Cylindrical explosion container design method based on liquid medium enhancement

Abstract

The invention discloses a cylindrical explosion container design method based on liquid medium enhancement. A radial dynamic balance equation for describing the dynamic response of a cylindrical explosion container is established. A pressure load model without packaging liquid is obtained based on a simplified finite element model, a time domain distribution model of a radial displacement field is constructed according to a similarity principle, a diffraction shielding effect and a momentum extraction effect are introduced to correct the pressure load model, and a pressure load model containing packaging liquid is obtained. A linear strengthening rigid-plastic model of a shell material is provided, and a theoretical model capable of quantitatively predicting the deformation rule of a traditional cylindrical explosion container in a time domain and a space domain is established in combination with displacement and bending moment boundary conditions. And finally, the dimensionless protection efficiency of the liquid medium enhanced cylindrical explosion container is defined, and the optimal design method of the packaging liquid size under the constraint condition is provided based on the ratio of the deformation reduction quantity to the quality of the protection structure. According to the method, the structure of the cylindrical explosion container can be quickly optimized.

Description

Technical field:

[0001] The present invention relates to the technical field of explosion protection, and in particular to a design method of a cylindrical explosion container based on liquid medium enhancement. Background technology:

[0002] An explosion container is a protective device that can effectively confine explosion energy and detonation products. With its advantages of large protection range, low cost, and easy maintenance, it has been widely used in many important fields such as urban emergency response, industrial production, laboratory research, and aerospace. Traditional explosion containers mainly rely on the strength and ductility of a single metal material to achieve the confinement and absorption of explosion energy. However, as the requirements for protection equivalent in practical applications continue to increase, the method of simply increasing the thickness of the metal layer to improve explosion-proof capabilities is increasingly difficult to meet the needs. Excessively thick metal structures will significantly increase the weight of the container, resulting in a decrease in the energy absorption efficiency per unit mass, and also increasing the difficulty of transportation and installation. Especially in fields such as aerospace that are extremely sensitive to weight, the application of traditional metal explosion containers is severely restricted.

[0003] In recent years, liquids such as water have been gradually introduced into explosion-proof vessels as a design strategy for reinforcing metal layers due to their physical properties such as low density and high specific heat. For example, patent document No. 202110950946.4 discloses a rigid-flexible composite explosion-proof tank containing a liquid layer of specific size. The liquid dispersed after the explosion can effectively reduce the ambient temperature and significantly reduce the destructive effects of the explosion shock wave pressure and flames. Patent document No. 202210356764.9 discloses a mushroom-shaped liquid container used inside the explosion-proof tank. By designing an explosion-proof liquid of specific size and shape, the concentrated explosion load can be spatially dispersed, reducing deformation in the weak parts of the explosion-proof tank. A large number of theoretical and experimental results have shown that the reasonable optimization of the liquid layer size can significantly reduce the final deformation of the container wall (by more than 40%), while increasing the overall mass by less than 5%. Therefore, it is of great significance to study the effect of the size optimization of the liquid reinforcement medium on the response characteristics of the cylindrical explosion-proof vessel.

[0004] Currently, the design of new explosive containment vessels relies primarily on trial and error, which is limited by testing time and safety requirements, resulting in low structural optimization efficiency. Theoretical models, however, can reduce testing costs and enable rapid structural iteration and optimization, offering significant advantages in the research and design of new explosive containment vessels. However, existing theoretical analysis methods primarily focus on single-layer metal structures and sandwich structures. Quantitative theoretical models for the interaction between liquid and metal containers are extremely limited, and there is a lack of quantitative prediction methods for the dynamic deformation of cylindrical explosive containment vessels reinforced by liquid media. Summary of the invention:

[0005] In view of this, the present invention provides a design method for a cylindrical explosion container reinforced with a liquid medium, which can quantitatively predict the dynamic deformation of the cylindrical explosion container reinforced with a liquid medium and obtain the optimal design scheme for the size of the encapsulated liquid under constraints based on the ratio of the deformation reduction amount to the mass of the protective structure.

[0006] The technical solutions for implementing the present invention are as follows:

[0007] A method for designing a cylindrical explosion container based on liquid medium reinforcement includes the following steps:

[0008] S1. Construct radial dynamic equilibrium equations for thin-walled cylindrical explosion container structures;

[0009] S2. Approximately characterize the pressure load model P(x, t) acting on the inner wall surface of the explosion container shell when there is no encapsulated liquid;

[0010] S3. For the pressure load model containing encapsulated liquid, the diffraction shielding effect and momentum extraction effect are introduced to modify the P(x, t) time domain and space domain distribution model. The maximum length l of the external shadow area that changes the pressure space distribution is obtained through the diffraction shielding effect. out , the equivalent area length l of the inner shadow area is obtained by the momentum extraction effect in , the shock wave overpressure on the inner wall of the explosion container shell in the outer shadow area and the inner shadow area is zero; thus, the pressure load model P containing the encapsulated liquid is obtained f (x,t);

[0011] S4. Based on the consistency of the dynamic displacement response of the explosion container shell and the excitation pressure pulse in spatial distribution, the time domain and spatial domain distribution law of the radial displacement field of the explosion container shell is obtained. ρ (x,t);

[0012] S5. A linear enhanced rigid-plastic model is used to characterize the yield stress-plastic strain relationship of the explosion container shell;

[0013] S6, the P obtained in S3 f (x, t), the temporal and spatial distribution law of S4 u ρ Substitute the yield stress-plastic strain relationship of (x, t) and S5 into the radial dynamic equilibrium equation of S1 to obtain the radial displacement time history curve u0(t) at the center of the inner wall of the explosion container shell. According to u0(t), the radial displacement field u ρ Numerical solution of (x,t);

[0014] S7, based on S6, get u0(t) and u ρ (x, t), adjust the thickness and height of the encapsulated liquid to achieve the optimal design of the explosion container protection efficiency.

[0015] Furthermore, the radial dynamic balance equation is:

[0016]

[0017] The radial dynamic balance equation is constructed in a cylindrical coordinate system with coordinate variables being radial ρ, circumferential θ and axial x; q ρ is the radial component of the external load, t is the time of the structural deformation process, and the moment when the pressure load begins to act on the explosion container shell is the zero point; u ρ is the radial displacement of the mid-plane of the explosion container shell; ρ, h, R and l0 represent the density, thickness, inner diameter and length of the explosion container shell respectively; N θ , Q x and Q θ They represent the hoop membrane force, axial shear force and hoop shear force per unit length of the mid-surface, respectively.

[0018] Furthermore, the pressure load model P(x,t) is:

[0019]

[0020] Wherein, P0 is the peak overpressure of the pressure pulse at the center of the inner wall of the explosion container shell 1 (x=0), a is the arrival time of the shock wave overpressure peak, and τ is the characteristic time constant describing the shock wave overpressure decay.

[0021] Furthermore, the pressure load model P containing the encapsulated liquid f (x,t) is:

[0022] P f (x, t) = P0P t (t)P x (x)

[0023] in

[0024]

[0025] Where, P t (t) is the normalized time domain distribution function of the reflected overpressure, P x (x) is the normalized spatial distribution function of the reflected overpressure.

[0026] Furthermore,

[0027]

[0028] Where H c and T c are the height and thickness of the encapsulated liquid respectively, and α is the propagation velocity ratio of the rarefaction wave to the shock wave in the encapsulated liquid, which is usually taken as α=0.33.

[0029] Furthermore,

[0030]

[0031] Where l1 is the length of the plastic deformation region, and u0(t) is the radial displacement time history curve at x=0.

[0032] Furthermore, the yield stress-plastic strain relationship of the explosion container shell is:

[0033]

[0034] Among them, σ y and σ0 are the flow stress and initial yield stress of the explosion container shell respectively; E p is the plastic hardening modulus, is the effective plastic strain;

[0035]

[0036] Among them, ε θ , ε ρ and ε x denote hoop strain, radial strain and axial strain respectively, γ xρ Represents the shear strain between the axial and radial directions.

[0037] Furthermore,

[0038]

[0039] in

[0040]

[0041] Furthermore, in S7, the dimensionless protection efficiency η is defined. The larger the value of η, the smaller the deformation of the structure under the same protection quality, and the higher the protection efficiency;

[0042]

[0043] Among them, m w is the mass of the encapsulated liquid, m s is the mass of the explosion container shell, ρ w and ρ are the densities of the encapsulated liquid and the explosion container shell respectively; u w+s and u s They are the maximum deformations of liquid medium enhanced explosion container and liquid medium free explosion container respectively.

[0044] Beneficial effects:

[0045] 1. The explosion wave pressure input used in the present invention is derived from a simplified finite element model, rather than directly using a commonly used empirical formula, thereby avoiding the order of magnitude error that may be caused by the empirical formula in the case of near-field explosions.

[0046] 2. The linear reinforcement rigid-plastic hypothesis proposed in this invention can fully consider the strain hardening effect of metal materials, breaking through the technical bottleneck of traditional vibration theory that is limited to small deformation analysis. It can directly guide the selection of the main metal material of the explosion container and avoid material waste caused by overly conservative design.

[0047] 3. The present invention is the first to decouple the liquid medium protection mechanism into a dual-effect synergistic model of diffraction shielding and momentum extraction, realizing the quantitative characterization of the liquid protection mechanism and providing a calculable parameter system for explosion container design. The theoretical prediction value is in good agreement with the experiment, filling the theoretical gap of traditional empirical formulas under near-field explosion conditions.

[0048] 4. The optimized design method of a liquid medium enhanced explosion container proposed in the present invention provides theoretical guidance for the design of this type of explosion container. Description of the drawings:

[0049] Figure 1 The figure is a flow chart of the method for designing a cylindrical explosion container for liquid medium reinforcement according to the present invention.

[0050] Figure 2 Schematic diagram of the dynamic response of a cylindrical explosion container under implosion load in the present invention.

[0051] Figure 3 Schematic diagram of the external shadow area caused by the diffraction shielding effect in the present invention.

[0052] Figure 4 Schematic diagram of the inner shadow area caused by the momentum extraction effect in the present invention.

[0053] Figure 5 This is a simplified structural diagram of Example 1 of the present invention.

[0054] Figure 6 1 is a comparison chart of theoretical prediction and experimental results in Example 1 of the present invention.

[0055] Figure 7 These are the optimization results of different packaged liquid sizes in the present invention.

[0056] Where: 1-explosion vessel shell, 1.1-plastic deformation area, 1.2-undeformed area, 1.3-AA circumferential section, 1.4-axial section, 2-explosive; 3-incident shock wave, 4-diffracted shock wave, 5-transmitted shock wave, 6-external shadow area, 7-encapsulated liquid; 8-internal shadow area, 9-scattering area Specific implementation method:

[0057] The present invention provides a method for designing a cylindrical explosion container based on liquid medium enhancement. The specific design process is as follows: Figure 1 shown.

[0058] First, for cylindrical thin shell structures, a radial dynamic equilibrium equation was established to describe the dynamic response of cylindrical explosive containers. Based on a simplified finite element model, a pressure load model was obtained in the absence of encapsulated liquid, and a time-domain distribution model of the radial displacement field was constructed based on the similarity principle. On this basis, the diffraction shielding effect and momentum extraction effect were further introduced to modify the pressure load model, and a pressure load model was obtained when encapsulated liquid was present. A linear reinforced rigid-plastic model of the shell material was proposed, and combined with displacement and bending moment boundary conditions, a theoretical model was established that can quantitatively predict the deformation law of traditional cylindrical explosive containers in the time and space domains. Finally, the dimensionless protection efficiency of liquid-reinforced cylindrical explosive containers was defined, and based on the ratio of deformation reduction to the mass of the protective structure, an optimal design method for the encapsulated liquid size under constraint conditions was proposed.

[0059] 1. Radial dynamic balance equation

[0060] Figure 5 The simplified explosion container consists of three main parts: the explosion container shell 1, the explosive 2, and the encapsulated liquid 7. Assume that the explosion container shell 1 is a thin-walled cylindrical shell (thickness / inner radius <5%). In the cylindrical coordinate system of radial (ρ), circumferential (θ), and axial (x), the dynamic equilibrium equation of the radial internal force governing the deformation region 1.1 is:

[0061]

[0062] in

[0063]

[0064] Where q ρ is the radial component of the external load, in this case the implosion load P generated by the explosive 2. t is the time of the structural deformation process, with the moment when the pressure load begins to act on the explosion container shell 1 as the zero point. u ρ is the radial displacement of the mid-plane of the explosion container shell 1. ρ, h, R and l0 represent the density, thickness, inner diameter and length of the explosion container shell 1 respectively. N θ , Q x and Q θ Respectively represent the hoop membrane force, axial shear force and hoop shear force per unit length of the mid-plane. x 、M θ and M xθ They represent the axial and hoop in-plane bending moments, and mid-plane torque per unit length, respectively.

[0065] The circumferential symmetry of the explosion container shell 1 and the explosive 2 results in the distribution of the internal force and bending moment in the mid-plane being independent of θ. Therefore, equations (1) and (2) can be simplified to:

[0066]

[0067] in

[0068]

[0069] N θ =σ y h (5)

[0070] Where P, N θ , Q x , M x , and u ρ are functions with x and t as independent variables. y is the flow yield stress of the explosion container shell 1. Figure 2 As shown, the explosion pressure P generated by explosive 2 acts on both the plastic deformation area 1.1 and the undeformed area 1.2, and is the only external load. The calculation range of x in the formula is [0, l1], that is, only the time domain and spatial domain deformation distribution of the plastic deformation area 1.1 is calculated. The undeformed area 1.2 only undergoes elastic deformation or no deformation and is not within the calculation range of the above formula. The AA circumferential section 1.3 shows the annular membrane force N generated by the annular expansion under the action of the explosion pressure P. θ , the resultant force direction points to the center of the circle, hindering the deformation of the explosion container shell 1. The axial section 1.4 shows the axial shear force Q caused by the uneven axial deformation under the action of the explosion pressure P. x , and its direction also points to the center of the circle, hindering the deformation of the explosion container shell 1.

[0071] 2. Pressure load model without encapsulated liquid

[0072] Near field explosion (proportional distance less than 0.5kg / m 1 / 3 ), commonly used empirical formulas can produce large errors, even orders of magnitude different from the true value. Therefore, the present invention preferably uses the pressure-time history curve obtained in the numerical simulation as the load input for the theoretical model. Numerical simulations can be performed using finite element software such as LS-DYNA, ABAQUS, or AUTODYN. Only the reflected pressure P0 acting at the center of the inner wall (x=0) of the explosion container shell 1 after the explosion of the explosive 2 is calculated, without the need for subsequent deformation calculations. When the encapsulated liquid 7 is not considered, the general form of the reflected overpressure P acting on the inner wall surface of the explosion container shell 1 can be described as follows:

[0073]

[0074] Where P0 is the peak overpressure of the pressure pulse at the center of the inner wall of the explosion container shell 1 (x = 0), and its specific value is calculated using a simplified finite element model. The spatial distribution of the pressure pulse is described by the shape function f(x), which is expressed as:

[0075]

[0076] Where 2l0 is the total length of the explosion container shell 1.

[0077] Since the explosion container shell 1 and the explosive 2 have circumferential symmetry, the distribution function g(θ) of the pressure pulse in the circumferential direction (θ direction) is 1, that is:

[0078] g(θ)=1 (8)

[0079] The temporal distribution of the pressure pulse is given by the shape function Description, its expression is in the form of piecewise function:

[0080]

[0081] Where a is the arrival time of the shock wave overpressure peak, and τ is the characteristic time constant describing the shock wave overpressure decay.

[0082] Without considering the encapsulated liquid 7, the time domain and spatial distribution of the reflected overpressure P acting on the inner wall surface of the explosion container shell 1 can be approximately expressed as:

[0083]

[0084] 3. Pressure load model with encapsulated liquid

[0085] On the basis of the model without encapsulated liquid pressure load, the diffraction shielding effect and momentum extraction effect are further introduced to modify the time domain and space domain distribution models of Equation (10), and then a theoretical method is proposed to quantitatively analyze the dynamic response characteristics of liquid medium reinforced cylindrical explosion container.

[0086] like Figure 3 As shown, due to the difference in wave impedance between the detonation products generated after the detonation of the explosive 2 and the encapsulating liquid 7, when the incident shock wave 3 interacts with the encapsulating liquid 7, a diffraction shock wave 4 and a transmission shock wave 5 are simultaneously generated. Among them, the diffraction shock wave 4 does not propagate closely to the surface of the encapsulating liquid 7, and a certain distance is formed between the two, thereby generating an external shadow area 6. The pressure of this shadow area is significantly lower than that of other areas affected by the incident shock wave 1. This phenomenon is the diffraction shielding effect. This effect effectively reduces the deformation of the structure by changing the spatial distribution of pressure on the explosion container shell 1. Under the premise that the internal explosion pressure wave propagates in a straight line, the length of the external shadow area H sIt can be calculated using the following formula:

[0087]

[0088] Where H c and T c are the height and thickness of the encapsulated liquid 7 respectively. out is the maximum length of the outer shadow area 6 that changes the pressure spatial distribution, which can be calculated by the following formula:

[0089]

[0090] In addition to the diffraction effect, when the detonation products come into contact with the encapsulated liquid 7, the incident shock wave 3 will partially penetrate into the liquid medium, forming a transmitted shock wave 5. Figure 3 As shown, the transmitted shock wave 5 propagates radially along the transmission surface A in the encapsulated liquid 7, while the rarefaction wave propagates into the liquid from the two free surfaces B. The inwardly propagating rarefaction wave induces axial scattering at the edge of the liquid, forming a scattering zone 9.

[0091] From a physical mechanism perspective, the encapsulated liquid 7 achieves momentum extraction by absorbing radial shock wave energy and converting it into axial kinetic energy. This energy conversion process is mainly dominated by the dynamic behavior of the rarefaction wave. To characterize the attenuation effect of the rarefaction wave on pressure, an internal shadow area 8 is introduced into the theoretical model. Figure 4 As shown, the inner shadow area 8 is two areas covered by the rarefaction wave, and its thickness is equal to the thickness T of the encapsulated liquid. c , height is αT c The cross section is triangular. Where α is the propagation velocity ratio of the rarefaction wave to the shock wave in the encapsulated liquid 7, which is usually α = 0.33. To simplify the calculation, the inner shadow area of ​​the triangular cross section is equivalent to a rectangular area, and the length of the area not affected by the rarefaction wave is l in It can be expressed as:

[0092]

[0093] The diffraction shielding effect and momentum extraction effect can be characterized as the outer shadow zone 6 and the inner shadow zone 8, respectively. These two mechanisms enhance the protective performance of the explosion container by changing the spatial distribution of the explosion overpressure. This is based on the following assumptions: (1) the shock wave overpressure in the outer shadow zone 6 and the inner shadow zone 8 is zero; and (2) the effect of the encapsulated liquid 7 on the shock wave propagation delay is negligible.

[0094] Considering the encapsulated liquid 7, the reflected overpressure P acting on the inner wall surface of the explosion container shell 1 is f The temporal and spatial distribution models of can be expressed as:

[0095] P f (x, t) = P0Pt (t)P x (x) (14)

[0096] in

[0097]

[0098] Where P t (t) is the normalized time domain distribution function of the reflected overpressure, P x (x) is the normalized spatial distribution function of the reflected overpressure, and the simplified deformation region length l1 = l out It should be noted that the reflected overpressure P on the inner wall surface of the explosion container shell 1 f (Equation (14)) is a function of x and t, and the effect of ρ on pressure has been ignored. Therefore, for the outer shadow area 6 and the inner shadow area 8, the size of the area is characterized only by the length in the x-axis direction, and the pressure distribution of the shadow area in the ρ direction is ignored.

[0099] 4. Spatial distribution model of radial displacement field

[0100] Considering that the explosive 2 is the only external load on the explosion container shell 1, according to the principle of structural dynamics similarity, the dynamic displacement response of the explosion container shell 1 is consistent with the excitation pressure pulse in spatial distribution. Based on this, the radial displacement field u ρ (x,t) can be expressed in the following analytical form:

[0101]

[0102] Where l1 is the length of the plastic deformation zone 1.1 and u0(t) is the radial displacement time history curve at x=0.

[0103] 5. Linear hardening rigid-plastic model

[0104] The explosion container shell 1, which serves as the load-bearing structure, is preferably made of steel with good ductility, such as Q235, Q345, or 316L. These materials exhibit significant strain hardening properties, and their plastic yield stress increases continuously with increasing plastic strain. To accurately describe the mechanical response of thin shell structures under explosive loads, the present invention innovatively employs a linear reinforced rigid-plastic model to characterize the shell's stress-strain relationship. This model can be expressed analytically as follows:

[0105]

[0106] Where σ y and σ0 are the flow stress and initial yield stress of the explosion container shell 1 respectively. E p is the plastic hardening modulus. is the effective plastic strain.

[0107] The linear hardened rigid-plastic model primarily studies the mechanical response characteristics of thin shell structures under uniaxial yield loading. Based on the model's assumptions, the influence of the elastic segment is ignored in subsequent analyses, and the distinction between plastic strain and total strain is no longer made. In a cylindrical coordinate system, the effective plastic strain can be expressed as follows:

[0108]

[0109] in

[0110]

[0111] Where ε θ , ε ρ and ε x denote hoop strain, radial strain and axial strain respectively, γ xρ Indicates the shear strain between the axial and radial directions. u ρ and w are radial displacement and axial displacement respectively. Since the structure is axially symmetrical, the circumferential displacement u θ and shear strain γ ρθ and γ xθ In the explosion container shell 1, the axial displacement w is much smaller than the radial displacement u ρ To simplify the theoretical model, the axial displacement w is neglected.

[0112] The explosion container shell 1 follows the plastic deformation isovolumetric law during the impact deformation process, and the variation of its thickness h during the expansion process satisfies the following relationship:

[0113] 2πRh0dx=2π(R+u ρ (x,t))h1dx (21)

[0114] Where h0 is the initial thickness of the explosion container shell 1 before deformation, h1 is the shell thickness during the explosive loading process, and dx is the axial unit length. The shell thickness h1 under explosive loading can be expressed as follows:

[0115]

[0116] Therefore, the plastic strain component in formula (19) can be specifically expressed as:

[0117]

[0118] Due to the radial displacement u ρ The magnitude of is much smaller than the shell radius R, so u is ignored in formula (24) ρThe deformation of the shell is mainly concentrated near the center area (x=0), at which time sin(πx / l1) approaches 0, cos(πx / 2l1) approaches 1, and the shear strain γ xρ Much smaller than the hoop strain ε θ .

[0119] Therefore, the effective plastic strain in formula (19) can be expressed as:

[0120]

[0121] 6. Boundary conditions and time domain distribution model of radial displacement field

[0122] Based on the pressure load model containing encapsulated liquid (Equation (14)) and the linear enhanced rigid-plastic constitutive relationship (Equations (18) and (27)), the radial dynamic equilibrium equation (Equation (3)) of the explosion container shell 1 can be specifically written as:

[0123]

[0124] Among them, P f (x, t) can be calculated by formula (14).

[0125] Considering that the explosion container shell 1 and the explosive 2 are symmetrical about the x=0 plane, the shear force Q in this plane is x (x,t) can be expressed as:

[0126]

[0127] The explosion container shell 1 forms annular plastic hinges at x = 0 and x = l1. Therefore, the bending moment M x The boundary conditions at (x,t) can be described as:

[0128] M x (0,t)=-M0,M x (l1,t)=M0 (30)

[0129] Where M0=(σh 2 ) / 4 is the critical bending moment of the explosion container shell 1 when it reaches the plastic flow stage under the action of pure bending moment.

[0130] According to the above boundary conditions of shear force and bending moment, excluding M x The dynamic equilibrium equation of the term can be described as:

[0131]

[0132] in

[0133]

[0134] And have the following initial conditions of displacement and velocity:

[0135]

[0136] From this we can get:

[0137]

[0138] The above formula describes the time domain distribution law of the displacement of the plastic deformation area 1.1 at x = 0 in the absence of liquid reinforcement medium, and its corresponding spatial domain distribution law is given by formula (17).

[0139] 7. Optimized design of structure

[0140] Based on the above theoretical model, the thickness T of the encapsulated liquid 7 is adjusted. c and height H c , to achieve the optimal design of explosion container protection efficiency. Define dimensionless protection quality :

[0141]

[0142] where m w is the mass of the encapsulated liquid 7 (ignoring the mass of the encapsulated structure), m s is the mass of the explosion container shell 1, which can be calculated by the following formula:

[0143] m w =ρ w π(R 2 -(RT c ) 2 )H c (36)

[0144] m s =2ρπ((R+h) 2 -R 2 )l0 (37)

[0145] Where ρ w and ρ are the densities of the encapsulating liquid 7 and the explosion vessel shell 1, respectively.

[0146] Define the dimensionless deformation reduction β for evaluating the protection effect:

[0147]

[0148] Where u w+s and u s They are the maximum deformations of liquid medium enhanced explosion container and liquid medium free explosion container respectively.

[0149] Define the dimensionless protection efficiency η:

[0150]

[0151] The larger the value of η, the smaller the structural deformation under the same protection quality, and the higher the protection efficiency. Among them, η = 1 represents the explosion container without liquid medium reinforcement, which is also the comparison benchmark for all optimization results.

[0152] Example 1:

[0153] The present invention provides an embodiment of a cylindrical explosion container with a protection equivalent of 100g TNT. Based on the aforementioned theoretical analysis method, the temporal and spatial deformation patterns of the plastic deformation region 1.1 of the explosion container shell 1 under the action of explosive 2 are predicted. This prediction is then compared with explosion test results to verify the accuracy of the theoretical model for liquid-enhanced explosion containers.

[0154] like Figure 5 As shown, the liquid-reinforced cylindrical explosion container comprises three parts: an explosion container shell 1, explosive 2, and encapsulated liquid 7. The explosion container shell 1 is welded from a ductile metal such as Q235, Q345, or 304 stainless steel. The explosive 2 is determined based on actual usage and is typically black powder or TNT. During calculation, it is converted to TNT equivalent based on the explosive heat ratio. The encapsulated liquid 7 is typically purified water, ethylene glycol, or a shear thickening fluid. The preferred encapsulation method is 3D-printed containers based on SLS (Selective Laser Sintering) nylon powder technology. Compared to traditional 3D printing and blow molding, this method requires no internal support, offers lower manufacturing costs, and significantly improved material strength.

[0155] A simplified numerical model of a cylindrical explosion container was established using ANSYS / LS-DYNA finite element software. The peak overpressure P0, linear growth coefficient a, and exponential decay coefficient τ acting on the inner wall of the explosion container shell 1 were calculated under different explosive equivalent loads. Taking 100g of TNT as an example, its reflected peak overpressure P0 is 228.76MPa, the linear growth coefficient a is 3.94μs, and the exponential decay coefficient is 13.8μs. Substituting into Equation (10), the reflected pressure load model of 100g of TNT is obtained as follows:

[0156]

[0157] The length l of the outer shadow area 6 out and the length l of the inner shadow area 8 in It can be calculated by formula (12) and formula (13) respectively:

[0158]

[0159] Substituting into formula (14) we can get:

[0160] P f(x, t) = 228.76 MPa*P t (t)P x (x) (43)

[0161] in

[0162]

[0163] Structural parameters of the explosion container shell 1, such as density (ρ), yield stress (σ), thickness (h), plastic hardening modulus (E p ), inner diameter (R) and axial length (l0) are shown in Table 1:

[0164] Table 1 Input parameters in the theoretical model

[0165]

[0166] Substituting into equation (17) we can get the radial displacement field u ρ Spatial distribution of (x,t):

[0167]

[0168] Substituting the above calculation results into equations (31) and (32), the dynamic equilibrium equation of the liquid medium reinforced explosion container shell 1 can be obtained:

[0169]

[0170] in

[0171]

[0172] By numerically solving the above differential equations, we can obtain the temporal and spatial distribution laws of the deformation of the explosion container shell 1 under the internal explosion load:

[0173]

[0174] The units in the above formula are the International System of Units (SI) of m-kg-s.

[0175] Figure 6 The displacement-time response of the explosion container shell 1, represented by Equation (49), is shown. As can be seen from the figure, the maximum deformation of the explosion container shell 1 without the encapsulating liquid 7 is 11.82 mm, while the maximum deformation of the explosion container shell 1 with the encapsulating liquid 7 for enhanced protection is only 4.75 mm, a reduction of 59.8%, indicating that the encapsulating liquid 7 has significant explosion-weakening capabilities. Furthermore, in the test, the maximum deformation of the explosion container shell 1 with the encapsulating liquid 7 for enhanced protection is 4.92 mm, and the theoretical model prediction error is only -3.5%, demonstrating the reliability of the theoretical model.

[0176] Based on the above calculation results, the thickness T of the encapsulated liquid 7 is adjusted. c and height H c , to achieve the optimal design of explosion protection efficiency of the explosion container. For the encapsulated liquid 7 in Example 1, its thickness T c Should be between 20mm-60mm, height H c Should be between 30mm-200mm. Too small T c and H c The packaging structure will account for too large a proportion of the packaging liquid 7, weakening the protection effect; too large T c and H c It will occupy the internal space of the explosion container shell 1, limiting the size of the explosive that can be accommodated. Substituting the above dimensions into formula (39) can obtain the influence of different packaging liquid sizes on the dimensionless protection efficiency η, as follows: Figure 7 shown.

[0177] Figure 7 Shows 20mm≤T c ≤60mm and 30mm≤H c The dimensionless protection efficiency η when ≤200mm, as can be seen from the figure, the larger the thickness T c and a maximum height H c The protection efficiency will be lower than 1. At this time, the addition of the encapsulation liquid 7 will bring about a significant negative effect. This is different from the conventional cognition that the greater the protection quality, the better the protection effect. c Smaller, thickness T c When it is larger, the protection efficiency gradually increases. c and H c When the depths are 60 mm and 30 mm respectively, the dimensionless protection efficiency is the highest, which is 6.43 times that of the condition without encapsulated liquid.

[0178] like Figure 7 As shown, at 20mm≤T c ≤60mm and 30mm≤H c Under the condition of ≤200mm, the variation trend of dimensionless protection efficiency η is shown. As can be seen from the figure, when the thickness T c and height H c When the height H of the encapsulated liquid 7 is larger, the protection efficiency is lower than 1, indicating that the addition of the encapsulated liquid 7 has a significant negative impact on the protection effect, which is different from the conventional belief that increasing the protection quality can improve the protection effect. Further analysis found that when the height H of the encapsulated liquid 7 is c Smaller and thicker than T c When T is larger, the protection efficiency gradually increases. c and H cWhen the thickness is 60 mm and 30 mm respectively, the dimensionless protection efficiency under this working condition reaches its maximum value, which is 6.43 times that of the working condition without encapsulated liquid.

[0179] The present invention realizes the quantitative characterization of the liquid protection mechanism, provides a calculable parameter system for the design of explosion containers, fills the theoretical gap of traditional empirical formulas under near-field explosion conditions, and proposes an optimized design method for liquid medium enhanced protection explosion containers, which is of great significance for guiding the engineering application of such explosion containers.

Claims

1. A design method for a cylindrical explosion container based on liquid medium reinforcement, characterized in that: The following steps are involved: S1. Construct radial dynamic equilibrium equations for thin-walled cylindrical explosion container structures; S2. Approximately characterize the pressure load model P(x, t) acting on the inner wall surface of the explosion container shell when there is no encapsulated liquid; S3. For the pressure load model containing encapsulated liquid, the diffraction shielding effect and momentum extraction effect are introduced to modify the P(x, t) time domain and space domain distribution model. The maximum length l of the external shadow area that changes the pressure space distribution is obtained through the diffraction shielding effect. out , the equivalent area length l of the inner shadow area is obtained by the momentum extraction effect in , the shock wave overpressure on the inner wall of the explosion container shell in the outer shadow area and the inner shadow area is zero; thus, the pressure load model P containing the encapsulated liquid is obtained f (x,t); S4. Based on the consistency of the dynamic displacement response of the explosion container shell and the excitation pressure pulse in spatial distribution, the time domain and spatial domain distribution law of the radial displacement field of the explosion container shell is obtained. ρ (x,t); S5. A linear enhanced rigid-plastic model is used to characterize the yield stress-plastic strain relationship of the explosion container shell; S6, the P obtained in S3 f (x, t), the temporal and spatial distribution law of S4 u ρ Substitute the yield stress-plastic strain relationship of (x, t) and S5 into the radial dynamic equilibrium equation of S1 to obtain the radial displacement time history curve u0(t) at the center of the inner wall of the explosion container shell. According to u0(t), the radial displacement field u ρ Numerical solution of (x,t); S7, based on S6, get u0(t) and u ρ (x, t), adjust the thickness and height of the encapsulated liquid to achieve the optimal design of the explosion container protection efficiency.

2. The method for designing a cylindrical explosion container according to claim 1, wherein: The radial dynamic balance equation is: The radial dynamic balance equation is constructed in a cylindrical coordinate system with coordinate variables being radial ρ, circumferential θ and axial x; q ρ is the radial component of the external load, t is the time of the structural deformation process, and the moment when the pressure load begins to act on the explosion container shell is taken as the zero point; u ρ is the radial displacement of the mid-plane of the explosion container shell; ρ, h, R and l0 represent the density, thickness, inner diameter and length of the explosion container shell respectively; N θ , Q x and Q θ They represent the hoop membrane force, axial shear force and hoop shear force per unit length of the mid-surface, respectively.

3. The method for designing a cylindrical explosion container according to claim 1, wherein: The pressure load model P(x,t) is: Wherein, P0 is the peak overpressure of the pressure pulse at the center of the inner wall of the explosion container shell 1 (x=0), a is the arrival time of the shock wave overpressure peak, and τ is the characteristic time constant describing the shock wave overpressure decay.

4. The method for designing a cylindrical explosion container according to claim 1, wherein: Pressure load model with encapsulated liquid P f (x,t) is: P f (x,t)=P0P t (t)P x (x) in Where, P t (t) is the normalized time domain distribution function of the reflected overpressure, P x (x) is the normalized spatial distribution function of the reflected overpressure.

5. The method for designing a cylindrical explosion container according to claim 1, wherein: Where H c and T c are the height and thickness of the encapsulated liquid respectively, and α is the propagation velocity ratio of the rarefaction wave to the shock wave in the encapsulated liquid, which is usually taken as α=0.

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6. The method for designing a cylindrical explosion container according to claim 1, wherein: Where l1 is the length of the plastic deformation region, and u0(t) is the radial displacement time history curve at x=0.

7. The method for designing a cylindrical explosion container according to claim 1, wherein: The yield stress-plastic strain relationship of the explosion container shell is; Among them, σ y and σ0 are the flow stress and initial yield stress of the explosion container shell respectively; E p is the plastic hardening modulus, is the effective plastic strain; Among them, ε θ , ε ρ and ε x denote hoop strain, radial strain and axial strain respectively, γ xρ Represents the shear strain between the axial and radial directions.

8. The method for designing a cylindrical explosion container according to claim 1, wherein: in 9. The method for designing a cylindrical explosion container according to claim 1, wherein: In S7, the dimensionless protection efficiency η is defined. The larger the value of η, the smaller the deformation of the structure under the same protection quality, and the higher the protection efficiency; Among them, m w is the mass of the encapsulated liquid, m s is the mass of the explosion container shell, ρ w and ρ are the densities of the encapsulated liquid and the explosion container shell respectively; u w+s and u s They are the maximum deformations of liquid medium enhanced explosion container and liquid medium free explosion container respectively.

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