ML17262A006
| ML17262A006 | |
| Person / Time | |
|---|---|
| Issue date: | 10/12/1976 |
| From: | Levine S Office of Nuclear Regulatory Research |
| To: | Rusche B Office of Nuclear Reactor Regulation |
| References | |
| RIL-0006 | |
| Download: ML17262A006 (11) | |
Text
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- J OCT 1 2 1976 lllMC1lllDOM Pm.: awn c.._..,,.., M.ncter Office of Jlacl.ear l*ctor._.iau.a Int:
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_t.rt.e, Ac.tiag tireccor Office of hclear hgilitory ~
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ftI 6: MAl'T UPO!tT: *.& CB.ITIQU'E 01 ml.aAll>-BALL
.:>DEL POR. THERMAL Dn'OliTIOllS DI TD W2-BA SYSTEM" hference: J!laaorandua of.b&Ut 19, 1'76 frca C. ** ltalber to I.. bbeu td.a entitled "'Plll'4ue ~
l'CKm!a t.1.ou l'ropoaal for CoutilluatiOD of the Work Iaitiated Under Contract lio. A.!(49-24)-018."
Enclosed for your f.nforaation 1* a U'aft copy of the ea.bject report prepared aa part of the af fort of die Off ice of 5uclear hgulatory l.e.searcb to detera.ine research Deed* in nu area. The autbor l*
l>r. David C. VilU.aaa of Sandia Laboratori.., and the pAper will M presented at the ANS-ENS "International Meeting of Faat l.eactor Safety and I.elated Physic*" at Chicago b October. This evalution 1.a relnant to the DPM-aupported experiment* at Pardue tJ-niver*ity on the *alidity of the Board-Ball aodel, and 1* the 'IES generated naluation of this aode.1 referred to in the reference ae.ora.zwha
- The Williams report eoncludea that the Board-Hall 90del for propagation of
- detonation-like thermal explosion in
- postulated. pre-mixed uo2 sodium 11yatm b not Talid for LMFBR accident conditions becaue of the very high magnitude of the shock pressure required for triggering, because of deficiencies ln the fragmentation 1a0del, and ~auae of Deglect of the dispersive characteristics of the pre-w.ixed uo2-sodium aystem.
The report d~ say, however, that the possibility of the occurrence and propagation of a detonation-like thermal explosion in a pre-tixed UO -a<>dium system by some mechanism other than the Board-Rall fragmenlation 9odel cannot at present be rule.d out completely.
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'MtJRLEY 10/6/76 us NORRY 10/ /76 RES LEVINE 10/ /76
I A CRITIQUE OF THE BOARD*BALL RODEL POR DETORATXHG THERMAL EXPLOSXONS AS.APPLXED TO 002-8a SYSTEMS
- David c. Williams Sandia Laboratories Albuquerque, Mew Mexico 87115 ABSTRACT The Board-Hall *odel for detonating thermal explosions is reviewed and
- ome criticisms are offered in terms of its application to 002-Na systems.
The basic concept of a detonation-like thermal explosion is probably valid provided certain fundamental conditions can be met1 however, Board and Ball's arguments as to just how these conditions can be met in 00 2-:a mixtures appear to contain aerious.flaws.
Even as given, the model itself predicts that a very large triggering event is needed to initiate the pro-cess.
More importantly, the model for shock-induced fragmentation greatly overestimates the tendency for auch fragmentation to occur.
~he shock-dispersive. effects of mixtures are ignored.
Altogether, the model's deficiencies iaply that, as given, it is not applicable to L~FBR accident analysis1 nonetheless, one can not completely rule out the possibility of meeting the fundamental conditions for detonati~n by other aechanisms.
UITRODOCTION Xn 1974, the British workers S.J. Board and R.W. Ball(l]proposed a model for the propagation of vapor explosions which was based upon a close analogy with chemi-
. cal detonations.
Since the *odel predicts that, under certain conditions,very powerful explosions can occur in molten oo.-Na mlxtures, it is of obvious interest to the LMFBR safety community.
Xn this paper, we review the model and its theoretical foundation, and then offer acme criticisms which suggest that Board and Hall may
-~------have overestimated the possibility that such ~xplosions could occur in LM?BR acci-dent situations.
We conclude with some additional discussion, including some cautionary remarks against over-interpreting the results offered.here.
SUMMARY
OF THE MODEL Since the Board-Hall aodel ls based upon shock and detonation physics, we briefly review this topic, omitting many refinements and qualifications that are required when dealing with solid materials (2).
~o~sider a severe stress wave propagating through a *edlum for which the sound speed c tends to increase as the material is compressed( aost materials satisfy this condition.
~he -high-pressure portion of the wave then tends to overtake J
- 1
I t
the leading edge, ao that the compression phase of the wave *teepena nto a near-diacont~nuous jump in the pressure called a shock.
By applyin~ the equations of aass, aomentum, and ener9y conservation, it aay be *hovn that the aaterial JJro~
pert~es be~ore and after *hock paasage aust be related by the well~knovn aankine-Bugoniot jW11p relations:
0 -vl ICP2 -
P 1 1/CV1
- V2)]\\
(la) u - [(P2 E -El+
2
.. P1 J Cv1.... v 2 )] \\
~(P2 +Pl) (Vl -
V2)
(lb)
(le)
Bere u, u, E, V and P are the *hock propagation velocity, the *hock~induced saterial velocity, *pecific energy) specific volume, and pressure, respectively1 subscripts l and 2 refer to conditions before and after ahockpassage, respectively.
Xn addition, the material must obey its own equations of *~ate; P
- P (E,V)
For a given set of initial conditio~s, ve have four equations Ln five unknowns (o, u, P2, V2, E2)*
Specifying any one of the latter in effect *pecifies the other four.
Xn,Particular, for any two of the quantities (Qi and Q., *ay), a plot of the states which may be obtained (from given initial conditions) by shocks of various strengths lies along a curve in the Qi -
QJ plane called the Bugoniot.
For many fully-dense (non-porous) materials, it has been found experimentally that the u-u Hugoniot approximately follows an especially simple form, tJ
- c 0 + *u, (2a)
- where s is an empirical, non-dimensional constant which usually lies between 1 and 21 we have also assumed that the initial *tate is the uncompressed reference state.
By combining Equation (2a) with Equations -(la) and (lb), it aay be shown that the P -
V Bugoniot will then be of the form 2
2 2
P.. c ~Iv u -
- El l
- E. El u - * £>
0 0
0 (2b) where the subscript o refers to the uncompressed reference state,E is in the volu-aetric strain (1 -
V/V ) and ~ is the bulk modulus.
Xt is *lso worth noting that the difference bEtveen°the Bugoniots and isentropes varies as E', and is therefore slight £or small£' in some of what follows, this difference~. ignored.
The detonation of chemical hi9h explosives!& aore complicated.
Xt involves the following sequence of events1 (1), The detonation subjects the unreacted explosive to a severe shock.
- .(2)
As a result, the explosive undergoes ene-r9etic decoaposition on a time scale,t, so short that the reaction zone thickness Ot is < 1 JDJD. 1 often
<< l llllDe (3)
The hot reaction gases expand with a substantial conversion of heat energy to work, which supplies further energy to continue driving the detonation wave.
-- --* \\.*
~igure 1 Scbeaatic P~V Diagram For a Detonating Explosive
- . ~
-~
~
<:t d'
f\\'11
... I '
t:_j
(~J) -~j)
R~.>' ~i7~
P,,"1 Sfe;.c.iffi'c. Volvme.. ~
The system is diagramed in terms of the P-V Bu9oniots in Fig. 1.
The lower curve represents the Hugoniot for the unreacted explosive initially in the state (P1,V1).
The upper curve represents theBugoniot for the high-temperature, gaseous reaction products.
It can be shown that the detonation vave vill propagate steadily, without attenuation or growth in amplitude, if and only if the line connecting the initial state with the state existing at the completion of the reaction is tangent to the reaction product Hugoniot.
The point of tangency, (PcJ*VcJ), gives the con-ditions at the end of the reaction and is called the Chapman -
Jouget point or C.J.
point, and is a characteristic constant for a given explosive at a given (P 1,V1).
From Eq. (3.la), the alope of the linf' connecting (P1,V1 ) and the C.J. point, called the Rayleigh line, is equal to o 2/v2.
Since the s~ock initially propagates
_____ through unreacted explosive, the initial pleasure must be given by the intersection of this line with the corresponding Bu9oniot at P 2v 2
- This still higher *pressure, PVN, is called the Von Neuman spiker it is eo narrow, however, that it attenuates
- very rapidly in a non-explosive aaterial and the CJ pressure is normally the quan-tity of interest.
The basis of the Board-Ball model was its authors' observation that thermal explosions can proceed vith an ~ssentially identical structure if the following three fundamental assumptions are valid:
.. A.
The ~iquid -
liquid system is initially in the form of a mixture that is too coarse to permit significant heat transfer on a time scale comparable to the time required for the detonation vave to traverse the eystem.
B.
A 11trong triggering shock is supplied.
- c.
~ shock having the CJ amplitude vill fragment the coarse initial mixfljre into a much finer mixture permitting extremely rapid heat transfer, with the total time required for fragmentation and thermal equilibration being much less than that required for the detonation wave to traverse the system.
Given these three assumptions, Board and Ball show that the explosion can pro-pagate with a structure identical to that of the chemical explosion, with the zone of rapid fragmentation and heat transfer corresponding to the reaction zone for the chemical case.
They also show that such a detonation can actually generate 3-
~reaauresconsiderably bi9her,-and work* potentials eoaevhat higher, 1:ban those cal-culated by Hicks and Menzies.
The reason is that, here, the aixture is first com-pressed by tne snock and heat is then transferred to the.olatile component at above normal densities; Ricks and Menzies assumed beat would be transferred at a constant *olume corresponding to the normal density thereby leading to PaM in Fig.
The author knovs of no ~law in the basic argument, but it is auch aore 4ebat-able as to whether the aodel's three fundamental assumptions are valid in practice.
The third assumption is -the crucial one in terms of the aodel'* internal structure1 tbe first tvo are actually assumptions about*tbe presumed initial conditions:
Board and Ball argue that this third assumption will be aet by noting that,
~ecauae of the large U0 2 -Na density difference. the shock will accelerate the tvo phases to quite different velocities, and the resulting velocity differential v will tend to induce U02 fragmentation due to Taylor instabilities.
Drawing an analogy with the data Simpkins an-d Bales t3J obtained for shock-induced breakup of 1iquid droplets in gases, they concluded that the time t required for fragmentation of a D02 drop of radius r1 is given by
- l.
(la) where P and p' are the Ha and uo 2 densities and the Bond number, B, is defined by 0
(lb) where 9 is the acceleration imparted by drag forces, a the surface tension,and c the drag coefficient.
It is then assumed that the drop fragments down to a fina1°
- ize rz governed by A Weber-type criterion, pv 2 r 2 g/a~ Bi r 2 turns out to be so small (microns or less) that heat transfer is essentially instantaneous compared vith the time required for fragmentation.
On the other hand, Board and Ball indicate that the relative velocities of the tvo fluids should tend to equilibrate during a characteristic time -t! given by (4)
I This estimate was evidently obtained simply bJ taking t
- v/g, where the accelera-tion, 9, is given by the drag force, F0 *
~pv CqA divide~ by the droplet mass,
~irp' r:/3, and A is the cross *ectional area 'Wr1 Based upon the resuI:t~. f_or ;_i:9l;J-ido
____ droplets, the drag coefficient, c0, vas taken to be about 2.
Boar~ land Ball the~ *
- argue that the third fundamental assumption will 1 be satisfied if t is greater than the fragmentation time, t.
Board and Hall consider the case of U02 at 3550 K, Na at 700 ~. a UOz/Na ratio of 10 by weight, and a 50' void (vapor) fraction by volume.
They find that the fragmentation criterion is indeed met, and calculate U
- 1.9 z 10 5 cm/sec, P
- 15 kbar, and.u
- 2.3 x 10~ cm/sec at the C.J. point1 if vapor is absent, they state that P is approximately doubled.
The authors also note that the reaction zone thickness, Xr
- Ut, is very much
- greater than for chemical explosives, of the order of 10 cm or more if r 1 s O.S cm, as they assumed. The model is one-dimensional and cannot apply unless the. dimensions ft-I. '
)
of the syst~m, L8, are auch greater than Ir* Thu*, the pheno*enon 1* predicted to be possible in full-scale LMFBR accidents but not in auch **aller*acale ~perimenta.
Xn part~cular, no auch explosions would be expected in any 002 -Na experiaents per-
~oraed to date, both because of their relatively **all scale and also because of the absence of a *trong trigger.
Thus, the fact that alaost all of these experi-wents yielded benign responses is not very relevant ~o the question of whether the aodel i* valid.
Xndeed, these £acts point to e ainqularly *exatious aspect of the Board-Ball aodel from the point of view of LMFBR safety analysis: the aodel predicts that extremely powerful explosions are possible in full-scale LMFBR accidents yet the aodel also predicts that it will be virtually impossible to 9ive the model any rigorous experimental test in an actual 00 2-Ha experiment of reasonable size.
Before attempting an experimental.test, it i* therefore worthwhile to review aome features of the model a little aore carefully.
SOME CRITICISMS OF THE MODEL Initiatinq Event.
It is instructive to estimate the aaqnitude of the trig-9ering event required to initiate the Board-Hall process.
Initiation requires a shock *above some minimum value Pm of duration at least t.
The magnitude of Pmis set by the need to meet* the fragmentation criterion.
By inserting numerical values for D02 and Na material properties (4] into Equations (3) and (4), we obtain
... 710 ***
1~*
12
, *'.. 13.l *~
(5)
For shocks below some limiting amplitude,*v will be low enough so that the frag-aentation criterion, t < t' 1 will not be met1 if r 1
- 0.5 ca, for example, Equa-tion (S) implies v > 4000 cm/sec is required.
~o estimate P, we assume v ~ u and assume that, ror Ha and UOz, the Buqoniot can be expressed b~ Eq (2) with s
- 1.27 and 1.5, respectively (results that fol-low are insensitive to s).
For the composite, we assume the P -
c curve can be constructed by evaluating £ individually for the two constituents at a given P &nd takinq & volume-weighted averaqe.
For the important case where void space (i.e.,
vapor or gas) is present, we let V0 represent the mean specific volume of the aixture without void space and represent the specific volume icluding voids as Vi
- av0 r thus *a
- 1 and a
- 2 correspond to no voids and SO' void fraction respectively.
We assume any reasonable final pressure completely collapses the voids and that the final volume v 1 is independent of a.
There are several approximations involved here, but refining them would not affect the basic conclu-sions to be given.
A computer code based upon these assumptions was written to estimate the value of P sufficient to give a velocity u, as calcula~ed from Equati~n (lb), to meet the 'rragmentation condition.
Equations (la) and (le) were then used to estimate the corresponding values of U and,E.
Since the initi~ting pressure must be applied for at least a time t, the initiation zone must be of
- thickness Xr
- Dt.
Xf.the initiation region must be an order of maqnitude greater in lateral extent than the thickness in order to preserve one-dimensionality, the volume of the initi-ation re~ion is of the order_lOO Xr 8 and the total enerqy Etot imparted to it is
-100 Xr E/(aV0 ).
The latter may be an over~estimate it the lateral extent of the initiation region need not be as great as assumedJ on the other hand~ we have only attempted to estimate the enerqy imparted to the.initiation region by virtue of its being subjected to the triqqerinq.ahock.
The total energy available to the triggering event itself must be considerably larger *
- ~-*
- e
- esults are summarized in Table I, where 1m* Xr, and Etot are given for
- arious v~lues of a and r1.
For r1
- o.s and a* 1, the *triqger* needed is extremely aassive, hardly less destructive than the fully-developed reactor-vide explosion, The aore realistic cases with a > 1 have lesser tri9gerin9 requirements but they are still very large.
If r1
- 0,05, total trigger energy needed is considerably less, but still substantial and~ is actually increased "Considerably, TABLE I Magnitude of the Initiating Event Required for Various Parameter Values r,.. 0.5 CD\\
r, - 0.05 cm x
(cm) p (bar.a)
Etot (J) x (cm)
- p. (bars)
Etot (J) a r
m r
1.0 180 3 x io*
J*x 10 1 7
io'
- l. s x lo' 1.11 60 700 e x 10 7 4
5 x io*
3 lit io 5 1.5 18 200 2 x 10 1 1.7 2 x io*
l.9 Jt 10'
..... 0 13 BO 4 x io 5 1.3 800 4 x *10 9
.~bus, even when taken at face value, the model itself 0predicts that the initial conditions required involve a combination of a rather idealized mix-ture and a strong initiating event that seems unlikely to be realized in practice.
D02 /Na Mass Ratio*
Even aore serious to the model, Equations (3) and (4) would at best be valid for an isolated drop of uo 2 in an infinite sea of sodium, yet they were applied to a situation vith a D0 2 /Na mass ratio ~f about 10.
The interfluid drag force applies equally to each component, and the acceleration of the sodium is therefore about ten times that of the 002.
Both velocity changes are, of course,
.in the direction to decrease v, so that the rate of velocity equilibration was
- eriously underestimated, and t'is correspondingly overestimated by Equation (4).
We estimate the importance of this effect by assuming the interfluid drag
~orce per unit volume, FD, for a mixture of two flu.ids, *,and b, to be where A is the perpendicular fluid-fluid interfacial area per unit volume, and
~ is the average density faPa + fbPb* where the f's and P's are the volume fractions and densities of the two fluids, respectively, for the moment, we iet Equation (6) be the effective 4efinition of CD*
The relative velocity decays at a rate given by be the volwne fraction of the less abundant fluid (i.e., fm
- rf we let f}m form of spherical drops of radius r1 Min lfa,fb) and assume this is ~n the 0 i it h as independently made points
- s. George Bankoff, of Northwestern n vers y, similar to those to be discussed here.
-.(-
(6)
(7)
- 1
i 1---
- ,,.. a
'1\\. *
- dispersed in the *ore-abundant flui4. A
- The reviaed value of the characteriatic equilibration time. t*. becomes (8)
(9)
J:f one fluid overvhelmin9ly predominates, Equatio"n (9) is easily shown to reduce to the same as Equation (4)1 hence the value of CD defined by Equation (6) reduces to the value appropriate for an isolat~d spherical drop of either fluid aovin9 in a sea of the other fluid, as it should1 of course, c0 aay also depend upon the aixin9 ratio for intermediate cases as well as upon the other usual parameters.
Xnsertin9 numerical values for the caae of interest.with fa* fb
- O.S ~ives ta: v/(dv/dt)
- 0.45 r /(vc0 >
- 1 (10)
-which implies tn<< t 1 as given by Equation (S) unless c0 << 1.
As a cross check, we may estimate t" by appro..xi_mat1n9 t:he flow of *odium relative to UOz as a flow throu9h a packed bed.
Startin9 with a correlation due to Er9un [5] for the resistance to such a flow, and omitting terms that are
- all in the present case, we obtain
~= v/(dv/~tl
- 0.57 r*/v (11)
.1 which is very close to (10) with c0 = 1.
~hough we are applyin9 Er9un's relation to values of v considerably hi9her th*n those for which it was established, this result au99ests our estimate for t# is of the right order of aagni:::~~atin9 t!' from Equation (10) vi th c0
- 1 and still evaluatin9 t from Equation (3) shows that, with a shock amplitude of 30 kbar, t! /t ranges from about o.os to 0.16 for all cases considered in ~able x.
That is, even for an initiatin9 shock with an amplitude equal to that of the fully-developed Board-Ball detonation, the fra9mentation criterion fails to met by about one order of magnitude.
Furthermore, if a still more powerful shock is applied, detona-tion theory itself tells us it will die down to the CJ amplitude even if fra9mentation does occur.
Hence, there appears to be no vay that a detonation-
--iike explosion can propagate in just the way *p.ro,Posed by Bo.ard and Ball unless t is also an order of magnitude or more shorter than those workers proposed.
~his is possible, but it is worth notin9 that eLther Equation (10) or (11) implies that the relative velocity will decay to less than 10\\ of its initial value before the total relative motion reaches the order of the mixture scale,
-2r1.
Since fragmentation implies liquid-liquid interpenetration, which presumably requires liquid relati~e motio~ at least of the order of the mixture scale, it is legitimate to raise the question as to whether the shock-induced velocity differential can cause complete fragmentation by any mech~nism.
As the Ha/UOz ratio increases toward infinity,. t' i as given.by -Equation (9) r increases toward t"' as given by Equation (3), but t*he amplitude* of the detonation wave decreases.
Xt seems very questionable as to whether one could find any mixture ratio such that, for a shock of the CJ amplitude, the necessary condition t" > t would be satisfied, however~ this question-has not been investi9ated in any det11iil
- 1
- c--*
~,.
/*
- .,l;l,.....
r
'l'hroughout this di;\\:-ion, ve b*ve aaauaed that th:-.evant shock amplitudes
~or, evalur. tipg fragmentatic;l should be PcJ, not the higher,{,.~ tue PvN.
- Actually,
- PvN is *not inearly high enou~ ** to reverse our conclusions.
h'ere fundamentally, the Von-WeuMann spike would be narrow compared with the fragmentation zone and the pressure wave causing fragmentation will have to be of at least the width
~f the latter.
Shock-Dispersive characteristics Board and Ball did not take into account the *hock-dispersive characteristics of composites.
Speaking roughly, a sharply~defined pres*ure wave undergoes aultiple, partial reflections at the interfaces between the two constituents.
'l'he wave profile therefore spreads and becomes rounded; it.also attenuates unless backed by a *ustained driving pressure.
~hese effects become very important when there is a large acoustic impedance mismatch between the two constituents, as is the case for 002-Na mixtures.
L. M. Barker (6] has analyzed composite response to *tress waves.
Be ahowed that composites, to a good approximation, could be modeled as a stress-relaxing aaterial.
Details cannot be given here, but the key point is that auch materials cannot aupport a steadily-propagating, *harply defined shock at all unless the amplitude exceeds a certain"blinimum value; lesser-amplitude steady waves must have a roundea profile.
Above the minimum value, part (but not all) of the pressure rise may appear as a near-discontinuous jump or shock.
'The author applied Barker's model to 00 2-Na mixtures, using simple stress-
- train relationships based upon Equation (2), *and it was found that the minimum value of the pressure permitting partial shock formation probably lies between 25 and SO kbars.
This is at least as high as the CJ pressure suggested by Board and Ball, and it is therefore questionable as to whether even the fully-developed detonation could propagate as a sharply defined shock.
Failure to achieve a sharp shock would reduce still further the driving force for fragmentation, which already appeared to be inadequate.
It would also require careful re-examination of the entire analogy vith chemical detonations.
The analysis just summarized would apply directly only vhen there is little or no void space.
With a substantial v~id fraction, the situation is more compli-cated and a relatively sharp pressure front cannot be ruled out, though it is not clear bow it can be much more sharply defined than the mixture scale.
In any case, *hock-dispersive effects are still expected and they must be considered.
If nothing else, they probably rule cut formation of a
~learly-de~ined Von Neumann
- pike, supporting still further the use cf the CJ pressure in the fragmentation analysis as vas done here.
SUMMARY
AND CONCLUSIONS If the criticisms offered here are valid, the Board-Ball aodel, in its present form, cannot be treated as a significant factor in LMFBR safety analysis.
When the Board-~all approach is refined along the lines indicated, the third of the three fundamental conditions for detonation-like behavior (shock-induced fragmen-tation) fails to be satisfied by rather wide margins, and the effects of shbck-dispersiveness and the need for very large trigg~rinq events cast further doubt upon the model's practical utility in safety analysis even if the idealized mix-ture considered could be achieved in practice, which is itself questionable.
On the other hand, this rather negative conclusion should not be over-inter-preted *. The present work was basically limited to refining certain aspects of the original study and showing that, with these refinements, some of the condi-tions required for internal self-consistency may no longer be satisfied. It is conceivable that quite different mechanisms could cause the rapid fragmentation required to generate detonation-like behavior.
Since fragmentation is a purely mechanical effect in the Board-Hall approach, there is no need to study it with hot-cold liquid pairs.
'l'hus. it could prove
~'.
1il
~
~
aseful ~o perform experiments subjecting mixtures of hi9hly dissimilar liquids (e.9., *ereury and water) to strong shocks, either with or without vapor pre-
- ent.
Care mu~t be taken to ensure that such experiments are consistent with the aodel's requirements.
Por example, the input pressure pulse *ust be relatively long in duration, not only because the Board-Ball aeehanism requires aueh pulses, but also because short pulses could induce Lragmentation by aeeha-nisms that would not b~ present in the lon9-dur&tion pulses of interest here.
%f fragmentation is observed, it would then be necessary to establish that it
- as a prompt effect rather than a delayed effect.
Finally, even if the Board-Ball approach could be shown to be totally in-T&lid, this would not necessarily mean that the possiblility of large-scale, coherent interactions between molten 00 2 and Ha can be laid to rest.
There is considerable experimental evidence (7] that both triggering and sealing effects are indeed important in vapor explosions, whatever the underlying reason.
Dnless major advances in the theoretical understanding of vapor explosions are made in the near future, it may eventually be desirable to conduct large-
- eale 002-Ha experiments with strong triggering pulses provided.
ACJl::NOWLEDGEMENT
~his work vas supported by the Ruclear Regulatory Commission.
REFERENCES l) s. J. Board and R. w. Ball, *propagation of Thermal Explosions -
Part 2:
A Theoretical Model,* Central E~ectricity Generating Board Report No.
RD(&/H3249 (December 1974).
- 2)
For more details see, for example, G. E. Duvall and E. R. Fowles, *shock Waves,* Chapter 9 in High Pressure Physics and Chemistry, R. S. Bradley, ed., Academic Press, N.Y. (1963).
- 3)
P. G. Simpkins and E. i. Bales, *water-drop Response to Sudden Accelera-tions,* J. Fluid Mech., 22.* p. 629-639 (1972).
~)
M. G. Chasanov, L. Leibowitz, and s. D. Gabelnick, *High Temperature Physical Properties of Fast Reactor Materials" J. Nuclear Materials, _!!,
- p. 129-135 (1973/1974).
- 5)
W. M. Rohsenow and H. Y. Choi, Heat, Mass, and Momentum ~ransfer, Prentice-Hall, Inc. (Englewood Cliffs, New Jersey, 1961), p. Bl *
- 6)
L. M. Barker, *A Model for Stress Wave Propagation in Composite Materials,*
J. Composite Materials,~* p. 140 (April, 1~71).
- 7)
L. D. Buxton and L. s. Nelson, *chapter 6:
St;am Explosions,* Core Meltdown Experi~ental Review, Sandia Laboratories Report SAND 74-0382 (August 1975).
'1-