Energy Skin Effect of Propellant Particles inElectrothermal-Chemical Launcher

Yong Jin and Baoming LiNational Key Laboratory of Transient PhysicsNanjing University of Science and Technology

Nanjing, ChinaEmail: kingdeyu@163.com

Abstract—A numerical model of the radiation has been em-ployed by a Monte Carlo method and statistical physics to simu-late the process of a capillary plasma source for Electrothermal-Chemical (ETC) Launcher. The effect on propellants with differ-ent physical parameters is discussed. The plasma-propellant in-teraction is also discussed when combined with a thermal model.Results show that radiant energy only causes a small field aroundthe plasma injector in the propellant bed. The responses of energyflux and propellant particles on radiation are both in the order ofpicosecond. The strong instantaneous radiation is responsible forthe transmission of energy to the propellant particles leadingto ignition. Compared with conventional ignition, the energyabsorbed by propellant particles is used to increase quickly thetemperature in the surface layer of propellant particles. Thisenergy skin effect in the propellant particle surface appears tobe the main cause of plasma ignition.

I. INTRODUCTION

Fundamental understanding of the electrothermal-chemical(ETC) plasma propulsion concept can potentially lead toan improvement regarding the performance of conventionalballistic weapons. It is known that plasma temperatures inthe electrothermal and electromagnetic accelerator are between0.35eV (4,000K) to 3eV (35,000K) [1]. At the moment thatplasma is injected into a propellant bed, energy is transferredquickly to the propellant particles via radiation. This is notonly the dominant effect for energy transport in hot plasma, butis also responsible for the transmission of energy to propellantparticles leading to ignition [2]. Before the ignition, there mustbe a strong instantaneous radiation that may potentially beused to optimize the ignition and combustion processes. Ex-perimentally, it is tedious to obtain instantaneous informationon radiation [3]-[9].

In this work, we employ a Monte Carlo method in attemptto understand the characteristics of plasma and its interactionwith propellant particles.

II. MODEL AND ASSUMPTIONS

A Monte Carlo method was used to simulate the radiationprocess. Our calculation model was established based on thefollowing assumptions.

978-1-4673-0305-7/12/$31.00 c⃝ 2012.IEEE

Plasma is a blackbody radiation, and the radiant energy 𝐸b

is𝐸b = 𝜎𝑇 4 (1)

where 𝜎 is Stefan-Boltzmann constant and 𝑇 is the plasmatemperature. The temperature inside a plasma injector isassumed to be finite and constant. The radiant energy consistsof 𝑛 energy beams and each energy beam has an energy 𝐸given by

𝐸 = 𝐸b/𝑛 = 𝜎𝑇 4/𝑛 (2)

We also assume that the radiation and absorption of propel-lant particles follow Kirchhoff’s law, based on local thermody-namic equilibrium (LTE) conditions [2], [10]. The propellantsare assumed to be spherical and have diffuse reflective sur-faces.Their quantum absorption Δ𝐸p is

Δ𝐸p = 𝛼 ⋅ 𝐸 = 𝛼 ⋅ 𝜎𝑇4

𝑛(3)

where 𝛼 is the average absorption coefficient. We also assumethat the scattering direction of the energy beam is random.All of the energy absorbed by the propellant particles areused to increase the temperature on their surfaces. And thewall of cartridge is assumed to have the same absorptioncharacteristics as the propellant particles.

The gases among the propellant particles are assumed tobehave as optical film, and also in thermodynamic equilibriumwith the attenuation to the energy beam 𝐸′ described as

𝐸′ = 𝐸 ⋅ exp(−𝛽𝑠) (4)

where 𝑠 is the length of the path and 𝛽 is the attenuationcoefficient of the gases in cartridge. 𝛽 is assumed to be 0.01in the calculations.

A two-dimensional model employed in our calculations isshown schematically in Fig. 1. All propellant particles areuniformly aligned around the serial arc plasma injector in thecenter of the cartridge, and are characterized by a porosity 𝑃and an average absorption coefficient 𝛼.

This radiation model is coupled with a thermal model asshown schematically in Fig. 2 to predict the surface tempera-ture of propellant particles and the temperature distributionin the cartridge [11], [12]. It is reasonable to assume thatradiative heat transfer from plasma source to the surface of

Plasma Injector

Propellant

Propellant Particles

a b c

Fig. 1. Schematic diagram of radiative model.

Propellant Particle

T0

Surface of Propellant

Energy Flux of Radiation

Heat Conduction fromthe Surface to theInner Propellant Particle

Ts

Fig. 2. Schematic diagram of thermal model.

propellant particles is extremely efficient in a strong instan-taneous radiation. Hence, heat transfer from the surface tothe inner propellant particles is relatively slow. Based on thisassumption, we define the surface layer of propellant particlesas the area in the dashed boundaries in Fig. 2, and it canbe approximated as an adiabatic boundary. If we consider theenergy of the 𝑖th propellant particle absorbed from plasma toincrease its surface temperature, we can write

𝑚 ⋅ 𝑘 ⋅ 𝐶𝑝 ⋅Δ𝑇𝑖 = (𝑞𝑖 − 𝜆 ⋅ ∂𝑇𝑖/∂𝑙) ⋅Δ𝑡 (5)

where 𝑞𝑖 is the energy flux reached in the surface of thepropellant particle, as calculated by the radiative model. 𝐶𝑝

and 𝜆 are the specific heat at constant pressure and thermalconductivity of propellant particles. Based on the parametersof JA2 [11], we selected 𝐶𝑝 and 𝜆 as 1520.45J/(kg⋅K) and0.28W/(m⋅K) respectively; 𝑚 is the mass of propellant particleand we set 𝑚=5.149g. Δ𝑡 is the actual time of radiation. 𝑘 isthe volume ratio of surface layer with propellant particle. Fora spherical particle, we have

𝑘 = (3𝑅2 − 3𝑅+ 1)/𝑅3 (6)

where 𝑅 is the ratio of the surface layer thickness 𝑟s to theradius of propellant particle 𝑟. The radius of propellant particle

is on the order of 10−3m, and the molecular structure fororganic large molecule is usually on the order of 10−7m,Hence, 𝑅 is assumed as 10,000 in our calculations with𝑘 ≈ 0.0003.

For an isotropic spherical particle, ∂𝑇𝑖/∂𝑙 is the temperaturegradient of the 𝑖th propellant particle

∂𝑇𝑖/∂𝑙 = Δ𝑇𝑖/𝑟 (7)

Substituting (7) into (5) yields

Δ𝑇𝑖 = 𝑞𝑖 ⋅Δ𝑡/(𝑚 ⋅ 𝑘 ⋅ 𝐶𝑝 + 𝜆 ⋅Δ𝑡/𝑟) (8)

Therefore, the surface temperature of the 𝑖th propellantparticle can be written as

𝑇s𝑖 = 𝑇0 +Δ𝑇𝑖 = 𝑇0 + 𝑞𝑖 ⋅Δ𝑡/(𝑚 ⋅ 𝑘 ⋅ 𝐶𝑝 + 𝜆 ⋅Δ𝑡/𝑟) (9)

where 𝑇0 is the initial temperature of propellant particles(288.15K).

It is anticipated that heat transfer from surface to the innerpropellant particle is minimal (𝑞𝑖 ≫ 𝜆 ⋅ ∂𝑇𝑖/∂𝑙). The mainfunction of radiation is the instantaneous heating to the surfacelayer of propellant particle, and the surface layer temperaturecan maintain a constant increasing trend as a result of theradiation.

Here we introduce an efficiency of “hot zone” 𝜂h by definingthe “hot zone” as the area in cartridge where the surfacetemperature of propellant particles is more than the ignitiontemperature of propellant particles 𝑇c (600K). The propel-lant particles have absorbed enough energy and the plasmaradiation can ignite these propellant particles instantaneously.Hence, we have

𝜂h = 𝑁h/𝑁 (10)

where 𝑁h is the number of propellant particles in “hot zone”and 𝑁 is the total number of propellant particles in thecartridge.

III. RESULTS AND DISCUSSION

All numerical results discussed in this work were obtainedafter the transfer with 10,000 energy beams in standard con-dition.

The radiant energy distribution in cartridge when𝑇=30,000K, 𝛼=0.1, and 𝑃=0.717257 is shown in Fig.3. It clearly shows that the effect of radiant energy is justover a small field around the plasma injector in the propellantbed [12]. The farther the radial distance, the fewer radiantenergy it has in the cartridge. The radiant energy becomeszero as the radial distance is more than 10 times of thepropellant particle’s diameter. In the actual propellant bed,the penetration depth of radiation is nearly 5 times of thepropellant particle’s diameter.

The radiation model is coupled with a thermal model toconduct an investigation in the response of propellant particlesin the cartridge. Fig. 4 shows the change of radiant intensityin the surface layer of propellant particles for 10ps, 100ps,and 1ns (a, b, and c are No. 1, 3, and 5 propellant particlesshown in Fig. 1), respectively. The stronger radiation is shown

Energy Flux (W/m2)

3.2E+083.0E+082.8E+082.6E+082.4E+082.2E+082.0E+081.8E+081.6E+081.4E+081.2E+081.0E+088.0E+076.0E+074.0E+072.0E+07

T=30,000K α=0.1 P=0.717257

Fig. 3. Distribution of radiant energy flux in cartridge when 𝑇=30,000K,𝛼=0.1, and 𝑃=0.717257.

100ps 1ns

(a)

10ps

(b)

(c)

Fig. 4. Radiant intensity in surface layer of propellant particles when𝑇=30,000K, 𝛼=0.1, and 𝑃=0.717257.

as bright white in Fig. 4. It can be seen intuitively that radiantintensity decreases from position a to c at different times as aresult of the rapid attenuation along the radial direction. Theradiant intensity of the surface layer of propellant particlesalso increases rapidly, suggesting that the surface layer ofpropellant particles has a high reaction rate with the radiation.

We also obtain quantitative results of this process. Fig. 5shows the radiant energy flux and temperature in the surfacelayer of the propellant particle (position a in Fig. 1) when𝑇=30,000K, 𝛼=0.1, and 𝑃=0.717257. As shown in Fig. 5, theradiant energy flux increases rapidly and reached a plateauin 0.15ns. Changes of the radiant energy flux and surfacetemperature of the propellant particle are synchronous withan average increasing rate of temperature of about 100K/ns.Therefore, this propellant particle has sufficient time to reachthe ignition temperature during the early pulse cycle whichis on the order of millisecond. It shows that this propellantparticle can be ignited simply by radiation. The responsesof energy flux and surface temperature of propellant particleswith radiation are both in picosecond. The main cause for the

Time (ps)

Ene

rgy

Flu

x(M

W/m

2 )

Sur

face

Tem

pera

ture

(K)

0 50 100 150 200 2500

50

100

150

200

250

300

290

295

300

305

310

315

Energy FluxSurface Temperature

T=30,000K α=0.1 P=0.717257

Position (a)

Fig. 5. Radiant energy flux and temperature in the propellant particle surfaceas a result of plasma radiation when 𝑇=30,000K, 𝛼=0.1, and 𝑃=0.717257.

Surface Temperature (K)

Num

ber

ofP

rope

llant

Par

ticle

s

400 600 800 1000 12000

500

1000

1500

2000

0s3.2ns1.0μs

Hot Zone

T=30,000K α=0.1 P=0.717257

Fig. 6. Distribution of particle number in 0s, 3.2ns, and 1.0 𝜇s when𝑇=30,000K, 𝛼=0.1, and 𝑃=0.717257.

fast response must be that the radiate heat transfer in highefficiency. And it is the main energy transfer mode in thisstage.

Fig. 6 shows the distribution of propellant particles in 0s,3.2ns, and 1.0 𝜇s when 𝑇=30,000K, 𝛼=0.1 and 𝑃=0.717257.It appears that we have a valid assumption that the ignitiontemperature of propellant particles is 600K, so that the “hotzone” is represented by the area to the right of the dashedline in Fig. 6. All propellant particles are at 288.15K at 0s.Through plasma radiation, more propellant particles would bestatistically entered in the “hot zone” (ignition temperature isreached) at 3.2ns. It is anticipated that this is the ignition timein the cartridge and more propellant particles will enter the“hot zone” after this time. This transport property of particlenumber in cartridge reflects the plasma and propellant inter-action. The transport velocity of propellant particles indicatesthe response rate of propellant bed to the plasma radiation.Similarly, this property can also be reflected by the changesof 𝜂h. Fig. 7 shows the changes of 𝜂h in different plasmatemperatures when 𝛼=0.1 and 𝑃=0.717257. The transportproperty of particle number reflected in Fig. 6 corresponds

Time (μs)

η h(%

)

0 1 2 3 4 50

10

20

30

40

50

60α=0.1 P=0.717257

T=30,000K

T=25,000K

T=20,000K

T=15,000K

T=10,000K

Fig. 7. 𝜂h in different plasma temperatures when 𝛼=0.1 and 𝑃=0.717257.

Plasma Temperature (K)

η hmax

(%)

5000 10000 15000 20000 25000 30000 350000

10

20

30

40

50

60α=0.1α=0.2α=0.3α=0.4α=0.5α=0.6α=0.7α=0.8α=0.9α=1.0

P=0.717257

Fig. 8. 𝜂hmax in different average absorption coefficients and plasmatemperatures when 𝑃=0.717257.

Plasma Temperature (K)

η hmax

(%)

5000 10000 15000 20000 25000 30000 350000

20

40

60

80

100

120P=0.214602P=0.497345P=0.717257P=0.874336P=0.968584

α=0.1

Fig. 9. 𝜂hmax in different porosities and plasma temperatures when 𝛼=0.1.

intuitively to the uppermost curve in Fig. 7. Apparently,the starting time of every curve in Fig. 7 appear to be theignition time in cartridge. Every curve has followed the similarapproach to its respective maximum 𝜂hmax which reflects thepropagation range of the radiation in cartridge.

Fig. 8 shows the changes of 𝜂hmax in different aver-

age absorption coefficients and plasma temperatures when𝑃=0.717257 and Fig. 9 shows the changes of 𝜂hmax indifferent porosities and plasma temperatures when 𝛼=0.1. Withthe increase in 𝛼, the radiation range remains approximatelyunchanged, but the radiant energy that reaches the surface ofpropellant particles increases. Thus, the radiation is more cen-tralized and 𝜂hmax decreases. It is notable that 𝜂hmax changessmoothly when 𝛼 is between 0.5 and 0.8. This phenomenamay have important implication to practical applications inengineering. Compared with 𝛼, 𝑃 has an opposite effectto 𝜂hmax. With the increase in 𝑃 , the energy attenuationincreases. However, the radiation can be transferred fartherand more uniformly. The radiation range and the number ofpropellant particles in “hot zone” also increases. Hence, 𝜂hmax

increases approximately linear.In plasma ignition, high efficiency heat transfer by plasma

radiation causes the radiant energy to aggregate in the pro-pellant particle surface layer rapidly during the early plasmaradiation. There is no sufficient time to transfer the energyfrom the surface to inner propellant particles by simple heatconduction. The energy absorbed by the propellant particles isused to increase the temperature in the surface layer of propel-lant particles quickly. Hence, the surface layer of propellantparticles can reach the ignition temperature instantly. This kindof energy skin effect in the propellant particle surface is themain cause of plasma ignition. Obviously, the use of plasmain ignition has a higher efficiency and more precise ignitiontime compared with conventional ignition.

IV. CONCLUSION

Monte Carlo and statistical physics have been employedto model plasma radiation in an electrothermal-chemicallauncher. Radiative energy distribution in the propellant bedand its interaction with propellant have been obtained. Wefound that a propellant bed has a screening effect on arcplasma radiation. And responses of energy flux and temper-ature in the propellant particle surface are both in the orderof picosecond due largely to the highly efficient radiate heattransfer.

Future analysis of this problem should include accountingin more detail for the properties of plasma and propellantparticles. The effect of high temperature gas [13] to the plasmaradiation will be considered more, and three-dimensionalmodel will conduce to understand this process more veritably.

REFERENCES

[1] G. L. Katulka, “Parametric study of high energy plasma forelectrothermal-chemical propulsion applications,” IEEE Trans. PlasmaSci., vol. 25, no. 1 pp. 66-72, Feb. 1997.

[2] K. Kappen and U. Bauder, “Simulation of Plasma Radiation inElectrothermal-Chemical Accelerators,” IEEE Trans. Magn., vol. 35, no.1, pp. 192-196, Jan. 1999.

[3] A. Koleczko, W. Ehrhardt, S. Kelzenberg, and N. Eisenreich, “Plasmaignition and combustion,” Propellants, Explosives, Pyrotechnics, vol. 26,no. 2, pp. 75-83, Apr. 2001.

[4] M. J. Taylor, “Measurement of the Properties of Plasma from ETCCapillary Plasma Generators,” IEEE Trans. Magn., vol. 37, no. 1, pp.194-198, Jan. 2001.

[5] K. Kappen and R. Beyer, “Progress in Understanding Plasma-PropellantInteraction,” Propellants, Explosives, Pyrotechnics, vol. 28, no. 1, pp.32-36, Jan. 2003.

[6] M. Keidar, I. D. Boyd, E. L. Antonsen, F. S. Gulczinski, and G. G.Spanjers, “Propellant Charring in Pulsed Plasma Thrusters,” J. Propul.Power, vol. 20, no. 6, pp. 978-984, Nov.-Dec. 2004.

[7] R. A. Beyer and R. A. Pesce-Rodriguez, “The Response of Propellantsto Plasma Radiation,” IEEE Trans. Magn., vol. 41, no. 1, pp. 344-349,Jan. 2005.

[8] M. A. Schroeder, R. A. Beyer, and R. A. Pesce-Rodriguez, “ScanningElectron Microscope Examination of JA2 Propellant Samples Exposedto Plasma Radiation,” IEEE Trans. Magn., vol. 41, no. 1, pp. 350-354,Jan. 2005.

[9] M. Das, S. T. Thynell, Jianquan Li, and T. A. Litzinger, “Transient Ra-diative Heat Transfer from a Plasma Produced by a Capillary Discharge,”J. Thermophys. Heat Transfer, vol. 19, no. 4,pp. 572-580, Oct.-Dec.2005.

[10] K. Kappen and U. Bauder, “Calculation of Plasma Radiation Transportfor Description of Propellant Ignition and Simulation of Interior Ballis-tics in ETC Guns,” IEEE Trans. Magn., vol. 37, no. 1, pp. 169-172, Jan.2001.

[11] A. J. Porwitzky, M. Keidar, and I. D. Boyd, “Modeling of the plasma-propellant interaction,” IEEE Trans. Magn., vol. 43, no. 1, pp. 313-317,Jan. 2007.

[12] A. J. Porwitzky, M. Keidar, and I. D. Boyd, “Numerical Parametric Studyof the Capillary Plasma Source for ElectrothermalCChemical Guns,”IEEE Trans. Magn., vol. 45, no. 1, pp. 574-577, Jan. 2009.

[13] K. Gruber, K. Kappen, A. Voronov, and H. Haak, “Radiation Absorptionof Propellant Gas,” IEEE Trans. Magn., vol. 37, no. 1, pp. 161-164, Jan.2001.