CN113553739B - Mixed explosive explosion output characteristic calculation method - Google Patents
Mixed explosive explosion output characteristic calculation method Download PDFInfo
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Abstract
The invention provides a method for calculating the explosion output characteristics of a mixed explosive, which is based on a fluid dynamics equation under a two-dimensional Euler coordinate system and comprises the following calculation steps: step 100, constructing a calculation model; step 200, constructing a state equation; step 300, constructing an explosive chemical reaction model; step 400, constructing an elastoplastic model; step 500, calculating mass migration; step 600, reassigns flow field variables. The calculation method comprises a plurality of chemical reaction models, can effectively describe the detonation reaction process of the mixed explosive, is suitable for the energy output characteristic calculation problem of a plurality of different processes, and has wider applicability. The calculation method has reliable calculation precision. By the method and the device, the calculation of multiple types and multiple times can be conveniently and repeatedly performed, the work efficiency is improved, and the work intensity of personnel is reduced.
Description
Technical Field
The invention belongs to the field of mixed explosives, relates to numerical calculation of detonation energy release rules of mixed explosives, and particularly relates to a method for calculating explosion output characteristics of mixed explosives.
Background
The evaluation of the detonation energy release characteristics of the mixed explosive is an important aspect for measuring the power of the mixed explosive. On one hand, researchers in the related field need to develop corresponding design work according to actual working conditions; on the other hand, the user also needs to make a reasonable choice according to the energy characteristics of the blended explosive.
The explosion output characteristic parameters of the mixed explosive are tested by adopting various experimental techniques, so that the method is the most direct evaluation method. However, since the mixed explosive belongs to dangerous chemicals, the sample preparation and experimental measurement are carried out with no small hidden risks. Moreover, the economic cost is often higher when experimental measurement is carried out, and the problem of high test data acquisition difficulty exists.
In order to reduce the dependence on experiments and improve the design level, the explosion energy release characteristics of the mixed explosive need to be designed and calculated. The detonation energy action process of the mixed explosive can be regarded as a time-varying flow process from physical substance, and the detonation reaction of the mixed explosive is described by combining various chemical reaction models. In the framework of the basic principle of fluid dynamics, the change rule of various physical quantities in an explosion flow field can be known by a numerical calculation method, so that the general process and characteristic rule of the energy output of the mixed explosive are reflected.
The Chinese patent of patent number ZL201610034329.9 discloses a design method of a high-energy high-frequency explosive source, which comprises the step of calculating by adopting different explosive explosion finite element models. However, the invention simply processes the explosive explosion process into a seismic source process, and does not calculate the energy output characteristics of the mixed explosive in detail.
Therefore, the invention needs to invent a method for calculating the explosion output characteristics of the mixed explosive, which calculates the detonation energy characteristic release and work output rules of the mixed explosive based on the general principle of fluid dynamics.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a method for calculating the explosion output characteristics of a mixed explosive, which solves the technical problem that the mixed explosive explosion flow field containing a chemical reaction process under Euler coordinates cannot be calculated in the prior art.
In order to solve the technical problems, the invention adopts the following technical scheme:
the method for calculating the explosion output characteristics of the mixed explosive is based on a fluid dynamics equation under a two-dimensional Euler coordinate system, and comprises the following calculation steps:
step 100, constructing a calculation model:
constructing a mass conservation equation in a two-dimensional Euler coordinate system as shown in a formula 1.1, a momentum conservation equation as shown in a formula 1.2 and a formula 1.3, and an energy conservation equation as shown in a formula 1.4;
mass conservation equation:
x-direction momentum conservation equation:
conservation of momentum in the y-direction equation:
energy conservation equation:
formula 1.1-formula 1.4:
ρ is the density;
u is the speed;
e is energy;
s is stress deflection;
p is the pressure;
t is time;
α is a symmetry coefficient, α=2 in the cylindrical coordinate system, and α=1 in the rectangular coordinate system;
subscripts x and y are components of the respective directions;
step 200, constructing a state equation:
describing the physical property change rule of the detonation product of the mixed explosive by adopting an HOM state equation, wherein the expression form is shown in the formula 1.5:
in formula 1.5:
p CJ is the pressure of detonation products in CJ state;
e CJ is the internal energy of detonation products in the CJ state;
T CJ the temperature of detonation products in CJ state;
subscript CJ refers to the CJ state;
V g is the volume of detonation product;
coefficients A, B, C, D and E, K, L, M, N and O, Q, R, S, U and X are fitting coefficients of the respective physical quantities, respectively;
step 300, constructing an explosive chemical reaction model:
the method comprises an Arrhenius chemical reaction model, a Taylor wave chemical reaction model, a square wave impact chemical reaction model, a CJ volumetric combustion chemical reaction model and a Forest-Fire heterogeneous combustion chemical reaction model;
step 400, constructing an elastoplastic model:
when the yield strength of the material is exceeded, describing the stress state of the object by using an elastoplastic model, the expression is shown in the formula 1.6:
in formula 1.6:
f represents the principal stress;
Y 0 indicating the yield strength of the material;
step 500, calculating mass migration:
migrating the mass according to the flow field movement speed, wherein the migrated mass flows into a new calculation grid;
step 600, reassigning flow field variables:
and (3) according to the mass migration calculation result in the step 500, reassigning flow field variables including density, mass fraction, x-direction speed, y-direction speed and internal energy.
The invention also has the following technical characteristics:
in step 300, the Forest-Fire heterogeneous combustion chemical reaction model further comprises a linear volumetric combustion chemical reaction model.
Step 300 further includes a step of adding a viscosity coefficient.
Compared with the prior art, the invention has the following technical effects:
the calculation method related by the invention comprises a plurality of chemical reaction models, can effectively describe the detonation reaction process of the mixed explosive, is suitable for the energy output characteristic calculation problem of a plurality of different processes, and has wider applicability.
The calculation method related to the invention has reliable calculation precision.
And (III) by applying the method, the calculation of multiple types and multiple times can be conveniently and repeatedly performed, thereby being beneficial to improving the working efficiency and reducing the working strength of personnel.
Drawings
FIG. 1 is a flow chart of a method for calculating the explosion output characteristics of the mixed explosive.
FIG. 2 is a cloud image of the pressure calculation results of the mixed explosive EX1 of example 1 when it is applied to a steel cylinder in an air medium.
Fig. 3 is a cloud image showing the pressure calculation result of the detonation of the mixed explosive EX2 in the aqueous medium in example 2.
Fig. 4 is a cloud image of the pressure calculation result of the combustion-detonation process of the mixed explosive EX3 in example 3.
The following examples illustrate the invention in further detail.
Detailed Description
In the present invention, the following is described.
All physical quantity units are common in the field.
CJ refers to the CJ theory of detonation waves, namely the planar one-dimensional hydrodynamic theory on detonation waves that Chapman and Jouget set forth at the beginning of the 20 th century, respectively.
HOM state equations are thermodynamic state equations describing the physical state of the unreacted mixed explosive and the detonation products of the mixed explosive.
Aiming at the defects existing in the prior art, the invention discloses a method for calculating the explosion output characteristics of a mixed explosive, which is based on the general principle of fluid dynamics, calculates the detonation reaction flow field of the mixed explosive containing a chemical reaction process by adopting a conservation equation under two-dimensional Euler coordinates, and reflects the main rule of the energy output characteristics of the detonation process of the mixed explosive.
The invention discloses a method for calculating the explosion output characteristics of a mixed explosive, which is analyzed from the aspect of a calculation principle, solves the problem of calculation of an explosion flow field of the mixed explosive containing a chemical reaction process under Euler coordinates, and can be applied to numerical calculation under a two-dimensional rectangular coordinate system or a two-dimensional cylindrical coordinate system.
For each calculation time step, three calculation links can be generalized.
The first calculation step is to calculate the chemical reaction process according to the state equation of the explosion product of the used mixed explosive, and obtain the pressure change and stress state change in the explosion flow field;
the second calculation link drives the flow field to migrate according to the pressure and stress change conditions obtained in the first calculation link, temporarily ignores the influence of a migration item, and calculates the flow field speed and energy by combining with the hydrodynamic conservation relation;
and a third calculation step, wherein the mass migration process is ignored in the second calculation step, the mass migration is calculated by using a donor-acceptor method, the mass is migrated to a new part, and then each physical quantity in the flow field is redistributed.
And completing the calculation of the current time step through the sequential connection of the three calculation links. And (3) carrying out reciprocating circulation on the three calculation links, thereby completing the calculation of the whole flow field change under the condition of expected time. And finally obtaining the calculation result of the output characteristics of the mixed explosive.
The three calculation links can be further refined into six calculation stages:
the first stage: calculation of pressure and stress variations, comprising:
(a) Calculating a state equation of a detonation product of the mixed explosive;
(b) Calculating the chemical reaction process of the mixed explosive;
(c) And calculating the bias stress.
And a second stage: calculation of elastoplasticity, comprising:
(d) Calculating a flow field probing speed;
(e) Calculation of elastoplasticity.
And a third stage: calculation of energy, comprising:
(f) Calculating the internal energy of detonation products;
(g) And calculating total energy of the flow field.
Fourth stage: a calculation of mass migration, comprising:
(h) And calculating the mass migration.
Fifth stage: reassignment of flow field variables, comprising:
(i) Reassignment of flow field variables.
Sixth stage: an elastoplastic flow comprising:
(j) Calculating elastoplastic flow of a flow field;
(k) Construction of various forms of partial derivatives.
From the aspect of operation analysis, when the mixed explosive explosion output characteristic calculation is specifically executed, three specific steps of calculation parameter file construction, solution calculation and calculation result visualization processing are included.
The construction of the calculation parameter file is combined with the specific practical problem, and the construction of the identifiable model parameter file for solving the calculation comprises the material property parameter, the state equation parameter, the calculation grid parameter, the initial condition parameter, the reaction model parameter, the calculation control parameter and the result output parameter.
The solution calculation is a numerical calculation process for the specified problem and is used for obtaining all calculation results of the detonation reaction flow field of the mixed explosive.
The calculation result visualization processing is to perform graphic processing on specified calculation result data by combining with the user requirement to form a distribution cloud chart and a time course curve.
The specific calculation comprises the following calculation steps:
step 100, constructing a calculation model, and constructing hydrodynamic mass, momentum and energy conservation equations under a two-dimensional Euler coordinate system, wherein the equations are respectively shown in the formulas 1, 2 and 3 and the formula 4:
mass conservation equation:
x-direction momentum conservation equation:
conservation of momentum in the y-direction equation:
energy conservation equation:
in equations 1 to 4, ρ is density, U is speed, e is energy, S is stress bias, p is pressure, t is time, α is a symmetry coefficient, α=2 in a cylindrical coordinate system, α=1 in a rectangular coordinate system, and subscripts x and y are components in the respective directions.
Under the Euler coordinate system, the mass conservation equation is automatically satisfied.
Step 200, constructing a state equation, describing the physical property change of the detonation product of the mixed explosive by adopting a HOM state equation in a gaseous form, wherein the form is shown as formula 5:
in formula 5, p CJ Is the pressure of detonation product in CJ state, e CJ Is the internal energy of detonation product in CJ state, T CJ The subscript CJ refers to the temperature of the detonation product in the CJ state, V g Coefficients A, B, C, D and E, K, L, M, N and O, and Q, R, S, U and X are fitting coefficients for the corresponding physical quantities for the volume of detonation product.
For the third expression in equation 5, the partial derivative of the polynomial function relation of temperature with respect to volume is calculated to obtain the Grunessen coefficient expression of the gas phase detonation product, as shown in equation 6:
the state change of other solids in the flow field is described by using a HOM state equation in a solid state form, and the form is shown in formula 7:
in 6, T H For the temperature under the Hugonlot impact curve, p H For the pressure under the Hugonlot impact curve, e H Is the internal energy of Hugonlot impact curve, V s Is solid volume Γ s Grunessen coefficient as solid, C V For the isovolumetric heat capacity of a solid, subscript H denotes the polynomial function fit coefficients for temperature versus solid volume with reference to the Hugoniot impact state, coefficients F, G, H, I and J.
If the solid Hugonlot impact curve relation expression 8 is taken as a reference:
U s ＝c+su p 8. The method is used for preparing the product
Then an expression for the impact pressure and impact internal energy of the solid can be derived as shown in equation 9:
in formula 8 and formula 9, U s For the wave velocity of the shock wave, u p For particle velocity, c and s are first order fitting coefficients, V 0 An initial volume of solid, p H 、e H And V s Is as defined in formula 7.
For a hybrid explosive, it is necessary to give the HOM state equation parameters in the unreacted state, i.e. in the solid, and the detonation product, i.e. in the gas, respectively.
For other solids or liquids in the flow field, only HOM state equation parameters in solid form need be given.
Step 300, constructing an explosive chemical reaction model, which comprises an Arrhenius chemical reaction model, a Taylor wave chemical reaction model, a square wave impact chemical reaction model, a CJ volume combustion chemical reaction model and a Forest-Fire heterogeneous combustion chemical reaction model.
The expression of the Arrhenius chemical reaction model is shown in formula 10:
in 10, W i Representing the mass fraction of the mixed explosive in the ith calculation grid, delta t being the calculation time step, Z being the pre-pointing factor, E a For activation energy, R is the gas universal constant, T i For the i-th calculation grid temperature, the superscripts n and n+1 represent the calculation time steps.
The expression of the Taylor wave chemical reaction model is shown in formula 11:
in 11, U CJ 、D CJ 、p CJ And V CJ Respectively representing the particle speed, the shock wave speed, the pressure and the volume under the CJ state, wherein gamma is the adiabatic index of detonation products, and ρ 0 For initial density V 0 For the initial volume ρ 0 V 0 ＝1。
The expression of the square wave impact chemical reaction model is shown in formula 12:
the meaning of each symbol in formula 12 is the same as that in formula 11.
The expression of the CJ volumetric combustion chemical reaction model is shown in formula 13:
the meaning of each symbol in formula 13 is shown in formulas 10 and 11.
The expression of the Forest-Fire heterogeneous combustion chemical reaction model is shown in formula 14:
in 14, W i The meanings of Δt and superscripts n and n+1 are the same as those of formula 10, coefficient a 0 、a 1 、a 2 .., and a m Polynomial fit coefficients for each order of power with respect to pressure p.
Further, the Forest-Fire heterogeneous fuel chemical reaction model also comprises a linear volume combustion chemical reaction model.
An expression of the linear volumetric combustion chemical reaction model is shown in formula 15:
in formula 15:
w is the mass fraction of the mixed explosive, (S) 0 /V 0 ) Denotes a combustion usable specific surface area, q denotes a shape factor, q=0 denotes planar constant combustion, q=1/2 denotes cylindrical particle combustion, and q=2/3 denotes spherical particle combustion; c represents a combustion linear coefficient, and b represents a combustion pressure index. The negative sign to the right of the equal sign indicates that the mass fraction decreases as the chemical reaction proceeds.
Further, in step 300, a step of adding a viscosity coefficient is further included, where the viscosity coefficient includes an artificial viscosity or a true viscosity, so as to stabilize the calculation result.
Step 400, constructing an elastoplastic model, and describing the stress state of the object by using the elastoplastic model when the yield strength of the material is exceeded, wherein the expression is shown in the formula 16:
in formula 16, f represents a principal stress; y is Y 0 The yield strength of the material is represented, S is the stress deflection, and the subscripts x and y are the components of the corresponding directions.
And 500, calculating mass migration, wherein the mass is migrated according to the flow field movement speed, and the migrated mass flows into a new calculation grid.
Mass migration was calculated using the donor-acceptor method. Mass migration in the donor and acceptor grids is calculated from the mass fraction of the material in the acceptor grid. The density and energy of the components corresponding to the migration mass in the donor mesh are calculated from the state equation in the first stage. Only one material reduction is allowed in one calculation time step.
For migration from the donor grid (i-1), j to the acceptor grid (i, j) along the x-direction, in the case of two-dimensional cylindrical symmetry coordinates, if the migration terms of energy, mass fraction, x-direction momentum, y-direction momentum, mass and density in the grid are expressed by DE, DW, DPU, DPV, DM and DMASS, respectively, their expressions are shown in equations 17-22:
DM i,j = (DMASS) (GEO) 21
In equations 17 to 22, subscript i, j is a calculation grid number, i represents an x direction, j represents a y direction, subscript n represents a calculation time step, U x For speed in x direction, U y The velocity in the y direction, ρ is the density.
In the formulas 17 to 22, the form factor is expressed as GEO, and the expression is shown in the formula 23:
in equation 23, i denotes an x-direction calculation grid number, and the sequential count starts from i=1.
In the formula 22, the discriminant is represented by Δ, and the expression is represented by the formula 24:
in formula 24, subscript i, j is a calculation grid number, i denotes x-direction, j denotes y-direction, and subscript n denotesCalculating time step, U x For x-direction velocity, Δt is the calculated time step and Δx is the calculated spatial step in the x-direction.
Step 600, reassigning flow field variables, and reassigning flow field variables including density, mass fraction, x-direction speed, y-direction speed and internal energy according to the mass migration calculation result in step 500.
According to the mass transfer calculation result, adding corresponding mass transfer terms to corresponding physical quantities, wherein expressions of density, mass fraction, x-direction speed, y-direction speed and internal energy are shown in the following formulas 25 to 29 respectively:
in the formulae 25 to 29, each symbol has the same meaning as in the formulae 17 to 22.
After the redistribution, the flow field is continuously flowed, the calculation of the current calculation step is completed, the corresponding calculation result is output and stored, circulation is continuously carried out until the expected calculation time is reached, and then the result visualization processing is carried out. Thus completing the calculation of the explosion output characteristics of the mixed explosive.
Based on the fluid dynamics principle, the invention carries out numerical calculation on the explosion reaction flow field of the mixed explosive containing chemical reaction under the Euler coordinate system frame, and reflects the general process and rule of the explosion output characteristic change of the mixed explosive. When the method is related to a specific technical scheme, based on hydrodynamic mass, momentum and energy conservation equations, a plurality of chemical reaction models are adopted to describe the reaction process of the mixed explosive, HOM state equations are used to describe the change rule of physical property states of detonation gas products and other solid materials in a flow field, elastoplastic mechanical responses of various materials are considered, and a control equation is solved by a numerical method, so that the calculation result of the change of each physical variable in the flow field along with time is obtained. When the numerical calculation is carried out, a trial-and-error method is used for carrying out loop iteration, so that the accuracy of a calculation result meets the requirement; the calculation process is also stabilized by adjusting the viscosity coefficient. When mass migration is involved, the intrinsic nature of mass migration and redistribution in the flow field can be reflected by treatment with the donor-acceptor method under the euler coordinate frame.
The invention relates to a method for calculating the explosion output characteristics of a mixed explosive, which is based on the general principle of fluid dynamics, carries out numerical calculation on a detonation reaction flow field of the mixed explosive containing a chemical reaction process under Euler coordinates to reflect the explosion output characteristics rule of the mixed explosive, and comprises the steps of constructing a calculation model, constructing a state equation, constructing a chemical reaction model, constructing an elastoplastic model, calculating mass migration and redistributing flow field variables. The invention adopts various chemical reaction models to describe the explosion reaction process of the mixed explosive, and is suitable for calculating the energy output characteristics of the mixed explosive in various different processes.
The following specific embodiments of the present invention are provided, and it should be noted that the present invention is not limited to the following specific embodiments, and all equivalent changes made on the basis of the technical solutions of the present application fall within the protection scope of the present invention.
Example 1:
according to the technical scheme, the mixed explosive EX1 is calculated on the steel cylinder explosion effect in an air medium by using the mixed explosive explosion output characteristic calculation method.
The mixed explosive EX1 comprises the following components in parts by mass: black-cord (RDX): polyisobutylene (PIB): dioctyl sebacate (DOP): oil (Oil) =91: 5.3:2.1:1.6.
the model contains three materials: mixing explosive, air and steel.
Step 100, constructing a calculation model comprising mass, momentum and energy conservation equations, wherein the number of calculation grids is 50 in the x direction, 100 in the y direction, 5000 in total, the initial temperature is 300K, the initial pressure is 0.1MPa, the calculation time step is 0.05 mu s, and the total calculation time length is 20 mu s;
step 200, constructing a state equation, wherein the state equation is described by adopting a solid phase HOM state equation when the mixed explosive is unreacted, and the state equation parameters are as follows: coefficients f=0.0000, g= -9.0419, h= -71.3185, i= -125.2050, and j= -92.0424;
the detonation reaction product is described by adopting a gas-phase HOM state equation, and the state equation parameters are as follows: coefficients a= -3.5391, b= -2.5774, c=0.2601, d=0.0139 and e= -0.0114, coefficients k= -1.6191, l=0.5215, m=0.0678, n=0.0043 and o= 1.0468 ×10 -4 The coefficients q=7.3642, r= -0.4937, s=0.0292, u=0.0330 and x= -0.0115;
air is described by a gas phase HOM state equation, coefficients a= -4.5060, b= -1.2755, c= -0.0037, d= 0.0124 and e= -0.0021, coefficients k= -1.6266, l= 0.0905, m= 0.0027, n= -5.4358 x 10 -5 And o= -1.5852 x 10 -6 The coefficients q=8.2264, r= -0.2515, s= -0.0134, u=0.0141 and x= -0.0022;
steel is described by adopting a solid phase HOM state equation; coefficient f=0.0000, g= -3.8238 ×10 3 ，H＝-7.0321×10 3 、I＝-4.8267×10 3 And J= -1.4668×10 3 ；
Step 300, constructing an explosive chemical reaction model, describing the mixed explosive by adopting a CJ volumetric fuel chemical reaction model, and the volume V under the CJ state CJ =0.407, the viscosity coefficient is 0.01;
step 400, constructing an elastoplastic model, wherein the shearing modulus of steel is 78GPa, and the yield strength is 690MPa;
step 500, calculating mass migration;
step 600, reassigns flow field variables.
According to the embodiment, the explosion effect output characteristics of the mixed explosive in the air medium can be calculated, the calculation accuracy meets the actual requirements, and the design level is improved.
Example 2:
according to the technical scheme, the explosion output characteristics of the mixed explosive EX2 in the water medium are calculated by using the mixed explosive explosion output characteristic calculation method.
The mixed explosive EX2 comprises the following components in parts by mass: black-cord (RDX): trientine ladder (TNT): aluminum powder (Al): wax (Wax) =40: 38:17:5.
the model contains two materials: and mixing the explosive and water.
Step 100, constructing a calculation model comprising mass, momentum and energy conservation equations, wherein the number of calculation grids is 100 in the x direction, 200 in the y direction, 20000 in total, the initial temperature is 300K, the initial pressure is 0.1MPa, the calculation time step is 0.05 mu s, and the total calculation time length is 30 mu s;
step 200, constructing a state equation, wherein the state equation is described by adopting a solid phase HOM state equation when the mixed explosive is unreacted, and the state equation parameters are as follows: coefficients f=0.0000, g= -8.6662, h= -58.3138, i= -69.7160, and j= -8.2010;
the detonation reaction product is described by adopting a gas-phase HOM state equation, and the state equation parameters are as follows: coefficients a= -3.6653, b= -2.4671, c= 0.2285, d= 0.0605 and e= -0.0193, coefficients k= -1.1592, l=0.5304, m=0.0956, n=0.0091 and o= 0.3444 ×10 -3 The coefficients q=7.5771, r= -0.4388, s=0.0923, u= 2.3668 ×10 -3 And x= -3.2434X 10 -2 ；
Water is described by a solid phase HOM state equation; coefficients f=0.0000, g=5.7206, h= 0.6926, i= 8.8139, and j= 36.0120;
step 300, constructing an explosive chemical reaction model, describing the mixed explosive by adopting a CJ volumetric fuel chemical reaction model, and the volume V under the CJ state CJ =0.357, viscosity coefficient of0.2；
Step 400, constructing an elastoplastic model;
step 500, calculating mass migration;
step 600, reassigns flow field variables.
The embodiment can calculate the output characteristics of the mixed explosive during the explosion in water, the calculation accuracy meets the actual requirements, and the design level is improved.
Example 3:
according to the technical scheme, the embodiment uses the mixed explosive explosion output characteristic calculation method to calculate the combustion-to-detonation characteristic of the mixed explosive EX 3.
The mixed explosive EX3 comprises the following components in parts by mass: octogen (HMX): fluororubber (F-Rubber) =95: 5.
the model contains two materials: a blended explosive and aluminum.
Step 100, constructing a calculation model comprising mass, momentum and energy conservation equations, wherein the number of calculation grids is 100 in the x direction, 200 in the y direction, 20000 in total, the initial temperature is 300K, the initial pressure is 0.1MPa, the calculation time step is 0.05 mu s, and the total calculation time length is 25 mu s;
step 200, constructing a state equation, wherein the state equation is described by adopting a solid phase HOM state equation when the mixed explosive is unreacted, and the state equation parameters are as follows: coefficients f=0.0000, g= -16.4687, h= -105.4688, i= -181.0623, and j= -129.3990;
the detonation reaction product is described by adopting a gas-phase HOM state equation, and the state equation parameters are as follows: coefficients a= -3.8489, b= -2.6707, c=0.2268, d=0.0780 and e= -0.0337, coefficients k= -1.5864, l=0.5244, m=0.0899, n=0.0077 and o= 0.2605 ×10 -3 The coefficients q=7.1167, r= -0.5500, s=0.0596, u=0.0112 and x= -0.0101;
aluminum is described by a solid phase HOM state equation; coefficients f=0.0000, g= -20.7547, h= -115.6178, i= -177.7626, and j= -114.2528;
step 300, constructing an explosive chemical reaction model, and adopting Forest-Fire heterogeneous combustion for the mixed explosiveAnd a linear volumetric combustion chemical reaction model, a coefficient a of a Forest-Fire heterogeneous combustion chemical reaction model 0 ＝-7.7583×10 5 、a 1 ＝7.7280×10 5 、a 2 ＝-3.0193×10 5 、a 3 ＝5.9730×10 4 、a 4 ＝-6.4367×10 3 、a 5 = 411.1578 and a 6 = -15.2642, linear volumetric combustion chemical reaction model coefficient, (S 0 /V 0 )＝75.0，q＝2/3；c＝0.0092，b＝2/3；
Step 400, constructing an elastoplastic model; the shear modulus of aluminum is 29GPa, and the yield strength is 260MPa;
step 500, calculating mass migration;
step 600, reassigns flow field variables.
The embodiment can calculate the combustion-detonation characteristics of the mixed explosive, the calculation accuracy meets the actual requirements, and the design level is improved.
Although the invention has been described herein with reference to a number of illustrative embodiments thereof, it should be understood that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the scope and spirit of the principles of this disclosure.
Claims (1)
1. The method for calculating the explosion output characteristics of the mixed explosive is based on a fluid dynamics equation under a two-dimensional Euler coordinate system and is characterized by comprising the following calculation steps:
step 100, constructing a calculation model:
constructing a mass conservation equation in a two-dimensional Euler coordinate system as shown in a formula 1.1, a momentum conservation equation as shown in a formula 1.2 and a formula 1.3, and an energy conservation equation as shown in a formula 1.4;
mass conservation equation:
x-direction momentum conservation equation:
conservation of momentum in the y-direction equation:
energy conservation equation:
formula 1.1-formula 1.4:
ρ is the density;
u is the speed;
e is energy;
s is stress deflection;
p is the pressure;
t is time;
α is a symmetry coefficient, α=2 in the cylindrical coordinate system, and α=1 in the rectangular coordinate system;
subscripts x and y are components of the respective directions;
step 200, constructing a state equation:
describing the physical property change rule of the detonation product of the mixed explosive by adopting an HOM state equation, wherein the expression form is shown in the formula 1.5:
in formula 1.5:
p CJ is the pressure of detonation products in CJ state;
e CJ is the internal energy of detonation products in the CJ state;
T CJ the temperature of detonation products in CJ state;
subscript CJ refers to the CJ state;
V g is the volume of detonation product;
coefficients A, B, C, D and E, K, L, M, N and O, Q, R, S, U and X are fitting coefficients of the respective physical quantities, respectively;
step 300, constructing an explosive chemical reaction model:
the method comprises an Arrhenius chemical reaction model, a Taylor wave chemical reaction model, a square wave impact chemical reaction model, a CJ volumetric combustion chemical reaction model and a Forest-Fire heterogeneous combustion chemical reaction model;
in step 300, the Forest-Fire heterogeneous combustion chemical reaction model further includes a linear volumetric combustion chemical reaction model;
step 300, further comprises a step of adding a viscosity coefficient;
step 400, constructing an elastoplastic model:
when the yield strength of the material is exceeded, describing the stress state of the object by using an elastoplastic model, the expression is shown in the formula 1.6:
in formula 1.6:
frepresenting the principal stress;
Y 0 indicating the yield strength of the material;
step 500, calculating mass migration:
migrating the mass according to the flow field movement speed, wherein the migrated mass flows into a new calculation grid;
mass migration was calculated using the donor-acceptor method; calculating mass migration in the donor and acceptor grids according to mass fraction of the material in the acceptor grid; the density and energy of the components corresponding to the migration mass in the donor mesh are calculated by the state equation in the first stage; allowing only one material reduction in one calculation time step;
for migration from the donor grid (i-1), j to the acceptor grid (i, j) along the x-direction, in the case of two-dimensional cylindrical symmetry coordinates, if the migration terms of energy, mass fraction, x-direction momentum, y-direction momentum, mass and density in the grid are expressed by DE, DW, DPU, DPV, DM and DMASS, respectively, their expressions are shown in equations 17-22:
In equations 17 to 22, subscript i, j is a calculation grid number, i represents an x direction, j represents a y direction, subscript n represents a calculation time step, U x For speed in x direction, U y The velocity in the y direction and ρ is the density;
in the formulas 17 to 22, the form factor is expressed as GEO, and the expression is shown in the formula 23:
In the formula 23, i represents an x-direction calculation grid number, and the sequential count is started from i=1;
in the formula 22, the discriminant is represented by Δ, and the expression is represented by the formula 24:
In formula 24, subscript i, j is the calculation grid number, i represents the x direction, j represents the y direction, subscript n represents the calculation time step, U x For the x-direction speed, Δt is the calculation time step, Δx is the x-direction calculation space step;
step 600, reassigning flow field variables:
reassigning flow field variables including density, mass fraction, x-direction speed, y-direction speed and internal energy according to the mass migration calculation result in the step 500;
according to the mass transfer calculation result, adding corresponding mass transfer terms to corresponding physical quantities, wherein expressions of density, mass fraction, x-direction speed, y-direction speed and internal energy are shown in the following formulas 25 to 29 respectively:
In the formulae 25 to 29, each symbol has the same meaning as in the formulae 17 to 22;
after reassigning, continuing to flow the flow field, completing the calculation of the current calculation step, outputting and storing the corresponding calculation result, continuing to circulate until reaching the expected calculation time, and then carrying out the result visualization processing; thus completing the calculation of the explosion output characteristics of the mixed explosive.
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