CN116246720A - Calculation method of swelling force of high polymer slurry - Google Patents
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- 239000002002 slurry Substances 0.000 title claims abstract description 194
- 229920000642 polymer Polymers 0.000 title claims abstract description 70
- 238000004364 calculation method Methods 0.000 title claims abstract description 26
- 230000008961 swelling Effects 0.000 title claims description 12
- 238000006243 chemical reaction Methods 0.000 claims abstract description 78
- 238000000034 method Methods 0.000 claims abstract description 23
- 230000008859 change Effects 0.000 claims abstract description 14
- 229920005862 polyol Polymers 0.000 claims abstract description 14
- 150000003077 polyols Chemical class 0.000 claims abstract description 14
- 239000012948 isocyanate Substances 0.000 claims abstract description 12
- 150000002513 isocyanates Chemical class 0.000 claims abstract description 12
- 230000008569 process Effects 0.000 claims abstract description 10
- CURLTUGMZLYLDI-UHFFFAOYSA-N Carbon dioxide Chemical compound O=C=O CURLTUGMZLYLDI-UHFFFAOYSA-N 0.000 claims description 58
- 239000004088 foaming agent Substances 0.000 claims description 31
- 229910002092 carbon dioxide Inorganic materials 0.000 claims description 29
- 239000001569 carbon dioxide Substances 0.000 claims description 26
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 19
- 238000005187 foaming Methods 0.000 claims description 16
- 239000004604 Blowing Agent Substances 0.000 claims description 15
- 239000007788 liquid Substances 0.000 claims description 12
- 229920002635 polyurethane Polymers 0.000 claims description 8
- 239000004814 polyurethane Substances 0.000 claims description 8
- 238000002309 gasification Methods 0.000 claims description 6
- 125000002887 hydroxy group Chemical group [H]O* 0.000 claims description 5
- 230000004913 activation Effects 0.000 claims description 3
- 208000012839 conversion disease Diseases 0.000 claims description 3
- 238000010521 absorption reaction Methods 0.000 claims description 2
- 238000001704 evaporation Methods 0.000 claims description 2
- 230000008020 evaporation Effects 0.000 claims description 2
- 238000001879 gelation Methods 0.000 claims 2
- 230000007246 mechanism Effects 0.000 abstract description 6
- 238000009792 diffusion process Methods 0.000 abstract description 4
- 230000003993 interaction Effects 0.000 abstract description 2
- 238000011160 research Methods 0.000 abstract description 2
- 230000036962 time dependent Effects 0.000 abstract description 2
- 238000012360 testing method Methods 0.000 description 9
- 238000009834 vaporization Methods 0.000 description 4
- 230000008016 vaporization Effects 0.000 description 4
- 230000009471 action Effects 0.000 description 3
- 238000004458 analytical method Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 239000000203 mixture Substances 0.000 description 2
- 230000003014 reinforcing effect Effects 0.000 description 2
- 239000000654 additive Substances 0.000 description 1
- 150000001412 amines Chemical class 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 229910002090 carbon oxide Inorganic materials 0.000 description 1
- 239000003054 catalyst Substances 0.000 description 1
- 238000005056 compaction Methods 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 238000001125 extrusion Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000006116 polymerization reaction Methods 0.000 description 1
- 229920005903 polyol mixture Polymers 0.000 description 1
- 230000036632 reaction speed Effects 0.000 description 1
- 239000011435 rock Substances 0.000 description 1
- 239000002689 soil Substances 0.000 description 1
- 230000002522 swelling effect Effects 0.000 description 1
- DQWPFSLDHJDLRL-UHFFFAOYSA-N triethyl phosphate Chemical compound CCOP(=O)(OCC)OCC DQWPFSLDHJDLRL-UHFFFAOYSA-N 0.000 description 1
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Abstract
The invention discloses a method for calculating the expansion force of high polymer slurry, which comprises the following steps: initializing related variables according to the proportion of each component of the slurry; solving a chemical reaction kinetic equation of the high polymer slurry by a Runge-Kutta algorithm to obtain the conversion rate change amount of isocyanate and polyol in the current time step; solving an energy balance equation to obtain the slurry temperature change amount, and accumulating to obtain the current slurry temperature; solving the slurry volume by combining an ideal gas state equation and determining a slurry expansion stage; setting the confining pressure of the slurry to be atmospheric pressure at the stage that the slurry is not filled in the slurry cavity, and freely expanding the volume of the slurry; after the slurry is filled in the slurry cavity, fixing the volume of the slurry, and calculating the expansion force of the slurry; updating parameters of density, volume, pressure and temperature according to the calculation result, and advancing the time step; the invention can solve the time-dependent change process of the expansion force of the high polymer slurry in real time, and lays a foundation for the deep research of the expansion and diffusion mechanism of the high polymer and the slurry-stratum interaction mechanism.
Description
Technical Field
The invention relates to the technical field of hydraulic engineering, in particular to a calculation method of swelling force of high polymer slurry.
Background
The high polymer grouting technology is widely used for civil engineering and hydraulic engineering such as highways, tunnels, dams, bridge engineering and the like due to the characteristics of rapid chemical reaction, large volume expansion rate, good durability, environmental protection and safety, and the like.
The principle of high polymer grouting is that the two-component high polymer slurry is injected into a medium, and the purposes of filling gaps, splitting a compaction soil body, lifting an upper structure, plugging leakage channels and reinforcing rock mass are realized by utilizing the characteristic that the volume of the slurry is rapidly expanded and solidified after the slurry reacts. The method is used for accurately mastering the change rule of the expansion force along with time in the high polymer slurry diffusion process, and is a key for researching the high polymer grouting repairing and reinforcing mechanism.
The carbon dioxide gas generated by the foaming reaction and the physical blowing agent are vaporized as the main causes for the expansion of the polymer slurry. The heat of reaction of the foaming reaction and the gelling reaction promotes vaporization of the physical foaming agent and an increase in gas volume, so that the expansion of the polymer slurry is a result of the combined action of the chemical reaction and the physical foaming agent. When the polymer slurry expansion process is constrained, a compressive force is generated on the surrounding medium.
The current research on the swelling properties of polymer slurries is still relatively poor. Based on the experimental expression of slurry density-expansion force obtained by the test, although a basis is provided for determining the expansion force of the high polymer slurry to a certain extent, only the final expansion force corresponding to the specific slurry density can be obtained, the time course change of the expansion force and the density in the reaction process of the high polymer cannot be reflected, the accuracy of calculation and analysis is restricted, and the guidance is difficult to provide for accurate grouting under the complex pressure environment. Because the expansion force of the high polymer is closely related to factors such as the chemical reaction progress of the slurry, the constraint condition of surrounding medium and the like, the expansion pressure of the high polymer slurry acting on the surrounding medium is continuously changed along with time in a certain grouting environment, the diffusion behavior of the high polymer slurry is closely related to the evolution process of the expansion pressure, and how to accurately calculate the expansion force of the high polymer slurry at different moments is not known at present.
Disclosure of Invention
The invention aims to provide a calculation method of the expansion force of polymer slurry, which solves the problems that the prior art only can obtain the final expansion force corresponding to specific slurry density, cannot reflect time course changes of the expansion force and density in the reaction process of the polymer, restricts the accuracy of calculation and analysis, is difficult to provide guidance for accurate grouting under a complex pressure environment, and is not effective in calculating how to accurately calculate the expansion force of the polymer slurry at different moments.
The invention is realized in that a method for calculating the swelling force of polymer slurry comprises the following steps:
initializing variables according to volume fixed boundary conditions and the distribution ratio of each component of the slurry, wherein the variables comprise pressure, slurry temperature, density and molar density;
solving a chemical reaction kinetic equation of the high polymer slurry in the current time step through a Runge-Kutta algorithm to obtain the conversion rate change amount of isocyanate and polyol;
step three, solving an energy balance equation to obtain a slurry temperature change amount, and accumulating to obtain the current slurry temperature;
step four, solving the slurry volume through an ideal gas state equation, so as to judge the slurry expansion stage;
step five, selecting different boundary conditions and calculation formulas according to different slurry expansion stages: setting the confining pressure of the fixed slurry to be 0.1MPa in the stage that the slurry is not filled in the slurry cavity, and freely expanding the volume of the slurry; after the slurry is filled in the slurry cavity, fixing the volume of the slurry, and calculating the expansion force of the slurry;
step six, updating parameters according to the new calculation result, wherein the parameters comprise density, volume, pressure, temperature and the reaction conversion rate of isocyanate and polyol components;
step seven, advancing the time step, and repeating the step two to the step six.
The invention further adopts the technical scheme that: the chemical reaction kinetic equation of the high polymer slurry in the second step comprises a gel reaction rate equation of the polyurethane high polymer slurry and a slurry foaming reaction rate equation, wherein the gel reaction rate equation of the polyurethane high polymer slurry is as follows:
the slurry foaming reaction rate equation is:
wherein c i,0 And X i The initial concentration and conversion of component i, respectively, i W, OH and NCO, respectively, represent water, polyol and isocyanate, A OH And A W Pre-finger factors, E, of the gelling and foaming reactions, respectively OH And E is W The activation energy of two reactions, r W R is the mass fraction of water BL Is the mass fraction of the liquid physical foaming agent, ρ BL For the density of the physical blowing agent ρ W Is the density of water ρ P Polyurethane density, R is the ideal gas constant, T is the slurry temperature.
The invention further adopts the technical scheme that: the second-order Runge-Kutta algorithm adopts a fourth-order Runge-Kutta algorithm to solve a chemical reaction kinetic equation, and the mathematical description of the fourth-order Runge-Kutta algorithm is as follows for a normal differential equation of the shape y' =f (x, y):
k 1 ＝f(x n ,y n )
k 4 ＝f(x n +h,y n +hk 3 )
wherein: h represents the time step selected in the calculation process, 0.1s is adopted in the program, the independent variable x is the time step, the dependent variable y is the conversion rate of hydroxyl or water in the chemical reaction, and k 1 Represents x n Slope at point; k (k) 2 Representation using k 1 X is calculated n Slope at +h/2 point; k (k) 3 Representation using k 2 X is calculated n Slope at +h/2 point; k (k) 4 Representation using k 3 X is calculated n Slope at +h point. The higher the order of the Dragon's library tower algorithm, the more accurate the calculation result.
The conversion of the components can be obtained by solving the above kinetic equation.
The invention further adopts the technical scheme that: substituting the conversion rate of hydroxyl and water obtained according to a range-Kutta algorithm into an energy balance equation, solving the energy balance equation to obtain a slurry temperature change amount, and accumulating to obtain the current slurry temperature, wherein in the step three, the energy balance equation of the self-expansion type high polymer slurry under the adiabatic condition is as follows:
wherein: c (C) P Is the heat capacity of the high polymer slurry,
is two (two)Carbon oxide heat capacity, C W Is the heat capacity of water, C BG Heat capacity of gaseous physical foaming agent, C BL Is the heat capacity of the liquid physical foaming agent +.>
Is the mass fraction of carbon dioxide, r W R is the mass fraction of water BG Is the mass fraction of the gaseous physical foaming agent, delta H OH As the reaction heat of the gel, delta H W Lambda is the evaporation heat absorption of the physical foaming agent for the heat of foaming reaction.
The invention further adopts the technical scheme that: in the fourth step, the slurry volume is solved through an ideal gas state equation: the initial stage is a slurry free expansion stage, the confining pressure of the fixed slurry is set to be 0.1MPa, and the volume of the slurry is calculated; judging the slurry expansion stage through the slurry volume: when the size is smaller than the cavity size, the size is not filled in the size cavity; the slurry has filled the cavity when the volume of the slurry is equal to or greater than the volume of the cavity.
The invention further adopts the technical scheme that: carbon dioxide gas generation amount in the chemical reaction process:
wherein m is 0 For the total mass of the high polymer slurry,
is carbon dioxide molar mass->
Initial mass fraction for carbon dioxide;
physical foaming agent gasification amount in the chemical reaction process:
r BG ＝r BL,0 -r BL
wherein r is BL,0 Represents the initial mass fraction of the liquid physical foaming agent, M B Represents the physical blowing agent molar mass;
according to an ideal gas state equation pv=nrt, under the condition of a certain pressure, the volume occupied by the gas is:
V＝(n CO2 +n BG ) RT/p can obtain slurry volume through gas volume and slurry original volume.
The invention further adopts the technical scheme that: in the fifth step, the carbon dioxide gas generation amount in the chemical reaction process is as follows:
wherein m is 0 For the total mass of the high polymer slurry,
is carbon dioxide molar mass->
Initial mass fraction for carbon dioxide;
physical foaming agent gasification amount in the chemical reaction process:
r BG ＝r BL,0 -r BL
wherein r is BL,0 Represents the initial mass fraction of the liquid physical foaming agent, M B Representation objectThe molar mass of the foaming agent is managed;
according to the ideal gas state equation pv=nrt, in the case of a certain volume, the pressure generated by the gas is:
The carbon dioxide gas generated by the foaming reaction and the physical blowing agent are vaporized as the main causes for the expansion of the polymer slurry. The heat of reaction of the foaming reaction and the gelling reaction promotes vaporization of the physical foaming agent and an increase in gas volume, so that the expansion of the polymer slurry is a result of the combined action of the chemical reaction and the physical foaming agent. When the polymer slurry expansion process is constrained, a compressive force is generated on the surrounding medium.
The invention has the beneficial effects that: the invention is based on the principle of conservation of energy, considers the slurry polymerization reaction mechanism, solves the chemical reaction kinetic equation describing the high polymer slurry reaction process by using a Dragon-Greek tower method, combines with an ideal gas state equation, improves the accuracy of calculating the high polymer slurry expansion force, can solve the time-dependent change process of the high polymer slurry expansion force in real time, and lays a foundation for further researching the high polymer expansion diffusion mechanism and the slurry-stratum interaction mechanism under different conditions;
the carbon dioxide gas generated by the foaming reaction and the physical blowing agent are vaporized as the main causes for the expansion of the polymer slurry. The heat of reaction of the foaming reaction and the gelling reaction promotes vaporization of the physical foaming agent and an increase in gas volume, so that the expansion of the polymer slurry is a result of the combined action of the chemical reaction and the physical foaming agent. When the high polymer slurry expansion process is restrained, the extrusion force is generated to the surrounding medium to be the high polymer slurry expansion force;
the initial stage is a slurry free expansion stage, the confining pressure of the fixed slurry is set to be 0.1MPa, and the volume of the slurry is calculated through an ideal gas state equation; judging the slurry expansion stage through the slurry volume: when the size is smaller than the cavity size, the size is not filled in the size cavity; when the volume of the slurry is larger than or equal to the volume of the cavity, the slurry is filled in the cavity, the volume of the slurry is fixed, and the expansion force of the slurry is calculated.
Drawings
FIG. 1 is a flow chart of a method of calculating the swelling force of a polymer slurry;
FIG. 2 shows a slurry density of 375 kg.m -3 A comparison chart of the time expansion force calculation result and the test value;
FIG. 3 shows a slurry density of 500 kg.m -3 A comparison chart of the time expansion force calculation result and the test value;
FIG. 4 shows a slurry density of 625 kg.m -3 A comparison chart of the time expansion force calculation result and the test value;
FIG. 5 shows a slurry density of 750 kg.m -3 A comparison chart of the time expansion force calculation result and the test value;
FIG. 6 shows the final densities of the slurries obtained by calculation of 800 kg.m -3 、850kg·m -3 、900kg·m -3 And 950 kg.m -3 Time course change curve of slurry expansion force.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention.
It should be noted that, the structures, proportions, sizes and the like shown in the drawings attached to the present specification are used for understanding and reading only in conjunction with the disclosure of the present specification, and are not intended to limit the applicable limitations of the present invention, so that any modification of the structures, variation of proportions or adjustment of sizes of the structures, proportions and the like should not be construed as essential to the present invention, and should still fall within the scope of the disclosure of the present invention without affecting the efficacy and achievement of the present invention. Also, the terms such as "upper," "lower," "left," "right," "middle," and "a" and the like recited in the present specification are merely for descriptive purposes and are not intended to limit the scope of the invention, but are intended to provide relative positional changes or modifications without materially altering the technical context in which the invention may be practiced.
Example 1:
the polymer slurry used in the test contained two components A and B, component A being isocyanate (PAPI), component B being a mixture of polyol, triethyl phosphate, physical blowing agent, amine catalyst and other additives. The mass percentages of each component relative to the polyol mixture are shown in table 1.
TABLE 1 composition of component B
The invention is realized by the following technical scheme:
a method for calculating the swelling power of a slurry of a polymer in consideration of chemical reaction, as shown in fig. 1, comprising the steps of:
step one, initializing all variables such as pressure, slurry temperature, density and molar density according to volume fixed boundary conditions and the distribution ratio of each component of the slurry.
The boundary condition is a fixed volume, the initial cavity volume is 3.33X10 -4 m 3 The initial density of the polyurethane-polymer slurry was 1140kg/m 3 The initial temperature was set at 305.15K.
And step two, solving a chemical reaction kinetic equation of the high polymer slurry in the current time step through a fourth-order Runge-Kutta algorithm to obtain the conversion rate change amount of isocyanate and polyol components.
The gel reaction rate equation of the polyurethane high polymer slurry is:
the slurry foaming reaction rate equation is:
wherein c i,0 And X i The initial concentration and conversion of component i are shown, respectively. i is W, OH and NCO represent water, polyol and isocyanate, respectively. Slurry pre-finger factor A OH 2.6460m 3 ·s -1 ·mol -1 ，A W 27.457m 3 ·s -1 ·mol -1 Activation energy E OH 35552.47 J.mol -1 ·K -1 ，E W 40175.42 J.mol -1 ·K -1 。r W R is the mass fraction of water BL Is the mass fraction of the liquid physical foaming agent, ρ BL For the density of the physical blowing agent ρ W 1000kg/m 3 ，ρ P 1140kg/m 3 R is 8.314J/(mol.K), polyol concentration c at initial time OH,0 2692.0 mol.m -3 Isocyanate concentration c NCO,0 Is 10430 mol.m -3 ；
And thirdly, solving an energy equation to obtain the slurry temperature change amount, and accumulating to obtain the current slurry temperature.
The energy balance equation of the self-expanding polymer slurry under the adiabatic condition is as follows:
wherein: specific heat C of polyurethane P 1800 J.kg -1 ·K -1 Heat capacity of carbon dioxide
1800 J.kg -1 ·K -1 Is the heat capacity C of water W 4200 J.kg -1 ·K -1 Specific heat C of gaseous physical blowing agent BG 1000 J.kg -1 ·K -1 Specific heat C of liquid physical foaming agent BL 1159 J.kg -1 ·K -1 ，
Is the mass fraction of carbon dioxide, r W R is the mass fraction of water BG The mass fraction of the gaseous physical blowing agent is the reaction heat (-delta H) of the polyol OH 7.075×10 4 J/g equiv，ΔH W For the heat of foaming reaction, the physical blowing agent had a heat of vaporization lambda of 206.8 kJ.kg -1 Polyol concentration at initial time ++>
2692.0 mol.m -3 The conversion rate of hydroxyl and water obtained according to the Runge-Kutta algorithm is substituted into an energy equation, so that the slurry temperature at different moments can be obtained;
step four, solving the slurry volume through an ideal gas state equation, so as to judge the slurry expansion stage;
the initial stage is a slurry free expansion stage, the confining pressure of the fixed slurry is set to be 0.1MPa, and the volume of the slurry is calculated through an ideal gas state equation; judging the slurry expansion stage through the slurry volume: when the size is smaller than the cavity size, the size is not filled in the size cavity; the slurry has filled the cavity when the volume of the slurry is equal to or greater than the volume of the cavity.
Specifically, the carbon dioxide gas generation amount in the chemical reaction process is as follows:
wherein m is 0 For the total mass of the high polymer slurry,
is carbon dioxide molar mass->
Initial mass fraction for carbon dioxide；
Physical foaming agent gasification amount in the chemical reaction process:
r BG ＝r BL,0 -r BL
wherein r is BL,0 Represents the initial mass fraction of the liquid physical foaming agent, M B Represents the physical blowing agent molar mass;
according to an ideal gas state equation pv=nrt, under the condition of a certain pressure, p=0.1 MPa, and the volume occupied by the gas is:
V＝(n CO2 +n BG )RT/p
the slurry volume is obtained by the gas volume and the original volume of the slurry.
Step five, selecting different boundary conditions and calculation formulas according to different slurry expansion stages: setting the confining pressure of the fixed slurry to be 0.1MPa in the stage that the slurry is not filled in the slurry cavity, and freely expanding the volume of the slurry; after the slurry is filled in the slurry cavity, fixing the volume of the slurry, and calculating the expansion force of the slurry; i.e., the slurry fills the slurry chamber, the gas generates a pressure that is the expansion force of the polymer slurry.
Carbon dioxide gas generation amount in the chemical reaction process:
wherein m is 0 For the total mass of the high polymer slurry,
is carbon dioxide molar mass->
Initial mass fraction for carbon dioxide;
physical foaming agent gasification amount in the chemical reaction process:
r BG ＝r BL,0 -r BL
wherein r is BL,0 Represents the initial mass fraction of the liquid physical foaming agent, M B Represents the physical blowing agent molar mass;
according to the ideal gas state equation pv=nrt, in the case of a certain volume, the pressure generated by the gas is:
wherein T is the temperature of the slurry, and V is the volume of the cavity of 3.33X10 -4 m 3 。
And step six, updating the density, volume, pressure, temperature and the reaction conversion rate of isocyanate and polyol components according to the new calculation result, advancing the time step, and repeating the steps two to five. The slurry expansion force at different moments can be obtained.
Solving the calculation method, the following assumption is made:
(1) The high polymer slurry has high reaction speed, and the expansion process is assumed to be in an adiabatic environment, so that heat exchange with the outside is avoided, and the influence of heat conduction is ignored;
(2) The reaction rate and density of each part of the slurry are the same.
And (3) analysis of calculation results:
FIGS. 2 to 5 show the slurry densities of 375 kg.m calculated under fixed volume conditions, respectively -3 、500kg·m -3 、625kg·m -3 And 750 kg.m -3 A comparison chart of the time expansion force calculation result and the test value; the final expansion force calculated values of the slurry under four working conditions are respectively 0.358MPa, 0.587MPa, 0.916MPa and 1.456MPa, and the test values are respectively 0.365MPa, 0.581MPa, 0.898MPa and 1.420MPa, and the relative errors of the two are respectively 1.92%, 1.03%, 2.00% and 2.53%. It can be seen that the slurry expansion force obtained by calculation under different working conditions has better matching trend with the test result along with time, and the final expansion force value is basically equal.
FIG. 6 shows the slurry density of 800 kg.m calculated under a fixed volume condition -3 、850kg·m -3 、900kg·m -3 And 950 kg.m -3 The expansion force of the material changes with time.
As can be seen from fig. 6, the expansion force variation trend of the slurries with different densities is basically the same, and in the slurry expansion process, the expansion force variation speed is firstly slow and then fast, and finally slows down and gradually approaches zero, and at the same time, the expansion force of the slurry increases along with the increase of the density, and the larger the density is, the larger the expansion force increment generated by the unit density is.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (7)
1. A method for calculating the swelling force of high polymer slurry is characterized in that: the calculation method comprises the following steps:
initializing variables according to volume fixed boundary conditions and the distribution ratio of each component of the slurry, wherein the variables comprise pressure, slurry temperature, density and molar density;
solving a chemical reaction kinetic equation of the high polymer slurry in the current time step through a Runge-Kutta algorithm to obtain the conversion rate change amount of isocyanate and polyol;
step three, solving an energy balance equation to obtain a slurry temperature change amount, and accumulating to obtain the current slurry temperature;
step four, solving the slurry volume through an ideal gas state equation, so as to judge the slurry expansion stage;
step five, selecting different boundary conditions and calculation formulas according to different slurry expansion stages: setting the confining pressure of the fixed slurry to be 0.1MPa in the stage that the slurry is not filled in the slurry cavity, and freely expanding the volume of the slurry; after the slurry is filled in the slurry cavity, fixing the volume of the slurry, and calculating the expansion force of the slurry;
step six, updating parameters according to the new calculation result, wherein the parameters comprise density, volume, pressure, temperature and the reaction conversion rate of isocyanate and polyol components;
step seven, advancing in time steps, and repeating the step two to the step six to obtain the condition that the expansion force changes along with time.
2. The method according to claim 1, wherein the equation of the chemical reaction kinetics of the polymer slurry in the second step includes an equation of the gelation reaction rate of the polyurethane polymer slurry and an equation of the foaming reaction rate of the slurry, and the equation of the gelation reaction rate of the polyurethane polymer slurry is:
the slurry foaming reaction rate equation is:
wherein c i,0 And X i The initial concentration and conversion of component i, respectively, i W, OH and NCO, respectively, represent water, polyol and isocyanate, A OH And A W Pre-finger factors, E, of the gelling and foaming reactions, respectively OH And E is W The activation energy of two reactions, r W R is the mass fraction of water BL Is the mass fraction of the liquid physical foaming agent, ρ BL For the density of the physical blowing agent ρ W Is the density of water ρ P Polyurethane density, R is the ideal gas constant, T is the slurry temperature.
3. The method for calculating the swelling power of a polymer slurry according to claim 1 or 2, wherein the step two-run-Kutta algorithm solves a chemical reaction rate equation using a fourth-order run-Kutta algorithm, and the fourth-order run-Kutta algorithm is described in terms of a normal differential equation of y' =f (x, y) as follows:
k 1 ＝f(x n ,y n )
k 4 ＝f(x n +h,y n +hk 3 )
wherein: h represents the time step selected in the calculation process, the independent variable x n The variable y is the conversion rate of hydroxyl or water in the chemical reaction, k, at the beginning of the nth time step 1 Represents x n Slope at point; k (k) 2 Representation using k 1 X is calculated n Slope at +h/2 point; k (k) 3 Representation using k 2 X is calculated n Slope at +h/2 point; k (k) 4 Representation using k 3 X is calculated n Slope at +h point.
4. The method according to claim 1 or 2, wherein in the third step, the energy balance equation of the self-expanding polymer slurry under adiabatic conditions is:
wherein: c (C) P Is the heat capacity of the high polymer slurry,
is carbon dioxide heat capacity, C W Is the heat capacity of water, C BG Heat capacity of gaseous physical foaming agent, C BL Is the heat capacity of the liquid physical foaming agent +.>
Is the mass fraction of carbon dioxide, r W R is the mass fraction of water BG Is the mass fraction of the gaseous physical foaming agent, delta H OH As the reaction heat of the gel, delta H W Lambda is the evaporation heat absorption of the physical foaming agent for the heat of the foaming reaction;
and substituting the conversion rate of hydroxyl and water obtained according to the Runge-Kutta algorithm into an energy balance equation to obtain the slurry temperature at different moments.
5. The method of claim 1 or 2, wherein in the fourth step, the slurry volume is solved by an ideal gas state equation: the initial stage is a slurry free expansion stage, the confining pressure of the fixed slurry is set to be 0.1MPa, and the volume of the slurry is calculated; judging the slurry expansion stage through the slurry volume: when the size is smaller than the cavity size, the size is not filled in the size cavity; the slurry has filled the cavity when the volume of the slurry is equal to or greater than the volume of the cavity.
6. The method for calculating the swelling power of a polymer slurry according to claim 5, wherein the amount of carbon dioxide gas generated during the chemical reaction:
wherein m is 0 For the total mass of the high polymer slurry,
is carbon dioxide molar mass->
Initial mass fraction for carbon dioxide;
physical foaming agent gasification amount in the chemical reaction process:
r BG ＝r BL,0 -r BL
wherein r is BL,0 Represents the initial mass fraction of the liquid physical foaming agent, M B Represents the physical blowing agent molar mass;
according to an ideal gas state equation pv=nrt, under the condition of a certain pressure, the volume occupied by the gas is:
V＝(n CO2 +n BG )RT/p
the slurry volume is obtained.
7. The method for calculating the swelling power of a polymer slurry according to claim 1 or 2, wherein in the fifth step, the amount of carbon dioxide gas generated during the chemical reaction is:
wherein m is 0 For the total mass of the high polymer slurry,
is carbon dioxide molar mass->
Initial mass fraction for carbon dioxide;
physical foaming agent gasification amount in the chemical reaction process:
r BG ＝r BL,0 -r BL
wherein r is BL,0 Represents the initial mass fraction of the liquid physical foaming agent, M B Represents the physical blowing agent molar mass;
according to the ideal gas state equation pv=nrt, in the case of a certain volume, the pressure generated by the gas is:
the swelling power of the high polymer slurry can be obtained.
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