Investigation of Local Heat Transfer Phenomena in a Pebble Bed HTGR Core Deliverable RES-07 ...

489 Pages·2009·24.95 MB·English

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Investigation of local Heat Transfer
Phenomena in a Pebble Bed HTGR Core
NROOl/RP/002 ROl
May 15, 2009
PreparC(! by: Prepared by:
R. St31nsby ~
Heat Transfer and flU:
Consultant
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Prepared by: ?rcpared by:
B. Mclaughlin ~
Analyst
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Prepared by: ~, .~~~c=.~~Aa~L~~~c-Z-=-~_
M. Worsley E. van Heerden
Senior Physicist Senior Analyst
A1'lEC Nudear (UK) AMECNSS
Prepared by: fT."\~/<. . J ." Reviewed by:
F. Dawson .7A . DennIer
Analyst TH Applkations and t-let~s
AJ.1EC Nuclear (UK)
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Principal Consultant Director - Thermal Hydraulics
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Revision Summary
Rev Date Author Comments
R00 March 2009 R. Stainsby For U.S.NRC Review
R01 May 2009 R. Stainsby Incorporate an Executive Summary per U.S. NRC’s request.

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Executive Summary
This report summarizes the research on Pebble Bed Reactors (PBR) Heat Transfer
from the study “Investigation of the Local Heat Transfer Phenomena in an HTGR
Core”, solicitation number RES-07-087.
The objective of this work is to identify the computational tools and techniques
available to resolve local fluid behavior in the core of a high temperature gas reactor
(HTGR). This information is needed for U.S. NRC staff to develop the evaluation model
that will be used to audit licensee calculations under normal operation and accident
conditions. This report summarizes the research performed on local heat transfer
phenomena in a pebble bed core. Several models have been developed and sensitivity
studies have been performed as part of this research based on the thermal fluids and
accidents analysis R&D phenomena tables developed by the U.S. NRC for HTGRs.
Based on this research, constitutive models will be developed for inclusion into
systems codes (such as the code MELCOR) that are being developed to predict the
system-wide thermal fluidic behavior of HTGRs.
This report is structured in thirteen sections. Sections 1 to 3 present an introduction, a
discussion of pebble bed HTGRs and a review of the U.S. NRC’s Thermofluid and
Accident Analysis PIRT exercise. Section 4 presents the scope of the research
programme covered by this report and how this is linked to the findings of the
aforementioned PIRT exercise.
The investigations were divided into four main themes with each theme targeted on
groups of the high-priority PIRT items. These themes were chosen to capture the
heat transfer mechanisms from the scale of individual coated particles out to the scale
of the whole core, and were identified as:
1. Mechanisms influencing fuel and moderator temperatures.
2. Investigation of pebble bed pressure losses and heat transfer mechanisms.
3. Effective thermal conductivity of the pebble bed in loss of forced circulation
(LOFC) conditions.
4. Production of a whole-core CFD model.
Sections 5 to 9 describe the work and results from the investigation of the first theme.
Within Section 5, multi-scale models were developed which are capable of predicting
the temperature distributions within individual coated particles and within individual
pebbles containing many particles. The multi-scale methods were developed by
starting from one-dimensional steady state conduction problems which featured
multiple embedded discrete heat sources. Analytical solutions exist for these problems
and the bounds of applicability of the multi-scale decomposition were investigated by
comparison with these solutions. It is shown that the decomposition of the discrete
heat sources into spatial average plus local perturbations resolves the temperature
field without approximation. However, averaging of fine-scale material property

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variations over longer length scales does introduce approximations and care is
required when considering such averaging. Generally, for practical application, the
degree of approximation is not large because the packing fraction of particles within
pebbles is small.
Section 6 investigates the statistical likelihood of clustering of the coated particles
within pebbles. A method was developed by which random arrangements of particles
with the correct average packing fraction could be generated and interrogated to
determine the frequencies of obtaining different sized clusters of particles. Finite
element predictions were made of the temperature enhancement experienced by the
centre particle in approximately spherical clusters. The largest such cluster examined
contained 14 particles, although a 13 particle cluster was found to be a worse case as
it was more spherical. The next largest spherical cluster size that could be considered
would contain about 61 particles and it was considered that the occurrence of such a
large cluster would be extremely rare. The thirteen particle cluster yielded a
temperature enhancement of approximately 4°C for a pebble with average power. In a
peak rated pebble, with assumed (paradoxically) highly irradiated graphite, the
temperature enhancement is 12°C. From this work it appears, tentatively, that a small
margin of about 20°C can be added to a best estimate calculated particle temperature
to allow for uncertainties associated with clustering, when considering fission product
release. Further work to improve the statistical treatment should be possible – the
current method of sampling introduces a scale effect in which the results are
influenced by the size of the volumes within which the particles are counted. A scale-
independent way of counting to identify the presence and size of clusters should be
possible.
Section 7 presented an analytical method, based on Maxwell’s method for determining
the effective conductivity of a pebble containing a mixture of coated particles and
graphite. The predictions of the analytical method were compared with finite element
predictions for three different structured arrangements of particles. Also, two
alternative treatments of the particles were considered in the finite element
simulations. In the first, the multiple layers of a single coated particle were
homogenized with a conductivity that was determined by Maxwell’s method. In the
second treatment, the fuel kernel and each of the coating layers was resolved
explicitly within the finite model. The finite element predictions showed that
alternative structured arrangements of particles had a negligible influence on the
effective conductivity, therefore, it can be concluded that a random arrangement
would have given the same result. Further, there was no significant difference in the
predicted conductivities between using homogenized and explicitly-layered particles.
Finally it was shown that the effective conductivities predicted by Maxwell’s method
was close to the values obtained from all of the finite element predictions with an
accuracy of better than 0.4%.
Section 8 presents a model by which the pebble-to-pebble power and temperature
differences that would occur in a multi-batch core can be taken into account.
Typically, a CFD calculation of a whole reactor core would calculate a single coolant
temperature and a single pebble surface temperature within each computational cell in
the core. The multi-batch model starts from these two batch-averaged macroscopic

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quantities within a given computational cell. The differences in power developed
between different batches, together with estimates of the batch-to-batch and cell-to-
cell heat exchange coefficients, are used to “de-average” these temperatures. Thus, it
is possible to back-out the pebble and particle temperatures of each of the fuel
batches within the given computational cell.
Section 9 is a review of available data and methods for the calculation of thermal
properties of irradiated graphite.
Section 10 covers the work of the second research theme, “investigation of pebble bed
pressure losses and heat transfer mechanisms”. A numerical method for generating
random arrangements of pebbles in cylindrical and annular geometries has been
developed. This was used to generate a large annular core assembly which has the
dimensions of the PBMR-400 core. From this assembly, two smaller assemblies were
extracted; a cylindrical assembly from a radial position that was midway between the
inner and outer boundaries, and a semi-elliptical assembly taken from the outer edge
of the pebble bed corresponding to the location of the outer reflector. Later, a wider
semi-cylindrical region was extracted from the outer reflector region to improve the
averaging of the results in the circumferential direction. Computational fluid dynamics
(CFD) models were developed for these sub-assemblies using the FLUENT code.
Meshing of the domains was not trivial. The point contacts between pebbles led to
severely skewed meshes in the vicinity of the contacts and the imposition of planes
bounding the models also gave rise to degenerate element shapes. The solution to
the contact problem was to build small cylindrical bridges between touching pebbles
and to impose a tightly controlled grid around the contacts. The issue with imposing
planar boundaries on the model was overcome by using curved boundaries that were
free from sharp corners. These methods resulted in high quality elements throughout
the entire fluid domain.
The CFD models were used to determine axial pressure drops and heat transfer
coefficients for each model. Initially, a Reynolds analogy approach was used to infer
the heat transfer coefficients as an alternative to performing thermal calculations.
However, problems in determining an appropriate reference velocity led to this being
abandoned in favor of modeling the power and temperature distributions directly.
Remote from the reflectors, the pressure drop predictions agreed very well with
established correlations. Close to the reflectors, the CFD models predicted
significantly lower pressure drops than the correlations. This was to be expected as it
is known that the phenomenon referred to as wall channeling should yield a lower
pressure drop for a given mass flow when compared with correlations derived for
complete pebble beds due to the lower packing fraction near the reflector wall. This
wall channeling effect was explored further using the semi-cylindrical model and a
strong correlation between the radial distributions of axial mass flux with observed
oscillations in pebble bed porosity was apparent.
Heat transfer coefficients derived from the Reynolds analogy were generally too high
when compared with existing correlations. Conversely, heat transfer coefficients
derived from thermal simulations were significantly lower than those obtained from

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correlations. It is too early to say that either are in error and more work is required to
investigate the influence of turbulence modeling and the methods by which local heat
transfer coefficients are determined and then averaged to ensure consistency of
approach with the methods used to derive the correlations.
A CFD model of an assembly of pebbles from a multi-batch core was developed to
compare with the predictions of the analytical model presented in Section 8. Three
different batches of pebbles were simulated with powers of average, 0.5 times
average and 1.5 times average power respectively. The temperature spread across
the batches of ±16.55°C agreed well with the values predicted by the analytical model
of ±16.1°C.
Section 11 addressed the third research theme and attempted to model heat transfer
through a pebble bed in the absence of any significant forced or natural convection.
This is an important scenario and represents the passive decay heat removal route in
a depressurized loss of forced circulation scenario. The intention was to compare the
predicted effective conductivity of a section of pebble bed, accounting for solid and
gaseous conduction plus thermal radiation heat transfers, with the established
correlations of Zehner and Schlünder, and Breitbach and Barthels. However, in the
specific case of no fluid flow, severe convergence problems were encountered with the
selected thermal radiation model in FLUENT. Many attempts were made to accelerate
the convergence and to execute simpler test problems in consultation with the code
vendors. Unfortunately, none of these attempts were successful and the investigation
was halted.
The fourth research theme is addressed in Section 12. A three-dimensional model of
the PBMR core was developed in Section 12. This model was based on the two-
dimensional benchmark problem that was part of the IAEA’s CRP-5 coordinated
research program on high temperature gas cooled reactor performance. Whilst the
current model has a three-dimensional representation of the riser and reactivity
control channels, the circumferential extent of the model was limited to a 20° sector to
remain representative of the two-dimensional benchmark problem and to limit the
geometrical description to what could be sourced from the open literature. Whilst the
flow channels in the reflector were represented explicitly, the pebble bed was
simulated as a porous medium. A simple homogeneous model was chosen as this was
adequate for the benchmark calculation which only required a steady state model and
had a very simple power distribution. The pebble bed hydraulic resistance was
specified using correlations and an analytical version of the multi-scale model of
Section 5 was used to determine the fuel and pebble temperatures. The model
predicted very similar coolant, fuel and moderator temperatures to the CRP 5
participants, showing a fuel temperature difference of 21oC and an overall coolant
temperature rise of 500oC. Further work is required to extend the model to be
applicable to more realistic power distributions and to transient conditions. Specifically,
a heterogeneous two-phase porous medium model is required so that separate energy
equations can be solved for the gas and solid fractions within the bed. Similarly,
models for the “geometrical” dispersion of heat and momentum within a packed bed
would need to be introduced. Further, the full finite difference form of the multi-scale

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model, as presented in Section 5, would need to be implemented to model fast
transients.
Overall conclusions and recommendations for further work are presented in
Section 13. The work of most of the sections can be extended and refined, but these
recommendations focus on two aspects where further work is definitely required.
These are:
1. Re-attempting the analysis of Section 11 but using a CFD code that can both
handle the large number of degrees of freedom and be able to simulate thermal
radiation in the absence of forced flow, and,
2. Further development of the whole-core CFD model to be applicable to realistic
power shapes and transient conditions.

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Table of Contents
Page
1.0 INTRODUCTION.......................................................................................1-1
1.1 References for Section 1..................................................................................1-2
2.0 PEBBLE BED REACTOR CORES.................................................................2-1
2.1 Purpose of Section 2.......................................................................................2-1
2.2 Early Pebble Bed HTRs....................................................................................2-1
2.2.1 AVR...............................................................................................................2-1
2.2.2 THTR-300......................................................................................................2-1
2.3 Current Operating HTRs..................................................................................2-2
2.3.1 HTR-10..........................................................................................................2-2
2.4 Pebble-Bed HTR Designs under Development....................................................2-3
2.4.1 PBMR.............................................................................................................2-3
2.4.2 HTR-PM.........................................................................................................2-5
2.5 References for Section 2..................................................................................2-6
3.0 REVIEW OF U.S. NRC THERMOFLUID AND ACCIDENT ANALYSIS PIRT
WITH REGARD TO PEBBLE BED CORES...................................................3-1
3.1 Purpose of Section 3.......................................................................................3-1
3.2 Findings of the PIRT........................................................................................3-1
3.3 Allocation of Research Priorities........................................................................3-3
3.3.1 Prioritised List of Phenomena and Scenario Pairings...........................................3-4
3.3.2 High Priority Research Items............................................................................3-4
3.4 References for Section 3..................................................................................3-7
4.0 SCOPE OF THE CURRENT PROGRAMME OF RESEARCH............................4-1
4.1 Purpose of Section 4.......................................................................................4-1
4.2 PBR Theme 1 .................................................................................................4-1
4.3 PBR Theme 2 .................................................................................................4-2
4.4 PBR Theme 3 .................................................................................................4-3
4.5 PBR Theme 4 .................................................................................................4-4
4.6 References for Section 4..................................................................................4-5
5.0 MICRO AND MESO-SCALE FUEL PARTICLES AND PEBBLE TEMPERATURE
MODELS – STEADY STATE AND TRANSIENT............................................5-1
5.1 Purpose of Section 5.......................................................................................5-1
5.2 Finite Element Models.....................................................................................5-2
5.2.1 Modelled Geometry.........................................................................................5-2

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5.2.2 Material Properties and Boundary Conditions.....................................................5-4
5.2.3 Steady State Results.......................................................................................5-5
5.2.4 Influence of Material Thermal Conductivities.....................................................5-7
5.2.5 Transient Model.............................................................................................5-10
5.3 Micro and Meso-Scale Models..........................................................................5-11
5.3.1 Previous Steady State Approach......................................................................5-12
5.3.1.1 Steady State Temperature Profile in a Pebble...................................................5-12
5.3.1.2 Steady State Temperature Profile in a TRISO Particle........................................5-13
5.3.2 Extension to Transients..................................................................................5-16
5.3.2.1 Revised Steady State Analytical Treatment in One Dimension............................5-16
5.3.2.2 Transient Solution in a One-Dimensional Linear Domain....................................5-24
5.3.3 Application to a Cylindrical Representation of a Pebble......................................5-29
5.3.4 Application to a Spherical Pebble.....................................................................5-34
5.4 Closure.........................................................................................................5-39
5.5 References for Section 5.................................................................................5-40
6.0 PARTICLE CLUSTERING...........................................................................6-1
6.1 Purpose of Section 6.......................................................................................6-1
6.2 Monte Carlo Modelling of Particles Clusters........................................................6-1
6.2.1 Nearest Neighbour Function.............................................................................6-2
6.2.2 Particle Clustering...........................................................................................6-3
6.2.3 Validation.......................................................................................................6-4
6.2.3.1 Nearest Neighbour Function.............................................................................6-4
6.2.3.2 Particle Clustering...........................................................................................6-5
6.2.4 Results...........................................................................................................6-6
6.2.4.1 Nearest Neighbour Function.............................................................................6-6
6.2.4.2 Particle Clustering...........................................................................................6-7
6.3 Finite Element Models of Particle Clusters.........................................................6-10
6.3.1 Material Properties.........................................................................................6-14
6.3.2 Results..........................................................................................................6-15
6.4 Closure.........................................................................................................6-19
6.5 References for Section 6.................................................................................6-20
7.0 DETERMINATION OF PEBBLE EFFECTIVE CONDUCTIVITY......................7-1
7.1 Purpose of Section 7.......................................................................................7-1
7.2 Determination of Pebble Effective Conductivity using Maxwell’s Equation.............7-1
7.2.1 TRISO Fuel Particle Properties..........................................................................7-1
7.2.2 Particle Packing Fraction in PBMR Fuel Pebbles..................................................7-2
7.2.3 Maxwell’s Theory of Conductivity of Composite Materials....................................7-2
7.2.4 Analytically Derived Effective Thermal Conductivities..........................................7-3
7.3 Finite Element Modelling..................................................................................7-3
7.3.1 Geometry Used for 3-D Finite Element Models...................................................7-3
7.3.2 Model Unit Cell Dimensions..............................................................................7-4
7.3.3 Boundary Conditions and Material Properties.....................................................7-4
7.3.4 Results...........................................................................................................7-5

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7.4 Closure..........................................................................................................7-8
7.5 References for Section 7..................................................................................7-8
8.0 MULTI-BATCH FUEL MODELS...................................................................8-1
8.1 Purpose of Section 8.......................................................................................8-1
8.2 Derivation of the Multi-Batch Model..................................................................8-2
8.2.1 Average Pebbles.............................................................................................8-2
8.2.2 Batch-Specific Pebbles.....................................................................................8-3
8.2.3 Assumptions...................................................................................................8-6
8.2.3.1 Batch-to-Batch Heat Exchange.........................................................................8-6
8.2.3.2 Distribution of the Cell-to-Cell Conductive Heat Transfer between Batches...........8-7
8.2.4 Revised Distribution of the Overall Conduction Term between Batches................8-8
8.2.5 Determination of Batch Surface Temperatures...................................................8-9
8.3 Extension to Transient Behaviour....................................................................8-10
8.4 Closure.........................................................................................................8-13
8.5 References for Section 8.................................................................................8-13
9.0 IRRADIATED GRAPHITE THERMAL PROPERTIES....................................9-1
9.1 Purpose of Section 9.......................................................................................9-1
9.2 Graphites Used in Past/Existing Reactor Cores...................................................9-1
9.3 Selection/Qualification of Graphites for Future HTGRs........................................9-2
9.4 Models Used for Predicting Graphite Specific Heat .............................................9-3
9.5 Models for Predicting Graphite Conductivity.......................................................9-6
9.5.1 Terminology...................................................................................................9-6
9.5.2 Existing Thermal Conductivity Data...................................................................9-7
9.5.3 Methodology..................................................................................................9-10
9.5.3.1 UK Methodology............................................................................................9-11
9.5.3.2 PBMR Methodology........................................................................................9-22
9.5.3.3 US Methodology.............................................................................................9-24
9.6 Through Life Variations in Density of Graphite..................................................9-24
9.7 Recovery of Thermal Conductivity at High Temperatures...................................9-25
9.8 Closure.........................................................................................................9-25
9.9 References for Section 9.................................................................................9-26
10.0 MODELS FOR THE INVESTIGATION OF PEBBLE BED PRESSURE LOSSES
AND HEAT TRANSFER MECHANISMS.....................................................10-1
10.1 Purpose of Section 10 ....................................................................................10-1
10.2 Random Packing of Spherical Pebbles within a Cylindrical or Annular Pebble Bed.10-2
10.2.1 Review of Existing Methods............................................................................10-2
10.2.2 Pebble Bed Generation Method Adopted in this Work........................................10-3
10.2.3 Generated Assemblies of Pebbles....................................................................10-3
10.3 Introduction to CFD Modeling .........................................................................10-4
10.3.1 Existing Literature for Explicit Modeling of Packed Beds.....................................10-5
10.3.2 Approach of Current Work..............................................................................10-5

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