EVOLVE Lithium Tray Thermal-Hydraulic Analysis

Mark AndersonJohn Murphy

Mohamed SawanIgor SviatoslavskyMichael Corradini

Fusion Technology InstituteThe University of Wisconsin

Siegfried Malang

Forschungszentrum Karlsruhe GmbHKarlsruhe, Germany

APEX Project MeetingNovember 16, 2000

Overview• Scenarios for boiling/evaporation process

• No MHD effect, normal boiling in stagnant pool

• Preliminary boiling vibration estimate

• Moderate MHD effect, channels produced (Malang concept)

• Large MHD effect (?), boiling severely affected

• Review proposed experiments to determine boiling curve (onset andflow visualization)

Pool Boiling No MHD Effect• Divide trays into “cells” and predict vapor fraction distribution in each cell

• Cell sizing calculation ( Taylor length scale, ~ 10 cm, 5 X 5 nodalization)

• Uniform vapor fraction distribution of 17% used for first estimate of heating

• Use energy deposited in Li pool and W wall to determine the vaporization rate

• Lithium vaporized used to determine volumetric vapor flux (jg) and thesuperficial gas velocity (Jg)

• Drift-flux model used, vapor fractions are driven by Li vapor density and bynuclear heat loads applied to the Li and W

• Vapor fraction must be matched with heating (iteration necessary)

• Once the vapor fraction distribution is finalized, nuclear performanceparameters will be updated, and the iteration continued (final vapor fractiondistribution on next page)

Pool Boiling No MHD Effect (continued)

• Final cell vapor fractions

0.52

0.56

0.60

0.64

0 5 10 15 20 Cell Depth (cm)

Vap

or F

ract

ion

Cell 1Cell 2Cell 3Cell 4Cell 5

Pool Boiling No MHD Effect (continued)

• “Void Distribution in Boiling Pools with Internal HeatGeneration”, Kazimi & Chen, (LMFBR core accidentswith molten fuel pools forming)

• Analytical expressions proposed

• Bubbly flow

α = 1- exp[-GY/(λρvBVinf)]

• Churn-turbulent flow

α = 1-1/[1+2GY/(λρvVinf)]1/2

Pool Boiling No MHD Effect (continued)

• Kazimi and Chen’s models are consistent with our drift-flux model (Casas and Corradini)

0.00.10.20.30.40.50.60.70.80.91.0

0 10 20

Cell Depth (cm)

Vap

or

Fra

ctio

n

Vapor Fraction(Kazimi non drift-flux)Vapor Fraction(Kazimi drift-flux)

Vapor Fraction(Corradini/Casasdrift-flux)

Pool Boiling No MHD Effect (continued)

• Vapor fractions appear to be significant (can be reduced by increasingoperating pressure and associated temperature)

• Vapor fractions in excess of 50% could be observed

0

0.1

0.2

0.30.4

0.5

0.6

0.7

0 10 20

Cell Depth (cm)

Vap

or

Fra

ctio

n (d

rift

-flu

x)

[1200 C, 0.037MPa][1300 C, 0.084MPa][1400 C, 0.169MPa][1500 C, 0.314MPa]

Preliminary Dynamic Response to Boiling

• Vapor fractions in excess of 50% could be observed• Natural frequency of beam/tray determined with and without lithium• If the tray is isolated on both ends the natural frequency is about 475

Hz, and may be as low as 423 Hz if the mass of lithium is includedwith the Tungsten beam

ωnatural=22.37[EI/(ml4)]1/2 (“Theory of Vibration”, Thomson)

• Estimating the boiling frequency from boiling mercury experiments(“Nucleate pool boiling of mercury in the presence of a magnetic field”,Lykoudis, 1998)¨ ωboiling= ~ 45 Hz– Using heat flux at Tungsten wall and comparing to mercury experiments

• Boiling frequency is a factor of 10 below the natural frequency of thetray

• This implies a static loading and minimal dynamics

Moderate MHD Effect

• Alternative boiling flow regime proposed by S. Malang (FzK)– MHD effects could hold channels open with minimal liquid lithium

movement with smaller vapor fractions and stable channels

– Moderate interaction where magnetic field dampens bulk liquid lithiummovement but does not affect nucleate boiling process

• Channels initiated at preferred nucleation sites and spaced as needed for heatremoval

• Potential for smaller vapor fractions with stable liquid/vapor channels

H

D _cell

D _channel

Schem atic of vapor channels (side view )

Liquid L ithium

N ucleation site

Vapor evaporation

Schem atic of vapor channels(top view )

D _channel D _cell

Moderate MHD Effect (continued)

• Conduction heat transfer analysis and liquid superheat woulddetermine maximum spacing of channels– To avoid liquid nucleation channels could be spaced ~ 8 cm apart (200K

superheat)

• Mass, pressure and energy balances are combined to determine vaporflow geometry and spacing– Balancing static head of liquid lithium with kinetic force from vapor,

frictional force from vapor and magnetic pressure drop of liquid lithium inchannel

∆P(static liquid head) = ∆P(kinetic) + ∆P(friction) + ∆P(magnetic)

l( ) gP static Hρ∆ =2

( )2

vvP kinetic

ρ∆ =

2( ) 0.03 ( )v HP friction vDρ∆ = 2( ) ( )2l LP magnetic vBσ∆ =

Moderate MHD Effect (continued)

• Parametric analyses performed to illustrate the effect of cell size onvapor channel size, and vapor fraction

0.0000.0020.0040.0060.0080.0100.0120.0140.0160.0180.020

0.00 0.03 0.06

Cell Diameter (m)

Ch

ann

el D

iam

eter

(m)

MHD Calcwith DchannelMHD Calcwith Dcell

Moderate MHD Effect (continued)

• Cell vapor fraction versus cell diameter

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.00 0.03 0.06

Cell Diameter (m)

Cel

l Vap

or

Fra

ctio

n

MHD Calc withDchannelMHD Calc withDcell

Large MHD Effects

• It is possible that MHD has a large effect on liquid metalboiling: bubble size and frequency ( Lykoudis et al. Int. J.Heat Mass Transfer 41 (1998) 3491-3500

• If this is confirmed for large magnetic fields (>> 1 T)boiling could be severely affected

• Current judgement is that this is not the case, but it must beexperimentally confirmed by boiling flow regimevisualization experiments

• These experiments are also needed to confirm the expectedflow regime with moderate MHD forces

• According to previous work and the current state ofknowledge regarding pool boiling of liquid metals in thepresence of a magnetic field, experiments are required toaccompany further analysis– Determine the onset of nucleate boiling and its characteristics for a

conductive fluid (lithium) at different magnetic field strengths toquantify the suppression of boiling

– Real-time visualization of flow patterns developed when boiling isachieved in the liquid metal as a function of magnetic fieldstrength

– Develop a physical model explaining the effects of the magneticfield for onset of boiling for liquid metals and boiling flow regime.This will allow us to determine the boiling rate and heat transferfor a given volumetric heat flux and will lead to the required depthof the pool needed to balance heat generation and heat removal