CN102592053A - Method for determining detonation parameters of liquid explosive - Google Patents

Abstract

The invention relates to detonation parameters of liquid explosive and provides a method for calculating CJ detonation pressure, detonation speed, detonation temperature and specific volume of the liquid explosive through a thermodynamic function of compounds and a minimal free energy method, and the invention belongs to the technical field of energetic materials. A VLW program is created on the basis of a BKW program and is used for calculating such function relations of the liquid explosive as CJ detonation pressure, detonation speed, detonation temperature, specific volume and the like through the thermodynamic function of compounds by utilizing the minimal free energy method.

Description

A kind of method of definite liquid explosive detonation parameter

Technical field

The present invention relates to the detonation parameter of liquid explosive, is the thermodynamic function through compound, and minimum free energy calculates the method for CJ detonation pressure, explosion velocity, quick-fried temperature and the specific volume of liquid explosive, belongs to the energetic material technical field.

Background technology

The liquid explosive detonation parameter calculates, and to understanding liquid explosive great importance is arranged.But the detonation of considering liquid explosive belongs to heterogeneous body detonation or out-phase detonation; Especially the characteristics of the existing volume blast of liquid explosive have the characteristic of point source explosion simultaneously again; Therefore; It is a kind of special detonation process, and this just causes the difference of detonation after it and condensed state explosive and hydrocarbon fuel and the air mixed.

Some liquefied compounds or its potpourri; Have inflammable, explosive characteristics like isopropyl nitrate, acetone, ether, nitromethane, diethlene glycol dinitrate, nitrine alkane, nitroglycerine and TATP (potpourri of acetone and hydrogen peroxide) etc., self can form explosive extremely strong cloud and mist explosive as liquid explosive or with air mixed.This research adopts VLW state equation and software for calculation thereof to study the explosion energy of these typical liquid explosives (liquefied compound).Therefore in calculating, nitroglycerine calculates as liquid single chmical compound explosive, and other liquefied compound or potpourri need absorb airborne oxygen, in explosion dispersion process, in fact forms the cloud and mist Air Explosives and explodes.

Liquid explosive are calculated, except that BKW program and Cordon-McBride Quatuor program, do not have better calculation procedure at present; But BKW program and Cordon-McBride Quatuor program have many weak points, and the error of calculation is bigger.Generally speaking, the liquid explosive component is simple, belong to out-phase detonation, so we selects the Fortran VLW program that is the basis with the BKW state equation to calculate for use.

Summary of the invention

The objective of the invention is in order to propose a kind of method of definite liquid explosive detonation parameter.

The objective of the invention is to realize through following technical scheme.

The method of a kind of definite liquid explosive detonation parameter of the present invention, concrete steps are following:

1) the VLW program is to be based upon on the BKW procedure basis, utilizes Free energy Minimization to calculate the funtcional relationships such as CJ detonation pressure, explosion velocity, quick-fried temperature and specific volume of liquid explosive through the thermodynamic function of compound;

Fundamental equation

In two phase detonation, a chemical reaction zone is arranged behind the detonation wave front, intense reaction and is taken place and emits big calorimetric by size degradation in drop in chemical reaction zone, chemical reaction terminal for reaction accomplish after formed detonation product.In the detonation process forward position shock wave with the back with chemical reaction propagate with same speed.If liquid explosive are ideal gas when detonation, and satisfy the various conditions under the standard state, the status values during the detonation reaction is calculated and should be found the solution within the scope in equation of state, and the kinetics equation group of used medium is:

$\left.\begin{array}{c}{\mathrm{\&rho;}}_0(D-u_0)-{\mathrm{\&rho;}}_1(D-u)=0\\ P_1-P_0={\mathrm{\&rho;}}_0(D-u_0)(u_1-u_0)\\ P_{1}u=P_0{u}_0+{\mathrm{\&rho;}}_0(D-u_0)[({\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="HDA0000129465170000032.png"\; state="\{\{state\}\}">E</figure-callout>}}_1+\frac{u_0^2}{2})\\ \frac{P-P_0}{V_0-{\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="HDA0000129465170000032.png"\; state="\{\{state\}\}">V</figure-callout>}}_1}=\mathrm{\&gamma;}\frac{P}{V_1}\\ P=f(V,T)\end{array}-(E_0+\frac{U_0^2}{2})]\right\}---\left(3.3\right)$

In the following formula:

The D-detonation rate;

ρ, P, u-are respectively density, pressure and particle velocity;

The E-specific internal energy;

Subscript 0 expression fuel;

Subscript 1 expression detonation product.

Consider

Suppose isentropic index γ again ₀=γ _CJ=γ, can as be write part arrangement in (3.3) formula:

$D=V_0\sqrt{\frac{P_{\mathrm{CJ}}-P_0}{V_0-V_{\mathrm{CJ}}}}---\left(3.4\right)$

$U_{\mathrm{CJ}}=(V_0-V_J)\sqrt{\frac{P_{\mathrm{CJ}}-P_0}{V_0-V_{\mathrm{CJ}}}}---\left(3.5\right)$

Because temperature of reaction is relevant with specific volume during liquid explosive detonation,

${\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="HDA0000129465170000032.png"\; state="\{\{state\}\}">E</figure-callout>}}_1=\frac{P_1{\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="HDA0000129465170000032.png"\; state="\{\{state\}\}">V</figure-callout>}}_1}{\mathrm{\&gamma;}-1}-\mathrm{\&lambda;Q}---\left(3.6\right)$

The specific energy that the detonation of Q-liquid explosive discharges in the formula;

λ-chemical reaction progress degree.

Theoretical according to CJ, only consider initial state and final state, then, have original state (λ=0):

$E_0=\frac{P_0{V}_0}{{\mathrm{\&gamma;}}_0-1}---\left(3.7\right)$

Final state (λ=0) is then had:

$E_{\mathrm{CJ}}=\frac{P_{\mathrm{CJ}}{V}_{\mathrm{CJ}}}{{\mathrm{\&gamma;}}_{\mathrm{CJ}}-1}-Q---\left(3.8\right)$

If further simplify, ignore original pressure P ₀Even, P ₀＜＜P _JThe time, (3.4) formula can be write as

(3.9)

$D=\sqrt{2({\mathrm{\&gamma;}}_1^2-1)Q}$

(3.10)

$P_{\mathrm{CJ}}=\frac{{\mathrm{\&rho;}}_0{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000129465170000021.png,HDA0000129465170000032.png"\; state="\{\{state\}\}">D</figure-callout>}}^2}{\mathrm{\&gamma;}+1}$

(3.11)

${\mathrm{\&rho;}}_{\mathrm{CJ}}=\frac{\mathrm{\&gamma;}+1}{\mathrm{\&gamma;}}{\mathrm{\&rho;}}_0$

(3.12)

$U_{\mathrm{CJ}}=\frac{D}{\mathrm{\&gamma;}+1}$

By above-mentioned equation is the fundamental equation that calculates the liquid explosive detonation parameter

2) VLW state equation

During liquid explosive calculated, the expression formula of VLW state equation was:

$\frac{\mathrm{PV}}{\mathrm{RT}}=1+B^{*}\left(\frac{b_0}{V}\right)+\frac{B^{*}}{T^{*}}\underset{n=3}{\overset{m}{\mathrm{\&Sigma;}}}{(n-2)}^{-n}{\left(\frac{b_0}{V}\right)}^{(N-1)}---\left(3.13\right)$

B in the formula ^*Be the dimensionless second virial coefficient, adopt the Lennard-Jones potential function to represent usually.

When pressure was little, the chance of the three molecules effect of running foul of each other was seldom, therefore, and the character that this equation is deployed into the second viral item when just enough correctly reflecting liquid explosive detonation.

Can derive by classical statistics thermodynamics:

ε in the formula and σ are the dimensionless parameter

$T^{*}=\frac{\mathrm{KT}}{\mathrm{\&epsiv;}}---\left(3.16\right)$

${\mathrm{\&gamma;}}^{*}=\frac{\mathrm{\&gamma;}}{\mathrm{\&sigma;}}---\left(3.17\right)$

Other adds a dimensionless parameter

$B^{*}=\frac{B}{b_0}---\left(3.18\right)$

Wherein $b_0=\frac{2}{3}\mathrm{\&pi;}\tilde{N}{\mathrm{\&sigma;}}^3$

Therefore

$B^{*}\left(T^{*}\right)=\underset{j=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[-\frac{2^{j+\frac{1}{2}}}{4j}\mathrm{\&Gamma;}(\frac{j}{2}-\frac{1}{4})T^{*-(2j+1)/4}]---\left(3.19\right)$

Under lower pressure, because the density of liquid explosive is less, thus can an intercepting VLW state equation first, that is:

$\frac{\mathrm{PV}}{\mathrm{RT}}=1---\left(3.20\right)$

Like this, the VLW state equation has just become equation for ideal gases.

Be noted that the calculating for the liquid explosive detonation parameter, the use of VLW state equation is arbitrarily, both can adopt cutting back formula (3.20); Also can adopt the monoblock type (3.13) of VLW state equation. this is that in this case, the high-order term of VLW state equation goes to zero basically because the density of liquid explosive is less; Therefore; No matter be to adopt cutting back or monoblock type, can obtain identical result of calculation. say that from this point the VLW state equation has certain universality.

Description of drawings

Fig. 1 is the result of calculation of TATP;

Fig. 2 is the result of calculation of isopropyl nitrate;

Fig. 3 is the result of calculation of ether;

Fig. 4 is the result of calculation of isoamyl nitrate;

Fig. 5 is the result of calculation of nitromethane;

Fig. 6 is the detonation pressure histogram of different liquid explosives;

Fig. 7 is the explosion velocity histogram of different liquid explosives.

Embodiment

Embodiment

The application of VLW program

Application V LW program is calculated the liquid explosive detonation parameter, is a very important problem for the given of initial input value, and the initial input value that must provide is: the chemical composition of liquid explosive; The enthalpy of formation of liquid explosive each component; The density of liquid explosive.

The density of liquid explosive be according to the percentage by weight of given fuel, and combining environmental pressure and temperature computation draw.

Application V LW program is calculated the liquid explosive detonation parameter; Hypothesis below need doing, with the premix combustible mixture of reaction system as whole gaseous states of equivalent, for compensate evaporate required when hot; The enthalpy of formation at this fuel adopts the liquid enthalpy of formation, temperature T at the beginning ₀Be 298.14K, original pressure P ₀Be 1atm..The enthalpy of formation and the detonation product of liquid explosive each component are as shown in table 1.

The enthalpy of formation of some liquid explosive of table 1

Use FORTRAN VLW program, calculated the detonation parameter of the liquid explosive of different component proportioning.Result of calculation is shown in Fig. 1～Fig. 5 and table 1.Wherein Fig. 1 is the result of calculation of TATP, and Fig. 2 is the result of calculation of isopropyl nitrate, and Fig. 3 is the result of calculation of ether, and Fig. 4 is the result of calculation of isoamyl nitrate, and Fig. 5 is the result of calculation of nitromethane.0 is explosion velocity among the figure, Δ-and be the superpressure value; Fig. 6 is the detonation pressure histogram of different liquid explosives, and Fig. 7 is the explosion velocity histogram of different liquid explosives;

Some liquid explosive such as isopropyl nitrate, acetone, ether, nitromethane, diethlene glycol dinitrate, nitrine alkane, nitroglycerine and TATP etc. have inflammable, explosive characteristics, and self can form explosive extremely strong cloud and mist explosive as liquid explosive or with air mixed.Their detonation parameter result of calculation is as shown in table 2.

Table 2 liquid explosive detonation parameter result of calculation

Can be found out that by Fig. 6 and Fig. 7 result of calculation the detonation pressure and the explosion velocity of nitroglycerine are the highest, detonation pressure reaches 21GPa, and explosion velocity is 7489m/s, is higher than the detonation pressure and the explosion velocity of other liquefied compound far away; Though the detonation pressure of other liquefied compound and explosion velocity are low than nitroglycerine because detonate moment and air have formed cloud and mist detonation, therefore have reach greatly, the characteristics of longer duration; In the compound or potpourri that form cloud and mist detonation, the detonation pressure of nitromethane and diethlene glycol dinitrate is higher, reaches 7～8MPa, and nitrine alkane and TATP take second place, and detonation pressure reaches 3～4MPa, and the detonation pressure of other three kinds of compounds is 2～3MPa; Their explosion velocity difference is little, is about 2000m/s, and wherein the explosion velocity of nitromethane and nitrine alkane is higher, surpasses 2000m/s.

Claims (1)

1. the method for a definite liquid explosive detonation parameter is characterized in that concrete steps are following:

1) the VLW program is based upon on the BKW procedure basis, utilizes Free energy Minimization to calculate the funtcional relationships such as CJ detonation pressure, explosion velocity, quick-fried temperature and specific volume of liquid explosive through the thermodynamic function of compound;

If liquid explosive are ideal gas when detonation, and satisfy the various conditions under the standard state, the status values during the detonation reaction is calculated and should be found the solution within the scope in equation of state, and the kinetics equation group of used medium is:

$\left.\begin{array}{c}{\mathrm{\&rho;}}_0(D-u_0)-{\mathrm{\&rho;}}_1(D-u)=0\\ P_1-P_0={\mathrm{\&rho;}}_0(D-u_0)(u_1-u_0)\\ P_{1}u=P_0{u}_0+{\mathrm{\&rho;}}_0(D-u_0)[(E_1+\frac{u_0^2}{2})\\ \frac{P-P_0}{V_0-V_1}=\mathrm{\&gamma;}\frac{P}{V_1}\\ P=f(V,T)\end{array}-(E_0+\frac{U_0^2}{2})]\right\}---\left(3.3\right)$

In the following formula:

The D-detonation rate;

ρ, P, u-are respectively density, pressure and particle velocity;

The E-specific internal energy;

Subscript 0 expression fuel;

Subscript 1 expression detonation product;

Consider

Suppose isentropic index γ again ₀=γ _CJ=γ, can as be write part arrangement in (3.3) formula:

$D=V_0\sqrt{\frac{P_{\mathrm{CJ}}-P_0}{V_0-V_{\mathrm{CJ}}}}---\left(3.4\right)$

$U_{\mathrm{CJ}}=(V_0-V_J)\sqrt{\frac{P_{\mathrm{CJ}}-P_0}{V_0-V_{\mathrm{CJ}}}}---\left(3.5\right)$

Because temperature of reaction is relevant with specific volume during liquid explosive detonation,

$E_1=\frac{P_1{V}_1}{\mathrm{\&gamma;}-1}-\mathrm{\&lambda;Q}---\left(3.6\right)$

The specific energy that the detonation of Q-liquid explosive discharges in the formula;

λ-chemical reaction progress degree;

Theoretical according to CJ, only consider initial state and final state, then, have original state (λ=0):

$E_0=\frac{P_0{V}_0}{{\mathrm{\&gamma;}}_0-1}---\left(3.7\right)$

Final state (λ=0) is then had:

$E_{\mathrm{CJ}}=\frac{P_{\mathrm{CJ}}{V}_{\mathrm{CJ}}}{{\mathrm{\&gamma;}}_{\mathrm{CJ}}-1}-Q---\left(3.8\right)$

Make P ₀＜＜P _JThe time, (3.4) formula can be write as (3.9)

$D=\sqrt{2({\mathrm{\&gamma;}}_1^2-1)Q}$

(3.10)

$P_{\mathrm{CJ}}=\frac{{\mathrm{\&rho;}}_0{D}^2}{\mathrm{\&gamma;}+1}$

(3.11)

${\mathrm{\&rho;}}_{\mathrm{CJ}}=\frac{\mathrm{\&gamma;}+1}{\mathrm{\&gamma;}}{\mathrm{\&rho;}}_0$

(3.12)

$U_{\mathrm{CJ}}=\frac{D}{\mathrm{\&gamma;}+1}$

By above-mentioned equation is the fundamental equation that calculates the liquid explosive detonation parameter;

2) VLW state equation

During liquid explosive calculated, the expression formula of VLW state equation was:

$\frac{\mathrm{PV}}{\mathrm{RT}}=1+B^{*}\left(\frac{b_0}{V}\right)+\frac{B^{*}}{T^{*}}\underset{n=3}{\overset{m}{\mathrm{\&Sigma;}}}{(n-2)}^{-n}{\left(\frac{b_0}{V}\right)}^{(N-1)}---\left(3.13\right)$

B in the formula ^*Be the dimensionless second virial coefficient, adopt the Lennard-Jones potential function to represent usually;

Can derive by classical statistics thermodynamics:

ε in the formula and σ are the dimensionless parameter

$T^{*}=\frac{\mathrm{KT}}{\mathrm{\&epsiv;}}---\left(3.16\right)$

${\mathrm{\&gamma;}}^{*}=\frac{\mathrm{\&gamma;}}{\mathrm{\&sigma;}}---\left(3.17\right)$

Other adds a dimensionless parameter

$B^{*}=\frac{B}{b_0}---\left(3.18\right)$

Wherein $b_0=\frac{2}{3}\mathrm{\&pi;}\tilde{N}{\mathrm{\&sigma;}}^3$

Therefore

$B^{*}\left(T^{*}\right)=\underset{j=0}{\overset{\&infin;}{\mathrm{\&Sigma;}}}[-\frac{2^{j+\frac{1}{2}}}{4j}\mathrm{\&Gamma;}(\frac{j}{2}-\frac{1}{4})T^{*-(2j+1)/4}]---\left(3.19\right)$

First of intercepting VLW state equation, that is:

$\frac{\mathrm{PV}}{\mathrm{RT}}=1---\left(3.20\right)$

Like this, the VLW state equation has just become equation for ideal gases.

Images