CN103267830B - Method for evaluating ablation characteristic of solid energetic material under plasma jet action - Google Patents

Abstract

The invention provides a method for evaluating the ablation characteristics of a solid energetic material under the action of a plasma jet: 1) Obtain the interaction time between the plasma jet and the energetic material, the pressure and temperature of the plasma jet, and the ablation quality through experiments ; 2) By simultaneously solving the heat conduction equation inside the energetic material and the ablation model of the energetic material by the plasma jet, the surface temperature, surface penetration depth and the total action process of the energetic material under the action of the plasma jet under the energy flow condition are obtained. 3) Adjust the input plasma jet energy flow data until the calculated ablation quality is consistent with the experimentally measured ablation quality, thereby determining the actual energy flow from the plasma jet; 4 ) using the calculated actual energy flow as the input condition to obtain information such as the actual surface temperature of the energetic material, the surface penetration depth, etc., and realize the evaluation of the interaction characteristics between the plasma jet and the energetic material.

Description

Method for Evaluating Ablation Properties of Solid Energetic Materials Under the Effect of Plasma Jet

technical field

The invention relates to a method for evaluating the interaction characteristics of plasma jets and energetic materials, in particular to a method for evaluating the interaction characteristics of plasma jets and energetic materials in an electrothermal chemical gun.

Background technique

Plasma jet, as a commonly used means to ignite and support solid energetic materials, has a very wide range of applications. For example, when the energetic material is a propellant, the plasma jet can be used as a plasma ignition source in an electrothermal chemical gun, and when the energetic material is a propellant, the plasma jet can be used as a means of ignition and auxiliary combustion of a spacecraft propulsion device .

The interaction process between plasma jet and solid energetic material can usually be divided into pre-ignition stage, ignition stage and stable combustion stage. Among them, in the stage before ignition, the solid energetic material is mainly affected by the ablation effect of the plasma jet. This process determines the initial conditions of the ignition stage and affects many important parameters of the ignition of energetic materials, including solid energetic The surface temperature of the material and the content of the energetic material in the gas phase in the surrounding environment have a very important influence on the comprehensive effect of the plasma jet and the solid energetic material. However, there is no effective method to evaluate the ablation characteristics of solid energetic materials under the action of plasma jets.

Contents of the invention

The purpose of the present invention is to provide a method for evaluating the ablation characteristics of solid energetic materials under the action of plasma jets.

To achieve the above object, the present invention adopts the following technical solutions:

1) First, the interaction time between the plasma jet and the energetic material, the pressure and temperature of the plasma jet at the surface of the energetic material, and the ablation quality of the energetic material are obtained through experiments;

2) After step 1), the surface temperature of the energetic material under the action of the plasma jet is calculated by simultaneously solving the heat conduction equation inside the energetic material and the ablation model of the plasma jet on the energetic material , ablation rate and ablation quality;

3) Adjust the given energy flow conditions until the calculated ablation mass is consistent with the experimentally obtained ablation mass, thereby determining the actual energy flow of the plasma jet;

4) Using the actual energy flow as the input condition, according to the method described in step 2), calculate the surface temperature and ablation rate of the energetic material when the given energy flow condition is the actual energy flow, and realize the comparison between the plasma jet and the energetic Evaluation of material action properties.

In the above step 2), in order to truly reflect the temperature of the surface of the energetic material, it is necessary to consider the process of the surface of the energetic material being continuously invaded under the action of plasma jet ablation in the calculation, so as to characterize the impact of the invasion process on the surface temperature and ablation impact on rate results. The specific method is:

To solve the equation, the energetic material is discretized into N layers, and the Indicates the temperature value of the location of the i-th layer of energetic material in the computational domain within the j-th time step, and represents the surface temperature at the jth time step. When starting to calculate the jth time step, it is necessary to use formula (8) to estimate the newly ablated layer in this time step according to the current ablation mass m ^j and the number of energetic material layers that have been ablated before. The number n ^j of energetic material layers ablated. Since the energetic material of the previous n ^j layers has been ablated, the n ^jth layer of energetic material in the previous time step becomes the surface layer (layer 0) of the energetic material in the current time step, and accordingly the upper The temperature value of layer n ^j in a time step which becomes the new surface temperature at the jth time step In the formula (8), "integer()" means that only the integer part is reserved for the value in the brackets (because the number of layers of the energetic material can only be an integer), the formula (8) is as follows, where m _l is the energy content of a single layer Quality of material:

${\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; integer</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>\underset{{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}^{{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

The process of the continuous intrusion of the surface of the energetic material under the action of plasma jet ablation is evaluated by the surface intrusion depth, and the calculation method of the inner surface intrusion depth in each time step is: The number of layers n ^j is multiplied by the thickness of each layer of energetic material.

The beneficial effects of the present invention are reflected in:

The present invention utilizes external parameters (discharge voltage, surface pressure of energetic material, and ablation quality of energetic material, etc.) The interaction theory of energetic materials is used to obtain more direct parameters that are difficult to measure directly through experiments during the interaction between plasma jets and energetic materials, including the surface temperature of energetic materials, ablation rate, and the average energy flow from the plasma, etc. In this way, a more comprehensive evaluation of the ablation characteristics of solid energetic materials under the action of plasma jets is realized.

The present invention proposes a method for considering the continuous intrusion process of the surface of the energetic material under the ablation action of the plasma jet, which can consider the actual intrusion process of the surface of the solid energetic material under the action of the plasma jet, so that it is more in line with the action theory and also makes The calculation results are more in line with the objective reality.

Description of drawings

Fig. 1 is the plasma discharge voltage under different voltages obtained in the experiment;

Figure 2 shows the plasma jet pressure on the surface of the energetic material under different voltages obtained in the experiment and the number density calculated from it;

Fig. 3 is a schematic diagram of a method for dealing with surface intrusion of energetic materials;

Figure 4 shows the difference in the calculation results of the plasma jet and SF3 propellant with and without considering the surface intrusion of energetic materials;

Fig. 5 is the flowchart of obtaining the average energy flow from the plasma jet during the action;

Figure 6 shows the average energy flow of the plasma jet calculated using different energetic materials;

Figure 7 shows the surface penetration depths of different energetic materials under the action of plasma jets.

Detailed ways

The present invention will be further described below in conjunction with drawings and embodiments.

The present invention comprises the following steps:

(1) First, the interaction time between the plasma jet and the energetic material, the pressure and temperature of the plasma jet on the surface of the energetic material, and the ablation quality of the energetic material are obtained through experiments;

(2) Based on the above experimental data and inputting the predicted energy flow from the plasma jet, the plasma jet under this energy flow condition is obtained by simultaneously solving the heat conduction equation inside the energetic material and the ablation model of the energetic material by the plasma jet Information such as surface temperature, ablation rate, surface penetration depth and total ablation quality of energetic materials under action;

(3) Adjust the input predicted energy flow data until the calculated total ablation mass is consistent with the experimentally measured ablation mass, thereby determining the actual energy flow from the plasma jet;

(4) Using the calculated actual energy flow as the input condition, use the method described in step 2 to recalculate the action process to obtain information such as the actual surface temperature, ablation rate, and surface penetration depth of the energetic material, so as to realize the Evaluation of the interaction properties of plasma jets with energetic materials.

In order to truly reflect the temperature of the surface of the energetic material, the continuous intrusion process of the surface of the energetic material under the action of plasma jet ablation needs to be taken into account in the calculation.

In the present invention, the specific steps for evaluating the ablation characteristics of solid energetic materials under the action of plasma jets are as follows:

(1) First, the interaction time between the plasma jet and the solid energetic material, the pressure and temperature of the plasma jet near the surface of the solid energetic material, and the ablation quality of the solid energetic material are obtained through experiments. Refer to the typical plasma discharge voltages obtained at 5kV and 7kV charging voltages in Figure 1. The discharge voltage is used to determine the interaction time between the plasma jet and the solid energetic material, and is usually obtained through the termination time of the voltage curve. Corresponding to the data in Figure 1, the interaction time between the plasma jet and the solid energetic material at 5kV and 7kV is 4.4ms and 5.5ms, respectively. Figure 2 shows the typical plasma jet pressure data obtained under the same experimental conditions as in Figure 1, and the plasma jet number density obtained using the equation of state (Equation (1)).

P ₂ =n ₂ kT ₂ (1)

Among them, P ₂ , n ₂ and T ₂ are the pressure, number density and temperature of the plasma respectively, and k is Boltzmann's constant, which is 1.38×10 ^-23 J·K ^-1 . Since the temperature of the air arc plasma is basically on the order of 10 ⁴ K and does not change much, for the sake of simplicity, the temperature of the plasma can be assumed to be constant, so that the plasma jet pressure can be obtained according to the experimentally measured The number density of the body jet.

(2) Based on the experimental data obtained in the previous step, input the predicted energy flow from the plasma jet, and obtain the energy flow by simultaneously solving the heat conduction equation inside the solid energetic material and the ablation model of the solid energetic material by the plasma jet Information such as the surface temperature, ablation rate, surface penetration depth and total ablation quality of the energetic material under the action of the plasma jet under certain conditions;

The heat conduction model inside the energetic material is shown in formula (2), and its boundary conditions are shown in formula (3). where T(x,t) is the temperature at position x inside the energetic material at time t, and q is the energy flow from the plasma jet, _Tr is the ambient temperature, L is the thickness of the energetic material in the calculation area, λ, C _p , ρ and ΔH are the thermal conductivity, specific heat, density and ablation enthalpy of energetic materials, respectively.

$\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; \&rho;</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{<span\; class="notranslate">\; \&PartialD;</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

$\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;H\&Gamma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

T(L,t)=T _r

Given the ablation rate Γ of the energetic material and the energy flow q of the plasma jet, the surface temperature T(0,t) of the energetic material can be obtained by solving equation (2), which is denoted as T ₀ below. The ablation rate of energetic materials can be solved through the dynamic ablation model, equations (4)-(7). Among them, (4)-(6) form a closed equation system with Y ₁ , Y ₂ , and α as the variables to be obtained. By solving it, the energetic material ablation rate Γ can be further obtained through formula (7).

${\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\sqrt{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\frac{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; erfc</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\sqrt{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\sqrt{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; \&alpha;\; exp</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; erfc</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\sqrt{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Where T ₂ , n ₂ and m ₂ are the temperature, number density and average particle mass of the plasma jet, respectively. Among them, n ₂ and m ₂ can be calculated by T ₂ and P ₂ . n ₀ and m ₀ are the number density and average particle mass on the surface of the energetic material, respectively, which are calculated by using the surface temperature T ₀ of the energetic material and the saturated vapor pressure P ₀ of the energetic material. If the composition of the energetic material is constant, the saturated vapor pressure P ₀ is usually a single-valued function of T ₀ , which can be obtained by taking the mass average of the saturated vapor pressure of each component of the energetic material. erfc(α) is an error function about α, and γ represents the specific heat ratio of the plasma. Solving the ablation model can obtain the ablation rate of the plasma jet on the energetic material to determine the boundary conditions in formula (3), thereby realizing the coupling with the heat conduction model.

During the interaction between the plasma jet and the energetic material, due to the continuous ablation effect of the plasma jet on the energetic material, the surface of the energetic material will gradually invade, so that the original internal energetic material is exposed and becomes an energetic material. The new surface of the energy material, its temperature also becomes the new surface temperature. The process of intrusion into the surface of energetic materials can be processed using the method shown in Figure 3. Assuming that the energetic material is discretized into N layers, then Indicates the temperature value at the location of the i-th layer of energetic material in the calculation domain within the jth time step, and the subscript 0 corresponds to the temperature value at the surface of the energetic material. When starting to calculate the jth time step, it is necessary to use formula (8), according to the current ablation mass m ^j and the number of energetic material layers that have been ablated before, to estimate the newly ablated layer in the current time step The number n ^j of energetic material layers ablated. Then the n ^j (from layer 0 to layer n ^j −1) layers of energetic material are removed from the calculation area, so that the n ^jth layer of energetic material becomes the surface of the energetic material. In order to avoid the problem of exhaustion of energetic materials due to the continuous intrusion into the surface of energetic materials, it is necessary to make up the corresponding number of layers at the other end of the calculation area (the back of the energetic materials), and set the temperature of the newly added energetic materials to Let it be room temperature T _r .

${\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; integer</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>\underset{{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}^{{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

where _ml is the mass of a single layer of energetic material.

The calculation method of the penetration depth of the inner surface at each time step is: multiply the number n ^j of layers ablated in the time step by the thickness of each layer of energetic material.

Figure 4 shows the influence of considering and not considering the surface intrusion effect of energetic materials on the interaction characteristics of SF3 energetic materials and plasma jets, from which it can be seen that ignoring the surface intrusion of energetic materials will seriously overestimate the surface temperature and Ablation rate.

(3) The predicted energy flow used in the calculation in the previous step should be selected to be small enough so that the cumulative ablation mass of the energetic material obtained by calculation is smaller than the experimental value. Afterwards, the value of the predicted energy flow is gradually increased, so that the calculated cumulative ablation quality is gradually increased until the obtained ablation quality exceeds the experimental value, as shown in the flow chart in Figure 5. The actual energy flow from the plasma jet can now be determined by interpolation from the previously obtained relationship between the predicted energy flow and the cumulative ablated mass. Figure 6 shows the plasma jet energy flow information obtained using typical experimental results.

(4) Using the calculated actual energy flow to recalculate the interaction process between the plasma jet and the energetic material, simultaneously solve the heat conduction model in the energetic material and the ablation model of the energetic material to obtain the actual energetic material Information such as surface temperature, ablation rate, and surface penetration depth can be used to evaluate the interaction characteristics of plasma jets and energetic materials. Figure 7 shows the calculated surface penetration depths of typical energetic materials (SF3 propellants and GR5 propellants) under the action of plasma jets. This method can also be used to evaluate the influence of different plasma discharge conditions and different energetic material formulations on the action process.

Claims (3)

1. evaluate a method for solid energetic material ablation characteristics under plasma jet effect, it is characterized in that, comprise the following steps:

1) action time of plasma jet and energetic material, the pressure of energetic material surface plasma jet and the ablation quality of temperature and energetic material is obtained first by experiment;

2) through step 1) after, calculate the surface temperature of energetic material under plasma jet effect, ablating rate and ablation quality under given energy flow condition by the equation of heat conduction of simultaneous solution energetic material inside and the dynamics ablating model of plasma jet to energetic material;

3) adjust given energy flow condition, until the ablation uniform quality that the ablation quality calculated obtains with experiment, determine the actual energy stream of plasma jet thus;

4) adopt actual energy stream as initial conditions, according to step 2) described in method, when to calculate given energy flow condition be actual energy stream, the surface temperature of energetic material and ablating rate;

The heat conduction model of energetic material inside is such as formula shown in (2), and its boundary condition is such as formula shown in (3), wherein T (x, t) is the temperature of the inner x position of t energetic material, and q is the energy flow from plasma jet, T _rfor environment temperature, L is the thickness of zoning embodied energy material, λ, C _p, ρ and the Δ H thermal conductivity of energetic material, specific heat, density and ablation enthalpy respectively, Γ is energetic material ablating rate:

$\frac{\&PartialD;T(x,t)}{\&PartialD;t}=\frac{\mathrm{\&lambda;}}{C_p\mathrm{\&rho;}}\&CenterDot;\frac{{\&PartialD;}^{2}T(x,t)}{{\&PartialD;x}^2}---\left(2\right)$

$\frac{\&PartialD;T(0,t)}{\&PartialD;t}=-\frac{1}{\mathrm{\&lambda;}}(q-\mathrm{\&Delta;H\&Gamma;})---\left(3\right)$

T(L,t)＝T _r

。

2. a kind of method evaluating solid energetic material ablation characteristics under plasma jet effect according to claim 1, it is characterized in that: in order to truly reflect the temperature on energetic material surface, need to consider energetic material surface in the calculation under plasma jet ablation effect by the process constantly invaded, concrete grammar is: by discrete for energetic material for N layer, and use represent the temperature value of i-th layer of energetic material position in computational fields in a jth time step, and use representing the surface temperature of a jth time step, when starting to calculate jth time step, utilizing formula (8), according to current ablation quality m ^jwith before this ablated fall the energetic material number of plies, to estimate in this time step newly ablated fall energetic material number of plies n ^j, then n-th in a time step is gone up ^jlayer energetic material just becomes the superficial layer of energetic material in current time step, correspondingly to go up in a time step n-th ^jthe temperature value of layer also surface temperature new in a jth time step is just become formula (8) is as follows, m in formula (8) _lquality for individual layer energetic material:

$n^j=\mathrm{integer}\left(\frac{m^j-\underset{j^{\&prime;}=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{n}^{j^{\&prime;}}{m}_l}{m_l}\right)---\left(8\right).$

3. a kind of method evaluating solid energetic material ablation characteristics under plasma jet effect according to claim 2, it is characterized in that: described energetic material surface is adopted surperficial depth of invasion to evaluate by the process constantly invaded under plasma jet ablation effect, and the computational methods of each time step inner surface depth of invasion are: by number of plies n ablated in this time step ^jbe multiplied by the thickness of every layer of energetic material.