EXPERIMENTAL EVALUATION OF BLAST WAVE PARAMETERS IN UNDERWATER EXPLOSION OF HEXOGEN CHARGES

Transcription

1 EXPERIMENTAL EVALUATION OF BLAST WAVE PARAMETERS IN UNDERWATER EXPLOSION OF HEXOGEN CHARGES E. Kowsarinia, Y Alizadeh*, H. S. Salavati Pour Departent of Mechanical Engineering, Airkabir University of Technology, Tehran, Iran ehsankowsar@aut.ac.ir, alizadeh@aut.ac.ir, hadi_salavati@aut.ac.ir *Corresponding Author (Received: October 8, 211 Accepted in Revised For: Deceber 15, 211) doi: /idosi.ije b.8 Abstract Behavior of blast wave in underwater explosion is of interest to etal foring counity and ship designers. Underwater detonation is, also a potential hazard to the water intakes or a plant spent fuel pool. In this paper, soe techniques for calculating free-field blast paraeters such as pressure and ipulse in underwater explosion and prediction of bubble pulsation paraeters are presented and they will be copared by experiental results of underwater detonation of Hexogen explosive charge. The details of pressure pulse curves generated by detonation of Hexogen in several standoff distances are obtained, that by using scaling laws, they can be used in analysis of practical underwater detonations. Finally, the equivalent ass of Hexogen charge relative to TNT in underwater explosion is calculated. Keywords Underwater explosion; Shock wave; Ipulse; Overpressure; Pressure-Tie Curve. چکیده مطالعه رفتار موج بلاست و پارامترهاي آن در انفجار زیر آب موضوعی است که همواره مورد توجه جامعه علمی شکل دهی مواد و طراحان کشتی بوده است. همچنین انفجارهاي زیر آب خطرات بالقوهاي براي تجهیزات زیر آب یا سکوهاي استخراج نفت و گاز به شمار میرود. در این مقاله تکنیکهاي محاسبه پارامترهاي بلاست میدان باز مانند فشار و ایمپالس در انفجارهاي زیرسطحی واقع در آب و پیشبینی پارامترهاي ضربان حباب بررسی شده و با نتایج تجربی به دست آمده براي انفجارهاي زیرسطحی نمونههاي خرج انفجاري هگزوژن مقایسه شده است. در این پژوهش جزي یات منحنیهاي پالس فشار در اثر انفجار زیر آب در فواصل مختلف به دست آمده که میتوان با استفاده از قوانین مقیاسگذاري از آنها در تحلیل پدیدههاي واقعی انفجار زیر آب استفاده کرد. در نهایت جرم معادل ماده منفجره هگزوژن نسبت ماده منفجره متداول تیانتی در شرایط انفجار زیر آب محاسبه شده است. 1. INTRODUCTION Underwater shock response of structures is studied by both ship designers and etal foring experts to understand the relation between the ipulsive forces and the structure deforation and fracture behavior. Effects of underwater explosion have been studied ever since it was realized that explosion underwater could be accoplished [1, 2]. Due to coplicated nature of the phenoenon, analytical works on study of explosion phenoena are very difficult and too any assuptions ust be taken to siplify analytical solutions [3]. It was reported that Rayleigh, for the first tie, took the assuption of incopressibility of fluid around the bubble and proposed an analytical odel for underwater explosion. Taylor and Shiffan, by energy equations, developed the otion equation of bubble that includes its contraction and expansion. Plesset used Bernoulli's equations and velocity potential generated by a source in an incopressible fluid and obtained the contractionexpansion otion of bubble [4]. Other researchers analyzed the proble by choosing the assuption of incopressibility of fluid in vicinity of bubble. Herring [5] chose the incopressibility assuption and by integration of Navier-Stokes in radial direction of spherical coordinates, proposed his theory and forula. Kirkwood and Bethe [6] developed an equation based on shock wave theory. Keller and Kolodner applied a unique ethod for developing of otion equations. They used wave equation instead of IJE Transactions B: Applications Vol. 25, No. 1, February

2 Noenclature c -1 Sound velocity (.s ) D Depth of explosion point ( ) E -3 sh Shock wave energy density ( J. ) I -2 Shock wave ipulse of unit area ( Pa.. s ) P Abient ediu pressure ( Pa ) a P Shock wave overpressure ( Pa ) p Pressure history function of shock wave ( Pa ) p Hydrostatic pressure ( Pa ) R Maxiu radius of gas bubble ( ) ax S Standoff distance to detonation point ( ) T Tie duration of bubble pulsation ( s ) t Tie variable ( s ) v -1 Flow velocity in the direction of shock wave (.s ) W Explosive charge weight ( kg ) Z Equivalent depth of charge for the total static pressure ( ) ρ -3 Abient ediu density ( kg. ) a θ Decay tie of shock wave pulse ( s ) Laplace equation for estiation of potential field [7]. In the other hand, the nature of explosion is too coplicated and the results of purely analytical and nuerical solutions are depended on several coefficients. These coefficients typically depend on type and coposition of explosive charge, and its density, shape and grain size. Therefore, estiation of shock wave paraeters by analytical and nuerical solutions is not too perfect or reliable and does have exact confority with experiental results [8]. In this paper, soe ethods that allow all these free-field blast paraeters for underwater explosions to be estiated by scaling fro available experiental data are described. The objective for analyzing the underwater explosion is to deterine the shock wave overpressure and shock wave positive ipulse as functions of target depth and radial distance fro the detonation point. Calculated paraeters needed for the underwater blasts include peak pressure and total positive ipulse for the shock wave of the explosions. These paraeters need to be deterined as functions of range extending out into the surrounding water fro a position iediately adjacent to the explosion. For this purpose, in this study soe experients have been done for easureent of pressure-tie history at different distances in underwater explosion of Hexogen charges. These experiental results are copared to available epirical equations of TNT charges and TNT weight equivalence of hexogen charge in underwater explosion is estiated. 2. SHOCK WAVE An explosive reaction is the break down of the original olecules into product olecules (such as CO, CO 2, NO, CH 4, H 2 as gases, and C, Pb, Al 2 O 3 as solids) together with the evolution of large aount of heat (4.2 MJ per kg of TNT explosive) [9]. The teperature in the product gas is of the order of 3 o C and the pressure about 5 MPa [1]. For a given type and size of charge, the efficiency of energy transfer depends greatly on the properties of the energy transfer ediu. Water has ore incopressibility than air, so it has uch higher energy transfer efficiency. In the underwater explosion, the cheical explosive is detonated and a gas bubble is produced under high pressure. A priary shock wave travels out fro the gas bubble through the surrounding water. At a short distance fro the source, this priary shock wave carries with it about 5% of the total energy of the charge. The 66 - Vol. 25, No. 1, February 212 IJE Transactions B: Applications

3 gas bubble expands until its internal pressure drops below of the surrounding water pressure. The expansion eventually ceases and the bubble begins to contract until it reaches a iniu size. The reduction in size results in increased pressure within the bubble. When the pressure increases, sufficiently the reduction in size stops. The pressure is greater than its surroundings and it begins to expand again. At the beginning of the second expansion, a secondary shock wave is generated in the water. A secondary shock wave is eitted each tie the bubble reaches a iniu size and carries only a sall fraction of the total energy. For reloading to occur, the head of the water above the charge ust be greater than twice the standoff distance. If this is not the case, the bubble bursts at the water surface and the energy transfer process stops. The coplex phenoenon of energy transfer fro an underwater explosion has not yet yielded a coplete atheatical description. Approxiate ethods are available for estiating the total energy delivered, the three coon ethods are: 1. The geoetrical ethod, based priarily on the specific energy of the explosive and the configuration relative to the charge. The influence of the energy transfer ediu is expressed relatively by an epirical factor. 2. The energy ethod, based on epirical energy density forulae derived fro easureents of underwater explosions that include the reloading effect. The energy density is integrated over the area of the structure. The use of this ethod is liited to explosives for which the appropriate epirical energy constants have been deterined. 3. The ipulse ethod, also based on epirical forulae obtained fro the easureent of shock pressures fro underwater explosions can only be used when the energy transfer ediu is water and when the reloading phenoenon is absent. Both the first and the second ethods provide upper bound estiates of the explosive energy delivered to the structure fro both the priary shock wave and reloading phenoenon. The third ethod gives lower bound estiation based on epirical pressure and ipulse forulae and does not include the energy delivered in the reloading phase. An iportant factor in deterining peak pressure is the copressibility of the energytransitting ediu and its acoustic ipedance, the product of the ass density and sound velocity in the ediu. The lower is the copressibility, the higher is the density of the ediu and the higher are the peak pressures. In this proble, there are five variables, which are charge weight W, standoff distance S, abient ediu density ρ a, its pressure P a, and shock wave overpressure P. The diensions are, respectively, M, L, ML -3, -1-2 ML T, and -1-2 ML T.There are only three diensions; therefore, two diensionless products should be fored. These are ( P / P a ) and ( S 3 ρ /W a ). Since water is relatively incopressible, its density, ρ a can be considered as constant and scaling paraeters of ( S 3 ρ a /W ) and ( P / P a ) can be written as follow [11]: 3 ( P / P ) f ( S W 1/ ) a = (1) The propagation velocity of shock wave drops rapidly to the sound velocity (approxiately 144 /s) within 1 ties the charge radius [12]. The underwater shock wave generated by the explosion is superiposed on the hydrostatic pressure. The pressure tie history, p ( t), at a fixed location starts with an instantaneous pressure increase to a 7 peak pressure, P, (in less than 1 s ) followed by a decay which in its initial portion is usually approxiated by an exponential function as [4]: p t = P exp -t / θ (2) with θ as the decay tie, valid for < t < θ. The peak pressure and the decay constant depend on the size of the explosive charge and the stand off fro this charge at which pressure is easured [4] /3 W P = S /3 1/3 W θ = 96.5( W ) S (3) (4) where, P is in MPa, θ is in icro seconds, W is expressed in kg of TNT and the stand off, S, is easured in eter. These forulae apply to any size of charge, fro a few grains to huge explosions, exploded at any depth, and describe the IJE Transactions B: Applications Vol. 25, No. 1, February

4 shock wave properly except in the iediate vicinity of the explosive charge (1 ties the charge radius), where the peak pressure is higher than what forula predicts. As the shock wave passes a fixed location and subjects the liquid at this point to a transient pressure p ( t), the liquid is siultaneously subjected to flow with a velocity v ( t) in the direction of the wave which is related to the transient pressure [13]: p ( t) = ρ cv( t) (5) A correction due to spherical flow is required and then the flow velocity becoes: ( ) p t 1 t v( t ) = + p ( t) dt ρc ρ S (6) The first ter is the velocity for a plane wave and the correction ter is called after flow ter. The after flow ter becoes significant in the close vicinity of the explosion, and for large tie intervals. The energy in the shock wave of the explosion consists of two equal coponents, one pertaining to the copression in the water and the other due to the associated flow. The shock wave energy density E for a plane shock wave is [14]: sh iportance. The energy is estiated for the whole length of the shock wave and the ipulse is integrated to a tie t = 6.7θ are given by: E sh = 98 W 1/3 ( ) 2.1 1/3 W S.891 1/3 1/3 W I = 576 ( W ) S 2 2 where, E is in J / and I is N s /. (1) (11) 2.1. Gas Bubble Pulsation The initial gas pressure is considerably decreased after the principal part of the shock wave has been eitted; but, it is still higher than the equilibriu hydrostatic pressure [14]. Up to 12 gas bubble pulsations have been observed using a detonator as the charge [15]. The first bubble pulse can have a peak pressure of 1 15 percent of the shock wave peak pressure. During the pulsation process, the bubble igrates upward because of the influence of the gravity, with the axiu igration occurring during the inia (Figure 1) [16]. 1 α E = p 2 ( t) dt ρc (7) For a fully exponential shock wave: E = 1 P 2 θ ρ c (8) The effectiveness of the shock wave depends on the tie integral of the pressure, or ipulse, ore significantly than on the detailed for of pressure versus tie. The ipulse of unit area of the shock wave front upto a tie t after the arrival is given by [13]: ( t) I = t p dt (9) Strictly, the pressure p( t) p in excess of hydrostatic pressure should be used in this equation. But for ost cases of interest, the shock wave pressure p( t ) is so large that the difference is of no Figure 1. Variation of the gas bubble generated by the explosion and its effect on pressure pulse The gas bubble generated by the explosion is nearly spherical during the initial expansion and contraction [17]. The two characteristic paraeters are the axiu radius R ax, reached during the first pulsation and the duration T of the pulsation (fro the explosion to the first following iniu). Both vary with the size of the 68 - Vol. 25, No. 1, February 212 IJE Transactions B: Applications

5 explosion charge and the depth at which the explosion occurs [13]. R ax =. 3 W 3 Z W T = 2.8 Z 1/ 3 5 / 6 1/ 3 (12) (13) where, Z = D + 1 represents the total static pressure at the location of the explosive. Here, D is the depth of the explosion in. Noogra was ade by Keil [1] for deterining the axiu gas bubble radius and the tie of first bubble pulsation. 1.5, and 1.6, three Endevco piezoelectric pressure sensors installed on the special fixtures. Using Mk79 electrical detonator (Figure 2), the charge is exploded and pressure versus tie data is recorded with 1 illion saples per second by a data acquisition syste. The experiental setup is shown in Figure 3. To ensure repeatability of results, tests repeated five ties. 3. EXPERIMENTAL PROCEDURE In this research, the blast shock waves for underwater detonation of Hexogen explosive charge (RDX or cyclotriethylene-trinitraine, C 3H 6N6O6 ) were experientally evaluated. The tests were set up in a water pool of diensions As entioned earlier, only experiental paraeters of shock wave for TNT charges were reported in the literature. Meanwhile, this data is ainly obtained about 6 years ago by Cole [4] or 4 years ago by Swisdak [13]. Therefore, these experiental results had soe liitations and deficiencies, due to technological restrictions. Not recording the details of blast waves is one of the liitations. It ust be noted that, the details of blast shock waves cannot still be evaluated by hydro-codes, because of intricacy and coplexity of the phenoenon [9]. Hexogen or RDX charge is a type of high explosive that has lot of industrial and ilitary applications. Detonation properties of this charge, siilar to other high explosives, depend on ass, density, shape, grain size and coposition. The saples of explosive charges used in the experients were cylindrical with L/D of one and ass of 2 gr. The density of hexogen charges was gr / c and it was obtained by pressing. The charges were coposed of 98 ass percentage of RDX and 2 ass percentage of wax. Charge placed at the id-depth point of the pool (2 depth) and at the distances of 1, 1.1, 1.25, 1.35, Figure 2. Electric detonator Figure 3. Setup of data acquisition syste 4. RESULTS AND DISCUSSION In Figure 4, a saple of experiental pressure pulse easured at 1. fro the detonation point is shown. In addition, the Cole's forula (Equations 2 to 4) for TNT is drawn for coparison. As expected, the pulse of Hexogen is larger than TNT, because of higher detonation energy [8]. Figure 5 shows coparison between shock wave pulses fro the detonation of 2 gr of Hexogen at distances 1., 1.25, and 1.5. Although, the behavior of shock wave pulse can be approxiated by an exponential curve, but its details are coplicated and the behavior of different pulses are not exactly the sae. IJE Transactions B: Applications Vol. 25, No. 1, February

6 14 14 RDX - 2 gr - 1. RDX - 2 gr RDX-Experient TNT-Cole Forula Tie (icrosecond) Figure 4. Pressure-tie record easured 1. fro the detonation of 2 gr of Hexogen (RDX). For coparison, pressure pulse curve of TNT based on Cole's equation is drawn Tie (icrosecond) Figure 7. Pressure-tie histories record easured 1.1 fro the detonation of 2 gr of Hexogen (RDX) for different tests RDX - 2 gr 14 RDX - 2 gr Tie (icrosecond) Figure 5. Coparison between shock wave pulses fro the detonation of 2 gr of Hexogen at distances 1., 1.25, and Tie (icrosecond) Figure 8. Pressure-tie histories record easured 1.5 fro the detonation of 2 gr of Hexogen (RDX) for different tests. The easured pressure versus tie histories for explosion of Hexogen at the distances of, 1., 1.1, 1.5, and 1.6 are shown in Figures 6, 7, 8, and 9, respectively. In these figures, every curve is belonging to a test repetition and siilarity of curves in each graph is noticeable RDX - 2 gr RDX - 2 gr Tie (icrosecond) Figure 9. Pressure-tie histories record easured 1.6 fro the detonation of 2 gr of Hexogen (RDX) for different tests Tie (icrosecond) Figure 6. Pressure-tie histories record easured 1. fro the detonation of 2 gr of Hexogen (RDX) for different tests. The values of overpressure and ipulse of easured blast shock waves are stated in Tables 1 and 2, respectively. 7 - Vol. 25, No. 1, February 212 IJE Transactions B: Applications

7 TABLE 1. The values of blast shock waves overpressure easured at different distances Distance () Values of overpressures in each test (bar) Average Ipulse (Pa.sec) RDX - 2 gr Distance () Figure 11. Measured shock wave ipulses as a function of distance to detonation point TABLE 2. The values of blast shock waves ipulse easured at different distances Distance () Values of ipulses in each test (Pa.s) Average Figures 1 and 11 show the variation of overpressure and ipulse, respectively, versus distance to detonation point. The correlation coefficients of the regression curves for these two charts are.9937 and.986, respectively. Overpressure (bar) RDX - 2 gr Distance () Figure 1. Measured shock wave overpressures as a function of distance to detonation point 5. CONCLUSION Previous events show the potential for terrorist attacks on the infrastructures involving waterborne explosions. Little inforation on how to deterine the potential daage fro such scenarios is publicly available yet. In addition, the underwater shock wave data for analysis of soe engineering practices such as explosive foring is necessary. The break down of the original olecule of an explosive into product olecules associated with the evolution of large aount of heat generates a shock front in the water ediu, followed by a gas bubble pulsation. The details of blast shock waves cannot be estiated by hydro-codes, because of coplexity of the explosion phenoenon and the purely nuerical or analytical solutions do not exactly confor to experients [9]. As entioned earlier, only experiental paraeters of shock wave for TNT charges were reported in the literature. Therefore, these experiental results had soe liitations and deficiencies due to technological restrictions. Not recording the details of blast waves is one of the liitations. For providing experiental data of shock wave pulses in underwater explosion of Hexogen charges, soe tests have been accoplished. Shock wave paraeters are obtained fro the easured pressure-tie curves. The experiental data can be used in practical engineering design, analysis applications and future theoretical researches. Coparison between these experiental results and Cole's forulae [4] shows that the equivalent ass of Hexogen to TNT explosive ust be taken as By this IJE Transactions B: Applications Vol. 25, No. 1, February

8 equivalence ass factor, behavior of underwater shock wave of Hexogen can be approxiately described by Coles' equations. 6. REFERENCES 1. Strosoe, E. and Eriksen, S. W., "Perforance of high explosives in underwater applications, Part 1: CHNO explosives, Propellants, Explosives and Pyrotechnics, Vol. 15, (199), Keil, A.H., "The response of ships to underwater explosions", Transactions of Social Naval Architect Marine Engineering, Vol. 69, (1961), Keicher, T., Happ, A., Kretscher, A., Sirringhaus, U. and Wild, R., "Influence of Aluiniu/Aoniu Perchlorate on the Perforance of Underwater Explosives", Propellants, Explosives and Pyrotechnics, Vol. 24, (1999), Cole, R.H., "Underwater explosions", Princeton University Press, Princeton, New York, (1948). 5. Bjarnholt, G., "Suggestions on standards for easureent and data evaluation in the underwater explosion test", Propellants, Explosives and Pyrotechnics, Vol. 5, (198.), Kirkwood, J.G. and Bethe, H.A., "Basic propagation theory", Office of scientific research and developent, (1942), Brett, J.M., "Nuerical odeling of shock wave and pressure pulse generation by underwater explosions", DSTO Report, TR-677, DSTO Platfors Sciences Laboratory, Australia, (1998). 8. Rajendran, R. and Narasihan, K., "Linear elastic shock response of plane plates subjected to underwater explosion", International Journal of Ipact Engineering, Vol. 25, (21), Geers, T.L. and Hunter, L.S., "An integrated waveeffects odel for an underwater explosion bubble", Journal of the acoustical society of Aerica, Vol. 4, (22), Brett, J.M., Buckland, M., Turner, T., Killoh, C.G. and Kiernan, P., "An experiental facility for iaging of ediu scale underwater explosions", DSTO-TR-1432, DSTO Platfors Sciences Laboratory, Australia, (23). 11. Held, M., "Siilarities of shock wave daage in air and in water", Propellants, Explosives and Pyrotechnics, Vol. 15, (199), Eneva, M., Stevens, J.L., Khristofrov, B.D., Murphy, J. and Adushkin, V.V., "Analysis of Russian hydroacoustic data for CTBT onitoring", Pure and Applied Geophysics, Vol. 158, (21), Haond, L., "Underwater shock wave characteristics of cylindrical charges", DSTO Report, GD-29, DSTO Platfors Sciences Laboratory, Australia, (1995). 14. Krueger, S.R., "Siulation of cylinder iplosion initiated by an underwater explosion", Naval Postgraduate School Thesis, Monterey, California, (26). 15. Swisdak, M.M., "Explosion Effects and Properties: Part II Explosion Effects in Water", NSWC/WOL/TR , Naval Surface Weapons Center, Dahlgren, VA, (1978). 16. Wardlaw, A.B.J. and Mair, H.U., "Spherical solutions of an underwater explosion bubble", Shock and Vibration, Vol. 5, (1998), Hung, C. F., Hsu, P. Y. and Hwang-Fuu, J. J., "Elastic shock response of an air-backed plate to underwater explosion", International Journal of Ipact Engineering, Vol. 31, (25), Vol. 25, No. 1, February 212 IJE Transactions B: Applications