A note on the pressure field within an outward moving free annulus

TLDR: In this paper, a model based on incompressible cylindrically symmetric flow is used to get a theoretical solution similar to that of the Rayleigh's solution for bubble dynamics.

Abstract: The outward radial expansion of a free liquid annulus is a common problem of both earlier and current ICF blanket design. Whether the annulus fractures or not depends on the internal pressure and surface stability. In this paper a model based on incompressible cylindrically symmetric flow is used to get a theoretical solution similar to that of the Rayleigh's solution for bubble dynamics. The pressure inside the annulus is found positive all time but the peak is lowering during the expansion. Besides, both surfaces are Taylor stable during such motion. Thus, it is concluded that an annulus in outward radial motion will not cavitate or breakup.

Full text

CERTAINDATA
CONTAINEDINTHIS
'DOC'uM'ENTMAYBE
DIFFICULT READ
IN IVI'ICROFI HE
PRODuCTS.

'II ' _ I-- BEP,::t<ELE"( bll It- LEt:-IFI._ EL 1',1,:,•'=:li_"f:'47''::''=':::=-'" " -- -- " I" ' 'i,':'t:'- ._':!: , '"t1"1_. J. c : t'-I1_, _, l'.l,:l . '"'":i:.. [:' . "'"
"iii
i't.
.,
• 8.(_,A._f-"-<.?<,'._[ _:_/.;,,,7....- i,,i"5
,>
UCRL-CR--- 10 3 81 9
DE91 000948
,A NOTE ON THE PRESSURE FIELD WITHIN AN OUTWARD
,MOVING FREE ANNULUS
o
X.M. Chen and Virgil E, Schrock
Department OfNuclear Engineering
University of California at Berkel,ey
Berkeley, CA 94720
(415) 642-6431
i,
Paper Proposed for
the Ninth Topical Meeting on I echnology of
Fusion Energy
October 7-11, 1990, Oak Brook, IL
Work performed under the auspices of the U.S. Department of Energy ....
by the Lawrence Livermore National Laboratory under contract W-7405-
Eng-.48
,_.: _::_%.
<;"i' _.-"
,_t_%_ITJ,ELITIONOF Tills lliJC'J_lTt,rl .IS UNI-t..M.!iTF.._)
i

i, ,,
A NOTE ON TIlE PRESSURE FIELD WITt-I{INAN OUTWARD MOVING FREE ANNULUS
i
X,M, ChertaM V,E. Schrock
Department of Nuclear Engineering
University of California at Berkeley
Berkeley,CA 94720
(415) 642-6431
ABSTRACT paper, L,'actures during its outward motion is
The outward radial expansion of a ft'ce!iquid annulus ;.,,,,_tl_,_t,,_,t_n.1ti<,,ll_,pr_O_r_._.,._fl_eTnYt__fr._
by
calcuLathal_
t),¢ radial
annulus, Irt this model,we
is a common problem of both ealier and current ICF treat thefluid asan incompressibleflow, Wecan obtain
blanket design, Whether the annulus fracturesor not a theoreucal solution following analysis similar tothat
depends on the internal pressure and surface stability, of Rayleigh forbubble dynamlcsL
In this, paper a model based on incompressible
cylindricallysymmetric flow is usedto geta theoretical THE INCOMPRESSIBLE GOVERNING
' solution similar to that of the Rayleigh's solution for EQUATIONS
bubble dy_mics, The pressure inside the annulus is
found posiUve ali time but the peak is loweringduring We view theannulus asa freecontinuous body which
the expartsion, Besides, both surfacesareTaylor stable has cylindrical innerand outersurfaces exposed to the
during such motion, ThUS,r ,t ISconcluded tKat an ambient pressure as illustrated in Figure 1. The
annulus in outward radial motion will not cavitate or following assumptionscan bereasonably made,
breakup,
THE BACKGROUND
In an Inertia Confinement Fusion (ICF) reactor, the
chamber wall may be protected from the neutron
radiationbya neutronabsorbtntg,fallingliquidblanket,
which surrounds the fusion site. The blar&et has a
geomeu'y.consisting of either a conthmous am_ulus
geomet_ or an array of discrete jets_,both of which
encLrcleacentral cavity. Shortly after a fusion event,
ali of the high.energyneutrons willleavethe fusionsite
' andbe mostlyabsorbed bythe fallingliquid, Moreovcr,
the attenuation of neutron energy by the liquid will
occur so quickly thatthe liquid wiUnot have sufficient
' time to esj}and. This process is known as iso_,horic
heating.. I,e,heatingatconslm_tvolun,c, The neutron
absorbing liquid thus finds itself suddenly possessing
much higher internal pressure tiron its surroundings
(dueto itsincreasedinternal energy), and willfragment
due to the propagation of a rarefaction wave into the
liquid, Interestingly, for the case of the dLscretejet
array, the fragmentation of the liquid results not in the
ft}rmatlonof small liquid chunks. On the contrary,
because of geoiaetj-y and neutr_ energy density
_radient, fcagmentataonresults ftrSi in thebreak-off of
mdtvld_aalannullhorn each jet, which thencollidewith Figure 1, The Description of Model
each other and consolidate into a roughly continuous
annulus, In eithergeometry, fragmentationis expected
to cause the outward radial motion of a single, free _II_I19_01
'n
liquid annulus, In previous studies_,it was assumed 1 The fluidis I compre.ss_ble
that this motioncausing fracture of the liquid. Inthis 2 The fluid is inviscid
3 The motionis one dimensional (radial)
Work ped'orrne<t under tl_ auspices oi'" the US
Department of Energy by the Lawrence Livermore Following these assumptions, wecan v_aqteout lbe
National Laboratoryunder Contract W-7405-Eng-48 governtng equations,

i _i,EFt KLE"_" I'ilIILEt:IF'._ IEI_ 1",.. ..::11'!:;_:,..::1:',':lr",::::"-,....... '!"Pf:' 2::: , ,:_.l.... ] L-.:,:-],.., 1.1,-,... i,.t:::.... F' .:_:1ii
,i