Experiment and Calculation for Expansion Process of Ablation Plasma Jets in Liquid

JOURNAL OF CHINA ORDNANCEExperiment and Calculation for Expansion Process ofAblation Plasma Jets in LiquidLIU Dong-yao(刘东尧)'，WANG Yu-wei(王育维)2 , ZHOU Yan-huang(周彦煌)'(1. School of Power Engineering, Nanjing Universty of Science and Technology, Nanjing 210094 Jiangsu, China;2. Northwestern Institute of Mechanical and Eletrical Engineering, Xianyang 712099 Shaanxi, China)Abstract: The expansion process of ablation plasma jet in liquid was experimentally investigated by using high speed digitalcamera. The sequential pictures show that, in the initial stage of the jet, the Taylor cavity expands in the axial and radialdirections simultaneously, and then, ig subjected to the constraint of chamber wall, in axial direction mainly. The maxi-mum axial speed of the cavity's head ranges from 240 m/s to 280 m/s. Some strong heat conduction and mass transmissioneffects can be found in the surface of Taylor cavity , where the plasma cools down and condenses a solid particles while theliquid vaporizes as gas. Compared the expansion processes of the cavities among the different discharge energies and thenozzle diameters, it can be seen that the expansion speed of the cavity is directly proportional to the discharge energy andinversely to the nozzle diameter, and the efect of the discharge energy is stronger than that of the nozzle diameter. A set ofequations describing the expansion process of ablation plasma jet was derived under the assumption of momentum conserva-tion. The calculated resuls by use of the equations coincide with the experimented results bltterKey Words: mechanics of explosion; ablation plasma jet; Taylor cavity; experimental study; numerical calculationCLC Number: TJ012Document Code: AArticle ID: 1673 002X(2010)01-0001-04graph, measured the expansion speed of Taylor cavityIntroductionand the mass loss of water, and proposed a theoreticalFor the electro-thermal chemical propulsionmodel to calculate the expansion speed and mass ex-(ETC) reduces the requirements of energetic proper-change in the surface of Taylor cavity.ties, a lot of low exothermal or even endothermic mate-The expansion process of ablation plasma jet inrials can be used as candidates for the propellants. Thwater was investigated experimentally and theoreticallyinteraction mechanism of plasma jets with liquid is oneby the authors. The continuous growing processes ofof the most important issues in the studies on the ETCTaylor cavity were recoded by a high-speed digitalinterior ballistics. And, water is widely used as work-camera, and the propagation speed of the frontal sur-ing medium in the study on plasma-liquid interactionface of Taylor cavity was calculated according to itsfor its safety and nontoxic.traces in the consecutive pictures. A set of algebraicIn the past decades, many experimental and theo-equations was presented under the assumption of mo-retical studies on the interactions of plasma jets withmentum conservation to calculate the expansion param-liquids were carried out. K K Kuo'" investigated theeters of Taylor cavity. The calculated expansion speedsplasma-liquid interaction mechanism by using higof Taylor cavity were compared with the experimentedspeed movie camera and X-ray radiography, observedresults.the interaction process when the plasma jet penetrated1 Experimental Investigationinto the liquid, calculated the speed of Taylor cavity'shead , and analyzed the plasma density distribution ac-1.1 Experiment Apparatuscording to the X ray pictures. Arensburg(2] studied therists of a cpillarypenetration of plasma jet into water by X-ray shadow-and e中国煤化工rig. 1. The capilTHCNMHGReceived 2009.04-30Sponsored by the National Nature Science Foundation of China (10302102)Blography LIU Dongyao( 1969- ), male, asistant rearcher, liudong@ mail. njus. edu. cn一1一JOURNAL OF CHINA ORDNANCE, 2010, Vol.6, No.1lary is also called as the plasma generation chamberal thin wire is evaporated as plasma to ablate the capil-( PGC), where plasma is generated by the discharge oflary material, and the metal diaphragm is broken whena pulse power system composed of a set of energy-stor-the pressure of ablation plasma in capillary is up to theage capacitors and some auxiliary circuits. The intensi-shear stress of the metal diaphragm. The ablation plas-ty of plasma jet can be adjusted by the voltage on thema forms jet injecting into the liquid. Some primary in-capacitor and the circuit parameters. The anode andjection phenomena of the plasma jets in water are ilus-cathode in the two ends of capillary are connected totrated in Fig. 2.the high voltage terminal of capacitors and ground, re-1;=25kV1,=201V "1,.=25kVt/msspectively. They are also connected each other by aφ=3.5 mnφ=3.5 mm0=2.5 mmmetal thin wire inside the capillary. It is evaporated in.to the plasma by the strong pulse current of the capaci-0tor discharge. The cathode also serves as a nozzlewhere the plasma in the capillary is injected into thechamber. The nozzle is sealed by a thin metal dia-0.025phragm to provide a preliminary pressure for the injec-tion of ablation plasma. The chamber is a cylindricalcontainer sized 118 mm in length and 36 mm in diame- 0.040ter, and its axis coincides with the capillary axis. Twoaxially symmetry slots sized 87 mm in length and 22mm in width are made in the chamber wall and covered0.074with quartz glass for the direct observation of the plas-ma jet. The plasma-liquid interaction process is recor-ded as sequential pictures by a high-speed digital cam-.099era with frame rate of 40500 f/s. The arc voltage andcurrent of capillary plasma are measured by a potenti-ometer and a Rogowsik coil current sensor, respective-ly， and recorded by a transient recorder typed 0.23DM7100.anode eapillary eathode nozzle chamber water optical slot0.1480.173Fig.1 Sketch of experiment apparatusfig.2 Sequential pictures of plasma jet1.2 Experimented Results and Discussionsexpandings in waterThe experiments were carried out under the condi-Generally, a highlight bulb occurs near the nozzletions of the capacitor voltage 2.0kV or2. 5 kV and thein the very beginning of jet injection, and the bulb ex-nozle diameter 2.5 mm or 3.5 mm. The experimentedpands downstream to form a Taylor cavity as the contin-results on the impedance, arc voltage and are currentuous中国煤化土eymerie Tgylrxof the ablation plasma in capillary indicate that the dis-cavitrections simultane-charge voltage, circuit parameter and nozzle diameterouslyMYHC N M H Graylor earity lokosall influence the generation process of the plasma-4.like a torch at 0. 049 ms, and then expands in axial di-Once the energy is released into the capillary, the met-rection primarily. It indicates that the axial speed ex-一2-LIU Dong-yao, et al. 1 Experiment and Calculation for Expansion Process of Ablation Plasma Jets in Liquidceeds the radial speed as the chamber wall constrictsas the downstream expansion of plasma jet. The maxi-the radial expansion of plasma jet. In the expansionmum expansion speeds of Taylor cavity range from 240process of Taylor cavity, the highlight plasma area ilul-m/s to 280 m/s. These results are in agreement withminates the liquid around Taylor cavity, but some dis-those of K K Kuo"] and A Arensburg'21.tinct dark areas exist in the head of Taylor cavity whereAlthough the pressure in capillary reaches to itsthe plasma interacts with the liquid. These dark areasmaximum value before the metal diaphragm is broken ,are totally different with the highlight plasma and graythe plasma jet does not get maximum speed in this in-liquid, and move downstream together with the Taylorstant. This result is dferent with that of K K Kuo". .cavity. This phenomenon can be explained as that theActually, the plasma jet can not be accelerated to theplasma cools down and condenses as opaque solid par-maximum speed instantaneously for it is subjected toicles when it interacts with water. It indicates that thethe resistance coming from the stationary liquid, andpenetration of plasma jet in liquid is a typical expan-this fact can not be explained by the momentum con-sion process of Taylor cavity, and the intensive heatservation theory also.conduction and mass transmission exist in the surface ofTaylor cavity where plasma interacts with liquid.2 Calculation of Expansion SpeedThe expansion speed of Taylor cavity can beA set of simplified equations was derived from themeasured according to its displacement and the timemomentum conservation law to calculate the expansiondifference between two adjacent pictures. Fig. 3 ilus-speed of Taylor cavity. For the derivation of thesetrates the expansion speeds in three different cases cor-equations, some assumptions were made according toresponding to Fig. 2. Compared the speed-time curvesthe expansion process of Taylor cavity'a. Firstly, theunder different conditions in Fig. 3, it can be foundTaylor cavity only expands axially. Secondly, the plas-that, for the constant nozzle diameter, the higher thema jet expands freely in liquid, i. e. the jet speedvoltage is, the higher the initial expansion speed ofalong axis keeps constant at each moment, and onceTaylor cavity is. This trend coincides with the subsonicthe liquid vaporizes it gets the same speed as the jet.flow theory of the plasma jet. With the increase of theFinally, and the vaporized liquid absorbs all the ra-voltage on energy-storage capacitors, the pressure ，diant energy of plasma jets. The injecting speed oftemperature and speed of the ablation plasma jet in-plasma jet near the nozzle is given by one-dimensioncrease. For the same voltage, the smaller the nozzlemodel of plasma discharge in capillary's.diameter is, the higher the expansion speed is, espe-Let u be the head speed of the plasma jet and setcially before it reaches to maximum speed. But, thethe origin of coordinates in the frontal surface of Taylorinfluence of the nozle diameter on the expansion speedis less than that of the voltage. It also can be seen thatcavity, the liquid moves toward to jet in a speed -ucorrespondingly. The momentum fluxes on both sidesthe head speed of the plasma jet gets its maximum val-ue shortly after it leaves the nozzle, and then decreasesof frontal surface of Taylor cavity are equal according tothe momentum conservation theory, thus,七U:=2 500 V.d=3.5 mm+U=2 000 Vd=3.5 mmρ.( -u)*=p(p-u)°,(1)士U=2500 V.d=2.5 mmwhere p. stands for the density of liquid, p; and Up thedensity and speed of plasma jet near the head of Taylorcavity, respectively. From Eq. (1), we can have100-(2)中国煤化工YHCNMHGtionsabove,”p，8.02 0.04 0.06 0.08 0.10 0.12 0.14mcan be replaced by the speed Um of plasma jet in theFig.3 Axial head speed of Taylor cavitynozzle, and ρa can be witen as一3-JOURNAL Of CHINA ORDNANCE, 2010, Vol.6, No. 1Ps=Pin +P,(3)case of Uc =2 000 V and nozzle diameter φ =3. 5 mm.where Pp represents the density of plasma jet in nozzle,The calculated results coincide with the experiment re-p. the density of vaporized liquid. Both Uy and Pm cansults better. It indicates that the above analyses andbe found in Ref. [4]. And p, can be derived based onassumptions about the Taylor cavity are reasonable.the energy conservation theory,3 Conclusionsdφ =g4oT,(4)Based on the experiment investigation and calcu-dtlation on the expansion process of plasma jet in liquid,whereσ is the Bolzman constant, h the enthalpy ofit can be concluded that 1) both the voltages of the en-the vaporized liquid, β the surface extension coefficientergy-storage capacitors and the nozzle diameter can af-owing to the Kelvin-Helmhotz unsteady effect in thefect the expansion speed of plasma jet, but the formergurface of Taylor cavity, A and V the surface area andhas more important influence on the speed than that ofvolume of an ideal smooth Taylor cavity respectively.the later; 2) in the two-phase interfaces between theAccording to the Taylor cavity's pictures taken in theplasma and liquid, the intensive heat conduction andexperiments, it can be divided into the front conicalmass transmission exist; 3) the head speed of the plas-part and the rear spherical part. Thus, A and V can bema jet reaches to its maximum value shortly after itwritten asleaves the nozzle; 4) the expansion speed of TaylorA=Tr T+7 +2πr ,(5)cavity can be calculated by using the equations basedon the momentum conservation theory, and the calcu-V=→rl+号m',(6)lated results are well in agreement with the testedwhere r is the maximum radius of Taylor cavity, and lones. The further theoretical investigation on the inter-the length of conical part of Taylor cavity. Observedaction mechanism should consider the multi-dimensionthe pictures, we find r equal to l. Thus, the totaland turbulent efects in the two-phase interface, for thelength of Taylor cavity can be written asl=r+h =2r.mass, momentum and heat conductions occur in theThe expansion speed of plasma jet can be derived fromsurface of Taylor cavity.the length of Taylor cavity ,Referencesdl_di=u.(7)[1] KuoK K, CheungFB, Hsieh W H, et al. Experimentsstudy of plasma/luid interaction in 8 simulated CAP gunUnder given intial and boundary conditions,[C] // Gannaway M T 27th JANNAF Combustion Sub-part of the parameters of Taylor cavity can be calculat-committee Meeting, Maryland, 1990: 365 -375.ed.[2] Arensburg A, wald s. X-ray diagnotics of a plasmajet-Figure 4 shows the comparison between the calcu-iquid interaction in electrothermal guns[J]. Journal oflated and tested head speeds of Taylor cavity in theApplied Physice, 1993, 73(5): 2145 -54. .28[3] LIU Dongyao, ZHOU Yan-huang, YU Yong-gang. Theexperimental study of the impedance of capillary plasma210J]. Journal of Bllistics, 199,11(2):74-77. (in .Chinese)g 140[4] GUO Haibo, LIU Dong-yao, ZHOU Yan-hang. Experi-+ experimentmental study of pulsed discharge property of plasma gen-.- - ealculationerator[J]. Jourmal of Nanjing University of Science and0-中国煤化工69. (in Chinee)[5]One-dimensional nu-0.040.080.12MHC N M H Gma[J]. Chinee lourt/msnal of High Pressure Physics, 2001, 15(4):249 -253.Fig.4 Calculation and experiment of head(in Chinese)speed of Taylor cavity一4-