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The Pebble-Bed AHTR Initial Pebble Recirculation Design Based on

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The Pebble-Bed AHTR Initial Pebble Recirculation Design Based on Powered By Docstoc
					    Pebble Bed Heat Transfer
Particle-to-Fluid Heat Convection
              Raluca Scarlat
      Thermal Hydraulics Laboratory
    Department of Nuclear Engineering
     University of California, Berkeley

              Group Meeting

           26 February 2009




                                          Jaeger Tripaks




                                                   UC Berkeley
                     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




                                             UC Berkeley
                           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
                                              UC Berkeley
                   Definitions: Sphere Packing


RHOMBOHEDRAL


         SC       BCC    FCC




              PB-AHTR Packing: random – 60% packing fraction




                                                               UC Berkeley
Definitions: Porous Bed Parameters




                                 UC Berkeley
      Momentum Equation: ΔP Correlation

• Ergun correlation:




• Other variants:




                                     UC Berkeley
           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                                     Forced        Natural
                                                                      circulation   circulation
     SC: vortex shedding observed.                          Re          1,700          66
     Rhombohedral: no vortex shedding observed.             uD          0.48         0.018
                                                         up = uD/ε       1.20         0.045
                                                        up = uD∙τ/ε      1.70         0.064

                                                                                UC Berkeley
                 Energy Equation: Nu Correlation

• Wakao et al 1982

         » Nusselt number:

         » Prandtl number:

         » Reynolds number:


• By analogy w/ mass transfer:

         » Schmidt number:

         » Sherwood number:




                                               UC Berkeley
                 Energy Equation: Nu Correlation
                          Packed Beds

• Wakao et al 1982                                         Forced      Natural
                                                         circulation circulation
         » Nusselt number:                    Re            1,700        66
                                               uD           0.48       0.018
                                           up = uD/ε        1.20       0.045
         » Prandtl number:
                                           up = uD∙τ/ε      1.70       0.064

         » Reynolds number:                   Inlet
                                               Pr           20.9       20.9
                                               Nu           265        39.5
• By analogy w/ mass transfer:                 kf           0.97       0.97
                                                h          17,127      2,554


         » Schmidt number:                  Outlet
                                             Pr              13          13
                                             Nu             226          34
                                              kf            1.00       1.00
         » Sherwood number:                   h            15,092      2,267




                                                         UC Berkeley
Energy Equation: Nu Correlation
         Packed Beds

                  (Wakao et al.)




                                   UC Berkeley
Literature Review by Wakao and Kaguei 1982
                 Packed Beds

                                                The sizes of the
                                                bubbles schematically
                                                represent the size of
                                                the parameter space
                                                (Pr or Sc x Re)
                                                covered by literature
                                                data.




                                                  No data:
                                                  Pr = 1 to 120




              Little data & high uncertainty:
              Re < 50


                                                  UC Berkeley
                Energy Equation: More Nu Correlations
      Packed Beds                                                     Disperse suspensions
      Wakao et al, 1982 (data: 0.7< Pr < 1, 15 < Re < 8 500 )
[1]

                                                                [6]


[2]


                                                                       Ahmad and Yavanovich, 1994
      Wilson and Jacobs, 1993 (numerical model)
[3]                                                             [7]



      Single Particle

[4]



       Vliet and Leppert, 1961 (single sphere in water)
[5]



                                                                                             UC Berkeley
          Energy Equation: More Nu Correlations

          Re = 66                                    Re = 1 700
                                                                                          Forced      Natural
                                                                                        circulation 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
            Pr = 13                                   Pr = 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
Solid = packed bed, Dashed = disperse/fluidized, Dotted = Single Sphere




                                                                                     UC Berkeley
                           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
                                                                           UC Berkeley
Experimental Set-Up that We’re Considering
       Transient, Step Change




                                     UC Berkeley
         Experimental Set-Up that We’re Considering
                Transient, Step Change
Scaling
• Geometric scaling coefficient: ξ.                                             Forced      Natural
                                                                              circulation circulation
   Subscript m = “model.”                                           Re           1,700        66
                                                                    uD           0.48       0.018
                                                                 up = uD/ε       1.20       0.045
                                                                up = uD∙τ/ε      1.70       0.064
• Momentum and Energy Equation Similarity:
                                                                   Inlet
                                                                    Pr           20.9        20.9
• Quasi Steady –State:                                              Nu
                                                                     kf
                                                                                 265
                                                                                 0.97
                                                                                             39.5
                                                                                             0.97
                                                                     h          17,127      2,554
  Stm = Strouhal n. =
                                                                  Outlet
                                                                   Pr             13          13
• Lumped capacity model for the sphere:                            Nu            226          34
                                                                   kf            1.00        1.00
                                                                    h           15,092      2,267

                                                                 Scaling
                                                                   Stm          105          25
Key assumptions                                                    Bim          41.7         6.2
• High pebble conductivity => lumped capacity model (no         Tm (Pr=Prm)     57 oC       85 oC

  conduction in the sphere)                                      ΔTf/ΔTo        3.0%        10%
                                                                 ΔTs/ΔTo        2.4%        9.0%
• High pebble heat capacity relative to fluid => quasi-steady
                                                                Subscript m = “model.”
  state heat flow from the spheres
                                                                              UC Berkeley
       Experimental Set-Up that We’re Considering
              Transient, Step Change
Scaling
• Momentum and Energy Equation Similarity:                                    Forced      Natural
                                                                            circulation circulation
                                                                  Re           1,700        66
                                                                  uD           0.48       0.018
• Quasi Steady –State:                                         up = uD/ε       1.20       0.045
                                                              up = uD∙τ/ε      1.70       0.064

                                                                 Inlet
                                                                  Pr           20.9        20.9
• Lumped capacity model for the sphere:                           Nu
                                                                   kf
                                                                               265
                                                                               0.97
                                                                                           39.5
                                                                                           0.97
                                                                   h          17,127      2,554

                                                                Outlet
                                                                 Pr             13          13
Challenges                                                       Nu            226          34
                                                                 kf            1.00        1.00
      Compared to the gas experiments, the oil has a high        h           15,092      2,267
       volumetric heat capacity => Harder to have quasi-       Scaling
       steady state at low Reynolds                              Stm          105          25
      Compared to the low Pr experiments, we have a             Bim          41.7         6.2
                                                              Tm (Pr=Prm)     57 oC       85 oC
       higher Nu and h => Harder to disregard conduction in
       the spheres at high Reynolds                            ΔTf/ΔTo        3.0%        10%
                                                               ΔTs/ΔTo        2.4%        9.0%
                                                              Subscript m = “model.”


                                                                            UC Berkeley
                        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?




                                                   UC Berkeley
                    Presentation Comments

1. Add hexagonal packing
2. Hydraulic conductivity in RELAP: permeability and hydraulic
   diameter
3. Mills Heat Transfer book: HTU
4. Periodically developed flow: Graetz number
5. Hollow spheres: blown glass, dimples
6. 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




                                                               UC Berkeley
                            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




                                                           UC Berkeley
                                                      Deep Burn
              Fuel Cycle          Fuel
                                                 DEEP BURN PROJECT OBJECTIVES
                                                 • Provide cost-effective recycle options for LWR
DB OVERVIEW
               Analysis        Development


                 Core and         TRU Fuel
                                                 spent fuel that will utilize minimal reprocessing
               Fuel Analysis      Modeling
                                                 and also rapidly and significantly reduce spent
                 Spent Fuel       TRU Fuel       fuel TRU stockpiles (particularly the weapons-
                                                 usable fraction).
                Management       Qualification



                 Fuel Cycle       HTR Fuel       •    Ensure that the HTR will consistently be
                                                 embraced as an important part of any large
                 Integration       Recycle



                                                 nuclear growth “global” scenarios (both for once-
                                                 through and recycle options).


     PARTICIPANTS                                                                   Multi-Scale
                                                                                     Thermo-
     • Universities: UC Berkeley, UN Las Vegas, Texas                               Mechanical
     A&M, Georgia Tech, Penn State, Idaho State,                                     Analysis
     University of Wisconsin, University of Tennessee
     • National Laboratories: Idaho, Oakridge, Los                         TRU FUEL MODELING
     Alamos, Argonne, LOGOS                                                Multi-Scale        TRISO Fuel
     • Private Entities: General Atomics, Graftech,                        Neutronic         Performance
     Studsvik                                                               Analysis            Model



                                                                                            UC Berkeley
                                             Deep Burn Fuel Cycle

                                                                    Deep Burn
                                                                    Recycle

                                                                         Recycle
                Deep Burn
                Power Reactor




                                                                      Uranium
                                                         LWR
                                                       Spent Fuel
                                                                                    Fission Product
                                                                                    Ultimate Disposal
Fuel particles, fuel compacts, fuel blocks

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




                                                  Transuranics
         DB-TRISO FAB

                                                                                      UC Berkeley
                       Advanced Nuclear Reactors




PBMR (Exelon/PBMR)       MHR (General Atomics)       PB-AHTR (UC Berkeley)
Pebble Bed Modular       Modular Helium Reactor      Pebble Bed Advanced High
Reactor                  Fuel Compact: Cylinder in   Temperature Reactor
Fuel Compact: Sphere     prismatic graphite block    Fuel Compact: Sphere
Coolant: He, 800oC       Coolant: He, 900oC          Coolant: FLiBe (BeF-LiF), 700oC
                                                                 UC Berkeley
                  Nuclear Fuel: TRISO Micro-Particles

                                    • Fuel Kernel (200 – 500 m in diameter)
             <1000 m
                                       – Example composition: PuO1.7 (85 mol %), Am2O3(9 mol %), Np
                                         oxide (5 mol%), and Cm2O3(1 mol %)
       • Bullets                    • Buffer layer (porous carbon layer, 50% TD, 100 m)
                                                           <1000 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

o Particles retain the fission products: advantageous for proliferation-resistance, and
  ultimate-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.
                                                                         UC Berkeley
                  Thermo-Mechanical Model

                                   Fuel Scale Thermo-
                                    Mechanical Model
                                         A. Pebble Fuel
                                    B. Prismatic Fuel (MHR)

1. Temperature-dependent
  TRISO properties, for a
   given temperature and               Constraints
      irradiation history               Peak stress               1. Steady-state and
  2. Power profile in the            Peak temperature            transient temperature
  fuel element, at a given         Thermal gradient across                profile.
 location in the core (from               TRISO                    2. Induced Material
      neutronic model)                                                   Stresses
   3. Thermal boundary                     Objective
conditions (from full core       Maximum power per TRISO
 thermal hydraulic model).


                       TRISO Scale
                         Models                    Multi-Scale
                     * Thermo-Mechanical        Neutronic Analysis
                      * Fuel Performance




                                                                           UC Berkeley
              Thermo-Mechanical Model


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

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

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




                                                                 UC Berkeley
Modeling Tools – COMSOL




                          UC Berkeley
Modeling Tools – COMSOL




                          UC Berkeley
Modeling Tools – COMSOL




                          UC Berkeley
Modeling Tools – COMSOL




                          UC Berkeley
            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




                                               UC Berkeley

				
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