TransAT Report Series
– Applications –
TransAT for Nuclear
Science & Technology
On Two-phase Flow, Heat
Transfer Phase Change
Simulation in Fuel Assemblies
Ascomp Switzerland
Edited by: Dr S. Thomas and Dr D. Lakehal
Release date: Sep, 2014.
References: TRS-A/ 04-2014
www.ascomp.ch - [email protected]
Table of Contents
1.
Introduction .................................................................................................................................................................... 2
2.
Simulation Possibilities using Transat (CFD & CMFD) ................................................................................ 3
3.
Single-Phase Flow & Heat Transfer in Fuel Assemblies .............................................................................. 4
3.1
RANS with IST: The Westinghouse 24-rod Mock-up of SVEA-96 Fuel Bundle ................................. 4
3.2
RANS with IST: The PBST Test-Case .................................................................................................................... 5
3.3
LES with BFC: The Scaled-down PSBT 5x5 case ............................................................................................. 8
4.
Multi-Phase Flow & Heat Transfer in Fuel Assemblies using ITMs...................................................... 12
5.
Multi-Phase Flow & Heat Transfer in Fuel Assemblies using Phase-Average Models ................. 14
5.1
DEBORA Test Case ..................................................................................................................................................... 14
5.2
BARTOLOMEI Test Case .......................................................................................................................................... 16
5.3
LEE, PARK & LEE and TU & YEOH Test Case .................................................................................................. 18
5.4
3D PWR SUB-CHANNEL Test Case ...................................................................................................................... 19
6.
Conclusions ................................................................................................................................................................... 22
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
1
Abstract
This note shows capabilities of the CMFD code TransAT for various scenarios of multiphase
flow and heat transfer simulations in fuel assemblies. The document highlights the unique
features of the code compared to others, including meshing complex geometries using the
coupled Immersed Surfaces Technology combined with Block Mesh Refinement (IST/BMR),
and phase-change physics using either interface tracking or phase-average models.
1. Introduction
Subcooled flow boiling in PWR’S occurs in the hot fuel assemblies when heat flux is supplied
to the wall, which is initially in contact with flowing liquid. Understanding and predicting
this complex phenomenon is crucial for efficient operations, safety, and development of new
PWRs, and more generally in light-water cooled reactor (Sugrue et al, 2012). For instance, in
U.S. PWR plants (Fig. 1), subcooled flow boiling occurs under normal operating conditions,
and determines the margin to Critical Heat Flux CHF (Toderas & Kazimi, 1990). Subcooled
flow boiling also determines the rate at which corrosion products in solution in the coolant
deposit on the surface of the zirconium alloy cladding, which can lead to localized corrosion
and neutronic distortions (axial offset), and ultimately cladding failure (Sugrue et al, 2012).
Figure 1: Schematic of subcooled flow boiling in a PWR assembly (not to scale).
The mainstream modelling approach for thermal-hydraulics systems involving two-phase
flow and heat transfer is based on the Eulerian-Eulerian, two-fluid model (Bestion et al,
2009; Lo, 2006 and In & Chun, 2009), which requires closure laws for the phase-to-phase
and wall-to-flow mass, momentum, and energy terms in the governing equations. The wallto-flow constitutive relation for energy captures subcooled boiling heat transfer. Examples
of mechanistic boiling heat transfer models are the heat flux partitioning model of Kurul
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
2
and Podowski (1991) and its recent modified variant of Krepper and Rzehak (2011).
Consensually, in the partitioning heat flux model, heat removal by the boiling fluid is split
into three contributions, (i) the latent heat of evaporation to form the bubbles, (ii) the heat
expended in re-formation of the thermal boundary layer following bubble departure, the socalled quenching heat flux, and (iii) the heat transferred to the liquid phase outside the zone
of influence of the bubbles by convective heat transfer (Fig. 1). This modeling strategy is
generally applicable to low heat flux boiling and has been based on speculative hypotheses
supported by a myriad of empirical correlations, assuming that single-phase convection and
nucleate boiling are analogous physical processes; e.g. the Rohsenow correlation. The
Achilles-Heel of existing wall boiling models is the definition of the bubble departure
diameter, which is a critical unknown. The flux-partitioning boiling model is in general
implemented within the two-fluid model, except in code TransAT, where it is implemented
with the homogeneous mixture model, coded within the general N-phase context.
Moving away from rough empiricism towards developing more mechanistic models of
boiling heat transfer requires high-quality/resolution DNS or experimental data made
available, including nucleation site density, bubble growth rate, bubble departure diameter
and frequency, and time-resolved temperature distribution on the boiling surface. While
efforts are underway on the experimental side notably to develop better data
acquisition/visualization systems, on the CMFD front, the interest has been shifted towards
high-end simulation (DNS) of boiling processes, using for example the so-called Interface
Tracking Methods (ITMs), in which the topology of the vapor/liquid interface is directly
calculated together with the Navier-Stokes equations. This is expected to play a major role
in the process of model development too. Note too that alternative treatments of wall heat
partitioning a la Kurul and Podowski (1991) are underway, accounting notably for other
hydrodynamics phenomena, including the effect of bubble merger and coalescence, bubble
size distribution, bubble sliding. This effort includes Kolev’s bubble interaction model
(1994), and the hybrid numerical-empirical model of Sanna et al (2009).
2. Simulation Possibilities using Transat (CFD & CMFD)
In TransAT, one can resort to various modelling combinations, depending on the needs in
terms of physics, the simulation capabilities (grid size and CPU resources). Fig. 2 below
presents these various modelling combinations. In short, as to turbulence first, TransAT can
simulate flows using either statistical time-average models (RANS, both isotropic and
algebraic stress, using wall functions or low-Re approaches) or scale-resolving approaches
(LES and V-LES). The same structure is available as to multiphase flow structures: use could
be made of phase-average models (N-phase approach) or interface tracking methods (ITM),
including Level Set and VoF. As to heat transfer phase-change, TransAT offers again two
routes: using interfacial and wall heat/mass transfer models (under both phase-average
models and ITM) or inter-phase direct heat-flux integration (under ITM). The same is true
as to meshing capabilities: TransAT uses either the Body-Fitted Coordinates approach (BFC)
or the Immersed Surface Technique (IST) combined with Block Mesh Refinement (BMR) or
Local Mesh Refinement (LMR). IST combined with BMR or LMR is infinitely faster than BFC,
in particular as to fuel assembly cases involving complex-shaped spacers.
These modelling and meshing combination possibilities offer indeed a great deal of
flexibility to the users. For instance the combination of ITM and LES is termed as LEIS, short
for ‘Large-Eddy & Interface Simulation’, and is a unique feature in TransAT. In extending the
modelling portfolio of TransAT, a new compressible, high-speed, N-phase formulation has
been developed and is under validation; another unique feature in TransAT. The next
sections will highlight these modelling combinations in terms of practical examples, with or
without direct comparison with experiments.
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
3
Figure 2: Schematic of the TransAT modelling combination capabilities.
3. Single-Phase Flow & Heat Transfer in Fuel Assemblies
3.1 RANS with IST: The Westinghouse 24-rod Mock-up of SVEA-96 Fuel Bundle
In Boiling Water Reactors (BWR), the nuclear core consists of multiple parallel channels,
connected at the inlet and outlet plena. This particular design feature effectively eliminates
coolant cross flows through the entire core and provides a more uniform and controllable
enthalpy distribution in various fuel rod assemblies. Thus, the issue of the optimization of
the thermal-hydraulic performance of nuclear fuel is shifted from the core-wide to the
assembly-wide analysis. This is only an apparent simplification of the task, since the
phenomena that govern the phase distribution within fuel assemblies are still very complex,
mainly due to various mechanisms such as diversion flows, void drift and turbulent mixing.
Clearly, prediction of the thermal-hydraulic performance of fuel rod assemblies and- in
particular- prediction of the occurrence of the Critical Heat Flux (CHF) requires that the
details of flow and phase distributions are known. Current computational methods cannot
be fully trusted in such complex applications and still require significant development of
new models as well as thorough validation of the existing ones. One of the important
components of the fuel rod assembly, whose important bi-function is to enhance the lateral
exchange of flow momentum and energy, is the spacer grid.
The experimental rig, schematically shown in Fig. 3 consists of a test section, a water
reservoir, a centrifugal pump (15 kW), flow control valves and stainless steel piping,
forming a closed loop. The water flow is measured by an electromagnetic flow meter
downstream of the pump. From the pump the water enters the plenum connected to the
lower part of the vertical test section. The plenum contains a honeycomb flow rectifier
suppressing large-scale vortices generated by the pump and tube bends. The test section
terminates in another plenum. A weir in the upper plenum maintains a constant water level
and a free surface at atmospheric pressure. The water from the upper plenum returns to the
reservoir passing a number of baffles giving time for air bubbles trapped in the water to rise
to the surface. All the measurements were performed in single-phase water flow. The crosssectional view of the test section, corresponding to one quarter of the SVEA–96 fuel
assembly, is shown in Fig. 3. The spacer part in the studied and surrounding sub-channels is
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
4
presented in the same figure together with the photographs of spacer elements, such as
dimple, spring and frame vane. The 24 rods are held in position by five spacers of the thinplate spring construction. The rods could slightly vibrate. The walls of the test section are
made of 10mm thick glass plates, allowing visibility techniques to be used to study the flow.
Figure 3: Real spacer photography and associated CAD file immersed in a coarse IST grid (for illustration).
3.2 RANS with IST: The PBST Test-Case
The PSBT benchmark, based on the NUPEC database (Rubin et al, 2010), focuses on
advancement in subchannel analysis of fluid flow in rod bundles, which has very important
relevance to the nuclear reactor safety margin evaluation. In this scaled down preliminary
work, steady state single phase flow with conjugate heat transfer in a PWR 5x5 rod bundle
with three different kind of spacers (the simple spacer, the non-mixing vane spacer and
mixing vane spacer; Fig. 4) is simulated and analysed. Turbulence effects are accounted for
using a standard k-ε model. The solids, including the spacers and the rods, were modelled
using the Immersed Surface Technique (IST). Commercial CMFD package TransAT was used
for the simulations.
Figure 4: The original CAD files of the two guiding-vane spacers
Steady state flow simulations were performed using TransAT employing the k- model for
turbulence with wall functions, modified to account for buoyancy forces for the production
and dissipation equations. The CAD files depicting the spacers (shown in Fig 4) could be
immersed in a Cartesian grid consisting of enough grid cells to mesh the fluid and solid
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
5
areas (Fig. 5). In TransAT, a minimum of 3 cells is needed to resolve solid components
immersed into the Cartesian grid. In this preliminary feasibility study, the problem has been
downgraded to simulate an axial heated length of 1m with five spacers along the length of
the rod bundle, requiring a total of 6.4 million cells. The project is expected to culminate
with the single state temperature analysis of the full PSBT geometry of 3.658m length with
17 spacers in total, which would require about 23-35 million grid cells, which is reasonable
compared to what might be needed with a BFC Grid (~ 100 million cells).
Figure 5: IST grid of the entire system with spacers; temperature iso-contours on the solids.
Fig. 6 displays a three-dimensional perspective view of the temperature iso-contours taken
on the solid walls, showing the details of the flow captured by the IST method. It shows in
particular the way heat evolves between the different spacers. Fig. 7 depicts the detailed
picture of the heat transfer on the rods and secondary flow-field immediately downstream
the upper mixing-vane spacer. The left panel shows clear heat streaks forming on the
surfaces of the rods enhanced by the mixing vane structure. The secondary flow is also
rather well predicted, although the method is more suitable to be used in the wall function
context, avoiding low-Re modelling requiring an extreme near-wall refinement.
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
6
Figure 6: Temperature contours on the surface of the entire assembly.
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
7
Figure 7: Temperature contours (left) and secondary flow (right) downstream the 1 st and 2nd spacers.
3.3 LES with BFC: The Scaled-down PSBT 5x5 case
This problem is inspired by the PSBT OECD sub-channel benchmark (Rubin et al., 2010) in
terms of radial dimensions, though the expected deliverables are different, in that the focus
is on detailed flow and temperature profiles in the subchannel, together with global
parameters including the heat transfer coefficient, the onset of nucleation, the pressure
drop and the thermal entry length (some only were required in the OECD benchmark). The
operating conditions of the present case are made on purpose different from PSBT, namely
the power and mass flow rate, which have been adjusted according to the reduced length
(1m instead of 3.65m). The PWR fuel assembly consists of a rod bundle with water coolant
flowing upward along the rods at a high Reynolds number. The rod diameter is 9.5mm, the
rod pitch is 12.6mm and the active fuel length is typically 3.7m. The hydraulic diameter for
a unit cell is De = 11.8mm. The coolant pressure is 15.5MPa with temperature ranging from
290C to 340C. The mass flux is G=3700 kg/m2s, corresponding to a Reynolds number
Re=GDe/=4.8105, shear velocity ~0.2m/s, and frictional Reynolds number ~104.
The problem has been scaled down to more reasonable conditions, i.e. Reτ = 300. Choosing
LES instead of DNS is motivated by the fact that in contrast to channel flow, this problem
should involve non-Cartesian meshing, e.g. BFC or unstructured grids, which are not
adequate for DNS. Finally, the length of the domain was reduced from the PWR case to relax
the meshing requirements in the axial direction. Since the distance to the onset of nucleate
boiling depends on the integrated power (heat flux times rod surface area) supplied to the
fluid, the heat flux was scaled accordingly. The heat flux is to be applied at the rod outer
surface. The actual operating conditions are summarized in Table 2.
Pressure
Sat. temp.
Inlet temperature
Mass flux
Heat Flux
Power
15.5 MPa
344.6C
290C
74.1 kg/m2s (or Re=300)
50 kW/m2
1.57 kW
Table 2: Test case 2 operating flow conditions.
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
8
Fuel Rod
Flow outlet
Heat flux q”
P=13.0 mm
Cross flow section
=450
=00
Figure 8: Computational domain: Dimensions & BC’s. (lower) Medium (left) and fine (right) grids for LES
(x-y). Arrows show 00 and 450 segments.
The dimensions of the simulation domain and boundary conditions are indicated in Fig. 8.
The case feature cross-sectional dimensions similar to the PSBT OECD case; rod diameter D
= 10 mm and pitch P = 13 mm. The length is reduced from 3.6 m to 1.0 m. A novel approach
was used to generate proper boundary conditions for this flow. First, periodic conditions
were applied in the radial and circumferential directions to mimic the effect of the
neighbouring rods. In the axial direction, however, a hybrid ‘Developed & Developing Flow
Hybrid Approach’ has been developed. It consists of first generating turbulence in a periodic
e, then the resulting fluctuating (scaled to maintain the mass flow
rate) field is imposed in the entire domain, recycled periodically: temperature is updated
using inflow-outflow BC’s, together with the steam-water interface in case of two-phase
flow calculations. Two BFC grids were employed: the medium one (208 // core blocks)
consists of 7984040 cells providing a near-wall resolution of y+~0.5-2.1, which allows
resolving the viscous sublayer. The second grid (832 // core blocks) consists of
1,600x60x60 cells, providing a near-wall resolution of y+~0.4-1.5.
Fig. 9 below depicts the cross-flow and heat transfer in the bundle. Panel a) and b) present
results of a 6 million cell still somewhat under-resolved DNS simulation. The lower panels
present LES results obtained with 1.6 million-cell grid (Caviezel et al, 2013). The panels
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
9
illustrate that dissipation in the numerical method captures some features of a subgrid scale
model and the wall temperatures of interest are reasonably predicted. What is also of
interest is the ability of under-resolved DNS to tackle problems of practical interest.
(a) Fine grid: instantaneous
(b) Fine grid: time average
(c) Medium grid: instantaneous (d) Medium grid: time average
Figure 9: Fine vs. medium resolutions: Instantaneous (a and c) and time averaged (b and d) crosssectional velocities and temperature contours.
Medium grid
Fine grid
Figure 10: Mean velocity profiles across the subchannel (0° & 45°) compared to the DNS of Eggels et al.
(1994); medium versus fine mesh simulations.
Time averaged results are presented in Figs. 10 and 11, including mean velocity and
temperature profiles. Since the flow resembles turbulent flow in a pipe, use was made of
available DNS data (Eggels et al, 1994) for comparison. The DNS data are not filtered. The
difference with the pipe flow is that the present one has two azimuthal segments, a short
one (=0°) with low Re effects and a full one (=45°) extending to the core with high Re
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
10
effects (see Fig. 10); the latter one should thus return the imposed shear Reynolds number
at the subchannel center point, in the form of y+¦centerline= Re. The mean flow profiles are
plotted in Fig. 9, compared to DNS. As explained earlier, the =0° segment profile achieves a
lower y+ than the =45° one. The profiles match very well the DNS data of Eggels et al
(1994), in particular the fine grid one which does not show the slight grid effect returned by
the medium grid simulation. This preliminary important result pleads in favour of a high
quality LES simulation achieved by TransAT. Another important measure is the normalized
temperature variance ’’>, which is plotted in Fig. 11 on both segments, at various crossflow locations, comparing once more the medium and fine grid results. It is only for this
higher-order quantity that the grid resolution shows an effect, with differences in peak
values of about 5% in the =0° segment and up to 10% in the =45° one. The medium grid
results still show a grid effect (kink). The fine grid results exhibit variations in this quantity
with elevation, which is not always the case in the medium grid results. This may be an
artefact of normalization; it could have shown a self-similar behaviour if it were normalized
by the average wall temperature. We also suspect that the fine grid simulations require still
more time to reach statistical convergence, in particular for second-order turbulent
quantities. Be it as it may, the results are similar to DNS data of a heated channel flow.
Fine grid: segment 0°
Fine grid: segment 45°
Figure 11: Mean temperature profiles across the subchannel at various locations.
Global parameters results are presented in Table 3. The LES results are compared here to
existing analytical and experimental correlations. The pressure drop between medium and
fine grid is accurate to 2.2% and 5% compared to the correlation. As to the heat transfer
coefficient (HTC), there are uncertainties for the case of interest, which in fact belongs to
the ‘transitional cases regime’, according to Incropera and DeWitt (1996), for which the
correlations, in particular the Colburn one (or Dittus-Boelter), could give up to 25% error.
When accounting further for the effect of neighbouring rods using the Weisman correction
(here =1.826p/D-1.043=1.33), the deviations between LES and correlation is high, and is
precisely 33%. If this correction is not accounted for, the LES results (fine grid in particular)
are comparable to the Colburn correlation, within -5%. With more sophisticated
correlations e.g. the Gnielinski and Petukov (see Incropera and DeWitt, 1996), the analysis
changes, in that the LES data are 6% than Gnielinski’s correlation and 1.9% only than
Petukov’s one.
Quantity
Pressure drop P [Pa]
Heat transfer coefficient
(HTC) at XONB
[kW/m2K]
Med. grid
10.223
Fine grid
10.52
1.495
1.535
Analytical/Exp.
10.0
1.62 (Colburn)
2.16 (Colburn -W*)
1.44 (Gnielinski)
1.99 (Gnielinski -W)
1.50 (Petukov)
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
11
Distance to XONB [m]
Thermal entry length [m]
Min-max
0.49–0.57
Min-max
0.21–0.28
Min-max
0.49–0.6
Min-max
0.21–0.29
2.0 (Petukov -W)
0.59 (Colburn)
0.79 (Colburn -W)
0.29–0.46
*W means with the Weisman (1959) correction factor
Table 3: Test case 2 operating flow conditions
The distance to the onset of boiling is questionable in the same way, since it is directly
based on the HTC correlation employed (here we took the Colburn one only). The
simulation results are within a few percent’s deviations from the Colburn correlation, but
24-35% off the Colburn–Weisman variant, which is in line with the HTC deviations
reported. Finally, as stated previously, there is no such a constant line indicating XONB since
the simulations have clearly shown that the effect of the secondary flow motion makes it
rather undulating by 5-7% around the mean.
4. Multi-Phase Flow & Heat Transfer in Fuel Assemblies using ITMs
The hydrodynamics of the convective boiling two-phase flow is the focus of this section. One
expects here the nucleating small bubbles to grow to non-spherical shapes – due to intense
shearing - and migrate to the core flow, possibly featuring coalescence, before condensing.
Starting from this hypothesis, the modeller – aiming at using ITMs - faces a dilemma as to
the way nucleation should be seeded, since there is no other alternative. Intuitively, the
choice would be to initiate individual resolved (super-grid) bubbles on the rod where the
wall temperature reaches saturation. But this could be questionable since it appeals to
making various hypotheses as to the statistical distribution of the bubbles, their size and
concentration, and the intensity of the nucleation of the sites. In other words, the potential
to make errors on the wall regions, which are instantaneously favourable for bubble
growth, is obviously high. Thus to avoid additional modelling assumptions, we have taken
another ‘novel’ route where boiling incipience is triggered using an unresolved (sub-grid)
vapour film instead of individual super-grid bubbles, without a-priori experimental
evidence. Here the only information available is the wall temperature. With the present
boiling incipience idea by means of a SGS vapour film, the physics of nucleate boiling cannot
be captured immediately past the onset of nucleate boiling where nucleation of individual
bubbles dominate heat transfer, unless the vapour film breaks in a later stage into
individual bubbles. But this again raises the issue of grid-dependent simulations; an
insufficient resolution should rather return large (discontinuous) patches of vapour on the
surface, as is the case in near-CHF situations.
The simulations started from the existing LES data basis, and initiated an ultra-thin-film of
vapour instantaneously on the rod surface where at Twall= Tsat. The film grows by the action
of heat/mass transfer from the wall; here use is made of the Level-Set technique (Sussman
et al., 1994) to track the vapour-water interface. Because a BFC grid is employed, a fastmarching approach on a narrow-band is used to re-distance the interface and conserve
mass; traditional re-initialization techniques are indeed suitable for Cartesian grids only. A
dynamic contact angle model based on the Yong’s triple force decomposition has been
employed. Combing advanced ITMs and LES is known as LEIS, short of Large-Eddy &
Interface Simulation (Lakehal, 2010). A near-interface damping approach is employed
(Liovic & Lakehal, 2007a,b). As to phase-heat transfer, direct heat flux integration is
performed to capture the exact rate of mass transfer across the interface, without resorting
to a model.
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
12
The ‘qualitative’ results shown next were obtained after 40.000 time steps only, which took
3 weeks on 892 processors. We estimate another 100.000 time steps before concluding.
Fig. 12 shows instantaneous temperature contours on the rod with the vapour-water
interface at positions of Tsat, at the end portion of rod. The film shown in a transparent way
suggests the occurrence of a patchy discontinuous structure of the interface. It is likely that
the film has not yet disintegrated into individual bubbles detaching towards the core flow.
The film is better visualized in Fig. 13, which does not show the temperature contours on
the rod; note that the film has been increased in size for visualization purposes only. The
size of the film is better depicted in Fig. 14 with a black line, displaying cross sections
coloured by temperature. It shows the turbulence activity and secondary flow motion as
well.
Figure 12: Instantaneous temperature contours on the rod with vapour at positions of Tsat
Figure 13: Vapour-water interface at positions of T sat
Figure 14: Cross-sectional temperature contours and interface.
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
13
5. Multi-Phase Flow & Heat Transfer in Fuel Assemblies using Phase-Average
Models
For solving the subcooled boiling problems in the following section, the channels are long
and thin (typically 5m long and 20mm width). The grid requirement to capture the sharp
interfaces in such slender domains is enormous. To resolve the issue, the Eulerian
multiphase (phase-average) model under its homogeneous form (Manninen et al, 1996) is
used to capture the evolution of the two phases with heat transfer. The vapor phase is
modeled as the secondary phase in the primary liquid flow. Under the original
homogeneous form of the Eulerian model, the conservation equations are solved for the
mixture quantities, including density, viscosity, velocity, pressure and temperature, and
phase volume fractions. The Eulerian Ensemble-Averaged model owing to its lower grid
resolution is faster to run. The details of the interface topology are not captured as well as
the Level-Set method, but it provides good comparison when looking at flow quantities, like
velocity, void fraction, temperature etc.
5.1 DEBORA Test Case
The motivation behind presenting the results of the DEBORA experiments (Manon, 2000;
Garnier et al, 2001) is that because we could compare the results of three different codes,
albeit using the same wall boiling model (Kurul and Podowski, 1991). Here we compare the
results of FLUENT and NEPTUNE (Lavieville et al, 2005) using the two-fluid approach
against TransAT’s results using the N-phase mixture model.
DEBORA experiments consist of Freon R12 flowing upwards in a vertical pipe heated with a
constant heat flux of 58.2 kW/m2 under a pressure of 30.06 bar. At the inflow, the liquid is
subcooled and is heated as it flows upwards and vapor bubbles are nucleated at the wall.
These bubbles break away from the wall and are dispersed in the turbulent flow. Internal
diameter of the pipe is 19.2mm. The whole pipe can be divided into three sections: inlet
adiabatic section – 1m long, heated section – 3.5m long and outlet adiabatic section 0.5m
long. The test cases are similar those simulated by Vyskocil and Macek [2008]. The
summary is listed in Table 4.
No.
kg/m2/s
°C
°C
Bubble
diameter
mm
1
2
3
4
5
6
7
1006.8
1007.4
999.5
1005
1004.8
1004.8
994.9
52.97
58.39
63.43
67.89
70.14
72.65
73.7
94.136
94.136
94.136
94.136
94.136
94.136
94.136
0.2
0.58
0.65
3.2
4.0
5.1
6.2
Case Mass flux
Tinlet
Tsat
Table 4: Selected DEBORA test cases
The bubble diameter is assumed to be constant for each case and does not vary within the
radial profile. The bubble diameters are different for every case. Computationally, the grid is
axisymmetric covered by 14 cells in the radial direction and 1000 cells in the axial direction.
The standard k-ε model is employed with wall functions for both velocity and thermal fields.
The turbulent dispersion coefficient is also employed for the diffusion of void fraction.
Properties of Freon-12 are extracted from the NIST Web Book (NIST, 2013). Initial flow
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
14
conditions are set according to the experiment, with a prescribed ratio of eddy-to-molecular
viscosity of 20. The numerical schemes used are second order in space. The void fraction is
initialized in the entire domain at 10-7. Following are the results for the test case. The
section is taken at the end of the heated part of the pipe.
The contours of void fraction, liquid temperature and streamwise gas velocity between
4.5m and 4.6m axially are shown in Fig. 15. It indicates a jump in the void fraction close to
the wall and the gas velocity is well developed at the end of the heated section. The liquid
temperature in the axial region is heated up close to the saturation temperature. Radial
profiles of the void fraction profiles are compared in Figures 16-18. From the 6 test cases
selected, the void fraction profiles compare well with the data. The vapour formation at the
wall gives a jump in the void fraction in that area. This behaviour is well captured for all the
cases by TransAT, except for Case 7, where the data show a sudden spike in the vapour
formation that all the CFD simulations fail to capture. As the inlet temperature increases
(constant mass flow rate), the void fraction at the wall increases. Results of TransAT and
Fluent show similar trends whereas NEPTUNE predictions do not return sufficient drop in
void fraction away from the wall.
Figure 15: Contours of void fraction, liquid temperature, streamwise gas velocity and temperature for Case
7
Figure 16: Void Fraction Comparison for Case 2 & 3:
Tin = 58.39 °C and Tin = 63.43 °C
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
15
Figure 17: Void Fraction Comparison for Case 4 & 5:
Tin = 67.89 °C and Tin = 70.14 °C
Figure 18: Void Fraction Comparison for Case 6 & 7:
Tin = 72.65 °C Tin = 73.7 °C
5.2 BARTOLOMEI Test Case
Figure 19: Problem Setup for the Bartolomei Test Case.
The next set of simulations experiments of Bartolomei et al. (1982). The set-up of
experiments is illustrated schematically in Fig. 19. Like in the DEBORA experiments
(Manon, 2000; Garnier et al, 2001), the heated lower section of the pipe sub-cooled boiling
occurs and steam is produced. The section above is adiabatic and vapor condensation
occurs due to the mixing of the vapor generated near the heated wall in the lower section
with the still subcooled liquid core. The pipe diameter is 12.03 mm, the heated section
length is L0=1 m and the total pipe length is L=1.4 m.
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
16
Subcooled water at temperature Tl enters the pipe at pressure Pl=6.89 MPa and mass flux Gl.
Heat flux at the channel wall in the heated section of the pipe is q=const. Saturation
temperature for these conditions is Tsat=558 K. The wall heat boundary condition in the
non-heated upper section of the pipe is q=0. Other conditions are listed in Table 5.
Heat flux mass flux Tinlet Tsat
MW/m2 kg/m2/s K
K
1.2
1500
495 558
Table 5: Parameters for the Bartolomei Test Case.
Figure 20: Radial distribution of void fraction.at different axial locations
Fig. 20 illustrates development of radial heating of water, changing of void fraction and
transport of steam due to lift and turbulent dispersion forces. By the end of the heated
section the water near the heated wall reaches saturation temperature, while the water at
the center of the pipe remains approximately 30K sub-cooled, The vapor fraction decreases
in the adiabatic section of the pipe due to condensation caused by turbulent mixing of the
two-phase mixture from the near-wall region with the sub-cooled liquid in the central
region. The experimental and numerical profiles of void fraction as shown in Fig. 21 are in
reasonably good agreement, although the discrepancy cannot be ignored. One probable
reason for the discepancy between the experimental results and the simulation results is
that the assumption of the bubble diameter and shape. The heat transfer rate predicted for
spherical bodies for condensation and evaporation is likely not to be accurate for complex
two-phase flow structures. The volumetric interfcial area balance equation proposed by Yao
at al (2004) to describe the geometrical structure of the two-phase flow, which takes into
account turbulence induced bubble coalescence and breakup, and modeling of the
nucleation of new bubbles on the volumteric interfacial area.
Figure 21: Average void fraction as a function of distance along the pipe.
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
17
5.3 LEE, PARK & LEE and TU & YEOH Test Case
Radial distribution of void fraction in a vertical (concentric) annulus in flow of subcooled
boiling water was studied in experiments of Lee, Park & Lee (2002), Tu & Yeoh(2003) and
Yeoh & Tu (2005). Schematic of the experimental section is presented in Fig. 22. The
experimental section is made as an annulus with inner diameter 19 mm, 37.5 mm, length
2.376 m and heated section of the inner pipe 1.67 m in length. Subcooled water is fed
upwards. The measurements were taken at the elevation of 1.61 m from the inlet. The
operating conditions are listed in Table 6.
Figure 22: Problem Setup.
Heat
flux
mass
Tinlet Tsat
flux
kg/m2/
MW/ m2
K
K
s
0.1523 474 371.5 383
Table 6: Computational Parameters.
Simulation was performed for the experiments with q=152.3 kW/m2, Gl=474 kg/(m2s),
P=0.14 MPa (saturation temperature Tsat=383 K), ΔTsub=11.5 K. The results from the
TransAT simulations are compared to the simulations performed by Ustinenko et al (2008)
using STAR-CD. The void fraction predictions match quite well with the published results as
seen in Fig. 23.
Figure 23: Void Fraction Distribution (Radial).
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
18
5.4 3D PWR SUB-CHANNEL Test Case
The present investigation is based on the CFD simulations for the international OECD/NRC
PWR subchannel and bundle tests (PSBT) benchmark (Rubin et al, 2010) provided by the
Nuclear Power Engineering Corporation (NUPEC), Japan. The benchmark specification
essentially compares and assesses numerical models and codes for the prediction of
detailed subchannel void distributions to full-scale experimental data on a PWR rod bundle.
Figure 24: Schematic of the NUPEC PWR Test Facility.
Figure 24 shows the schematic of the corresponding subchannel test section with an
effective heated length of LH=1555mm and the measurement cross section being located
LM=1400mm downstream the horizontal inlet of the coolant to the subchannel test section.
As can be seen from the schematic diagram, no special measures had been undertaken in
the experiment to control flow conditions or level of turbulence at the inlet cross section of
the subchannel test section, e.g. flow straighteners, honeycombs or similar, and it is hoped
that the length of the test section is sufficiently long (L/D~112) to prevent too large
influence from deviations of the necessary inlet condition assumptions in the CFD setup
from the real but unknown experimental inlet conditions.
Testcase
1.2211
1.2223
1.2237
1.4411
1.4325
1.4326
Measured
Inlet
Power
Pressure Temperature
[kW]
[MPa]
[°C]
15
15
15
10
10
10
295.4
319.6
329.6
238.9
253.8
268.8
90
70
60
60
60
60
Mass Flux
[kg m-2 s-1]
11
11
11
5
2
5
Table 7: Computational Parameters for the S1 subchannel.
The sub-channel test section, as shown in Fig. 24, simulates a single channel of a PWR fuel
assembly. The effective heated length is 1500 mm where the void measurement section is
located near close to the top end at 1400 mm from the bottom of the heated section. For the
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
19
CFD analyses 10 tests in the pressure region of 5 to 15 MPa, the mass flux range of 2.106 –
11.106 kg m-2 h-1 heating powers of 20 – 90 kW and inlet subcooling of about 15 to 50 K
were selected (see Table 7). The S1 subchannel consists of a typical central subchannel of a
fuel assembly where all four adjacent walls of heater rods are homogeneously heated by
constant power over the total length of the heated part of the test section. Due to the 90°
symmetry, only 1/4th of the geometry will be simulated in the CFD simulations.
The simulations are run unsteady (with adaptive time-stepping) till the flow properties
become quasi-constant. Fig. 25 shows the evolution of the vapour production over time, till
steady state is reached. The production of vapour is generated towards the end of the
heated section. The maximum production can be seen close to the exit. Due to the high
speed of the flow through the channel, the vapour produced does not drift towards the axis
of symmetry.
Figure 25: Evolution of the void fraction for test case 1.2237 (Scale – 1:20 lengthwise)
It is vital to know the minimum grid resolution to confidently perform accurate simulations.
Table 8 below shows the cell sizes used for running the test case 1.2223 in order to know
the grid resolution needed for grid independence. It also shows the additional
computational resources that are required to run the test case at higher grid resolution.
The wall clock time going from a cell-size 5.31 mm to 0.885 mm goes up 12 times with the
number of processors going up to 128 from 1.
Table 8: Computational Setup for the grid independence
Fig. 26 shows the average void fraction taken at a location close to the exit. It is seen that
the void fraction increases with better grid resolution. Between grid resolution of 1.328
mm and the 0.885 mm, the average void fraction is nearly constant. In the interest of
balancing the computational resources and accuracy, a grid resolution of 1.328 mm is
acceptable. Figure 27 shows the steady state void fraction distribution close to the exit. For
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
20
four different test cases listed in Table 7. It can be seen that the larger quantities of vapour
are produced when the inlet temperature is higher and when the fluid velocity is lower.
Figure 26: Average Void Fraction with increasing grid resolution.
Figure 27: Steady State Void Fraction Distribution for test cases 1.2211, 1.2436, 1.4326 and 1.4411
Fig. 28 shows the cross-sectional averaged void fraction distribution for the six test cases.
The results from TransAT are compared to the experimental results and CFX (Frank et al,
2011 and Krepper & Rzehak, 2013). TransAT show good agreement with the experiments
and performs better than CFX in four of the six test cases.
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
21
Figure 28: Steady State Void Fraction Distribution for four test cases (1.2211, 1.2436, 1.4326 and
1.4411)
6. Conclusions
This note describes the way computational thermal-hydraulics is migrating to more
sophisticated meshing techniques for problems involving complex geometries as well as
more complex physics. The proposed techniques for complex geometries, called IST/BMR,
helps describe the wall-surface of any component simply using CAD-based information. The
CAD file is immersed in a Cartesian grid. The method can be successfully combined to
generate realistic transient simulations of turbulent flows in reasonable computing times,
since it reduce the grid size and thus the simulation time. Further, the BMR technique helps
to better solve the boundary layer zone along with the IST technique. In BMR, more refined
sub-blocks are automatically generated around solid surfaces. An unlimited number of subblocks of various refinements can be generated, leading to a saving of up to 75% of cells in
3D. The advanced turbulence models involved in solving the complicated problems include
LES, Steady and Unsteady RANS. The methods for capturing heat transfer, including phase
change go from Level-Set to Ensemble-Averaged Model depending on the scale of the
problem. Plans are afoot at ASCOMP to create a hybrid approach that combines the level of
detail of the Level-Set Method and the large-scale applicability of the Ensemble-Averaged
Method.
In conclusion, through several examples, the ability of TransAT to simulate different aspects
of industrial thermal-hydraulics is demonstrated. With a combination of advanced physical
models, numerical algorithms and computational resources, ASCOMP can tackle the most
complex problems within a reasonable time-frame.
References
G. G. Bartolomei, V. G. Brantov, Y. S. Molochnikov, Y. V. Kharitonov, V. A. Solodkii,,G. N.
Batashova, & V. N. Mikhailov, “An experimental investigation of true volumetric vapor
content with subcooled boiling in tubes”, Thermal Engineering, 29(3), 132-135 (1982).
D. Bestion, D. Lucas, M. Boucker, H. Anglart, I. Tiselj, Y. Bartosiewicz, "Some lessons learned
from the use of Two-Phase CFD for Nuclear Reactor Thermalhydraulics", N13-P1139, Proc.
of NURETH-13. Kanazawa, Japan, September 27-October 2 (2009).
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
22
D. Caviezel, M. Labois, C. Narayanan and D. Lakehal, , “Highly resolved multiphase flown
topology in vertical pipes and risers”, International Conference on Multiphase Flow 2013
ICMF2013 (Paper 860), May 26-31 (2013).
J.G.M. Eggels, F. Unger, M. H. Weiss, J. Westerweel, R. J. Adrian, R. Friedrich, and F. T. M.
Nieuwstadt. "Fully developed turbulent pipe flow: a comparison between direct numerical
simulation and experiment." Journal of Fluid Mechanics 268, 175-210 (1994).
T. Frank, F. Reiterer and C. Lifante, “Investigation of the PWR subchannel void distribution
benchmark (OECD/NRC PSBT benchmark) using ANSYS CFX”, NURETH-14, paper 85,
Toronto, Canada, September 25-29 (2011).
J. Garnier, E. Manon & G. Cubizolles, “Local measurement on flow boiling of Refrigerant 12 in
a vertical tube”, Multiphase Science and Technology, Vol.13, pp.1-58 (2001).
W.K. In, and T.-H. Chun, "CFD Analysis of a Nuclear Fuel Bundle Test for Void Distribution
Benchmark, N13-P1259", Proc. of NURETH-13, Kanazawa, Japan, Sep. 27-Oct. 2 (2009).
H. Incropera & J. DeWitt,. Introduction to Heat Transfer, Wiley & Sons. Third Ed. 1996
N.I. Kolev, The influence of mutual bubble interaction on the bubble departure diameter,
Experimental thermal and fluid science, 8(2), pp. 167-174 (1994).
E. Krepper, and R. Rzehak. "CFD for subcooled flow boiling: Simulation of DEBORA
experiments", Nuclear Engineering and Design, 241(9), pp. 3851-3866 (2011).
E. Krepper and R. Rzehak, “ CFD Analysis of a void distribution benchmark of the NUPEC
PSBT tests”, The 15th International Topical Meeting on Nuclear Reactor Thermalhydraulics,
NURETH-15, paper 336, Pisa, Italy May 12-15 (2013).
N. Kurul, and M. Z. Podowski, “Multidimensional Effects in Forced Convection Subcooled
Boiling”, Proc. of 9th Int. Heat Transfer Conference, Jerusalem, Israel, 21-26 August (1990).
M. Labois & D. Lakehal, “Very-Large Eddy Simulation (V-LES) of the flow across a tube
bundle”, Nuclear Engineering and Design, 241, 6, pp. 2075-2085 (2011).
D. Lakehal, “LEIS for the prediction of turbulent multifluid flows applied to thermalhydraulics applications”, Nuclear Engineering and Design, 240, 9, pp. 2096-2106 (2010).
J. Lavieville, E. Quemerais, S. Mimouni, M. Boucker, N. Mechitoua: “NEPTUNE CFD V1.0
Theory Manual”, EDF (2005).
T. H. Lee, G. C. Park & D. J. Lee, “Local flow characteristics of subcooled boiling flow of water
in a vertical annulus”. Int. J. Multiphase Flow, Vol.28, p.1351-1368 (2002).
P. Liovic, D. Lakehal, “Interface-turbulence interactions in large-scale bubbling processes”,
Int. J. Heat & Fluid Flow, 28, 127-144, 2007a.
P. Liovic, D. Lakehal, “Multi-Physics Treatment in the Vicinity of Arbitrarily Deformable
Fluid-Fluid Interfaces”, J. Comp. Physics, 222, 504-535, 2007b.
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
23
S. Lo, “Progress in modeling boiling two-phase flows in boiling water reactor fuel
assemblies”, Proc. of Workshop on Modeling and Measurements of Two-Phase Flows and
Heat Transfer in Nuclear Fuel Assemblies, October 10-11, KTH, Stockholm, Sweden (2006).
M. Manninen, V. Taivassalo and S. Kallio, “On the mixture model for multiphase flow”, Espoo,
Technical Reseacrh Centre of Finland, VTT Publications, pp. 288-354 (1996).
E. Manon, “Contribution à l'analyse et à la modélisation locale des écoulements bouillants
sous-saturés dans les conditions des réacteurs à eau sous pression”, Thèse de Doctorat.
Ecole Centrale Paris (2000).
NIST Chemistry WebBook, Thermophysical Properties of Dichlorodifluoromethane (R12),
http://webbook.nist.gov/
A. Rubin, A. Schoedel, and M. Avramova, “OECD/NRC Benchmark Based on NUPEC PWR
Subchannel and Bundle Tests (PSBT). Volume I: Experimental Database and Final Problem
Specifications,” NEA/NSC/DOC(2010)1, January 2010.
A. Sanna, C. Hutter, D.B.R. Kenning, T.G. Karayiannis, K. Sefiane, R.A. Nelson, “Nucleate Pool
Boiling Investigation on a Silicon Test Section with Micro-Fabricated Cavities”, ECI
International Conference on Boiling Heat Transfer, Florianópolis, Brazil, 3-7 May (2009).
R. Sugrue, T. McKrell and J. Buongiorno, “On the effects of orientation angle, subcooling,
masflux, heat flux and pressure on bubble growth and detachment in subcooled flow
boiling”, Advances in Nuclear Energy Disciplines (ANED) Series, MIT-ANED-TR-001 (2012).
M. Sussman, P. Smereka & S. Osher, “A level set approach for computing solutions to
incompressible two-phase flow”, Journal of Computational physics, 114(1), 146-159 (1994).
N. Todreas and M. Kazimi, “Nuclear Systems I: Thermal Hydraulics Fundamentals”, Taylor
and Francis Group (1990).
J. Y. Tu & G. H. Yeoh, “Development of a numerical model for subcooled boiling flow”, Third
Int. Conf. CFD in the Minerals and Process Industries CSIRO, Melbourne, Australia,
December 10-12 (2003).
F. Unger, and R. Friedrich. "Numerical Simulation of Fully Developed Turbulent Pipe Flow."
Notes on Numerical Fluid Mechanics 38, 201-201 (1993).
V. Ustinenko, M. Samigulin, A. Ioilev, S. Lo, A. Tentner, A. Lychagin, A. Razin and V. Girin, Y.
Vanyukov, "Validation of CFD-BWR, a new two-phase computational fluid dynamics model
for boiling water reactor analysis" Nuclear Engineering and Design, 238(3), 660-670
(2008).
L. Vyskocil and J. Macek, “Boiling Flow Simulation in NEPTUNE CFD and FLUENT Codes”,
XCFD4NRS, Grenoble, France, 10 - 12 Sep. (2008).
W. Yao and C. Morel, “Volumetric interfacial area prediction in upward bubbly two-phase
flow”, Intl. J. Heat Mass Transfer, 47, 307-328 (2004).
G. H. Yeoh & J. Y. Tu, “A unified model considering force balances for departing vapour
bubbles and population balance in subcooled boiling flow”, Nucl. Engineering Design,
Vol.235, p.1251-1265 (2005).
TransAT for Nuclear Science & Technology: On Two-phase Flow & Heat Transfer Simulation in Fuel Assemblies.
24