ADIT DEBRIS PROJECTION DUE TO AN EXPLOSION IN AN UNDERGROUND AMMUNITION STORAGE MAGAZINE

Transcription

1 ADIT DEBRIS PROJECTION DUE TO AN EXPLOSION IN AN UNDERGROUND AMMUNITION STORAGE MAGAZINE Froe Opsvik, Knut Bråtveit Holm an Svein Rollvik Forsvarets forskningsinstitutt, FFI Norwegian Defence Research Establishment P.O. Box 5, N-007 Kjeller, Norway ABSTRACT The main hazars from acciental explosions in unergroun ammunition storage magazines are the air blast propagation an the structural ebris projection exposing the terrain outsie the tunnel. In this paper we focus on the ait ebris projection part of the problem, which is not as thoroughly examine as the air blast propagation. The existing preiction methos for the ait ebris quantity istance are base on a fairly small number of trials. The sparse test ata available makes it ifficult to establish reliable formulas for the maximum ebris projection istance an the lethal ebris ensity limit. Great care must be taken when analysing such a sparse set of ata, because interpolation, an especially extrapolation, may lea to non-physical relations. In this paper we escribe a metho which combines theory an test ata in orer to extract as much knowlege as possible from the available trial results. Only the ominating physical processes are escribe by the moel, using simple analytical formulas. Test ata are use to escribe the processes that can not be approximate analytically. The simulation results from a numerical coe hanling the require calculations are consistent with the available test ata. INTRODUCTION Acciental explosions in unergroun ammunition storage magazines are characterise by the strong irectional effect ue to the ait. A large amount of the energy release in an explosion is irecte through the ait, an the main hazars are the air blast propagation an the structural ebris projection exposing the terrain outsie the tunnel. In aition, breaching of the overhea cover of the magazine may occur, leaing to blast venting an ebris ejection, which further complicates the hazar assessments. The present stuy is constraine to the cases where such breaching oes not occur. The part of the problem concerning the air blast propagation is stuie an fairly well unerstoo, an the resulting preiction methos for the quantity istance are well establishe, although numerical preictions so far ten to overestimate the sie on air blast. In this paper we focus on

2 Report Documentation Page Form Approve OMB No Public reporting buren for the collection of information is estimate to average hour per response, incluing the time for reviewing instructions, searching existing ata sources, gathering an maintaining the ata neee, an completing an reviewing the collection of information. Sen comments regaring this buren estimate or any other aspect of this collection of information, incluing suggestions for reucing this buren, to Washington Heaquarters Services, Directorate for Information Operations an Reports, 5 Jefferson Davis Highway, Suite 04, Arlington VA Responents shoul be aware that notwithstaning any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it oes not isplay a currently vali OMB control number.. REPORT DATE AUG 996. REPORT TYPE 3. DATES COVERED to TITLE AND SUBTITLE Ait Debris Projection Due to an Explosion in an Unergroun Ammunition Storage Magazine 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Norwegian Defence Research Establishment,P.O. Box 5,N-007 Kjeller, Norway, 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 0. SPONSOR/MONITOR S ACRONYM(S). DISTRIBUTION/AVAILABILITY STATEMENT Approve for public release; istribution unlimite. SPONSOR/MONITOR S REPORT NUMBER(S) 3. SUPPLEMENTARY NOTES See also ADM Proceeings of the Twenty-Seventh DoD Explosives Safety Seminar Hel in Las Vegas, NV on -6 August ABSTRACT see report 5. SUBJECT TERMS 6. SECURITY CLASSIFICATION OF: 7. LIMITATION OF ABSTRACT a. REPORT unclassifie b. ABSTRACT unclassifie c. THIS PAGE unclassifie Same as Report (SAR) 8. NUMBER OF PAGES 9a. NAME OF RESPONSIBLE PERSON Stanar Form 98 (Rev. 8-98) Prescribe by ANSI St Z39-8

3 the ait ebris projection part of the problem, which is not as thoroughly examine as the air blast propagation. The existing quantity istance preiction methos for ait ebris projection are base on a fairly small number of trials. The sparse test ata available makes it ifficult to establish reliable formulas for the ebris projection istance an the lethal ebris ensity limit. When analysing such a sparse set of ata, exclusive use of interpolation an extrapolation techniques may lea to non-physical relations. Fining the correct functional relations between the various parameters involve, requires that the physics of the unerlying processes is applie in the analysis. The comply of the problem makes it ifficult to establish these relations through a purely analytical approach, using the test ata only to confirm the theory. In this paper we try to reprouce the available trial results by establishing a simple moel that combines the use of theory an test ata. If this can be achieve, the moel can be use to stuy other initial conitions than those of the trials since the moel enables a physically correct extrapolation. It has not been the intention of this stuy to provie a etaile mathematical escription of the ifferent physical phenomena, but rather to outline the basic ieas of the moel. THE MODEL Consier a simple storage site characterise by the chamber volume V, the net explosive quantity Q an the length L A an iameter D of the ait. Given these initial parameters, we want to establish a proceure for preicting the projection istance for one piece of structural ebris with known mass, shape an initial location. Base on the various unerlying physical processes, it is natural to ivie the moel into the following sub-problems: i) The etonation in the chamber will create a blast wave followe by a flow of etonation proucts through the ait. A relation between the particle flow velocity in the ait, U, an the initial parameters of the problem must be foun. This can be one through analytical approximations. ii) The rag force ue to the particle flow (the ynamic pressure impulse) will accelerate the piece of ebris own the tunnel. A relation between the ebris velocity at the tunnel, v, an the particle flow velocity, U, must be establishe, when assuming that no collisions with the tunnel walls occur. This relation can also be approximate analytically. iii) The piece of ebris may however collie several times with the ait walls an its velocity will consequently be reuce. The more collisions the larger reuction of the velocity, an the number of collisions increases with the istance from the initial location of the piece of ebris to the tunnel, L, an ecreases with the tunnel iameter, D. Even if the initial orientation of the ebris is known, it is impossible to exactly foresee how a piece of ebris is lifte by the blast wave, an what rotation an trajectory it is given, see however (). Therefore the number of collisions is not uniquely given, but will be istribute aroun a mean value. A

4 velocity reuction factor possessing these features must be foun. Assuming the factor to have an exponential form, the velocity can be expresse by v = v e L β D, (.) as iscusse in section 3.5. In equation (.) β is a stochastic parameter influence by the inertia of the ebris, the structure of the tunnel walls, etc. The β -istribution must be etermine experimentally. iv) The acceleration of the ebris is assume to cease at the tunnel, an the ebris trajectory outsie the ait is etermine by the velocity an angle, an the acting air rag an gravity forces. The projection istance from the tunnel to the ebris groun impact, R, must be foun. This can be one analytically when assuming a rag coefficient. v) The stochastic parameter β will be istribute aroun a mean value, hence the projection istance R will be istribute accoringly. This statistical aspect must be hanle by the moel. The sub-problems i)-iv) of the moel are escribe in etail in chapter 3. 3 IMPLEMENTATION 3. Particle flow velocity The particle flow following a etonation in the chamber is primarily etermine by the net explosive quantity Q an the chamber volume V. In aition the ratio of the tunnel cross section to the chamber cross section will effect the venting of the chamber. The roughness of the walls will also effect how the particle flow velocity U evolves, an generally U is given by the pressure time history in the tunnel. A rough estimation of U can be foun using a one imensional shock tube analogy, assuming the pressure to be constant throughout the tunnel; U c a ( M ) =, (3.) M ( γ a + ) where M = v c is the Mach number of the shock propagating own the tunnel, c a the soun spee an γ a the specific heat ratio in the unisturbe air in the tunnel. In this simplifie analogue U is constant, giving an estimate for the velocity of the etonation proucts as well as for the air behin the shock. The Mach number can be foun from shock tube relations ()(3) provie that the post-etonation pressure in the chamber can be estimate. This can be one by assuming that all the chemical energy of the explosive is use to aiabatically heat up the mixture of air an etonation proucts to a final equilibrium. The effects of heat conuction into the surrouning rock an mechanical interaction with the surrouning rock (chamber expansion) are

5 neglecte. When all the original mass of the explosive is assume converte to etonation proucts, the equilibrium gas ensity in the chamber becomes ρ c Q =. (3.) V Here the relatively small amount of air present is neglecte. When assuming that the ieal gas law applies, the equilibrium chamber pressure becomes p = E( γ ) ρ, (3.3) c c c where E is the release energy per unit mass an γ c is the specific heat ratio. Even though the gas of etonation proucts is non-ieal, the use of an effective value of γ c gives a fairly goo approximation. 3. Debris velocity The ominating force accelerating the piece of ebris is the rag force ue to the velocity ifference, V r = v-u, relative to the surrouning gas; F ( V ) ρ AC ( V ) V, (3.4) r = r r where ρ is the gas ensity, A is the expose area of the ebris an C (V r ) is the rag coefficient which is a function of V r an ebris shape. The integral of F represents the ynamic pressure impulse. The equation of motion is, when V r = v-u: m v t = ρ AC ( v U), (3.5) where m is the mass of the piece of ebris, v is the ebris velocity. Here, the rag coefficient is suppose to be constant an equal to the initial value, C (U). This is a goo approximation because the changes in V r, an hence in C, are relatively small. By introucing K A = m C ρ, (3.6) the solution of the equation becomes U K t v( t) =. (3.7) + UK t The istance covere by the piece of ebris is x(t) = Ut ln( + UK t). (3.8) K

6 The piece of ebris reaches the tunnel at time t = t. This time must be etermine numerically from equation (3.8), an the velocity is then v = v( t ). The initial acceleration ue to the passage of the shock front is neglecte in this estimate. 3.3 Velocity reuction ue to collisions The piece of ebris may collie several times with the tunnel walls an consequently lose some of its velocity. Therefore the velocity is generally smaller than the velocity v calculate above. This may be written v = K v, (3.9) where K is a factor between 0 an. The actual value of K can not be preetermine even if the initial location an orientation of the piece of ebris are known ue to the stochastic nature of the collision process. K is roughly given by the number of collisions, which increases with the istance from the initial location of the piece of ebris to the tunnel, L, an ecreases with the tunnel iameter, D. Therefore, K is suppose to be a function of L/D, as alreay state in equation (.). The actual form of the velocity reuction factor can be foun by analysing the test ata, see section 3.5. In orer to o this the ebris flight outsie the ait must be treate. 3.4 Debris flight outsie the ait The forces acting on a flying piece of ebris outsie the ait are the gravity an the air rag, resulting in the following equations of motion: t v v A m C v vv a x = ρ ( ) A g m C v vv, (3.0) ρa ( ) y x y where g is the gravitational constant an x an y are the co-orinates in the horizontal an the vertical irection. The velocity v is given as v = v + v. (3.) x y The initial conitions may be written v v x y ( 0) v ( 0) = v cosθ sinθ, (3.) where v is the velocity an θ is the angle. The angle will also be a stochastic variable influence by the collision process. For convenience the angle is kept constant in this stuy.

7 3.5 Velocity reuction factor The form of the velocity reuction factor K can now be foun using parts of the establishe moel to analyse the test ata. In this stuy we use the results of the Älvalen (4) an China Lake (5) trials. These trials are briefly escribe in appenix A. For each of the surveye pieces of artificial ebris in the trials, we calculate the v as escribe by the moel in sections 3. an 3.. The test ata gives the projection istance for each piece of ebris, which can be use to calculate the corresponing v by integrating the equations of section 3.4 "backwars". For convenience the θ is set constant to 9 uring this analysis. The ratio of the two calculate velocities, v v, is plotte against the L/D in figure 3. for all the pieces of artificial ebris surveye in the tests. 0.9 Velocity reuction factor L/D Älvalen-5 Älvalen-6 China Lake Curve fit Figure 3.: Velocity reuction factor, K; results from the tests at Älvalen an China Lake an a fitte exponential curve. The plot in figure 3. inicates that K shoul have an exponential form. The exponential form possess the correct limiting behaviour. If L equals 0, no collisions takes place an K shoul be, an if L becomes large K shoul approach 0. Assuming an exponential form, the velocity reuction factor can be expresse by L D K = e β, (3.3) where β is a stochastic parameter. There is a consierable scatter aroun the least squares fitte curve in figure 3., which can be interprete as the manifestation of the stochastic nature of β. The calculate values of K can be

8 use to calculate the corresponing values of β, given by equation 3.3. Figure 3. shows the β values for the surveye ebris of the tests. The β seems to be normally istribute with mean 0.4 an stanar eviation This β -istribution can now be use to escribe the collision process of any piece of ebris, an the moel escribe in i)-iv) is complete Relative ensity Experiments Normal istribution β Figure 3.: Experimental istribution of β -values an a normal istribution with mean 0.4 an stanar eviation REPRODUCTION OF THE TEST DATA 4. Artificial ebris To test the moel we try to reprouce the available test ata. At China Lake (5) mm projectiles were place about 8 m from the tunnel, of these were surveye after the shot. The initial conition can be escribe by Q/V=00 an L/D=.7. The columns in figure 4. show the istribution of the projecte ebris ivie in range intervals of 00 m. The meian of this istribution is 443 m, the 75th percentile is 664 m an the 90th percentile is 789 m. The curve in figure 4. shows the ebris istribution prouce by the moel when subjecte to the China Lake initial conitions. To satisfy the statistical requirements of step v) of the moel, the simulation was performe with 400 ( 00) cyliners, an the result normalise to a total of cyliners. The meian of the simulate istribution is 476 m, the 75th percentile 679 m an the 90th percentile 89 m. Hence the moel seems to reprouce the test ata well. For other combinations of Q/V an L/D, the trials at Älvalen (4) an China Lake (5) have only two pre-locate pieces of ebris for each initial conition. This makes it ifficult to ecie if the

9 simulation results are consistent with the trials. Table 4. shows the meian, 75th an 90th percentile for the istribution of ebris projection istances for the other combinations of Q/V an L/D, as well as the trial results for these combinations. 5 4 No. of fragments 3 China Lake Trial, Artificial Debris Simulation Projection istance, interval mipoint [m] Figure 4.: Comparison of simulation results an test ata for the China Lake artificial ebris survey. Initial conitions Simulation results Trial results Projection istance istribution [m] Projection Q/V L/D meian 75th percentile 95th percentile istance [m] Table 4.: Comparison of simulation results an test ata for various combinations for Q/V an L/D. China Lake an Älvalen artificial ebris survey.

10 The simulation gives consistent projection istances when the ebris are initially locate near the chamber. For pieces of ebris initially locate near the tunnel, the moel tens to unerestimate the projection istance. This inicates that the approximations mae when escribing the unerlying processes might be too rough, an that the escription shoul be refine. One way to explain the unerestimation of the projection istances is that the acceleration of the ebris o not cease at the tunnel mouth as assume, but continue to some istance outsie the. 4. Natural ebris At China Lake the naturally forme ebris of rock an concrete weighing more than 0 kg were surveye an their mass an projection istances measure. A total of 8 pieces of natural ebris were surveye an their mass istribution can be represente by a log-normal istribution with mean 5. an stanar eviation.4. The moel can be use to reprouce the projection istances for the natural ebris at China Lake. An extra element of uncertainty is ae in this simulation since the initial locations of the ebris are unknown an their shapes are not well efine. In the simulation it is assume that the ebris are initially uniformly istribute in the ait, an that their masses are log-normally istribute an their shape cubic. In figure 4. the columns show the istribution of the projection istances for the 8 surveye pieces of natural ebris. The meian of this istribution is 473 m, the 75th percentile 7 m an the 90th percentile 770 m No. of fragments China Lake Trial, Natural Debris Simulation Projection istance, interval mipoint [m] Figure 4.: Comparison of simulation results an test ata for the China Lake natural ebris survey.

11 The curve in figure 4. shows the simulation results for the projection of 6400 (8 00) pieces of natural ebris using the China Lake initial conitions, normalise to a total of 8 pieces of ebris. The calculate istribution has a meian of 307 m an a 75th percentile of 496 m an a 90th percentile of 677 m. For the projection of the natural ebris the moel tens to unerestimate the projection istances. This might be ue to an incorrect assumption of uniform initial location of the ebris, or the velocity reuction factor establishe for cylinrical ebris might overestimate the velocity reuction for cube-like ebris. Consiere the rough assumptions mae in the simulation, the test ata are reprouce to an unexpecte high egree. 5 CONCLUSIONS The simulation results prouce by the moel seems to be consistent with the test results. This inicates that the establishe moel represents a mainly correct escription of the physical phenomena of the problem. This also inicates that the steps i)-iv) of the moel represents a correct ivision of the problem. The main parameters etermining the projection istance can be ientifie to be Q/V, L/D an the istributions of mass, location an shape of the expecte ebris. The moel is recommene use to preict ebris projection istances an to etermine quantity istance preiction methos for actual storage magazines. 6 RECOMMENDATIONS FOR FURTHER WORK The escription of the physical processes of i)-iv) shoul however be refine, to achieve an even better reprouction of the trial results. When refining the moel, it is important to maintain a balance egree of refinement between the various processes escribe. In our moel several short cuts have been mae which shoul be reconsiere when improving the moel: The particle flow velocity in the ait (or ynamic pressure impulse) shoul be etermine base on a better representation of the pressure time history in the ait. The effect of the choking of the flow an the shock attenuation ue to wall roughness shoul be consiere. The ratio of the tunnel cross section to the chamber cross section will effect the amount of time neee to vent the chamber. The ynamic pressure impulse epens on this venting time an on the total amount of energy available, which inicates that Q as a representation of the available energy shoul be a separate parameter of the problem. The acceleration of the ebris o not cease at the tunnel mouth as assume, but continues to some istance outsie the. The ebris angle is kept constant in the moel even though this parameter clearly is istribute. This simplification shoul be reconsiere. When analysing the test results, the measure projection istance is taken to be the istance to the first groun impact for the ebris. This is probably not correct ue to ricochets before the ebris finally stops.

12 The β -istribution in this stuy is entirely base on cylinrical ebris. The experimental basis leaing to the β -istribution shoul be extene, an the effect of various ebris shapes stuie. Survey of pre-locate natural rock ebris shoul be inclue in future tests, to ensure that the β -istribution represents a correct escription of their collision process. Before the moel can be use to establish the quantity istance preiction methos, some aitional problems must be aresse: The angular istribution of the ebris must be escribe. Accoring to the test ata a normal istribution seems to be a goo representation of the angular istribution. The initial mass istribution of potential ebris for typical storage magazines must be etermine by inspection. The effect of various safety measures in actual storage magazines must be estimate. These measures might be the geometry of the tunnels, constrictions, expansion chambers, ebris traps, blast oors etc. The effect of the topography of the expose terrain shoul also be taken into account when etermining the quantity istance preiction methos. References () Ethrige N H, Flory R A (993): Use of cube isplacements as a measure of air blast, Proceeings of the 3th International Symposium on the Military Application of Blast Simulation, Volume, The Hague, The Netherlans. () Lanau L D, Lifshitz E M (984): Flui mechanics, Volume 6 of Course of Theoretical Physics, Secon Eition, Pergamon Press, Oxfor. (3) Whitham G B (974): Linear an non-linear waves, John Wiley & Sons, New York. (4) Vretbla B (987): The 986 Klotz-Club Tests, report A3:87, Fortifikationsförvaltningen, Forskningsbyrån, Eskilstuna, Sween. (5) Halsey C C, Durbin W F, Berry S L (989): Klotz unergroun magazine trial ata report, Naval Weapons Center, China Lake, California, USA. APPENDIX A DESCRIPTION OF THE TRIALS Very few full-scale experiments inclue survey of ait ebris. Two tests incluing measurements of ait projection istances are the Älvalen trials (4) in Sween an the China Lake trials (5) in USA.

13 At the 986 Älvalen test series, the installation consiste of a tunnel with two chambers as figure A. shows. The volume of chamber A an B was 300 m 3 an 00 m 3 respectively. The cross section of the tunnels was 6.3 m. For test shots 5 an 6 at Älvalen, there exist ata for the iniviual positions of the place artificial ebris before an after the shots. In these tests, the charge consiste of totally 000 kg TNT, place in the mile of the chambers. In test 5 the charge was in chamber A an in test 6 in chamber B. The artificial ebris were steel pipes fille with concrete, an their mass was 47 kg, the length 68 cm an the iameter 6 cm. Pairs of cyliners were place on the tunnel floor on three (test 5) or four (test 6) locations as figure A. shows. All the pipes were marke to make it possible to ientify them after the shots. 5 m A 6 m 58 m B Figure A.: Tunnel an chambers at Älvalen. The installation of the 988 China Lake trial, consiste of a chamber an a tunnel as shown in figure A.. The chamber ha a m cross section an a volume of 0 m 3, while the cross section of the tunnel was 5.6 m. The charge was equivalent to 000 kg TNT an positione in the centre of the chamber. 5 m Charge 8 m 5 m Figure A.: Tunnel an chamber at China Lake. As in the Älvalen tests, pieces of artificial ebris were place in the tunnel an in the chamber, see figure A.. The ebris were san-fille 55 mm projectiles with mass 43 kg an length 90 cm. Initially 4 projectiles were place in the installation, 5 of these were surveye, an their projection istances measure.