IAAl?90NVAL RSEARCH LAB WASHINGTON DC FG1/S SCT SIMULATION OF HB AIRBLAST PHENOMENA U

I EP 81 A L KUHL. M A FRy M PICONE. DL BOOK

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NRL Memorandum Report 4613 At: g c' L4. TITLE (W4d Su~btitle) S. TYPE OF REPORT 6 PERIOD COVERED

FCT IMUATIO OFHOB IRBASTInterim report on a continuingFCT IMULTIONOF OB ARBLAT INRL roblem.PHENOMENA S.P~OMIN G ORG. REPORT NUMBER

7. AUTHOR(*) 0, CONTRACT OR GRANT NUMOER(.t

A. L. Kuhl*, M. A. Fry**, M. Picone, D. L. Book andJ. P. Boris

9. PERFORMING GRGANIZA1ION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

Naval Research Laboratory AE OR O UBR

Washington, DC 20375 62715H; 44-0578-0-1

It. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Defense Nuclear Agency September 29, 1981Washington, DC 20305 5"3UME ~ AE

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**Present address: Science Applications, Inc., McLean, Virginia 22102

(Continues)19 KEY FIORDS (Contirnue on reverse olde If noceeewiy, end Idenfy by block nueser)

HOB (Height-of-burst) Hemispherical HE (High explosive)Airbiast EnvironmentDetonation(s) Overpressure

%AIISTRACT (Colltin... on reverse side If necesele And identify by block mnwiteb.)

Height-of-burst (HOB) detonations can create airblast environments which are moresevere than surface burst environments at high overpressures (> 100 psi). A double Machstem structure develops during shock reflection from the ground at a range approxi-mately equal to the HOB. This creates double peak static pressure waveforms withenhanced early-time impulses. Blast diffraction on above pround structures also

(Continues)

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18. Supplementary Notes (Continued)

This work was supported by the Defense Nuclear Agency under Subtask XY99QAXSG,work unit 00001, and work unit title "Flux-Corrected Transport."

This paper was presented at the Seventh International Symposium on MilitaryApplications of Blast Simulation, July 13-17, 1981, Medicine Hat, Alberta, Canada,under the title "Simulation of High Overpressure HOB Airblast Environments on a\ Large Scale."

20. Abstract (Continued)

contains multiple peaks with enhanced loads and impulses. There is an ongoing interestin simulating these HOB environments for military applications. High explosives (HE)charges can be used to simulate the nuclear surface burst case below about 100 psi forreasonable yields (100T or more), but it appears that it is impractical to elevate largeHE charges above grade to simulate the HOB case. In this paper we propose a newmethod for naturally simulating such HOB environments on a large scale. A hemi-spherical HE charge could be detonated near a natural slope which had been graded toform a large ramp. When the spherical blast wave reflects from this ramp a shockstructure and environment is created which is similar to the HOB case. Validity of thisconcept is demonstrated by numerical simulations with a nonsteady 2-D FCT hydrocode.These calculations indicate that a 30°, ramp located 200 ft from a 500T hemisphericalHE charge will create 400 to 600 psi double peak static pressure waveforms at distancesof 40 to 60 ft up the ramp; time betwen peks is 1 ms. These waveforms correspondto a nuclear detonation at 100 to 120 ftKTrT and a ground range of 190 to 210 ft/

.AD

seNl[ llY CL.ASIIrCATION OP TI1S PAOE(W?'. DE1*l EU~lt~ltE)

ii

CONTENTS

I. INTRODUCTION 1.. . . . . . .. . . . .. . . . . . . . . . . .

11. CONCEPTUAL DESIGN OF THE HOB SIMULATOR........................3

III. COMPUTATIONAL TECHNIQUE ....................................... 4

IV. CALCULATIONAL RESULTS......................................... 6

V. SUMMARY AND CONCLUSIONS ....................................... 8

VI. RECOMMENDATIONS ............................................... 9

ACKNOWLEDGMENTS .................................................. 9

REFERENCES........................................................23

A ccession For

NTIS GRA&IDTIC TABUnannounced.Justif'ication

By-- - - - --Distribution/ _

-Availability Codes D I!Avail and/or FL E ZT E

Dist Special DC~ 3 1

DEC1 1,6

FCT SIMULATION OF HOB AIRBLAST PHENOMENA

I. INTRODUCTION

It is now recognized that height-of-burst (HOE) detova-tions can create more severe airblast environments thansurface burst (SB) detonations, especially at high over-pressures. In the HOB case, the spherical blast wave re-flects from the ground, initially as a regular reflection.Then at a ground range approximately equal to the height-of-burst, the shock reflection makes a transition to adouble Mach shock structure. This double shock structurecreates secondary peaks in the static pressure at and nearthe ground and thus enhances the early-time HOB airblastimpulses compared to the SB case. As shown experimentallyby H. J. Carpenter at MABS-IV (Ref. 1), these secondarypeaks of the HOB case can be much greater than the firstpeaks.

When a double Mach shock structure reflects from anabove-ground structure, it can produce enhanced diffractionloads. HOB diffraction loads are compared with SB loads inFig. 1 which was constructed by scaling data from the1000-lb Pentolite sphere experiments on the recent MIGHTYMACH test series (Ref. 2). As is evident from this figure,the early-time HOB loading impulses are about twice theSB values. Similar effects are shown in Fig. I for thestatic pressure histories and impulses which apply to loadson flush mounted structures.

For military applications, there is a need to simulatethese HOB blast environments on a large scale in order totest the response and survivability of large-scale or full-scale military systems. Explosive yields from kilotons tomegatons are required. Suspension of such large high explo-sive (HE) charges is impractical and could lead to poorquality blast fields due to interference effects from thecharge support structure.

In this paper we propose a novel approach for simulatingHOB blast environments on a large scale. The concept isshown in Fig. 2. A hemispherical surface burst HE chargewould be used to create a free-field blast wave. The chargewould be situated near an up-slope which had been graded toform a large ramp. When the spherical blast reflects fromthe ramp, a double Mach shock structure can be created(within certain constraints on wedge angle, OW , and inci-dent shock Mach number). This concept relies on the simi-larity between the HOB-produced environments on horizontalsurfaces and the environments produced by shock reflectionson wedges or ramps. In Fig. 3 we compare some recent

Manuscript submitted July 22, 1981.

calculations with the FAST2D code:* a nuclear detonation atHOB = 10L ft/KTN1 /3 versus a Mach seven square wave shockreflection from a wedge. The pressure contours show thatfor similar sho-k strengths and angles, the shock structuresin the wedge and HOB cases are qualitatively similar; den-sity contours are also qualitatively similar with a slipliae emanating from the primary triple point. There are,however, quantitative differences: the Mach stem structurein the nuclear HOB case is more complex, with a bulge atthe foot of the Mach stem; also, in the nuclear case, thereflected shock races rapidly through the high temperature(104 to 105 OK) fireball, while in the wedge case, thereflected wave propagates slowly into the lower (10 3 OK)temperature constant field behind the incident square waveshock. We believe, however, that these differences are ofsecondary importance.

A remaining question is: how well does the blast wavefrom a hemispherical HE charge simulate the nuclear free-field environment? In Figure 4 we compare the static anddynamic pressure waveforms for the HE and nuclear casesfrom Brode's one-dimensional (l-D) free air burst calcula-tions (Refs. 3,4) at shock overpressures of approximately100, 200 and 400 psig. In the HE case a contact surface(CS) separates the air from the detonation products. Thiscontact surface causes a sharp jump in dynamic pressure dueto the high densities ot the products. Also evident in theHE case is a secondary shock, S2, which faces inward but isbeing swept outward by the rapid expansion of the charge.The HE-driven blast wave gives a rather poor simulation ofthe complete nuclear waveform at high overpressures, dueprincipally to the HE contact surface and secondary shock.However, the HE blast wave outside the contact surface is areasonably good simulation of the nuclear case. We proposeto use precisely this part of the HE blast wave and reflectit from the ramp to simulate the early-time nuclear HOBcases.

The remainder of the paper is organized as follows:Section II gives a conceptual design of the ramp HOB simu-lator; Section III describes the 2-D finite difference vscheme which we used to investigate numerically the flowfields on and near the ramp; Section IV presents the resultsof these calculations, while conclusions and recommenda-tions are offered in Sections V and VI.

This code uses the Flux Corrected Transport (FCT) aigor-ithm,described in Section III, to maintain sharp disconti-nuities.

2

II. CONCEPTUAL DESIGN OF THE HOB SIMULATOR

The design objective for this simulator is to producethe high overpressure (say 100 to 1000 psi) double-peakflow fields which simulate nuclear HOB detonations in theMach reflection regime with high fidelity. The simulatorshould be reasonably inexpensive and readily constructed.The design concept should be extendable to large yields.

The primary design parameters for the simulator are thelocation of the front edge of the ramp, GRR, and the rampangle, 8W. The conceptual design process begins with an HEfree-air pressure-range curve for 1 lb of Pentolite. Aramp was assumed to be located at a GRR corresponding tofree field shock overpressures of 500 psi or 150 psi.Assuming various ramp angles, we used reflection factors(Ref. 1) to determiue the peak static pressure versus rampground range, RGR. Parametric results are presented in

Fig. 5. Inserts give the results scaled to a 500Tsurface burst which are equivalent to about a one-kilotonnuclear surface burst case. Examination of the results in

Fig. 5 indicates the following trends:

o A requirement for a high pressure (400 psi to 600psi) simulator forces one to either move the rampcloser to the charge, or increase the ramp angle,or both.

o One would prefer to move the ramp away from thecharge so that the HE free field is closeto thenuclear case; however, this leads to large (andpresumably impractical) ramp angles.

o Decreasing the ramp angle tends to make the Machstem rise more rapidly thus increasing the separa-tion between the first and second peaks; we specu-late that this could lead to a yield amplificationon the front-end of the waveform.

o Transition to Mach reflection occurs at the leadingedge of the ramp for 8W = 300 and 400; the transi-tion point (TP) for the OW = 600 occurs at aboutone-half the distance up the ramp.

The 300 ramp at the 500 psi station appears to be aninteresting case--it is feasible to construct and the 600-psi shock overpressure will occur at about 50 ft up theramp, thus allowing plenty of time for the Mach stem heightto grow. Peak pressures will range from 1500 psi at thebeginning of the ramp to about 300 psi at the far end.

3

III. COMPUTATIONAL TECHNIQUE

A numerical simulation of the shock diffraction for theramp HOB simulator (a 300 ramp starting at 200 feet from a500T hemispherical HE charge) was performed with a nons-eadytwo-dimensional (2-D) hydrocode, FAST2D. The objectives ofthe calculation were to validate the ramp HOB simulatordesign and to evaluate, in detail, the flow field in thevicinity of the ramp. The FAST2D code solves the balancelaws of gasdynamics on a sliding grid in the general form:

O J dV =- (a-u) dA +7 TdA()SV(t) 6A.(t)- -- 6A(t)

where represents the mass, momentum, energy or species massdensity (for multi-material calculations) in cell 6V(t),u and Ug represent the fluid and grid velocities, respect-ively, and T represents the pressure/work terms. The finite-difference approximation to Eq. (1) uses a vectorized Flux-Corrected Transport (FCT) algorithm, ETBFCT (Ref. 5), whichgives an accurate and well-resolved description of shockwave propagation without the necessity of an a priori know-ledge of the number, location or character of the gas-dynamic discontinuities in the problem. The linear portionof this algorithm is fourth-order-accurate spatially forconstant-velocity advection problems, and has a nonlinearflux-corrected antidiffusion stage which automatically pro-vides the local dissipation needed to accurately model dis-continuities. The formulation of the algorithm allows thegrid to slide with respect to the fluid without introducingadditional numerical diffusion. This general adaptiveregridding technique permits fine zones to be concentratedin the region of greatest physical interest, thus reducingcomputational costs with no serious loss in resolution.

Since the ETBFCT algorithm is one-dimensional,time-splitting must be employed to solve two-dimensionalproblems. Time-splitting makes the boundary condition onthe ramp particularly easy to implement. The ramp isrepresented as a series of "stairsteps" (of varying heightand depth) along the interface between the extremal interiorzones and a corresponding set of guard cells. A guard cellis defined as the right-most cell in the r-directionduring the r-sweep, and the bottom-most cell in the z-direction during the z-sweep. The stairstep boundary con-ditions are reflective,which requires pressure, densityand energy to be continuous and the corresponding velocitynormal to the stairstep to vanish.

4

The numerical simulation began with a 1-D FCT calcula-tion of the blast wave driven by a one pound sphericalcharge of PBX-9404 in air. The initial conditions, whichare shown in Fig. 6, were taken to be the self-similarflow field corresponding to a spherical Chapman-Jouguetdetonation wave (Ref. 6), at the time the M onation wavereaches the charge radius, ro - 3.89 cm/lb . A Jones-Wilkins-Lee (JWL) equation of state (EOS) was used forthe detonation products and a real air equation of statewas used outside the HE/air interface. These EOS specifythe pressure as a function of density and internal energy.The HE/air interface was followed by solving a conserva-tion law for the mass fraction pf (where f=l in the pure HEand f-0 in the pure air). The equations of state wereblended in the mixed cells (O<f<l) according to Dalton'slaw. A fixed grid 9f 500 cells was used with a mesh spacingAr - 0.1025 cm/lbl/3, so that the initial flow field in thecharge occupied about 38 computational cells. The flowfield resultsl t the end of the 1-D calculation (cycle 1281,t - 152 Ps/lbI/ 3) are shown in Fig. 6. The shock over-pressure is 445 psig. The density distribution shows ajump at the HE/air interface; inside the interface is asecondary inward-facing shock which is being swept outwardby the supersonic flow.

These results were scaled up to the 500 ton HE surfaceburst case by multiplying all times and ranges by the sca!.:factor, SF = (2xi06)I/3 = 125.992. The shock radius atthis time of 19.15 ms/50OT1/

3 was found to be 198 ft/500T I/3

with an overpressure of 445 psig (note that this pointchecks with the HE free air curve in Fig. 5). Theseresults were then inserted as initial conditions in thecylindrical r-z FAST2D code, with one approximation. Sincethe y's ahead and behind the HE/air interface were quiteclose (YHE = 1.25 versus Yair = 1.30), the HE products weremodeled with the real air equation of state, and the 2-Dinterface was not followed specifically with a mass speciesconservation law. The 2-D mesh consisted of 150 x 150cells with a moving fine mesh region (55 x 55 cells, Ar5 cm and Az - 2.8868 cm with Az/Ar = tan 300) which followedthe Mach stem. The calculation was run 5601 cycles. Diag-nostics for the 2-D calculation consisted of 46 environmenttime histories (at 40 stations on the ramp and 6 stationsperpendicular to the ramp at a RGR - 60.5 ft) and contourplots of the flow field every 200 cycles. Times aredenoted by the label At=t-t, which references everythingto the incident shock arrival time at the foot of the rampto-19. 2 ms.

5

IV. CALCULATIONAL RESULTS

An overall picture of the spherical shock reflectionfrom the ramp is displayed in Fig. 7 which gives the cal-culated pressure and density contours at various times(. t=3, 5.61, 9.27 and 13.4 ms/500Tl/3); Fig. 8 gives a

magnified view of the flow field at At=9.61 ms/500T I / 3 .The shape of the shock structure for the simulator (i.e.,

the geometry of the incident wave, the Mach stem, and thekinked reflected wave) more c>osely resemble the shock

structure for square wave reflections from a ramp (Ref. 7)than the nuclear HOB case (see Fig. 3). The densitycontours indicate that a contact surface (a slip line)emanates from the triple point (the confluence of the inci-

dent, Mach and reflected waves) and approaches the ramp at0

an angle of about 60 . Pressure contours indicate that ahigh pressure region is located in the vicinity of where

the projection of the contact surface would strike the ramp.

Figure 9 gives an experimental shadowgraph of the shockwave structure formed by an 8 lb TNT driven blast wave(HOB - 1.04 ft/1bl / 3 ) diffracting on a 310 ramp. The inci-

dent shock pressure was about 120 psi at the foot of theramp and about 75 psi at the time of the photograph (com-

pliments of W. Dudziak, Ref. 8). The shock structure isqualitatively similar to that in Figs. 7 and 8. Fig. 9

shows that tha reflected wave pushes the TNT products awayfrom the ramp, thus maintaining a clean air flow (unpolluted

by HE products) in the Mach stem region--a truly beneficial

result! Note that this happens even in the low HOB casewhere the TNT products squish along the ground and push theTNT/air interface closer to the shock.

The calculated shock properties for the ramp HOB simu-

lator are shown in Fig. 10 as a function of ramp groundrange, RGR. The primary Mach stem pressure, Pl, ranged

from about 600 psi to 400 psi. The second peak pressure,

P2, decayed from 1300 psi at the foot of the ramp to 400psi at the 60 foot station. The peak pressures were deter-

mined from two methods: for RGR < 30 ft peaks were evaluated

from pressure distributions at a fixed time, and these dataare somewhat noisy due to the stairstep boundary condition

modeling of the ramp; for RGR > 30 ft, peaks were evaluatedby smoothing the pressure time histories two cells above

the ramp, giving a smooth pressure-range curve. * Note

that the second peaks are in reasonably good agreement with

Unfortunately the pressure histories for RGR < 30 ft werenot available for data analysis.

6

the prediction technique used to design the simulator. Alsonote that for RGR > 40 ft the first and second peaks areequal.

The calculated shock arrival times for the first andsecond static pressure peaks are included in Fig. 10The arrival time difference between peaks grows rapidly forthe first 30 feet up the ramp, and then remains constant atabout lms/500T1 1 3 . In addition, Fig. 10 depicts the Machstem growth versus ramp ground range. The top of the Machstem traces a path at an average angle of about 9 degreesabove the ramp surface, which is consistent with shock tubedata for square wave shock reflections from wedges (Ref. 7).Note that the Mach stem growth for the equivalent nuclearcase is more rapid than in the case of the simulator.

Calculated static pressure histories are presentedin Fig. 11 for various stations on the ramp (34 ft < RGR <60 ft). The second peak dominates for RGR < 34 ft, andthen gradually melts into backside of the waveform. ForRGR > 60 ft, the second peak has essentially disappeared.Comparisons of static pressure histories at h = 0, 1 and5.5 ft normal to the ramp for station 17 indicate thatthere is no vertical pressure gradient on the front end ofthe waveform.

Fig. 12 gives the calculated dynamic pressure his-tories on the ramp at stations corresponding to the staticpressure histories of Fig. 11. At small ground ranges,the second peak dominates the first peak. The second peakdecays in magnitude and duration as the Mach stem pro-gresses up the ramp, and has essentially disappeared forRGR > 60 ft. Comparisons of dynamic pressure histories ath = 0, 1 and 5.5 ft normal to the ramp for station 17 indi-cate very little vertical gradient for times less than 0.8ms after shock arrival. However, the h = 1 ft stationshows a strong second peak at about 1 ms which is absentfrom the h - 0 and 5 ft records. We believe that this iscaused by a high density slug of gas at this altitude. Aslip line (with high density material above and lower den-sity material below) emanates from the triple point. Asthe slip line approaches the ramp it curls forward forminga region of high density fluid near the ramp surface (h "11 ft/500T1 /3) while the Mach stem at this station is about10 ft high. This effect is similar to the contact surfacerollup observed in numerical simulations of nuclear HOBdetonations and square wave shock reflections from wedges(Ref. 9). This increase in dynamic pressure near the rampcan be very important to airblast loads on above ground

7

structures--it increases both the peak loads and theimpulses to approximately 2 ms/50OTl/3.

Let us now relate the simulator environment to an equi-valent nuclear height-of-burst case. Fig. 13 gives theideal, nuclear peak overpressure HOB curves as constructed

by H. J. Carpenter (Ref. 10). Region A corresponds to theregular reflection regime, and region B corresponds to theMach reflection regime where the static pressure waveformson the ground contain two peaks. In regions B1 and B2 ,first and second peaks dominate, respectively. Along thedashed curve the first and second peaks are equal. Figure9 indicates that for 30 ft < RGR < 60 ft, first and secondpeaks are equal and range from 600 psi down to 400 psi.Figure 13 then indicates that for this range in pressure,the nuclear HOB parameters are the following:

100 ft/KT1/ 3 < HOB < 120 ft/KT

1/ 3

190 ft/KT1 / 3 < GR < 210 ft/KT

1 / 3

Thus the simulator as analyzed in this report gives an air-blast environment which is equivalent to a nuclear detona-tion at height-of-burst of about 110 ft/KT I 3 and a groundrange of about 200 ft/KT1 /3.

Finally, let us consider the effective yield of thesimulator. A 500T high explosives surface burst producesa blast wave flow field which is equivalent to about a I-KTnuclear surface burst (or a 2-KT nuclear free air burst).Nuclear static pressure waveforms in the 400 psi to 600 psiMach reflection regime have double peqks with a time separa-tion between peaks of about 2 ms/KTN1' 3 (Ref. 10). TheFAST2D calculation of the simulator flow field indicates atime separation between peaks of about 1 ms/500ESB' i.e.,

the time separation for the simulator is too small by afactor of about two. We believe that the time separationbetween peaks can be increased by making the Mach stemclimb more rapidly. This can be accomplished by simul-taneously decreasing the ramp angle and moving the ramptoward the charge.

V. SUMMARY AND CONCLUSIONS

Height-of-burst detonations create airblast environmentsand diffraction loads which are more severe than the surfaceburst case in the high overpressure Mach reflection regime.There is an ongoing need to simulate these HOB environmentson a large scale to validate the survivability of militarysystems to blast effects. We propose using an existinghigh explosives test bed, say a 500T hemispherical charge,

8

to create the ?ree field blast environment. A large rampwould be located near the charge. Shock diffraction on theramp generates, in a rather natural way, a flow field whichsimulates the HOB blast environment with high fidelity.

A parametric analysis of such HOB simulators indicatesthat a 300 ramp situated about 200 feet from a 500T hemis-pherical charge would give useful environments. The flowfield details near such a ramp were investigated with a 2-Dhydrocode calculation. The calculation indicates thatdouble peaked static and dynamic pressure waveforms werecreated near the ramp surface. In the 400 to 600 psi range,the calculated first and second static pressure peaks wereequal. By use of the nuclear HOB curves, it was determinedthat the blast flow field corresponds to a nuclear detona-tion at a height-of-burst of 100 to 120 ft/KTNI/3 and aground range of 190 to 210 ft/KTN1/ 3 . Time separationsbetwen static pressure peaks were found to be about 1 ms/500ThsB; this value was too small by about a factor oftwo for the nuclear case.

VI. RECOMMENDATIONS

Additional analysis should be performed to refine theHOB simulator design. The 2-D hydrocode simulations arequite useful because they allow one to examine the entireflow field in a non-interfering way. Am improvement isneeded on the boundary condition modeling of the ramp--thestairstep model gave very noisy results on the ramp surface.Small charge (say 4-lb hemispherical PBX-9404 charges) testscan provide an experimental definition of the blast environ-ment. Ramp angle, location and surface curvature could bevaried parametrically in such tests. Pressure gauges onthe ramps can measure static pressure histories with highfidelity, while shadowgraph photography can capture theshock structure on the ramp. These results could be usedto design a simulator which, we suggest, should be fieldedon the next 500T HE test.

ACKNOWLDEGMENTSWe would like to acknowledge the contributions of

H. J. Carpenter in this work. In July of 1980, he and oneof the authors (A. Kuhl) first postulated the idea that alarge ramp, in conjunction with an HE charge, could be usedto simulate HOB environments on a large scale. His carefulcritique of the manuscript and his stimulating discussionson this subject are greatly appreciated.

This work was sponsored by the Defense Nuclear Agencyunder Contract Number DNAOO-81-C-0023. Dr. George Ullrichwas project officer for this effort.

9

5000 50

Average loads, A5 f 0Ap dy/h ~ 4 0 psi

HOB h =1.67 ft/KTl7I 4 t

100\BHO1

soE

- SHB = 30 f/KT1 3 . SR 21 ft/T 11

SB cas

100.

SH tB= (10ms/KTI/3 ) G 1 f/T/

Fig. 1 - Comparison of nuclear surface burst and height-of-burst loadsand impulses at the 400-psi station

10

Fig. 2- OB simultorGconept (Rade ap)op)aresae Et

11i

2.5mPressure Pesr

C, 460a 40

=i 5.4 M .

033.5 mn 38.5 mn

2.5 rn DensityDest

a 46040

MI=5.4 M .

00033.5 mn 38.5 rn

1-KT nuclear burst at HOB 104 ft = 7.0 shock on a 500 wedge (7 -4/3)(t - 11.15 ins)

Fig. 3 - Comparison of calculated pressure and density contours for a nuclearHOB case and a square wave shock on a wedge

12

100

-N~cear 0 -KTAS)- E

29.2 bd,

CS (409 ps9

1 12.1 ba2.nbr

A/ 1176 / (76 sr

110 -p45,(13p)

- N 1 a 11 K T B 'I . p I2 . a

171

I S2S,

I I - /

S/

0.01 1 01 J, j. .. . L..0 20 40 60 80 100 0 20 40 60 s0 100

R.d~us (./KTN'/3) Radius (m1KT1/~

3

Fig. 4 - Comparison of HE and nuclear free-air burst static and dynamicpressure waveforms at shock overpressures - 100, 200, and 400 psi

13

Peak reflected pressures onramps at the 500 psi station '0"Shock N

TP

1000 Ow =400

- Peaks reflected pressures on- ramps at the 150-psi station

Ramp~~~~~ grun rage00/0 T

u040

a)

100 10

150 ~T 20 503 0w5 40045

Ramp ~ ~ Rng gfround rag (t50 S100 0

Ramgudrnge (ft/50 SB

teRape HOB50 smlTor/

143

4!i 1

Icaq1 0

~~15

Pressure Density85 85

At 3 ms At 3 ms

Cycle - 601 Cycle 601

N

0 0200 297 200 297

85 .5

At = 5.61 ms 4t = 5.61 ms

*- Cycle =2001 Cycle = 2001

' ',

0 0

200 297 200 297

85 85

At 9.27 ms At 9.27 ms

Cycle 4001 Cycle = 4001

I-

N

0O 0200 297 200 297

85 85

N

13.4 ms At - 13.4 ms

Cycle = 5601 Cycle - 560O 0

200 297 200 297GR (ft/500 T113) GR 3ft/5O0T1/3

Fig. 7 - Calculated pressure and density contours at times At - 3.0, 5.61,

9.27, and 13.4 ms/500 T 1I3 (to = 19.2 ms/500 T1 13 )

16

Density (10-3 g/cm3)

-7

02519425

Pressure (bars)49 4 4

p 9.8 bars11.9.. 13.9\16J,. 18N 20

.2520

21020

194 253

Velocity (105 cm/S)

49 ... :...............

Umax =1.89 x 105 cm/s

0194 253

Ground range (ft)

Fig. 8 - Calculated flow details at At 9.61 ms/500 T113

17

NominalTNT/airinterface

Shockperturbations

Infornitatin Science, Inc.

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0 -q

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to w C4 0 0 co CY 0 E

C/ 09/ILL 4'14la -01 L ~ eVWD

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0 L

(Rsd) d 'aJnssaid

19

506 I

Station 10RGR = 34.1 ft

0. A

..... Station 14

0 RGR = 49.2 ft

689 493

Station 11RGR = 37.5 ft

Station 15

RGR 53.0 ft0 0

572 i 471 A

0. I

! ' Station 12 '

i, RGRSta4t.on 16

Station 16

0 0 RGR = 56.8 ft

590 433Station 17

F M Station 13 RGR = 60.5 ft

RGR =45.5 fth=Oft

,a (Sta. 17)

CL h 1ft(Sta. 34)h = 5.5 ft(Sta. 39)

0 0

5.15 13.4 5.15 13.4

Time, At (ms/500 T1/ 3) Time. At (ms/500 T1/3

Fig. 11 - Calculated static pressure time histories at various stations on the ramp(to 19.2 ms/500 T 1 /3)

20

MLi I I ' -I I . . . I ' "' :

1967 j1479

Station 10 Station 14

RGR 34.1 ft RGR 49.2 ft

L0

1479 1276

Station 11 0Station 15

. RGR=4.RR 568ft 'RGR 530

Cr , I f t0 01-

1682 1128

Station 12 Station 16

RGR =41.7 ft RGR $6.8 it

o 0f

1726 1009Station 17 \iSi Statio n 13 G 60 S f

RGR = 45.5 ft

''h -- 0 fta'(Sta. 17) A

(Sta. 34)--- ------ h - 5.5 ft

(Sta. 39) 3"0 . . . ' - - 0 O f - --5.1S 13.4 5.15 13.4

Time, At (ms/500 T1/31 Time, At (ms/500 T1/3 )

Fig. 12 - Calculated dynamic pressure time histories at various stations onthe ramp (t o - 19.2 ms/500 T 1 /3 )

21

500-

(Reguiar relcA n

(re(macr reflection)

.15

00

00

30 10 0 0 0

22

REFERENCES

1. Carpenter, H. J., "Height-of-Burst Blast at High Over-pressure," 4th Int. Symposium on Military Applications

of Blast Simulation, (1974).

2. Keefer, J. and Reisler, R., U. S. Ballistic ResearchLaboratory, (private communication, 1979).

3. Brode, H. L., A Calculation of the Blast Wave from aSpherical Charge of TNT, Rand Report RM-1965 (1957).

4. Brode, H. L., Theoretical Description of the Blast andFireball for a Sea-Level Kiloton Explosion (U), RaudReport RM-2246-PR (1966).

5. Boris, J. P., Flux-Corrected Transport Algorithms forSolving Generalized Continuity Equations, NRL Report3237 (1976).

6. Kuhl, A. L., Seziew, M. R., Analysis of Ideal. Strong.Chapman-Jouguet Detonations, TRW Report 78.4735.9-13

(1978).

7. Ben-Dor, G., Glass, I. I., "Domains and Boundaries ofNon-stationary Oblique Shock-Wave Reflections: 1.Diatomic Gas," J. Fluid Mechanics, Vol. 92, Pt. 3,

pp. 459-496 (1979).

8. Dudziak, W. F., Infotuation Science, inc. (privatecommunication, May 9, 1981).

9. Book, D., Boris, J., Kuhl, A., Oran, E., Picone, M.,Zalesak, S., "Simulation of Complex Shock Reflectionsfrom Wedges in Inert and Reactive Gaseous Mixtures,"

Seventh Int. Conference on Numerical Methods in Fluid

Dynamics, Springer-Verlag (1981).

10. Carpenter, H. J., RDA (private communication, 1979).

23

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