Thermal Fluid Characteristics for
Pebble Bed HTGRs.
Frederik Reitsma
Oct 22-26, 2012
IAEA Course on High temperature Gas Cooled Reactor Technology
Beijing, China
Oct 22-26, 2012 IAEA Course on High temperature Gas Cooled Reactor Technology
Overview
• Background
• Key T/F parameters
• Key T/F characteristics
• Heat transfer modeling
• T/F modeling challenges
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Background
• Analysis of thermal-fluid systems – Often complicated because of the complex nature of fluid
flow and heat transfer
• Characteristics of thermal-fluid systems – Time-dependent – Multidimensional – Complex geometries – Complicated boundary conditions – Coupled transport phenomena – Turbulent flow – Structural and phase change – Energy losses and irreversibilities – Variety of energy sources
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Basic principles
• Need to solve the governing equations in:
– Conservation of mass
– Conservation of momentum
– Conservation of energy
• Heat transfer
– Conduction
– Convection
– Radiation
Oct 22-26, 2012 IAEA Course on High temperature Gas Cooled Reactor Technology
Typical thermal-dynamic cycles
• The T/F conditions of the reactor are determined from the type of thermodynamic cycle used
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Oct 22-26, 2012 IAEA Course on High temperature Gas Cooled Reactor Technology
Typical reactor T/F parameters
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Key T/F characteristics • Helium is a single phase coolant
– No phase change in the cycle to deal with – Helium has excellent heat transfer properties – Compressible gas
• Large ΔT across reactor inlet to outlet – Requires a smaller coolant mass flow rate resulting in lower pumping
requirements
• High coolant outlet temperatures – Allows for higher thermal efficiency in power conversion cycles and process heat
applications
• Small ΔT between fuel and coolant (~70 °C) • Large temperature margins in the fuel (~600-1000 °C) • Slow thermal transients
– Large thermal capacitance in the fuel and graphite combined with a low power density results in slow transients
• Pebble bed is one flow channel – Strong coupling in the pebble bed does not require throttling of flow channels or
adjusting for flow distribution through the core
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Thermal fluid considerations
• In the Thermal-Fluid design of a pebble bed core, the following aspects need to be considered:
– Positions of heat generated
– Flow path design to keep the metallic components cool
– Identification of all intentional and unintentional flow paths
– Pressure zoning to prevent hot gas impingement
– Temperature stratification in the outlet flow
– Component Temperatures
– Needs to design both an active (forced flow) and passive (natural) heat transfer path
Oct 22-26, 2012 IAEA Course on High temperature Gas Cooled Reactor Technology 9
Heat generation input
• Heat is generated in both local (in the fuel) and non-local sources
Heat sources: – Fuel – Reflectors – Control rods – Lateral restraints – Core barrel – Reactor vessel
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Coolant flow design
• The coolant flow path design needs to consider the following aspects: – cool the metallic
structures where necessary
– reduce bypass flows – provide a uniform
temperature distribution – mix the bypass flows to
lower the thermal lower the thermal stratification in the outlet gas
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Secondary flow paths
• Engineered
– Control rod cooling flow
– Central reflector cooling flow
– Pressurisation flow
• Leakage paths
– Across side reflector
– Inlet-to-outlet
– Along side reflector
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Passive heat transfer path description
• Inherent post-shutdown decay heat removal is achievable through conduction, natural convection and radiation heat transfer. Design choices include core geometry, low power density and high thermal capacity of the core structures.
Centre Reflector Pebble Bed Side Reflector Core Barrel RPV RCCS Citadel
RadiationConduction
Conduction
Conduction
Convection
Radiation
Convection
Conduction
Radiation
Convection
Conduction
Convection
Radiation
Convection
Conduction
Radiation
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Effect of Different Residual Heat Removal Mechanisms on Peak Fuel Temperature
• Active and passive heat removal • CCS is an active heat removal system
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T/F Correlations • Helium properties
– Given by KTA 3102.1 Calculation of the Material Properties of Helium
• Heat transfer from sphere to gas – Given by KTA 3102.2 Heat Transfer in Spherical Fuel Elements – Function of ΔT, sphere diameter, Pr, Re, coolant properties, bed porosity
• Pressure loss through a pebble bed – Given by KTA 3102 3 Loss of Pressure through Friction in pebble bed cores – Function of bed porosity, sphere diameter, coolant properties, bed
height, bed diameter, mass flow
• Effective thermal conductivity of a pebble bed – Given by Zehner-Schlünder correlation – Function of bed porosity, sphere material properties which in turn is
dependent on temperature and dose
IAEA Course on High temperature Gas Cooled Reactor Technology
Bypass flow
LRD
Pebble Bed CROD
channel
Core flow Bypass
Leakage
Needs to predicts leak flows Use systems code like or detailed CFD
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Effects of modelling bypass flows
• Bypass flows could increase thermal gradients and thus stresses in components
IAEA Course on High temperature Gas Cooled Reactor Technology
Example of test facility and required Modelling
Proximity refinement
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Reactor Neutronics and Thermal Fluid
Analysis
Reactor Power Profile
Reactor Flow Distribution and Temperatures
Structural Analysis
Thermal Fluid Analysis
Computational Fluid Dynamics
(CFD)
Cycle Flow Conditions
Detailed Flow Distributions
Detailed Component Temperatures
Analysis Requirements (A typical picture needed)
Detailed Flow Distributions and Neutronic Data
Fluid/Structure Interaction
Oct 22-26, 2012 IAEA Course on High temperature Gas Cooled Reactor Technology 19
Physical Phenomena • FLUID FLOW
– Very hot helium gas under high pressure flows through an inlet, riser channels, leakage paths, inlet plenum, pebble bed, outlet plenum
– Frictional resistance (mainly in the pebble bed core, riser channels and leakage paths) cause pressure drops
– Heat transfer from the solid through convection (mainly in the pebble bed and riser channels)
– Internal heat redistribution in the gas through heat conduction and “braided” turbulent flow (in the pebble bed)
– Secondary helium circuit for cooling purposes • SOLID HEAT TRANSFER
– Nuclear heat sources (mainly in the pebbles) – Pebble-pebble heat transfer through solid and stagnant gas
conduction, radiation, etc. Heat transfer in the reflector through conduction and radiation
– Heat transfer to the gas through convection (mainly in the pebble bed and riser channels, couples the solid and gas temperatures)
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Heat transfer in the Pebble Bed
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The Lumped Parameter Approach
• Could also be described as a “macroscopic” approach • Uses a relatively coarse grid for the gas (as opposed to CFD
simulations) • The gas is treated as inviscid (no turbulence models, etc.) • The porous medium approximation is used in the core • Makes use of (non material property) empirical correlations (e.g. for
frictional resistance and heat transfer via convection) because the flow field around each pebble is not resolved and the gas is inviscid
• Programs like RELAP, FLOWNEX and CFD programs using the porous medium approximation are also lumped parameter models
• Many of the earlier codes used for HTR-Pebble-Bed modeling is 2D, which enforces the lumped parameter approach
• In the core these programs predict different temperatures for the gas and solid, this the pseudo-heterogeneous approach (not to be confused with the term heterogeneous which refers to subdivided pebbles and kernels)
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Unique features to take into account…
• Fast reactivity transients – kernel modelling – In normal operation very small difference (normally
not modelled at all)
– Essential to model the kernel temperature behaviour explicitly (with all the coatings)
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Critical thermal heat transfer modelling
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Time [sec]
Po
wer [
% o
f N
om
inal]
Homog
SS Triso - no gap
Core Power (% of full) in PBMR400 / HTR-Modul after Large Reactivity Insertion
Because the fuel is dispersed in a matrix, simplistic energy deposition assumptions can lead to large errors when modeling reactivity insertions (e.g., control rod withdrawal or water ingress)
Oct 22-26, 2012 IAEA Course on High temperature Gas Cooled Reactor Technology 24
Other pebble specific aspects to remember
• Different fuel spheres of different “batches” in multi-pass have:
– Different heat sources
– Different graphite thermal conductivity (temperature, fluence and irradiation T dependent)
– Thus different surface temperatures
– (may want to include kernel – buffer layer gap and fission product buildup...)
– Variations in pebble packing fractions
Oct 22-26, 2012 IAEA Course on High temperature Gas Cooled Reactor Technology 25
Ultimate heat sink
• Significant amount of work was performed to find a passive Reactor Cavity Cooling System (RCCS).
• Different systems were investigated using coupled CFD models: – Direct passive air cooled
– Indirect passive air cooled
– Direct passive water cooled
– Indirect active water cooled
– Direct active water cooled with boil-off
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Summary
• Flow phenomena in a pebble bed is straightforward and well characterized
• Thermo physical properties of helium is well understood and characterized
• Modeling challenges stems from defining flow paths with “loosely” packed side reflector blocks that creates leak flow paths
• Modern modeling and calculation methods are used to calculate design inputs for components in lieu of measurements from operating plants
Materials and design shape the core neutronics and thermal flow characteristics
• Graphite is the moderator and structure, not metal and water – high temperature solid
moderator – hard thermal spectrum – fixed burnable poison possible – large physical dimensions – low power density
• Helium is the coolant not water – Coolant is transparent to
thermal neutrons – Coolant has no phase change
• Fuel is carbide-clad, small ceramic, particles not metal clad UO2 – PyC/SiC carbide clad is primary
fission product release barrier – Fuel operates at high temperatures
with wide margin to failure – Double heterogeneity in physics
modelling in fuel
• Heat removal path through core structures – Modular requires metallic vessel – For increased power (and lower
maximum fuel temperature in DLOFC) - have to go to annular core
Oct 22-26, 2012 IAEA Course on High temperature Gas
Cooled Reactor Technology 27
Oct 22-26, 2012 IAEA Course on High temperature Gas Cooled Reactor Technology
• Source material used: – HTGR Technology Course for the Nuclear Regulatory
Commission, May 24 – 27, 2010
– HTR/ECS 2002 High temperature Reactor School, 2002
– Advanced Reactor Concepts Workshop, PHYSOR 2012
– Coupling of neutronics and thermal-hydraulics codes for the simulation of transients of pebble bed HTR reactors, T. Rademer, W. BERNNAT and G. Lohnert, Paper C22, HTR2004
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