NOLTR 64-40

THE FLOW FIELD BEHIND A SPHERICALDETONATION IN TNT USING THE LANDAU-

, STANYUKOVICH EQUATION OF STATE FOR

DETONATION PRODUCTS

10 DE$.OE_ 2 ',?•

UNITED STATES NAVAL ORDNANCE LABORATORY, WHITE OAK, MARYLANDo

T

DDC IRA C

, r-• , ,',-•". •,,

NOLTR 64-40

THE FLOW FIELD BEHIND A SPHERICAL DETONATION IN TNT USING THE LANDAU-STANYUKOVICH EQUATION OF STATE FOR DETONATION PRODUCTS

Prepared by:M. Lutzky

ABSTRACT: Calculatlons have been made of the flow field in the isentropicregion behind a detonation wave in TNT, using the Landau-Stanyukovichequation of state for the detonation products (as described by Zeldovichand Kompaneets). Adjustable constants in this equation have been evalu-ated by imposing ideal gas behavior on the detonation products in thelarge expansion (low density) limit, and by fitting to an experimentalcurve of detonation velocity versus loading density. Calculated valuesof Chapman-Jouguet variables correspond fairly well with experimentalvalues at various loading densities, with the exception of the tempera-tures, which seem to be far too low. This is cormected with the fact thatthe theory predicts an upper limit to the loading density at which anexplosive will detonate; at this point the thermal energy vanishes andonly the elastic energy contributes to the energy of detonation.

PUBLISHED FEBRUARY 1965

Air-Ground Explosions DivisionExplosions Research DepartmentU. S. NAVAL OPDNANCE LABORATORY

WHITE OAK, MARYLAND

i

NOLTR 64-40 10 December 1964

THE FLOW FIEU) BEHIND A SPHERICAL DETOMaTION IN TNT UESING THE LANDAU-STANYUKOVICH EQUATION OF STATE FOR DETONATION PRODUCTS

Calculations of the airshock motion produced by a spherical TNT explo-sion, with the reaction products considered to be gaseous, have givensatisfactory agreement with experimental results However, theexperimental motion of the explosive interface and the seccnd shockhave not agreed with the theoretical calculations. An attempt toclarify these discrepancies has led to consideration of the Landau-Stanyukovich solid state model for the reaction products of a condensedexplosive. The Landau-Stanyukovich equation of state has been utilizedto calculate the flow field in the reaction products behind theCbapman-Jouguet zone - the so-called Taylor Wave distribution - andthe results are presented in this report Preliminary determinationsof this distribution have already been used as initial conditions forthe calculation of the subsequent explosion motion, and have beenreported elsewhere.

Support for this investigation has been provided by the Defense AtomicSupport Agency under Nuclear Weapons Effects Research Subtask 01.002(NOL-428).

This report has been approved for open publication by the Departmentof Defense, Office of Assistant Secretary of Defense (Public Affairs).

R. E. ODENINGCaptain, USNColmnder

I. KA.BIBy direction

ii

NOLTR 64-40

SCONTENTS Pg S~Page

INTRODUCTION ........................................................ 1

THE LSZK EQUATION OF STATE .......................................... 2

ISENTROPIC PROCESSES ................................................ 4

CHAPMAN-JOUDUET CONDITIONS .......................................... 6

EVALUATION OF PARAMETERS ............................................ 9

FLOW FIELD BEHIND DETONATION SHKCK .................................. 11

CONCLUDING REMARKS .................................................. 13

ACKNOWLIEDGMENT ..................................................... 14

REFEREWCES .......................................................... 15

TABLES

Table Title

1 Comparison of Detonation Velocities Calculated for ISZKSubstance with Detonation Velocities Determined at Bruceton

2 Detonation Paraeeters Calculated with LSZK Equation of State,for TNT, Q a 1018 cal/gm

3 Experimental Values for Detonation Parameters of TNT(Dremin, et al)

4 Detonation Wave for TNT (p - 1.625 gm/cc)5 Detonation Wave for TNT (P - 1.59 gm/cc)6 Detonation Wave for TNT (p - 1.45 gm/cc)7 Detonation Wave for TNT (P - 1.30 gm/cc)8 Detonation Wave for TNT (a - 1.14 gm/cc)9 Detonation Wave for TNT (s - 1.00 gm/cc!

( iii

tr

NOLTR 64-0

INTRODUCTION

The theory of the detoration process for a Y-law gas, whosedeto'atior product is also a y-law gas, has been quite completelyworked out and is available i' many places.192 In particular, theconditions at the Chaprar'-Jougue+ state car be derived, and it canbe shown that the detoration velocity i3 a function only of the heatof detonation and the Y for the detonation products, for sufficientlylarge detonation pressLres. In addition, differential equations havebeen derived for the flow behind the detonation wave, and have beensolved for certain explosives and geometries, a9 3 94

The theory of the detonation of a solid explosive, on the otherharnd, is in a much less satisfactory state. Experiments' have shownthat the detonation velocity of a solid explosive depends on the initialdensity, unlike the detonation velocity of gaseous detonations. Further-more, the explosion products of condensed explosives are obtained atpressurea of the order of megabars, and ot densities approa:hing 2 grams/cm?, under which conditlons their behavior becomes extremeln complex.Consequently, various attempts have been made to find an equation ofstate for the explosion products by treating the highly compressedgas as a solid.

The first such attempt is due to H. Jones,7 who developed anequation of the Gr~ineisen type, based on the Einstein model of asolid, of the form p - Ae-av-B+fRT, where a, A, B and f are constants.The equation of state which we consider in this paper, however, wasderived by Landau and Stanyukovich,,i 9,ho also approached the problemby drawing an analogy between the s'*.ate of the detonation productsof a condensed explosive and the crystal lattice of the solid state.,It is well known that the energy of a solid body has a two-fold origin:it is made up of an elastic energy arising from the binding forcesbetween the atoms and molecules and a thermal energy connected withoscillations of the atoms or molecules about their positiona of stableequilibrium., Landau and Stanyukovich have attempted to describe thebehavior of the detonation product by considering it as a solid withthe property that the elastic energy and the elastic part of the pres-sure are predominant. The theory has been described and expanded byZeldovitch and Kompaneets, so that we refer to it as the LSZK theory.The purpose of this papei. is to make some computations using the LSZKequations of state, and, in particular, to calculate the flow fieldbehind the detonation shock in a condensed explosive.

1\

NOLTR 64-40

THE LSZK EQUATION OF STATE

For the sake of completeness, we present here a description ofthe LSZK equation of state, and a derivatio-, of some of its properties.

The LSZK equation of state may be written8

p.B + , T()vy V

E B + C T , (2)(Yl)vy-l

where P a pressureE 0 energy density (per unit mass)v n specific volumeT = temperature

and B, Cvy, OG •id y are constants. y is a dimensionless constantserving ms a polytropic index connected with the intermolecularforces; Cv is the specific heat at constant volume; Cv1 is a specificheat associated with the appropriate lattice vibrations; and B isa constant having the units a calnries The elastic

cm grampart of the pressure is B and B is the elastic part of

vy (y _)v• rthe energy.

Eliminating T between (1) and (2), we obtain the expresbion

p.E ÷B 1 l (3)

C rwhere M a 1I

or is a convenient variable which will be used in this report. Interms of o, (1) and (2) may be written:

B CTP=B +vC

P 7 v- Y- (5)

2

NOLmR 64-4o

E B + CT (6)(Y-l)v•y v

Another convenient parameter which we will find useful is thequantity y, defined as the ratio of the thermal part of the pressureto the elastic part:

(ClT/cev) .C vT y_ (7)Y B/ = aB

Clearly, (5) and (6) may now be written in Lhe form:

p L (l + y) (8)

VY

E +

NOLTR 64-40

iSENTROPIC PROCESSES

It is possible t, obtain an expression for the pressure of theform P - P (p), valid for isentropic processes of an LSZK substance,by combining equation (3) with

dE =- dp, (10)

which is the differential equation of ar isentropic process Dif-ferentiating (3), we obtain

dP -1 (pdE + Edo) +BYp •,-1i- -• -l d (11)

Using (10) to eliminate dE from (11), we obtain

lPdP -1(-Pd p +Ed p) + ypY11- 1 d (12)

Solving (3) for E and substituting into (12), we obtain the differentialequat:.on

d_ _ (1 + L () BY-1 ( 1-I) (13)dp a p

which has the solution:

1I+•

P )-K p-3 + By(14)

where K is a constant of integration., We are now in a position toobtain expressions for E, the sound speed c , the temperature T,etc. as functions of density alone, valid for isentropic processesof an LSZK substance.: Thus, putting (14) into (3), and solvingfor E, we obtain:

E(p) - AKr 1 BP ) Y-l (15)

4

NOLTR 64-4o

Similarly,

T - -K (16)Cv

and1

c" K(- -•)p + (17)

5

NOLTR 64-40

CHAPMAN-JOUGUET CONDITIONS

We now obtain the initial conditions at an LSZK detonation, interms of the variable y., We consider that the detonation wave consistsof a shock traveling at speed D, followed immediately by a region ofisentropic expansion. The region of chemical reaction behind theshock is considered to be infinitely thin., Values of the hydro-dynamic parameters in the undetonated explosive ahead of the shockare given a subscript o so that v. is the specific volume of theoriginal explosive. We first obtain v as a function of y, From

the Rankine-Hugoniot (R-H) relations at the shock, we have

_. D--q ;(18)

where u - particle velocityD - detcnation velocity.

Using the detonation property D - u + c (19)

equation (18) becomes

va -c- + 1. (20)v c

Another R-H relation yields

P - Du/Vo (21)

which my be written in the form

S(22)c c c

Using P-Boy (l + y) and the equation (20), (22) may be put into theform

Y-iBP (I + y(23)

v

6

NOLTR 64-40

ca may be obtained as a function of p and y by eliminating K between(14) and (17), and then using P a BpY (i + y) to eliminate P; theresult is

ca B - (Y + ', 1 (24)

Inserting (24) into (23) we obtain Y& as a function of y:V

+ ( + -- (25)v Y l+ +

The next step is to obtain vo itself as a function of y; this willenable us to solve for the parameter y as a function of the knownquantity vo.

We write the R-H equation for the energy in the form

1 1E + P (V0 - V)m + ýPv (,- -- 1) ,(26)

where Q is the chemical energy released by each grain of explosive;and using (25), this becomes:

EQ + Pv ( + y (27)

Eliminating P by using P - BpY (i + y) we obtain

E 1 + B (1+ y) 1 T7 (26)

Another expression for E/Q may be obtained from equation (9)

E*B c + 1(29)

7

NOLTR 64-40

Equating (28) and (29), and solv-.g for v, we oota'-:

y B (cry + + - (30)

Q '~'1,2(Y +

Eliminating v between (30) and (25), we obtain t'L expression:

1 1Vo ) I y + + + __ +o 1)

where

w-,- 'y (32)

Since vo , the specific volume of the solid explosive, is a knownquantity, we may solve (31) for y, by an iterative process. Sincev is a known fanction of y, by virtue of (30), we can find P byusing the expression B (1 4,y); Emay be found from (28) or

(29); and ce may be found from equation (24).

The particle velocity at the front, u, may be found from (20),and is given by

u " c(l + y) (33)Y + + '

Finally, the detonation velocity can be found from

D - u + c - c 1 + 1 + X (34)1+ ý

Thus, the detonation velocity is seen to be a function of vo, theinitial specific volune, corresponding to the well-known experimentalresult for solid explosives.

8

NOLTR 64-4o

EVALUATION OF PARAMETERS

The three undetermined parameterb, Y, c, and B/Q, which appear inthe LSZK equItion of state, must be evaluated by using experimental data.It can be seer, from equation: (14), which descrites the Isentropic P-prelation for an LSZK substance, that if 1).+ 0' < Y P (0 approaches

I + o 3

Kp a as p approaches zero. We assume that in the limit of low pres-

sures the detonation products behave as ideal gases, with a constantvalue of the specific heat ratio, denot.ed here by K. (A reasonable valuefor K seems to be 1.34. obtainable by averaging the gams for the variousgaseous constituents accrrding to the composition of the products at lowpressure.) It is thus clear that in order to obtain the correct behaviorof the detonaticn products at low pressures, we must set ca 1

K-i

The remaining constants may be evaluated by referring to the experi-mental results for the dependence of the detonation velocity on thedensity. After a particular value. is assigned for Y (v',-, a series ofvalues for B/Q may be obtained by carrying out a point by point comparisonof •he theoretical plot of in D vs. (lnpe + 1 in (obtainable from

equations (31) and (34)) with the experimental plot of ln D vs. In •.Since B/Q must be a constant, the accuracy of the fit is determined bythe amount of variation in the values of B/Q obtairnd, and Y may be adjustedto make this variation a minimum.

This process has been carried out for TNT, using an empirical relationbetween detonation velocity and loading density determined at theExplosives Research Laboratory, at Bruceton. 8 This relation may be writtenD - 0.1785 + 0.3225 P,, where D is in centimeters per microsecond and Ois in grams per cubic centimeter. Using K - 3..31, and with the heat ofdetonation chosen" to be 1018 cal/gm, the results are Y - 2.78, B/Q -

0.53562 and a - 2.9412.

Equations (31) and (34) may now be utilized to provide the dependenceof the detonation velocity on the loading density, by letting the parametery run through a rarge of values. Table 1 gives a comparison of thistheoretical curve with the empirical relationship, and it can be seen thatthe fi. is quite good.

It is interesting to note that this formalism predicts an upperdensity limit to the detonability, at thu loading density pe - 1.793 gm/ccand detonation velocity D a 0.757 cm/usec. This comes about because ofthe fact that at this point the value of the parameter y is zero (ydecreases with increasing loading density), and y cannot be negative,because of its physical meaning as a ratio of pressures (see equation (7)).

9

NOLTR 6•4-40

In fact, e-•iation (7) implies that at this limiting point, the onlycontribution to the pressure comes from the elastic part, while the thermlpressure vanishes. Zeidovich and Kompaneets have the following to sayabout the physical significance of this phenomenon: "It is possible tohave charge densities for which the thermal energy is much smaller thanthe elastic part. This corr"aponds to y being nearly zero ... It is notquite clear what happens when the charge density is large. It can beassumed that in this case the dissociation reaction does not go tocompletion, since the supply of chemical energy ib insufficient for over-coming the work required by the elastic repulsion forces between themolecules. It appears as though the chemical energy does not sufficefor the mcleculAr rearrangement which leads to an explosion." Thispre-diction is especially interesting inasmuch as it is known that TNTexhibits increa'ing resistance to detonation with increasing loadingdensity, as, in fact, do most solid explosives.

Nov that values for the ccnstants in the LSZK equation have be-enarrived at, t he conditions at the Chapman-Jouguet state may be computedby "ming the expressions developed in the preceding section. This hasbeen done for TNT at several loading densities and the results arepresented in Table 2. (The temperatures were calculated using Cv = 0.3

cal/gm-legree.) Table 3 presents experimental values for the C-J state,determined by Dremin, et al; ' the correspondence between calculatedvalues and experiment appears good, except for the temperatares, whichseem to be far below the generally accepted values for detonation tem-peratures of several thousand degrees.

The fact that the ratio of elastic pressure to total pressureincreases as the loading density increases may be verified in the lastcolumn of Table 2. For instance, for p - 1.625, this ratio is 0.974,which means that, for the isentrope given in equation (14), 97.4% of thepressure comes from the eltstic pressure term. For p - 1.00 gm/cc, thisratio is 0.805.

Conseq,,*ntly, in the vicinity of the Chapman-Jouguet state, the L5Z7Kisentrope my be approximated by a polytropic relation, with exponentequal to 2.78. In this connection, it is interesting to note the experi-mental results of Deal,s which indicate that the explosion productsisentrope for RDX-TWT may be fitted quite closely to a polytropic P-prelation, with '' o 2.77, at least down to 500 bars. It thua seems likely

that the ISZK equation of state for TNT not only yields the proper D vspe relationship, but also provides the proper isentrope, both in thevicinity of the Chapman-JougwL state and in the larg- expansion limitof low pressure and density.

10

NOLTR 64-40

FLOW FIELD BEHIND DETONATION SHOCK

The isentropic flow behind a detonation shock in a sphericalexplosive is governed by the differential equations :"

du ' 2 uc(d-: (36)

where u particle velocity

r radial distance of detonation shock from origin-rE"" , t = time

c sound speed

f - J. where p- density 1 (38)

Calculating f by means of (14), we obtain:1

K (10 +) + BY (Y 1)p1f W Ci a -i- (39)

K(I1)+ G' + Fe p

To utilize (39) in the system of differential equations (36), (37),it is necessary to express f as a function of cý. This may be done(in principle) by solvtng (17) for p in terms of c2, and substitutingthe result into (39). Unfortunately, it is not possible to invert(17) analytically, in closed form, so that an alternative approachmust be used. The procedure chosen here is to convert equations(36) and (37) into a set in whicb the dependent variables are uand p, rather than u and cý. In this case, we can use f in theform (39), as a function of p. To effect this change of variablewe make use of the equation

dci. dc1 A (40)d• dp dp

11

NOLTR 6'4-4o

Since c2 - dP/ddc in the isertropic flow, we may put dc2/dr - d&P/deand using (17) we get:

1 -dcld . K +I Of) C + BY (Y 1) Y 2 (41)

a0 a- 'I

Consequently, + + By (Y 1 )0 Y and the

differential equations become:

du 2 u (42)

2 ue -u) fC () (3

where c2 - K (-)p + BY , and f(p) is given by (39). These

equations are to be solved subject to the conditions u a uD) P a PDat P - D, where

D - detonaticn veiocity

uD =particle velocity at the detonation shock

SD =deneity at the detonation shock.

v, and DD may be found from (33) and (25), after y has been found fromequation (31).

These calculations have been carried out for TNT on an IBM-7090electronic computer, for the loading densities 1.625, 1.59, 1.45, 1.30,1.14, and 1.00 g1m/cc. The results are given in Tables 4-9. The firstcolumn 's a dimensionless dis~ance, the radius of the original chargebeing taket, as the unit. Pressures are in megabars, velocities in centi-meters per microsecond, energy densities in mwgabar-cc per gram anddensities in grams per cubic centimeter. It will be seen that the para-meters vary in the well-known way first demonstrated by Taylor, 3 with theregion of constant state surrounding the origin.

12

NOLTR 64-4o

CONCLUDING REMARKS

4 Up until now, very little has been said about the temperature. Toevaluate this quantity, we must know the value of Cv, which is notdetermined by the other constznts. (Only the ratio Cv/Cv, 13 determinedby equation (4).) If Cv is taken to be 0.3 cal/gm, aBr approximate averagevalue for detonation products, the C-J temperature (for g - 1.625 gm/cc)turns out to be 582.9"K, which seems to be too low. This is connectedwith the phenomenon of the decreasing importance of the thermal pressurewith increasing loading density, which was mentioned above. Though this

4 phenomenon is consistent with the known resistance to detonation of TNT athigh densities, and with the experimental results of Deal,s it is not yetcertain whether it is a real effect or whether it is a result of theincompleteness of the LSZK theory* In any case, it is believed thatin all applications where the temperature is not needed, and only an(E, p, v) equation of state is iequired (such as the calculation of thenon-reactive, isentropic expansion of detonation products by means ofhydrodynamic computer codes), the LSZK equation of state (in particular,equation (3)) my be used with confidence.

It is probably not possible to decide on the correctness of theLSZK equation of state by experimental observations of the detonationprocess alone. A possible approach is to use the results for the distri-bution behind the detonation as initial conditions for a hydrodynamiccode computation of the detonation of a sphere of TNT in air, using theLSZK equation of state for the expanding detonation products. The motionof the second shock through the product gases is expected to be asensitive function of the equation of state used, and one can attemptto compare the calculated results with the evidence obtained fromphotographic records. The behavior of the air shock, though a much lesssensitive function of the equation of state for explosion products,might also provide a useful check.

Preliminary hydrodynamic calculations have already been carried outon an IBM-7090 and are reported elsewhere; 10 more refined computationsare in progress at the present time.

* Jacobs'. has pointed ouT that a reiriter'pretat~or, of the partitionbetweer elastllc and thermal energy leads to a theory which does rotinvolve a limtAtrg density, or vanishW.ng thermal pressure, Thistheory retains the LSZK form for the equation of state, but doesnot make use o Zeldovich's argumeits for the physical mear.ing of.the cot stants CV, Cv., and Cv.

13

NOLTR 64-40

ACKNOWLEDlGMENT

The author grmtefully acknowledges fruitfu! and e: lightening dscus-slons with L. RtdLin, S. J. Jacobs, H. M. Sternberg, H. Hurwftz, andJ. W. Enig.

NOLTR 64-4O

FEFEFECIý3

1. Penner, S., S. and Mullin- , B. P., Expioeiors , Detonations,Flammbility and Ignition, Pergamon Press, 1959, Chapter 5

2. Landau, L. D. and Lifshitz, E. M., Fluid Mec-anics, PergamonPress, 1959 (Addison-Wesley Publishing Co., Inc.) Chapter 14

3. Taylor, G. I., The Dynfamics of the Combustion Products BehindPlane and Spherical Detonation Fronts in Explosives, Proc. Roy.Soc. A200, 1061, Pgs 235-247 (1950)

4. Lutzky, M., The Spherical Taylor Wave for the Gaseous Productsof Solid ExDplosives, NAVWEPS Report 6W48 (1961)

5. Deal, W. E., Measurement of the Peflected Shock Hugoniot and Isentropefor Explosion Reaction Products, Physics of Fluids, 1, 6) P. 523 (1958)

6. MacDougal•, D. P., Messerly, G. H., Hurwitz, M. D., et al, "The Rateof Detonation of Various Explosive Com.pounds and M-ixtures ," OSRD-5611.See also: Urizir, M. J., Jamsi Jr., E., Smith, L. C., Detonation

Velocity of Pressed TNT, Physics of Fluids, 4, 2, P. 262 (1961)

7. Jor.es, H. , 1-41. See C.cle, -.. H. , U. er-ate, xps-s ,(Prir.2etor. '-..iv-rs.'y Press, -1+c)

8. Laniau, L. D. and Stanyukov~ch, K. P. , On the S .'. of -e-cra. c-in Conder.sed Explosives, Dckialy .Jkad. Nauk 33SSR 46. 3Q (lm

9. Zeldovich, Iu.B. , ai.d Kcrnpar.!eta, -. S. , Tneory of letor.a icr.,Academic Press (1poO), Cnapter 14

10. Rudlin, L., On the Origin of 5hockwaves from Sljherical CondensedExplosions in Air, U. S., Naval Ordnance Laborato-y NOLTR b3-220,Part 3, Appendix B (to oe pulish1ed)

1l. Rudlin, L.., tn Approximate Solution of the Flow Within theReaction Zone Behind a Spherical Detonation Wvre in TNT, U.: S.Naval Ordnance Laboratory, NAVWEPS Report 73W, ,Ajril 1960

12. Dremin, A. N., Zaitsev, V. M., Ilyukh1n, V. S., Pokhil, P. •.,Detonation Parmmeters, Eighth Symposium (International) on Combustion,Williams and Wilkins Co., Baltimore, P. 610 (1962)

13. Jacobs, S. J., A New Interpretatlor. of the Zeldovich-Kcrnpar.eetsTreat,-e " of the Equation of State foe [etonation I'roducts, U. S.Naval Ordnance Laboratory Internal Memorar.dum, 5 June l-T

15

NOLTR 64-4o

Table 1

Comparison of Detonation Velocities Calculated forLSZK Substance with Detonation Velocities Determined at Bruceton

PD(-cm); ISZK Dcm );(Bruceton)ccuse c usec

1.7935 0.7572 0.7569

1. 662o 0.7146 0. 7145

1.5535 0.6795 o.6795

1.4412 o.6433 o.6433

1.3655 o.6189 0.6189

1.2995 0.597 0.5976

1.2412 0.5791 0.5788

1.1773 0.5588 0.5582

1.1320 0.55444 0.5436

1.1009 0.5345 0.5335

1.0034 0.5039 0. 50210. 9590 o. 4900 o. 48780.9256 o.4797 0. 4770

0.901o o.4720 0.4691

!1o. 8565 0.4584 o.4547

o.8o82 0.4437 0.4391

0.7703 0.4322 0.4269

0.7331 0.4211 0.4149

NOLTR 64-40

Table 2

Detonation Parameters Calculated withLSZK Equation of State, for TNT, Q a 1018 cal/gm

%(gm/cc) P(Kbars) E(*egaa"rcc) p(P) u_ cm) D( cm T(edegree) -icgram cc usec tuec Kelvin I~t{tal}

1.625 214.3 m.06022 2.217 0.188 0.703 582.9 o.974

1.59 203.5 0.05973 2.171 o.185 o.691 698.4 o.9681.45 163.8 0.0579 1.988 0.175 c.646 1141.7 0.941

1.30 127.6 0.05607 1.792 0.164 0.598 1582.5 0.905

1.14 95.4 0.05431 1.583 0.153 0.547 2013.3 0.857

1.00 72.2 0.05293 1.400 0.144 0.503 2356.7 O0.85_______________________________I

NOLTR 64-WO

Table 3

Experimntal Values for Detonation Parametersof TNT (Dremin, et al)

,|cm

P(kbears) u(C)D( sC)

1.59 202 0.183 o.694

1.45 162 0.172o.168 0.6501. 30 123 o. 158 .o0.156

1.30 123 0.165 0.5571.1• •"0.142

1.. 0130 0.510

_________________________________ ______________________ ___________________________ ________________________________________________ _____0____________1________________

OIA!R 604-4o

¶able 4

Dttonation Wave for T (fb " 1.6-5 gm/cc)

DISTANCE VELOCITY CEtSITY PRESSUI'L ENERGY DENSX/RADILS Civ/USEC GtV/CC MEGABMAS ftEG-CC)/GM

0. C. 1.29163E 0,- 4.91537E-52 2.63C-62E-C24.57265E-02 C. 1.291o3[ O0 4.91537E-02 2.63'•62F-C29.14531E-,12 C. 1.29163E 0. 4.91b37E-)2 2. 63.)62E-C21.37180E-GI C. I.29163E 0- 4.9 1 37E-C02 2.E3ý62F-C21.82936E-,CI C. 1.29163E 0C, 4.91I.37E-C2 2.63f'2F-022.28633E--0l C. 1.29163E 0,s 4.91537E-02 2.6,3C62E-C22.7435gE-01 C. 1.29163E O." 4.91537F-02 2. 6 32C.2E- D23.20086E-Cl C. 1.29163E 0,, 4.91537E-C2 2.63r621:--23.65812F-01 C. 1.29163E J0 4.91537E-32 2.63"'62E-C24.11539E-01 C. 1.29163E 0G 4.91537E-32 2.63-62E-C24. 57265E-O1 5.62295E-05 1.29163E JO 4.915J7E-)2 2.632 LZE-C24.8573CE-01 2.864C9E-03 I.30326E Ou 5.235R8E-02 2.66499E-C25.14195E-01 6 .72 5 65E-03 1.31989E OC' 5.21153E-02 2.71453E-C25.42659E-01 1.11811E-02 1.33975E 0Cv 5.42632E-02 2.77425r-c25.71124cE-01 1.60719E-02 1.36220E O0 5.67594E-C2 2.84252F-C25.99589E-0i 2.13167L-02 1.3869.E 0: 5.0 9595E-02 2.91858e-C26.28053E-01 2.68724E-02 1. 4 1367E 90 6.2759'1E-02 3.OC2C8E-C26.56518E-01 3.27201E-02 1.44242E 0- 6.62796E-92 3.C9299rg-c26.84983E-OI 3.88586E-02 1.47311E 06 7.C1775E-02 3.l'd52E-C27.13447E-01 4 .53,24E-02 1.50582E O0 7.448991-02 3.29814r-c27.41912E-01 5.20822C-02 1.!'40,7E O0' 7.92682E-02 3.41357F-C'27.70377E-'11 5.92466E-02 1.57788E 0j 6.4582HE-02 3.53P93E-C27.98841E-01 6.68685E-02 1.61777E * 9 .053--H-02 3.67566F-C28 .273')6E-01 7.50551E-02 1.6608!)E c,' 9 .7246'8E-C2 3.E261CE-C214.55771IE-1 8.39o76E-07 1.707b5E 0%, 1.0493?7-01 3.99349E-GZ8.84235E--I 9.38oC4E-02 1.75995C O .1,13896E-01 4.183CIE-C29.CO523L-!:1 1.O')119-O1 1.79278E Gu 1.19769E-o1 4.30454E-C29.15477E-31 1.06-375C-01 1.82544E OC 1.258l,3E-01 4.427C9F-C29.29105E-c'1 &.12b32[-Oj 1.85790[ O0 1.3205-C-01 4.55C45F-021.18417E-S1 1.1RF~OL-O0 1.89010E O- 1.38399E-O1 4.67442F-C29.52435E-1- 1.25 147E-01 1.922u'jE 0C'j 1.44880E-01 4.7SP77E-C29.62185E-ol 1.314C5E-01 1. 9 53)7E 0C, 1.51482E-01 4.92332E-C29.70701E-01 1.37662E-01 1.98476E 0C 1.58192E-01 5.C4786E-029.78C22E-01 1.43919E-01 2.01555E OC 1.6500JE-01 5.17220r-C29.84193E-01 1.50177L-01 2.04590E 00 1.71892E-01 5.2S615F-C29.89262E-01 1.564,34E-01 2.07578E Oj 1.78856E-01 5.41953F-029.93282E-OI 1.62691E-01 2.10517E Ou 1.8588oc-01 5 .54217F-029.96309E-01 1.68949E-01 2.13405E Ou i.92952E-01 5. 6392E-C29.98398E-01 1.752061-01 2.16240E OC 2.0006'E-O1 5.7E46iC-C29.99609E-Ol 1.81463E-01 2.19020E 0. 2.0719'IE-O1 5.9C411E-02I.CO0000E 00 1.87721tC-01 2.21743E 3u 2.14333[-G1 6.C222EF-C2

w)NTR 64-wo

¶Iabl~e S5

Detonation Wave for TNT (c• , 1.59 gm/cc)

DISTANCE VELCCITY EEMITY PRESSURE ENERGY CENS

X/RADILS CPI/WSEC GMw/(C MECABARS (MEr,-CC)/GM

0. C. 1.26271E C.- 4.67753E-C2 2.671C8E-C24.56064E-"2 C. 1.26271E 02- 4.67753E-02 2.671C8E-C2

9.12129E-,',2 C. 1.26271E 0>. 4.67753E-02 2.671C8E-C21.36819-')1 C. 1.26271E Gu 4.67753E-02 2.671C8E-C21.82426E-^I ,". 1.26271E OL 4.67753E-02 2.671C8E-022.28032E-01 C. 1.26271E 06 4.677:,3E-02 2.671C8E-C22.73639E-31 C. 1.26271E 06 4.67753E-02 2.671CRE-C23.19245E-C•I C. 1.26271E OL. 4.67753E-C' 2.071(8E-C23.64851E-C1 C. 1.26271E 03 4.67753E-02 2.71CPE-C24.10458E-01 C. 1.26271E 0.#, 4.67753E-02 2.671C8E-C2

4.56064E-CI 9.91348E-05 1.26271E OD 4.67753E-02 2.671C81-024.84596E-31 2.72!187E-03 1.27354E 01-i 4.78596E-02 2.7C294E-C25.13127E-CI 6.52P04E-03 1.2898)E Oý 4.95179E-02 2.75111E-02

5.41659E-01 1.09217E-02 1.33925E OJ 5.155".9E-02 2.FC933E-025.70191E-I I.57492E-02 1.3312RE 03 5.39162E-02 2.87595E-C2

5.98722E-01 2.09282E-02 1.35553E 00 5.66005E-02 2.95CIgE-02

6.27254E--I 2.64154E-02 1.38182E OC 5.96061E-02 3.C317IE-C26.55785E-CI 3.219146-02 1.41005E OC 6.29463E-02 3.12047F-026.84317E-^I 3.82 5461-02 1.44021E 00 6.66453E-02 3.21667E-C2

7.12848E-91 4.46192E-02 1.47235E OL' 7.07384E-02 3.32074E-027.4138CE-01 5.131511-02 1.50660E Ou 7.52742E-02 3.4334CE-C2

7.69912E-SI 5.83403L-C2 1.54317E OC 8.C3196E-02 3.55570E-027.98443E-Cl 6.59166E-02 1.58238E 00 8.59663E-02 3.68914E-02

8.26975E-1% 7.39999E-02 1.62471E 0. 9.2343SE-02 3.83587E-C2

8.55506E-01 8.27990t-02 1.67091[ 0C 9.96419E-02 3.S'912E-028.84038E-01 9.25653E-02 1.72213E 01: I.C8155E-O1 4.1839CE-C29.C0348E-C1 9.87363L-02 1.7543FE 0C I.1374(E-01 4.3C226E-G29.15325E-01 1.049G7C-01 1.7864iE Ou 1.19491E-01 4.4216CE-02

9.28974E-01 I.11''78E-01 1.8183.,E 06 1.25382E-01 4.554171E-02

9.41307E-01 1.17249E-01 1.84995E OC 1.314')8E-01 4.66241F-C29.5234AE-01 1.2342UE-01 1.88124E 03, 1.37559E-01 4.7el47E-C2

9.62112E-01 1.295i91E-01 1.9123)E 00 1.43825E-01 4.90471E-C29.70643E-C1l 1.35762E-01 1.9429.E O0 1.50195E-CL 5.02593F-C2

9.77978E-01 1.41933E-C1 1.97319E 06 1.56656E-01 5.14694E-C29.84161E-01 1.48104E-01 2.003U0E 0 1.63199E-01 5.26756E-C2

9.8924CE-0l 1.542751-01 2.03236E 00 1.69810E-01 5.30762E-C2

9.93269E-LI 1.60446E-01 2.06124E OC 1.76479E-01 5.5C696F-02

9.96301E-C'l 1.66617E-01 2.08961E 0& 1.83193E-C1 5. 6254CE-02

9.98395E--Ol 1.72789E-01 2.11746E Ou 1.89941E-01 5.74282E-02

9.99609E-Cl 1.78960E-01 2.1447TE 36 1.96712E-01 5.859C6E-02

,.OOOOE )G 1.85131E-01 2.17153E OCc 2.G3493E-O1 5.9740OE-C2

Dstamtlai m fcr 91! (lb 1-5 90/00fo)

DISTANCE VELOCITY CENSITY PR ESSURF~ [NFRI I r)Ews

X/RADI US, CM/USEC 10,M/C C KL'CABAS (I',EG-tCCI/GP'

0.0 I146blE !I, 3.R0136E-"2 2oS2422t.-rZ4*53543E-02 0. 1.146o1E 0O 3.80Ž136E- 'i2 2 . t24 2 2'-C- 29.G7081E-02 C. 1 *14&t) IE T"i 3,60136E-G2 2.82422!7-'%'-1.36063E-01 0. 1.14661[ OZ 3.80136F-C.2 2.82422r--r(?1*81411E-31 0. 1.l46colE Q~ 3.8(-,136E-C2 2. P,24 2 2F-t) 22*26?72E-OI. 0. 1.14661E OZ2 3.80136E-C2 2.92422E-,722.72126E-01 0. 1-14661C Ov 3.60136"5C2 2. -r~2E-~3.17480E-O1 0, 1.14661C ZD'- 3.AvCI36E-%'2 2.824i221$- .3.42835E-01 0. 1.14661E 0-" 3.PIi0136E-r,2 2.824229:-C.24.08189E-10 1.14661E OC 3.80136r-0~2 2.82422E-024.53543E-01 1.716L61-04 1.14661[ 0ý 3.0013(6C-C2 2.82422F-C24.82184E-01 2.46944E-03 1.15583E 02- 3.SfI149F--.^2 2.85394F-'-25.10825E-C1l 6.35588E-33 1.17077E Zj 4 .;w3~WC L.95F~5.39465E-:)l 1.021571-02 1.183871E Ou 4.17629E-/'-' 2.94732E-)25.6S106E--Dl 1.47906L-02 1*2,)966E 0,' 4.36576C-02 3.ýIMIPF-Cl5.96?47E-01 1.97303E-32 1.23149F 30- 4.580'94E-02 3..07513[-026,25387E-01 2.4901*tE-02 1.255bl[1Ot 4.8219CE-)2 3.14905E-026.54028E-01 3.03746L-32 1.28194E 03 5..38989E-02 3.22947F-026.82669E-01 3.6118DE-02 1.3,)98bE 6iC 5.38t,63:-02 3.31653F-C27*11309E-01 4.21442E-02 1.339b2E 22 5.714'ThE-0? 3.41CE.,3E-(,27.399SOE-O1 4.84C80L-32 1.37133E OC 6.C78'3E-02 3.51237P-C27.69590E-01 5.51725E-02 1.40519E OL. 6.4835i3F-iQ2 3.62?ERF-C?7.97231E-01 6.22664E-'2 1.44149E C"4 6.9364krv-L2 3.74287F-1128.25872E-01 6.99216L-02 19480o9E OC 7.4477701---2 3.8748BLE-029.54512E-Dl 7.82267E-02 1.52345F 00 8.032hi0E-C2 4.241rC8,83153E-01 8.74366E-02 1*51CdI3E 0'. 8.714 197E-0 2 ',.I1P7F~-'2B.99565E-01 9.32657E-02 1.6.)073E 300 9*1639J;E-0.2 4.293,2P-r-29*14641E-01 9.9994SE-O2 1.63048[ 0(- 9.62536[-032 4.40C)Q5."-3f9.28386E-01 1.04924E-31 1 o6b0(.,bE 00' 4.0'I- e5CF42F-C.?9,40811E-01 1.1'4753E-01 1.68941E 0J 1C83!EC 4.61642F-'29.51934E-01 1.16582E-01 1.7185OF OC, 1.1c477SC-01 4.7249IF-029*617S0E-0l 1.22411E-01 1.74728k 01" 1.15814E-01 4.R3350F-r29*70383E-01 1.Z824%'Oe-Gl1 .77574E Q.1.20937t-:71 4.942^4F-:29o7?78lE'-01 1.34369E-01 1.80383E OC 1.26136r--,i 5*5'34FC2c9984018E-01 1.39899E-01 1.831,2(. 0) 1.314'OE-O1 5.15?25F-C20,89142E-01 1.4572SE-01 1.85i879E Ot' 1.36721E-01 5.2&562F-C29,93207E-01 1.51557E-01 1.885b1E Oc 1.4?8w9L-,)l 5.37229r-"29*96267E-0l 1.57386k-Ol 14991197E 01, 1*47494E-.'f 5.4?PI 3F-L29,9S3R0E-01 1.63215E-01 I.93Tb4E O)u 1.529261-01 5.5P3ý'CF-C9.99605E-01 1.69044E-%'1 1.96321E 0'. 1.58377E-01 5.689679F-C*.21,OOOOOE 00 1.74873E-01 1.988,6E 0,j 1.63836r-fa 5.78936[-()2

NOLTR 64-40

Table 7

Detonation Wave for TNT (p 6 1.30 gm/cc)

DISTANCE VELOCITY CENSITY PRESSURL ENERGY UENS

X1RADIUS CMI/USEC GMw/CC MECAIBARS (MEG-CC)/GM

0. G. 1.02138E 00 2.990C 5E-02 2. 97234E-C2

4.53858E-02 0. 1.02138E 00 2.9901)5[-02 2.c;7234E-C29.07715E-02 0. 1.02138E 00 2.990j5E-02 2.97234F-021.36157E-01 0. 1.02138E 00 2.990:j5E-02 2.97234F-021.81543E-01 0. 1.02138E 00 2.990'5E-02 2.97234E-C22.26929E-01 0. 1.02138E 00 2.99005E-02 2.97234E-C22.72315E-01 0. 1.02138E 00 2.99005(-02 2.97234E-C23.177O0E-01 0. 1.02138E 00 2.990C5r-02 2.q7234E-C23.63086E-01 0. 1.02138E 00 2.99015F-02 2. 97234E-C24.08472E-01 0. 1.02138E 00 2.99005E-02 2.S7234[-024.53858E-01 4.92819[-05 1.02138F 00 2.99005E-02 2.97234F-C24.82401E-01 2.52551F-03 1.03098E 00 3.C6106E-02 2.999941-C25.10944E-01 5.93218E-03 1.04474E 00 3.164b6E-02 3.03970E-C25.39487E-01 9.86973E-03 1.06118E 00 3.29137E-02 3.08755F-025.68030E-01 1.41695[-02 1.07977E 00 3.43860E-02 3.142121-n25.96573E-01 1.87854E-02 1.10022E 00 3.60553E-02 3.2C276F-026.25116E-01 2.36693E-02 1.12239E OC 3.79229E-02 3.26914E-C2

6.53659E-01 2.88034[-02 1.14619E 00 3.99979L-02 3.34120F-026.82202E-01 3.41857E-02 1.17161E 0C 4.22921E-02 3.41905F-C27.10745E-01 3.98276E-02 1.19870E 00 4.48297E-02 3.5C3C2E-C2

7.39288E-01 4.57546L-02 1.22754E 00 4.76396E-92 3.59362E-027.67831E-01 5.20076E-02 1.25833E 00 5.07624E-02 3.69165E-C27.96374E-01 5.8648iE-02 1.29133E 0,0 5.42537E-02 3.79822F-028.24917E-01 6.57666E-02 1.32694E 00 5.81922E-02 3.91499F-028.53460E-01 7. '4985[-02 1.36576E O0 6.26922E-02 4.C4437E-C28.82003E-01 8.2056 9 L- 0 2 1.40873E 00 6.79313[-02 4.19C141-02

8.98544E-01 8.75274E-02 ,.43b13E 00 7.1414CE-02 4.2P4451-C29.13748E-01 9.29978E-02 1.46341E O0 7.49958E-02 4.37944E-02-).27617E-01 9.84683E-02 1.49053E 00 7.86718E-02 4.47496F-02

9.40161E-01 1.03939E-01 1.51746E Ou 8.24330E-02 4.57084E-C29.51395E-01 1.09409E-01 1.54416E 00 8.62759E-02 4.66693E-02

9.61344E-01 1.14880E-01 1.57059E 00 9.01929E-02 4.76306F-029.70040E-01 1.20350E-0l 1.59672E 00 9.4 176'E-02 4.85909F-C2

9.77520E-01 1.25821E-01 1.62251E O0 9-82206E-02 4.95486r-029.83828E-01 1.31291L-01 1.64795E 00 1.02317C-01 5.05024[-02

9.89012E-01 1.36762E-01 1.67301E 00 1.06457E-01 5.145C8F-02

9.93125E-01 1.42232E-01 1.69765E 00 i.10635E-01 5.23926E-029.96222E-O 1.47702E-01 1.72187E 00 1.14842E-01 5.332661-02

9.98361E-01 1.53173E-01 1.74565E 00 1.19072E-01 5.42515E-C29.99600E-01 1.58643E-01 1.76896E 00 1.23316[-01 5.51663E-C2

1.O0000E 00 1.64114E-01 1.79180E 00 1.27567E-01 5.6C700E-C2

NoIITP 64 -4o

Table 8

Detonation Wave for TNT (a a 1.14 gm/cc)

DISTANCE VELOCITY EENSITY PRESSURE ENERGY DENSX/RADIUS CM/USEC GM/CC MEGABARS (MEG-CC)/GM

0. 0. 8.88453E-01 2.26994E-02 3.11573E-024.52631E-02 0. 8.88453E-0l 2.26994E-02 3.11573E-02

9.C5262E-02 0. 8.88453E-01 2.26994E-C2 3.11573E-C21.35789E-01 0. 8.88453E-01 2.26994E-02 3.11573F-621.81052E-01 0. 8.88453E-01 2.26994E-02 3.11573F-022.26316E-01 0. 8.88453E-01 2.269941-C2 3.11573E-C22.71579E-01 0. 8.88453E-01 Z.26994F-02 3.11573E-023.16R42E-01 0. 8.88453E-01 2.26994E-02 3.11573E-C23.62105E-01 0. 8.88453E-01 2.26994E-02 3.11573E-C24.07368E-01 0. 8.88453E-01 2.26994E-C2 3.11573E-024.52631E-01 8.34041L-05 8.88453E-01 2.26994E-02 3.11573E-C24.95417E-0I 3.96314[-03 9.03023E-O 2.35974E-02 3.15776E-C25.38202E-01 9.32355E-03 9.24314E-01 2.4951,)E-02 3.21966E-025.80988E-01 1.54886E-02 9.49978E-01 2.664RSE-C2 3.29503E-C26.23774E-01 2.22482E-02 9.79245E-01 2.86750E-02 3.38200E-C26.66560E-O0 2.95268E-02 1.01182E OC 3. C453E-02 3.4P8008E-C27.C9345E-01 3.73264E-02 1.04769E Ou 3.3800IF-02 3.5P97CE-027.52131E-01 4.57134C-02 1.08713E 00 3.70077E-02 3.71218E-C27.94917E-O1 5.48296[-02 1.13074E 00 4.07783E-(,2 3. 84999E-028.37703E-01 6.49320E-02 1.17961E 00 4.52926E-02 4.0C747F-C28.80488E-01 7.64985E-02 1.23582E 00 5.08731t-02 4.1S2561-028.93143E-01 8.03235E-02 1.25408E 00 5.28096E-02 4.25463E-029.05047E-01 8.41484E-02 1.27290E 00 5.4789.-'E-02 4.317C2E-029.I6197E-0I 8.79733[-02 1.29136E 00 5.68u95E-02 4.37967F-029.26595E-01 9.17982E-02 1.30975E 00 5.P8694E-02 4.44253E-C29.36243E-01 9.56232E-02 1.32804E OC 6.09666F-02 4.5C553E-029.45147E-01 q.94481E-02 1.34622E 00 6.30992E-02 4.56862E-C29.53316E-O1 1.03273E-01 1.36429E OC 6.526b1E-02 4.63173r-C29.60760E-01 1.07098E-01 1.38222E 00 6.746211-02 4.694P2F-029.67491E-O1 1.10923E-01 1.40003E 00 6.96819L-02 4.75782F-C29.73526E-01 1.147'.8E-0I 1.41761E O, ?.119402E-02 4.82668E-029.78880E-01 1.18573E-01 1.435061 OC 7.42167E-02 4.88334E-029.83573E-01 1.22398E-01 1.45233E 00 7.65149E-02 4.94577E-029.87625E-01 1.26223E-01 1.46940E O0 7.88324[-02 5.00789E-029.91058E-OI 1.30047E-01 1.48627E 00 8.11668E-02 5.06968F-029.93896E-01 1.33872[-01 1.50292E 00 8.35156E-02 5.13107E-029.96161E-01 1.37697E-01 1.51936E 00 8.58764E-02 5.19203F-029.97879E-01 1.41522E-01 1.53557E 00 8.82467E-02 5.25252F-C29.99074E-01 1.45347E-01 1.55155E 00 9.06240E-02 5.31249rI-';29.99773E-01 1.49172E-01 1.56729E 00 9.30061E-02 5.37191E-C21.O0000E 00 1.52997E-01 1.58278E OC 9.53905E-02 5.43073E-C2

£IJ'.A -40

Table 9

Detonation Wave for TNT (p* 1.00 gMAC)

DISTANCE VELUCITY CEASNIfY PRCSSUIJVF ENERGY DENS

X/RADIUS CMIJSEC (;i/cc M LGAB AP (MES-CC)/GM

3. C. 7.72354:-'J 1.74753E-: 2 3.22656F-024.46409E-D2 1. 7.7235MF-I11 I.747:.1-C2 3.22656E-02

8.92817E-12 " 7.723:i6-)I 1.747:,E-'ý 3.22656E-021.33923E-'d C. 7.7 L3 ,"P5C-L-1 1.747sPE-32 3.22656E-021.78563E-CI J. ?.723'..-Li 747i-,"-C'2 3.22656E-022.23204E-31 0. 7.723,8E-Oi 1.7475PL-r2 3.22656E-022.67845E-'al L'. 7. 723:RE-ii 1. 7475P[--02 3. 22656E-0•2

3.12486E-31 3. 7.72392F-31 1.747)'8L-'32 3. 22656E-02S3.57127E-01 3o 7.723564- 1 2.74734B!- 0 2 3.22656E-02+. O768E-al "4.5 7.725?-5E -. )1 2. 9u747:AE- 02 3.22656E-02.49272E-11 1 . 2• R19 1 t-24 79. 73 V'3 -1 1.7475,-2 3. 22656E-02

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1.00000E 10 1.436819E-% 1 .43)12E ,OC 7.2247oL-02 5.29266F-02

ARMY

COP I ES

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UNCLASSIFIEDSecunty Classificanon

DOCUMENT CONTROL DATA - R&D(S~ectanry cI...tlrcatiori of tile bodý of , ra'nd $4 es a -. ' - " -4,.-r~#''tC ~ ''- . .

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U. S. NAVAL ORDNANCE LABORATORY UNCLASSIFIEDWHITE OAK, SILVER SPRING, MARYLAND N//A

3 REPOR" TITLE

THE FLOW FIELD BEHIND A SPHERICAL DETONATION IN TNT USING THELANDAU-STANYUKOVICd EQUATION OF STATE FOR DETONATION PRODUCTS

4 DESCRIPTIvE NOTES 'Tvp3 of rep<rt &r,dn tu .e dares

FinalS AUTHOR(S) (Last name first nra.e initi.al

Lutzky, Morton

6 REPORT DATE 7a ''ýA. NO OF PA&O; lb NC : QF"3

10 December 1964 27 138. CC%'RACT OR GRAN" 'NO 95 R.AOS 'c .~

SPOJCT NO Task NOL-428 NOLTR 64-4o

C 9bý 1-- Cq REP 0R Q ~ A' t'e- e -'a d~'.

d

10 AV•AILABILITY LIMITATION NOTICES

Released to DDC without restriction.

11 SUPPLEMENTARY NOTES '2 SPONSORING k" ., ARY AZ

Defense Atomic Support AgencyThe Pentagon, Washington, D.C.

13 ABSTRACT

Calculations have been made of the flow field in the isentropicregion behind a detonation wave in TNT, using the Landau-Stanyukovichequation of state for the detonation products (as described byZeldovich and Kompaneets). Adjustable constants in this equationhave been evaluated by imposing ideal gas behavior on the detonationproducts in the large expansion (low density) limit, and by fittingto an experimental curve of detonation velocity versus loadingdensity. Calculated values of Chapman-Jo'guet variables correspondfairly well with experimental values at various loading densities,with the exception of the temperatures, which seem to be far too low.This is connected with the fact that the theory predicts an upperlimit to the loading density at which an explosive will detonate; atthis point the thermal energy vanishes and orly the elastic energycontributes to the energy of detonation.

DD F 1473Set uritO (.'!,,;-,ifi ,, on

14 LINK A T LINK B LINK CAF OD OL. E ftT PiO E R. OLE 7-w T

Detonation ProductsHigh ExplosivesEquation of StateTaylor Wave

TNTI

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