Numerical Simulation on Laser Propulsion Capability of Polymer Target

doi:10.4236/opj.2013.32B003

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Optics and Photonics Journal, 2013, 3, 11-14

doi:10.4236/opj.2013.32B003 Published Online June 2013 (http://www.scirp.org/journal/opj)

Numerical Simulation on Laser Propulsion Capability of

Polymer Target

Nanlei Li, Jifei Ye, Weijing Z hou

State Key Laboratory of Laser Propulsion and Application, Academy of Equipment, Huairou, Beijing, China

Email: [email protected]

Received 2013

ABSTRACT

A computational model of laser ablated polymer was established. Set the ablation criterion based on threshold energy.

Put forward the polymer ablation criterion in the numerical model. It established the energy distribution equation to

describe the laser ablation process. When the ablation products ejected, the target gained recoil impulse from ejection

process. Get the ejection energy and the recoil momentum of target based on momentum conservation law. The numer-

ical analysis model can reflect the propulsion capability of different polymer propellant, revealed the law of propulsion

parameters in laser ablation process.

Keywords: Laser Propulsion; Laser Ablatio n; Polymer Target

1. Introduction

Laser propulsion as a new concept propulsion technology,

it is given more and more extensive concern by the main

astronautic powers. As one of the practical application

achievements, laser ablation micro thruster is one of th e-

focus[1,2]. With its hig h specific impulse, wide dynamic

range o f i mpuls e, s mal l mi nimu m i mp u lse bit, lo w power

and easy to realized the lightweight and digital control

etc, laser ablation micro thruster has wide application

prospects on high-precision task of satellite attitude ad-

justment, orbit maintain and networking formation con-

trol. Ba sed on these applications, the generation of micro

thrust using a middle or low intensity laser ablation was

studied. The principle of laser ablation micro thruster is

that using small portable laser ablated target can generate

micro thrust. Due to low thermal conduction, low abla-

tion threshold, polymer material was easily ablated to

generate thrust[3,4]. Based on the summary of domestic

and international laser micro propulsion development,

this paper studied the polymer propulsion properties

thro ugh establishing the theoretical calculation model.

Simulated the micro-thruster working vacuum envi-

ronment, a computational model of low intensity laser

ablated polymer was established. Put forward the poly-

mer ablation criterion based on the experimental pheno-

mena. The polymer doesn’t have fixed fusion point, so

building the ablation criterion based on threshold energy,

whic h has obs erve d in many e xpe ri ments o f re fere nce. In

the numerical model, the target ablation phenomenon

happens when inner deposited energy achieves the thre-

shold value. Along with inner deposited energy increas-

ing, ablation phenomenon continually happened and ab-

lation depth rose. It established the energy distrib ution

model to describe the ablation process of temperature

rise, phase change and the influence of chemical exo-

thermic process. When ablation phenomenon happened

the ablation products would ejected, and the target gained

recoil impulse from ejection process. Based on the con-

servation law, assumed that in the ablation process the

laser deposited energy consume in such aspects: fusion

and vaporization process, target inner energy which

made temperature rose, the exothermic energy in chemi-

cal reaction, product ejection energy. According to ener-

gy distribution equations we can get the ejection energy,

and then get the recoil momentum of target based on

momentum conservation law. Propulsion capability of

laser ablated polymer was studied through the numerical

analyse model. The generation law of impulse, thrust,

impulse coupling coefficient, specific impulse, ejection

velocity and ablation efficiency was calculated. And it

analyzed the propulsion capability of different polymer

targets.

The conclusions showed that, the numerical analysed

model can reflect the propulsion capability of different

polymer propellant, revealed the law of propulsion pa-

rameters in laser ablation process. The results for propel-

lant selection, micro-thruster design and improve ment of

propulsion performance are valuable.

2. Numerical Modeling

N. L. LI ET AL.

Laser ablated a target can caused micro-thrust, the direc-

tion is showed in Figure 1. Based on the physical

process of interaction between laser and polymer materi-

al, a numerical model was set up to simulate the ablation

thru s t and moment um coupli ng coefficient.

2.1. Thermal Conduction Equation

The first equation for interaction between laser and po-

lymer is thermal conduction energy conservation equa-

tions for column symmetric case.

1( )()

T TT

CK rq

trrrz z

∂∂ ∂∂∂



= ++



∂∂ ∂∂∂



(1)

where ρ, C and K are the target density, specific heat and

thermal conductivity, qi is target inner deposited power

whe n laser is heating.

(1)exp(), 0

I Rzrb

qbrb

αα

−− −≤≤



=

>



(2)

where I0 and b are laser power and radius, R is target

reflectivit y, α is laser absorption coefficient in tar get.

2.2. Ablation Threshold Energy

Summarizing laser ablated polymers experiment results,

the ablation process is described by the following equa-

tion[5,6]

( )ln()

dF F

(3)

where F and Ft are laser fluence and ablation threshold

fluence; d(F) is the ablation rate; α is the laser absorption

coefficient. In the process of laser ablation, The polymer

don’t have fixed fusion point, so in this paper we build

the ablation criterion based on threshold energy, which

has observed i n the experiment. In our numerical model,

the target ablation phenomenon happens when inner de-

posited energy achieve the threshold value. Along with

inner deposited energy increasing, ablation phenomenon

continually happened and ablation depth rose. According

to Eq.(3), the ablation threshold energy is

th t

exp( )EF z

αα

(4)

Laser

Target

Products

Ejection

Thrust

Direction

Figure 1. Sketch of laser ablated polymer target.

After laser ir rad iation la st t ime t, the t ar ge t i nner d epo-

sited energy is

0(1 )exp()

E IRzt

αα

=−−

(5)

When inner deposited energy is larger than ablation

threshold ener gy, the ablation phenomenon happened, so

the ablation criterion is

i th

EE≥

(6)

2.3. Energy Distribution Equation

When Eq.(6) achieves, it means the ablation phenomeno n

happened, and the ablation products would ejected, the

target gained recoil impulse from ejection process. Based

on the co nservation law, we assume that in the ablation

process the laser deposited energy consume in such as-

pects: fusion and vaporization process, target inner ener-

gy which made temperature rose, the exothermic energy

in chemical reaction, product ejection energy. the distri-

bution equation of energy Ei is

[( )]

ifv caej

Ehh h CT TE

=+−+− +

(7)

where hf,hv and hc are fusion heat, vaporiza tio n heat and

exothermic energy; Ta and T0 are ablation temperature

and initial temperature; Eej is ejection energy. According

to all above equations we can get the ejection energy Eej,

so the mome n tum Pej is

eja ej

P mE=

(8)

where ma is ablation mas s. Based on mo mentum conser-

vation law, Pej is equal to the recoil momentum P of tar-

get.

2.4. Simulation Setting

Considering the symmet ry configuration of laser and tar-

get, planar symmetric column coordinate is used in si-

mulation model. In actual ablation process, the ablated

products would eject form target and dissipated , so i n the

simulation model we set a ablation moving boundary, see

Figure 2.

In this paper, chose PVC (Poly vinylchloride), POM

(Polyoxymethylene), GAP (Glycidylacide polymer) as

targets in computation example, the parameters[7,8] of

pol ymer in Table 1. It analyzed the propulsion capability

of d iffere nt polymer s .

3. Numerical Results and Analysis

3.1. Momentum Coupling Coefficient

Figure 2 shows the relation of momentum coupling

coeffici entwith laser power. When ablation begin, the

momentum coupling coefficient increased rapidly and

reach the peak then fall slowly, the reason is plasma

screening e ffect weakened reaction of laser and target.

N. L. LI ET AL.

The exother mic polymer GAP has the maxim al momen-

tum coupling coefficient48dyn/W, because released

chemical energy in the ablation process, but PVC and

POM don’t have additional energy in ablation.

3.2. Specific Imp uls e

Figure 3 shows the relation of specific impulse with la-

ser power. When ablation begins, the exothermic poly-

mer GAPreleased chemical energy in the ablation

progress so has the maximalspecific impulse200s. The

PVC and POMincreased slowly, the stab iliz ation are

120s and 50s.

3.3. Compare with Experiment

The Figure 4 shows the comparison between experiment

and numerical model. According to literature description,

using our numerical model to calculate the experiment

results, lines represent experiment data and dots

represent simulation result s [9,10]. The simulation re sults

are basically accord with the experiment data. But there

is a little differe nt, the simulat ion results are le ss than the

experiment data in short laser pulse width. The reason

maybe in short width the m echanismis more complex,

and the model can’t simulatevery well.

020 40 60 80100

Cm (dyn/W )

(GW/m

)

PVC POM GAP

Figure 2. Moment um coupling coeff icient of polymers .

Table 1. Parameters of p olymer target.

PVC POM GAP

Densityρ Kg/m3 1439 1410 1290

Thermal conductivityK W/ (m K) 0.15 0.36 0.40

Specific heatC J/( kg K) 1700 1450 1800

ReflectivityR 0.2 0.2 0.2

Absorptioncoefficientα 1/m 1.7×105 1.0×105 2.0×104

Vaporization heathv J/kg 2.8×105 5.0×105 1.9×106

Chemical heathc J/kg 0 0 3.0×106

Ablation thresholdFt J/m2 9.0×103 1.0×104 3.1×104

02040 60 80100

100

120

140

160

180

200

220

240

(s)

(GW/m

)

PVC POM GAP

Figure 3. Specific impulse of poly mers .

(dyn/W ), P (n Ns ), I

(s)

(ms)

simulation: C

experiment: C

Figure 4. Comp a r e simulation with exper ime nt.

4. Conclusions

Numerical model of laser ablated polymer was founded

to analyzed the propulsion capability of PVC, POM,

GAP. The results show that, the exothermic polymer

GAP has great propulsion capability because released

chemical energy in the laser ablation process. Its max-

imalmomentum coupling coefficient and specific impulse

are 48 dyn/W and 200s, more than PVC and POM. Po-

lymer GAP is an excellent propellant in laser ablation

propulsion.

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