Method for calculating wide-temperature environment ignition delay of multi-component propellant

Abstract

The invention discloses a method for calculating ignition delay of a multi-component propellant in a wide-temperature environment. The multi-component propellant is an aluminum-containing composite propellant. The calculation method comprises the following steps: establishing a low-temperature ignition model of the aluminum-containing composite propellant; the low-temperature ignition model is the relationship between the temperature and the substance concentration and the reaction time; performing discrete and finite difference processing on each control equation in the low-temperature ignition model according to a reaction time step length and a step length of a distance from a combustion surface; setting the temperature and the substance concentration at the position where the reaction time is 0 as the initial state of the low-temperature ignition model, carrying out iteration on the gas-phase temperature, the solid-phase temperature, the adhesive concentration, the oxidant concentration and the ammonium nitrate concentration at each grid point obtained through discretization, and carrying out continuous iteration until the termination condition is reached; the total step length of the reaction time corresponding to the termination condition is ignition delay; according to the method, the ignition delay of the multi-component propellant in a relatively large initial temperature environment domain (-60 to 150 DEG C) and the temperature distribution in the ignition process can be calculated.

Description

Technical Field

[0001] The present invention belongs to the field of multi-component propellant performance testing, and particularly relates to a calculation method for ignition delay of multi-component propellant in a wide temperature environment. Background Art

[0002] Multicomponent propellant refers to a rocket propellant composed of three or more chemical components, which realizes characteristics such as high energy density and controllable combustion through the synergistic effect of different components.

[0003] With continuous development, the propellant faces an increasingly complex working environment. There are many studies on the ignition model of double-base composite propellant, while there are few studies on the ignition model of composite propellant containing aluminum particles. Since the existing ignition models of double-base composite propellant are unclear about the action mechanism of aluminum during the entire ignition process and ignore the influence effect of aluminum, the calculation accuracy of ignition delay will be relatively low. Summary of the Invention

[0004] The purpose of the present invention is to provide a calculation method for ignition delay of multi-component propellant in a wide temperature environment, which can calculate the ignition delay of multi-component propellant in a large initial temperature environment range (-60 to 150 °C) and the temperature distribution during the ignition process.

[0005] The present invention adopts the following technical solutions: A calculation method for ignition delay of multi-component propellant in a wide temperature environment, the multi-component propellant is an aluminum-containing composite propellant; the calculation method includes:

[0006] Step 1: Establish a low-temperature ignition model of the aluminum-containing composite propellant according to each control equation; the low-temperature ignition model is the relationship between temperature, substance concentration and reaction time;

[0007] Step 2: Discretize and perform finite difference processing on each control equation in the low-temperature ignition model with a step size of reaction time and a step size of distance from the burning surface;

[0008] Step 3: Set the temperature and substance concentration at the reaction time of 0 as the initial state of the low-temperature ignition model, and iterate the gas-phase temperature, solid-phase temperature, binder concentration, oxidizer concentration, and ammonium nitrate concentration at each grid point obtained by discretization until the termination condition is reached. The total step size of the reaction time corresponding to the termination condition is the ignition delay.

[0009] Further, the control equation in Step 1 includes the energy heat flux equation at the solid-gas interface of the burning surface, specifically:

[0010]

[0011] where k2 is the thermal conductivity of the solid phase, T2 is the temperature of the solid phase, x is the distance from the burning surface, t is the reaction time, k1 is the thermal conductivity of the gas phase, and T1 is the temperature of the gas phase. is the volume fraction of Al in the composite propellant, and ΔH ox is the heat of the oxidizer thermal decomposition reaction, and ρ ox is the density of the oxidizer, A i is the pre-exponential factor of the reaction, E i is the activation energy of the reaction, i is the number of components of the composite propellant; R is the gas constant, and T S is the propellant surface temperature, and ΔH F is the heat of the binder thermal decomposition reaction, and ρ F is the density of the binder, and ΔH An is the heat of the ammonium nitrate thermal decomposition reaction, and ρ An is the density of the ammonium nitrate, and ΔH s is the heat of the heterogeneous reaction, and C ox is the concentration of the oxidizer in the gas phase, and F0 is the external surface heat flux.

[0012] Furthermore, the control equation in step 1 also includes the oxidizer decomposition control equation on the propellant surface, specifically:

[0013]

[0014] where D is the gas phase diffusion coefficient;

[0015] The control equation in step 1 also includes the binder thermal decomposition control equation, specifically:

[0016]

[0017] where C F is the concentration of the binder in the gas phase;

[0018] The control equation in step 1 also includes the ammonium nitrate thermal decomposition control equation, specifically:

[0019]

[0020] where C An is the concentration of the ammonium nitrate in the gas phase.

[0021] Furthermore, the control equation in step 1 also includes the heat flow diffusion equation of the solid phase, specifically:

[0022]

[0023] where a2 is the thermal diffusion coefficient of the solid phase.

[0024] Furthermore, the control equation in Step 1 also includes the heat flow diffusion equation of the gas phase, specifically:

[0025]

[0026] where a1 is the thermal diffusion coefficient of the gas phase; Z is the pre-exponential factor of the gas phase reaction, P is the ambient pressure, P0 is the standard atmospheric pressure, n is the pressure exponent, Y F is the mass fraction of the binder in the gas phase, Y ox is the mass fraction of the oxidizer in the gas phase, ΔH g is the reaction heat of the gas phase reaction, ρ1 is the gas phase density, c p1 is the specific heat capacity, Y An is the mass fraction of ammonium nitrate in the gas phase.

[0027] Furthermore, the control equation in Step 1 also includes the diffusion equation of the oxidizer in the gas phase, specifically:

[0028]

[0029] where β is the stoichiometric coefficient of the oxidizer gas phase reaction.

[0030] Furthermore, the control equation in Step 1 also includes the diffusion equation of the binder in the gas phase, specifically:

[0031]

[0032] Furthermore, the control equation in Step 1 also includes the diffusion equation of ammonium nitrate in the gas phase, specifically:

[0033]

[0034] where γ is the stoichiometric coefficient of the ammonium nitrate gas phase reaction.

[0035] Furthermore, the boundary conditions of the low-temperature ignition model in Step 1 are:

[0036] T1(+∞,t) = T1(+∞,0)

[0037] T2(-∞,t) = T2(-∞,0)

[0038] C F (+∞,t) = C F (+∞,0)

[0039] C ox (+∞,t) = C ox (+∞,0)

[0040] C An (+∞,t) = C an(+∞, 0).

[0041] The beneficial effects of the present invention are as follows:

[0042] The present invention can calculate the ignition delay and the temperature distribution during the ignition process of multi-component propellants in a relatively large initial temperature environment range (-60 to 150 °C);

[0043] The present invention can convert the ignition heat flux into high temperature in the gas phase, calculate the propellant ignition process caused by the high temperature. The low-temperature ignition model of the present invention simplifies a large number of chemical reaction calculation processes in the calculation process through a one-step overall reaction. Compared with general numerical calculation methods, the calculation speed of the low-temperature ignition model of the present invention is greatly improved;

[0044] During the calculation process, the low-temperature ignition model of the present invention can track the energy exchange generated by surface thermal decomposition, gas-phase reactions, external heat flux, and heat conduction, and can clearly understand the energy influence of each part during the ignition process, and verify it by comparing with experimental phenomena. Description of the Drawings

[0045] Figure 1 It is a comparison of the ignition delay calculated at different temperatures for aluminized and non-aluminized propellants with the actual ignition delay;

[0046] Figure 2 It is the ignition delay of propellants with different aluminum contents calculated by the present invention at different temperatures;

[0047] Figure 3 It is the ignition delay of the propellant calculated by the present invention at different temperatures and pressures;

[0048] Figure 4 It is the ignition delay of the propellant of the present invention without external heat flux at different ambient temperatures. Detailed Embodiment

[0049] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0050] The present invention discloses a calculation method for the ignition delay of multi-component propellants in a wide-temperature environment, including:

[0051] Step 1: Establish a low-temperature ignition model of aluminized composite propellants according to each control equation; the low-temperature ignition model is the relationship between temperature, substance concentration and reaction time.

[0052] The low-temperature ignition model mainly controls the heat flow through the partial differential equations describing heat conduction in the condensed phase, gas phase and burning surface, and controls the distribution of reaction substances in the gas phase through the gas diffusion equation in the gas phase.

[0053] During the ignition process, thermal decomposition reactions and heterogeneous reactions occur on the propellant surface. Aluminum does not participate in these reactions. Instead, aluminum reduces the reaction area of the binder and oxidizer on the propellant surface, thereby leading to a decrease in the exothermic heat and products of oxidizer thermal decomposition. It reduces the heating rate of the propellant and increases the ignition delay. Here, the Dupuit-Forchheimer assumption is adopted, which allows the definition of the volume fraction of porosity to be extended to the area fraction. Therefore, the volume fraction of Al is regarded as the volume fraction of porosity, and thus we have:

[0054]

[0055] where A is the burning surface area of the propellant, A a is the surface area occupied by aluminum, which means that aluminum will reduce the reaction rate of the propellant Therefore, the governing equations are as follows.

[0056] The governing equations in Step 1 include the energy heat flux equation at the solid-gas interface at the burning surface, specifically:

[0057]

[0058] where k2 is the thermal conductivity of the solid phase, T2 is the temperature of the solid phase, x is the distance from the burning surface, t is the reaction time, k1 is the thermal conductivity of the gas phase, T1 is the temperature of the gas phase, is the volume fraction of Al in the composite propellant, ΔH ox is the heat of the oxidizer thermal decomposition reaction, ρ ox is the density of the oxidizer, A i is the pre-exponential factor of the reaction, E i is the activation energy of the reaction, i is the number of components in the composite propellant; R is the gas constant, T s is the propellant surface temperature, ΔH F is the heat of the binder thermal decomposition reaction, ρ F is the density of the binder, ΔH An is the heat of the ammonium nitrate thermal decomposition reaction, ρ An is the density of the ammonium nitrate, ΔH s is the heat of the heterogeneous reaction, C ox is the concentration of the oxidizer in the gas phase, F0 is the external surface heat flux.

[0059] The governing equations in Step 1 also include the oxidizer decomposition control equation on the propellant surface, specifically:

[0060]

[0061] where D is the gas-phase diffusion coefficient;

[0062] The control equations in Step 1 also include the control equation for the thermal decomposition of the binder, specifically:

[0063]

[0064] where C F is the concentration of the binder in the gas phase;

[0065] The control equations in Step 1 also include the control equation for the thermal decomposition of ammonium nitrate, specifically:

[0066]

[0067] where C An is the concentration of ammonium nitrate in the gas phase.

[0068] The control equations in Step 1 also include the heat flow diffusion equation in the solid phase, specifically:

[0069]

[0070] where a2 is the thermal diffusivity of the solid phase.

[0071] The control equations in Step 1 also include the heat flow diffusion equation in the gas phase, specifically:

[0072]

[0073] where a1 is the thermal diffusivity of the gas phase; Z is the pre-exponential factor of the gas phase reaction, P is the environmental pressure, P0 is the standard atmospheric pressure, n is the pressure exponent, Y F is the mass fraction of the binder in the gas phase, Y ox is the mass fraction of the oxidizer in the gas phase, ΔH g is the reaction heat of the gas phase reaction, ρ is the gas phase density, c p1 is the specific heat capacity, Y An is the mass fraction of ammonium nitrate in the gas phase.

[0074] The control equations in Step 1 also include the diffusion equation of the oxidizer in the gas phase, specifically:

[0075]

[0076] where β is the stoichiometric coefficient of the gas phase reaction of the oxidizer.

[0077] The control equations in Step 1 also include the diffusion equation of the binder in the gas phase, specifically:

[0078]

[0079] The control equations in Step 1 also include the diffusion equation of ammonium nitrate in the gas phase, specifically:

[0080]

[0081] where γ is the stoichiometric coefficient of the gas-phase reaction of ammonium nitrate.

[0082] The boundary conditions of the low-temperature ignition model in Step 1 are:

[0083] T4(+∞,t) = T1(+∞,0)

[0084] T2(-∞,t) = T2(-∞,0)

[0085] C F (+∞,t) = C F (+∞,0)

[0086] C ox (+∞,t) = C ox (+∞,0)

[0087] C An (+∞,t) = C An (+∞,0).

[0088] The ignition criterion refers to Bradley's summary of the thermal explosion theory. The maximum temperature rise before thermal explosion (defined by the rapid temperature rise rate) is usually very small compared to the initial temperature. During the heating process, the inflection point on the surface temperature curve that changes with time is used as the ignition criterion. When the ignition system successfully ignites, the surface reaction rate of the propellant will increase significantly and generate a large amount of heat, resulting in a very high level of the heating rate of the propellant burning surface, exceeding 5×10 5 K / s. Therefore, when the following equation holds, it is considered that the propellant ignition is successful:

[0089]

[0090] Step 2: Discretize and perform finite difference processing on each control equation in the low-temperature ignition model with a step size of reaction time and a step size of the distance from the burning surface.

[0091] The control equations of the low-temperature ignition model are seven partial differential equations, and it is basically impossible to obtain the analytical solution of the equation set through derivation. The partial differential equations will be transformed into constant equations by the method of model discretization. The low-temperature ignition model is discretized according to the reaction time and the distance from the burning surface. Among them, preferably, the step size of the reaction time is 0.1 millisecond, and the step size of the distance from the burning surface is 10 micrometers.

[0092] Each point represents the state of the point at a distance of iΔh from the burning surface in the system at jΔt, and the finite difference processing is carried out as follows:

[0093]

[0094] Step 3: Set the temperature and substance concentration at the reaction time of 0 as the initial state of the low-temperature ignition model, and iterate the gas-phase temperature, solid-phase temperature, binder concentration, oxidizer concentration, and ammonium nitrate concentration at each grid point obtained by discretization until the termination condition is reached. The total step length of the reaction time corresponding to the termination condition is the ignition delay.

[0095] After discretization and finite difference processing, set the state at t = 0 as the initial state of the system. Then, take Δh and Δt as the step lengths to iterate the gas-phase temperature, solid-phase temperature, binder concentration, oxidizer concentration, and ammonium nitrate concentration at each point from the burning surface, and simultaneously track and calculate the value of. When is greater than 5×10 5 , it is determined that ignition is successful, and the ignition delay is jΔt.

[0096] Experiment and calculate the ignition delays of aluminized propellant and non-aluminized propellant at different initial temperatures respectively. The results are as Figure 1 shown. It can be seen from Figure 1 that the calculated ignition delay is basically consistent with the experimental ignition delay, and the error of the calculated ignition delay is within 10%, which indicates that the calculation method of the present invention has high accuracy.

[0097] Calculate the ignition delays of propellants with different aluminum contents at different temperatures. The results are as Figure 2 shown. It can be seen from Figure 2 that the aluminum content and the calculated ignition delays at different temperatures have a similar changing trend, indicating that the calculation method of the present invention has high robustness in calculating the ignition delay with the coupled change of aluminum content and initial temperature.

[0098] Calculate the ignition delays at different temperatures and pressures. The results are as Figure 3 shown. It can be seen from Figure 3 that the ignition delays at different temperatures and pressures have a similar changing trend. The ignition delay gradually decreases with the increase of pressure, and the decreasing speed gradually slows down, which is consistent with the trend in previous literature. This indicates that the calculation method of the present invention has high robustness in calculating the ignition delay with the coupled change of pressure and initial temperature.

[0099] Calculate the ignition delays of ignition relying on ambient temperature at different ambient temperatures. The results are as Figure 4 shown. It can be seen from Figure 4 that within a certain range, the ignition delay gradually decreases with the increase of temperature, and the changing trend is basically stable. This proves the feasibility of the calculation method of the present invention in calculating the ignition delay of ignition relying on ambient temperature.

[0100] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A calculation method for ignition delay of multi-component propellants in a wide-temperature environment, characterized in that, The multi-component propellant is an aluminum-containing composite propellant; the calculation method includes: Step 1: Establish a low-temperature ignition model of the aluminum-containing composite propellant according to each control equation; the low-temperature ignition model is the relationship between temperature, substance concentration and reaction time; Step 2: Discretize and perform finite difference processing on each control equation in the low-temperature ignition model with the step lengths of reaction time and distance from the burning surface; Step 3: Set the temperature and substance concentration at the reaction time of 0 as the initial state of the low-temperature ignition model, and iterate the gas-phase temperature, solid-phase temperature, binder concentration, oxidizer concentration, and ammonium nitrate concentration at each grid point obtained by discretization until the termination condition is reached. The total number of reaction time steps corresponding to the termination condition is the ignition delay.

2. The calculation method for ignition delay of a multi-component propellant in a wide temperature environment according to claim 1, characterized in that The control equation in Step 1 includes the energy heat flux equation at the solid-gas interface at the burning surface, specifically: where k2 is the thermal conductivity of the solid phase, T2 is the temperature of the solid phase, x is the distance from the burning surface, t is the reaction time, k1 is the thermal conductivity of the gas phase, and T1 is the temperature of the gas phase. is the volume fraction of Al in the composite propellant, ΔH ox is the heat of the oxidizer thermal decomposition reaction, ρ ox is the density of the oxidizer, A i is the pre-exponential factor of the reaction, E i is the activation energy of the reaction, i is the number of components of the composite propellant; R is the gas constant, T s is the propellant surface temperature, ΔH F is the heat of the binder thermal decomposition reaction, ρ F is the density of the binder, ΔH An is the heat of the ammonium nitrate thermal decomposition reaction, ρ An is the density of the ammonium nitrate, ΔH s is the heat of the heterogeneous reaction, C ox is the concentration of the oxidizer in the gas phase, and F0 is the external surface heat flux.

3. The calculation method for ignition delay of multi-component propellants in a wide-temperature environment according to claim 2, characterized in that The control equation in Step 1 also includes the control equation for the decomposition of the oxidizer on the propellant surface, specifically: where D is the gas-phase diffusion coefficient; The control equation in Step 1 also includes the thermal decomposition control equation of the binder, specifically: Among them, C F is the concentration of the binder in the gas phase; The control equation in Step 1 also includes the thermal decomposition control equation of ammonium nitrate, specifically: Among them, C An is the concentration of ammonium nitrate in the gas phase.

4. The method for calculating the ignition delay of a multipropellant in a wide temperature environment according to claim 2 is characterized in that: The control equation in Step 1 also includes the heat flow diffusion equation of the solid phase, specifically: where a2 is the thermal diffusion coefficient of the solid phase.

5. The calculation method for ignition delay of multi-component propellants in a wide temperature environment according to claim 3, characterized in that The control equation in Step 1 also includes the heat flow diffusion equation of the gas phase, specifically: Among them, a1 is the thermal diffusion coefficient of the gas phase; Z is the pre-exponential factor of the gas-phase reaction, P is the ambient pressure, P0 is the standard atmospheric pressure, n is the pressure exponent, Y F is the mass fraction of the binder in the gas phase, Y ox is the mass fraction of the oxidizer in the gas phase, ΔH g is the heat of reaction of the gas-phase reaction, ρ1 is the gas-phase density, c p1 is the specific heat capacity, Y An is the mass fraction of ammonium nitrate in the gas phase.

6. The calculation method for ignition delay of multi-component propellants in a wide temperature environment according to claim 5 is characterized in that, The control equation in Step 1 also includes the diffusion equation of the oxidizer in the gas phase, specifically: where β is the stoichiometric coefficient of the gas-phase reaction of the oxidizer.

7. The calculation method for ignition delay of multi-component propellants in a wide temperature environment according to claim 5, characterized in that The control equation in Step 1 also includes the diffusion equation of the binder in the gas phase, specifically:

8. The method for calculating the ignition delay of a multipropellant in a wide temperature environment according to claim 5 is characterized in that: The control equation in Step 1 also includes the diffusion equation of ammonium nitrate in the gas phase, specifically: where γ is the stoichiometric coefficient of the gas-phase reaction of ammonium nitrate.

9. The calculation method for ignition delay of multi-component propellants in a wide temperature environment according to claim 3 is characterized in that, The boundary conditions of the low-temperature ignition model in Step 1 are: T1(+∞,t) = T1(+∞,0) T2(-∞,t) = T2(-∞,0) C F (+∞, t) = C F (+∞, 0) C ox (+∞,t)=C ox (+∞,0) C An (+∞, t) = C An (+∞, 0).

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