A method for establishing a reaction kinetics model in the preparation process of gradient nitrocellulose propellant

Abstract

The present invention discloses a method for establishing a reaction kinetics model in the preparation process of gradient nitro propellant, comprising the following steps: S1, establishing model assumptions; S2, establishing a chemical reaction-controlled mass transfer model; S3, establishing an internal diffusion-controlled mass transfer model for the solid residual film layer; S4, establishing a mixed-controlled mass transfer model for interfacial mass transfer and diffusion of the solid residual film layer; S5, experimentally verifying the models described in steps S2, S3, and S4, and comparing to obtain the optimal reaction kinetics model for the preparation process of gradient nitro propellant. The present invention clarifies that the reaction process is affected by the internal diffusion control of the solid residual film layer, and has important guiding significance for the fine regulation of the structure of the gradient nitro layer and the reaction process in the preparation of gradient nitro propellant.

Description

Technical Field

[0001] The present invention relates to the field of gunpowder, and particularly to a method for establishing a reaction kinetic model in the preparation process of gradient nitro propellant. Background Art

[0002] Achieving a high gradual increase in the energy release of propellant from slow to fast has become the core and key technology determining weapon performance, and the research on its control technology has always been a hot topic at home and abroad. The innovation and development of propellant play a huge role in promoting the improvement of weapon systems. Propellant that takes into account both the high gradual increase in energy release and low harmful phenomena is the demand for the development of weapon equipment systems. Gradient nitro propellant is a new type of propellant with a gradually increasing energy release that meets the development needs of weapon equipment systems. It uses a chemical tailoring method to make the -O-NO 2 groups be positioned, quantified, and distributed in a gradient along the surface normal direction, achieving a high gradual increase in the energy release of the propellant.

[0003] The preparation conditions of gradient nitro propellant determine the structure of the gradient nitro layer, and the structure of the gradient nitro layer determines the quality of the gradually increasing energy release of gradient nitro propellant. The preparation process of gradient nitro propellant is a solid-liquid chemical reaction process, that is, a denitration chemical reaction between solid propellant and denitration reaction solution. The mass transfer and two-phase reaction in the preparation process of gradient nitro propellant are both interfacial reactions between the solid phase (unreacted nitrocellulose, unreacted nitroglycerin, nitrocellulose with low nitrogen content, and nitroglycerin with low nitrate ester group) and the liquid phase (denitration reaction solution). Therefore, studying the interfacial chemical reaction model in the preparation process of gradient nitro propellant has important guiding significance for the structure of the gradient nitro layer of gradient nitro propellant and the refined control of the reaction process. Summary of the Invention

[0004] The present invention aims to provide a method for establishing a reaction kinetic model in the preparation process of gradient nitro propellant to guide the study of the interfacial chemical reaction model in the preparation process of gradient nitro propellant for the structure of the gradient nitro layer of gradient nitro propellant and the refined control of the reaction process.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for establishing a reaction kinetic model in the preparation process of gradient nitro propellant, comprising the following steps,

[0007] S1. Establish model assumptions:

[0008] a. Assume that the reaction system reacts under a constant temperature environment;

[0009] b. Approximately assume that the reaction interface is stationary and regard the reaction process as a pseudo-steady state process;

[0010] c. Assume that the denitration reaction is a first-order irreversible chemical reaction, and its expression is simplified as:

[0011] A(l) + bB(s) → fF(l) + sS(s) (1)

[0012] d. Assume that the gradient nitro propellant is a spherical solid;

[0013] S2. Establish a chemical reaction-controlled mass transfer model:

[0014] When the denitration reaction is controlled by a chemical reaction, the mathematical expression of the reaction model is:

[0015] 1 - (1 - x B ) 1 / 3 = k 1 t (18)

[0016] S3. Establish an internal diffusion-controlled mass transfer model for the solid residue film layer:

[0017] When the denitration reaction is controlled by the internal diffusion of the solid residue film layer, the mathematical expression of the reaction model is:

[0018]

[0019] S4. Establish a mixed-controlled mass transfer model for interfacial mass transfer and diffusion of the solid residue film layer:

[0020] When the denitration reaction is controlled by the mixed control of interfacial mass transfer and diffusion of the solid residue film layer, the mathematical expression of the reaction model is:

[0021]

[0022] S5. Experimentally verify the models described in steps S2, S3, and S4, and compare to obtain the optimal reaction kinetic model for the preparation process of the gradient nitro propellant;

[0023] In the above formula, A represents the denitration reaction solution, B represents the unreacted solid propellant, F represents the liquid product after denitration reaction, S represents the solid product after denitration reaction; x B represents the conversion rate of the solid-phase reactant B, and k 1 , k 2 , k 3 are constant coefficients.

[0024] Furthermore, step S1 further includes analyzing the denitration reaction based on the model assumptions:

[0025] (1) The external diffusion rate of the denitration reaction solution A through the stagnant film is:

[0026]

[0027] (2) The internal diffusion rate of the denitrification reaction liquid A through the solid residue film layer is:

[0028]

[0029] Among them,

[0030]

[0031] (3) The chemical reaction rate of the first-order irreversible reaction between the denitrification reaction liquid A and the unreacted solid propellant B is:

[0032]

[0033] (4) The relationship between the radius R c of the unreacted core and the reaction time is:

[0034]

[0035] (5) The conversion rate x B of the solid-phase reactant B and R c is:

[0036]

[0037] In the above formula, k G is the mass transfer coefficient of the denitrification reaction liquid A, with the unit of m / s; C 0 is the concentration of the unreacted denitrification liquid; C s is the concentration of the denitrification liquid on the outer surface of the propellant; D eff is the effective diffusion coefficient of component A in the solid residue film layer, with the unit of m 2 / s; C A is the concentration of the reaction denitrification solution at R = R c .

[0038] Furthermore, the experiment in step S5 includes:

[0039] Step 1: Dissolve 3.54 g of hydrazine hydrate with a concentration of 80 wt% into 16.5 mL of deionized water to prepare a hydrazine hydrate solution with a concentration of 14.15%;

[0040] Step 2: Preheat the prepared solution to 30 °C, weigh 10 g of dry spherical propellant, place the propellant in a 150 mL three-necked flask with a stirring device, pour the preheated hydrazine hydrate-aqueous solution, and carry out denitrification reaction under the conditions of heating in a 30 °C water bath and a stirring speed of 260 rap / min. After the reaction for 4 h, stop the reaction, filter to remove the reaction solution, and obtain the denitrified propellant;

[0041] Step 3: Place the denitrified propellant in deionized water for boiling and washing to remove the hydrazine hydrate remaining on the surface of the propellant grains. The boiling and washing temperature is 80 °C, and the boiling and washing time is 30 min;

[0042] Step 4: Place the boiled and washed propellant in a water bath oven at 60 °C for drying, and the drying duration is 48 h;

[0043] Step 5: Weigh the dried propellant, record the mass data of the dried propellant before and after the experiment, and calculate the corresponding denitrification percentage;

[0044] Step 6: Repeat Steps 1 to 5, set up another three experiments, and extend the reaction times to 6 h, 8 h, and 12 h respectively. Linearly fit the experimental data according to the models described in Steps S2, S3, and S4;

[0045] Step 7: Repeat Steps 1 to 6, set up another three groups of experiments, and adjust the denitrification reaction temperature and set the reaction times at the corresponding reaction temperatures;

[0046] Step 8: According to the fitted linear correlation coefficient R 2 , obtain the optimal reaction kinetic model for the preparation process of gradient nitro propellant.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] The present invention uses the research method of the shrinking unreacted core model in the chemical reaction process to establish and deduce the solid-liquid chemical reaction model for the preparation process of gradient nitro propellant, and uses a simple weighing method to verify the established model, clarifying that the reaction process is affected by the internal diffusion control of the solid residual film layer. Establishing the reaction kinetic model for the preparation process of gradient nitro propellant will provide an important guiding role for the preparation of the gradient nitro layer structure of gradient nitro propellant and the refined regulation of the reaction process. Description of the Drawings

[0049] Figure 1 It is a schematic diagram of the shrinking unreacted core model and the substance concentration distribution of the gradient nitro propellant of the present invention;

[0050] Figure 2 It is a schematic diagram of the actual verification scheme of the model in the preparation process of the gradient nitro propellant of the present invention;

[0051] Figure 3 It is a graph showing the variation law of the denitrification rate with time for Examples 1 to 4 of the present invention (a: 30 °C; b: 50 °C; c: 70 °C; d: 90 °C);

[0052] Figure 4 It is a data fitting graph of three models for Examples 1 to 4 of the present invention (a: 30 °C; b: 50 °C; c: 70 °C; d: 90 °C). Detailed implementation mode

[0053] The present invention will be further described in detail below with reference to the accompanying drawings and implementation modes:

[0054] A method for establishing a reaction kinetic model in the preparation process of gradient nitro propellant, comprising the following steps:

[0055] S1. Establish model assumptions:

[0056] When studying the overall rate characterizing the macroscopic kinetics in the preparation process of gradient nitro propellant, it is assumed that the entire reaction system reacts under a constant temperature environment. The reaction interface in the preparation process of gradient nitro propellant gradually moves towards the center. However, since its moving rate is much smaller than the diffusion rate of the fluid reactant through the solid product layer, it can be approximately assumed that the reaction interface is stationary, and the reaction process is regarded as a pseudo-steady state process. It is assumed that the denitration reaction in the process of preparing gradient nitro propellant is a first-order irreversible chemical reaction, and its expression can be simplified as:

[0057] A(l)+b B(s)→f F(l)+s S(s) (1)

[0058] Wherein, A represents the denitration reaction liquid, B represents the unreacted solid propellant, F represents the liquid product after denitration reaction, and S represents the solid product after denitration reaction. It is assumed that the propellant is a spherical solid.

[0059] The external diffusion rate of the denitration reaction liquid A through the stagnant film is:

[0060]

[0061] In the formula, k G is the mass transfer coefficient of the denitration reaction liquid A, with the unit of m / s; C 0 is the concentration of the unreacted denitration liquid; C s is the concentration of the denitration liquid on the outer surface of the propellant.

[0062] The internal diffusion rate of the denitration reaction liquid A through the solid residue film layer is:

[0063]

[0064] In the formula, D eff is the effective diffusion coefficient of component A in the solid residue film layer, with the unit of m 2 / s; C A is the concentration of the reaction denitration solution at R = R c .

[0065] In the formula can be calculated by the diffusion process of A in the solid product layer. Under steady state, there is no accumulation, then:

[0066]

[0067] That is:

[0068]

[0069] When the above formula is integrated twice and the conditions: R = R s are applied, C A = C s ; R = R c are applied, C A = C c are substituted, and we get:

[0070]

[0071] When R = R c , differentiating R in the above formula gives:

[0072]

[0073] Substituting into the formula, we can obtain:

[0074]

[0075] The chemical reaction rate of the denitrification reaction liquid A and the unreacted solid propellant B undergoing a first-order irreversible reaction is:

[0076]

[0077] In the formula, k is the reaction rate constant of the denitrification reaction liquid, with the unit of m / s.

[0078] The relationship between the radius R c of the unreacted core and the reaction time is:

[0079]

[0080]

[0081] The conversion rate x B of the solid-phase reactant B and R c is:

[0082]

[0083] S2. Establish a chemical reaction-controlled mass transfer model:

[0084] During the preparation of gradient nitro propellant, it is assumed that the flow rate of the denitrification reaction liquid is high, the structure of the solid-phase product layer is relatively loose, and relatively speaking, the resistance of the chemical reaction is greater than that of other steps. The concentration of the denitrification reaction solution A at different positions of the solid propellant is C 0 = Cs = C c , at this time, the preparation process of the gradient nitrocellulose propellant is controlled by chemical reactions, that is:

[0085]

[0086]

[0087] Integrating, we get:

[0088]

[0089] When the reaction is complete, R c = 0, x B = 1, at this time the reaction time t f is:

[0090]

[0091] The relationship between t and t f is:

[0092]

[0093] When the denitration reaction is controlled by chemical reactions, the mathematical expression of the reaction model is:

[0094] 1 - (1 - x B ) 1 / 3 = k 1 t (18)

[0095] S3. Establish the internal diffusion-controlled mass transfer model of the solid residue film layer:

[0096] When the denitration reaction is controlled by internal diffusion in the solid residue film layer, the external diffusion resistance and the surface chemical reaction resistance are both smaller than the internal diffusion resistance. The concentration comparison of the denitration reaction solution A at different positions of the solid propellant is: C 0 ≈ C s >> C c ≈ 0, that is:

[0097]

[0098]

[0099] Integrating, we get:

[0100]

[0101] When the reaction is complete, R c = 0, x B = 1, at this time the reaction time t f is:

[0102]

[0103]

[0104] When the denitration reaction is controlled by internal diffusion of the solid residue film layer, the mathematical expression of the reaction model is:

[0105]

[0106] S4. Establish a mass transfer model of mixed control of interfacial mass transfer and diffusion of the solid residue film layer:

[0107] In the preparation process of gradient nitro propellant, assuming that the flow rate of the denitration reaction solution is slow, the structure of the solid-phase product layer is relatively dense, it is difficult for the denitration solution A to penetrate into the solid propellant B, the depth of the denitration reaction is very small, the resistance of interfacial mass transfer and diffusion of the solid residue film layer is greater than that of other steps, and the concentration of the denitration reaction solution A at different positions of the solid propellant is C 0 >C s >>C c ≈0. At this time, the preparation process of the gradient nitro propellant is under the mixed control of interfacial mass transfer and diffusion of the solid residue film layer (or product layer), that is:

[0108]

[0109]

[0110] Integrating, we get:

[0111]

[0112] When the reaction is complete, R c =0, x B =1. At this time, the reaction time t f is:

[0113]

[0114]

[0115] When the denitration reaction is controlled by internal diffusion of the solid residue film layer, the mathematical expression of the reaction model is:

[0116]

[0117] The present invention also includes the application of the reaction kinetic model in the preparation process of the gradient nitro propellant, that is, applying this model to verify and apply in the solid-liquid denitration chemical reaction in the preparation process of the gradient nitro propellant, which is expected to provide a research plan for the refined control in the preparation process of the gradient nitro propellant.

[0118] Verify the model described in steps S2, S3, and S4 through experiments, and compare to obtain the optimal reaction kinetic model for the preparation process of gradient nitro propellant:

[0119] Example 1

[0120] 1) Dissolve 3.54 g of hydrazine hydrate with a concentration of 80 wt% into 16.5 mL of deionized water to prepare a hydrazine hydrate solution with a concentration of 14.15%. Preheat the prepared solution to 30°C. Weigh 10 g of dry spherical propellant, place the propellant in a 150 mL three-necked flask equipped with a stirring device, and pour the preheated hydrazine hydrate - aqueous solution at 30°C for denitration reaction. React under the conditions of 30°C water bath heating and a stirring speed of 260 rap / min. Stop the reaction after 4 h of reaction, filter to remove the reaction solution, and obtain the denitrated propellant.

[0121] 2) Place the denitrated propellant in deionized water for boiling and washing to remove the hydrazine hydrate remaining on the surface of the propellant grains. The boiling and washing temperature is 80°C, and the boiling and washing time is 30 min. After boiling and washing, place the prepared gradient nitro propellant in a 60°C water bath oven for drying, and the drying duration is 48 h. After drying, the gradient nitro propellant is obtained. Weigh the obtained dried gradient nitro propellant and record the mass data of the dried propellant before and after the experiment. Calculate the corresponding denitration percentage.

[0122] Under the same other conditions, extend the reaction times to 6 h, 8 h, and 12 h respectively. The corresponding data are shown in Figure 3 (a), and the data fitted according to the model are shown in Figure 4 (a).

[0123] Example 2

[0124] 1) Dissolve 3.54 g of hydrazine hydrate with a concentration of 80 wt% into 16.5 mL of deionized water to prepare a hydrazine hydrate solution with a concentration of 14.15%. Preheat the prepared solution to 50°C. Weigh 10 g of dry spherical propellant, place the propellant in a 150 mL three-necked flask equipped with a stirring device, and pour the preheated hydrazine hydrate - aqueous solution at 50°C for denitration reaction. React under the conditions of 50°C water bath heating and a stirring speed of 260 rap / min. Stop the reaction after 2 h of reaction, filter to remove the reaction solution, and obtain the denitrated propellant.

[0125] 2) Place the denitrated propellant in deionized water for boiling and washing to remove the hydrazine hydrate remaining on the surface of the propellant grains. The boiling and washing temperature is 80 °C, and the boiling and washing time is 30 min. After the boiling and washing is completed, place the prepared gradient nitro propellant in a water bath oven at 60 °C for drying, and the drying duration is 48 h. After drying, the gradient nitro propellant is obtained. Weigh the obtained dried gradient nitro propellant, and record the mass data of the dried propellant before and after the experiment. Calculate the corresponding denitration percentage.

[0126] Under the same other conditions, the reaction time is extended to 4 h, 6 h, 8 h, and 10 h respectively. The corresponding data can be seen in Figure 3 (b), and the data fitted according to the model can be seen in Figure 4 (b).

[0127] Example 3

[0128] 1) Dissolve 3.54 g of hydrazine hydrate with a concentration of 80 wt% in 16.5 mL of deionized water to prepare a hydrazine hydrate solution with a concentration of 14.15%. Preheat the prepared solution to 70 °C. Weigh 10 g of dry spherical propellant, place the propellant in a 150 mL three-necked flask equipped with a stirring device, and pour in the preheated hydrazine hydrate - aqueous solution for denitration reaction. React under the conditions of water bath heating at 70 °C and a stirring speed of 260 rap / min. Stop the reaction after 1 h of reaction, filter to remove the reaction solution, and obtain the denitrated propellant.

[0129] 2) Place the denitrated propellant in deionized water for boiling and washing to remove the hydrazine hydrate remaining on the surface of the propellant grains. The boiling and washing temperature is 80 °C, and the boiling and washing time is 30 min. After the boiling and washing is completed, place the prepared gradient nitro propellant in a water bath oven at 60 °C for drying, and the drying duration is 48 h. After drying, the gradient nitro propellant is obtained. Weigh the obtained dried gradient nitro propellant, and record the mass data of the dried propellant before and after the experiment. Calculate the corresponding denitration percentage.

[0130] Under the same other conditions, the reaction time is extended to 2 h, 3 h, 4 h, and 5 h respectively. The corresponding data can be seen in Figure 3 (c), and the data fitted according to the model can be seen in Figure 4 (c).

[0131] Example 4

[0132] 1) Dissolve 3.54 g of hydrazine hydrate with a concentration of 80 wt% into 16.5 mL of deionized water to prepare a hydrazine hydrate solution with a concentration of 14.15%. Preheat the prepared solution to 90 °C. Weigh 10 g of dry spherical propellant, place the propellant in a 150 mL three-necked flask equipped with a stirring device, and pour the preheated hydrazine hydrate - aqueous solution for denitration reaction. React under a water bath heating at 90 °C and a stirring speed of 260 rap / min. Stop the reaction after 15 min of reaction, filter to remove the reaction solution, and obtain the denitrated propellant.

[0133] 2) Place the denitrated propellant in deionized water for boiling and washing to remove the hydrazine hydrate remaining on the surface of the propellant grains. The boiling and washing temperature is 80 °C and the boiling and washing time is 30 min. After the boiling and washing is completed, place the prepared gradient nitro propellant in a water bath oven at 60 °C for drying, and the drying duration is 48 h. After drying, the gradient nitro propellant is obtained. Weigh the obtained dried gradient nitro propellant and record the mass data of the dried propellant before and after the experiment. Calculate the corresponding denitration percentage.

[0134] Under the condition that other conditions are the same, extend the reaction times to 30 min, 1 h, 90 min, and 2 h respectively. The corresponding data are shown in Figure 3 (d). The data fitted according to the model are shown in Figure 4 (d).

[0135] This invention takes spherical propellant as the research object, establishes a denitration reaction kinetic model for surface gradient nitro propellant. Through experimental data, the correlation between the denitration percentage x(NO 2 - ), reaction temperature, and reaction time is obtained; the linear correlation coefficient R obtained by fitting the shrinking core model equation of the solid residue layer 2 All remain above 0.99, indicating that 1 - 2x(NO 2 - ) / 3 - (1 - x(NO 2 - )) 2 / 3 Has a good linear relationship with t, and is better than the linear correlation coefficients obtained by fitting the other two shrinking core model equations. It can be seen that this reaction process is affected by the internal diffusion control of the solid residue film layer.

[0136] Substitute the experimental results in the above examples into the corresponding mathematical models, and summarize the experimental conditions and experimental results in Table 1.

[0137] Table 1 Linear fitting correlation parameters of each kinetic equation at different temperatures

[0138]

[0139] The above are only embodiments of the present invention, and common general technical solutions and / or features in the solutions are not described in detail herein. It should be noted that for those skilled in the art, without departing from the technical solution of the present invention, several modifications and improvements can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the implementation effect of the present invention and the practicality of the patent. The protection scope required by this application shall be subject to the content of its claims, and the specific implementation manners and the like recorded in the specification can be used to interpret the content of the claims.

Claims

1. A method for establishing a reaction kinetics model in the preparation process of gradient nitro propellant, characterized in that, it includes the following steps, S1. Establish model assumptions: a. Assume that the reaction system reacts under a constant temperature environment; b. Approximately assume that the reaction interface is stationary, and regard the reaction process as a pseudo-steady state process; c. Assume that the denitration reaction is a first-order irreversible chemical reaction, and its expression is simplified as: A(l)+b B(s)→f F(l)+s S(s) (1) d. Assume that the gradient nitro propellant is a spherical solid; S2. Establish a chemical reaction-controlled mass transfer model: When the denitration reaction is controlled by chemical reaction, the mathematical expression of the reaction model is: 1-(1-x B ) 1 / 3 =k 1 t (18) S3. Establish an internal diffusion-controlled mass transfer model of the solid residue film layer: When the denitration reaction is controlled by the internal diffusion of the solid residue film layer, the mathematical expression of the reaction model is: S4. Establish a mixed-controlled mass transfer model of interfacial mass transfer and diffusion of the solid residue film layer: When the denitration reaction is controlled by the mixed control of interfacial mass transfer and diffusion of the solid residue film layer, the mathematical expression of the reaction model is: S5. Experimentally verify the models described in steps S2, S3, and S4, and compare to obtain the optimal reaction kinetics model for the preparation process of gradient nitro propellant; The experiments in step S5 include: Step one. Dissolve 3.54 g of hydrazine hydrate with a concentration of 80 wt% into 16.5 mL of deionized water to prepare a hydrazine hydrate solution with a concentration of 14.15%; Step two. Preheat the prepared solution to 30 °C, weigh 10 g of dry spherical propellant, place the propellant in a 150 mL three-necked flask with a stirring device, pour in the preheated hydrazine hydrate-aqueous solution, and carry out the denitration reaction under the conditions of 30 °C water bath heating and a stirring speed of 260 RPM. Stop the reaction after 4 h of reaction, filter to remove the reaction solution, and obtain the denitrated propellant; Step three. Place the denitrated propellant in deionized water for boiling and washing to remove the hydrazine hydrate remaining on the surface of the propellant grains. The boiling and washing temperature is 80 °C, and the boiling and washing time is 30 min; Step four. Place the boiled and washed propellant in a 60 °C water bath oven for drying, and the drying duration is 48 h; Step five. Weigh the dried propellant and record the mass data of the dried propellant before and after the experiment, and calculate the corresponding denitration percentage; Step six. Repeat steps one to five, set up three other experiments, and extend the reaction times to 6 h, 8 h, and 12 h respectively. Linearly fit the experimental data according to the models described in steps S2, S3, and S4; Step seven. Repeat steps one to six, set up three other groups of experiments, and adjust the denitration reaction temperature and set the reaction times at the corresponding reaction temperatures; Step 8. Based on the fitted linear correlation coefficient R 2 , obtain the optimal reaction kinetic model for the preparation process of gradient nitrocellulose propellant; In the above formula, A represents the denitrification reaction solution, B represents the unreacted solid propellant, F represents the liquid product after denitrification reaction, and S represents the solid product after denitrification reaction; x B represents the conversion rate of the solid-phase reactant B, and k 1 , k 2 , k 3 are constant coefficients.

2. According to the method for establishing a reaction kinetics model in the preparation process of gradient nitro propellant described in claim 1, characterized in that, step S1 further includes performing denitration reaction analysis based on the model assumptions: (1) The external diffusion rate of the denitration reaction liquid A through the stagnant film is: (2) The internal diffusion rate of the denitration reaction liquid A through the solid residue film layer is: Wherein, (3) The chemical reaction rate of the denitration reaction liquid A and the unreacted solid propellant B in a first-order irreversible reaction is: (4) Unreacted core radius R c The relationship with the reaction time is as follows: (5) Conversion rate x of solid-phase reactant B B and R c is related as follows: In the above formula, assuming that the propellant is spherical solid, k G is the mass transfer coefficient of the denitrification reaction liquid A, with the unit of m / s; C 0 is the concentration of the unreacted denitrification liquid; C s is the concentration of the denitrification reaction liquid on the outer surface of the propellant; D eff is the effective diffusion coefficient of component A in the solid residue film layer, with the unit of m 2 / s; C A is the concentration of the denitrification reaction solution at R = R c ; R s is the radius of the propellant, R c is the radius of the unreacted core of the propellant, C c is the concentration of the denitrification reaction liquid at R = R c ; k is the reaction rate constant of the denitrification reaction liquid, m 0 is the original mass of the solid-phase reactant B, m t is the real-time mass of the solid-phase reactant B.

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