CN117592389A - Gas temperature-pressure change rule calculation method for semi-closed exploder - Google Patents
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Abstract
The invention provides a method for calculating the gas temperature-pressure change rule of a semi-closed exploder, which is used for quickly determining the hole breaking pressure of the semi-closed exploder and obtaining the gas temperature and pressure change rule of gunpowder after hole breaking; calculating the gas leakage rate in the combustion chamber after the hole is broken by combining a compressible gas state equation and a gas dynamics method, and deducing the pressure change rule before and after the hole is broken by the semi-closed exploder; the algorithm does not need to solve a combustion dynamics differential equation, can provide a new method and a new thought for calculating the temperature-pressure change rule of the gas in the semi-closed explosive device for scientific researchers, and can be applied to the fields of dynamic ablation simulation research of barrel materials and the like.
Description
Technical Field
The invention belongs to the technical field of explosives and powders, relates to a semi-closed explosive device, and particularly relates to a method for calculating a gas temperature-pressure change rule of the semi-closed explosive device.
Background
Ablation of barrel materials by gunpowder and gas is a major factor affecting the operational performance and service life of barrel weapon systems. The ablative property of gunpowder is generally evaluated by a semi-closed exploder ablation tube method, and the method can effectively eliminate the interference of mechanical factors and study the ablation effect of thermal-chemical factors. The basic principle of the semi-closed exploder ablation experiment is as follows: the powder burns in the closed chamber to produce high temperature and high pressure gas, when the pressure value of the gas reaches the breaking pressure of the bursting disc in the closed chamber, the bursting disc is opened, the closed chamber is communicated with the outside environment, and the powder gas is accelerated to wash the ablation tube to simulate the ablation effect of the high temperature and high pressure powder gas on the barrel material. The hole breaking pressure of the rupture disk usually takes the maximum pressure generated by the combustion of gunpowder in a closed chamber, and is an important parameter of a semi-closed exploder experiment. The change rule of the temperature and pressure of the gunpowder gas after the hole of the semi-closed exploder is broken is a precondition for the construction of a dynamic barrel ablation model.
The hole breaking pressure of the existing semi-closed explosive device is basically determined by an empirical formula on the powder strength, powder filling density and powder gas residual capacity and a closed explosive device pre-experiment, and an accurate and reliable calculation method is lacked. Meanwhile, the pressure release time of the gunpowder gas in the experiment of the semi-closed explosion device is usually in the millisecond level, the temperature is above 2000 ℃, and the temperature change of the gunpowder gas before and after the hole breaking of the semi-closed explosion device is difficult to measure by the traditional temperature measuring method.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a method for calculating the gas temperature-pressure change rule of a semi-closed exploder, which solves the technical problems that the practicability and operability of the calculation method in the prior art are to be further improved.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for calculating the temperature-pressure change rule of a semi-closed exploder gas comprises the following steps:
step one, the structural size, filling density, initial temperature and pressure and hole breaking pressure of the semi-closed explosive are given, and the physical and chemical properties of gunpowder, parameters of a gunpowder type structure and physical parameters of gunpowder gas are given.
Step two, setting a time step and total calculated time length.
And thirdly, calculating the gas generation delta m (t) in time steps at different moments in the gunpowder combustion process.
And step four, calculating the temperature of the newly generated gunpowder gas in a time step after mixing with the original gas in the semi-closed exploder.
And fifthly, calculating the gas temperature reduction caused by radiation heat loss, and updating the gas temperature in the semi-closed exploder.
And step six, deducing the pressure of the gunpowder gas.
Step seven, judging whether the pressure in each time step in the earlier stage is larger than the rupture disc hole-breaking pressure p cr If the judgment result is true, the powder gas is considered to start to leak, the mass delta w (t) of the gas leaked in a time step is calculated, and then the mass m (t) of the residual gas in the semi-closed burst is updated; if the judgment result is false, the judgment result shows that the gas pressure in the semi-closed exploder does not reach the hole breaking pressure yet, and the deltaw (t) is constantly zero.
And step eight, accumulating the combustion depth in each time step to obtain the combustion depth e (t) at the current moment.
Step nine, judging whether the depth of the burnt gunpowder is smaller than the thickness of the gunpowder arc, if the judgment result is true, returning to the step three to continuously calculate the gas generation amount in the gunpowder combustion process; if the judgment result is false, returning to the step five to continuously calculate the radiation heat loss of the gas.
And step ten, after the total calculation time length is up, preserving the temperature and the pressure of gunpowder gas in each time step, and outputting a T-T curve and a p-T curve before and after the hole breaking of the semi-closed exploder.
Compared with the prior art, the invention has the following technical effects:
the calculation method disclosed by the invention can flexibly adjust the time step, the physicochemical property of gunpowder, the size of the semi-closed exploder and the fragment pressure, avoids solving the combustion dynamics differential equation, has strong practicability and operability, and can provide support for the dynamic ablation simulation research of the barrel materials.
(II) according to the calculation method, the energy release equation of the gunpowder and the hole breaking pressure of the rupture disk are preset, so that the combustion process of the gunpowder in the semi-closed space is simulated; and calculating the gas leakage rate after hole breaking by using a gas dynamic method, and further deducing the temperature and pressure change in the semi-closed chamber.
(III) the calculation method of the invention gradually converts chemical energy of gunpowder combustion into gas internal energy according to time step length, and the gas temperature change rule in the semi-closed explosion device is obtained after considering the gas radiation heat loss; and deducing a pressure change rule before and after the hole breaking of the semi-closed exploder by combining a compressible gas state equation and the gas leakage rate after the hole breaking.
The calculation method can quickly determine the hole breaking pressure of the semi-closed explosive device and acquire the temperature and pressure change rule of the gunpowder gas after hole breaking, and helps to construct a dynamic ablation model of the barrel material.
The invention provides a new method and a new thought for calculating the temperature and pressure change rule of the gunpowder combustion body before and after the hole breaking of the semi-closed exploder, which can be applied to the fields of hole breaking pressure determination of the semi-closed exploder, material high-temperature ablation simulation research and the like.
Drawings
FIG. 1 is a flow chart of a computing method of the present invention.
FIG. 2 is a graph comparing T-T curves and p-T curves at different pore-breaking pressures.
The following examples illustrate the invention in further detail.
Detailed Description
All materials and equipment used in the present invention are known in the art, unless otherwise specified.
The invention aims to provide a method for calculating the temperature-pressure change rule of gas of a semi-closed exploder, which simulates the combustion process of gunpowder in a semi-closed space by presetting an energy release equation of the gunpowder and the pressure of a broken hole of a rupture disk; and calculating the gas leakage rate after hole breaking by using a gas dynamic method, and further deducing the temperature and pressure change in the semi-closed chamber. The algorithm can provide a new method and a new thought for calculating the temperature-pressure change rule of the gas in the semi-closed explosive device for scientific researchers, and can be applied to the fields of dynamic ablation simulation research of barrel materials and the like.
The embodiment provides a method for calculating the temperature-pressure change rule of a semi-closed explosive, which comprises the steps of firstly calculating a temperature change (T-T) curve of gunpowder gas, then calculating the gas leakage rate in a combustion chamber after hole breaking by adopting a compressible gas state equation and a gas dynamics method, and deducing a pressure change (p-T) curve.
The invention provides a method for calculating the gas temperature-pressure change rule of a semi-closed exploder, which is used for quickly determining the hole breaking pressure of the semi-closed exploder and obtaining the gas temperature and pressure change rule of gunpowder after hole breaking; calculating the gas leakage rate in the combustion chamber after the hole is broken by combining a compressible gas state equation and a gas dynamics method, and deducing the pressure change rule before and after the hole is broken by the semi-closed exploder; the algorithm does not need to solve a combustion dynamics differential equation, can provide a new method and a new thought for calculating the temperature-pressure change rule of the gas in the semi-closed explosive device for scientific researchers, and can be applied to the fields of dynamic ablation simulation research of barrel materials and the like.
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.
Examples:
the embodiment provides a method for calculating a gas temperature-pressure change rule of a semi-closed exploder, as shown in fig. 1, which comprises the following steps:
step one, the structural size, filling density, initial temperature and pressure and hole breaking pressure of the semi-closed explosive are given, and the physical and chemical properties of gunpowder, parameters of a gunpowder type structure and physical parameters of gunpowder gas are given.
In the step, the initial values of temperature and pressure are required to be matched with the ignition conditions of gunpowder, so that the condition that the gunpowder burns slowly or even is not burnt is avoided.
In the first step, parameters of the physicochemical properties of the gunpowder and the shape structure of the gunpowder comprise the combustion speed, arc thickness, explosion temperature, explosion heat, density and energy release equation coefficients; parameters of physicochemical properties and shape structure of the powder are used to calculate the gas generation rate and energy release rate of the powder.
In the first step, the physical parameters of the gunpowder gas comprise specific heat capacity and specific heat ratio; the specific heat capacity is used for calculating the heating rate of the gunpowder gas after absorbing heat, and the specific heat ratio is used for calculating the mass flow of the leakage of the gunpowder gas after the hole of the rupture disc is broken.
Step two, setting a time step and total calculated time length.
Thirdly, obtaining the combustion depth e (t) at the current moment by accumulating the combustion depths in each time step, and calculating the total generation quality of the fuel gas at the current moment by combining the geometric structure of the gunpowder and the loading quantity of the gunpowder
The gas generation amount Δm (t) in the time step at different times of the gunpowder combustion process was calculated using equation 1.
Wherein:
Δm (t) is the gas production in the time steps at different moments of the gunpowder combustion process;
the total generation quality of the fuel gas at the current moment;
t is the time t;
Δt is the time step in s;
delta is the gunpowder filling density, and the unit is kg.m -3 ；
V is the volume of the semi-closed exploder, and the unit is m 3 ；
e (t) is the depth of combustion of the gunpowder, and the unit is m;
e 1 the unit is m;
mu, lambda and chi are geometric structure coefficients.
Step four, the newly generated gunpowder gas is fully mixed with the existing gas in the semi-closed exploder, and the temperature of the generated gunpowder gas in delta T time can be regarded as the gunpowder explosion temperature T b The temperature of the gas in the semi-closed explosion device before mixing is T (T); and calculating the temperature of the newly generated gunpowder gas in a time step and the original gas in the semi-closed exploder by adopting the method 3.
Wherein:
t (t+Deltat) is the temperature of the newly generated gunpowder gas in a time step after being mixed with the original gas in the semi-closed exploder;
m (t) is the mass of the gas in the closed space at the moment t, and is the sum of the initial gas mass of the semi-closed explosive device and the generation amount of gunpowder gas, wherein the unit is kg;
C v the specific heat capacity of the gunpowder gas is J.kg -1 ·K -1 ；
T (T) is the temperature of the gas in the semi-closed exploder, and the unit is K;
T b the unit is K for explosive explosion temperature;
p 0 the initial pressure value is Pa;
T 0 the unit is K, which is the initial value of the temperature;
the gas constant of the initial filling gas of the semi-closed exploder is expressed as J.kg -1 ·K -1 。
Fifthly, assuming that gas in the semi-closed explosive device does not flow before the hole is broken by the rupture disc, the gunpowder gas exchanges heat with the inner wall of the explosive device through thermal radiation, so that the temperature of the gunpowder gas is reduced. Calculating the gas temperature reduction caused by radiation heat loss by adopting a formula 5, and updating the gas temperature in the semi-closed exploder by adopting a formula 6;
t (T) =t (T) - Δt (T) formula 6;
wherein:
deltat (T) is the gas temperature decrease in K;
sigma is Stefin-Boltzmann constant, 5.6704 ×10 -8 W·m -2 ·K -4 ；
S is the inner surface area of the semi-closed exploder, and the unit is m 2 。
Step six, after the temperature of the gunpowder gas is determined, deducing the pressure of the gunpowder gas according to the gas temperature and a Nobel-Abel state equation by adopting a formula 7;
wherein:
p (t) is the gas temperature reduction amount in Pa;
alpha is the residual capacity, and the unit is m 3 ·kg -1 ；
The gas constant of the gunpowder gas is J.kg -1 ·K -1 ；
ρ is the density of powder in kg.m -3 ；
And step seven, according to the aerodynamic theory, the gas in the large cavity is discharged from the small hole to belong to the necking flow, and the flow speed of the gas flow can only be accelerated to Mach number (namely, the local sonic speed) at the highest. Because the hole-breaking pressure of the semi-closed exploder is usually 10 2 The MPa, the gas of the gunpowder is considered to be discharged from the broken hole at Mach number.
Judging whether the pressure in each time step in the earlier stage is larger than the rupture pressure p of the rupture disk cr If the determination result is true, the gas mass Δw (t) of the powder gas discharged in one time step is calculated by equation 8, and then the remaining gas mass m (t) in the semi-closed burst is updated by equation 9. If the judgment result is false, the gas pressure in the semi-closed exploder does not reach the hole breaking pressure, and the deltaw (t) is constantly zero;
m (t) =m (t) - Δw (t) formula 9;
wherein:
Δw (t) is the mass of gas vented in a time step;
a is the broken hole area, m 2 ；
Gamma is the specific heat ratio of the gunpowder gas;
and step eight, accumulating the combustion depth in each time step by adopting the formula 10 to obtain the combustion depth e (t) at the current moment.
Wherein:
i is the i-th time step, i=1, 2, …, n;
u s is a combustion rate constant;
n s is the burning rate index;
p (t) is the gas pressure in Pa in each time step;
Δt is the time step in s;
step nine, judging whether the depth of the burnt gunpowder is smaller than the thickness of the gunpowder arc, if the judgment result is true, returning to the step three to continuously calculate the gas generation amount in the gunpowder combustion process; if the judgment result is false, returning to the step five to continuously calculate the radiation heat loss of the gas;
and step ten, after the total calculation time length is up, preserving the temperature and the pressure of gunpowder gas in each time step, and outputting a T-T curve and a p-T curve before and after the hole breaking of the semi-closed exploder.
Application example:
the embodiment provides a gas temperature-pressure change rule calculation method of a semi-closed explosion device based on the embodiment.
In the application example, taking spherical insensitive powder with the radius of 5mm as an example (the insensitive layer thickness is 1 mm), calculating a T-T curve and a p-T curve of the semi-closed exploder under different hole breaking pressures, and verifying an algorithm; the physicochemical properties of the powder are shown in the following table 1, the powder charge density in the semi-closed explosive is 0.2g/ml, the powder charge amount is 0.011g/ml, the ignition pressure is 10MPa, the hole breaking pressure is 100MPa, 200MPa and 300MPa respectively, the time step is 0.01ms, and the calculated temperature change curve and pressure change curve pair are shown in fig. 2.
TABLE 1 physicochemical Properties of gunpowder
The results show that the temperature and pressure curves at the early stage of hole breaking are consistent under three hole breaking pressures of 100MPa, 200MPa and 300 MPa; when the hole breaking pressure is smaller, the pressure in the semi-closed exploder can also rise after the rupture of the rupture disc (for example, the pressure change curve of the hole breaking pressure is 100 MPa), and when the hole breaking pressure is larger, the pressure in the semi-closed exploder rapidly drops after the rupture of the rupture disc. The temperature curves under different hole breaking pressures are relatively close, and the temperature dropping rate is accelerated after the hole breaking pressure is reached.
Claims (4)
1. The method for calculating the gas temperature-pressure change rule of the semi-closed exploder is characterized by comprising the following steps of:
step one, setting the structural size, filling density, initial temperature and pressure and hole breaking pressure of a semi-closed explosive device, and setting the physical and chemical properties of gunpowder, parameters of a gunpowder type structure and physical parameters of gunpowder gas;
step two, setting a time step and calculating the total calculated time length;
step three, calculating gas generation delta m (t) in time steps at different moments in the gunpowder combustion process;
step four, calculating the temperature of the newly generated gunpowder gas in a time step after being mixed with the original gas in the semi-closed exploder;
step five, calculating the gas temperature reduction caused by radiation heat loss, and updating the gas temperature in the semi-closed exploder;
step six, deducing the pressure of the gunpowder gas;
step seven, judging whether the pressure in each time step in the earlier stage is larger than the rupture disc hole-breaking pressure p cr If the judgment result is true, the powder gas is considered to start to leak, the mass delta w (t) of the gas leaked in a time step is calculated, and then the mass m (t) of the residual gas in the semi-closed burst is updated; if the judgment result is false, the gas pressure in the semi-closed exploder does not reach the hole breaking pressure, and the deltaw (t) is constantly zero;
step eight, accumulating the combustion depth in each time step to obtain the combustion depth e (t) at the current moment;
step nine, judging whether the depth of the burnt gunpowder is smaller than the thickness of the gunpowder arc, if the judgment result is true, returning to the step three to continuously calculate the gas generation amount in the gunpowder combustion process; if the judgment result is false, returning to the step five to continuously calculate the radiation heat loss of the gas;
and step ten, after the total calculation time length is up, preserving the temperature and the pressure of gunpowder gas in each time step, and outputting a T-T curve and a p-T curve before and after the hole breaking of the semi-closed exploder.
2. The method for calculating the temperature-pressure change law of the gas of the semi-closed exploder according to claim 1, which is characterized by comprising the following steps:
step one, setting the structural size, filling density, initial temperature and pressure and hole breaking pressure of a semi-closed explosive device, and setting the physical and chemical properties of gunpowder, parameters of a gunpowder type structure and physical parameters of gunpowder gas;
step two, setting a time step and calculating the total calculated time length;
step three, calculating the gas generation delta m (t) in time steps at different moments in the gunpowder combustion process by adopting a formula 1;
wherein:
Δm (t) is the gas production in the time steps at different moments of the gunpowder combustion process;
the total generation quality of the fuel gas at the current moment;
t is the time t;
Δt is the time step in s;
delta is the gunpowder filling density, and the unit is kg.m -3 ；
V is the volume of the semi-closed exploder, and the unit is m 3 ；
e (t) is the depth of combustion of the gunpowder, and the unit is m;
e 1 the unit is m;
mu, lambda and χ are geometric structure coefficients;
step four, calculating the temperature of the newly generated gunpowder gas in a time step and the original gas in the semi-closed exploder by adopting a formula 3;
wherein:
t (t+Deltat) is the temperature of the newly generated gunpowder gas in a time step after being mixed with the original gas in the semi-closed exploder;
m (t) is the mass of the gas in the airtight space at the moment t, and the unit is kg;
C v the specific heat capacity of the gunpowder gas is J.kg -1 ·K -1 ；
T (T) is the temperature of the gas in the semi-closed exploder, and the unit is K;
T b the unit is K for explosive explosion temperature;
p 0 the initial pressure value is Pa;
T 0 the unit is K, which is the initial value of the temperature;
the gas constant of the initial filling gas of the semi-closed exploder is expressed as J.kg -1 ·K -1 ；
Step five, calculating the gas temperature reduction caused by radiation heat loss by adopting a formula 5, and updating the gas temperature in the semi-closed exploder by adopting a formula 6;
t (T) =t (T) - Δt (T) formula 6;
wherein:
deltat (T) is the gas temperature decrease in K;
sigma is Stefin-Boltzmann constant, 5.6704 ×10 -8 W·m -2 ·K -4 ；
S is the inner surface area of the semi-closed exploder, and the unit is m 2 ；
Step six, deducing the pressure of the gunpowder gas by adopting a formula 7;
wherein:
p (t) is the gas temperature reduction amount in Pa;
alpha is the residual capacity, and the unit is m 3 ·kg -1 ；
The gas constant of the gunpowder gas is J.kg -1 ·K -1 ；
ρ is the density of powder in kg.m -3 ；
Step seven, judging whether the pressure in each time step in the earlier stage is larger than the rupture disc hole-breaking pressure p cr If the judgment result is true, considering that the gunpowder gas starts to leak, calculating the mass delta w (t) of the gas leaked in one time step by the formula 8, and then updating the mass m (t) of the residual gas in the semi-closed burst by the formula 9; if the judgment result is false, the gas pressure in the semi-closed exploder does not reach the hole breaking pressure, and the deltaw (t) is constantly zero;
m (t) =m (t) - Δw (t) formula 9;
wherein:
Δw (t) is the mass of gas vented in a time step;
a is the broken hole area, m 2 ；
Gamma is the specific heat ratio of the gunpowder gas;
step eight, accumulating the combustion depth in each time step by adopting the method 10 to obtain the combustion depth e (t) at the current moment;
wherein:
i is the i-th time step, i=1, 2, …, n;
u s is a combustion rate constant;
n s is the burning rate index;
p (t) is the gas pressure in Pa in each time step;
Δt is the time step in s;
step nine, judging whether the depth of the burnt gunpowder is smaller than the thickness of the gunpowder arc, if the judgment result is true, returning to the step three to continuously calculate the gas generation amount in the gunpowder combustion process; if the judgment result is false, returning to the step five to continuously calculate the radiation heat loss of the gas;
and step ten, after the total calculation time length is up, preserving the temperature and the pressure of gunpowder gas in each time step, and outputting a T-T curve and a p-T curve before and after the hole breaking of the semi-closed exploder.
3. The method for calculating the temperature-pressure change law of gas in a semi-closed exploder according to claim 1, wherein in the first step, the parameters of the physicochemical properties and the shape structure of the powder include the firing rate, arc thickness, explosion temperature, explosion heat, density and energy release equation coefficient.
4. The method for calculating the temperature-pressure variation law of gas in a semi-closed explosion device according to claim 1, wherein in the first step, the physical parameters of the powder gas include specific heat capacity and specific heat ratio.
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