CN117789879B - Bubble pulsation and impact cover layer coupling response calculation method - Google Patents
Bubble pulsation and impact cover layer coupling response calculation method Download PDFInfo
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Abstract
The invention relates to a bubble pulsation and impact cover layer coupling response calculation method, which comprises the steps of establishing a one-dimensional impact theoretical model of an impact cover layer under the combined action of hydrostatic pressure and impact load, wherein the model comprises the pre-stress of the impact cover layer under the action of the hydrostatic pressure and the dynamic compression process under the action of the impact load; fluid-solid coupling of the impact cover layer with water; a secondary loading process caused by occurrence and collapse of cavitation in water; based on a theoretical model, analyzing the complete impact process of the impact resistant coating, wherein the analysis comprises S1, dynamic compression process analysis, S2, fluid-solid coupling analysis, and S3, cavitation occurrence and collapse process analysis. The invention forms a theoretical calculation method of the impact-resistant coating under the combined action of the hydrostatic pressure and the shock wave on the basis of a theoretical model, can be used for analyzing the impact protection effect of the coating, and provides theoretical support for researching the impact protection mechanism of the pressure-resistant impact-resistant coating.
Description
Technical Field
The invention relates to the technical field of impact resistance calculation of submarine cladding, in particular to a dynamic response calculation method of a submarine impact resistance cladding structure under the action of short-distance underwater explosion impact load.
Background
For underwater structures, underwater blast impact loads pose a fatal threat. How to alleviate the destructive effect of the underwater explosion impact is a key problem for guaranteeing the safety of the underwater structure. At present, an effective measure is to add an impact-resistant coating to the surface of the structure, however, not all coatings can alleviate the impact of underwater explosions. The cover layer with the sound absorption cavity may instead reduce the impact resistance of the structure under the action of the blast shock wave. The main mechanism of the impact-resistant coating for relieving the damage of the underwater explosion shock wave is as follows: for long-distance underwater explosion load, the energy absorption performance of the covering layer can effectively reduce the peak value of the impact wave acting on the structure; for short-distance underwater explosion load, the impact-resistant covering layer can generate large deformation and crushing, and an in-water bubble effect is generated, so that continuous and strong impact load of the shock wave on the surface of the structure due to wave reflection and diffraction is reduced. In the close-range underwater explosion process, high-speed water jet which is generated when explosion bubbles collapse and faces to a structural object is more deadly, and the whole hull can be broken. In order to analyze the impact protection mechanism of the impact-resistant coating and improve the impact-resistant protection performance of the coating under the close-range underwater explosion load, the research of an underwater explosion theory calculation method of the coupling response of bubble pulsation and the impact-resistant coating is necessary to be carried out. The research process mainly has two technical problems: (1) The evolution rule of the bubble load at the flexible interface is unclear, and an effective load prediction method is lacked; (2) Fluid-solid coupling effect under strong impact load is lacking in effective theoretical analysis method.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for calculating the coupling response of bubble pulsation and impact-resistant coating, which aims at the technical problem existing in the prior art, and the method establishes a one-dimensional impact-resistant theoretical model of the submarine coating under the combined action of high hydrostatic pressure and underwater explosion shock waves, and comprises the dynamic compression, fluid-solid coupling, cavitation formation and collapse processes of the coating; on the basis of a theoretical model, a theoretical calculation method of the impact-resistant coating under the combined action of hydrostatic pressure and shock waves is formed, so that the method can be used for analyzing the impact protection effect of the coating and providing theoretical support for researching the impact protection mechanism of the pressure-resistant impact-resistant coating.
The technical scheme adopted by the invention for solving the technical problems is as follows:
A bubble pulsation and impact cover layer coupling response calculation method establishes a one-dimensional impact theoretical model of an impact cover layer under the combined action of hydrostatic pressure and impact load, wherein the model comprises three parts: (1) A dynamic compression process of the impact-resistant coating under the action of prestress and impact load under the action of hydrostatic pressure; (2) fluid-solid coupling of the impact cover layer with water; (3) A secondary loading process caused by occurrence and collapse of cavitation in water;
On the basis of a theoretical model, analyzing the complete impact process of the impact resistant coating layer comprises the following steps:
s1, analyzing a dynamic compression process:
according to the theory of shock waves, the shock wave load is described in the form of exponential decay waves, and the propagation speed of the shock waves is obtained according to the law of conservation of momentum and the conservation of mass equation; obtaining the internal energy variation of the cover layer according to the law of conservation of momentum;
When the surface of the covering layer is made of a plastic porous material, strong intermittent elastic precursor waves and subsequent plastic shock waves exist in the material, and the wave speed and wave surface stress of the material are respectively calculated;
the unloading process generated under the action of plastic shock waves needs to consider the strain hardening effect to obtain a control equation of an unloading area;
according to Newton's second law, get the motion equation of the pressure-proof shell and crushed porous material;
S2, fluid-solid coupling analysis:
According to the reflection rule of the incident shock wave, obtaining the reflection wave caused by reflection and the sparse wave caused by deformation of the covering layer, and under the combined action of hydrostatic pressure and shock wave, obtaining the total pressure on the fluid-solid coupling surface under the condition of not considering cavitation and bubble collapse;
S3, analyzing cavitation occurrence and collapse process:
The cavitation phenomenon is generated in the water due to the reflected wave and the sparse wave, and the cavitation time of any position in the water can be obtained according to the cavitation generation condition and the pressure and the speed of water particles in the water area, so that the position and the moment of the first cavitation are further obtained; combining the water particle velocity expression, the velocity of the water particles at the cavitation position can be calculated;
The bubbles generated after cavitation collapse, and the pressure at the reconstructed wave generated by collapse is the sum of the pressure of the front of the reconstructed wave, the pressure of the radiation wave of the reconstructed wave and the hydrostatic pressure; the reconstructed wave front pressure can be obtained by the reflected wave and the sparse wave;
Compression of water particles can be generated in the collapsing process, and according to a displacement continuous equation, the propagation speed of the wave front of the reconstructed wave, the pressure at the reconstructed wave and the radiation wave pressure of the reconstructed wave can be obtained by combining the conservation of momentum of the wave surface of the reconstructed wave; the true incident shock wave of the coating and the wet surface pressure taking cavitation effects into account are then determined.
In the above scheme, in step S1, the propagation speed of the shock wave is:
Where Vs represents the propagation velocity of the shock wave, σ - is the wavefront stress, σ + is the back stress, ε - is the wavefront strain, ε + is the back strain, and ρR is the initial density of the plastic porous material.
In the above-described scheme, in step S1, the internal energy per unit mass of the porous material at the shock wave front is changed to:
where E - represents the internal energy in the wavefront unit mass porous material and E + represents the internal energy in the back unit mass porous material.
In the above scheme, in step S1, before the impact wave acts, the impact-resistant coating is in an equilibrium state under the action of the hydrostatic pressure pst, and the stress, strain and particle velocity in the coating are respectively: pst, εst, 0;
After the elastic precursor wave, the stress, strain and particle velocity in the cover layer are noted as: σ 0、ε0、V0, according to the conservation of mass and conservation of momentum equations:
V0＝C0(ε0-εst),σ0-pst＝ρRC0V0 (8)
wherein C 0 is the wave velocity of elastic wave, satisfying Es is Young's modulus of the porous material in the elastic stage;
The state of the plastic shock wave front particle is the state after the elastic precursor wave, namely the stress, the strain and the particle speed in the covering layer are respectively as follows: sigma 0、ε0、V0; the stress, strain and particle velocity in the cover layer after plastic shock wave recording are respectively: σd, εd, V, according to the conservation of mass and conservation of momentum equations:
V-V0＝Vs(εd-ε0),σd-σ0＝ρRVS(V-V0) (9)
Then, the dynamic stress after the plastic impact wavefront is:
in the above scheme, in step S1, the control equation of the unloading area is:
in the method, in the process of the invention, Indicating the strain of elastic unloading, t indicating time,Indicating the speed of elastic unloading, X indicates the initial transversal coordinates of the plastic cellular material,Representing the stress of elastic unloading, σm and εm represent the stress and strain, respectively, achieved by plastic deformation prior to unloading, and Es is the Young's modulus of the porous material wire in the elastic phase.
In the above scheme, in step S1, according to newton' S second law, the pressure shell is considered to be fixed at the same time, and the equation of motion of the plastic porous covering layer under the action of hydrostatic pressure and shock wave is obtained as follows:
Wherein mf is the mass per unit area of the cover layer panel; ρ 0 is the initial density of the plastic porous material; u is the displacement of the cover front panel; h is the thickness of the crushed part; σd is the stress in the cover layer after plastic impact; pwet is the total wet surface pressure, taking into account the effects of fluid-solid coupling and cavitation.
In the above scheme, in step S2, the reflected wave generated after the underwater explosion shock wave is transmitted to the fluid-solid coupling surface is pr; meanwhile, the covering layer is required to generate large deformation to form sparse waves-rho wcwV, wherein rho represents the density of an aqueous medium, and cw is the propagation speed of sound waves in water;
taking into account the combined action of hydrostatic pressure and shock waves, the total overburden wet surface pressure can be expressed as:
pwet＝pst+pin+pr-ρwcwV (23)
Wherein pst is the hydrostatic pressure before the shock wave acts and pin is the incident shock wave.
In the above scheme, in step S3, after the impact wave acts on the impact-resistant cover layer, the reflected wave and the sparse wave propagate in the water along the direction opposite to the propagation direction of the incident impact wave, and the moment when the incident impact wave is transmitted to the fluid-solid coupling surface is 0 moment, at the moment t, the distance between the reflected wave and the sparse wave is cwt, and in the water area with-cwt < x <0, the pressure and the speed of the water particles are respectively:
When cavitation occurs in water, pw (x, t) =0 is satisfied, and for any position x in water, the cavitation time tcav can be obtained by solving the equation;
for a series of (x, tcav) combinations, wherein the position at which tcav takes the minimum value is the position at which cavitation occurs for the first time, the position and time at which cavitation occurs for the first time is (xf, tf);
Bringing cavitation time tcav into the water particle velocity expression and taking pw (x, tcav) =0, gives the velocity at which the water particle cavitation at x is:
Wherein pin (x, tcav) represents the incident shock wave of the water particle at time tcav at x, pst (x, tcav) represents the hydrostatic pressure of the water particle at time tcav at x.
In the above scheme, in step S3, the propagation speed of cavitation collapse is subsonic, the wave of cavitation collapse radiation is a reconstructed wave, the pressure applied to the reconstructed wave front along the-x direction is pCF ,in, which is the sum of the reflected wave and the sparse wave, assuming that the reconstructed wave front is at xCF at this time, namely:
pCF,in＝pr-ρwcwV (26)
The radiation wave pressure at which cavitation collapses the reconstructed wave front is noted as pCE ,out, and the pressure and velocity of the water particles at the reconstructed wave front can then be expressed as:
The radiation wave pressure pCF ,out includes:
Wherein pCF represents the pressure at dx of cavitation zone after collapse of cavitation, eta is the fraction of cavitation in dx thickness, cCF is the propagation speed of reconstructed wave front, and parameter lambda can be expressed as:
In the above-described scheme, in step S3,
When the reconstructed wave of the collapsing radiation is transmitted to the fluid-solid coupling surface for the first time, the incident shock wave is replaced by acting on the impact-resistant cover layer, so the actual incident shock wave can be expressed as:
Wherein ta is the time when the wave radiated by cavitation collapse is transmitted to the fluid-solid coupling surface for the first time;
finally, considering the effect of cavitation, the expression of the total pressure of the wet surface can be rewritten as:
pwet＝pst+pa+pr-ρwcwV (34)。
the invention has the beneficial effects that:
1. Aiming at the technical problems of unclear evolution rule of bubble load at a flexible interface and lack of an effective load prediction method, a one-dimensional impact theoretical model under the combined action of high hydrostatic pressure and underwater explosion shock waves is established, the model considers the combined action of the hydrostatic pressure and the underwater explosion shock waves, and the whole impact action process is covered: the dynamic compression process of the coating, the fluid-solid coupling process and the cavitation generation and collapse process in the flow field. On the basis of a theoretical model, a theoretical calculation method of the impact-resistant coating under the combined action of hydrostatic pressure and shock waves is formed, so that the method can be used for analyzing the impact protection effect of the coating and providing theoretical support for researching the impact protection mechanism of the pressure-resistant impact-resistant coating.
2. In order to solve the technical problem of the fluid-solid coupling effect under the strong impact load and the lack of an effective theoretical analysis method, the influence of the impact carried by fluid between the position where cavitation occurs for the first time and the wet surface on the covering layer is considered. Compared with the theory of a free Taylor plate, the model can not only consider the action of a plastic porous material, but also consider the impulse carried by fluid between the first cavitation position and the wet surface, and the estimated impulse transferred to the fluid-solid coupling surface is more accurate.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a material model of a plastic porous material of the method of the present invention;
FIG. 2 is a one-dimensional theoretical model of the pressure resistant impact blanket of the method of the present invention under hydrostatic pressure and shock wave action;
FIG. 3 is a schematic representation of the propagation of shock waves in a porous material in accordance with the present invention;
FIG. 4 is a graph showing the movement of the pressure resistant impact blanket of the method of the present invention under hydrostatic pressure and impact loading;
FIG. 5 is a cavitation formation process and collapse process of the method of the present invention;
FIG. 6 is a graph showing the results of calculating cavitation formation and collapse processes and cavitation particle velocity using the method of the present invention;
FIG. 7 is a graph showing the results of the calculation of the true incident pressure and total pressure of a wet surface using the method of the present invention.
Detailed Description
For a clearer understanding of technical features, objects and effects of the present invention, a detailed description of embodiments of the present invention will be made with reference to the accompanying drawings.
Because the impact cover of submarines is continuously subjected to high hydrostatic pressure, the cover material needs to have a high modulus of elasticity and a significant stress plateau phase, such as a plastic cellular material. The material model of the plastic porous material can be simplified to an equivalent rigid plastic model, as shown in fig. 1. The equivalent rigid-plastic model mainly uses two parameters to describe the stress-strain characteristics of a plastic porous material: platform stress (σpl) and densification strain (εD), which is generally defined as the strain at which energy absorption efficiency is greatest. And carrying out uniaxial compression experiments on the selected plastic porous material to obtain a nominal stress-strain curve of the plastic porous material. The energy absorption efficiency Ea is defined as the quotient of the energy absorption at a nominal strain of sn and the stress corresponding to this strain, namely:
According to And determining densification strain epsilon D, and obtaining corresponding platform stress sigma pi according to the densification strain. The plateau stress is defined as the average stress from the yield strain epsilon 0 to the densification strain epsilon D, i.e.:
the invention provides a bubble pulsation and impact cover layer coupling response calculation method, which uses a plastic porous material with higher elastic modulus and obvious stress platform stage as a cover layer material to establish a one-dimensional impact theoretical model of an impact cover layer under the combined action of hydrostatic pressure and impact load, wherein the model mainly comprises three parts, as shown in figure 2: (1) A dynamic compression process of the impact-resistant coating under the action of prestress and impact load under the action of hydrostatic pressure; (2) fluid-solid coupling of the impact cover layer with water; (3) The cavitation in water, the collapsing process and the secondary loading process caused by collapsing.
On the basis of a theoretical model, analyzing the complete impact process of the impact resistant coating layer comprises the following steps:
s1, analyzing a dynamic compression process of an impact-resistant covering layer under the action of hydrostatic pressure and shock waves:
According to the theory of shock waves, the shock wave load is described in the form of exponential decay waves, and the propagation speed of the shock waves is obtained according to the law of conservation of momentum and the conservation of mass equation; and obtaining the internal energy change quantity of the cover layer according to the law of conservation of momentum. When the surface of the covering layer is made of plastic porous material, strong intermittent elastic precursor wave and subsequent plastic shock wave exist in the material, and the wave speed and wave surface stress are respectively calculated. The unloading process generated under the action of plastic shock waves needs to consider the strain hardening effect to obtain a control equation of an unloading area. And obtaining the motion equation of the pressure shell and the crushed porous material according to Newton's second law.
The specific analysis process is as follows:
S1.1, shock wave propagation control equation
The far-field underwater explosion shock wave can be described in the form of an exponentially decaying wave, and the plastic porous material is an unloading process with strong interruption under the load, and can be described by adopting a shock wave theory. When the shock wave is applied to the porous material and the shock wave strength is greater than the yield strength of the porous material, plastic collapse of the porous material occurs. For plastic porous materials, there are two waves propagating simultaneously in the porous material: one is elastic precursor wave, and propagates at the wave speed of the elastic wave; one is a plastic shock wave.
Whether it is an elastic precursor wave or a plastic shock wave, the mass continuity and momentum conservation equations are satisfied at the wave fronts during propagation, and the derivation process is independent of the specific form of the load acting on the pressure-resistant impact-resistant coating, so long as the input is a strong intermittent unloading load. Let the wavefront state be: wave front stress sigma -, wave front strain epsilon -, wave front speed V - and wave front density rho -; the post-wave state is: the initial density of the material is ρR, the post stress σ +, the post strain ε +, the post velocity V +, and the post density ρ +. The propagation of the shock wave in the plastic porous material is shown in fig. 3.
The propagation speed of the shock wave is: where t represents time, X represents the abscissa of the wavefront plastic porous material, and X represents the initial transversal coordinate of the plastic porous material (with the shock wave loading direction as the positive direction and the fluid-solid coupling contact surface as the origin).
The mass conservation is satisfied on the wave front: ρ -dx＝ρ+[dx-(V+dt-V- dt) ] (2)
Relationship of density to strain: ρr=ρ +(1-ε+)＝ρ-(1-ε-) (3)
The infinitesimal thickness dx on the wavefront satisfies the conservation of momentum:
(σ+-σ-)dt＝ρ-dx(V+-V-)
the propagation speed of the shock wave obtained by combining the mass conservation equation and the momentum conservation equation is as follows:
According to the energy conservation condition, the work of the external force is balanced with the change of the internal energy and kinetic energy of the system, and E is set as the internal energy in the porous material with unit mass, and the method comprises the following steps:
where E - represents the internal energy in the wavefront unit mass porous material and E + represents the internal energy in the back unit mass porous material.
The mass and momentum conservation equations are brought into the above equation:
the internal energy change per unit mass of porous material at the shock wave front is:
for plastic porous materials, which are incrementally hardened materials, there are duplex waves under the action of a shock wave: strong intermittent elastic precursor wave and subsequent shock wave. The propagation velocity of the subsequent shock wave is generally much smaller than that of the precursor shock wave. The propagation of these two waves in the plastic porous material is described below, respectively.
Elastic precursor wave: before the impact wave acts, the impact cover layer is in an equilibrium state under the action of hydrostatic pressure pst, and the stress, strain and particle speed in the cover layer are respectively as follows: pst, εst, 0; after the elastic precursor wave, the stress, strain and particle velocity in the cover layer are noted as: σ 0、ε0、V0. According to the mass conservation and momentum conservation equations:
V0＝C0(ε0-εst),σ0-pst＝ρRC0V0 (8)
wherein C 0 is the wave velocity of elastic wave, satisfying Es is the Young's modulus of the porous material in the elastic phase of the wire.
Plastic shock wave: the state of the plastic shock wave front particle is the state after the elastic precursor wave, namely the stress, the strain and the particle speed in the covering layer are respectively as follows: sigma 0、ε0、V0; the stress, strain and particle velocity in the cover layer after plastic shock wave recording are respectively: σd, εd, V, according to the conservation of mass and conservation of momentum equations:
V-V0＝Vs(εd-ε0),σd-σ0＝ρRVS(V-V0) (9)
Then, the dynamic stress after the plastic impact wavefront is:
S1.2, unloading wave control equation
The far-field underwater explosion shock wave is an exponentially decaying wave, so that the plastic wave of the porous material under the action of the exponentially decaying shock wave is an unloading wave with strong intermittent characteristic. The unloading process and the loading process follow different stress-strain relations and have different control equations. If the plastic deformation before unloading reaches the stress sigma m, whether or not the plastic deformation is reloaded after unloading, the stress and the strain have a linear relation as long as the stress no longer exceeds sigma m, and the slope of the stress and the strain is equal to the initial slope of the elastic part of the loading curve. Obviously, from the plastic deformation occurring after unloading, the yield limit is increased to σm, a so-called work hardening or strain hardening effect.
Under one-dimensional stress, the stress-strain relationship of elastic unloading is as follows: in the method, in the process of the invention, Indicating the stress of the elastic unloading,Indicating the strain of elastic relief.
The control equation for the unloading process is the same as that for loading, and still comprises a kinematic equation (conservation of mass), a kinetic equation (conservation of momentum) and an constitutive equation.
The unloading process strain and speed are: where ε represents unloading process strain, u represents displacement of the front panel of the cover layer, and X represents initial transverse coordinates of the plastic porous material (with the direction of shock wave loading as positive direction and the fluid-solid coupling contact surface as origin).
The compatibility equation, namely the continuous equation (mass conservation equation), is:
Conservation of momentum is: Where ρ 0 represents the initial density of the plastic porous material, a 0 represents the initial cross-sectional area of the covering layer, P (X) is the pressure applied at the position X of the covering layer, and P (x+dx) is the pressure applied at the position x+dx of the covering layer.
Also known is σ=p/a 0, then there isWherein σ represents stress.
The control equation for the unload region is:
in the method, in the process of the invention, Indicating the strain of the elastic relief,Indicating the speed of the elastic unloading,Representing the stress of elastic unloading, σm and εm represent the stress and strain achieved by plastic deformation, respectively, prior to unloading.
For plastic porous materials, the elastic strain is negligible with respect to the plastic strain. Thus, the first and second substrates are bonded together,Independent of t, there is
The velocity of the plastic strong intermittent unloading wave in the porous material is consistent with the velocity of the plastic wave front particles, namely, the region after the plastic wave is transmitted is in rigid motion, and V (X, t) =v (t) (18).
S1.3 equation of motion of the impact-resistant coating under the action of hydrostatic pressure and impact load
Under the combined action of hydrostatic pressure and shock wave, the porous material of the crushed part of the cover layer and the front panel of the cover layer do rigid motion together. According to Newton's second law, considering the fixation of the pressure-proof shell, the equation of motion of the plastic porous covering layer under the action of hydrostatic pressure and shock wave is expressed as:
Wherein mf is the mass per unit area of the cover layer panel; ρ 0 is the initial density of the plastic porous material; h is the thickness of the crushed part; σd is the stress in the cover layer after plastic impact; pwet is the total wet surface pressure, taking into account the effects of fluid-solid coupling and cavitation. The movement of the pressure resistant and impact resistant cover layer under hydrostatic pressure and impact load is shown in figure 4.
S2, fluid-solid coupling analysis of the impact coating layer and water:
according to the reflection rule of the incident shock wave, the reflection wave caused by reflection and the sparse wave caused by deformation of the covering layer are calculated, and under the combined action of hydrostatic pressure and shock wave, the total pressure on the fluid-solid coupling surface under the condition of not considering cavitation and bubble collapse is calculated.
The specific analysis process is as follows:
For underwater explosion problems, the load on the pressure-resistant impact blanket, which is associated with the coupled movement of the fluid and the pressure-resistant impact blanket, is not known in advance. According to the description in Cole, underwater explosion, for far-field shock waves, it can be described as exponentially decaying waves propagating at sonic speed, namely:
Where cw is the propagation velocity of the acoustic wave in the water, p 0 is the peak value of the incident shock wave, θ is the attenuation coefficient, and can be expressed as a function of the explosive weight and the explosive distance:
Where W is the weight (kg) of the explosive, R is the distance (m), and K 1、K2、A1、A2 is a constant related to the type of explosive, for TNT explosives: k 1＝53.4,K2＝0.0925,A1＝1.13,A2 = -0.22.
After the underwater explosion shock wave is transmitted to the fluid-solid coupling surface, the underwater explosion shock wave is reflected, and the reflected wave is pr; meanwhile, the cover layer is required to be greatly deformed to form sparse waves-rho wcwV, wherein rho represents the density of the water medium, and cw is the propagation speed of sound waves in water.
Taking into account the combined action of hydrostatic pressure and shock wave, the total wet surface pressure can be expressed as:
pwet＝pst+pin+pr-ρwcwV (23)
Wherein pst is the hydrostatic pressure before the shock wave acts and pin is the incident shock wave.
The formula is established before cavitation occurs, and cavitation occurs under the action of sparse wave-rho wcwV because water cannot bear tensile stress. Cavitation can block the propagation of incident shock wave pin, but collapse can occur due to the pressure-resistant impact-resistant cover layer. During cavitation collapse, new shock waves are radiated to act on the pressure resistant impact cover layer, which is further described in S3.
S3, analyzing cavitation occurrence and collapse process:
The cavitation phenomenon is generated in the water due to the reflected wave and the sparse wave, and the cavitation time of any position in the water can be obtained according to the cavitation generation condition and the pressure and the speed of water particles in the water area, so that the position and the moment of the first cavitation are further obtained; by combining the water particle velocity expression, the velocity of the water particles at the cavitation position can be calculated. The bubbles generated after cavitation collapse, and the pressure at the reconstructed wave generated by collapse is the sum of the pressure of the front of the reconstructed wave, the pressure of the radiation wave of the reconstructed wave and the hydrostatic pressure; the reconstructed wave front pressure can be obtained from the reflected wave and the sparse wave. Compression of water particles can be generated in the collapsing process, and according to a displacement continuous equation, the propagation speed of the wave front of the reconstructed wave, the pressure at the reconstructed wave and the radiation wave pressure of the reconstructed wave can be obtained by combining the conservation of momentum of the wave surface of the reconstructed wave; the true incident shock wave of the coating and the wet surface pressure taking cavitation effects into account are then determined.
The specific analysis process is as follows:
s3.1 cavitation formation Process
After the impact wave acts on the impact cover layer, the reflected wave and the sparse wave can propagate in water along the direction opposite to the propagation direction of the incident impact wave, the moment when the incident impact wave is transmitted to the fluid-solid coupling surface is recorded as 0 moment, the transmission distance between the reflected wave and the sparse wave is cwt at t moment, and the pressure and the speed of water particles in a water area with the cwt < x <0 are respectively as follows:
When cavitation occurs in water, pw (x, t) =0 is satisfied, and for any position x in water, the cavitation time tcav can be obtained by solving the equation. For a series of (x, tcav) combinations, the position at which tcav takes the minimum value is the position at which cavitation occurs for the first time, and the position and time at which cavitation occurs for the first time is (xf, tf). For the free Taylor plate, the first place of cavitation occurs on the fluid-solid coupling face, while for the pressure-resistant impact coating, the first place of cavitation occurs in water at a distance from the pressure-resistant impact coating.
Bringing cavitation time tcav into the water particle velocity expression and taking pw (x, tcav) =0, gives the velocity at which the water particle cavitation at x is:
Wherein pin (x, tcav) represents the incident shock wave of the water particle at time tcav at x, pst (x, tcav) represents the hydrostatic pressure of the water particle at time tcav at x.
Cavitation occurs and propagates at supersonic speeds both toward and away from the wet surface. Wherein xBF is the position of the cavitation wavefront.
S3.2 cavitation collapse process
The propagation speed of cavitation collapse is subsonic, and the wave of cavitation collapse radiation is recorded as a reconstructed wave, as shown in fig. 5. Assuming that the reconstructed wavefront is at xCF at this time, the pressure applied to the reconstructed wavefront in the-x direction is noted as pCF ,in, which is the sum of the reflected and sparse waves, namely:
pCF,in＝pr-ρwcwV (26)
The radiation wave pressure at which cavitation collapses the reconstructed wave front is noted as pCF ,out, and the pressure and velocity of the water particles at the reconstructed wave front can then be expressed as:
Assuming that at time t the reconstructed wavefront is at xBF, during the dt time the reconstructed wavefront passes the distance dx, i.e. the cavitation region with dx collapses. Before the reconstructed wave is transmitted, the pressure in the area is the critical pressure of cavitation and is recorded as 0, and the particle speed is Vcav when cavitation occurs; after cavitation collapse, the pressure at this point was pCF and the particle velocity was vCF. The compression of dx at the reconstructed wavefront is (Vcav-vCF) dt. The compression amount is composed of two parts, one part is the compression amount caused by changing the pressure from 0 to pCF, and the other part is the collapse of the cavitation part, namely:
The displacement continuity equation can be expressed as:
ρwcw2(vCF-Vcav)＝[ρwcw2η+pCF(1-η)]cCF (29)
wherein eta is the fraction of cavitation in dx thickness, The vcf is the propagation speed of the reconstructed wavefront, satisfying vcf=dx/dt.
The reconstructed wave front simultaneously meets the conservation of momentum:
-ρw(1-η)dx(vCF-Vcav)＝-pCFdt (30)
the equation can be integrated to obtain:
Wherein the parameter λ can be expressed as:
When the reconstructed wave of the collapsing radiation is transmitted to the fluid-solid coupling surface for the first time, the incident shock wave is replaced by acting on the impact-resistant cover layer, so the actual incident shock wave can be expressed as:
Wherein ta is the time when the wave radiated by cavitation collapse is transmitted to the fluid-solid coupling surface for the first time;
finally, considering the effect of cavitation, the expression of the total pressure of the wet surface can be rewritten as:
pwet＝pst+pa+pr-ρwcwV (34)。
in one embodiment of the invention, according to a one-dimensional impact-resistant theoretical model under the combined action of high hydrostatic pressure and underwater explosion shock waves, a plastic polyurethane foam material is selected as a submarine cover layer, and is simplified into a rigid plastic model, when the hydrostatic pressure is 1MPa, the shock wave load is p 0 = 15.4MPa, and θ = 1.178ms, cavitation formation and collapse processes and cavitation particle speeds in fluid can be calculated (figure 6), real incident pressure and total pressure results of a wet surface can be calculated, the theoretical results are well matched with the finite element results, and the accuracy of the one-dimensional impact-resistant theoretical model can be verified.
The embodiments of the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and many forms may be made by those having ordinary skill in the art without departing from the spirit of the present invention and the scope of the claims, which are to be protected by the present invention.
Claims (6)
1. A method for calculating coupling response of bubble pulsation and impact cover layer is characterized in that a one-dimensional impact theoretical model of the impact cover layer under the combined action of hydrostatic pressure and impact load is established, and the model comprises three parts: (1) A dynamic compression process of the impact-resistant coating under the action of prestress and impact load under the action of hydrostatic pressure; (2) fluid-solid coupling of the impact cover layer with water; (3) A secondary loading process caused by occurrence and collapse of cavitation in water;
On the basis of a theoretical model, analyzing the complete impact process of the impact resistant coating layer comprises the following steps:
s1, analyzing a dynamic compression process:
according to the theory of shock waves, the shock wave load is described in the form of exponential decay waves, and the propagation speed of the shock waves is obtained according to the law of conservation of momentum and the conservation of mass equation; obtaining the internal energy variation of the cover layer according to the law of conservation of momentum;
When the surface of the covering layer is made of a plastic porous material, strong intermittent elastic precursor waves and subsequent plastic shock waves exist in the material, and the wave speed and wave surface stress of the material are respectively calculated;
the unloading process generated under the action of plastic shock waves needs to consider the strain hardening effect to obtain a control equation of an unloading area;
according to Newton's second law, get the motion equation of the pressure-proof shell and crushed porous material;
S2, fluid-solid coupling analysis:
According to the reflection rule of the incident shock wave, obtaining a reflected wave p r caused by reflection and a sparse wave-rho wcw V caused by deformation of a covering layer, wherein rho w represents the density of an aqueous medium, c w represents the propagation speed of sound waves in water, and V represents the particle speed in the covering layer after plastic shock waves; under the combined action of hydrostatic pressure and shock wave, the total pressure of the wet surface of the covering layer is calculated without considering cavitation and bubble collapse:
pwet＝pst+pin+pr-ρwcwV (23)
wherein, p st is the hydrostatic pressure before the impact wave acts, and p in is the incident impact wave;
S3, analyzing cavitation occurrence and collapse process:
The cavitation phenomenon is generated in the water due to the reflected wave and the sparse wave, and the cavitation time of any position in the water can be obtained according to the cavitation generation condition and the pressure and the speed of water particles in the water area, so that the position and the moment of the first cavitation are further obtained; combining the water particle velocity expression, the velocity of the water particles at the cavitation position can be calculated; specific: after the impact wave acts on the impact cover layer, the reflected wave and the sparse wave can propagate in water along the direction opposite to the propagation direction of the incident impact wave, the moment when the incident impact wave is transmitted to the fluid-solid coupling surface is recorded as 0 moment, the distance between the reflected wave and the sparse wave is transmitted as c w t at the t moment, and the pressure and the speed of water particles in the water area with the speed of-c w t < x <0 are respectively as follows:
when cavitation occurs in water, p w (x, t) =0 is satisfied, and for any position x in water, the cavitation time t cav can be obtained by solving the equation;
For a series of (x, t cav) combinations, wherein the position at which t cav takes the minimum value is the position at which cavitation occurs for the first time, the position and time at which cavitation occurs for the first time are recorded as (x f,tf);
Bringing the cavitation time t cav into the water particle velocity expression and taking into account p w(x,tcav) =0, the velocity at which the water particles cavitation at x is obtained is:
Wherein, p in(x,tcav) represents the incident shock wave of the x-ray particle at time t cav, and p st(x,tcav) represents the hydrostatic pressure of the x-ray particle at time t cav;
The bubbles generated after cavitation collapse, and the pressure at the reconstructed wave generated by collapse is the sum of the pressure of the front of the reconstructed wave, the pressure of the radiation wave of the reconstructed wave and the hydrostatic pressure; the reconstructed wave front pressure can be obtained by the reflected wave and the sparse wave; specific: the propagation speed of cavitation collapse is subsonic, the wave of cavitation collapse radiation is recorded as a reconstruction wave, the pressure acting on the reconstruction wave front along the-x direction is recorded as p CF,in on the assumption that the reconstruction wave front is at the position of x CF at the moment, and the pressure is the sum of a reflected wave and a sparse wave, namely:
pCF,in＝pr-ρwCwV (26)
the pressure of the radiation wave at the reconstructed wave front, where cavitation collapses, is noted as p CF,out, and thus the pressure and velocity of the water particles at the reconstructed wave front can be expressed as:
Regarding the radiation wave pressure p CF,out, there are:
Wherein, p CF represents the pressure at dx of cavitation zone after collapse of cavitation, eta is the fraction of cavitation in dx thickness, c CF represents the propagation speed of reconstructed wave front, and parameter lambda is expressed as:
Compression of water particles can be generated in the collapsing process, and according to a displacement continuous equation, the propagation speed of the wave front of the reconstructed wave, the pressure at the reconstructed wave and the radiation wave pressure of the reconstructed wave can be obtained by combining the conservation of momentum of the wave surface of the reconstructed wave; further obtaining the real incident shock wave of the coating and the wet surface pressure considering cavitation influence; specific: when the reconstructed wave of the collapsing radiation is transmitted to the fluid-solid coupling surface for the first time, the incident shock wave is replaced by acting on the impact-resistant cover layer, so the actual incident shock wave can be expressed as:
Wherein t a is the time when the wave radiated by cavitation collapse is transmitted to the fluid-solid coupling surface for the first time;
finally, considering the effect of cavitation, the expression of the total pressure of the wet surface can be rewritten as:
pwet＝pst+pa+pr-ρwcwV (34)。
2. The method of calculating a bubble pulsation and impact cover layer coupling response according to claim 1, wherein in step S1, a propagation speed of the shock wave is:
Where V s denotes the propagation velocity of the shock wave, σ - is the wavefront stress, σ + is the back stress, ε - is the wavefront strain, ε + is the back strain, and ρ R is the initial density of the plastic porous material.
3. The method of calculating the bubble pulsation and impact cover layer coupling response according to claim 2, wherein in step S1, the internal energy change per unit mass of the porous material at the shock wave front is:
where E - represents the internal energy in the wavefront unit mass porous material and E + represents the internal energy in the back unit mass porous material.
4. The method of claim 3, wherein in step S1, before the impact wave is applied, the impact coating is in an equilibrium state under the action of hydrostatic pressure p st, and the stress, strain and particle velocity in the coating are respectively: p st、εst, 0;
After the elastic precursor wave, the stress, strain and particle velocity in the cover layer are noted as: σ 0、ε0、V0, according to the conservation of mass and conservation of momentum equations:
V0＝C0(ε0-εst),σ0-pst＝ρRC0V0 (8)
wherein C 0 is the wave velocity of elastic wave, satisfying E s is the Young's modulus of the porous material at the elastic stage of the wire;
the state of the plastic shock wave front particle is the state after the elastic precursor wave, namely the stress, the strain and the particle speed in the covering layer are respectively as follows: sigma 0、ε0、V0; the stress, strain and particle velocity in the cover layer after plastic shock wave recording are respectively: σ d、εd, V, according to the mass conservation and momentum conservation equations:
V-V0＝VS(εd-ε0),σd-σ0＝ρRVS(V-V0) (9)
Then, the dynamic stress after the plastic impact wavefront is:
5. The method of claim 4, wherein in step S1, the control equation of the unloading zone is:
in the method, in the process of the invention, Indicating the strain of elastic unloading, t indicating time,Indicating the speed of elastic unloading, X indicates the initial transversal coordinates of the plastic cellular material,Representing the stress of elastic unloading, σ m and ε m represent the stress and strain, respectively, reached by plastic deformation before unloading, E s is the Young's modulus of the porous material wire in the elastic phase.
6. The method for calculating the coupling response of bubble pulsation and impact cover layer according to claim 5, wherein in step S1, according to newton' S second law, the motion equation of the plastic porous cover layer under the hydrostatic pressure and shock wave action is obtained by considering the fixation of the pressure shell at the same time:
Wherein m f is the mass per unit area of the cover panel; ρ 0 is the initial density of the plastic porous material; u is the displacement of the cover front panel; h is the thickness of the crushed part; σ d is the stress in the cover layer after plastic impact; p wet is the total wet surface pressure, taking into account the effects of fluid-solid coupling and cavitation.
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