an investigation of the fluid dynamics aspects of thin...

AN INVESTIGATION OF THE FLUID DYNAMICSASPECTS OF THIN LIQUID FILM PROTECTIONSCHEMES FOR INERTIAL FUSION ENERGYREACTOR CHAMBERSM. YODA,* S. I. ABDEL-KHALIK, and ARIES-IFE TEAM Georgia Institute of TechnologyG. W. Woodruff School of Mechanical Engineering, Atlanta, Georgia 30332-0405

Received June 1, 2003Accepted for Publication October 7, 2003

Experimental and numerical studies of the fluid dy-namics of thin liquid film wall protection systems havebeen conducted in support of the ARIES-IFE study. Boththe porous “wetted wall” concept, involving low-speedinjection through a porous wall normal to the surface,and the “forced film” concept, involving high-speed in-jection through slots tangential to the surface, have beenexamined. These initial studies focus upon the “preshot”feasibility of these concepts, between chamber clearingand the fusion event.

For the wetted wall, a three-dimensional level con-tour reconstruction method was used to track the evolu-tion of the liquid film on downward-facing walls fordifferent initial conditions and liquid properties with evap-oration and condensation at the free surface. The effectsof these parameters on the film dynamics, the free sur-face topology, the frequency of liquid drop formation anddetachment, the minimum film thickness between explo-sions, and the equivalent diameter of detached dropshave been analyzed. Initial experimental results are inreasonable agreement with the numerical predictions.Generalized nondimensional charts for identifying ap-propriate “design windows” for successful operation of

the wetted wall protection concept have been developed.The results demonstrate that a minimum repetition rate isrequired to avoid liquid dripping into the reactor cavityand that a minimum injection velocity is required in orderto maintain a minimum film thickness over the first wall.

For the forced film concept, experimental investiga-tions of high-speed water films injected onto downward-facing flat and curved surfaces at angles of inclinationup to 45 deg below the horizontal were conducted. Meandetachment length and the lateral extent of the film weremeasured for a wide range of liquid-solid contact anglesat different values of the initial film thickness, liquidinjection speed, and surface orientation. The results showthat the film detaches earlier (i.e., farther upstream) fornonwetting surfaces and for flat (versus curved) sur-faces. The nonwetting flat surface data are therefore usedto establish a conservative “design window” for filmdetachment. Initial observations of film flow around cy-lindrical obstacles suggest that cylindrical dams are in-compatible with forced films.

KEYWORDS: thin liquid protection, forced films, wetted wall

I. INTRODUCTION

In inertial fusion, the energy released from the ex-ploding fuel pellets consists of energetic neutrons, pho-tons, and charged particles that eventually dissipate theirkinetic energies in the walls of the reactor chamber. Theenergy from the soft X rays and charged particles is de-posited within an extremely thin surface layer, causingrapid surface heating of the reactor chamber first wall.

These photon and ion irradiations may cause excessivewall erosion by numerous mechanisms, including evap-oration, spallation and macroscopic erosion due to shockwave destruction, high thermal stresses, and intergranu-lar pore explosion.

Numerous studies of the thermal-mechanical re-sponse of inertial fusion energy~IFE! reactor chamberfirst walls for different wall materials, target yields~i.e.,wall loadings!, repetition rates, and target designs~i.e.,spectra! have been reported.1–6The results of these stud-ies point to the need for a first wall protection scheme to*E-mail: [email protected]

FUSION SCIENCE AND TECHNOLOGY VOL. 46 NOV. 2004 451

assure wall survival at practical cavity sizes. Several firstwall protection schemes have been proposed over the lastthree decades, including the use of a thin sacrificial liq-uid film to protect the first wall from damaging radiationand thermal stresses. The Prometheus study,7,8which con-sidered thin liquid film protection for both heavy-ion-beam and laser ignition, proposed using a film of liquidlead to protect the silicon carbide~SiC! first walls of thereactor chamber, a vertical cylinder with hemisphericalend caps. The film was created using two differentmethods:

1. a “wetted wall”~a concept originally proposed byLosAlamos National Laboratory in 1972~Ref. 9!!,with a 0.5-mm-thick layer of liquid lead suppliedthrough a porous SiC structure

2. a “forced film,” where molten lead is injected atspeeds exceeding 7 m0s through slots at the top ofthe chamber to create a few-millimeter-thick at-tached film over the upper chamber end cap.

The X rays produced by the exploding targets deposittheir energy in the liquid lead, which prevents surfaceheating of the silicon carbide first wall. The ionic debristhat arrives a few microseconds thereafter deposits itsenergy either in the lead vapor cloud produced by theX-ray energy deposition or in the remaining liquid film,thereby causing further evaporation. Recondensation ofthe vapor allows the energy deposited in the film to berecovered prior to the next target explosion, albeit over alonger time period, thereby limiting first wall heatingand thermal stress. More recently, the feasibility of thinliquid layers attached to the first walls and controlled inpart by electromagnetic forces has been explored as partof the APEX study on innovative concepts for magneticfusion energy chamber technologies to attenuate neu-trons and reduce surface heat flux.10

Prometheus envisioned injecting the forced film froma single point at the top~apex! of the reactor cavity. If thefilm is completely destroyed by the fusion event, how-ever, and the film must be reestablished after each shot,this appears to be infeasible. For a cavity radiusR5 5 mand a time between shots of 0.2 s~or a repetition rate of5 Hz!, the fluid must travel a distance ofpR, over theupper hemispherical end cap, or 15.7 m, within 0.2 s,giving a minimum flow velocity of 78.5 m0s, which is avalue well above speeds at which flowing liquids willerode the first wall. The only feasible method for imple-menting the forced film concept therefore appears to in-volve “tiling” the upper hemispherical end cap of thereactor cavity with multiple coolant injection and re-moval slots.

In 2001, the ARIES study began to develop designwindows for IFE reactors using thin liquid film protec-tion schemes based upon the Prometheus conceptual de-sign. To this end, numerical and experimental studieshave been performed by the Georgia Institute of Tech-

nology to examine the basic fluid dynamics of the wettedwall and forced film concepts. We have focused in theseinitial studies upon the “preshot” dynamics, or the evo-lution of these flows over the time period after the cham-ber is cleared until target ignition. The critical questionfor establishing the viability of these concepts is the fol-lowing: Can a minimum film thickness be maintained toprovide adequate protection during subsequent targetexplosions?

Among the most important fluid dynamics issues inthin liquid film protection are~a! preventing “dry patch”formation on the first wall;~b! preventing film detach-ment that may partially uncover the surface, thereby ne-gating its effectiveness as a wall protectant; and~c!minimizing drop formation and detachment to avoid in-terference with target injection and beam propagation. Inboth the wetted wall and forced film concepts, film de-tachment and drop formation under the influence of grav-ity is most likely to occur on the downward-facing surfacesover the upper end cap of the reactor chamber. Moreover,this flow geometry—where a dense “heavy” liquid flowsabove a less dense “light” near-vacuum—may be suscep-tible to drop and even dry patch formation due to Rayleigh-Taylor instability~Refs. 11, 12, and 13, among others!.

In the wetted wall concept, the appropriate modelproblem is that of a liquid film on a downward-facing flatsurface at various angles of inclination with respect tothe horizontal. Neglecting the first wall curvature is areasonable assumption given that the radius of curvaturefor the Prometheus chamber upper end cap is;5 m, ormore than three orders of magnitude greater than filmthicknesses ofO~1023 m!, and the flow velocities par-allel to the wall are negligible. For the forced film, thelarge flow speeds tangential to the curved first wall gen-erate a centrifugal force that stabilizes the film by drivingthe fluid outward against the wall. Forced film flowsover both downward-facing flat and curved surfaces witha radius of curvature of 5 m were therefore investigated.

There have been several previous studies of the fluiddynamics and heat transfer of forced and free-falling lam-inar and turbulent liquid films on vertical and upward-facing inclined flat surfaces~Refs. 14 through 17, forexample!. Most of these studies have either focused uponthe evolution and statistics of the free-surface waves onthese films, or on modeling heat transfer in and minimumthickness of these flows. There has, however, been littlework on liquid film flows on downward-facing solid sur-faces, where a significant component of the gravitationalforce acts normal to the flow direction. We are aware ofonly one experimental study of forced film flow on adownward-facing surface, which reported that surfaceroughness had a major impact on detachment length forlaminar water films in ambient air on flat acrylic surfacesup to 30 deg below the horizontal.18

A numerical investigation has therefore been con-ducted to examine the hydrodynamics of the wetted wallconcept, which is modeled as a thin liquid film formed on

Yoda et al. THIN LIQUID FILM PROTECTION FOR IFE REACTOR CHAMBERS

452 FUSION SCIENCE AND TECHNOLOGY VOL. 46 NOV. 2004

the downward-facing surface of a flat porous wall.19–21

These simulations are being validated by experiments onwater injected through a porous stainless steel surface.An experimental investigation is also being conducted tostudy the fluid dynamics of the forced film concept, mod-eled as a high-speed film of water injected tangentiallyonto the underside of both flat22,23and curved plates witha radius of 5 m. The objective of both efforts is to develop“design windows” to provide guidance for power plantdesigners on how important flow parameters~e.g., filmthickness, liquid injection speed, surface orientation, andsurface wettability! affect phenomena such as film de-tachment, drop formation and detachment, and minimumfilm thickness.

In this overview, Sec. II describes the numerical andexperimental studies of the wetted wall concept, whileSec. III discusses the experiments on the forced filmflow. Section IV summarizes the conclusions derived fromthese investigations and discusses the implications ofthese results for both of these thin liquid film protectionconcepts in IFE power plants.

II. WETTED WALLS

In the numerical study of the wetted wall concept, astate-of-the-art level contour reconstruction technique hasbeen developed and used to track the three-dimensionalevolution of a thin liquid film with injection through aporous downward-facing wall with evaporation and con-densation at the film free surface. The aim is to determinethe effect of different design and operational parameters~initial film thickness, liquid injection velocity, mass fluxat the film free surface, wall inclination angle, liquidproperties, and surface disturbance amplitude and con-figuration! on the liquid film stability between explo-sions. Here, we report on the effects of these parameterson the transient, three-dimensional topology of the filmfree surface and the frequency of liquid drop formationand detachment. Formation and detachment of liquid dropsfrom the downward-facing sections of the cavity surfacemay interfere with subsequent target and0or beam prop-agation and may render such a wall protection schemeunsuitable, at least for the upper sections of the cavity.Additionally, the effects of various parameters on theminimum film thickness prior to drop detachment areexamined.

II.A. Numerical Formulation

The numerical technique is based upon a finitedifference0front tracking method originally developedfor two- and three-dimensional isothermal multifluidflows.24,25One of the major advantages of this method isits ability to naturally and automatically handle interfacemerging and breakup in three-dimensional flows. A more

detailed description of the numerical techniques is givenby Shin.25

One set of transport equations, valid for both fluids~namely, the liquid injected through the porous wall andthe cavity “gas”!, is solved. This local, single-field for-mulation incorporates the effect of the interface in theequations as delta-function source terms, which act onlyat the interface.

The interface is advected in a Lagrangian fashion byintegrating

dx f

dt{n 5 V{n , ~1!

where

x f 5 x~s, t ! 5 parameterization of the interface

n 5 unit normal to the interface

V 5 interface velocity vector.

In the absence of mass exchange~i.e., evaporation orcondensation! at the gas-liquid interface, the interfacevelocity will be equal to the fluid velocity at the inter-face, orV 5 uf 5 u~x f !. On the other hand, when massexchange takes place, the interface velocity componentsare given by

dx f

dt5 uL 1

_mf''

rL

n , ~2!

where

uL 5 heavier fluid~liquid! velocity at the interface

rL 5 liquid density

_mf'' 5mass flux from the gas to the liquid at the in-

terface~positive for condensation and nega-tive for evaporation!.

Equation ~2! specifies only the normal component ofthe interface motion; we assume that the interface andfluid at the interface have the same tangential velocitycomponent.

The momentum equation is written for the entireflow field, and the forces due to surface tension are ap-plied at the interface as body forces that act only at theinterface. For the confined Rayleigh-Taylor instabilitysimulation performed here, mass exchange at the inter-face is accounted for parametrically. We can thereforeuse a single nondimensional momentum equation for bothfluids, without having to solve the energy equation. Moreimportantly, by parametrically accounting for mass ex-change at the interface, we can address all the relevantphysical phenomena without restricting this analysis tospecific target output spectra, chamber design, or fluidproperties. Hence, we have accounted for the dominantnonisothermal effects, i.e., evaporation and condensationat the interface, by introducing a parametrically specified



interfacial mass flux _mf'' as a source term in the conser-

vation of mass and interface advection.In nondimensionalizing the governing equations

and boundary conditions, we define the length scalel 5

!s0@g~rL 2 rG !#, the velocity scaleUo 5 !gl, thepressure scalePo 5 rL Uo

2, and the time scaleto 5 l0Uo.Here, the subscriptL refers to the film liquid injectedthrough the porous wall~heavy fluid!, while the sub-scriptG refers to the low-pressure gas~vacuum! withinthe reactor cavity~light fluid!. Thus, the governing non-dimensional momentum equation can be expressed as

]r1u

]t1 ¹{~r1uu!

5 2¹p 1 r1g 11

Re¹{m1~¹u 1 ¹uT!

1EA

1

Weknd~x 2 x f ! dA , ~3!

where

rG

rL

5 r* ;mG

mL

5 m* ~4!

r1 [ r~x, t !0rL 5 1 1 ~r* 2 1! I ~x, t ! ~5!

m1 [ m~x, t !0mL 5 1 1 ~m* 2 1! I ~x, t ! ~6!

Re5rL Uo l

mL

; We5rL Uo

2 l

s5

rL

rL 2 rG

, ~7!

where

p 5 pressure

g 5 gravitational acceleration

s 5 surface tension coefficient

k 5 twice the mean interface curvature

d~x 2 x f ! 5 three-dimensional delta function that isnonzero only whenx 5 x f .

The important nondimensional groups, the Reynolds andWeber numbers Re and We, respectively, are defined inEq. ~7!. The integral term in Eq.~3! accounts for surfacetension acting on the interface. In order to limit the scopeof our study, we have assumed that the surface tensioncoefficient is constant, and thus, without loss of gener-ality, we ignore tangential variations ins along the in-terface. We have also assumed the light fluid~IFE chambercavity gas! to be inviscid, so the viscosity ratio defined inEq. ~4! is zero.

By including condensation and evaporation as a sourceterm at the interface, the nondimensional conservation ofmass can be written as

¹{r1u 5 u{¹r1 12~r* 2 1!

r* 1 1E

A_mf*d~x 2 x f ! dA ,

~8!

where the nondimensional mass flux is defined as_mf*5

_mf''0~rL Uo!. Interface advection with finite phase

change@Eq. ~2!# can be expressed in nondimensionalform as

dx f

dt5 uL 1 _mf

*n . ~9!

The selected definitions for the length and velocityscales make the Weber number a function of only thedensity ratiorL0rG @Eq. ~7!# . Parametric calculationshave been performed to quantify the effect ofrL0rG

on the nondimensional drop detachment time, detacheddrop equivalent diameter, and liquid penetration dis-tance prior to drop detachment.19 These results showthat for rL0rG $ 20 ~i.e., We # 1.053!, the resultsare insensitive to further increases inrL0rG ~note thatWe r 1 asrL0rG r `!. Obviously,rL0rG .. 20 inIFE applications. Nevertheless, the results of the para-metric calculations demonstrate that the effect ofrL0rG

can be ignored for values above 20. The results pre-sented here therefore userL0rG 5 20, or, equivalently,We 5 1.053, to reduce the computing time required forthe analyses.

II.B. Boundary Conditions and Initial Perturbations

Figure 1 shows the calculation geometry and bound-ary conditions used to model horizontal, downward-facing surfaces with liquid injection through the surface.

Fig. 1. Initial surface configuration and boundary conditionsused to model horizontal downward-facing surfaceswith liquid injection through the surface.



This corresponds to the uppermost point in the reactorcavity inner surface. The film is along thex-yplane of theflow, with the z direction oriented normal to the filmpointing upward. Because of symmetry, periodic bound-ary conditions are used in the horizontal directions acrossthe four vertical sides. Liquid is injected at a specifiednormal velocitywin at the upper solid boundary, while anopen boundary condition is used at the bottom surface.The calculation geometry and boundary conditions usedto model films on downward-facing inclined surfaces areshown in Fig. 2. Although the upper and lower surfaceboundary conditions are the same as those for the hori-zontal surface case, we impose Neumann conditions onthe side boundaries for velocity and hydrostatic pressureconditions for thex andy directions. Gravity acts at anangleu with respect to the vertical.

Clearly, in the relatively hostile environment follow-ing target explosion and chamber clearing, the initial filmsurface geometry would be highly uncertain. The effectsof three different initial surface perturbation geometries,namely, the “sinusoidal,” “saddle,” and “random” per-turbations~Fig. 3!, on drop detachment time were con-sidered at different mode numbers.19The results generallyshow that the saddle-type initial surface perturbation witha mode number of 1 produces the shortest drop detach-ment time, in agreement with previous studies of theRayleigh-Taylor instability.19 Grid convergence studiesshowed that simulations with nodal resolutions of~50350 3 50! and ~1003 1003 100! gave nearly identicaldrop detachment times. Therefore, all the results pre-sented here were generated using the saddle-type pertur-bation with a mode number of unity over a 503 503 50mesh with a perturbation amplitude of half the initialsurface thicknesszo

*. The large perturbation amplitude

was chosen to represent the strongly disturbed film aftertarget explosion and subsequent chamber clearing.

II.C. Numerical Results

The effects of initial film thickness, liquid injectionvelocity, evaporation0condensation mass flux, and Reyn-olds number on the free-surface evolution and drop de-tachment timetd have been examined. Figure 4 showsfour snapshots over time~with time increasing from leftto right! of the film free surface for a thin film~nondi-mensional initial film thicknesszo

*5 0.1! and moderateinjection velocity ~normalized injection velocitywin

* 50.01! at nondimensional mass flux_mf

*5 20.005~evap-oration! @left# , 0.0 @center# , and 10.01 ~condensation!@right# . For lead at 800 K, these values correspond to aninitial film thickness of 0.2 mm and injection velocity of1.4 mm0s, giving a Reynolds number of 2000, and massfluxes of27.6, 0, and 15.2 kg0~m2{s!, respectively. Thelast snapshot for each case corresponds to the momentwhere a drop detaches; the nondimensional drop detach-ment timet* [ td0to is given at the bottom for all threecases. These results indicate that evaporation delays dropdetachment~i.e., increasest*!, while condensation re-sults in earlier detachment compared to the baseline casewith _mf

*5 0. The nondimensional detachment timest*531.35, 27.69, and 25.90 correspond to detachment timestd 5 0.46, 0.41, and 0.38 s, respectively.

Similar calculations have been performed for a higherinjection velocity ofwin

* 5 0.05 ~Fig. 5!, while all otherparameters remain unchanged. These results show that aswin increases, evaporation and condensation have rela-tively little impact upontd; t*5 25.69, 25.13, and 25.74for _mf

* 5 20.005~evaporation! @left# , 0.0 @center# , and

Fig. 2. Initial surface configuration and boundary conditions used to model inclined downward-facing surfaces with liquidinjection through the surface.



Fig. 3. Sketch of the three initial surface perturbation geometries~sinusoidal, random, and saddle! examined in this investigation.

Fig. 4. Evolution of the film free surface over time~time progressing from left to right!, with drop detachment occurring in therightmost snapshot, showing the effect of evaporation0condensation at the interface on nondimensional drop detachmenttime t* for thin liquid films ~zo

*5 0.1! with moderate injection velocity~win* 5 0.01!: _mf

*5 20.005~evaporation! @left# ,0.0 @center# , and 0.01~condensation! @right# . In all cases, Re5 2000.

Fig. 5. Evolution of the film free surface showing the effect of evaporation0condensation at the interface on nondimensional dropdetachment timet* for thin liquid films ~zo

*5 0.1! at a higher injection velocity~win* 5 0.05!: _mf

*5 20.005~evaporation!@left# , 0.0 @center# , and 0.01~condensation! @right# . In all cases, Re5 2000.



10.01~condensation! @right#, respectively. Figure 6 showssimilar calculations at a larger initial film thickness ofzo* 5 0.5, corresponding to an initial film thickness of

;1 mm for lead at 800 K~all other parameters are thesame as those in Fig. 5!. As expected, higher initial filmthickness~with correspondingly larger initial distur-bance amplitude! leads to smaller detachment time, witha reduction of nearly 30% compared with the cases shownin Fig. 5. For the thicker film,t* 5 17.11, 16.94, and17.83 for _mf

*5 20.005~evaporation! @left# , 0.0@center# ,and 10.01 ~condensation! @right# , respectively. Never-theless, the effects of mass transfer at the gas-liquid in-terface are relatively small for thicker films.

Generalized charts showing the nondimensional dropdetachment time as a function of Reynolds number fordifferent values of nondimensional mass flux_mf

* at thegas-liquid interface ranging from20.005 to10.02 areshown in Fig. 7 for three different values of initial filmthickness and liquid injection velocity:~a! zo

*5 0.1 andwin* 5 0.01,~b! zo

*5 0.5 andwin* 5 0.05, and~c! zo

*5 0.5and win

* 5 0.01. Figure 7a shows that detachment timedecreases at a given Re as mass flux increases for thinfilms ~zo

* 5 0.1!. Figures 7b and 7c show that for rela-tively thick films ~zo

* 5 0.5!, the effect of all other pa-rameters~including _mf

*! on t* is relatively minor andthat the detachment time is essentially constant for thesecases.

Figure 7 can be used by the system designer to de-termine the expected drop detachment time, or fre-quency, for different design and operating conditions.Although the target explosion will generate numerousdrops and clearing these drops, or “chamber clearing,” isa major issue for liquid protection schemes, these simu-lations demonstrate that even an isothermal film will dripin the preshot interval between chamber clearing and thenext target explosion. These drop detachment time re-sults therefore imply that target explosions must occur ata frequency above a minimum repetition rate to mini-

mize interference with target injection and ignition dueto formation of preshot drops.

Figure 8 shows the evolution of the nondimensionalminimum film thicknessdmin

* [ dmin0l, wheredmin is theminimum film thickness observed over the entire film atany given timet, as a function of nondimensionalizedtime t *[ t0to # t* at different Reynolds numbers~50#Re# 2000! for two cases:~a! zo

*5 0.1 andwin* 5 0.05 and

~b! zo* 5 0.5 andwin

* 5 0.05, both with no evaporation0condensation~mf

*5 0.0!. Figure 8 shows thatdmin* grad-

ually increases with injection and then decreases to aminimum value prior to drop separation. Figure 8a showsthat for an initially thin film ~zo

* 5 0.1!, the minimumfilm thickness over the entire transient is actually higherthan the initial value ofdmin

* . The opposite is true forinitially thick films ~zo

*5 0.5!, as shown in Fig. 8b.Recognizing the importance of this parameter to

system designers, generalized nondimensional charts fordmin* as a function of Re for different evaporation and

condensation rates have been developed for three differ-ent cases, as shown in Fig. 9:~a! zo

* 5 0.5 andwin* 5

0.05,~b! zo* 5 0.1 andwin

* 5 0.01, and~c! zo* 5 0.5 and

win* 5 0.01. These results suggest that the injection ve-

locity must exceed a minimum value to keep the filmthickness from decreasing below a designer-specifiedminimum value. Clearly, condensation at the liquid-gasinterface reduces the minimum injection velocity re-quired to prevent film dryout. Moreover,dmin

* increaseswith _mf

* at a given Re for all three cases. Figure 9 canbe used to determine the minimum film thickness forvarious design conditions and fluid properties. Alterna-tively, these generalized charts can be used to deter-mine the necessary injection velocity corresponding toa desired value for the minimum film thickness anda given set of fluid properties and evaporation0condensation rates.

The nondimensional detached drop equivalent diam-eter D * [ D0l shown in Fig. 10 as a function of Re

Fig. 6. Evolution of the film free surface~time progressing from left to right!, with drop detachment occurring in the finalsnapshot, showing the effect of evaporation0condensation at the interface on nondimensional drop detachment timet* forthicker liquid films ~zo

*5 0.1! at a higher injection velocity~win* 5 0.05!: _mf

*5 20.005~evaporation! @left# , 0.0 @center# ,and 0.01~condensation! @right# . In all cases, Re5 2000.



represents the diameter of a spherical dropD with a vol-ume equal to that of the liquid spike that separates fromthe liquid film att 5 td. Figure 10 shows curves for sevendifferent values of the nondimensional mass flux at thefree surface~20.005# _mf

* # 10.02!. Graphs are pre-sented for three different initial film thicknesses and in-jection velocities:~a! zo

*50.5 andwin* 50.05,~b! zo

*50.1andwin

* 5 0.01, and~c! zo* 5 0.5 andwin

* 5 0.01. Theseresults suggest thatD * depends weakly on Re, increaseswith _mf

* at a given Re, and is strongly dependent upon theinjection velocity and initial film thickness. Again, theresults given in Fig. 10 allow the designer to estimatethe size of detached drops from the liquid film for dif-ferent design parameters and liquid properties.

Fig. 7. Generalized charts for nondimensional drop detach-ment timet* as a function of Reynolds number Re@logscale# for different values of the normalized interfacialmass flux _mf

* ~see legend!. Three different initial filmthicknesses and injection velocities are presented:~a!zo* 0.1 andwin

* 5 0.01,~b! zo*5 0.5 andwin

* 5 0.05, and~c! zo

*5 0.5 andwin* 5 0.01. Note that the vertical scale

of ~a! is different from that for~b! and~c!.

Fig. 8. Variation of the normalized minimum film thicknessdmin* with nondimensionalized timet * at Reynolds

numbers Re~see legend! for two cases:~a! zo*5 0.1 and

win* 5 0.05 and~b! zo

* 5 0.5 andwin* 5 0.05. In both

cases,mf*5 0.0.



Fig. 9. Generalized charts for the normalized minimum filmthicknessdmin

* as a function of Reynolds number Re@log scale# for different values of the normalized inter-facial mass flux _mf

* ~see legend!. Three different initialfilm thicknesses and injection velocities are presented:~a! zo

*5 0.5 andwin* 5 0.05,~b! zo

*5 0.1 andwin* 5 0.01,

and~c! zo*5 0.5 andwin

* 5 0.01.

Fig. 10. Generalized charts for the normalized detached dropequivalent diameterD* as a function of Reynolds num-ber Re@log scale# for different values of the normal-ized interfacial mass flux _mf

* ~see legend!. Threedifferent initial film thicknesses and injection veloc-ities are presented:~a! zo

* 5 0.5 andwin* 5 0.05, ~b!

zo* 5 0.1 andwin

* 5 0.01, and~c! zo* 5 0.5 andwin

* 50.01.



II.D. Experimental Validations

Table I gives values of the length, velocity, and time-scales, along with the Re for several fluids at differenttemperatures. Table I shows that Re' 500 for water at300 K, suggesting that water can be used as a simulantfluid for a number of candidate IFE reactor coolants.Experiments using water as the working fluid can there-fore provide useful data to validate the results given inSec. II.C. An experimental recirculating test facility hasbeen constructed where water supplied by a constant-head tank flows continuously through a porous stainlesssteel rectangular plate~nominal dimensions 12318 cm!at an adjustable orientation angleu with respect to thehorizontal.20 Different plate porosities and tank levelsare used to vary the film thickness and injection velocitywin.

Typical results showing the evolution of a liquidwater drop from a horizontal porous surface~u 5 0 deg!at win 5 10 mm0s are shown in Fig. 11. Initial data forthe drop detachment time atu 5 0 deg andwin 52.4 mm0s over 40 different drops give a mean dropdetachment timetd 5 0.39 s, with a standard deviation60.04 s, and a mean detached equivalent drop diameterPD 5 5.796 0.77 mm. Based on an estimated film thick-

ness of 1.0 mm, these results compare well with the

model predictions oftd 5 0.36 s andD 5 5.5 mm. Weare currently developing techniques to accurately andnonintrusively measure the initial film thickness usingoptical techniques to obtain more accurate comparisonswith the numerical simulations.

III. FORCED FILMS

This section deals with the fluid dynamics aspects ofthe forced thin liquid film wall protection scheme, wherethe liquid is tangentially injected along the first wallsurface. As discussed previously, avoiding the formationof dry patches is a major issue for effective thin filmprotection. For dry patch formation in a forced film flowdriven by forces tangential to the surface~e.g., thermo-capillary and surface forces!, recent results using mini-mum total energy criteria17 show that for an isothermalliquid film flowing down a vertical adiabatic wall, theminimum film thickness required to rewet any dry patchdmin is given by the empirical relation

Dmin [ dminS15mL2 s

rL3g2 D5 ~12 cosuo!0.22 , ~10!

TABLE I

The Length, Velocity, and Timescales~l, Uo, andto, respectively!, Along with the Reynolds Number Re, for DifferentFluids of Interest at Various TemperaturesT

Water Lead Lithium Flibe

T ~K ! 293 323 700 800 523 723 773 873 973l ~mm! 2.73 2.65 2.14 2.12 8.25 7.99 3.35 3.22 3.17Uo ~mm0s! 163.5 161.2 144.7 144.2 284.4 280.0 181.4 177.8 176.4to ~ms! 16.7 16.4 14.8 14.7 29.0 28.6 18.5 18.1 18.0Re 445 771.2 1618 1831 1546 1775 81.80 130.8 195.3

Fig. 11. Typical images showing the evolution of a film of water on the underside of a horizontal porous plate at timest 5 0.05,0.1, 0.15, and 0.2 s for an injection velocitywin 5 10 mm0s.



whereDmin is the nondimensional minimum film thick-ness anduo is the contact angle of the liquid on the wall.The minimum mass flow rate per unit perimeter requiredto rewet any dry patchgmin is then

Gmin [ gminS g

rL mL s3D0.2

5 0.67Dmin2.831 0.26Dmin

9.51 ,

~11!

whereGmin is the nondimensional flow rate. Applicationof Eqs.~10! and ~11! shows thatdmin , 1 mm and theminimum film average speed required for a stable fullywetted liquid film,1 m0s for most IFE coolants of in-terest and water with 0 deg# uo # 90 deg. The minimumrequired film thickness scales asg2, while the minimumrequired film speed is weakly dependent on gravity, scal-ing asg20.2. Dry patch formation and rewetting in forcedfilm flow over a vertical wall is hence the “worst case”from a purely hydrodynamic viewpoint at the expectedliquid film velocities in IFE systems~which are muchgreater than 1 m0s! since the streamwise component ofgravity is greatest for this orientation. Based on theseresults, our efforts have focused on the detachment ofthin liquid films flowing along downward-facing sur-faces where gravitational and surface tension effects be-come dominant.

Turbulent films on downward-facing surfaces wereexperimentally studied by injecting water through rect-angular slot nozzles tangentially onto the underside offlat and curved surfaces in ambient air at atmosphericpressure. Although the film in Prometheus is injectedinto a near-vacuum, a simple force balance across anarbitrary control volume of fluid starting at the film freesurface demonstrates that atmospheric pressure acts acrossthe entire film~neglecting the small weight of the fluidinside the control volume!. The forces due to atmo-spheric pressure balance across the film and can there-fore be neglected.

Four different surfaces—glass, stainless steel, Plexi-glas, and glass coated with a commercial product to makeit “nonwetting,” with varying surface wettability charac-terized by water-solid contact anglesaLS ' 25 to 85deg—were investigated. Both flat and curved surfaceswith a radius of curvatureR 5 5 m were studied. Themean film detachment length downstream of the nozzleexit xd and the average film lateral extentW at variousdownstream locations were measured for various valuesof initial film ~i.e., nozzle! thicknessd, initial film injec-tion velocityU, and plate orientation with respect to thehorizontalu. The important dimensionless groups in thisflow are the Weber and Froude numbers, or We5rLU 2d0s and Fr5 U 0!g~cosu!d, respectively. In thesestudies,d 5 1 to 2 mm,U 5 1.9 to 11 m0s, andu 5 0 to45 deg, giving We5 100 to 3200 and Fr5 15 to 120. Inall cases,d $ 1 mm andU $ 1 m0s to prevent dry patchformation. Our results on film detachment and lateralspread are the first~to our knowledge! for turbulent liq-uid films on downward-facing flat and curved surfaces.

III.A. Experimental Apparatus

Accurate numerical predictions of detachment andlateral spread in this free-surface turbulent flow are ef-fectively impossible because of the prohibitive compu-tational cost~at present! of simulating a moving interfacein a turbulent flow and difficulties in determining ap-propriate boundary conditions for the meniscus formednear the detachment point. An experimental study wastherefore conducted. As shown in Fig. 12, water is drivenby a 0.5-hp centrifugal pump~Teel 2P39C! through aflexible coupling and then a flow straightening sectionand exits through a rectangular nozzle at an adjustableangle u with respect to the horizontal. The water isinjected by the nozzle tangentially onto the undersideof either a flat or curved plate with a width of;0.4 mextending a distance of 1.83 m downstream of the noz-zle exit. The nozzle was mounted in a bracket designed

Fig. 12. Sketch of the flow loop@left# and film nozzles@right# for the forced film experiments. All dimensions are given inmillimeters.



so that its vertical position and angular orientation aboutthe x andy directions could be independently adjustedto ensure that the inner lip of the nozzle was flush withand parallel to the upstream end of the plate to ensurethat the water would be injected tangential to the platesurface. The flow, which either detaches from the plateor hits a vertical splash guard at the downstream end ofthe plate, then falls into a 840-, ~220-gal! receivingtank below, where it is recirculated by the pump. Thecurvilinear coordinate system for this flow is defined asfollows: x along the~attached! flow direction and theplate surface,y along the long dimension of the film orparallel to the plate surface, andz downward along theshort dimension of the film~i.e., thickness! or normalto the plate surface. Further details of the experimentsare given by Anderson26 and Shellabarger.27

Three different nozzles with azdimension at the exitd 5 1, 1.5, and 2 mm and ay dimensionWo 5 5 cm ~oraspect ratiosAR 5 50, 33, and 25, respectively! werefabricated using stereolithography rapid prototyping witha minimum fabrication tolerance of 0.1 mm~based uponthe spatial resolution of the rapid prototyping machine!.The nozzles were two-dimensional fifth-order poly-nomial contractions, followed by a straight channel at theexit, to produce uniform flow with thin boundary layers~see Fig. 12 right!. The flow straightening section con-sisted of a perforated plate~53.6% open area ratio, 0.21-cm-diam staggered holes!, followed by a 1.8-cm sectionof honeycomb~cell diameter 0.16 cm!, both of stainlesssteel. The edge-to-edge spacing between the perforatedplate and honeycomb, and the honeycomb and the nozzleinlet, were 7 and 50 mm, respectively.

The Prometheus study proposed using a molten leadfilm on the SiC first wall for thin liquid film protection.Since lead is essentially nonwetting on SiC surfaces, andlittle is known about the effect of surface wettability onthe detachment and lateral spread of turbulent liquid films,experimental studies were also carried out on the effectof surface wettability on the film flow. Four differentsurfaces were studied:

1. glass~contact angleaLS 5 25 deg!

2. stainless steel~aLS 5 50 deg!

3. Plexiglas~aLS 5 75 deg!

4. “nonwetting glass,” or glass coated with a verythin-layer of Rain-Xt ~Pennzoil-Quaker StateCompany! ~aLS 5 85 deg!.

The contact angle for all four surfaces was estimated byvisual inspection of a 0.04-, drop of water~illuminatedby white light from above! on each surface.

In the Prometheus study, the large flow speeds tan-gential to the first wall over the hemispherical upper endcap of the reactor chamber generated a centrifugal forcethat helped to stabilize the film by keeping it attached tothe first wall. For the flow speeds proposed for Prometheus

of U . 7 m0s, the centrifugal accelerationU 20R ~wherethe radius of curvature of the hemispherical end capR55 m! easily exceeds that due to gravityg. Forced filmflows were therefore investigated over flat plates of glass,stainless steel, Plexiglas, and nonwetting glass, and curvedplates withR5 5 m about they axis of stainless steel andPlexiglas. The curved Plexiglas surface was formed bybolting a 183-3 40- 3 0.56-cm~x 3 y 3 z! flexiblePlexiglas plate along both its~183-cm dimension! edgesto two identical concave wooden forms cut in the shapeof an arc with a radius of curvature of 5 m. The woodenforms were braced at their upstream and downstreamends by crossbars to ensure consistent overall surfacecurvature. The curved stainless steel surface was formedby bolting a 183-3 40-3 0.064-cm~x3 y3 z! flexiblestainless steel plate over the curved Plexiglas plate. Notethat the surface angle of inclinationu for the curvedsurfaces was measured with respect to the tangent to thesurface at the nozzle exit~i.e., the upstream end of theplate!. The detachment length and the lateral extent ofthe film flow were then measured for water films flowingover all six surfaces.

The Prometheus-H study, which used 14 heavy-ionbeams with a total energy of 7 MJ, proposed using theforced film concept over the upper end cap of the reactorchamber. Since then, the number of ignition beams pro-posed for various IFE power plant design concepts hassteadily increased, with 72 heavy-ion beams proposedfor an updated HYLIFE-II design28 and 192 laser beamsunder construction for the National Ignition Facility.29

With this large a number of ignition beams, penetrationsthrough the first wall for beam ports will be required overmost of the interior of the reactor cavity, including theupper end cap. Therefore, protecting these beam portsfrom the flowing thin liquid film represents an importantdesign issue for this type of protection.

As an initial study of protective dams around beamport penetrations, cylindrical dams were placed on theunderside of both the flat glass and curved Plexiglas plateswith their leading edge atx 5 7.62 cm. The dams wereheld in place by a permanent rare-earth magnet~Ray-theon 62428D! on the upper side of the plate. Galvanizedsteel tubing with outer diameterd 5 25.4 mm and thick-nesst 51.8 to 76.2 mm and carbon steel shims withd515.9 to 25.4 mm andt 5 0.51 to 2.36 mm were used.

III.B. Flow Visualization

After contacting the plate surface, the film propa-gates some distance along thex direction and then de-taches at some distance downstream of the nozzle exit.The detachment length was measured by takingx-z “sideviews” of the flow in which the detachment point is clearlyvisible, as shown in Fig. 13. The film detaches at slightlydifferent x locations across the lateral~ y! extent of thefilm, especially for smaller values ofU. In all cases, thedetachment distance on each image was therefore taken



to be the location farthest upstream~i.e., the smallestxvalue! at which film detachment occurred.

Individual frames with an exposure of 8 ms wererecorded at 30 Hz by a progressive scan monochromecharge-coupled-device camera~Pulnix TM-9701! ontothe RAM of a personal computer using a framegrabbercard~ImageNation PX610A! as 8-bit grayscale 640 col-umn3 480 row images. Each individual image spans 7tto 90t, where the flow convective timescalet 5 d0U 50.09 to 1.1 ms. A ruler or tape measure attached to theupper side of the plate was used to measure the detach-ment distancexd ~in inches! along the plate surface forboth flat and curved surfaces. Since the detachment dis-tance can vary by up to62 cm between frames for thisturbulent flow, the values reported here for mean detach-ment lengthxd are the average of 40 consecutive inde-pendent realizations obtained from images taken of theflow over a time period of 1.3 s.

For the glass and nonwetting glass surfaces, or thesurfaces with the lowest and highest contact angles, re-spectively, the film width~ y extent! W~x! was measuredby visualizing the film through the top of the plate. Inall cases,W~x! varied by less than61 mm over time atany given downstream locationx. Direct visual inspec-tion was therefore used to measureW~x! every 5 cm forx , xd. Although drop formation was typically observedat the film free surface upstream of the detachment point,no dry patch formation was observed before detachment,as expected.

III.C. Experimental Results

Figure 14 showsxd as a function of the Weber num-ber We for the flat glass~C!, stainless steel~▫!, Plexiglas~L!, and nonwetting glass~n! surfaces, all atu 5 0 deg,for d 5 1 mm ~open!, 1.5 mm~black!, and 2 mm~gray!symbols. If no data are presented for a given case~usu-ally for large We andu! in this and the subsequent graphs,detachment was not observed within the limits of theexperimental apparatus~i.e.,xd . 183 cm!. The detach-ment distance increases with Weber number and is smaller

for a more nonwetting surface~i.e., a surface with higheraLS! at a given We, demonstrating that surface wettabil-ity has a significant impact upon this flow. Moreover,xd

is essentially independent ofd for a given We. The small-est or most conservative estimates ofxd are hence for themost wetting glass surface.

Figure 15 showsxd versus We for the~a! flat glassand ~b! nonwetting glass surfaces, or the surfaces withthe lowest and highest contact angles, respectively. Dataare shown foru 5 0 deg~L!, 30 deg~n!, and 45 deg~C!andd 5 1 mm ~open!, 1.5 mm~black!, and 2 mm~gray!symbols. Detachment length increases withu for a givenWe, as expected since the component of gravity actingnormal to the surface to detach the film decreases asuincreases. Although the data are not shown here, similartrends are observed for the two other surfaces.27 Themost conservative estimates of detachment are thereforefor horizontal surfaces, oru 5 0 deg.

Fig. 13. Typical image showing detachment of the forced film from a flat glass surface atu510 deg for We51390 and Re59200.Note that the ruler above the glass plate is in inches.

Fig. 14. Graph ofxd as a function of We for flat glass~C!,stainless steel~▫!, Plexiglas~L!, and nonwetting glass~n! surfaces atu 5 0 deg andd 5 1 mm ~open!,1.5 mm~black!, and 2 mm~gray! symbols.



Figure 16 showsxd versus We for the flat~▫! andR5 5-m curved Plexiglas~C! surfaces atu 5 0 deg andd 5 1 mm ~open!, 1.5 mm ~black!, and 2 mm~gray!symbols. As expected, surface curvature stabilizes thefilm, delaying detachment and increasingxd by as muchas 50%. Figure 17 showsxd versus We for the curvedPlexiglas surface ford 5 1 mm ~open!, 1.5 mm~black!,and 2 mm~gray! symbols atu 5 0 deg~L!, 10 deg~▫!,and 308 ~n!. As seen in Fig. 15 for the flat surfaces,xd

increases withu for a given We.Figure 18 shows the normalized average detachment

distancexd0d plotted as a function of Froude number Frfor the flat glass~C!, stainless steel~▫!, Plexiglas~L!,and nonwetting glass~n! surfaces atu 5 0 deg andd 51 mm~open!, 1.5 mm~black!, and 2 mm~gray! symbols.The normalized detachment distance increases approxi-mately linearly with Fr. As seen in Fig. 14, detachmentoccurs much closer to the nozzle~i.e., smallerxd! for

the relatively nonwetting~i.e., higheraLS! surfaces—Plexiglas and nonwetting glass. Edge effects due to noz-zle geometry~characterized byd for a constant nozzleydimension! appear to have almost no impact on the non-wetting glass surface data~n!, probably because thissurface “pins” the lateral edges, and hence fixes theyextent, of the flow~see discussion of Fig. 19!. The dataalso show thatxd0d increases asd decreases for all thevalues ofu studied. We hypothesize that this is due to areduction in edge effects asd decreases~for a constantnozzley extent! so that the flow would become more“two-dimensional.”

Fig. 15. Plot ofxd versus We for~a! flat glass and~b! nonwet-ting glass surfaces atu 5 0 deg~L!, 30 deg~n!, and45 deg~C! andd 51 mm~open!, 1.5 mm~black!, and2 mm ~gray! symbols.

Fig. 16. Graph ofxd as a function of We for flat~▫! and curvedPlexiglas~C! surfaces atu 5 0 deg andd 5 1 mm~open!, 1.5 mm~black!, and 2 mm~gray! symbols.

Fig. 17. Plot ofxd versus We for the curved Plexiglas surfaceat u 5 0 deg ~L!, 10 deg~▫!, and 30 deg~n! ford 5 1 mm ~open!, 1.5 mm~black!, and 2 mm~gray!symbols.



Since these data atu 5 0 deg have the smallestdetachment lengths, the most conservative estimatefor detachment length is then given by the solid line inFig. 18, or

~xd 0d!min 5 11.56Fr2 16.1 . ~12!

Equation~12! can be used by designers to predict theminimum spacing for injection slots for the forced filmconcept over both wetting and nonwetting surfaces.

The estimated errors inxd0d are 5, 6.8, and 10% ford 5 2, 1.5, and 1 mm, respectively. The major source oferror in these data is slight misalignments between thenozzle and the surface, along with variations in the initialfilm thicknessd due to fabrication tolerances. The max-imum misalignment between they axis of the nozzle andthe surface of the glass plate is 0.4 deg, resulting in aheight difference of 0.4 mm, or 0.2 to 0.4d, across the5-cmy extent of the nozzle exit. The minimum geometrictolerance for the nozzles, based upon the spatial resolu-tion of the rapid prototyping machine used to fabricatethem, is 0.1 mm absolute, or 5 to 10% ofd. The resultantvariation in initial film thickness over they extent of thenozzle with respect to the glass surface due to these twofactors can affect detachment distance and film width byintroducing local variations in pressure gradient and flowspeeds. We expect that errors due to local variations inthe wettability of the various plate surfaces due to sur-face and water contamination are minimal since littlevariation was observed in either mean detachment lengthor film width over independent experimental runs underotherwise identical conditions.

Finally, Fig. 19 compares the average lateral~ y! ex-tent of the film normalized by its initial extentW0Wo asa function of normalized downstream distancex0d forthe wetting~gray symbols! and nonwetting~black sym-bols! surfaces atu 5 0 deg andd 5 2 mm for We5 100~C! and 1540~▫!. The error inW0Wo is estimated to be62% in all cases. The nonwetting surface has negligiblelateral spread and contracts much more rapidly than thewetting surface. The nonwetting surface appears to fix,or “pin,” the contact line for the film flow at the edges ofthe nozzle, thereby preventing the marked lateral growthof the flow observed for the wetting case. Numericalsimulations of a three-dimensional wall jet, a flow sim-ilar to the forced film except that the injected and ambi-ent fluids are identical, indicate that the remarkable lateralspread of these flows is due to the flow creating signifi-cant streamwise vorticity.30 The lack of lateral spread forthe nonwetting surface is therefore likely correlated to adecrease in streamwise vorticity in this flow.

The flow parameters proposed in Prometheus for theforced film over the upper part of the hemispherical endcap~whereu 5 0 to 45 deg! were We5 5900 to 190 000and Fr5 100 to 680, versus the flow parameters rangestudied here of We5 100 to 3200 and Fr5 15 to 121.Moreover, the liquid lead films are nonwetting~i.e., havea contact angle of 90 deg! on the SiC walls proposed forPrometheus. These experimental data are therefore validfor the lower-speed~i.e., less turbulent! forced film cases,with the nonwetting glass and Plexiglas results beingmost relevant to the Prometheus design.

Equation~12!, which gives a conservative estimateof film detachment over wetting or nonwetting surfaces,

Fig. 18. Graph ofxd0d as a function of Fr for flat glass~C!,stainless steel~▫!, Plexiglas~L!, and nonwetting glass~n! surfaces atu 5 0 deg andd 5 1 mm ~open!,1.5 mm~black!, and 2 mm~gray! symbols. The solidline, given by Eq.~12!, represents the lower bound onall these data obtained using a linear regression curve-fit.

Fig. 19. Nondimensional film widthW0Wo as a function ofnormalized downstream distancex0d for the wetting~gray! and nonwetting~black! symbols surfaces atu 5 0 deg andd 5 2 mm for We5 100 ~C! and 1540~▫!.



suggests that the film may detach as soon as 0.46 mdownstream of the injection slot~at Fr5 100 andd 50.5 mm!. The upper end cap has a colatitudinal extent of7.85 m. Although surface curvature may increase thisvalue by as much as 50%, these results—and the exces-sive flow velocities required to reestablish the forcedfilm between shots for a single injection slot—suggestthat multiple injection slots~with corresponding regionsdownstream to remove the film fluid before it detaches!will be required to provide robust and complete cover-age. The inner surface of the reactor chamber upper endcap may consist of several “tiles,” or modular filminjection0removal units. Moreover, the greater lateral con-traction of these flows implies that injection slots musthave significantly smaller longitudinal and colatitudinalspacing for nonwetting~versus wetting! surfaces. Bothresults indicate that forced film flows over curved wet-ting surfaces—which may require considering either al-ternative candidate coolant or first wall materials~orcoating the SiC to create a wetting surface for liquid lead,as suggested in the Prometheus study!—with their markedlateral spread and greater detachment length, may besignificantly more advantageous for IFE reactor chambers.

III.D. Cylindrical Dams

Our experimental results for cylindrical dams to pro-tect the beam ports showed that they were not compatiblewith the forced film concept. In all the cases studied here,the film either detached from either the flat glass or curvedPlexiglas surface at the leading~upstream! edge~Fig. 20top! or from the inside trailing edge of the obstruction~Fig. 20 center! and created a spray of drops falling intothe “reactor cavity.” In some cases, the film flowedsmoothly over the entire obstruction, thus blocking theport ~Fig. 20 bottom!. Obviously, these are all unaccept-able outcomes for effective forced film protection since aviable protective dam geometry requires that the filmflow smoothly around~versus over! the dam, recoversome distance downstream, and remain attached to thesurface.

The APEX study has numerically simulated hydro-dynamically shaped penetrations and backwall modifi-cations to ensure that the film flow closes downstream ofvarious penetration geometries.10 We are therefore start-ing experiments on forced film flows around both stream-lined dams and a scaled model of one of the ellipticalpenetrations with a linearly sloped and recessed back-wall considered in the APEX study. This work will ex-tend the results of the APEX study to film flows overshaped penetrations and backwalls with liquid-surfacecontact angles exceeding 0 deg.

These results suggest that designing penetration andbackwall geometries that minimize disturbances to forcedfilm flows may present a significant challenge to design-ers of IFE chambers utilizing the forced thin film wallprotection concept. Alternatively, the driver beam array

may be designed to avoid the reactor chamber upper endcap~difficult given the large number of beams in currentIFE designs!.

IV. CONCLUSIONS

Over the last two years, numerical and experimentalstudies have been conducted on two types of thin liquidfilm protection, namely, the wetted wall and forced filmconcepts, as part of the ARIES-IFE study. These detailedinvestigations of the fluid dynamics aspects of these twoconcepts for protecting IFE reactor chamber first wallshave identified several of the important design param-eters for these concepts and identified the “design win-dows” for successful implementation of these concepts.

A numerical investigation has been performed to an-alyze the fluid dynamics aspects of the porous wettedwall protection scheme for IFE reactor first walls, focus-ing upon drop formation and detachment. The numericalresults are in good agreement with initial experimentalresults. The model extends earlier work on the Rayleigh-Taylor instability by including the effect of a boundingwall through which the heavier fluid is continuously in-jected with mass transfer~evaporation0condensation! atthe interface between the liquid film and chamber “gas.”The results suggest that the stability of the liquid film

1. imposes a lower bound on the repetition rate inorder to avoid liquid “dripping” into the reactorcavity between shots~Fig. 7!

2. imposes a lower bound on the liquid injectionvelocity in order to maintain the film thicknessover the entire surface above some given mini-mum value to assure adequate wall protection fromsubsequent shots~Fig. 9!.

The generalized charts presented in Figs. 7 and 9 make itpossible for system designers to establish “design win-dows” for successful implementation of the wetted wallprotection scheme with various coolants under a varietyof operating conditions.

Experimental studies have been conducted on thehydrodynamics aspects of the forced film protectionscheme for IFE reactor first walls, focusing upon filmdetachment, film lateral growth, and film flow aroundprotective dams surrounding chamber penetrations typi-cal of beam ports. The data confirm that surface wetta-bility has a major impact upon the flow: The film detachesmore closely to the injection point and has much lesslateral growth over a nonwetting surface compared witha wetting surface. The experimental data are used to ob-tain a bounding relation@Eq. ~12!# for conservative esti-mates of detachment length suitable for design purposes.The results imply the following:

1. Awetting chamber first wall surface is much moredesirable from a design perspective, requiring far fewerinjection slots than a nonwetting surface.



Fig. 20. Typical images of film detachment and spray formation at the cylindrical dam leading edge ford 5 1.5 mm, We5 530,andt 5 2.36 mm@top image#; film detachment and spray formation at the inner trailing edge for a similar case except thatWe5 200@center image#; smooth film flow over the entire dam ford 51 mm, We5 200,t 5 0.51 mm@bottom image# .In all cases,d 5 25.4 mm. These images are obtained from below the glass plate looking upward.



2. Cylindrical protective dams around chamber pen-etrations for beam or target injection appear to be incom-patible with effective forced film protection.

Currently, experimental studies of various dam shapes~including those considered by the APEX study10! arebeing conducted to determine if there exist viable alter-native protective dam geometries to shield the beam portswhere the film separates around the dam and then recov-ers downstream of the dam, while remaining attached tothe surface.

ACKNOWLEDGMENTS

This research would not have been possible without thecontributions of the other members of the Georgia Institute ofTechnology Fusion Engineering Group: F. F. Abdelall, J. K.Anderson, D. Juric, D. L. Sadowski, B. Shellabarger, and S.Shin. We wish to thank the ARIES-IFE Team for their sugges-tions and the U.S. Department of Energy Office of FusionEnergy Sciences for its support of this work through contractDE-FG02-01ER54656.

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