UC Berkeley

Raluca ScarlatThermal Hydraulics Laboratory

Department of Nuclear EngineeringUniversity of California, Berkeley

Group Meeting

26 February 2009

Pebble Bed Heat TransferParticle-to-Fluid Heat Convection

Jaeger Tripaks

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Outline

1. Porous Media

2. Pressure Drop and Flow Regimes in Packed Beds

3. Heat Transfer in Packed Beds

4. Planned Experimental Set-up

5. Deep-Burn TRU Fuel Modeling

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Motivation

• Why we care:

– PB-AHTR, LIFE, and Deep Burn

o core thermal-hydraulic analysis, and

o fuel thermo-mechanical modeling

• Why others care:

– Solids Drying

– Bubbles: liquid-liquid or liquid-gas

– Solids dissolving

– Catalytic Reactions

– Coal combustion

– etc

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Definitions: Sphere Packing

RHOMBOHEDRAL

SC BCC FCC

PB-AHTR Packing: random – 60% packing fraction

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Definitions: Porous Bed Parameters

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Momentum Equation: ΔP Correlation

• Ergun correlation:

• Other variants:

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Momentum Equation: Flow Regimes• Darcy Flow: Re<1

Local pore geometry effects only

Wall channeling: uwall/ubulk ≈ 2, 1-2 d from the wall

Entrance region: ≈ 3d; Developed region: periodic velocity profile

• Inertial flow: 1-10 < R < 150

Lower Re: more pronounced boundary layer in the pore

Developing boundary layer in the pore (higher ΔP in entrance region): ΔP dependent on lateral & longitudinal pore dimensions

Wider pores: more significant inertial effect

• Unsteady laminar flow: 150 < R < 300

Oscillations: frequency ≈ a few Hz, amplitude ≈ d/10

Possible oscillation cause: laminar wake instability

• Turbulent/unsteady chaotic flow: Re > 300

Turbulent mixing in the pores

SC: vortex shedding observed.

Rhombohedral: no vortex shedding observed.

Forced

circulation

Natural

circulation

Re 1,700 66

uD 0.48 0.018

up = uD/ε 1.20 0.045

up = uD∙τ/ε 1.70 0.064

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Energy Equation: Nu Correlation

• Wakao et al 1982

» Nusselt number:

» Prandtl number:

» Reynolds number:

• By analogy w/ mass transfer:

» Schmidt number:

» Sherwood number:

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Energy Equation: Nu CorrelationPacked Beds

• Wakao et al 1982

» Nusselt number:

» Prandtl number:

» Reynolds number:

• By analogy w/ mass transfer:

» Schmidt number:

» Sherwood number:

Forced

circulation

Natural

circulation

Re 1,700 66

uD 0.48 0.018

up = uD/ε 1.20 0.045

up = uD∙τ/ε 1.70 0.064

Inlet

Pr 20.9 20.9

Nu 265 39.5

kf 0.97 0.97

h 17,127 2,554

Outlet

Pr 13 13

Nu 226 34

kf 1.00 1.00

h 15,092 2,267

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Energy Equation: Nu CorrelationPacked Beds

(Wakao et al.)

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Literature Review by Wakao and Kaguei 1982

Packed Beds

No data:Pr = 1 to 120

Little data & high uncertainty:Re < 50

The sizes of the

bubbles schematically

represent the size of

the parameter space

(Pr or Sc x Re)

covered by literature

data.

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Energy Equation: More Nu Correlations

Single Particle

Vliet and Leppert, 1961 (single sphere in water)

Ahmad and Yavanovich, 1994

Disperse suspensionsPacked Beds

Wilson and Jacobs, 1993 (numerical model)

Wakao et al, 1982 (data: 0.7< Pr < 1, 15 < Re < 8 500 )[1]

[2]

[3]

[4]

[5]

[6]

[7]

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Energy Equation: More Nu Correlations

Forced

circulation

Natural

circulation

Re 1,700 66

uD 0.48 0.018

up = uD/ε 1.20 0.045

up = uD∙τ/ε 1.70 0.064

Inlet

Pr 20.9 20.9

Nu 265 39.5

kf 0.97 0.97

h 17,127 2,554

Outlet

Pr 13 13

Nu 226 34

kf 1.00 1.00

h 15,092 2,267

Re = 66 Re = 1 700

Solid = packed bed, Dashed = disperse/fluidized, Dotted = Single Sphere

Pr = 13 Pr = 20.9

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Experimental Set-Ups

• Transient:

– Frequency response

» Heat inlet gas with mesh, measure gas temp at inlet and outlet and calculate transfer function from the Fourier spectra [Littman et al]

– Shot response

» Heat inlet gas in empty column, measure outlet gas temp at inlet and outlet and calculate transfer function from the response [Shen et al]

– Step change:

» drop cold particles in a hot stream, measure gas outlet temperature as a function of time [Wamsley and Johanson]

• Steady-State:

– Water evaporation:

» Fluidized bed of water-imbibed particles in hot gas, measure amount of water vapor [Ketterig et al]

» Evaporation from droplets

– Fluidized bed of coal in air, measure bed (thermo-couple) and gas (suction thermo-couple) temperatures [Walton et al]

– Induction heating

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Experimental Set-Up that We’re ConsideringTransient, Step Change

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Experimental Set-Up that We’re ConsideringTransient, Step Change

Scaling

• Geometric scaling coefficient: ξ.

Subscript m = “model.”

• Momentum and Energy Equation Similarity:

• Quasi Steady –State:

• Lumped capacity model for the sphere:

Key assumptions

• High pebble conductivity => lumped capacity model (no conduction in the sphere)

• High pebble heat capacity relative to fluid => quasi-steady state heat flow from the spheres

Forced

circulation

Natural

circulation

Re 1,700 66

uD 0.48 0.018

up = uD/ε 1.20 0.045

up = uD∙τ/ε 1.70 0.064

Inlet

Pr 20.9 20.9

Nu 265 39.5

kf 0.97 0.97

h 17,127 2,554

Outlet

Pr 13 13

Nu 226 34

kf 1.00 1.00

h 15,092 2,267

Scaling

Stm105 25

Bim 41.7 6.2

Tm (Pr=Prm) 57 oC 85 oC

ΔTf/ΔTo3.0% 10%

ΔTs/ΔTo2.4% 9.0%

Stm = Strouhal n. =

Subscript m = “model.”

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Experimental Set-Up that We’re ConsideringTransient, Step Change

Scaling

• Momentum and Energy Equation Similarity:

• Quasi Steady –State:

• Lumped capacity model for the sphere:

Challenges

Compared to the gas experiments, the oil has a high volumetric heat capacity => Harder to have quasi-steady state at low Reynolds

Compared to the low Pr experiments, we have a higher Nu and h => Harder to disregard conduction in the spheres at high Reynolds

Forced

circulation

Natural

circulation

Re 1,700 66

uD 0.48 0.018

up = uD/ε 1.20 0.045

up = uD∙τ/ε 1.70 0.064

Inlet

Pr 20.9 20.9

Nu 265 39.5

kf 0.97 0.97

h 17,127 2,554

Outlet

Pr 13 13

Nu 226 34

kf 1.00 1.00

h 15,092 2,267

Scaling

Stm105 25

Bim 41.7 6.2

Tm (Pr=Prm) 57 oC 85 oC

ΔTf/ΔTo3.0% 10%

ΔTs/ΔTo2.4% 9.0%

Subscript m = “model.”

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Summary

• We need to characterize overall heat transfer coefficients in pebble beds, for 10 < Pr < 30

• Should we characterize local heat transfer coefficients for pebble beds, to be able to couple with Deep Burn?

• The Fuel Thermo-Mechanical model will be highly flexible – possibly use for PB-AHTR, LIFE?

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Presentation Comments

1. Add hexagonal packing2. Hydraulic conductivity in RELAP: permeability and hydraulic

diameter3. Mills Heat Transfer book: HTU4. Periodically developed flow: Graetz number5. Hollow spheres: blown glass, dimples6. Natural circulation in a packed bed: what sets of experiments

does it makes sense to design?7. Options for heating pebbles:

• larger heated pebble; check Grashoff number (may not have to match it if buoyancy effects are insignificant – see Archimedes number).

• PBMR test facility uses square array

• See e-mails from Ronen

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References

[1] “Principles of Convective Heat Transfer,” Kaviany• Ch 5: Solid-Fluid Systems with Large Specific Interfacial Area

[2] “Principles of Heat Transfer in Porous Media,” Kaviany• Ch 7: Two-Medium Treatment

[3] “Heat and Mass Transfer in Packed Beds”, Wakao and Kaguei• Ch 2: Fluid Dispersion Coefficients• Ch 6: Thermal Response Measurements• Ch 4: Particle-to-Fluid mass transfer coefficients• Ch 8: Particle-to-Fluid heat transfer coefficients

[4] “Heat Transfer Handbook,” Bejan and Kraus 2003• Ch 19: External Convection to Spheres

[5] “Handbook of Heat Transfer,” Rohsenow, Warren, Cho 1998• Ch 9: Heat Transfer in Porous Media• Ch 13: Heat Transfer in Packed and Fluidized Beds

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Deep Burn

PARTICIPANTS• Universities: UC Berkeley, UN Las Vegas, TexasA&M, Georgia Tech, Penn State, Idaho State,University of Wisconsin, University of Tennessee• National Laboratories: Idaho, Oakridge, Los Alamos, Argonne, LOGOS• Private Entities: General Atomics, Graftech,Studsvik

DEEP BURN PROJECT OBJECTIVES• Provide cost-effective recycle options for LWRspent fuel that will utilize minimal reprocessingand also rapidly and significantly reduce spentfuel TRU stockpiles (particularly the weapons-usable fraction).• Ensure that the HTR will consistently beembraced as an important part of any largenuclear growth “global” scenarios (both for once-through and recycle options).

Fuel Cycle Analysis

Core and Fuel Analysis

Spent Fuel Management

Fuel Cycle Integration

Fuel Development

TRU Fuel Modeling

TRU Fuel Qualification

HTR Fuel Recycle

DB

OV

ER

VIE

W

Multi-Scale Thermo-

Mechanical Analysis

TRISO Fuel Performance

Model

Multi-Scale Neutronic Analysis

TRU FUEL MODELING

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Deep Burn Fuel Cycle

Transuranics

FP

DB-TRISO FAB

LWR Spent Fuel

Ura

niu

m

RecycleDeep Burn Power Reactor

Deep Burn Recycle

FP = 800 kg/yrfor 0.6 GW TRU= 35-75 kg /yr

UREX

Fuel particles, fuel compacts, fuel blocks

Fission ProductUltimate Disposal

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Advanced Nuclear Reactors

PBMR (Exelon/PBMR)Pebble Bed Modular ReactorFuel Compact: SphereCoolant: He, 800oC

PB-AHTR (UC Berkeley)Pebble Bed Advanced High Temperature ReactorFuel Compact: SphereCoolant: FLiBe (BeF-LiF), 700oC

MHR (General Atomics)Modular Helium ReactorFuel Compact: Cylinder in prismatic graphite blockCoolant: He, 900oC

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Nuclear Fuel: TRISO Micro-Particles

• Bullets

o Particles retain the fission products: advantageous for proliferation-resistance, andultimate-disposal of spent fuel.

o 10,000 particles in a graphite matrix form a fuel compact (cm-sized cylinder or sphere): reduced energy and materials inputs for fuel fabrication vs. conventional LWR.

<1000 m

• Fuel Kernel (200 – 500 m in diameter)– Example composition: PuO1.7 (85 mol %), Am2O3(9 mol %), Np

oxide (5 mol%), and Cm2O3(1 mol %)

• Buffer layer (porous carbon layer, 50% TD, 100 m)– Attenuates fission recoils– Provides void volume for fission gases and kernel swelling

• Inner Pyrocarbon (IPyC, 82-90% TD, 35 m)– Retains gaseous fission products– Provides structural support for SiC– Shrinks during irradiation, holding SiC in compression

• Silicon Carbide (SiC, ~ 100% TD, 35 m)– Primary load-bearing layer– Retains gas and metal fission products (except Ag)

• Outer Pyrocarbon (OPyC, 82-90% TD, 40 m)– Provides structural support for SiC– Fission product barrier in particles with defective SiC– Prevents SiC damage during fuel element fabrication

<1000 m

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Thermo-Mechanical Model

Fuel Scale Thermo-Mechanical Model

A. Pebble Fuel

B. Prismatic Fuel (MHR)

1. Steady-state and transient temperature

profile.

2. Induced Material Stresses

TRISO Scale Models

* Thermo-Mechanical

* Fuel Performance

Multi-Scale Neutronic Analysis

1. Temperature-dependent TRISO properties, for a given temperature and

irradiation history

2. Power profile in the fuel element, at a given

location in the core (from neutronic model)

3. Thermal boundary conditions (from full core thermal hydraulic model).

ConstraintsPeak stress

Peak temperatureThermal gradient across

TRISO

ObjectiveMaximum power per TRISO

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Thermo-Mechanical Model

• Micro-Scale: A packed sphere array with an initial set of boundaryconditions will be used to compute the temperature and burn-updependent effective thermo-mechanical properties. These results willfeed into the model at the fuel element scale.

• Fuel Element Scale: A homogeneous fuel element model (pebble, orcylindrical fuel compact) will be used to calculate the thermal profile,and the thermal stresses. These results will feed back into the boundaryconditions for the micro-scale model.

• Full Core Temperature Profile: A full core temperature profile isneeded as an input for neutronic analysis, and it will be generated basedon the results of the fuel element model.

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Modeling Tools – COMSOL

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Modeling Tools – COMSOL

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Modeling Tools – COMSOL

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Modeling Tools – COMSOL

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Deep Burn Work in Progress

• Import segments of SolidWorks model in COMSOL/Ansys

• Ansys vs. COMSOL

• Compiling temperature and Burn-up dependent material properties

• Identify best method to couple the multi-scale models: material property homogenization