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 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

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

Technical field

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

Background technology

Plasma jet carries out lighting a fire and combustion-supporting means to solid energetic material as conventional, is widely used.Such as when energetic material is propellant powder, plasma jet can be used for the plasma igniting source in electrothermal chemical gun, and when energetic material is 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, solid energetic material is mainly subject to the impact of the ablation effect of plasma jet, this process determines the primary condition in ignition stage, affect many important parameters of Ignition of Energetic Materials, comprise the content of gas phase energetic material in solid energetic material surface temperature and surrounding environment, therefore the comprehensive function effect of plasma jet and solid energetic material has very important impact.But also there is no the method for a kind of effectively evaluating solid energetic material ablation characteristics under plasma jet effect at present.

Summary of the invention

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

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

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) after step 1), the surface temperature of energetic material under plasma jet effect, ablating rate and ablation quality under given energy flow condition is calculated by the equation of heat conduction of simultaneous solution energetic material inside and the 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, realize the assessment of plasma jet and energetic material action characteristic.

Described step 2) in, in order to truly reflect the temperature on energetic material surface, need to consider energetic material surface in the calculation by the process constantly invaded under plasma jet ablation effect, to characterize the impact of invasion procedure surface temperature and ablating rate result.Concrete grammar is:

In order to solve equation, by discrete for energetic material be N layer, and to use represent the temperature value of i-th layer of energetic material position in computational fields in a jth time step, and represent the surface temperature of a jth time step.When starting to calculate jth time step, need to utilize 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.Due to front n ^jthe energetic material of layer is ablated, then go up n-th in a time step ^jlayer energetic material just becomes the superficial layer (the 0th 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 in formula (8), " integer () " represents and only retains integer part (because the number of plies of energetic material can only round numbers) to the numerical value in bracket, and formula (8) is as follows, wherein m _lquality for individual layer energetic material:

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

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.

Beneficial effect of the present invention is embodied in:

The present invention utilizes the external parameter (discharge voltage that usual laboratory facilities can be utilized to obtain in plasma jet and solid energetic material interaction process, energetic material surface pressure, and energetic material ablation quality etc.), obtain in plasma jet and energetic material mechanism more direct according to plasma and solid energetic material intreractive theory, be difficult to the parameter directly measured by experiment, comprise the surface temperature of energetic material, ablating rate and the mean energy flows etc. from plasma, thus achieve the evaluation more comprehensively of solid energetic material ablation characteristics under plasma jet action.

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

Accompanying drawing explanation

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

Fig. 2 is energetic material surface plasma jet pressure and calculate the number density that obtains by it under the different voltages obtained in experiment;

Fig. 3 is the schematic diagram of process energetic material surface intrusion method;

Fig. 4 considers and does not consider that energetic material surface invades the difference of article on plasma jet and SF3 propellant powder effect result of calculation;

Fig. 5 obtains the flow chart from plasma jet mean energy flows in mechanism;

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

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

Detailed description of the invention

Below in conjunction with drawings and Examples, the invention will be further described.

The present invention includes following steps:

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

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

(3) the predict energy flow data of adjustment input, until the ablation uniform quality that the total ablation quality calculated records with experiment, determines the actual energy stream from plasma jet thus;

(4) adopt the actual energy stream calculating and obtain as initial conditions, the method described in step 2 is utilized to recalculate mechanism, obtain the information such as actual energetic material surface temperature, ablating rate and surperficial depth of invasion, realize the assessment of plasma jet and energetic material action characteristic.

In order to truly reflect the temperature on energetic material surface, need to take into account the continuous invasion procedure of energetic material surface under plasma jet ablation effect in the calculation.

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

(1) action time of plasma jet and solid energetic material is obtained first by experiment, the pressure of solid energetic material near surface plasma jet and temperature, and the ablation quality of solid energetic material.See the classicalpiston discharge voltage obtained under 5kV and 7kV charging voltage in Fig. 1, discharge voltage, for determining the action time of plasma jet and solid energetic material, is obtained by the end time of voltage curve usually.Data in corresponding diagram 1, under 5kV and 7kV, the action time of plasma jet and solid energetic material is respectively 4.4ms and 5.5ms.Give in Fig. 2 and the classicalpiston jet pressure data that obtains under Fig. 1 same experimental conditions, and the plasma jet number density that utilization state equation (formula (1)) obtains.

P ₂=n ₂kT ₂（1）

Wherein P ₂, n ₂with T ₂be respectively the pressure of plasma, number density and temperature, and k is Boltzmann constant, value is 1.38 × 10 ^-23jK ^-1.Because the temperature of air arc-plasma is substantially all 10 ⁴the K order of magnitude and change is little, therefore for simplicity, the temperature of plasma can be assumed to be constant, the plasma jet pressure that just can experimentally record thus obtains the number density of plasma jet.

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

As the formula (2), and its boundary condition as the formula (3) for the heat conduction model of energetic material inside.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.

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

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

T(L,t)=T _r

Just can obtain by solving formula (2) when given energetic material ablating rate Γ and plasma jet can flow q energetic material surface temperature T (0, t), be below designated as T ₀.And energetic material ablating rate is by dynamics ablating model, formula (4)-(7) solve.Wherein (4)-(6) constitute with Y ₁, Y ₂, α is the Closure equation group of unknown variable.It is solved and just can obtain energetic material ablating rate Γ further by formula (7).

$Y_1={[\sqrt{1+\mathrm{\π}{(\frac{\mathrm{\γ}-1}{\mathrm{\γ}+1}\·\frac{\mathrm{\α}}{2})}^2}-\sqrt{\mathrm{\π}}\frac{\mathrm{\γ}-1}{\mathrm{\γ}+1}\·\frac{\mathrm{\α}}{2}]}^2---\left(4\right)$

$Y_2=\sqrt{\frac{1}{Y_1}}[({\mathrm{\α}}^2+\frac{1}{2})\exp \left({\mathrm{\α}}^2\right)\mathrm{erfc}\left(\mathrm{\α}\right)-\frac{\mathrm{\α}}{\sqrt{\mathrm{\π}}}]+\frac{1}{{2Y}_1}[1-\sqrt{\mathrm{\π}}\mathrm{\αexp}\left({\mathrm{\α}}^2\right)\mathrm{erfc}\left(\mathrm{\α}\right)]---\left(5\right)$

${\mathrm{\α}}^2=\frac{1}{2}\frac{(\frac{n_2{T}_2}{n_0{T}_0}\frac{1}{Y_1{Y}_2}-1)}{(1-Y_2\frac{m_0{n}_0}{m_2{n}_2})}---\left(6\right)$

$\mathrm{\Γ}=\mathrm{\α}\·m_0{n}_0\·\sqrt{\frac{2k{T}_0}{m_0}}{Y}_2\sqrt{Y_1}---\left(7\right)$

Wherein T ₂, n ₂with m ₂be respectively the temperature of plasma jet, number density and mass average particle.Wherein n ₂with m ₂by 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 ₀normally T ₀monotropic function, on average obtain by doing quality to the saturated vapor pressure of each component of energetic material.Erfc (α) is the error function about α, and γ represents the specific heat ratio of plasma.Solve ablating model and can obtain the ablating rate of plasma jet to energetic material, to determine the boundary condition in formula (3), realize and being coupled of heat conduction model thus.

In the mechanism of plasma jet and energetic material, due to the ablation effect that plasma jet continues energetic material, the surface of energetic material can progressively invade, make originally to be positioned at inner energetic material be exposed and become the new surface of energetic material, its temperature also becomes new surface temperature.The method shown in Fig. 3 can be utilized to process the invasion procedure on energetic material surface.Suppose energetic material by discrete for N layer, then represent the temperature value of i-th layer of energetic material position in computational fields in a jth time step, 0 label subscript correspond to the temperature value of energetic material surface.When starting to calculate jth time step, need to utilize formula (8), according to current ablation quality m ^jwith before this ablated fall the energetic material number of plies, to estimate in current time step newly ablated fall energetic material number of plies n ^j.Then by this n ^j(from 0 layer to n ^j-1 layer) layer energetic material remove in zoning, makes n-th ^jlayer energetic material becomes the surface of energetic material.And in order to avoid because consider that energetic material is surperficial constantly invade the problem causing energetic material to run out, need to supply the corresponding number of plies at the other end (back side of energetic material) of zoning, and the energetic material temperature newly covered is set to room temperature T _r.

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

Wherein m _lfor the quality of individual layer energetic material.

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.

Fig. 4 gives and considers and do not consider that energetic material surface invades the impact of effect on SF3 energetic material and plasma jet action characteristic, therefrom can find out and ignore surface temperature and the ablating rate that the surperficial intrusion of energetic material seriously can over-evaluate energetic material.

(3) the predict energy stream that previous step adopts in calculating should be chosen enough little, makes to calculate the energetic material accumulation ablation quality obtained and is less than experiment value.After this then progressively improve the numerical value of predict energy stream, progressively promote, until the ablation quality obtained exceedes experiment value, as shown in the flow chart that Fig. 5 provides to make the calculating accumulation ablation quality obtained.Now just can pass through the relation of predict energy stream and the accumulation ablation quality obtained before this, determine the actual energy flow from plasma jet by interpolation.And Fig. 6 gives the plasma jet energy flow utilizing typical experimental result to obtain information.

(4) mechanism calculating actual energy stream plasma jet and the energetic material obtained is adopted to recalculate, heat conduction model in simultaneous solution energetic material and the ablating model of energetic material, obtain the information such as actual energetic material surface temperature, ablating rate and surperficial depth of invasion, realize the assessment of plasma jet and energetic material action characteristic.Fig. 7 gives typical energetic material (SF3 propellant powder and GR5 propellant powder) the surperficial depth of invasion under plasma jet effect calculating and obtain.Adopt this method can also make assessment on different plasma discharge conditions from the impact of different energetic material formulas on mechanism.

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:

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

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

T(L,t)＝T _r

。

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:

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

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.