Pebble Bed Heat Transfer Particle-to-Fluid Heat Convection

Transcription

1 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

2 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

3 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

4 Definitions: Sphere Packing RHOMBOHEDRAL SC BCC FCC PB-AHTR Packing: random 60% packing fraction

5 Definitions: Porous Bed Parameters

6 Momentum Equation: ΔP Correlation Ergun correlation: Other variants:

7 Momentum Equation: Flow Regimes Darcy Flow: Re<1 Local pore geometry effects only Wall channeling: u wall /u bulk 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, u D u p = u D /ε u p = u D τ/ε

8 Energy Equation: Nu Correlation Wakao et al 1982» Nusselt number:» Prandtl number:» Reynolds number: By analogy w/ mass transfer:» Schmidt number:» Sherwood number:

9 Energy Equation: Nu Correlation Packed 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, u D u p = u D /ε u p = u D τ/ε Inlet Pr Nu kf h 17,127 2,554 Outlet Pr Nu kf h 15,092 2,267

10 Energy Equation: Nu Correlation Packed Beds (Wakao et al.)

11 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

12 Packed Beds Energy Equation: More Nu Correlations Disperse suspensions [1] Wakao et al, 1982 (data: 0.7< Pr < 1, 15 < Re < ) [6] [2] Ahmad and Yavanovich, 1994 [3] Wilson and Jacobs, 1993 (numerical model) [7] Single Particle [4] [5] Vliet and Leppert, 1961 (single sphere in water)

13 Energy Equation: More Nu Correlations Re = 66 Re = Forced circulation Natural circulation Re 1, u D u p = u D /ε u p = u D τ/ε Pr = 13 Pr = 20.9 Inlet Pr Nu kf h 17,127 2,554 Solid = packed bed, Dashed = disperse/fluidized, Dotted = Single Sphere Outlet Pr Nu kf h 15,092 2,267

14 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: Steady-State:» drop cold particles in a hot stream, measure gas outlet temperature as a function of time [Wamsley and Johanson] 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 thermocouple) temperatures [Walton et al] Induction heating

15 Experimental Set-Up that We re Considering Transient, Step Change

16 Experimental Set-Up that We re Considering Transient, Step Change Scaling Geometric scaling coefficient: ξ. Subscript m = model. Momentum and Energy Equation Similarity: Quasi Steady State: St m = Strouhal n. = 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 Natural circulation circulation Re 1, u D u p = u D /ε u p = u D τ/ε Inlet Pr Nu kf h 17,127 2,554 Outlet Pr Nu kf h 15,092 2,267 Scaling St m Bi m T m (Pr=Pr m ) 57 oc 85 oc ΔT f /ΔT o 3.0% 10% ΔTs/ΔT o 2.4% 9.0% Subscript m = model.

17 Experimental Set-Up that We re Considering Transient, 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 quasisteady 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 Natural circulation circulation Re 1, u D u p = u D /ε u p = u D τ/ε Inlet Pr Nu kf h 17,127 2,554 Outlet Pr Nu kf h 15,092 2,267 Scaling St m Bi m T m (Pr=Pr m ) 57 oc 85 oc ΔT f /ΔT o 3.0% 10% ΔTs/ΔT o 2.4% 9.0% Subscript m = model.

18 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?

19 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 s from Ronen

20 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

21 DB OVERVIEW Deep Burn Fuel Cycle Analysis Core and Fuel Analysis Spent Fuel Management Fuel Cycle Integration Fuel Development TRU Fuel Modeling TRU Fuel Qualification HTR Fuel Recycle DEEP BURN PROJECT OBJECTIVES Provide cost-effective recycle options for LWR spent fuel that will utilize minimal reprocessing and also rapidly and significantly reduce spent fuel TRU stockpiles (particularly the weaponsusable fraction). Ensure that the HTR will consistently be embraced as an important part of any large nuclear growth global scenarios (both for oncethrough and recycle options). PARTICIPANTS Universities:, UN Las Vegas, Texas A&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 Multi-Scale Thermo- Mechanical Analysis TRU FUEL MODELING Multi-Scale Neutronic Analysis TRISO Fuel Performance Model

22 Uranium TRU= kg /yr Deep Burn Fuel Cycle Deep Burn Recycle Deep Burn Power Reactor LWR Spent Fuel Recycle Fission Product Ultimate Disposal Fuel particles, fuel compacts, fuel blocks UREX FP FP = 800 kg/yr for 0.6 GW Transuranics DB-TRISO FAB

23 Advanced Nuclear Reactors PBMR (Exelon/PBMR) Pebble Bed Modular Reactor Fuel Compact: Sphere Coolant: He, 800 o C MHR (General Atomics) Modular Helium Reactor Fuel Compact: Cylinder in prismatic graphite block Coolant: He, 900 o C PB-AHTR () Pebble Bed Advanced High Temperature Reactor Fuel Compact: Sphere Coolant: FLiBe (BeF-LiF), 700 o C

24 Nuclear Fuel: TRISO Micro-Particles <1000 m Bullets Fuel Kernel ( m in diameter) Example composition: PuO 1.7 (85 mol %), Am 2 O 3 (9 mol %), Np oxide (5 mol%), and Cm 2 O 3 (1 mol %) Buffer layer (porous carbon <1000 layer, m 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 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.

25 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 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). Constraints Peak stress Peak temperature Thermal gradient across TRISO Objective Maximum power per TRISO 1. Steady-state and transient temperature profile. 2. Induced Material Stresses TRISO Scale Models * Thermo-Mechanical * Fuel Performance Multi-Scale Neutronic Analysis

26 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 onthe results of the fuel element model.

27 Modeling Tools COMSOL

28 Modeling Tools COMSOL

29 Modeling Tools COMSOL

30 Modeling Tools COMSOL

31 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