Underwater columnar charge numerical simulation method based on equivalent amplification

Abstract

The invention discloses an equivalent amplification-based underwater columnar charge numerical simulation method, which comprises the following steps of: selecting a small-diameter high-detonation-velocity explosive underwater columnar charge, and drawing an underwater shock wave P-v curve and a sparse wave P-v curve in an explosive product; obtaining a relational expression of the shock wave array surface particle velocity vx and the shock wave array surface pressure Px of the explosive-water interface through an intersection point of the two curves, and calculating a shock wave peak value of a cylindrical shock wave in water at a certain point to equivalently amplify the underwater columnar charge of the small-diameter high-detonation-velocity explosive into the large-diameter low-detonation-velocity columnar charge. And solving the detonation velocity D3 and the density rho3 of the large-diameter low-detonation-velocity columnar charge, and establishing an explosive detonation state equation so as to simulate the detonation state of the underwater columnar charge explosive. According to the method, the explosion state can be well described, the modeling effect is good, deformed grids are not generated, the calculation time can be greatly shortened, and the storage memory is saved.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation and analysis technology for blasting engineering, and in particular to a numerical simulation method for underwater cylindrical charges based on equivalent amplification. Background Technology

[0002] In various numerical simulation analyses of underwater columnar charge blasting, *MAT_HIGH_EXPLOSIVE_BURN (high-energy explosive material) is generally used to simulate the explosive explosion. When simulating the damage of seismic waves generated by the explosive explosion to nearby buildings and structures in numerical calculations, the diameter of the explosive cartridge is several centimeters, while the distance between the buildings and structures under study and the explosive is tens to hundreds of meters, a difference of 3 to 4 orders of magnitude. The diameter of the explosive cartridge is very small relative to the distance between the nearby buildings and structures. When performing numerical modeling, it is necessary to divide the mesh of the blast hole and the explosive cartridge into very small grids, which leads to distorted meshes, excessively long calculation time, or even no results during numerical calculations.

[0003] Therefore, how to prevent malformed meshes from causing incomprehensible calculations during numerical computation, and how to save computer computation time and storage memory, are technical problems that urgently need to be solved. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a numerical simulation method for underwater cylindrical charges based on equivalent amplification. Utilizing the principle that the total energy released during the explosion of a small-diameter, high-detonation-velocity (typically 3–30 cm in diameter and 2800–5500 m / s) underwater cylindrical charge is equal to the total energy released during the explosion of a large-diameter, low-detonation-velocity cylindrical charge, the corresponding explosive detonation state equation is established after equivalent amplification. This method effectively describes the explosion state, provides good modeling results, avoids distorted meshes, and significantly reduces computation time and saves storage memory.

[0005] The embodiments of the present invention provide the following solutions:

[0006] This invention provides a numerical simulation method for underwater cylindrical charges based on equivalent scaling, the method comprising:

[0007] Step 1: Select a small-diameter, high-detonation-velocity underwater cylindrical charge with a density of ρ2 and a detonation velocity of D.

[0008] Step 2: Plot the Pv curve of the shock wave in water and the Pv curve of the rarefaction wave in the explosion products. The intersection of the two curves gives the particle velocity v of the shock wave front at the explosive-water interface. x and the shock wave front pressure P x Relationship;

[0009] Step 3: Calculate the peak value of the shock wave at a certain point using the attenuation law of the cylindrical shock wave in water.

[0010] Step 4: Based on the principle of decreasing detonation velocity with constant density, the underwater cylindrical charge of small-diameter high-detonation-velocity explosive is equivalently enlarged into a large-diameter low-detonation-velocity cylindrical charge. Solve for the detonation velocity D3 and density ρ3 of the large-diameter low-detonation-velocity cylindrical charge.

[0011] Step 5: Using the detonation velocity D3 and density ρ3 of the large-diameter, low-detonation-velocity cylindrical charge obtained from the above calculations as conditions, establish the detonation state equation of the explosive to simulate the detonation state of the underwater cylindrical charge explosive.

[0012] In an optional embodiment, when the small-diameter high-explosive underwater cylindrical charge described in step one is a deep-water charge, then step two uses the following formula to plot the underwater shock wave Pv curve:

[0013]

[0014] Where P1 is the pressure of the initial shock wave in the water, ν w Let Pv be the velocity of particles moving on the front of the shock wave in water; plot the rarefaction wave Pv curve in the explosion products using the following formula:

[0015]

[0016] Among them, P x and v x These are the velocities at the interface between the detonation products and water, respectively.

[0017] In an optional embodiment, when the small-diameter high-explosive underwater cylindrical charge described in step one is a shallow-water charge, then step two uses the following formula to plot the underwater shock wave Pv curve:

[0018]

[0019] Where P1 is the pressure of the initial shock wave in the water, ν w Let Pv be the velocity of particles moving on the front of the shock wave in water; plot the rarefaction wave Pv curve in the explosion products using the following formula:

[0020]

[0021] Among them, P x and v x These are the velocities at the interface between the detonation products and water, respectively.

[0022] In an optional embodiment, the peak value of the underwater cylindrical shock wave at a certain point as described in step three is... Calculated using the following formula:

[0023]

[0024] in, R is the distance from the axis of the medicine roll, W c The TNT equivalent of the charge per meter of length.

[0025] In an optional embodiment, the detonation velocity D3 of the large-diameter low-detonation-velocity explosive described in step four is obtained by combining the following formulas:

[0026] P3 = P x =ΔP φ (twenty four)

[0027]

[0028] Where P3 is the average initial detonation pressure of a large-diameter, low-detonation-velocity cylindrical charge, ρ3 is the density of the large-diameter, low-detonation-velocity cylindrical charge, and γ is the isentropic exponent of the explosive.

[0029] In an optional embodiment, the detonation state equation for the explosive described in step five is the JWL equation, which is described as follows:

[0030]

[0031] Where P is pressure, A, B, R1, R2, and ω are material constants related to the explosive; V is relative volume, E0 is initial specific internal energy, and V0 is the initial internal energy. CJ A is the explosive volume of the explosive, ρ is the density of the explosive, and A = 5.35545ρv 2 B = 0.094983ρv 2 , R1=4.2, R2=0.27R1, ω=0.33,

[0032] In one alternative embodiment, the explosive used is No. 2 rock emulsion explosive.

[0033] The beneficial effects of this invention based on its technical solution are as follows:

[0034] In numerical simulations of the damage to nearby buildings caused by seismic waves from an explosive explosion, the diameter of the explosive cartridge is several centimeters, while the buildings under study are located tens to hundreds of meters away from the explosive. The difference in distance is 10. 3 -10 4When the diameter of an explosive charge is very small relative to the distance between it and adjacent structures, the mesh for the borehole and the explosive charge needs to be very small during numerical modeling. This results in distorted meshes, excessively long computation times, and even no results. To solve this problem, this invention provides a numerical simulation method for underwater cylindrical charges based on equivalent scaling. It utilizes the principle that the total energy released when a small-diameter, high-velocity explosive charge explodes is equal to the total energy released when a large-diameter, low-velocity explosive charge explodes. After equivalent scaling, the corresponding detonation state equation is established, thus accurately describing the explosion state. This method provides good modeling results, avoids distorted meshes, and significantly reduces computation time and saves storage memory. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart illustrating a numerical simulation method for underwater cylindrical charges based on equivalent amplification, provided by the present invention.

[0037] Figure 2 This is a schematic diagram of a deep-water cylindrical charge of a small-diameter, high-explosive-velocity explosive.

[0038] Figure 3 This is a schematic diagram of physical quantities before and after the shock wave.

[0039] Figure 4 This is a graph showing the detonation velocity decay of emulsion explosives in deep water.

[0040] Figure 5 This is a schematic diagram of the underwater shock wave diagram in deep water conditions.

[0041] Figure 6 This is a schematic diagram of a shallow water column charge of a small-diameter, high-explosive-velocity explosive.

[0042] Figure 7 This is a schematic diagram of the underwater shock wave diagram in shallow water conditions.

[0043] Figure 8 Screenshot of the modeling results for a small-diameter, high-explosive-velocity explosive charge.

[0044] Figure 9 This is a screenshot of the modeling results of a large-diameter, low-explosion-velocity explosive charge.

[0045] Figure 10 This is a screenshot of the background data showing the time taken to model a small-diameter, high-velocity explosive charge.

[0046] Figure 11 This is a screenshot of the background data showing the time taken to model a large-diameter, low-explosion-velocity explosive charge.

[0047] Figure 12 This is a screenshot of the memory usage data for modeling a small-diameter, high-velocity explosive charge.

[0048] Figure 13 This is a screenshot of the memory usage data for modeling a large-diameter, low-explosion-velocity explosive charge. Detailed Implementation

[0049] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the protection scope of the embodiments of the present invention.

[0050] This embodiment provides a numerical simulation method for underwater cylindrical charges based on equivalent scaling, referring to... Figure 1 The method includes:

[0051] Step 1: Select a small-diameter, high-explosive, high-velocity underwater cylindrical charge, such as... Figure 2 As shown, the explosive used is No. 2 rock emulsion explosive with a density of ρ2 and a detonation velocity of D.

[0052] Step 2: Plot the Pv curve of the shock wave in water and the Pv curve of the rarefaction wave in the explosion products. The intersection of the two curves gives the particle velocity v of the shock wave front at the explosive-water interface. x and shock wave front pressure P x The relationship between the two curves is as follows: The derivation process and principle of the two curves are:

[0053] Physical quantities of the shock wave before and after the explosive-water interface, such as Figure 3 As shown. Figure 3 As shown in (1), P0, ρ0, E0, and v0 are the pressure, density, internal energy, and particle velocity of the undisturbed water medium, respectively; P1, ρ1, E1, and v1 are the pressure, density, internal energy, and particle velocity of the water medium instantaneously after the impact front passes; D is the shock wave velocity. When the explosive detonates in water, it satisfies the conservation of mass, momentum, and energy. Taking the coordinates on the wavefront, the mass flowing in from the right side of the wavefront per unit time is ρ0(D-v0), and the mass flowing out from the left side is ρ1(D-v1), as shown in (1). Figure 3 As shown in (2).

[0054] According to the law of conservation of mass, the mass of medium flowing into the right side of the wavefront per unit time is equal to the mass flowing out from its left side, that is:

[0055] m=ρ0(D-v0)=ρ1(D-v1) (1)

[0056] The change in momentum of the medium per unit time is m(v1-v0), and the impulse acting on the medium is P1-P0. According to the law of conservation of momentum, during the propagation of the shock wave, the impulse acting on the medium per unit time is equal to its change in momentum, therefore:

[0057] P1-P0=m(v1-v0)=ρ0(D-v0)(v1-v0) (2)

[0058] The energy flowing into the right side of the wavefront per unit time consists of three parts: the internal energy mE0 of the medium, the kinetic energy of the medium, and the energy of the medium. The work done by the medium pressure is P0(D-v0). Similarly, the energy flowing out from the left side of the wavefront is... According to the law of conservation of energy, during the propagation of a shock wave, the energy flowing into the right side of the wavefront per unit time should be equal to the energy flowing out of the left side of the wavefront, that is:

[0059]

[0060] Substituting equations (1) and (2) into equation (3) and rearranging, we get:

[0061]

[0062] Rearranging equations (1), (2), and (4), we obtain the basic equations as follows:

[0063]

[0064] E1-E0=1 / 2(P1+P0)(1 / ρ0-1 / ρ1) (7)

[0065] To solve the above system of equations, we also need the water state equation, which is required when the pressure range is greater than 2.5 × 10⁻⁶. 3 At MPa, the equation of state for water adopts the impact (Poisson) adiabatic equation:

[0066] (P+α) / P * =(ρ / ρ * ) k(s) (8)

[0067] In the formula, α = 529 MPa, ρ * =2530kg / m 3 P* = 8940 MPa, the exponent k(s) is a function of entropy s, and entropy is a function of pressure, which depends on the strength of the shock wave.

[0068] After an underwater explosive charge detonates, the detonation wave front will first impact the water at the edge of the charge, generating a high initial pressure underwater shock wave. Generally, since the borehole is filled with water, the isentropic exponent of the detonation products can be approximated as constant, and their pressure and density will not decrease sharply. Therefore, it can be assumed that the detonation products decompose according to pV... γ =const's regular expansion.

[0069] The detonation wave is incident perpendicularly from the explosive into the water. To simplify the discussion, we assume the entire process is one-dimensionally planar symmetric. The point velocity of the explosion products at the interface between the explosion products and the water is obtained as follows:

[0070]

[0071] In the formula: γ is the adiabatic index of the detonation products, which is taken as 3 here; P x P is the pressure at the interface between the detonation products and water; D is the detonation velocity of the explosive; L Let be the pressure on the detonation wave front. Substituting the values, we get:

[0072]

[0073] In the formula: v x The velocity at the interface between the detonation products and water.

[0074] When v0 = 0, the velocity of the particles on the shock wave front in the water is obtained from equation (5):

[0075]

[0076] Based on the continuity condition of the interface, we know that:

[0077] P x =P1, v x =v1 (12)

[0078] In the formula: ρ1 and P1 are the density and pressure of the initial shock wave in the water; ρ0 and P0 are the density and pressure of the undisturbed water medium.

[0079] Based on kinetic experiments, when pressure 0 < P1 < 4.5 × 10⁻⁶, 4 At MPa, the impact adiabatic equation in water is:

[0080]

[0081] In the formula D w and ν w These represent the frontal velocity of the shock wave in water and the velocity of the moving particles, respectively, in m / s. The momentum equation for the shock wave in water is:

[0082] P1=ρ0D m v1 (14)

[0083] Substituting (13) into equation (14) above, we get:

[0084]

[0085] 1. Deep water conditions

[0086] The borehole depth is h0, and the charge length is 1m, so the explosive is located at a water depth of h0.

[0087] Research on cofferdam demolition blasting in deep water conditions shows that water pressure in deep water reduces the detonation velocity of emulsion explosives. Experimental results on the reduction in detonation velocity of commonly used industrial emulsion explosives under water pressure in deep water are as follows: Figure 4 As shown.

[0088] The relationship between water pressure P0 and water depth h0 is shown in equation (16):

[0089] P0=ρ0gh0 (16)

[0090] In the formula, ρ0 is the density of water, 1000 kg / m³. 3 g is the acceleration due to gravity, 10 m / s². 2 .

[0091] Depend on Figure 3 Equation (16) shows the relationship between the detonation velocity D of the emulsion explosive and the water depth h0 when the water depth is 30m. When the water depth h0 = 30m, the detonation velocity D of the emulsion explosive is 3000m / s.

[0092] ρ2 is the density of the explosive, 1061 kg / m³. 3 The detonation velocity of the emulsion explosive is 5000 m / s, and the pressure on the detonation wave front in equation (10) is... γ is the adiabatic index of the detonation products, taken as 3, resulting in P. L .

[0093]

[0094] After transformation, we get:

[0095]

[0096] ρ0 is the density of the undisturbed water medium, 1000 kg / m³. 3 P0 is the pressure of the undisturbed water medium; the hydrostatic pressure is ignored and is taken as 0.

[0097]

[0098] ρ1 is the density of the initial shock wave in the water.

[0099] On the Pv plane, the Pv curve of the shock wave in water can be plotted using equation (15); the Pv curve of the rarefied wave in the explosion products can be plotted using equation (18). The graphical method for shock waves in water is as follows: Figure 5 As shown.

[0100] The particle velocity v on the shock wave front can be obtained from the intersection of the rarefaction curve of the explosion products and the shock wave in the water. x and shock wave front pressure P x Then, substituting into equations (13) and (19), we obtain the water shock wave velocity D. w The density ρ1 of the initial shock wave in the water.

[0101] 2. Shallow water conditions

[0102] The overall derivation process is similar to that in deep water. For example... Figure 6 As shown, since the explosive is buried relatively shallowly in the water, its density of 1061 kg / m³ can be directly taken. 3 The detonation velocity D of the emulsion explosive is 5000 m / s. Substituting into equation (10), we get:

[0103]

[0104] After transformation, we get:

[0105]

[0106] ρ0 is the density of the undisturbed water medium, 1000 kg / m³. 3 P0 is the pressure of the undisturbed water medium; the hydrostatic pressure is ignored and is taken as 0.

[0107]

[0108] ρ1 is the density of the initial shock wave in the water.

[0109] On the Pv plane, the Pv curve of the shock wave in water can be plotted using equation (15); the Pv curve of the rarefied wave in the explosion products can be plotted using equation (18'). The graphical method for shock waves in water is as follows: Figure 7 As shown.

[0110] Then, substituting into equations (13) and (19), we obtain the shock wave velocity D in the water. w The density ρ1 of the initial shock wave in the water.

[0111] Step 3: Calculate the peak value of the shock wave at a certain point using the attenuation law of the cylindrical shock wave in water. The attenuation law of a cylindrical shock wave in water is as follows:

[0112]

[0113] In the formula, ΔP(t) is the amount of shock wave pressure attenuation within time t from the start of detonation, with t in seconds; R is the distance from the axis of the explosive cartridge in meters; C0 is the shock wave velocity in water in m / s; σ0 is a function of time t, expressed by the following formula:

[0114]

[0115] Let be the peak shock wave value at a certain point, 10⁵ Pa, which is a function of distance R. For a TNT pack, we have:

[0116]

[0117] in, It is a proportional distance, in units. W c This is the TNT equivalent of the charge per meter of length, expressed in kg / m; calculated using the following formula:

[0118] W c =W cs Q Ws / Q WT (twenty three)

[0119] In the above formula, W cs Q is the relative mass of the given explosive charge (per unit length), expressed in kg. Ws Q is the heat of explosion (specific energy) of the explosive under consideration, in kcal / kg; WT ≈1000kcal / kg.

[0120] The borehole diameter is 0.146m, the explosive diameter d is 0.06m, and ρ2 is the density of the explosive, 1061kg / m³. 3 The heat of explosion Q of No. 2 rock emulsion explosive Ws The heat of explosion is 881 kcal / kg (1 cal = 4.18 J), which is the heat of explosion of a shallow-water coupled explosive charge. Since the explosive properties (such as detonation velocity, intensity, and work capacity) of an explosive are directly proportional to its heat of explosion, the heat of explosion at a depth of 30 m in water is 528.6 kcal / kg.

[0121] The relative mass per unit length is obtained. 3kg; TNT equivalent per meter of length (W) c =W cs Q Ws / Q WT The value is 2.64 kg / m; proportional distance for

[0122] Step 4: Based on the principle of decreasing detonation velocity with constant density, the underwater cylindrical charge of a small-diameter, high-detonation-velocity explosive is equivalently enlarged to a large-diameter, low-detonation-velocity cylindrical charge. The detonation velocity D3 and density ρ3 of the large-diameter, low-detonation-velocity cylindrical charge are then calculated. This is obtained by simultaneously solving the following formulas:

[0123] P3 = P x =ΔP φ (twenty four)

[0124]

[0125] In the formula: P3 is the average initial detonation pressure of a large-diameter low-detonation-velocity explosive; ρ3 is the density of a large-diameter low-detonation-velocity explosive; D3 is the detonation velocity of a large-diameter low-detonation-velocity explosive; γ is the isentropic index of the explosive, which is generally taken as 3 for industrial explosives.

[0126] The detonation velocity D3 of a large-diameter, low-detonation-velocity explosive is derived.

[0127] Step 5: Using the detonation velocity of the large-diameter, low-detonation-velocity explosive obtained from the above calculations as a condition, establish the detonation state equation of the explosive to simulate the detonation state of the coupled-charge explosive. The detonation state equation of the explosive is described by the JWL equation:

[0128]

[0129] Where P is pressure, A, B, R1, R2, and ω are material constants related to the explosive; V is relative volume, E0 is initial specific internal energy, and V0 is the initial internal energy. CJ A is the explosive volume of the explosive, ρ is the density of the explosive, and A = 5.35545ρv 2 B = 0.094983ρv 2 , R1=4.2, R2=0.27R1, ω=0.33,

[0130] This embodiment uses a deep-water cylindrical explosive charge as an example to illustrate the effect.

[0131] For small-diameter, high-detonation-velocity explosives, substitute their explosive density ρ1 and detonation velocity D into ρ and v2 in equation (27):

[0132] A = 5.35545ρ1D 2 =1.42×10 11 Pa; B = 0.094983ρ1D 2 =2.52×10 9 Pa; R1 = 4.2;

[0133] R2=0.27R1=1.13;ω=0.33; E0=ρ1D 2 (0.204-0.0734ρ1)=3.35×10 9Pa;

[0134]

[0135] For large-diameter, low-detonation-velocity explosives, substitute their explosive density ρ3 and detonation velocity D3 into equation (27):

[0136] R1 = 4.2;

[0137] R2=0.27R1=1.13;ω=0.33;

[0138]

[0139] The result of directly substituting the properties of a small-diameter high-explosive charge into equation (27) for modeling is as follows: Figure 8 As shown, the result of substituting the properties of a large-diameter, low-detonation-velocity explosive charge into equation (27) for modeling is as follows: Figure 9 As shown, the model directly built from small-diameter, high-detonation-velocity data contains distorted meshes (i.e., the meshes marked in red), which will affect the calculation accuracy. However, the model built by equivalently enlarging the small-diameter, high-detonation-velocity explosive into a large-diameter, low-detonation-velocity explosive charge does not have distorted meshes.

[0140] Screenshots of the backend data showing the modeling time for small-diameter high-explosive velocity explosive charges and large-diameter low-explosive velocity explosive charges are shown below. Figure 10 and Figure 11 As shown, for the same amount of explosives, the numerical simulation time was reduced from 33 minutes and 56 seconds to 17 minutes and 14 seconds, saving nearly half of the calculation time. If modeling larger data for real experiments, the time saved would be considerable.

[0141] Screenshots of the background data showing the memory usage for modeling small-diameter high-explosive-velocity explosive charges and large-diameter low-explosive-velocity explosive charges are shown below. Figure 12 and Figure 13 As shown, for numerical simulations of the same amount of explosives, the number of cells used decreased from 21609 to 19965, saving nearly 10% of memory. If modeling larger datasets for real experiments, the memory savings would be equally considerable.

[0142] This invention provides a numerical simulation method for underwater cylindrical charges based on equivalent amplification. It utilizes the principle that the total energy released when a small-diameter high-velocity explosive charge with radial water coupling in water explodes is equal to the total energy released when a large-diameter low-velocity cylindrical explosive charge explodes. After equivalent amplification, the corresponding explosive detonation state equation is established, which can well describe the explosion state, achieve good modeling results, avoid producing distorted meshes, and significantly reduce computation time and save storage memory.

[0143] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0144] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (modules, systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0145] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0146] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0147] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0148] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A numerical simulation method for underwater cylindrical charges based on equivalent scaling, characterized in that, The method includes: Step 1: Select a small-diameter, high-detonation-velocity underwater cylindrical charge with a density of ρ2 and a detonation velocity of D. Step 2: Plot the Pv curve of the shock wave in water and the Pv curve of the rarefaction wave in the explosion products. The intersection of the two curves gives the particle velocity v of the shock wave front at the explosive-water interface. x and shock wave front pressure P x Relationship; Step 3: Calculate the peak value of the shock wave at a certain point using the attenuation law of the cylindrical shock wave in water. Step 4: Based on the principle of decreasing detonation velocity with constant density, the underwater cylindrical charge of small-diameter high-detonation-velocity explosive is equivalently enlarged into a large-diameter low-detonation-velocity cylindrical charge. Solve for the detonation velocity D3 and density ρ3 of the large-diameter low-detonation-velocity cylindrical charge. Step 5: Using the detonation velocity D3 and density ρ3 of the large-diameter, low-detonation-velocity cylindrical charge obtained from the above calculations as conditions, establish the detonation state equation of the explosive to simulate the detonation state of the underwater cylindrical charge explosive.

2. The numerical simulation method for underwater cylindrical charges based on equivalent scaling as described in claim 1, characterized in that: When the small-diameter high-explosive underwater cylindrical charge described in step one is a deep-water charge, then step two uses the following formula to plot the underwater shock wave Pv curve: Where P1 is the pressure of the initial shock wave in the water, ν w Let Pv be the velocity of particles moving on the front of the shock wave in water; plot the rarefaction wave Pv curve in the explosion products using the following formula: Among them, P x and v x These are the velocities at the interface between the detonation products and water, respectively.

3. The numerical simulation method for underwater cylindrical charges based on equivalent scaling as described in claim 1, characterized in that: When the underwater cylindrical charge of the small-diameter high-explosive explosive described in step one is used in shallow water, then step two uses the following formula to plot the underwater shock wave Pv curve: Where P1 is the pressure of the initial shock wave in the water, ν w Let Pv be the velocity of particles moving on the front of the shock wave in water; plot the rarefaction wave Pv curve in the explosion products using the following formula: Among them, P x and v x These are the velocities at the interface between the detonation products and water, respectively.

4. The numerical simulation method for underwater cylindrical charges based on equivalent scaling as described in claim 1, characterized in that: The peak value of the underwater cylindrical shock wave at a certain point, as described in step three. Calculated using the following formula: in, R is the distance from the axis of the medicine roll, W c The TNT equivalent of the charge per meter of length.

5. The numerical simulation method for underwater cylindrical charges based on equivalent scaling as described in claim 1, characterized in that: The following formulas are used to obtain the detonation velocity D3 of the large-diameter low-detonation-velocity explosive described in step four: P3=P x =ΔP φ (24) Where P3 is the average initial detonation pressure of a large-diameter, low-detonation-velocity cylindrical charge, ρ3 is the density of the large-diameter, low-detonation-velocity cylindrical charge, and γ is the isentropic exponent of the explosive.

6. The numerical simulation method for underwater cylindrical charges based on equivalent scaling as described in claim 1, characterized in that: The detonation state equation for the explosive described in step five adopts the JWL equation and is described as follows: Where P is pressure, A, B, R1, R2, and ω are material constants related to the explosive; V is relative volume, E0 is initial specific internal energy, and V0 is the initial internal energy. CJ A is the explosive volume of the explosive, ρ is the density of the explosive, and A = 5.35545ρv 2 B = 0.094983ρv 2 , R1=4.2, R2=0.27R1, ω=0.33, 7. The numerical simulation method for underwater cylindrical charges based on equivalent scaling as described in claim 1, characterized in that: The explosive used is No. 2 rock emulsion explosive.

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