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Journal ArticleDOI

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

01 May 1991-Fusion Technology (American Nuclear Society)-Vol. 19, pp 727-731

AbstractThe 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.

Topics: Annulus (firestop) (65%), Internal pressure (50%)

Summary (1 min read)

THE BACKGROUND

  • In an Inertia Confinement Fusion (ICF) reactor, the chamber wall may be protected from the neutron radiation bya neutron absorbtntg,falling liquidblanket, which surrounds the fusion site.
  • I,e, heating at conslm_tvolun,c, The neutron absorbing liquid thus finds itself suddenly possessing much higher internal pressure tiron its surroundings (due to its increasedinternal energy), and will fragment 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 the break-off of mdtvld_aal annullhorn each jet, which thencollide with Figure 1.

O=?(R')-e(R)

  • The integradon (over timO of Equation la gives a global continuity equation, During the outward motion, the velocity profllo is known from thecontinuity equation.
  • The pressure is close to zero, That is, ZO.litl.h_l:Itrdgu_ EQUATION.
  • The,total momentum can becalculated also by an integration of over the whole annulus P(R)--O . (3b).

,, CONCLUSIONS

  • Wher_ the p-bi-is the rate of the momentum ctmnge Aaad flus is _hievable in the simple tmmodeal caleutetton along with the other calcutadons.
  • The total rate of find outisthe total momentumof the annuluscalculated ¢tmnge can be obtained by integration over the v,,hole from this equation (l-V)exactly overlaps on tyre, curve body.

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,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
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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,

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