Liquid metal coolants

Janne Wallenius

Reactor Physics, KTH

Outline

Why liquid metals?

Which liquid metal?

Calculation of clad temperatures

Why liquid metals?

In order to achieve a fast spectrum in a power reactor, a coolant with high heat capacity and low moderation power is required

Liquid water or organic coolants are excluded

Liquid metals or gases possible options

Gases need to operate under high pressure

Loss of pressure accident difficult to survive in a fast neutron reactor with passive safety systems only (Generation IV-objective!)

Which liquid metal?

Liquid metal or metal alloy properties

ρ[ kgm3 ] Cp[

JkgK

] k [ Wm K

] σ c [mb]Coolant Tmelt [K] Tboil [K]

Hg 234 630 13600 140 12 107

Na 371 1156 850 1277 68 1.3

Pb 601 2016 10500 147 17 4.4

NaK 260 1058 780 1200 22 5.9

PbBi 399 1943 10200 144 14 3.6

Mercury

+ Liquid at room temperature

+ Experience from operation of Clementine & BR-2

– Very low boiling temperature – high vapour pressure

– High cross section for capture

Sodium

+ High heat capacity

+ High thermal conductivity

+ Low density (low pumping power)

+ Low neutron capture cross section

+ Large body of operational experience

– Solid at room temperature

– Low boiling temperature – risk for boiling

– High chemical reactivity with water

NaK

+ Liquid at room temperature

+ Experience from operation of EBR-I & DFR

– Chemically reactive with water

– Higher vapour pressure than sodium

– Lower boiling temperature than sodium

– Lower thermal conductivity than sodium

DFRDounreay, UK

Lead coolant

+ Lead has a boiling temperature above the clad melting temperature. Coolant boiling no longer an issue.

+ Large density change with temperature permits decay heat removal by natural circulation.

+ Lead is inert with respect to water

– High freezing temperature

– No operational experience

– Lead is highly corrosive above T = 720 K. Optimised steel composition, oxygen control and/or surface treatment is required.

– Coolant flow rate is limited to < 2 m/s by erosion concerns.

Lead-bismuth eutectic (LBE)

+ Lower melting temperature than lead

+ 80 years of operational experience from Soviet submarines

– Activation of 210Po due to neutron capture in 209Bi

– Resources limited (~ 100 reactors)

K745Soviet Union

Choice of liquid metal

Sodium: Proven to work under semi-industrial conditions (Phénix, BN-600)

Lead: May permit reduction of costs for operation & maintenance. Lifetime limits due to corrosion & erosion have to be addressed.

Thermal hydraulics of liquid metals

Lead and sodium have different heat removal performance

Lead velocity limited by erosion

Coolant volume fraction must be larger for same power density

Safety coefficients depend on coolant cross sections and leakage factors.

Calculation of clad temperatures relatively straight forward for liquid metals

Fast neutron reactor geometry

Hexagonal geometry (triangular unit cell) standard choice for fast neutron reactors

Close packing, minimises leakage

In hexagonal geometry, one coolant channel transports heat from half a pin.

Lead cooling suggests larger coolant volume fraction. Square lattice may be applied (BREST, ELSY)

Area

Diameter

Pitch

Methodology

Calculate mass flow corresponding to the desired temperature increase in the coolant.

Applying maximum permitted coolant velocity, find minimum P/D satisfying temperature limits for the cladding:

Calculate axial temperature profile in bulk coolant

Calculate axial dependence of temperature drop in film between clad and bulk coolant

Axial power profile

Axial power distribution in fast reactors well described by cosine function (far away from control rods).

Extrapolation length in sodium: 135% of fuel column height.

Axial peaking factor: ~ 1.26

Extrapolation length in lead:

150% of fuel column height

Axial peaking factor: ~ 1.20

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.60

5

10

15

20

25

30

35Linear power [kW/m]

z [m]

Coolant temperature (hexagonal geometry)

Half the linear power is removed by one coolant channel:

Mass flow is a constant, determined e.g. by density and velocity at the inlet of the coolant channel.

To perform analytical integration, we may approximate Cp with its value at the inlet

T (z) = Tin +

1m

χ(z)2Cp

dz−L /2

z

∫

T (z) = Tin +χave

4ρinVinA Cp1+

sin πzL0

⎛

⎝⎜

⎞

⎠⎟

sin πL2L0

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

�0.4 �0.2 0.0 0.2 0.4650

700

750

800

z �m�

Coolant temperature �K�

Physical properties

The density of liquid lead is one order of magnitude higher than the density of liquid sodium.

The opposite holds for the respective heat capacities

The product of density and heat capacity is ~ 40% higher for lead.

600 700 800 900 1000 11000

2000

4000

6000

8000

10 000

12 000

Temperature [K]

Density [kg/m3]

Lead

Sodium

600 700 800 900 1000 11000

200

400

600

800

1000

1200

1400

Temperature [K]

Heat capacity [J/(kg K)]

Lead

Sodium

Density

Sodium density as function of temperature:

ρNa (T ) =1012 − 0.2205T −1.923×10−5T 2 + 5.637 ×10−9T 3

Lead density as function of temperature:

ρPb (T ) =11367 −1.1944T

Relative expansion of sodium larger than for lead (2.2% for ∆T = 100 K)

Absolute expansion of lead larger than for sodium (120 kg/m3 for ∆T = 100 K)

Velocity limitation

Upper limit for sodium velocity: 7–9 m/s

Limiting phenomenon: mechanical vibration of fuel assembly

Upper limit for lead velocity: 1.8 – 1.9 m/s

Erosion of protective iron oxide film on steel cladding surface

ΔTcool =

QmCp

= QρAvCp

Coolant flow area in lead must be ~ 3 times larger than in sodium to achieve the same heat removal rate!

Coolant channel dimensions

Refence design parameters

Cladding diameter: 8.6 mm

Average linear power: 30 kW/m

Fuel column height: 1.0 m

Sodium velocity: 8.0 m/s

Hexagonal geometry

∆TNa = 100 K -> P/D = 1.20

Lead velocity: 1.75 m/s

∆TPb= 100 K -> P/D = 1.62

Area

Diameter

Pitch

�0.4 �0.2 0.0 0.2 0.4650

700

750

800

z �m�

Coolant temperature �K�

Clad temperature

Heat transfer from fuel clad to bulk coolant leads to temperature difference:

h (Tsurf −Tcool ) =χ(z)πD

The heat transfer coefficient depends on thermal conductivity of coolant, on the dimensionless Nusselt number and on the so called hydraulic diameter:

h = Nu × kDh

Dh =4APwet

Pwet =12πD

Dh

Physical properties

Thermal conductivity of sodium larger than for lead

700 800 900 1000 1100 12000

20

40

60

80

T[K]

Sodium

Lead

Thermal conductivity [W/(m K)]

kNa (T ) =109.7 − 0.0645T +1.173×10−5T 2

700 800 900 1000 1100 12000

10

20

30

40

T[K]

Nusselt number

Lead

Sodium

Nusselt number depends on density, heat capacity, velocity, geometry and thermal conductivity.

kPb (T ) = 9.2 + 0.011T

Nu = 0.047(1− e−3.8(P /D−1) )(Pe0.77 + 250)

Pe =ρCpvDh

k

Reference configuration: Nu[Pb] > Nu[Na]

Temperature difference

Nu x k ~ same for lead and sodium

Dh ~ 3 times larger for lead

For same bulk coolant temperature, temperature difference between clad and coolant several times larger in lead

∆ T (z) = χ(z)πD

Dh

Nu × kDh =

4APwet

700 800 900 1000 1100 12000

10

20

30

40

T [K]

Tsurf - Tcool [K]

Sodium

Lead

Cladding temperatures

Due to larger hydraulic diameter (ratio between flow area and wetted perimeter), cladding temperatures are significantly higher with lead coolant, even if bulk coolant temperature is the same.

Maximum cladding temperature is located below the top of the fuel column.

-0.4 -0.2 0.0 0.2 0.4

680

700

720

740

760

780

800

z [m]

Clad surface temperature [K]

Pb

Na

Natural circulation

Hot coolant above core has lower density than cold coolant at the outlet of the heat exchanger

Buoyancy pressure head: Pb = gHHX (ρcold − ρhot )

For fully established natural convection, buoyancy pressure equals pressure losses in core and heat exchanger.

Pressure drop is proportional to coolant velocity square, e.g. is the channel friction pressure drop:

ΔPch = f Hchρv

2

2Dh

= f Hch m2

2DhρA2

ρcold

ρhot

HHX

Hch

Volumetric expansion &buoyancy pressure head

Pb = gHHX (ρcold − ρhot )

ρNa (T ) = 1012 − 0.2205T −1.923×10−5T 2 + 5.637 ×10−9T 3

ρPb (T ) = 11367 −1.1944T

∆ T = 100K ⇒

∆ ρNa ≈ 22kg / m3

∆ ρPb ≈ 119kg / m3

Five times higher pressure head in lead cooled reactors!

Pressure drop due to channel friction

ΔPch = f Hchρv2

2Dh

= f Hch m2

2DhρA2

f = 0.316Re0.25

, Re = ρvDh

µ

600 700 800 900 1000 1100 1200 1300

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030Dynamic viscosity [Pa s]

T [K]

Pb

Na

600 700 800 900 1000 1100 1200 1300

50 000

100 000

150 000

200 000

250 000

300 000Reynolds number

T [K]

Pb

Na

Reynolds numbers and hence friction factors are similar for the reference configurations.

Coolant Na Pb

ρ 1 12

v2 1 0.05

Dh 1 3

∆Pch 1 0.2

Heat removal during transient

If pumping power is lost without scram of reactor (Unprotected Loss of Flow, ULOF), coolant temperatures will increase.

Buoyancy forces increase, leading to increase in natural convection flow velocity.

Finally, equilibrium is obtained and temperatures stabilise!

For lead cooled reference core: vPb ~ 0.4 m/s, ∆TPb ~ 500 K

Short term (30 minutes) permitted clad temperatures:

1000 K for ferritic martensitic steels (may not survive)

1200 K for austenitic steels (would probably survive!)