1457 IEPC-93-165

SEMI- EMPIRICAL INTERIOR BALLISTICS SIMULATIONMODEL OF ARC HEATED LIGHT GAS GUN

A.M. GlukhovIPERAS

18 Dvortsovaya, SLPetersburg, 191065, Russia

ABSTRACT aX Covolume

A mathematical model of hypervelocity p Densityelectrical arc heated light gas gun has beendeveloped that enables to predict all the major P Pressuregas dynamics parameters of AHLGG vs timeand co-ordinate and also the components of R Gas Constantenergy conversion during the launchingprocess. The laws of electric energy delivery T Gas Temperatureand arc current are used as the initial data.The model is based upon a set of equations of f Electric ChargeS- D non - steady motion of compressible gas,combined with empirical relations, Ce Erosion Law Constant

describing losses of energy during arc heating t Timeprocess and ingress of the metal vapor into thelight gas due to the electrode erosion. The I Arc Currentworking gas is considered as a binary one,which composition and properties depend on U Arc Potential. Averaged Over Timeelectric parameters of discharge and type ofthe electrodes material. The empirical data W Closed Vessel Volumeused were obtained at the arc current up to 1.5MA and the hydrogen density of 10-30 Ee Arc Electric Energy, Ee= Ukg/m 3 . The system of equations was solvednumerically by means of the Godunov's Ein Internal Energy Incrementmethod. The model and the software had beenverified by the series of 43 tests and the H Electrodes Enthalpy of Destructionquantitative parameters of deviations had beenobtained. T1 Arc Heating Efficiency

NOMENCLATURE V Muzzle Velocity

AHLGG Arc Heated Light Gas Gun Vo Muzzle Velocity at Zero Metal VaporInjection Conditions

g Pure Gas Subscript

INTRODUCTIONm Metal Vapor Subscript

Inspite of the AHLGG had been describedy Mass Fraction more than 30 years ago, 1 reports on numerical

models of electrothermal launchers haveCO Mass of Gas Component appeared only in recent time. Probably, that is

caused by relatively recent appearance ofM Molecular Mass effective methods of gas dynamics equations

solution and experimental data on features ofC Specific Heat the interior ballistics of the AHLGG. The major

feature is, first of all, electrode erosion, thatk Specific Heats Ratio consumes a lot of electric energy (20-70 % as

usual) and causes metal vapor ingress into the

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0 100 describing arc heating, which are obtained inS/ dedicated experiments. 2 These relations, being080 - - combined with the gas dynamics system of

So equations for the pure gas and erosion

v 60 -- -- products mixture, give the entire mathematicalmodel of interor ballistics of the AHLGG. In

S40 general, such a model is similar to modernO 4 classical gun models, where empirical relations

20 / 0 for the powder burning are currently in use.

S0 / - - EMPIRICAL RELATIONS

S0 1 2 3 4 5S 4 Dedicated experiments were carried out byeroded mass, g means of the closed vessel technique.

Experiments with heavy projectiles were usedFig.l Energy losses vs eroded mass of as well, because their conditions are prettyelectrodes for tungsten and hydrogen. close to that of the constant volume. In each

experiment electrodes weighing was carriedout, that enabled to establish the relationbetween the eroded mass and electric charge :

light gas. This causes formation of the mixtureof the light gas and erosion products, which .m = C 2properties differ much from that of the pure

e

gas. These processes have a considerable effecton the AHLGG performance. That is why The relation is obtained for various metals andattempts to use quite perfect gas dynamics tests conditions.3 For tungsten the value of Ce

models without erosion consideration lead to is found to be about 40 mg/C.

remarkable disagreement of computational andexperimental results, which grows with the The arc heating efficiency was studied byvelocity increase. As the experimental means of the closed vessel only. The

investigation of arc burning at gun pressure experimental conditions are described in.2

and megaampere current is extremely difficult, Assume that all the energy loss is consumed

there are no sufficient data for creation of the by an ablation of the electrodes metal and

theoretical model of light gas arc heating. there is a linear function between the lost

Therefore one has to use empirical relations, energy and eroded metal mass, then the

Fig.2 Total density (upper curves) and metal vapor density (lower curves) vs time and co -ordinate.

1459 IEPC-93-165

process in the vessel can be described by the The state equation was adopted in a Duprefollowing equations of mass and energy form P(l/p-ayg)=RT, and the covolume aconservation: was considered as the function of the pressure

up to 10 kbar.

Wdp m = I (1) 0-D equations of continuity and energy fordt , the chamber included terms, describing metal

vapor ingress and energy loss, related to theW- -d m electrode erosion.

W dP_dE dPm (2)S- HW The barrel process was described by two

k-1 dt dt dt continuity equations (for each mixturecomponent); momentum equation, including

Substituting Eq.(1) in Eq.(2) and integrating the the gas skin friction; energy equation,resulting equation over the burning time, we including convective heat transfer to walls ofget the expression for the energy loss: the barrel. The skin friction and the heat

transfer were evaluated for the conditions of

E - E = HC 0 the gas flow in the tube behind theSaccelerating piston. The dependence of the gasviscosity and thermal conductivity on

Defining h= Ein/Ee as the arc heatingSa t a temperature was represented by exponentialefficiency we obtain: approximations.

S=approximations.

HCe (3) The projectile motion equation included the~ l ~ projectile friction force and the ambint back

U pressure. The piston friction was evaluatedusing the experimentally found friction

The validity of the assumed proportionality coefficientbetween the energy loss and the eroded massis confirmed by the experimental data (see SOLUTION OF THE PROBLEMFig.l). The estimated value of the enthalpy ofdestruction for tungsten is close to 20 MJ/kg. The problem was solved by means ofNote, that, according to the arc efficiency Godunov's discontinuity decay on a movingdefinition, the product in the fraction grid technique. 4 The chamber was treated as anumerator in Eq.(3) is the electrode potential single mesh. Mass fluxes of the twodrop. For tungsten this value is about 750 V. componenets were computed separately by theOn the basis of Eq.(3) we can make an uniform procedure. Probably it was theimportant remark: for the efficiency increase Godunov's approach that prevented thethe total arc potential should be increased, troubles of negative mass fractions. 5 TheThis equation enables to estimate practically program had been written down in VAX-attainable arc heating efficiency. If the value of FORTRAN language. The runtime was withinU is 8-10 kV, which corresponds to the 10-70 minutes depending on the bore andcapacitor bank maximum voltage of 20-25 velocity. The output data were presented inkV, then r should be greater than 0.9. table and graphic form.

MODEL DESCRIPTION Besides ordinary projectile and gas motionparameters, the program puts out the metal

The assumption had been made, that the pure vapor density as the function of the time andgas and erosion products form a homogenious, co-ordinate (Fig. 2). The graph is plotted forthermally equilibrium mixture, behaving as a the example with the burning time exceedingbinary gas. Taking into account real properties 1/2 of the total launching time and the muzzleof metals and gases and also reasonable pure velocity of 4.2 km/s. The program also putsgas mass fraction, the following binary gas out the istantaneous energy balance table forparameters were derived: M= M/yg, C= C/g, any moment of the launching which is prettyk=kg.The isentropic exponent was treated as useful for estimation of the role of separatea function of temperature and pressure up to processes in the entire launching process.104 K and 10 kbar.

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1.4 0 0 CONLUSIONS1.4 , 0

S1. o The phenomenological approach in arc1. burning process represntation proved to be

1.0 -- valid for application in the AHLGG simulation.So ° o a 000o a% The simulation model of the AHLGG based onS0.8 empirical relations for arc burning predicts

oo o° o° satisfactorily the major gun parameters.

1 2 3 4 5 ACKNOWLEDGEMENTVpredited, km/s

The author would like to acknowledge thefriendly cooperation of Mr. S.A. Kudryavtsev in

Fig.3 Coincedence of predicted and measured the software developmentvelocities.

REFERENCES

I Journeau A., Capelier C., Leboucher,EXPERIMENTAL VERIFICATION Lecomte C. Rapport de mission aux Etats-

Unis., LRBA, Vernon, 1961.The accuracy of produced simulation modelhad been evaluated by comparison of 2 Budin A.V., Glukhov A.M., Kolikov V.A.,computations results and experimental data. Rutberg F.G., Shirokov N.A. MegaampereFor this purpose a series of 43 shots3 had been Current Pulse Generation in High Densityused. The gun parameters were the following: Hydrogen. Megagauss Fields and Pulsedbore 30 mm, barrel length 4 m, chamber Power Systems (MG -V). Nova Science Publ.,volume 0.59-1.5 1, arc energy 0.2-1.7 MJ, New.York, 1990.cold hydrogen pressure 17-43 MPa. Therange of the projectille mass was 13.5-250 g. 3 Glukhov A.M., Kolikov V.A., Levchenko B.P.,The coicidence of results can be described by Rutberg Ph.G. Electrical Light Gas Gun as anthe ratio of measured to predicted velocity as Effective Hypervelocity Launcher. Megagaussthe function of the predicted velocity (Fig. 3). Fields and Pulsed Power Systems (MG -VI).The distribution law of values is close to Nova Science Publ., New.York, 1992.normal with the mean value of 1.0 and thestandard deviation of 0.2. The values of the 4 roAyHos C.K. 'HcAeHHoe pemeHHemaximum chamber pressure were processed in MHOroMepHUX 3aAa' ra3oBo~f AHHaMHKH. M.the same manner. The following parameters of HayKa, 1976.accuracy had been obtained: the mean value ofmeasured-to-predicted ratio was 0.73, the 5 Larrouturou B. How to Preserve the Massstandard deviation was 0.2. Fraction Positivity When Computing

Compressible Multi-components Flows. J.APPLICATIONS Comp. Phys., v.95, 59-84, 1991.

The created software proved to be a very 6 Glukhov A.M. Numerical Modelling andconvinient and reliable istrument for AHLGG Optimization of Arc Heated Light Gasanalysis and design. It was used effectively for Launcher. 4th European Symposium onenergy balance studies and for AHLGG Electromagnetic Launch Technology. Celle,optimization.6 In particular the model was used 1993.for estimation of eroded metal injection effecton the muzzle velocity. The example of thegun with the total eroded mass of about that ofthe pure gas was investigated. The two sets ofcomputations were carried out for variousmasses of projectiles: one with consideration ofinjection (velocity V) and another - without(velocity Vo). For the values of V 1.8, 3.8 and7.0 km/s the corresponding values of V/Vo1.04, 0.96and 0.76 have been obtained.