Concept Description and Thermalhydraulics of Liquid Surface FW/Blankets for High Power Density Reactors

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1 Concept Description and Termalydraulics of Liquid Surface FW/Blankets for Hig Power Density Reactors A. Ying, N. Morley, K. Gulec, B. Nelson (1), M. Youssef, and M. Abdou Mecanical and Aerospace Engineering Department, UCLA 45 Hilgard Avenue Los Angeles, CA ABSTRACT Te attractive features and scientific callenges offered by te liquid wall systems render tem strong candidates for investigation in te APEX project[1]. In particular, teir ig power density capabilities make te fusion reactors economically competitive. In tis paper, as part of evolving a practical design based on tis evolutionary idea, issues concerning termalydraulics of liquid surface first wall/blankets were analyzed. Design approaces as presently envisioned include bot liquid films over te solid surface and gravity driven tick liquid jets using litium and flibe as working fluids. Te analyses involved defining liquid systems operating conditions, suc as velocity and inlet/outlet temperatures, as well as to calculate free surface temperature so tat te evaporation rate from te free surface would not jeopardize plasma operation wile maintaining te liquid temperature witin te operating windows for ig termal efficiencies. All analyses were performed for a neutron wall load of 1 MW/m and its corresponding surface eat flux of MW/m. Te results indicated tat ig velocities, ard x-ray spectra and turbulent eat transfer enancement were necessary conditions for keeping flibe first wall temperature low. On te oter and, at velocities of m/s or iger, it appears possible to maintain litium film evaporation rate below 1 #/m s in an ARIES-RS type configuration. Neverteless, present analyses ave not uncovered any basic flaws or major sortcomings in te underlying scientific or tecnical arguments for te concepts. Yet, engineering innovations of ow to maintain and control te flow and te associated analyses are still needed. INTRODUCTION Free liquid surfaces appear to be suitable for andling te ig neutron wall load and ig surface eat flux in future ig power density fusion reactors. Te general liquid wall approac as some very obvious attractive features including te reduction of radiation effect in structural material, te elimination (or reduction) of FW termal stresses, te elimination of tick plasma facing armor materials, and a possibly significant reduction of (1) Oak Ridge National Laboratory Oak Ridge, TN te replacement time. Design ideas as presently envisioned for magnetic fusion devices include bot fast moving, tin liquid films flowing over te FW solid surface, and tick liquid jets acting as bot FW and blanket flow. Te tick liquid wall concept was first proposed for an FRC device in te late 196s, were te plasma volume were surrounded by a 75cm tick, free surface litium blanket flowing at m/s []. Te concept was recently extended to a tokamak configuration in wic a slug flow, straigt troug inboard and two counter rotating outboard sections were introduced []. In contrast to tat te jet flows witout any structure or container, te liquid film aderes to te surface by te centrifugal force. Te FW liquid is injected into te vacuum camber at a rate great enoug to actively convect away surface eat and initial ig intensity neutron energy deposition. Te liquid could ten be used as a free surface divertor and recirculated as coolant troug te blanket to eat it to efficient power conversion temperatures as sown in Figure 1. Te amount of ot liquid in te vacuum environment raises concerns regarding plasma contamination by evaporated liquids. Tere are also fundamental questions regarding te adaptation of liquid flows to te topological constraints of toroidal plasma devices including penetrations. MHD issues will need to be investigated in order to validate te possibility tat suc films can indeed be created and sustained along teir required flow lengt wen te fluid is an electrical conductor. In tis paper, termalydraulics aspects of te flow caracteristics and te associated ydrodynamic stability issues as well as of te eat transfer capabilities are analyzed for bot litium and flibe as working liquid. Flibe is te favored liquid from te viewpoints of te sielding, pumping and safety caracteristics. However, litium is a low Z material and may be more compatible wit plasma operation. Utilization of litium will ave to deal wit te MHD effects, not just in te surface flows, but in supply lines and feed systems, and so may still require electrical insulating coatings. It is believed tat an understanding of te basic termal-ydrauilcs

2 performance of te free surface liquid flows is imperative for te ultimate development of a practical design. ( V ) d θ = (continuity) dθ Vθ 1 dp = + g cosθ (r - mom) R ρ dr Vθ dvθ 1 dp = + g sinθ R dθ ρr dθ F friction ( θ - mom) (1) () () Te conservation equations can be manipulated into te following form by making te assumption tat te film is tin (/R << 1). V θ = q o p( R, θ ) = ( V R gρ cosθ ) d Rg sinθ + R F = dθ g cosθ + q o friction (4) (5) (6) Te equations can ten be solved to produce profiles of V θ, and p as a function of location on te arc. Te quantity p is an indicator of te aderence of te film, and is always positive for attaced flows. Te equilibrium eigt can be determined by setting te numerator of te equation for equal to zero. Tis is te point were friction balances gravitational acceleration. Te equations are tus very sensitive to te definition of te friction term. Vθ θ r wall R Figure 1 Scematic View of Convective Liquid Wall Design THIN FILM FLOWS W/O MHD EFFECTS One of te difficulties involving te use of free surface films for fusion reactors relates to te flow on a concave surface. To ensure a compact flow trajectory along te plasma contour lines and yet not to interfere wit plasma operation, te flow as to carry adequate centrifugal inertia against te gravity, friction and MHD forces. Te ydraulics of a tin flow on a typical plasma topological surface is predicted using te simplified conservation equations for mass and momentum in cylindrical coordinates (see figure ). liquid film Figure Simplified cylindrical geometry for ydraulics calculations of tin films Te appropriate friction term is determined by te type of flow. For an electrical semi-conductor like flibe, te flow is turbulent and te friction is estimated from te

3 Darcy-Weisbac formula applied to open cannels using te appropriate friction factor, f F friction = fq 8 For an electrical conductor like litium, te flow is most likely laminarized, depending on te flow velocity, and te friction is estimated using te fully-developed Hartmann flow profile to determine te sear at any sidewalls (due to te toroidal field) and te back plate (due to any radial field component). F friction BT = w B + σν R q o ρ It sould be noted tat tis formula assumes te all wall to be electrically insulated from te flow, and tat electrical currents beave as in fully-developed flows. Developing MHD flows will require a muc more sopisticated treatment tan tat given ere. In te event tat eiter of tese terms are smaller tan te parabolic velocity profile sear stress (e.g. B R ), ten te parabolic sear stress is applied instead. F friction ν q = o Hydraulic calculations indicate tat flow dept equilibria in te range of cm can be acieved for bot litium and flibe flows at teir respective speeds (see figures and 4). A ticker/faster film leads to a ig volumetric flow Film Dept, ff =.17 Film Velocity, ff =.17 Film Dept, ff =.1 Film Velocity, ff = Flow Lengt (m) Figure : Flow Profiles for Flibe film on an 8 m arc cylindrical surface (θ = 45 to 15 ). Te friction factors of.17 and.1 are used for smoot and roug surfaces, respectively. (7) (8) (9) rate inside te camber in wic a large pumping power is needed to drive te flow. Te dept equilibrium for te turbulent flibe flow is not extremely sensitive to te exact value of te friction factor. A 5% increase in te smoot pipe friction factor, wic is likely due to Taylor- Gortler boundary layer instabilities resulting from flow on a curved plate, does not significantly cange te ydraulic results. Te flow is still very near te inlet conditions in tis case. Te litium flow, owever, is sensitive to te selection of te strengt and orientation of te magnetic field. Te presence of a small radial field component, B R =.5 T, causes a significant reduction in te velocity of te film flow over te 8 m flow lengt. Te slower/ticker litium flow will remain in contact wit te plasma for a longer time tan desired, and te surface temperature rise may be too ig Film Dept, Br = T Film Velocity, Br = T Film Dept, Br =.5 T Film Velocity, Br =.5 T Flow Lengt (m) Figure 4 Flow Profiles for Litium films on an 8 m arc cylindrical surface (θ = 45 to 15 ). Litium flow as a 7 T tordoidal field, a widt of 1 m, and sows significant retarding effect of a relatively small radial field normal to te surface. THERMAL ANALYSIS OF THE FW LIQUID SURFACES A key issue of liquid first walls is weter or not te evaporated liquid can be removed witout critically contaminating te plasma. Tis quantity is generally proportional to te amount of vapor evaporated out of te first wall surface wic is a function of liquid surface temperature. Witout detailed edge plasma calculations, te simplest way to answer tis question is to examine wat magnitudes of te liquid FW surface temperatures can be acieved under te specified eat load conditions.

4 Te temperature profile of te liquid FW is calculated using a tree-dimensional finite difference eat transfer code for a combined surface eat load of MW/m and neutron wall load of 1 MW/m. Te code takes te velocity profile as an input parameter and solves te energy equation: T T T ρcp Vx + Vy + Vz = k T + q x y z (1) Te volumetric eating due to bot neutron and x-ray interactions are accounted in te source term, q. Details of te neutronics analysis are included in paper in ref. [4]. In cases were x-ray penetration is insignificant, te surface eat flux is accounted for as a boundary condition. To adequately simulate te sarp eat deposition gradient, finer meses are required in te first 1 cm of te liquid wall close to te plasma side. Te surface and bulk temperature distributions as fluids proceed downstream are sown in Figures 5 and 6 for litium and flibe slug jets, respectively; wile temperature profiles into te jets at about. m downstream are sown in Figure 7. As sown, accounting for x-ray penetration significantly reduces te jet surface temperature, particularly in te case were 64 6 Surface eating Hard Bremsstralung radiation spectrum Bulk temperature Temperature (K) Flibe surface is exposed to a ard Bremsstralung radiation spectrum (for example as te case sown: a classical Bremsstralung radiation spectrum corresponding to an average T e of 1 KeV). Neverteless, most of te Bremsstralung radiation is deposited witin te 1 st cm of te jet. Furtermore, being a low termal-conductivitymedium, te amount of eat conducted into te jet is insignificant wic results in a muc sarper temperature gradient across te flibe jet as compared to tat of litium jet [Figure 7]. Te peak surface temperatures as sown for 1 cm tick litium and Flibe jets under te ard Bremsstralung radiation eating for te coolant velocity of m/s are 7 and 74 C, respectively. Te corresponding evaporation rates for te aforementioned temperatures are 1 19 and 1 atoms/m s, respectively. Te maximum litium surface temperature increases to 75 C if litium flows at a lower velocity of 1 m/s Surface eating Hard Bremsstralung radiation eating Bulk temperature Flibe Surface Temperature Temperature (k) Litium surface temperature Distance away from te inlet (m) Figure 6 Flibe jet surface and bulk temperatures as jet proceeds downstream (For a surface eat load = MW/m combined wit a neutron wall load = 1 MW/m and jet velocity = m/s) Distance away from te inlet (m) Figure 5 Litium jet surface and bulk temperatures as jet proceeds downstream (For a surface eat load of MW/m combined wit a neutron wall load of 1 MW/m and jet velocity = m/s) For te preceding cm Flibe film flowing at 1 m/s, te maximum surface temperature exposed to a ard Bremsstralung radiation of te same eating condition reaces 86 C wit an average exit temperature of 54 C wic is about 19 C iger tan te inlet temperature. Tese results indicate tat some amount of eat transfer enancement is needed to reduce te flibe FW surface temperature. Since te jet is igly turbulent, te existences of eddies/pockets are expected to elp acieve tis goal.

5 Local Temp. - Inlet Temp. (K) Li jet wit surface eating Li jet wit ard Bremsstralung radiation eating Flibe jet wit surface eating Flibe jet wit ard Breemsstralung radiation eating Li: Hig termal conductivity Distance into te jet (m) Flibe: Low termal conductivity Figure 7 Temperature increases inside te jets at about m downstream under different eating conditions (jet velocity = m/s, 1 cm tick jet) LIQUID BLANKET DESIGN: GRVITY-DRIVEN JETS Beind te first wall, te simplest way to form a tick liquid is to drive te liquid jet using gravity force in contrast wit te mecanical force driven rotating flow as proposed in [5]. Suc a type of jet flow is modeled wit RIPPLE; a -D, incompressible, free-surface, transient computer code developed at LANL including surface tension effects. Te RIPPLE solution of Figure 8 sows tat free tick liquid jet tends to be tinned due to te acceleration of gravity. More specifically, te jet tickness is rapidly reduced from 1 cm to cm and stays at around cm for te bottom part of te plasma core if te jet is injected at 1 m/s (Figure 9). Te jet tinning effect can be overcome by increasing te initial jet velocity; and a uniform tick liquid jet can be obtained trougout te plasma core if te jet is injected at 7 m/s or above. However, wit te flow rate increases te pumping power increases even more significantly as sown in Figure 1. Te tinning reduces liquid s potential for radiation protection of solid first walls beind te liquid. Furtermore, te ig eat capacity of te liquid results in an unnoticeable temperature rise of less tan C even severely eated by a neutron wall load of 1 MW/m. Altoug a fairly uniform liquid temperature could be a favorable condition for te termal cycle, te blanket liquid needs to operate at ig temperatures to acieve a ig termal conversion efficiency. Tis implies tat a tick liquid wall concept would comprise Figure 8 RIPPLE result of Flibe slab jet configurtion wit initial jet velocity and tickness of.5 m/s and 1 cm, respectively(travelling distance = m, final jet tickness= cm) multiple slab jets including a ig-speed jet facing te plasma aving a lowest surface temperature to avoid jeopardizing plasma operation. It is conceivable tat, to combat tinning and acieve an appreciable amount of radiation sielding, one could recirculate and subsequently re-inject te fluid at different vertical eigts/radial positions. To te extent of aving te lifetime structure beind te liquid, a tick liquid wall approac could involve te use of flow reflectors to elp restrain te liquid inside a pocket structure. Te fast moving jet in front of te pocket provides resistive forces for preventing te liquid entering te plasma core. Te fluid temperature inside te pocket is maintained by continuously circulating a small amount of liquid in and out of te pocket. Tese specially designed reflectors tat protect te liquid entering te Jet tickness (m) Initial jet velocity 1 m/s m/s 5 m/s 7 m/s Distance away from inlet (m) Figure 9 Flibe Jet tickness reduces as jet proceeds downstream due to te gravitational force

6 plasma core ave to be periodically replaced. More analyses are planned to elp proceed wit a realistic design based on tis approac. Pumping power (MW) Initial jet tickness.15 m.1 m.5 m.5 m 5 MW = 1% termal power Initial jet velocity (m/s) Figure 1 Pumping power requirement increases significantly for ig speed tick Flibe blanket jets HYDRODYNAMICS STABILITY OF FLIBE FW FILM Te fluid dynamic beavior of te liquid first-wall system is an important issue in addressing te feasibility of te liquid first wall concepts. Te stability of te liquid first wall sould be maintained for efficient eat extraction from ig neutron and surface eat loads wile satisfying safe and reliable operation for te fusion power system. It sould be noted tat te stability of te liquid first wall is not only effected by liquid first wall operation and geometry parameters but also by te existence of te components in te liquid first wall system suc as flow straigtener, contraction nozzle, back plate geometry and drain system. Te mecanisms affecting te dynamic beavior of te liquid first-wall over a concave surface may be related to: (a) Taylor-Gortler vorticity formations in te liquid first wall boundary layer along te concave surface, (b) boundary layer relaxation on te liquid wall surface as it leaves te nozzle exit, (c) ydraulic jump, (d) eddy generation due to ig velocity gradients in te boundary layers along te nozzle inner walls, (e) inviscid searlayer instabilities (Kelvin-Helmoltz). Considering te neutron wall loading, carged particle and radiation energy deposition in te liquid first wall, te dynamic beavior of te first wall may furter be affected by: (f) stratification (Rayleig-Taylor), (g) carged particle liquid first wall momentum interaction () termal relaxation of te liquid first wall. Te mecanisms stated ere may introduce or enance te turbulence in te firstwall flow and at its free surface. An increase in te turbulence intensity at te free surface may increase convective eat transfer rate. Tis condition may decrease te required minimum liquid wall velocity so tat uniform and more eat deposition in te first wall can be assured wile maintaining te evaporation rate witin te constraint limits [6]. Terefore, any of tose mecanism sould not be eliminated unless it destabilizes te first wall flow completely or increases mass loss in te first wall due to evaporation or splasing. A case wit a first wall operating condition of 1 m/s average velocity,. m of tickness flowing over a 4 m radius of concave surface is investigated using flibe as a working fluid at an operating temperature of 6 o C Table 1: Operating condition and non-dimensional flow parameter of te case Avg. Vel. m/s Liq. Wall δ(m) Re (1 5 ) Fr= U / (g.δ) Fr* We (1 5 ) (U /R) /g Caracteristic lengt is taken as liquid first wall tickness (δ). As seen in Table 1, te flow regime is expected to be turbulent since Reynolds number (Re) is iger tan. Furtermore, te modified Froude (Fr*) number (ratio of inertia forces to centripetal forces (U /R)) is muc greater tan one. Terefore flow regime is expected to be supercritical (any disturbance on te first wall surface will not propagate upstream) and a ydraulic jump may occur. Hydraulic jump may cause an increase in te first wall tickness. An increase in te first wall tickness results in a smaller modified Froude number. Terefore tere is a stabilizing mecanism for ydraulic jump. Also, tere is a component of gravitational acceleration in te flow direction tat may minimize te possibility of ydraulic jump. But it sould be noted tat any transient cange in te first wall tickness may be a source of perturbation to te liquid first-wall surface. Waves may form on te first wall surface due to te relaxation of te boundary layer leaving te nozzle exit from no-slip boundary condition to free-sear boundary condition [7]. Momentum tickness of te liquid wall on te upper wall of te nozzle is a function of pressure distribution (nozzle contraction ratio, upper wall surface

7 curvature) in te nozzle as well as operating parameters. Momentum tickness of te liquid wall on te upper wall of te nozzle is estimated using nozzle design data developed for FMIT [8]. Surface waves are expected wen te momentum tickness (δ m : m) and Reynolds number based on momentum tickness of te present case (Re δm : 168) is compared to te experimental results obtained by Brennen [9], Hoyt et al. [1] and Hassberger [8]. Te average wavelengts of surface waves is expected to be.1 cm. Te inverse Weber number based on momentum tickness of te boundary layer on te first wall surface (σ/(δ m ρv ): ) is more tan experimentally obtained values 1-4 [11,8] terefore, surface waves are expected to be stable. Te flow field of a boundary layer on a concave wall is unstable wen [11] r ρδ mv δ m µ It sould be noted tat stability mecanism is inviscid and viscosity only damps te motion. Assuming tat liquid flows over a meter of flat surface in te nozzle before it reaces to te concave back plate region, te momentum tickness of te liquid first wall flow system is determined using te momentum tickness relationsip for turbulent boundary layer over a flat plate [1]. Te inequality in te relationsip above is satisfied for te first wall operation parameters and estimated momentum tickness of m. Terefore, Gortler vortices are expected to exist randomly in te turbulent boundary layer. Te average eigt of te vortices for mildly curved back plate is expected to be approximately 5υ/u τ [1] wic corresponds m. CONCLUSIONS (11) Tis paper addressed several fundamental termalydraulics questions tat must be answered before a realistic liquid wall design concept can be drawn. Over a travelling distance of 5 m ARIES-RS type geometric configuration, te ydraulics analyses sowed tat a cm tick film can be maintained at a flibe velocity of 1 m/s. However a iger velocity of m/s is required for litium to overcome additional MHD forces. At te velocity of m/s, te termal analyses sowed tat te liquid surface evaporation rate can be maintained below 1 #/m s for litium flows under a 1 MW/m neutron wall load and its corresponding MW/m surface eat load. However, a arder Bremsstralung radiation eating as opposed to te surface eating in conjunction wit a turbulent eat transfer enancement are te necessities for te Flibe first wall to satisfy te same criterion. If litium is preferred due to its attainable lower surface temperature, MHD pressure drop appears too ig for te liquid films, tus R&D on te electrical insulator coatings is unavoidable. For non-mhd gravity driven jet flows, te fluid tends to contract as flow proceeds downstream due to te gravitational acceleration. As a result, te liquid loses its potential wit respect to te radiation protection. Ideas to combat te effect of tinning were proposed. Yet, te exact configuration of te tick liquid walls is still te subject of te detailed investigation in te near future. Te instability mecanisms investigated in te present study confirm te existence of eat transfer enancement turbulent pockets, wile te film surface is wavy yet stable under te specified operating conditions. Aside from te termalydraulics issues regarding eat transfer into turbulent jets, free turbulent jet flow caracterizations, MHD developing flow and surface stability, tere remains many concerns over plasma contamination by evaporated liquids, tritium flow, radiation damage, etc. Penetrations for pumping, fueling and beams will need to ave a ydrodynamic design so as not to introduce excessive drag. Innovative engineering solutions endorsed by detailed analyses are needed to fully realize te profound advantages of te liquid wall approaces and proceed wit a practically attractive design. NOMENCLATURE B T,R Tordoidal and radial magnetic field components Cp eat capacity D Caracteristic lengt (First wall tickness) (m) Fr Froude number g acceleration of gravity film tickness k termal conductivity p pressure q o flowrate, V θ q eat source R arc radius Re Reynolds number U Average first wall velocity (m/s) u τ Friction velocity (m/s). V velocity V Free stream velocity (m/s). w widt of te module segment We Weber number Greek σ electrical conductivity ν kinematics viscosity ρ density δ FW liquid film tickness

8 δ m Momentum tickness (m) Subscripts r,θ cylindrical coordinates x, y, z Cartesian coordinates ACKNOWLEDGEMENTS Tis work was performed under U.S. Department of Energy Contract DE-FG-88ER515 A8. REFERENCES 1. M. Abdou, APEX Overview, in tese proceedings.. N. C. Cristofilos, Design for a Hig Power- Density Astron Reactor, Journal of Fusion Energy, Vol. 8, Nos. ½, (1989) 97.. R. W. Moir, APEX Presentation, January 1-14, 1998, Los Angeles. 4. M. Youssef, N. Morley, and E. Anter, X-Rays Surface and Volumetric Heat Deposition and Tritium Breeding issues in Liquid-Protected FW in Hig Power Density Devices, in tese proceedings. 5. R. W. Moir, Rotating Liquid Blanket wit No First Wall for Fusion Reactors, Fusion Tecnology, Vol. 15, Mar. (1989) Moir, R.W., Liquid First Walls for Magnetic Fusion Energy Configurations, Nuclear Fusion 7, (1997) Brennen, C. E., `Cavitation and Bubble Dynamics', Oxford University Press, (1995) Hassberger, J. A., Stability of te FMIT Hig Speed, Free Surface Liquid Jet Flowing Along a Curved Back Wall, J. Fluid Mec. 191, (1988) Brennen, C. E., Cavity Surface Wave Patterns and General Appearance, J. Fluid Mec. 44, (197). 1. Hoyt, J.W. and Taylor, J.J., Waves on Water Jets, J. Fluid Mec. 8, (1977) Howard, J. E., On te Stability of te Flow Tin Liquid Litium Flows, Nuc. Science Eng., 69, (1979) Blackwelder R. F., Analogies Between Transitional and Turbulent Boundary Layers, Pys. Fluids, 6, (198) Sclicting, H., Boundary Layer Teory, 1955 Mc Graw Hill Book Co. p. 5.