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Journal Article•DOI•

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

X.M. Chen, V.E. Schrock
01 May 1991-Fusion Technology (American Nuclear Society)-Vol. 19, pp 727-731
TL;DR: 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.

Summary (1 min read)

Jump to: [THE BACKGROUND] – [O=?(R')-e(R)] and [,, CONCLUSIONS]

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
,_.: _::_%.
<;"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
Citations
More filters
Journal Article•DOI•
HYLIFE-II: A Molten-Salt Inertial Fusion Energy Power Plant Design — Final Report

[...]

Ralph W. Moir1, R. L. Bieri1, Xiang M. Chen1, T. J. Dolan1, M. A. Hoffman1, P.A. House1, R. L. Leber1, J. D. Lee1, Y. T. Lee1, J. C. Liu1, G. R. Longhurst1, Wayne R. Meier1, P. F. Peterson1, Ronald W. Petzoldt1, V. E. Schrock1, M. Tobin1, W. H. Williams1 •
Lawrence Livermore National Laboratory1
01 Jan 1994-Fusion Technology
TL;DR: In this article, the liquid-wall HYLIFE-II conceptual design has been presented, which has been shown to reduce the electricity cost by using a neutronically thick array of flowing molten-salt jets, which will not burn, has a low tritium solubility and inventory, and protects the chamber walls.
Abstract: Enhanced safety and performance improvements have been made to the liquid-wall HYLIFE reactor, yielding the current HYLIFE-II conceptual design. Liquid lithium has been replaced with a neutronically thick array of flowing molten-salt jets (Li[sub 2]BeF[sub 4] or Flibe), which will not burn, has a low tritium solubility and inventory, and protects the chamber walls, giving a robust design with a 30-yr lifetime. The tritium inventory is 0.5 g in the molten salt and 140 g in the metal of the tube walls, where it is less easily released. The 5-MJ driver is a recirculating induction accelerator estimated to cost $570 million (direct costs). Heavy-ion targets yield 350 MJ, six times per second, to produce 940 MW of electrical power for a cost of 6.5 cents/kW[center dot]h. Both larger and smaller yields are possible with correspondingly lower and higher pulse rates. When scaled up to 1934 MW (electric), the plant design has a calculated cost of electricity of 4.5 cents/kW[center dot]h. The design did not take into account potential improved plant availability and lower operations and maintenance costs compared with conventional power plant experience, resulting from the liquid wall protection. Such improvements would directly lower the electricity cost figures. For example,more » if the availability can be raised from the conservatively assumed 75% to 85% and the annual cost of component replacement, operations, and maintenance can be reduced from 6% to 3% of direct cost, the cost of electricity would drop to 5.0 and 3.9 cents/kW[center dot]h for 1- and 2-GW (electric) cases. 50 refs., 15 figs., 3 tabs.« less

273 citations

Journal Article•DOI•
Hylife-II Inertial Fusion Energy Power Plant Design

[...]

Ralph W. Moir1•
Lawrence Livermore National Laboratory1
01 May 1992-Fusion Technology
TL;DR: In this article, an inertial fusion power plant design study uses a liquid fall, in the form of jets, to protect the first structural wall from neutron damage, x rays, and blast to provide a 30-y lifetime.
Abstract: The HYLIFE-II inertial fusion power plant design study uses a liquid fall, in the form of jets, to protect the first structural wall from neutron damage, x rays, and blast to provide a 30-y lifetime. HYLIFE-I used liquid lithium. HYLIFE-II avoids the fire hazard of lithium by using a molten salt composed of fluorine, lithium, and beryllium (Li2BeF4) called Flibe. Access for heavy-ion beams is provided. Calculations for assumed heavy-ion beam performance show a nominal gain of 70 at 5 MJ producing 350 MJ, about 5.2 times less yield than the 1.8 GJ from a driver energy of 4.5 MJ with gain of 400 for HYLIFE-I. The nominal 1 GWe of power can be maintained by increasing the repetition rate by a factor of about 5.2, from 1.5 to 8 Hz. A higher repetition rate requires faster re-establishment of the jets after a shot, which can be accomplished in part by decreasing the jet fall height and increasing the jet flow velocity. In addition, although not adequately considered for FIYLIFE-I, there is liquid splas...

35 citations

Journal Article•DOI•
The Soft-Sphere Equation of State for Liquid Flibe

[...]

Xiang M. Chen1, Virgil E. Schrock1, Per F. Peterson1•
University of California, Berkeley1
10 Mar 1992-Fusion Technology
TL;DR: In this article, a soft sphere model for describing liquid metals was deployed with slight modifications for fitting the available experimental data for liquid Flibe, and the results show that the model has good thermodynamic behavior, although for a material like Flibe the "critical point" phenomenon is more complex than for pure component material.
Abstract: Molten Flibe (Li2BeF4) salt is a candidate material for the liquid blanket in the HYLIFE-II inertial confinement fusion reactor. The thermodynamic properties of the liquid are very important for the study of the thermohydraulic behavior of the concept design, particularly, the compressible analysis of the blanket isochoric heating problem. In this paper, a soft sphere model equation of state, which was used for describing liquid metals previously, is deployed with slight modifications for fitting the available experimental data for liquid Flibe. It is found that within the available temperature range the model gives a good agreement with experimental data for density, enthalpy and speed of sound. Additionally the model provides reasonable isotherms, spinodal line and predicts a “critical point”. The results show that the model has good thermodynamic behavior, although for a material like Flibe the “critical point” phenomenon is more complex than for pure component material.

14 citations

Hylife-ii inertial confinement fusion power plant design

[...]

Ralph W. Moir
14 Dec 1990
TL;DR: The HYLIFE-II inertial fusion power plant design study uses a liquid fall, in the form of jets, to protect the first structural wall from neutron damage, x rays, and blast to provide a 30-y lifetime.
Abstract: The HYLIFE-II inertial fusion power plant design study uses a liquid fall, in the form of jets, to protect the first structural wall from neutron damage, x rays, and blast to provide a 30-y lifetime. HYLIFE-I used liquid lithium. HYLIFE-II avoids the fire hazard of lithium by using a molten salt composed of fluorine, lithium, and beryllium (Li 2BeF4) called" Flibe". Access for heavy-ion beams is provided. Calculations for assumed heavy-ion beam performance show a nominal gain of 70 at 5 MJ, producing 350 MJ, about 5.2 times less yield than the 1.8 GJ from a driver energy of 4.5 MJ with gain of 400 for HYLIFE-I. The nominal 1 gigawatt electrical (GWe) of power can be maintained by increasing the repetition rate by a factor of about 5.2, from 1.5 to 8 Hz. A higher repetition rate requires faster re-establishment of the jets after a shot, which can be accomplished in part by decreasing the jet fall height and increasing the jet flow velocity. Multiple chambers may be required. In addition, although not adequately considered for HYLIFE-I, there is undoubtedly liquid splash that must be forcibly cleared because gravity is too slow, especially at high repetition rates. Splash removal can be accomplished by either pulsed or oscillating jet flows. The cost of electricity is estimated to be 0.09 $/kWh in constant 1988 dollars, about twice that offuture coal and light-water-reactor nuclear power. The driver beam cost is about one-halfthe total cost.

7 citations

Journal Article•DOI•
Computer modeling of ICF target chamber phenomena

[...]

Gregory A. Moses, Robert R. Peterson
01 Jun 1994-Laser and Particle Beams
TL;DR: In this article, physical models for ion, electron, and X-ray deposition are discussed, along with physical and numerical modeling of the resulting phase changes intarget chamber structures, and hydrodynamics and radiative transfer in the target chamber vapors and plasmas are central topics.
Abstract: The target chamber of an inertial confinement fusion (ICF) power plant or high-yield test facility must be designed to absorb the target produced Xrays and ions and survive the resulting effects. The target chamber conditions must be restored in fractions of a second for high repetition rate power applications. Computer modeling of these phenomena is essential because equivalent conditions cannot be produced in laboratory experiments prior to the first ignition of high-yield ICF targets. Choices of models are dictated by specific reactor design strategies. The two major strategies, gas protection and sacrificial first surfaces, are used as a guide to our discussion. Physical models for ion, electron, and X-ray deposition are discussed, along with physical and numerical modeling of the resulting phase changes intarget chamber structures. The hydrodynamics and radiative transfer in the target chamber vapors and plasmas are central topics.

6 citations

References
More filters
Journal Article•DOI•
The Instability of Liquid Surfaces when Accelerated in a Direction Perpendicular to their Planes. I

[...]

Geoffrey Ingram Taylor
22 Mar 1950-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences
TL;DR: In this article, it was shown that when two superposed fluids of different densities are accelerated in a direction perpendicular to their interface, this surface is stable or unstable according to whether the acceleration is directed from the heavier to the lighter fluid or vice versa.
Abstract: It is shown that, when two superposed fluids of different densities are accelerated in a direction perpendicular to their interface, this surface is stable or unstable according to whether the acceleration is directed from the heavier to the lighter fluid or vice versa. The relationship between the rate of development of the instability and the length of wave-like disturbances, the acceleration and the densities is found, and similar calculations are made for the case when a sheet of liquid of uniform depth is accelerated.

2,839 citations

Journal Article•DOI•
VIII. On the pressure developed in a liquid during the collapse of a spherical cavity

[...]

Lord Rayleigh
01 Aug 1917-Philosophical Magazine Series 1

2,532 citations

Journal Article•DOI•
On the motion following isochoric heating of concentric liquid annuli

[...]

L.A. Glenn1•
Lawrence Livermore National Laboratory1
01 Oct 1980-Nuclear Engineering and Design
TL;DR: In this article, the inertial confinement fusion (ICF) design was studied in connection with the design of an IC fusion reactor in which an array of concentric liquid lithium annuli, or close-packed jets, is suddenly penetrated by high-energy neutrons and simultaneously exposed to surface deposition of X-rays and ionic debris.
Abstract: When adjacent liquid slabs are separated by void gaps and suddenly heated throughout, each slab will split into two parts, which then move away from each other. If there are n initial gaps, there will eventually be at least n(n + 1) 2 collisions. If the initial heating is non-uniform, the collisions will act to smear or average out the momentum generated within the fluid. Moreover, if the flow field is divergent, cavities will form in the liquid, the collisions will be inelastic, and energy will be dissipated. These phenomena were studied in connection with the design of an inertial confinement fusion reactor in which an array of concentric liquid lithium annuli, or close-packed jets, is suddenly penetrated by high-energy neutrons and simultaneously exposed to surface deposition of X-rays and ionic debris. It is shown that such a design can be very effective in reducing the outward-directed momentum and thus the impulse imparted to the reactor walls.

11 citations

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