CN103267830A - 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 characteristic of a solid energetic material under the plasma jet action. The method comprises the following steps: 1, carrying out experiments to obtain the plasma jet and energetic material action time, the pressure and temperature of the plasma jet, and the ablation mass; 2, carrying out simultaneous solution of the internal thermal conduction equation of the energetic material and the plasma jet energetic material ablation model to obtain the surface temperature, the surface intrusion depth and the total ablation mass in the action process under the plasma jet action under an energy flow condition; 3, adjusting the input plasma jet energy flow data until the ablation mass obtained through calculation is consistent with the ablation mass measured through the experiment to determine the practical energy flow from the plasma jet; and 4, adopting the practical energy flow obtained through calculation as an input condition to obtain the practical surface temperature, the surface intrusion depth and the like of the energetic material in order to realize the evaluation of the plasma jet and energetic material action characteristic.

Description

Estimate the method for solid energetic material ablation characteristics under the plasma jet effect

Technical field

The present invention relates to assess the method for plasma jet and energetic material action characteristic, be specifically related to a kind of method of assessing electrothermal chemical gun ionic medium body jet and energetic material action characteristic.

Background technology

Plasma jet is lighted a fire and combustion-supporting means to the solid energetic material as commonly used, is widely used.For example when energetic material was propellant powder, plasma jet can be used for the plasma igniting source in the electrothermal chemical gun, and when energetic material was propellant, plasma jet can be used for igniting and the auxiliary combustion means of spacecraft propulsion device.

The mechanism of plasma jet and solid energetic material can be divided into ignition last stage, ignition stage and smooth combustion stage usually.Wherein in the ignition last stage, the solid energetic material mainly is subjected to the influence of the ablation effect of plasma jet, this process has determined the starting condition in ignition stage, affect many important parameters of energetic material igniting, the content that comprises gas phase energetic material in solid energetic material surface temperature and the surrounding environment, so the combined action effect of article on plasma body jet and solid energetic material has very significant effects.Yet the method that does not also have a kind of effectively evaluating solid energetic material ablation characteristics under the plasma jet effect at present.

Summary of the invention

The object of the present invention is to provide a kind of method of estimating solid energetic material ablation characteristics under the plasma jet effect.

For achieving the above object, the present invention has adopted following technical scheme:

1) obtains the 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 at first by experiment;

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

3) adjust given energy stream condition, up to the ablation uniform quality that the ablation quality that calculates and experiment obtain, determine the actual energy stream of plasma jet thus;

4) adopt actual energy stream as initial conditions, according to step 2) described method, when calculating given energy stream condition and being actual energy stream, the surface temperature of energetic material and ablating rate are realized the assessment of article on plasma body jet and energetic material action characteristic.

Described step 2) in, for the temperature on true reflection energetic material surface, need in calculating, consider the process that the energetic material surface is constantly invaded under plasma jet ablation effect, to characterize invasion procedure to surface temperature and ablating rate result's influence.Concrete grammar is:

For equation is found the solution, it is the N layer that energetic material is dispersed, and uses

The temperature value of representing i layer energetic material position in the interior computational fields of j time step, and

Representing the surface temperature of j time step.When beginning to calculate j time step, need utilize formula (8), according to current ablation quality m ^jWith the ablated energetic material number of plies of falling before this, estimate the new ablated energetic material number of plies n that falls in this time step ^jBecause preceding n ^jThe energetic material of layer is ablated, then goes up the n in the time step length ^jLayer energetic material just becomes the superficial layer (the 0th layer) of energetic material in the current time step-length, correspondingly goes up n in the time step length ^jThe temperature value of layer

Also just become new surface temperature in j the time step

" integer () " expression only keeps integral part (because the number of plies of energetic material can only round numbers) to the numerical value in the bracket in formula (8), and formula (8) is as follows, wherein m _lQuality for the individual layer energetic material:

$n^j=\mathrm{integer}\left(\frac{m^j-\underset{j^{\′}=1}{\overset{j-1}{\mathrm{\Σ}}}{m}^{j^{\′}}{m}_l}{m_l}\right)---\left(8\right)$

。

The process that described energetic material surface is constantly invaded under plasma jet ablation effect adopts surperficial invasion depth to estimate, and the computing method of each time step inside surface invasion depth are: with number of plies n ablated in this time step ^jMultiply by the thickness of every layer of energetic material.

Beneficial effect of the present invention is embodied in:

The present invention utilizes the external parameter (sparking voltage that can utilize common laboratory facilities to obtain in plasma jet and the solid energetic material interaction process, energetic material surface pressure, and energetic material ablation quality etc.), obtain in plasma jet and the energetic material mechanism more direct according to plasma and solid energetic material intreractive theory, be difficult to the direct parameter of measuring by experiment, the surface temperature that comprises energetic material, ablating rate and from mean energy flows of plasma etc. has been realized the evaluation more comprehensively of solid energetic material ablation characteristics under the jet action of article on plasma body thus.

The present invention proposes the method for considering energetic material surface continuous invasion procedure of quilt under plasma jet ablation effect, can consider the actual invasion procedure on solid energetic material surface under the plasma jet effect, thereby more meet intreractive theory, also make result of calculation more meet objective reality.

Description of drawings

Fig. 1 is plasma sparking voltage under the different voltages that obtain in the experiment;

Fig. 2 reaches the number density that is obtained by its reckoning for energetic material surface plasma jet pressure under the different voltages that obtain in the experiment;

Fig. 3 is for handling the synoptic diagram of energetic material surface intrusion method;

Fig. 4 does not invade the difference of article on plasma jet and SF3 propellant powder effect result of calculation for considering with not considering the energetic material surface;

Fig. 5 is for obtaining in the mechanism process flow diagram from the plasma jet mean energy flows;

Fig. 6 is the plasma jet mean energy flows of utilizing different energetic materials to calculate;

Fig. 7 is the surperficial invasion depth of different energetic materials under the plasma jet effect.

Embodiment

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

The present invention includes following steps:

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

(2) based on above-mentioned experimental data, and the energy stream from plasma jet of input prediction, the heat-conduction equation by simultaneous solution energetic material inside and plasma jet obtain under this energy stream condition the total information such as ablation quality of surface temperature, ablating rate, surperficial invasion depth and the mechanism of energetic material under the plasma jet action to the energetic material ablating model;

(3) adjust the prediction energy flow data of importing, up to the total ablation quality that calculates and the ablation uniform quality that experiment records, determine the actual energy stream from plasma jet thus;

(4) adopt the actual energy that calculates acquisition to flow as initial conditions, utilize the method described in the step 2 that mechanism is recomputated, obtain actual information such as energetic material surface temperature, ablating rate and surperficial invasion depth, realize the assessment of article on plasma body jet and energetic material action characteristic.

Temperature for true reflection energetic material surface need take into account the continuous invasion procedure of energetic material surface under plasma jet ablation effect in calculating.

The present invention is as follows to solid energetic material evaluation concrete steps of ablation characteristics under the plasma jet effect:

(1) obtains action time of plasma jet and solid energetic material at first by experiment, pressure and the temperature of solid energetic material near surface plasma jet, and the ablation quality of solid energetic material.Referring to the classicalpiston sparking voltage that obtains under 5kV among Fig. 1 and the 7kV charging voltage, sparking voltage is used for determining the action time of plasma jet and solid energetic material, obtains constantly by the termination of voltage curve usually.Data in the corresponding diagram 1, be respectively 4.4ms and 5.5ms the action time of plasma jet and solid energetic material under 5kV and the 7kV.Provided among Fig. 2 with Fig. 1 same experimental conditions under the classicalpiston jet pressure data that obtains, and the plasma jet number density of utilizing state equation (formula (1)) to obtain.

P ₂=n ₂kT ₂ （1）

P wherein ₂, n ₂With T ₂Be respectively pressure, number density and the temperature of plasma, and k is Boltzmann constant, value is 1.38 * 10 ^-23JK ^-1Because the temperature of air arc-plasma is basically all 10 ⁴The K order of magnitude and variation are little, therefore for simplicity, the temperature of plasma can be assumed to be constant, just can obtain the number density of plasma jet thus according to the plasma jet pressure that experiment records.

(2) experimental data that obtains based on previous step, the energy stream from plasma jet of input prediction, the heat-conduction equation by simultaneous solution solid energetic material inside and plasma jet obtain under this energy stream condition the total information such as ablation quality of surface temperature, ablating rate, surperficial invasion depth and the mechanism of energetic material under the plasma jet action to solid energetic material ablating model;

The heat conduction model of energetic material inside as the formula (2), and its boundary condition is as the formula (3).Wherein (x be the t temperature of the inner x of energetic material position constantly t), and q is the energy stream from plasma jet to T, T _rBe environment temperature, L is the thickness of zoning embodied energy material, λ, C _p, ρ and Δ H thermal conductivity, specific heat, density and the ablation enthalpy of energetic material respectively.

$\frac{\∂T(x,t)}{\∂t}=\frac{\mathrm{\λ}}{C_p\mathrm{\ρ}}\·\frac{{\∂}^{2}T(x,t)}{{\∂x}^2}---\left(2\right)$

$\frac{\∂T(0,t)}{\∂t}=-\frac{1}{\mathrm{\λ}}(q-\mathrm{\ΔH\Γ})---\left(3\right)$

T(L,t)=T _r

Just can flow at given energetic material ablating rate Γ and plasma jet under the situation of q can by find the solution the temperature T that formula (2) obtains the energetic material surface (0, t), below be designated as T ₀And the energetic material ablating rate can pass through the dynamics ablating model, and find the solution formula (4)-(7).Wherein (4)-(6) have been formed with Y ₁, Y ₂, α is the sealing system of equations of unknown variable.Finding the solution just further to it, through type (7) obtains energetic material ablating rate Γ.

${\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HDA00003165244000021.png,HDA00003165244000031.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1={[\sqrt{1+\mathrm{\&pi;}{(\frac{\mathrm{\&gamma;}-1}{\mathrm{\&gamma;}+1}\&CenterDot;\frac{\mathrm{\&alpha;}}{2})}^2}-\sqrt{\mathrm{\&pi;}}\frac{\mathrm{\&gamma;}-1}{\mathrm{\&gamma;}+1}\&CenterDot;\frac{\mathrm{\&alpha;}}{2}]}^2---\left(4\right)$

${\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HDA00003165244000011.png,HDA00003165244000012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2=\sqrt{\frac{1}{Y_1}}[({\mathrm{\&alpha;}}^2+\frac{1}{2})\exp \left({\mathrm{\&alpha;}}^2\right)\mathrm{erfc}\left(\mathrm{\&alpha;}\right)-\frac{\mathrm{\&alpha;}}{\sqrt{\mathrm{\&pi;}}}]+\frac{1}{{2Y}_1}[1-\sqrt{\mathrm{\&pi;}}\mathrm{\&alpha;exp}\left({\mathrm{\&alpha;}}^2\right)\mathrm{erfc}\left(\mathrm{\&alpha;}\right)]---\left(5\right)$

${\mathrm{\&alpha;}}^2=\frac{1}{2}\frac{(\frac{n_2{T}_2}{n_0{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA00003165244000012.png,HDA00003165244000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}\frac{1}{Y_1{Y}_2}-1)}{(1-Y_2\frac{m_0{n}_0}{m_2{n}_2})}---\left(6\right)$

$\mathrm{\&Gamma;}=\mathrm{\&alpha;}\&CenterDot;m_0{\mathrm{<figure-callout\; id="0"\; label="n"\; filenames="HDA00003165244000012.png,HDA00003165244000021.png"\; state="\{\{state\}\}">n</figure-callout>}}_0\&CenterDot;\sqrt{\frac{2k{T}_0}{m_0}}{Y}_2\sqrt{Y_1}---\left(7\right)$

T wherein ₂, n ₂With m ₂Be respectively temperature, number density and the mass average particle of plasma jet.N wherein ₂With m ₂Can pass through T ₂With P ₂Calculate.n ₀With m ₀Be respectively number density and the mass average particle on energetic material surface, utilize energetic material surface temperature T ₀, in conjunction with the saturated vapor pressure P of energetic material ₀Calculate.If the composition of energetic material is certain, then saturated vapor pressure P ₀T normally ₀Single-valued function, can on average obtain by the saturated vapor pressure of each component of energetic material is done quality.Erfc (α) is the error function about α, and γ represents the specific heat ratio of plasma.Find the solution ablating model and can obtain plasma jet to the ablating rate of energetic material, to determine the boundary condition in the formula (3), realize the coupling with heat conduction model thus.

In the mechanism of plasma jet and energetic material, because the ablation effect that plasma jet continues energetic material, the surface of energetic material can progressively be invaded, make to be positioned at originally that inner energetic material is exposed and the new surface that becomes energetic material, its temperature also becomes new surface temperature.Invasion procedure to the energetic material surface can utilize the method shown in Fig. 3 to handle.Supposing that energetic material is dispersed is the N layer, then

Represent the temperature value of i layer energetic material position in the interior computational fields of j time step, 0 label subscript correspondence the temperature value of energetic material surface.When beginning to calculate j time step, need utilize formula (8), according to current ablation quality m ^jWith the ablated energetic material number of plies of falling before this, estimate the new ablated energetic material number of plies n that falls in the current time step-length ^jThen with this n ^j(from 0 layer to n ^j-1 layer) a layer energetic material remove in the zoning, makes n ^jLayer energetic material becomes the surface of energetic material.And for fear of constantly invading the problem that causes energetic material to run out because consider the energetic material surface, need supply the corresponding number of plies at the other end (back side of energetic material) of zoning, and the energetic material temperature that will newly cover is made as room temperature T _r

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

M wherein _lQuality for the individual layer energetic material.

The computing method of each time step inside surface invasion depth are: with number of plies n ablated in this time step ^jMultiply by the thickness of every layer of energetic material.

Fig. 4 has provided and has considered not invade effect to the influence of SF3 energetic material and plasma jet action characteristic with not considering the energetic material surface, therefrom ignores surface temperature and ablating rate that energetic material can be seriously over-evaluated in energetic material surface intrusion as can be seen.

(3) the prediction energy stream that adopts during previous step is calculated should be chosen enough for a short time, makes the energetic material accumulation ablation quality of calculating acquisition less than experiment value.After this then progressively improve the numerical value of prediction energy stream, progressively promote so that calculate the accumulation ablation quality that obtains, surpass experiment value up to the ablation quality that obtains, shown in the process flow diagram that Fig. 5 provides.Just can flow the relation with accumulation ablation quality this moment by the prediction energy that obtains before this, determines actual energy stream from plasma jet by interpolation.And Fig. 6 has provided the plasma jet energy stream information that utilizes typical experimental result to obtain.

(4) mechanism that adopts the actual energy that calculates acquisition to flow article on plasma body jet and energetic material recomputates, heat conduction model in the simultaneous solution energetic material and the ablating model of energetic material, obtain actual information such as energetic material surface temperature, ablating rate and surperficial invasion depth, realize the assessment of article on plasma body jet and energetic material action characteristic.Fig. 7 has provided and has calculated the surperficial invasion depth of typical energetic material (SF3 propellant powder and GR5 propellant powder) under the plasma jet effect that obtains.Adopt this method to make assessment with different energetic material prescriptions to the influence of mechanism to different plasma discharge conditions.

Claims (3)

1. a method of estimating solid energetic material ablation characteristics under the plasma jet effect is characterized in that, may further comprise the steps:

1) obtains the 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 at first by experiment;

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

3) adjust given energy stream condition, up to the ablation uniform quality that the ablation quality that calculates and experiment obtain, determine the actual energy stream of plasma jet thus;

4) adopt actual energy stream as initial conditions, according to step 2) described method, when calculating given energy stream condition and being actual energy stream, the surface temperature of energetic material and ablating rate.

2. according to the described a kind of method of estimating solid energetic material ablation characteristics under the plasma jet effect of claim 1, it is characterized in that: for the temperature on true reflection energetic material surface, need in calculating, consider the process that the energetic material surface is constantly invaded under plasma jet ablation effect, concrete grammar is: energetic material is dispersed is the N layer, and uses

Represent the temperature value of i layer energetic material position in the interior computational fields of j time step, and use

Represent the surface temperature of j time step, when beginning to calculate j time step, utilize formula (8), according to current ablation quality m ^jWith the ablated energetic material number of plies of falling before this, estimate the new ablated energetic material number of plies n that falls in this time step ^j, then go up the n in the time step length ^jLayer energetic material just becomes the superficial layer of energetic material in the current time step-length, correspondingly goes up n in the time step length ^jThe temperature value of layer

Also just become new surface temperature in j the time step

Formula (8) is as follows, m in the formula (8) _lQuality for the individual layer energetic material:

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

。

3. according to the described a kind of method of estimating solid energetic material ablation characteristics under the plasma jet effect of claim 2, it is characterized in that: the process that described energetic material surface is constantly invaded under plasma jet ablation effect adopts surperficial invasion depth to estimate, and the computing method of each time step inside surface invasion depth are: with number of plies n ablated in this time step ^jMultiply by the thickness of every layer of energetic material.

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