CN110082384B - Method for predicting time for generating holes or cracks by high-energy solid propellant grains through gas generation - Google Patents

Method for predicting time for generating holes or cracks by high-energy solid propellant grains through gas generation Download PDF

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CN110082384B
CN110082384B CN201910400623.0A CN201910400623A CN110082384B CN 110082384 B CN110082384 B CN 110082384B CN 201910400623 A CN201910400623 A CN 201910400623A CN 110082384 B CN110082384 B CN 110082384B
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CN110082384A (en
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曹蓉
程海燕
彭松
赵程远
张峰涛
杨根
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Hubei Institute of Aerospace Chemical Technology
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Abstract

The method for predicting the time for generating the cavity or the crack by the gas generation of the high-energy solid propellant grain is provided, and comprises the following steps: establishing a prediction model of gas production and cracking time of the high-energy solid propellant according to theory and test results, and quantifying some parameters of the model to a small-size solid propellant sample with reduced equal proportion; and then, by measuring the size, the thermal weight loss, the tensile strength and the gas production cracking time of the small-size solid propellant sample and the size of the high-energy solid propellant column, substituting the parameters into a prediction model of the gas production cracking time, predicting the gas production cracking time of the high-energy solid propellant under the normal-temperature storage condition, and ensuring the structural reliability of the column. The invention can realize nondestructive and quantitative evaluation of the gas production and cracking time of the large-scale engine and has the advantages of safe test, simple and convenient operation, economy and quickness.

Description

Method for predicting time for generating holes or cracks by high-energy solid propellant grains through gas generation
Technical Field
The invention relates to the technical field of high-energy solid propellant grains, in particular to a method for predicting gas generation and perforation or cracking time of high-energy solid propellant grains.
Background
The high-energy solid propellant grain is a thermosetting cross-linked propellant which takes polyether plasticized by mixed nitrate as an adhesive and is filled with a large amount of high-energy oxidants of HMX, AP, aluminum powder (Al) and the like, integrates the advantages of a modified double-base propellant and a composite solid propellant, and has excellent energy performance and mechanical performance. Because of containing a large amount of nitrate, the thermochemical decomposition or gasification of the explosive column can occur in the storage process to cause gas accumulation, internal looseness, microcracks and cavities are generated, the explosive column finally generates structural damage (cracks and holes), the structural integrity and combustion stability of an engine are influenced, the ignition failure and even explosion of the engine are caused, and the use safety of the missile is seriously threatened. Therefore, it is an essential matter of high-energy propellants to evaluate the structural destruction of high-energy propellants due to thermal aging. The propellant grains, particularly the propellant grains for strategic missiles, are large in size, and are uneconomical and unsafe if a live bomb is used for testing, in order to evaluate whether internal cracking behaviors occur in the grains containing nitrate under the common storage condition, a high-energy propellant gas-generating cracking model containing temperature and size effects is established, and a small-size propellant sample is used for simulating the cracking condition of the grains in the storage process of an engine, so that the gas-generating cracking time of the large-size high-energy solid propellant grains is predicted, and the structural integrity of the engine is guaranteed.
Disclosure of Invention
The invention aims to provide a method for predicting the gas generation and cracking time of a high-energy solid propellant grain due to gas generation.
The technical idea of the invention is as follows: firstly, based on theoretical derivation and experimental conclusion, establishing a prediction model of the gas generation and hole generation or cracking time of the high-energy solid propellant grain, and replacing some parameters or variables in the model by small-size propellant samples, or establishing a functional relation between the high-energy solid propellant grain and the small-size propellant samples which are reduced in equal proportion on the same parameter; then, carrying out a high-temperature accelerated aging test by adopting a small-size propellant sample, and measuring the thermal weight loss rate, the high-temperature tensile strength and the cracking time of the propellant; and (3) measuring parameters of the propellant such as the normal temperature thermal weight loss rate, the normal temperature tensile strength and the like. The obtained parameters are substituted into the model, so that the time of cracking of the large-scale engine grain due to gas generation under the normal-temperature storage condition can be predicted.
The technical scheme of the invention is that a high-energy solid propellant grain gas generation hole or cracking time prediction method is based on a prediction model of high-energy solid propellant grain gas generation hole or cracking time of tensile strength, weight loss rate, grain size, time and temperature T, and the prediction model is represented by the following formula (1):
Figure BDA0002059627800000021
wherein:
σm,1、σm,2respectively high-energy solid propellant grains at T1、T2Maximum tensile strength at two different temperatures; rw,t,1、Rw,t,2Respectively high-energy solid propellant grain at temperature T1Elapsed time tR,1Later weight loss rate, and at temperature T2Elapsed time tR,2The later weight loss rate is dimensionless; t is tR,1、tR,2Respectively at a temperature T1When the weight loss rate of the high-energy solid propellant grain reaches Rw,t1Time elapsed, and temperature T2When the weight loss rate of the high-energy solid propellant grain reaches Rw,t2Time elapsed in units of day; t is1、T2Respectively two different test temperatures, where T2The conventional storage temperature of the high-energy solid propellant grain; r is1The radius r of a small-size solid propellant sample is reduced according to the equal proportion of a high-energy solid propellant grain2The radius of the high-energy solid propellant grain; t is t1According to the time for producing holes or cracks of the small-size solid propellant samples with the same specific shrinkage of the high-energy solid propellant grains, t2Time to produce a perforation or crack for the high energy solid propellant charge; e is the base of the natural logarithm and has a value equal to about 2.71828.
The method of the invention deduces the time for generating the holes or cracks of the high-energy solid propellant grains by the experiment of the time for generating the holes or cracks of the small-size solid propellant samples with the same specific shrinkage of the high-energy solid propellant grains, can avoid destructive experiment of the high-energy solid propellant grains, improves the test safety, has simple and convenient operation, is economic and fast, and can be used for quantitatively evaluating the gas generation and cracking time of a large-scale engine.
Further, the establishment of the prediction model shown in the above formula (1) includes the following steps:
s11, setting the time T for a certain high-energy solid propellant grain to pass by at the temperature TRAfter-weightlessness ratio RwThe amount of the gaseous substance generated per unit mass and per unit time at that temperature is expressed by the following formula (2):
Figure BDA0002059627800000022
wherein:
tRwhen the temperature is T, the weight loss rate of the high-energy solid propellant grain sample reaches RwElapsed time, day;
Rw,t-at temperature T, sample of high energy solid propellant charge over time TRThe later weight loss rate is dimensionless;
average molar mass, g.mol, of gas generated by decomposition of M-high energy solid propellant grains-1；
S12, determining the rate of thermal weight loss of the propellant at different temperatures as a constant conclusion according to experimental research results, and obtaining the gas production rate of the high-energy solid propellant grain per unit volume at a certain temperature according to the relation V between the volume and the mass and the density as shown in the formula (3):
Figure BDA0002059627800000023
wherein:
Figure BDA0002059627800000024
is a constant;
q-the rate of gas generation per unit volume of the high-energy solid propellant charge at the temperature T, i.e. the amount of gas product in the high-energy solid propellant charge per unit time and unit volume, mol m-3·day-1；
Rho-density of solid propellant, kg m-3；
S13, theoretical analysis and experimental verification show that when the temperature is constant, the gas accumulated concentration at the center of the high-energy solid propellant grain is in exponential growth relation with the radius r of the grain, and the gas amount at the center is expressed by the formula (4):
q′＝q·k′er (4)
wherein when q' is temperature T, the gas production rate per unit volume of propellant gas product at the center of the high-energy solid propellant grain with radius r is mol.m-3·day-1(ii) a k' is a constant;
s14, according to Henry' S law, the internal stress of the center of the propellant is equal to the pressure of generated gas, and the calculation formula is shown as formula (5):
p＝qvt/H (5)
in the formula:
t-storage time, day, of the high-energy solid propellant grain;
h-coefficient of solubility of the gas formed in volume in solid propellants, m.Pa-1·m-3；
p-the pressure, Pa, to which the high-energy solid propellant grains are subjected;
qvgas production in m day per unit volume of propellant at the centre of the high-energy solid propellant grain expressed as gas production volume-1·m-3；
S15 equation of state of ideal gas
Figure BDA0002059627800000031
And obtaining the gas production rate of the propellant in unit volume at the center of the high-energy solid propellant grain expressed by the gas production volume as qvThe calculation formula is shown as formula (6):
Figure BDA0002059627800000032
in the formula:
p is the pressure, Pa, to which the high-energy solid propellant grains are subjected;
r-gas constant, 8.314J. mol-1·K-1；
T-propellant storage temperature, K;
substituting equation (6) into equation (5) yields equation (7):
Figure BDA0002059627800000033
s16, because the density rho of the propellant and the average molecular weight M of the generated gas at room temperature are basically unchanged at different temperatures, the relationship of the pressures received by the high-energy solid propellant grains at different temperatures and storage times is obtained by the formulas (3), (4) and (7), see the formula (8):
Figure BDA0002059627800000034
wherein:
P1、P2respectively high-energy solid propellant grains at T1、T2The maximum pressure that can be withstood at two different temperatures;
s17, assuming that the dissolution parameter of the decomposition product gas in the propellant does not change with the temperature, i.e. letting H2/H1＝1；
Then converting the formula (8) into the relation of the cracking time of the high-energy solid propellant grain due to gas generation at different temperatures, see the formula (9):
Figure BDA0002059627800000041
s18, when the internal pressure of the high-energy solid propellant grain reaches or exceeds the maximum tensile strength of the propellant, setting the high-energy solid propellant grain to crack, and writing the formula (9) as shown in the formula (1):
Figure BDA0002059627800000042
the method of the invention can be seen in that the model establishment process for deducing the time for generating the holes or cracking of the high-energy solid propellant grains by utilizing the experiments of the time for generating the holes or cracking of the high-energy solid propellant grains and other small-size solid propellant samples with reduced specific ratios is based on theoretical calculation and experimental conclusions, does not deviate from actual assumptions and limiting conditions, and has scientific and reasonable model establishment and strong applicability.
Further, the high-energy solid propellant grain is at the temperature T1Maximum tensile strength σ ofm,1And at a temperature T2Maximum tensile strength σ ofm,2Obtained by measuring a dumbbell-shaped solid propellant sample with the same component as the high-energy solid propellant grain. The dumbbell type solid propellant sample can be tested according to a conventional method as long as the dumbbell type solid propellant sample meets the condition that the components are the same as the high-energy solid propellant grains, and the size of the sample can be designed according to experimental practice.
Further, the high-energy solid propellant grain is at the temperature T1Elapsed time tR,1Later weight loss ratio Rw,t1And at a temperature T2Elapsed time tR,2Later weight loss ratio Rw,t2Obtained by measuring the thermal weight loss rate of a cubic propellant sample with the same components as the high-energy solid propellant grains.
Similarly, the cubic propellant sample only needs to meet the condition that the components are the same as those of the high-energy solid propellant grain, and the size is designed according to the experimental requirements.
Furthermore, the size of the dumbbell-shaped solid propellant sample and/or the cubic propellant sample is obviously smaller than that of the high-energy solid propellant grain.
Further, the above method further comprises the steps of:
preparing a small-size solid propellant sample which is reduced according to the equal proportion of the high-energy solid propellant grains, and measuring the radius r of the small-size solid propellant sample1While measuring the radius r of the engine charge2，；
Developing propellant sample high temperature T1And normal temperature T2Thermogravimetric test underRecord Rw,t,1，Rw,t,2，tR,1，tR,2；
Determination of propellant sample high temperature T1And normal temperature T2Tensile Strength σm,1And σm,2；
Determination of high temperature T of small-sized solid propellant sample1Time t for generating holes or cracking by generated gas1(ii) a Then, the measured parameters are brought into the prediction model of the formula 1) to obtain the time t for generating holes or cracking by gas generated under the normal-temperature storage condition of the high-energy solid propellant grain engine grain2。
Compared with the prior art, the invention has the advantages that:
1) the invention establishes a prediction model of gas production and cracking of the high-energy solid propellant grain, and realizes non-destructive and quantitative evaluation of gas production and cracking time of a large-scale engine.
2) The method for predicting the integrity of the charging storage structure of the large-scale engine is small in sample consumption, and can safely, simply, conveniently and quickly predict the integrity of the charging storage structure of the large-scale engine.
Detailed Description
The present invention will be described in further detail below with reference to specific embodiments in order to make the present invention better understood by those skilled in the art.
A method for predicting the time for generating holes or cracks by gas generation of high-energy solid propellant grains comprises the following steps:
(1) selecting an engine charge formula, and measuring the radius r of the engine charge column2High temperature and Normal temperature (temperature is denoted as T respectively)1And T2) Maximum tensile strength σ of lower propellantm.1And σm.2。
(2) And (5) testing the thermal weight loss rate. Cutting propellant samples into cubes with certain side length, sealing and then respectively putting the cut propellant samples into a high-temperature test box and a dryer for normal-temperature storage, regularly weighing the sample mass of the samples under two storage conditions, calculating the thermal weight loss ratio, and respectively recording the thermal weight loss ratio as R and Rw,t,1/tR,1、Rw,t,2/tR,2。
(3) And carrying out a high-temperature accelerated gas production cracking test. Cutting the sample into pieces with radius r1The side length is more than or equal to 3r1Cylinder at a temperature T1In the high-temperature test box, the sampling time is reasonably arranged, the sample is taken out from the oven, and the section is cut and observed. The end point of the test is when cracks or air holes are observed in the section, and the time is recorded as t1。
(4) From the above data, according to formula (1) shown in the specification, the time of cracking due to gas generation under the normal temperature storage condition of the engine can be predicted.
Example 2
The method for predicting the time for generating holes or cracks by gas generation of the high-energy solid propellant grains comprises the following steps:
1) the NEPE propellant has engine charge column diameter of 200mm and tensile strengths at 90 deg.C and 25 deg.Cm,90℃0.32MPa (test temperature 90 ℃, pull rate 2mm/min) and σm,25℃0.62MPa (test temperature 25 ℃, pull rate 2 mm/min).
2) The propellant sample is cut into cubes with certain side length, the cubes are sealed and then are respectively placed into a constant temperature box at 90 ℃ and a constant temperature drier at 25 ℃, and the thermal weight loss rate at different temperatures is shown in table 1.
TABLE 1 thermal weight loss ratio of propellant at different temperatures
T/℃ tR/day Rw,/％
90 11 0.77
25 1032 0.28
3) The propellant is made into a cylinder with the diameter of 20mm and the height of 90mm, and the cylinder is put into a thermostat with the temperature of 90 ℃. The cut observation section is taken out periodically. The end point of the test is observed when cracks or air holes are observed in the cut surface. The cracking time was recorded as tb,1＝6d。
4) The results of the thermal weight loss test, the gas generation cracking test and the mechanical property test at two temperatures show that:
T1＝90℃＝363.15K，r1＝10mm，tR,1＝11d,Rw,t1＝0.77％，t1＝6d，P1＝σm,90℃＝0.32MPa
T2＝25℃＝298.15K，r2＝100mm，tR,2＝1032d，Rw,t2＝0.28％，P2＝σm,25℃＝0.62MPa
substituting the data into
Figure BDA0002059627800000061
Calculating the cracking time t of the engine grain at normal temperature2＝t25℃Approximately equal to 17.7a, namely the normal-temperature storage cracking time of the engine with the radius of 200mm is at least 17.7 a.
Example 3
1) The tensile strength of certain formula NEPE propellant at 90 ℃ and 70 ℃ is respectively sigmam,90℃0.33MPa (test temperature 90 ℃, pull rate 2mm/min) and σm,25℃0.38MPa (test temperature 70 ℃, pull rate 2 mm/min).
2) The propellant sample is cut into cubes with certain side length, the cubes are sealed and then are respectively placed into a constant temperature box at 90 ℃ and a constant temperature drier at 70 ℃, and the thermal weight loss rate at different temperatures is shown in table 2.
TABLE 2 thermal weight loss ratio of propellant at different temperatures
T/℃ tR/day Rw,/％
90 14 0.72
70 234 0.47
3) The propellant is made into cylinders with the diameter of 20mm and the height of 90mm, and the cylinders are respectively put into thermostats at 90 ℃ and 70 ℃. The cut observation section is taken out periodically. The end point of the test is observed when cracks or air holes are observed in the cut surface. The cracking time was recorded as tb,1＝6d、tb,2＝96d。
4) The results of the thermal weight loss test, the gas generation cracking test and the mechanical property test at two temperatures show that:
T1＝90℃＝363.15K，r1＝10mm，tR,1＝14d,Rw,t1＝0.72％，t1＝6d，P1＝σm,90℃＝0.33MPa；
T2＝℃＝243.15K，r2＝10mm，tR,2＝234d，Rw,t2＝0.47％，P2＝σm,25℃＝0.38MPa；
substituting the data into
Figure BDA0002059627800000062
Determine the propulsion at 70 DEG CTime to crack of agent sample t2＝t75℃91 d. The actual gas production cracking time t at 70 ℃ of the propellantb,2Compared with 96d, the method for estimating the gas generation and cracking time of the high-energy solid propellant grain in normal-temperature storage is safer.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (5)

1. A method for predicting the time for generating holes or cracks by the gas generation of high-energy solid propellant grains is characterized in that the method is based on a prediction model of the time for generating holes or cracks by the gas generation of the high-energy solid propellant grains with tensile strength, weight loss rate, grain size, time and temperature T, and the prediction model is represented by the following formula (1):
Figure FDA0003116976990000011
wherein:
σm,1、σm,2respectively high-energy solid propellant grains at T1、T2Maximum tensile strength at two different temperatures;
Rw,t,1、Rw,t,2respectively high-energy solid propellant grain at temperature T1Elapsed time tR,1Later weight loss rate, and at temperature T2Elapsed time tR,2The later weight loss rate is dimensionless;
tR,1、tR,2respectively at a temperature T1When the weight loss rate of the high-energy solid propellant grain reaches Rw,t1Time elapsed, and temperature T2When the weight loss rate of the high-energy solid propellant grain reaches Rw,t2Time elapsed in units of day;
T1、T2respectively two different test temperatures, where T2The conventional storage temperature of the high-energy solid propellant grain;
r1the radius r of a small-size solid propellant sample is reduced according to the equal proportion of a high-energy solid propellant grain2The radius of the high-energy solid propellant grain;
t1in order to generate holes or cracks according to the time of the small-size solid propellant samples with the same specific shrinkage of the high-energy solid propellant grains, t2Time to produce a perforation or crack for the high energy solid propellant charge;
e is the base of the natural logarithm and has a value equal to about 2.71828;
the method comprises the following steps:
preparing a small-size solid propellant sample which is reduced according to the equal proportion of the high-energy solid propellant grains, and measuring the radius r of the small-size solid propellant sample1While measuring the radius r of the engine charge2，；
Developing propellant sample high temperature T1And normal temperature T2Thermogravimetric testing under conditions of recording Rw,t,1，Rw,t,2，tR,1，tR,2；
Determination of propellant sample high temperature T1And normal temperature T2Tensile Strength σm,1And σm,2；
Determination of high temperature T of small-sized solid propellant sample1Time t for generating holes or cracking by generated gas1(ii) a Then, the measured parameters are brought into the prediction model of the formula (1) to obtain the time t for generating holes or cracking by gas generation of the high-energy solid propellant grain engine grain under the normal-temperature storage condition2。
2. The method for predicting the gas generation and perforation or cracking time of the high-energy solid propellant grain according to claim 1, wherein the establishment of the prediction model shown in the formula (1) comprises the following steps:
s11, setting the time T for a certain high-energy solid propellant grain to pass by at the temperature TRAfter weight lossRate RwThe amount of the gaseous substance generated per unit mass and per unit time at that temperature is expressed by the following formula (2):
Figure FDA0003116976990000012
wherein:
tRwhen the temperature is T, the weight loss rate of the high-energy solid propellant grain sample reaches RwElapsed time, day;
Rw,t-at temperature T, sample of high energy solid propellant charge over time TRThe later weight loss rate is dimensionless;
average molar mass, g.mol, of gas generated by decomposition of M-high energy solid propellant grains-1；
S12, determining the conclusion that the rate of thermal weight loss of the propellant is constant at different temperatures according to experimental research results, and obtaining the gas production rate of the high-energy solid propellant grain per unit volume at a certain temperature according to the relation V between the volume and the mass and the density as W/rho shown in the formula (3):
Figure FDA0003116976990000021
wherein:
Figure FDA0003116976990000022
is a constant;
q-the rate of gas generation per unit volume of the high-energy solid propellant charge at the temperature T, i.e. the amount of gas product in the high-energy solid propellant charge per unit time and unit volume, mol m-3·day-1；
Rho-density of solid propellant, kg m-3；
S13, theoretical analysis and experimental verification show that when the temperature is constant, the gas accumulation concentration at the center of the high-energy solid propellant grain is in exponential growth relation with the radius r of the grain, and the gas production rate of the propellant gas product per unit volume at the center is represented by the formula (4):
q′＝q·k′er (4)
wherein when q' is temperature T, the gas production rate per unit volume of propellant gas product at the center of the high-energy solid propellant grain with radius r is mol.m-3·day-1(ii) a k' is a constant;
s14, according to Henry' S law, the internal stress of the center of the propellant is equal to the pressure of generated gas, and the calculation formula is shown as formula (5):
p＝qvt/H (5)
in the formula:
t-storage time, day, of the high-energy solid propellant grain;
h-coefficient of solubility of the gas formed in volume in solid propellants, m.Pa-1·m-3；
p-the pressure, Pa, to which the high-energy solid propellant grains are subjected;
qvgas production in m day per unit volume of propellant at the centre of the high-energy solid propellant grain expressed as gas production volume-1·m-3；
S15 equation of state of ideal gas
Figure FDA0003116976990000023
And obtaining the gas production rate of the propellant in unit volume at the center of the high-energy solid propellant grain expressed by the gas production volume as qvThe calculation formula is shown as formula (6):
Figure FDA0003116976990000024
in the formula:
p is the pressure, Pa, to which the high-energy solid propellant grains are subjected;
r-gas constant, 8.314J. mol-1·K-1；
T-propellant storage temperature, K;
substituting equation (6) into equation (5) yields equation (7):
Figure FDA0003116976990000031
s16, because the density rho of the propellant and the average molecular weight M of the generated gas at room temperature are basically unchanged at different temperatures, the relationship of the pressures received by the high-energy solid propellant grains at different temperatures and storage times is obtained by the formulas (3), (4) and (7), see the formula (8):
Figure FDA0003116976990000032
wherein:
P1、P2respectively high-energy solid propellant grains at T1、T2The maximum pressure that can be withstood at two different temperatures;
s17, assuming that the dissolution parameter of the decomposition product gas in the propellant does not change with the temperature, i.e. letting H2/H1＝1；
Then converting the formula (8) into the relation of the cracking time of the high-energy solid propellant grain due to gas generation at different temperatures, see the formula (9):
Figure FDA0003116976990000033
s18, when the internal pressure of the high-energy solid propellant grain reaches or exceeds the maximum tensile strength of the propellant, setting the high-energy solid propellant grain to crack, and writing the formula (9) as shown in the formula (1):
Figure FDA0003116976990000034
3. the method for predicting gas generation and perforation or cracking time of high-energy solid propellant grain according to claim 1Method, characterized in that the high-energy solid propellant grains are at a temperature T1Maximum tensile strength σ ofm,1And at a temperature T2Maximum tensile strength σ ofm,2Obtained by measuring a dumbbell-shaped solid propellant sample with the same component as the high-energy solid propellant grain.
4. The method for predicting the gas generation perforation or cracking time of the high-energy solid propellant grain according to claim 1, wherein the high-energy solid propellant grain is at a temperature T1Elapsed time tR,1Later weight loss ratio Rw,t1And at a temperature T2Elapsed time tR,2Later weight loss ratio Rw,t2Obtained by measuring the thermal weight loss rate of a cubic propellant sample with the same components as the high-energy solid propellant grains.
5. The method for predicting the gas generation and perforation or cracking time of the high-energy solid propellant grain according to claim 3 or 4, wherein the size of the dumbbell-shaped solid propellant sample and/or the cubic propellant sample is significantly smaller than that of the high-energy solid propellant grain.
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