.
FIG. 3 is a schematic diagram of a boundary approximation search for fluid grid-to-node distances, fluid grid-to-line segment distances, and fluid grid-to-plane shortest distances.
Fig. 4 is a schematic diagram 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 material propeller.
Fig. 8 is a pressure cloud of the flow field at different times during the shock phase and deformation of the propeller.
Fig. 9 shows the evolution of the bubbles and the deformation of the propeller at different times during the bubble phase.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention discloses a three-dimensional multiphase compressible fluid-solid coupling rapid calculation method, which comprises the following steps:
(1) Establishing a three-dimensional model of the impacted material and dividing a Cartesian non-uniform grid;
(2) Establishing mass, momentum and energy equations and state equations of the non-viscous compressible fluid under Cartesian coordinates;
(3) Performing multiphase compressible fluid-solid coupling calculation;
(4) Providing an initial pressure to the structural field through a fluid-solid coupling solver, and simultaneously obtaining an initial node speed provided by the structural field;
(5) And simulating the whole period and the whole flow of the underwater impact by using 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:
Wherein,
Ρ is the fluid density, p is the pressure, u, v, w is the velocity in the x, y, z direction, g gravitational acceleration;
total energy e t＝e+0.5(u2+v2+w2), where e is the internal energy.
2. The state equation can be expressed as:
p＝p(ρ,e),ρ＝ρ(p,e),ore＝e(ρ,p).。
in general, the state equations may be described in a unified format of Mie-Gruneisen, and the state equations for various mediums may be as shown in the following table:
3. As shown in fig. 1, the two interfaces divide three media, the first LevelSet function (Φ=0) defining the interface between media 1 (Med 1) and media 2 (Med 2), while the second LevelSet function (ψ=0) defines the interface between media 2 (Med 2) and media 3 (Med 3).
The definition of each medium is as follows:
Here Med2 is generally considered the main medium, med1& Med2 comprising the first two-phase flow and Med3& Med2 comprising 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 a three-phase flow final solution. For each medium, the distance function may be obtained by solving the following transient transport equation:
φt+uφx+vφy+wφz＝0
ψt+uψx+vψy+wψz＝0
Where u, v, w are the velocity of the fluid in the x, y, z directions; phi t,φx,φy,φz is the time-space variation of the distance function of the first two-phase flow interface, and ψ t,Ψx,Ψy,Ψz is the time-space variation of the distance function of the second two-phase flow interface.
If the two interfaces coincide, this calculation Med1 is relevant to Med2, in which case the calculation Med1/Med3 requires information from Med3/Med1, so the method of the patent defines different media by the following equation:
4. As shown in fig. 2, assuming that the material interface is located between grid nodes i and i+1 at time t=t n, we calculate the flow field for the next time t=t n+1. The new location of the interface is first obtained using LevelSet techniques of distance function, in order to calculate the flow field of Med1, the grid nodes i+1, i+2 or more need to be defined as Med1 virtual fluidic nodes, depending on the accuracy of the algorithm used. The state of the virtual fluid node is defined by the same state equation as Med1, and the virtual fluid node (i, i-1, i-2.) and the virtual fluid node point of Med2 can be defined using the same method.
The virtual fluid state of the virtual node can define and solve a multi-medium Riemann problem at the two-phase flow interface by two nonlinear characteristic equations at the interface:
along
along
The subscripts "I", "IL" and "IR" herein refer to the interface as well as to the left and right sides of the interface; ρ IL(ρIR) and c IL(cIR) are fluid density and sound velocity on the left and right sides of the interface; u I,pI is the speed and pressure of the interface; u IL,UIR may be interpolated from two non-linear feature lines of the interface that are regressible to the corresponding medium, or simply set as U IL＝Ui-1,UIR＝Ui+2. Since u IL(pIL) and u IR(pIR) are discontinuous (intermittent) across the interface when the shock impacts the interface, an approximate Riemann solution must be performed at the interface as follows:
ρ L(pI),ρR(pI) is the fluid density of the shock flow at the interface pressure p I.
5. In a fluid-solid coupling solver, the first step is to determine a 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 method searches for fluid mesh-to-node distances, fluid mesh-to-line segment distances, and fluid mesh-to-plane shortest distances. To reduce the computational cost, the distance search is performed only in a narrow area of the structure surface.
Using the distance function provided above, the second step is a solver that couples the euler function and the lagrangian function. The fluid calculations are performed on a fixed cartesian grid, while the structural calculations are performed using and structural finite element calculations. The fluid-solid coupling interface is eventually stepped as shown in fig. 4.
The key to the fluid-solid coupled 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 functionAnd (5) performing calculation. Virtual nodes inside a structure can be projected by the following equation:
Where q= (ρ, p, u, v, w) is an array of extrapolation quantities. Calculating tau along the normal direction by adopting a simple windward format, when reaching a steady state In this case, the non-physical extrapolated velocity field at the virtual node can be reconstructed by the following equation:
Wherein the method comprises the steps of Is the velocity obtained by extrapolation of the actual fluid grid velocity, v s is the solid interface velocity, which is the velocity at the intersection point, as shown in fig. 5.
6. The compressible algorithm can simulate including shock wave and bubble dynamics, however the computational cost and CPU time of this approach results in the inability to simulate the full cycle and full flow of an underwater shock in a reasonable time. The patent develops a combined transformation solution algorithm, 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 breaks. The key of the conversion solving algorithm is to construct flow field initial conditions during conversion.
The flow of this algorithm is illustrated with compressible flow converted to incompressible flow:
(1) At the time of conversion, the compressible algorithm has physical parameters of flow and fluid in all volume meshes;
(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 ideal bubbles and the positions of free interfaces according to the calculation result of the compressible fluid;
(4) Generating a potential flow boundary element grid;
(5) Interpolation is carried out on the flow field of the compressible fluid during conversion to obtain a normal speed field of the boundary element grid;
(6) Applying the flows (1) - (5) on the fluid-solid interface
(7) The green's equation is applied to solve for the potentials on the BEM grid;
(8) And performing BEM calculation and outputting a result.
Implementation case:
(1) Composite underwater impact case-case physical schematic model
The geometric topology of the impacted composite propeller is shown in fig. 6, and the propeller is mainly used for researching the response under impact.
(2) Composite underwater impact case-calculation grid
The computational grid of the case of underwater impact on the composite material is shown in fig. 7, which produces a cartesian non-uniform grid. For accurate calculation of the shock wave stage, a denser structural grid is generated in the physical area of the impact source.
(3) Composite underwater shock case-shock stage computation
In the shock wave stage, a multiphase compressible fluid-solid coupling calculation method is mainly applied, and fig. 8 shows pressure cloud patterns 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, and a boundary element fluid-solid coupling calculation method is mainly applied, and fig. 9 shows the evolution process of bubbles and 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 characteristics 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 (3)
1. A three-dimensional multiphase compressible fluid-solid coupling rapid calculation method is characterized in that: 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 mass, momentum and energy equations and state equations of the non-viscous compressible fluid under Cartesian coordinates;
the mass, momentum and energy equations of the non-viscous compressible fluid in the step (2) under the Cartesian coordinates are expressed as follows:
Wherein,
Ρ is the fluid density, p is the pressure, u, v, w is the velocity in the x, y, z direction, g gravitational acceleration;
Total energy e t＝e+0.5(u2+v2+w2), where e is the internal energy;
The state equation in the step (2) is expressed as:
p＝p(ρ,e),ρ＝ρ(p,e),or e＝e(ρ,p).；
(3) Performing multiphase compressible fluid-solid coupling calculation;
The multiphase compressible fluid-solid coupling calculation in the step (3) comprises the following steps of
Determining the position of the interface through a distance function;
defining a virtual fluid state of the virtual node and performing approximate Riemann solution at the interface;
the distance function is obtained by solving the following transient transport equation:
φt+uφx+vφy+wφz＝0
ψt+uψx+vψy+wψz＝0
where u, v, w are the velocity of the fluid in the x, y, z directions; phi t,φx,φy,φz is the time-space variation of the distance function of the first two-phase flow interface, and ψ t,Ψx,Ψy,φz is the time-space variation of the distance function of the second two-phase flow interface;
The approximate Riemann solution is expressed as:
Wherein, subscripts "I", "IL" and "IR" refer to the interface and the left and right sides of the interface; ρ IL(ρIR) and c IL(cIR) are fluid density and sound velocity on the left and right sides of the interface; u I,pI is the speed and pressure of the interface; u IL,UIR is obtained by interpolation of two nonlinear characteristic lines of the interface which can return to the corresponding medium, or set as U IL＝Ui-1,UIR＝Ui+2;ρL(pI),ρR(pI) is the fluid density of the left and right shock wave flow at the interface pressure p I;
(4) Providing an initial pressure to the structural field through a fluid-solid coupling solver, and simultaneously obtaining an initial node speed provided by the structural field;
(5) And simulating the whole period and the whole flow of the underwater impact by using a compressible-incompressible conversion solving algorithm, and outputting a calculation result.
2. The method for rapidly computing three-dimensional multiphase compressible fluid-solid coupling according to claim 1, wherein: and (3) the fluid-solid coupling solver in the step (4) is a solver for coupling the Euler function and the Lagrangian function.
3. A method of fast computing a three-dimensional multiphase compressible fluid-solid coupling according to claim 2, wherein: the flow of the compressible-incompressible transformation solving algorithm in the step (5) comprises the following steps: at the time of conversion, the compressible algorithm has physical parameters of flow and fluid in all volume meshes;
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 ideal bubbles and the positions of free interfaces according to the calculation result of the compressible fluid; generating a potential flow boundary element grid; interpolation is carried out on the flow field of the compressible fluid during conversion to obtain a normal speed field of the boundary element grid; the flow is applied to a fluid-solid interface; the green's equation is applied to solve for the potentials on the BEM grid;
And performing BEM calculation and outputting a result.
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