Progress on Gravity & Momentum Driven Thick Liquid WallConcepts for High Power Density MFE FW/Blanket Designs

Presented by

Alice YingAPEX VUCLA

Nov. 2, 1998

Presentation Outline

1. Considerations for “Idea Conceptualization”

2. Progress on GMD with Pocket Concept

3. Role of Turbulent Heat Transfer in Surface Heat Transport (Flibe)

Flibe GMD with Pocket Design Case Studies(10 MW/m2 neutron wall load, 2 MW/m2 surface heat load)

ARIES –RS reactor parameters/Total fusion power = 5479.75 MW

Case 1 Case 2 Case 3 Case 4 Case 5 Case 6FW thickness (δ, m) 0.01 0.02 0.01 0.02 0.01 0.02Inlet velocity (m/s) 10 10 15 15 20 20

Outlet velocity (m/s) 15.448 15.448 19.116 19.116 23.18 23.18Mass flow rate (kg/s) 13104.2 26233.2 19656.3 39349.8 26208.4 52466.4Desired blanket Tout 650 oC 650 oC 650 oC 650 oC 650 oC 650 oCTotal FW T increase 28.11 C 14.04 C 18.74 C 9.36 C 14.05 C 7.02 C

Total Bk T increase, C 140.56 70.21 93.7 46.806 70.28 35.105FW T inlet, oC 481.33 565.75 537.56 593.834 565.67 607.815Reynolds No. 13148 36453 25042.7 68815 36453 91753.6

Heat transfer coeff. (1) 18926.5 18776 28798.87 24468.84 37550.6 35832.9Heat transfer coeff. (2) 32012.5 26435 45960 43060.8 74776 62910Heat transfer coeff. (3) 15589.17 15589.17 23386.68 23386.68 31164 31164

Τsurface− Τbulk (2), oC 62.475 75.65 43.52 46.45 26.75 31.79

Τsurface− Τbulk(3), oC 128 128 85.52 85.52 64.17 64.17

Tsurface(2), oC 571 655.44 599.8 649.64 606.46 646.68

Tsurface(3), oC 637.44 707.79 641.82 688.74 643.89 679

Hartmann No. (12 T,δ) 12.22 28.788 13.776 32.29 14.4 32.3Re/Ha 1075 1266 1817 2130 2532 2840

FW fluid pumping power 1.31 MW 2.62 MW 4.422 MW 8.85 MW 10.48 MW 20.99 MW(1) Dittus-Boelter heat transfer coefficient for channel turbulent fluid flow(2) and (3) Reynolds analogy h calculated based on the mass transfer coefficients (2) J. Davies for turbuletn restrained jets and (3) M.

Rashidi surface renewal theorey

Temperature Distribution Inside Flibe Blanket Pocket[Cylindrical Outlet Located at the Mid-plane of the Pocket. Suction begins at 5.66 seconds.]

(The hottest spot located below the cylinder outlet.)

Flibe Blanket Pocket Velocity Vector Plots at 4 Time Steps[Cylindrical Outlet Located at the Mid-plane of the Pocket. Suction begins at 5.66 seconds.]

Flibe Blanket Pocket Velocity Vector Plots at 4 Time Steps[ Semi-Cylindrical/Elliptical Outlet Located at the Mid-plane of the Pocket]

Velocity Vector Plot Showing Flow Re-circulation Inside the Pocket[ Semi-Cylindrical/Elliptical Outlet Located at the Mid-plane of the Pocket]

Flibe Blanket Pocket Temperature Distribution Plots at 4 Time Steps[ Semi-Cylindrical/Elliptical Outlet Located at the Mid-plane of the Pocket]

Velocity Vector Plot Showing Flow Re-circulation inside the Blanket PocketElliptical outlet located below the mid-plane of the blanket pocket. The liquid level stays low.

Flibe Temperature Distribution Inside the Blanket PocketElliptical outlet located below the mid-plane of the blanket pocket. The hottest spot is located near

the outlet.

The idea was proposed due to its economical competitive potential

• Advantages

– High wall loadingscapability making highpower density systemsattainable

– High fluence capacityeliminating many of thematerial radiation damageproblems

– Simplified maintenanceincreasing plant systemavailability

Moir’s vision

Questions

How do we form and maintain the liquid?

Plasma-liquid interface stability

“Temperature management”?

Characteristics of Non-Structure Thick Liquid Wall Concepts for Different Confinement Schemes

ARIES-RS ARIES-RS*1 FRC ST BCSS(H2O/SB)

Fusion Power (MW) 2170 5480/16439.2 2072 5470 5000 MWAverage Neutron Wall Load(MW/m 2)

3.96 10/30 30 8.085 5

First Wall Area (m 2) 438.38 438.38 55.26 541 1000Flow Area for 45 cm thick liquid 30 m2 30 m2 3.744 m2 14 m2 NACoolant Velocity (m/s) 10 10 10 10Mass Flow Rate (Kg/s) Flibe 5.89x105 5.89x105 7.35x104 2.748x105 3.6x104

(Kg/s) Dai-Kai‘s Sn-Li 1.877x106 1.877x106 2.343x105 8.762x105

Pumping Power (MW) Flibe 58.89 58.89 7.35 27.48 49.5*2

(MW) Dai-Kai‘s Sn-Li 187.74 187.74 23.43 87.62Temperature Rise (K) Flibe 1.87 4.53/13.6 13.74 9.70 40 (K) Dai-Kai‘s Sn-Li 4.21 10.64/27.52 32.24 22.76*1 Assuming that beta is increased proportionally.*2 Estimated for the whole primary loop system. The pumping power for the in-vessel pressure drop of 0.2 MPa & associated massflow rate is 7.2 MW.*3 Pumping power requirement for recovering the coolant from losing its kinetic energy.

• Huge mass inventories result in low temperature rises- It appears difficult to simultaneouslyachieve low surface temperature and high bulk coolant temperature (for Flibe and Li).

• Pumping power requirements appear reasonable for FRC, ST and the extreme neutron wall loadARIES-RS configurations.

• The difficulty for Flibe (and Li) is how to keep the surface temperature low. The concept oftwo coolant streams was meant to overcome this difficulty particularly for the ARIES-RSconfiguration.

The Pumping Power Requirement Becomes Less a Concern for a High VelocityThick Liquid Wall Concept Under Extreme Neutron Wall Load Conditions

0

100

200

300

400

500

8 10 12 14 16 18 20 22

ARIES-RSSTFRC

(con

serv

ativ

e) P

umpi

ng P

ower

(M

W)

Velocity (m/s)

FRC (30. MW/m2)

Blanket thickness = 45 cm

Bulk Temperature = 650 C Power conversion efficiency = 42%Net efficiency = 40%

ARIES-RS (10 MW/m2)

FRC (10 MW/m2)

ARIES-RS 30 MW/m2)

Flibe

900

950

1000

1050

1100

1150

0 0.01 0.02 0.03 0.04 0.05

Velocity = 10 m/sVelocity = 7.5 m/sVelocity = 5 m/s

Tem

pera

ture

(k)

Distance into the fluid (m)

900

950

1000

1050

1100

1150

1200

1250

0 1 2 3 4 5

Velocity =10 m/sVelocity = 7.5 m/sVelocity = 5 m/s

Sur

face

Tem

pera

ture

(K

)

Distance away from inlet (m)

How low can the “Sn-Li” velocity go without exceeding the maximumallowable surface temperature? And how much pumping power requirement?

0

50

100

150

200

4 6 8 10 12 14 16 18 20

Dai-Kai's Sn-Li at ARIES-RSThick Flibe at FRC

Pum

ping

pow

er r

equi

rem

ent f

or d

eliv

erin

g 45

cm

thic

k liq

uid

(MW

)

Velocity (m/s)

2 % thermal powerARIES-RS (10 MW/m2)

2 % thermal power ARIES-RS (3.96 MW/m2)

2 % thermal power FRC (31 MW/m2)

Derivation of Turbulent Jet Heat Transfer Coefficient Based on Reynolds Analogy

Background: Tremendous experimental and numerical studies have been performed to understandand quantify mass transfer into turbulent jets. Yet, almost no direct work was done in deriving theheat transfer properties.

Approach

A. Long-time constant approach

Numerical simulation takingaccount of turbulent velocitystructures and free surfaceboundaries (will be presented byGuo)

Experimental Study

B. Short-time constant approach

Reynolds Analogy –first cut data needed now for ideaconceptualization

Restrained turbulent jetshowing the surfacedeformations whichmake visible the eddyfluctuations near thesurface.The diameter of the jetleaving the nozzle is1.3 mm.

Reynolds Analogy

Mass transfer: Heat transfer:

Assuming that the eddy diffusivities are approximately equal, we obtain the Reynoldsanalogy given as:

(The expression can be used to predict heat and mass transfer data for fluids which have a Lewis number, whichrelates the thermal and mass diffusivities or α/D, close to unity.)

Mass Transfer Coefficient Based on Eddy Diffusivity (Mass transfer into restrained turbulent jets)

D

l

ED

kYY +

==∂∂

0φ

)(0EEc

hYY +

==∂∂

αρφ

mm

l

cU

h

U

kSt

ρ==*

165

21

21

(Re))()(028.0 WeScD

dkSh l ==

DSc ν=

21

)(2/1

σρd

uWe m=

Mass Transfer Coefficient Derived from the Surface Renewal Phenomena

Non-wavy shear-free interface

where T may be thought of as the mean time between surface renewals, u* the friction velocity.

Flibe

0077.0)( *

21

=wm

l

uU

SckTDkl /=

1 104

2 104

3 104

4 104

5 104

6 104

7 104

8 104

1000

1200

1400

1600

1800

2000

2200

2400

2600

8 10 12 14 16 18 20 22

Hea

t Tra

nsfe

r C

oeffi

cien

t (W

/m2k

)

Re/H

a @12 T

Velocity (m/s)

Dittus-Boelter correlationSurface renewal phenomena

Eddy diffusivity correlation (2 cm jet)Eddy diffusivity correlation (1 cm jet)

Fluid Characteristics of Fast Moving FW Jet and Slow Re-circulation Blanket Pocket Flow (beforepocket is filled)

Fluid Characteristics of Fast Moving FW Jet and Slow Re-circulation Blanket Pocket Flow (afterpocket is filled.)

Flibe Temperature Magnitudes at 1 Second after the Pocket is Filled

Summary

The idea of “GMD with pocket” thick liquid wall was introduced:

- to use Flibe as the liquid breeder while applied to advanced Tokamak configurations- to ensure that the first wall surface temperature can be maintained within the maximum

allowable value while achieving a high exit temperature for a high power conversionefficiency [“temperature management”]

- without using a continuous first wall structure

The concept appears “attractive” if the turbulent heat transfer coefficient approaches that of Dittus-Boelter’s prediction. The optimum design has a 1cm thick fast moving of 20 m/s jet as the first wall.

The pumping power requirements for a 45 cm thick Flibe flowing at 10 m/s appearreasonable for FRC, ST, and high wall load (> 20 MW/m2) tokamaks. However, thetemperature management is somewhat complicated. Innovative ideas are needed to keepthe FW surface temperature low.

Indeed, “Sn-Li” relaxes this “temperature management” requirement due to its lowvapor pressure. However, its high density counteracts this benefit if a thick liquid wallis favored. The “temperature window” for a non-structure-thick-liquid wall design maynot be as big as desired (for high power density tokamaks).