# An Overview of the Pressurized Thermal Shock Issue in  the Context of the NURESIM Project

Authors: D. Lucas; D. Bestion; E. Bodèle; P. Coste; M. Scheuerer; F. D'Auria; D. Mazzini; B. Smith; I. Tiselj; A. Martin; D. Lakehal; J.-M. Seynhaeve; R. Kyrki-Rajamäki; M. Ilvonen; J. Macek
Journal: Science and Technology of Nuclear Installations
 (2009)

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## Abstract

Within the European Integrated Project NURESIM, the simulation of PTS is investigated. Some accident scenarios for Pressurized Water Reactors may cause Emergency Core Coolant injection into the cold leg leading to PTS situations. They imply the formation of temperature gradients in the thick vessel walls with consequent localized stresses and the potential for propagation of possible flaws present in the material. This paper focuses on two-phase conditions that are potentially at the origin of PTS. It summarizes recent advances in the understanding of the two-phase phenomena occurring within the geometric region of the nuclear reactor,that is, the cold leg and the downcomer, where the “PTS fluid-dynamics" is relevant. Available experimental data for validation of two-phase CFD simulation tools are reviewed and the capabilities of such tools to capture each basic phenomenon are discussed. Key conclusions show that several two-phase flow subphenomena are involved and can individually be simulated at least at a qualitative level, but the capability to simulate their interaction and the overall system performance is still limited. In the near term, one may envisage a simplified treatment of two-phase PTS transients by neglecting some effects which are not yet well controlled, leading to slightly conservative predictions.


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## Body

## 1. Introduction

Pressurized thermal shock (PTS) in
general denotes the occurrence of thermal loads on the reactor pressure vessel (RPV)
under pressurized conditions. PTS was identified by the European project
EUROFASTNET as one of the most important industrial needs related to nuclear
reactor safety since the integrity
of the RPV has to be assured throughout the reactor lifetime; it is one of the
barriers against fission product release, and its replacement is not feasible. A very severe PTS scenario is cold
water emergency core cooling (ECC) injection into the cold leg during a
hypothetical small-break loss of coolant accident (SB-LOCA). The injected water
mixes with the hot fluid present in the cold leg, and the mixture flows towards
the downcomer where further mixing with the ambient fluid takes place (see Figure1). High thermal gradients may occur in the structural components while the
primary circuit pressurisation is partially preserved. Therefore, the transient
fluid temperature must be reliably assessed to predict the loads upon the RPV
and the pressure wall toughness. The cooling fluid can either be in
single-phase or in two-phase condition, depending on the leak size, its
location, and on the operating conditions of the nuclear power plant considered.
The PTS has been the objective of a number of international cooperative
programmes in the past, for example, the OECD-ICAS as given by [1].Figure 1
Most important flow phenomena during a PTS situation with
partially filled cold leg.PTS-scenarios were considered in
the NURESIM project for the French 900 MW CPY PWR, the German 1300 MW Konvoi
reactor, the Loviisa 500 MW VVER, and the Russian VVER-1000. Typical diameters
of the cold leg are between 700 mm and 850 mm while the sizes of the ECC
injection nozzle vary between 170 mm and 225 mm. Loss of coolant accident
(LOCA) scenarios, with different leak sizes and leak locations, are considered
as initial events leading to ECC injection, which can
create PTS situations. For all the scenarios, there is a high-pressure
injection (HPI) into the cold leg. For some of the scenarios, the pressure can
be stabilized to remain within single-phase flow conditions in the cold leg.
However, for all reactor concepts, there are also scenarios that lead to
two-phase flow situations in the cold leg. Injection from the hydroaccumulators
needs to be considered in addition to the HPI. While the accumulators are
connected to the cold leg for some PWR, the accumulators inject the cooling
water into the downcomer and into the upper plenum in case of the VVER
reactors. In the two-phase flow scenario, the cold leg is either partially
uncovered or totally uncovered. Both situations have to be covered by two-phase
flow simulations; in particular, stratified flow with a void fraction range
from 0 to 100% needs to be considered for a partially filled cold leg.In all the
two-phase flow scenarios, the pressure is below 7.5 MPa. The liquid flow rates
in the cold leg at the exit of the pumps are close to zero but may have
fluctuations in the range from−100kg/s to +100kg/s. Maximum steam flow rates
in the considered scenarios are up to 50 kg/s in case of a steam flow from the
downcomer towards the steam generator and up to 15 kg/s for a flow from the
steam generator towards the downcomer. Mass flow rates from the HPI are limited
to a maximum value of 80 kg/s, while the temperatures are in the range between
283°C and 298°C. The maximum accumulator flow rates for the reactor
designs with an injection into the cold leg are up to 30 kg/s. The temperature
of the injected water is between 25°C and 60°C.The PTS work
package within the frame of the NURESIM Integrated project of the 6th Framework
Programme focuses on a two-phase flow configuration resulting from a partially or
fully uncovered cold leg. In the case of a partially uncovered cold leg, a stratification
of cold water on the bottom of the cold leg with counter-current flow of hot
water and steam on top of this cold-water layer may occur (see Figure1). There
is a mixing between hot and cold water. Condensation takes place at the free
surfaces of the cooling water jet and of the stratified flow. The process is
strongly dependent on the turbulence in the fluids. If the water level in the
downcomer has dropped below the cold leg nozzle, cold water is injected into
vapor with direct contact condensation on the steam-water interface and heating
along walls of both the cold leg and the downcomer. Stripe cooling will occur
in the downcomer. Direct contact condensation (DCC) is of prime importance in
this situation since it is the main heat source for the cold water. Interfacial
transfers (momentum—including turbulence—mass and energy) have then to be considered in
the jet area as well as in the stratified flow.As shown in Figure1, different flow
phenomena occur. There are flows with separated surfaces (jet interface,
horizontal interface), but also dispersed flows occur due to bubble entrainment
(at jet impingement and possibly also in the horizontal flow region by
entrainment caused by waves). Since there is a strong thermal nonequilibrium at
these interfaces, momentum transfer as well as heat and mass transfer have to
be considered. The various two-phase phenomena taking place are strongly
coupled, both within the fluids and in regard to the
heat transfer to walls. The different phenomena depend on very different
characteristic length-scales, from the size of the smallest eddy up to the
system scale. Some of the involved phenomena are not yet well understood
regarding their physics. The simulations of the whole system during the ECC
injection process and then accurate reproduction of the thermal loads on the
RPV are thus a considerable challenge.In
detail, the following “geometrical” flow regions or flow patterns connected
with the listed single phenomena can be distinguished for the two-phase PTS
situation (e.g., [2], see also Figure 1).(i)
Free liquid jet:(a)
momentum transfer at the jet interface, including instabilities,(b)
splitting of the jet,(c)
condensation on the jet surface.(ii)
Zone of the impinging jet:(a)
surface deformation by the jet including generation of waves,(b)
steam bubble entrainment,(c)
bubble migration and de-entrainment,(d)
turbulence production below the jet.(iii)
Zone of horizontal flow:(a)
momentum exchange at the gas-liquid interface, including generation of
waves and growth or damping of these waves,(b)
heat and mass transfer (condensation) at the gas-liquid interface
including its influence on the momentum transfer,(c)
heat transfer to the walls,(d)
turbulence production at the interface,(e)
turbulence production at the walls,(f)
influence of the phase change on turbulence and on wave pattern,(g)
mixing/stratification of hot and cold water streams.(iv)
Flow in the downcomer in the case of a partially filled cold leg:(a)
turbulence production at the walls,(b)
mixing/stratification of hot and cold water,(c)
heat transfer to the walls.(v)
Flow in the downcomer in the case of the water level being below the
cold leg nozzle:(a)
separation of the incoming water jet from the downcomer wall or not,(b)
momentum transfer at the jet interface, including instabilities,(c)
splitting of the jet,(d)
phase change at the jet surface,(e)
heat transfer to the walls.There are
strong interactions between the listed flow regions and related flow
patterns. The effect of noncondensable
gases has to be considered due to nitrogen degassing from ECCS water.It is not
possible to reproduce experimentally in full scale, the whole ECC injection
process, starting from the injection location to the inner downcomer, considering
the various two-phase flow regimes. Reliable numerical simulations are
required, and two-phase PTS constitutes one of the most challenging exercises
for a computational fluid dynamics (CFD) simulation. Improvements of the
two-phase modelling capabilities have to be undertaken to qualify the codes for
the simulation of such flows. A really accurate simulation of all the phenomena
that occur in the scenario will only be possible in the far future. To reach
this aim, it is necessary to go step-by-step and to improve the quality of the
forecasts. However, the use of CFD in industrial studies related to PTS is already
possible, but with some limitations.The main goal
of the NURESIM project is the development of a common European multiscale and multidisciplinary
platform for NUclear REactor SIMulation (NURESIM). During the current NURESIM project, the simulation of PTS,
including DCC scenarios, should be enhanced beyond the current state of the art
by improving substantially the two-phase flow modelling capabilities of current
CFD-codes. The Neptune_CFD (see [3, 4]) code is used as the initial framework for the common platform, and both
the CFX and FLUENT CFD tools are also used for PTS investigations.Within the above framework, the
objective of the paper is on the one hand to provide a critical evaluation on
the present status in the simulation of thermal-hydraulic aspects of PTS and on
the other hand to show how the NURESIM project uses available experimental data
for improving and validating the models. A detailed presentation of scenarios
leading to two-phase PTS situations as well as a discussion on the status of
CFD capabilities for PTS at the beginning of the NURESIM was given by Lucas [5].


## 2. Experimental Data Basis

CFD methods
use many turbulence and two-phase flow models which have a certain degree of
empiricism. The accuracy and universal validity of these models have to be
assessed by comparison of the numerical results with experimental data.
Depending on the suitability of the data, test cases are used for validation
and calibration of statistical models and for demonstration of model
capabilities.


### 2.1. Validation Experiments

Validation
cases focus on separate effects as they test different aspects of a CFD code
and its physical models. The successful simulation of the single separated
effects is a prerequisite for a complex industrial PTS flow simulation. In a validation
test, the quality of the statistical model is checked for a given flow
situation. Validation tests are the only method to minimize and quantify modelling
errors and to ensure that new models are applicable with confidence to certain
types of flows. In an ideal case, a validation test case gives sufficient
details to allow for an improvement of the physical models. In NURESIM,
validation data are also obtained from direct numerical simulation (DNS)
studies.In the
NURESIM database [6], test cases were selected which clearly
identify the main features of the CFD models that are to be tested and which
are dominant in the validation case. In order to ensure completeness of
information, all experiments are described according to the following template:
(i)
general description and flow features,(ii)
description of measurements and geometry,(iii)
detailed information on boundary and initial conditions,(iv)
availability of experimental data,(v)
information on previous work and related experiments.Next to the
completeness of the data, their quality is of primary importance for a successful
validation exercise. The quality of the data is mainly evaluated by error
bounds provided by the experimentalists. Unfortunately, most experiments still
do not provide this information. Moreover, even if error estimates are
available, they cannot exclude systematic errors by the experimentalist. In
addition to error bounds, it is therefore desirable to have an overlap of
experimental data, which allow for testing of the consistency of the
measurements. To this end, experiments have been gathered investigating the
same or similar PTS phenomena but performed by different experimental groups in
different facilities using different experimental techniques.Experiments investigating jet impingement
on a free surface and bubble entrainment were performed by Bonetto and Lahey [7] and Iguchi [8] as follows.
(i)
The Bonetto and Lahey experiment
investigates jet impingement on a free surface using an axisymmetric, turbulent
jet impinging orthogonally on a free surface. The flow was statistically
steady-state; the fluid was water in an air environment. A laser Doppler
anemometer (LDA) system was used to measure the liquid gas velocities (both
mean and fluctuations), and both a fiber phase-Doppler anemometer (FPDA) and an
impedance probe were used to measure the void fraction, depending on the bubble
size created by the impinging jet. The void fraction was measured at varying
depths below the undisturbed surface.(ii)
A turbulent nonfragmented water jet
impinging on a free surface in air environment was investigated by Iguchi et al. [8] at the University of Hokkaido. LDA was used to measure mean
velocities and RMS values of the vertical and radial velocity below the free
surface. However, no measurements of bubble entrainment were made.Air water flows in horizontal channels were investigat-
ed at Forschungszentrum Dresden-Rossendorf (FZD) by Vallée et al. [9] and at INP Toulouse by Fabre et al. [10]:
(i)
A horizontal channel with rectangular
cross section was built at FZD for the investigation of co- and counter-current
air water flow at atmospheric pressure. The measurements were focused on the behaviour
of slug flow. Optical techniques, like video observation, were used to record
the flow pattern and to determine the water level. Velocity-fields are measured
using particle image velocimetry (PIV). Data is available for all NURESIM
partners on the basis of bilateral agreements.(ii)
In the Fabre experiment, air-water
turbulent stratified flow was investigated in a quasi horizontal (descending)
rectangular channel. Systematic measurements of the components of the mean
velocities and Reynolds stresses were performed with LDA and hot wire
anemometry under carefully controlled inlet conditions. The data was used by
[11] for validating the turbulence modelling near a free surface and
below the free surface in the liquid including the interfacial production terms
in adiabatic conditions. Selected data is made available to NURESIM partners by
CEA.Stratified steam water flows with
condensation were inves-
tigated by Lim et al. [12] and Ruile [13] as follows.
(i)
Lim investigated steam-water turbulent
stratified flow with condensation in a horizontal channel with a rectangular
cross-section. In the experiment, Pitot tubes were used to measure the local
mean steam velocity, and conductivity probes to measure the water height at
five locations. The data was used to validate interfacial condensation models
by Yao et al. [14].(ii)
Ruile [13], Hein et al. [15], and Goldbrunner [16] investigated contact condensation
in horizontal stratified flows of subcooled water and saturated steam in the
LAOKOON test facility at the University of Munich. The
experimental equipment was designed to set up co-current and counter-current
flow conditions in a straight channel with adiabatic walls. Available measured
data include the water and steam flow rates at the water feed cross section,
the inlet water temperature, and the temperature distribution across the water
layer at one location, where a vertical array of thermocouples was installed.
The pressure level inside the channel and the water layer height were also
measured. Data for selected test cases is available for NURESIM partners.Water hammer in a horizontal section of
a steam-line, induced by the injection of the cold water, was experimentally analysed
at PMK-2 test facility of the Hungarian Atomic Energy Research Institute KFKI
[17]. For the NURESIM project, mesh sensor data
can be useful for the development and verification of the heat and mass
transfer models in a horizontally stratified flow. However, it is well known
that due to the Helmholtz instability measurement error can be as large as 50%.Condensation
pool studies
were performed
in the Nuclear Safety Research Unit at Lappeenranta University of Technology, LUT
[18]. They were designed to correspond to the conditions of a
postulated accident in BWRs in Finland. In the first tests, the formation, size, and distribution of noncondensable gas
bubbles were studied in the condensation pool facility POOLEX. In the frame of
the national SAFIR programme, steam instead of noncondensable gas was injected
into the condensation pool test rig in order to study bubble dynamics issues
such as bubble growth, upward acceleration, detachment, and breakup. The
experiments usually consisted of several individual steam blows, where the key
parameters of the experiments (pool subcooling, steam mass flux) were varied. High-frequency
instrumentation and a high-speed camera were used in the experiments.
Structural loads were evaluated with the help of strain gauge measurements.


### 2.2. Demonstration Experiments

The purpose of a demonstration
exercise is to build confi-
dence in the ability of a CFD method to simulate
complex flows. While validation studies show for a number of building block
experiments that the physical models can cover the basic aspects of the PTS
application, demonstration cases test the ability of the CFD methods to predict
combined effects, including geometrical complexity. Typically, the level
of completeness of the data for demonstration cases is much lower than for
validation cases. Even though the density of data is usually lower, the NURESIM
selection required that the quality satisfies the same criteria as for
validation cases. Error estimates are desirable and so are independent measurements.Suitable
demonstration experiments were selected with complex flow phenomena for
PTS-scenarios as follows.(i)
The 1 : 2 scaled HYBISCUS experiments where
local temperature measurements were taken in the cold leg and in the downcomer
of a PWR simulating ECC-injection. However, data is property of EDF and only
available on special bilateral agreement.(ii)
The COSI experiments (see [19]) which provide temperature measurements for ECC injection scenarios
in a cold leg with focus on direct contact condensation in the injection zone. The
analysis of COSI tests data concluded that the jet-induced local turbulence in
the water was the main phenomenon controlling the global condensation rate
since most of the total condensation occurs close to the jet where this jet-induced turbulence enhances heat mixing below the free surface. Data is
property of CEA and EDF, and there is no published data available.(iii)
Selected 1 : 1 scaled UPTF experiments
where condensation and mixing phenomena during ECC injection were studied in
the test series TRAM C1 and TRAM C2. Temperature measurements were taken in the
cold legs, downcomer, lower, and upper plenum and in the core region. A
detailed description of the geometry, the instrumentation, and selected data is
made available in the frame of the NURESIM project.(iv)
The 1 : 48 volumetrically scaled ROSA test facility which was originally designed for the
investigation of system behaviour. However, several spinoff experiments in the
ROSA-IV and ROSA-V test programmes are focused on stratified flows. Data for
temperature and concentration measurements are restricted to the ROSA group. Future experiments are planned with focus on
the simulation of ECC injection and temperature stratification.(v)
Structural mechanics data resulting from
thermal stresses assuming PTS conditions are also made available in the NURESIM
database. They relate to thermal shock cryogenic experiments on steel plates
which were performed at the University of Pisa, DIMNP.Although
there are a number of experiments available where flow phenomena are
investigated as separate effects and as integral effects, there is still a need
for well-instrumented validation data and demonstration experiments where
experimental parameters are varied in order to investigate PTS phenomena. The
data are required in a high resolution in space and time for the whole domain
of interest and should include local and time-dependent information on
interface between the phases, mean, and fluctuations (turbulence parameter)
values for temperature and velocity.For this
purpose, theTOPFLOW PTS experimental
programme has been conceived. Its objective is to provide a well-informed
experimental database for both validation of CFD modelling of the two-phase
flow in the cold leg and the downcomer including flow-wall heat transfer, and
the improvement of the understanding of key thermal hydraulic (TH) phenomena
involved. Besides the operational standard instrumentation (pressure,
differential pressure, temperature, flow rates), the instrumentation will
comprise thermocouples, heat-flux probes, wire-mesh sensors, local void probes
equipped with a microthermocouple, high-speed camera observation, infrared
camera observations and a local conductivity probe. It is planned to operate
the test mockup in steady-state conditions with and without mass transfer due
to condensation as well as in transient operation.


## 2.1. Validation Experiments

Validation
cases focus on separate effects as they test different aspects of a CFD code
and its physical models. The successful simulation of the single separated
effects is a prerequisite for a complex industrial PTS flow simulation. In a validation
test, the quality of the statistical model is checked for a given flow
situation. Validation tests are the only method to minimize and quantify modelling
errors and to ensure that new models are applicable with confidence to certain
types of flows. In an ideal case, a validation test case gives sufficient
details to allow for an improvement of the physical models. In NURESIM,
validation data are also obtained from direct numerical simulation (DNS)
studies.In the
NURESIM database [6], test cases were selected which clearly
identify the main features of the CFD models that are to be tested and which
are dominant in the validation case. In order to ensure completeness of
information, all experiments are described according to the following template:
(i)
general description and flow features,(ii)
description of measurements and geometry,(iii)
detailed information on boundary and initial conditions,(iv)
availability of experimental data,(v)
information on previous work and related experiments.Next to the
completeness of the data, their quality is of primary importance for a successful
validation exercise. The quality of the data is mainly evaluated by error
bounds provided by the experimentalists. Unfortunately, most experiments still
do not provide this information. Moreover, even if error estimates are
available, they cannot exclude systematic errors by the experimentalist. In
addition to error bounds, it is therefore desirable to have an overlap of
experimental data, which allow for testing of the consistency of the
measurements. To this end, experiments have been gathered investigating the
same or similar PTS phenomena but performed by different experimental groups in
different facilities using different experimental techniques.Experiments investigating jet impingement
on a free surface and bubble entrainment were performed by Bonetto and Lahey [7] and Iguchi [8] as follows.
(i)
The Bonetto and Lahey experiment
investigates jet impingement on a free surface using an axisymmetric, turbulent
jet impinging orthogonally on a free surface. The flow was statistically
steady-state; the fluid was water in an air environment. A laser Doppler
anemometer (LDA) system was used to measure the liquid gas velocities (both
mean and fluctuations), and both a fiber phase-Doppler anemometer (FPDA) and an
impedance probe were used to measure the void fraction, depending on the bubble
size created by the impinging jet. The void fraction was measured at varying
depths below the undisturbed surface.(ii)
A turbulent nonfragmented water jet
impinging on a free surface in air environment was investigated by Iguchi et al. [8] at the University of Hokkaido. LDA was used to measure mean
velocities and RMS values of the vertical and radial velocity below the free
surface. However, no measurements of bubble entrainment were made.Air water flows in horizontal channels were investigat-
ed at Forschungszentrum Dresden-Rossendorf (FZD) by Vallée et al. [9] and at INP Toulouse by Fabre et al. [10]:
(i)
A horizontal channel with rectangular
cross section was built at FZD for the investigation of co- and counter-current
air water flow at atmospheric pressure. The measurements were focused on the behaviour
of slug flow. Optical techniques, like video observation, were used to record
the flow pattern and to determine the water level. Velocity-fields are measured
using particle image velocimetry (PIV). Data is available for all NURESIM
partners on the basis of bilateral agreements.(ii)
In the Fabre experiment, air-water
turbulent stratified flow was investigated in a quasi horizontal (descending)
rectangular channel. Systematic measurements of the components of the mean
velocities and Reynolds stresses were performed with LDA and hot wire
anemometry under carefully controlled inlet conditions. The data was used by
[11] for validating the turbulence modelling near a free surface and
below the free surface in the liquid including the interfacial production terms
in adiabatic conditions. Selected data is made available to NURESIM partners by
CEA.Stratified steam water flows with
condensation were inves-
tigated by Lim et al. [12] and Ruile [13] as follows.
(i)
Lim investigated steam-water turbulent
stratified flow with condensation in a horizontal channel with a rectangular
cross-section. In the experiment, Pitot tubes were used to measure the local
mean steam velocity, and conductivity probes to measure the water height at
five locations. The data was used to validate interfacial condensation models
by Yao et al. [14].(ii)
Ruile [13], Hein et al. [15], and Goldbrunner [16] investigated contact condensation
in horizontal stratified flows of subcooled water and saturated steam in the
LAOKOON test facility at the University of Munich. The
experimental equipment was designed to set up co-current and counter-current
flow conditions in a straight channel with adiabatic walls. Available measured
data include the water and steam flow rates at the water feed cross section,
the inlet water temperature, and the temperature distribution across the water
layer at one location, where a vertical array of thermocouples was installed.
The pressure level inside the channel and the water layer height were also
measured. Data for selected test cases is available for NURESIM partners.Water hammer in a horizontal section of
a steam-line, induced by the injection of the cold water, was experimentally analysed
at PMK-2 test facility of the Hungarian Atomic Energy Research Institute KFKI
[17]. For the NURESIM project, mesh sensor data
can be useful for the development and verification of the heat and mass
transfer models in a horizontally stratified flow. However, it is well known
that due to the Helmholtz instability measurement error can be as large as 50%.Condensation
pool studies
were performed
in the Nuclear Safety Research Unit at Lappeenranta University of Technology, LUT
[18]. They were designed to correspond to the conditions of a
postulated accident in BWRs in Finland. In the first tests, the formation, size, and distribution of noncondensable gas
bubbles were studied in the condensation pool facility POOLEX. In the frame of
the national SAFIR programme, steam instead of noncondensable gas was injected
into the condensation pool test rig in order to study bubble dynamics issues
such as bubble growth, upward acceleration, detachment, and breakup. The
experiments usually consisted of several individual steam blows, where the key
parameters of the experiments (pool subcooling, steam mass flux) were varied. High-frequency
instrumentation and a high-speed camera were used in the experiments.
Structural loads were evaluated with the help of strain gauge measurements.


## 2.2. Demonstration Experiments

The purpose of a demonstration
exercise is to build confi-
dence in the ability of a CFD method to simulate
complex flows. While validation studies show for a number of building block
experiments that the physical models can cover the basic aspects of the PTS
application, demonstration cases test the ability of the CFD methods to predict
combined effects, including geometrical complexity. Typically, the level
of completeness of the data for demonstration cases is much lower than for
validation cases. Even though the density of data is usually lower, the NURESIM
selection required that the quality satisfies the same criteria as for
validation cases. Error estimates are desirable and so are independent measurements.Suitable
demonstration experiments were selected with complex flow phenomena for
PTS-scenarios as follows.(i)
The 1 : 2 scaled HYBISCUS experiments where
local temperature measurements were taken in the cold leg and in the downcomer
of a PWR simulating ECC-injection. However, data is property of EDF and only
available on special bilateral agreement.(ii)
The COSI experiments (see [19]) which provide temperature measurements for ECC injection scenarios
in a cold leg with focus on direct contact condensation in the injection zone. The
analysis of COSI tests data concluded that the jet-induced local turbulence in
the water was the main phenomenon controlling the global condensation rate
since most of the total condensation occurs close to the jet where this jet-induced turbulence enhances heat mixing below the free surface. Data is
property of CEA and EDF, and there is no published data available.(iii)
Selected 1 : 1 scaled UPTF experiments
where condensation and mixing phenomena during ECC injection were studied in
the test series TRAM C1 and TRAM C2. Temperature measurements were taken in the
cold legs, downcomer, lower, and upper plenum and in the core region. A
detailed description of the geometry, the instrumentation, and selected data is
made available in the frame of the NURESIM project.(iv)
The 1 : 48 volumetrically scaled ROSA test facility which was originally designed for the
investigation of system behaviour. However, several spinoff experiments in the
ROSA-IV and ROSA-V test programmes are focused on stratified flows. Data for
temperature and concentration measurements are restricted to the ROSA group. Future experiments are planned with focus on
the simulation of ECC injection and temperature stratification.(v)
Structural mechanics data resulting from
thermal stresses assuming PTS conditions are also made available in the NURESIM
database. They relate to thermal shock cryogenic experiments on steel plates
which were performed at the University of Pisa, DIMNP.Although
there are a number of experiments available where flow phenomena are
investigated as separate effects and as integral effects, there is still a need
for well-instrumented validation data and demonstration experiments where
experimental parameters are varied in order to investigate PTS phenomena. The
data are required in a high resolution in space and time for the whole domain
of interest and should include local and time-dependent information on
interface between the phases, mean, and fluctuations (turbulence parameter)
values for temperature and velocity.For this
purpose, theTOPFLOW PTS experimental
programme has been conceived. Its objective is to provide a well-informed
experimental database for both validation of CFD modelling of the two-phase
flow in the cold leg and the downcomer including flow-wall heat transfer, and
the improvement of the understanding of key thermal hydraulic (TH) phenomena
involved. Besides the operational standard instrumentation (pressure,
differential pressure, temperature, flow rates), the instrumentation will
comprise thermocouples, heat-flux probes, wire-mesh sensors, local void probes
equipped with a microthermocouple, high-speed camera observation, infrared
camera observations and a local conductivity probe. It is planned to operate
the test mockup in steady-state conditions with and without mass transfer due
to condensation as well as in transient operation.


## 3. CFD Capabilities for the Simulation of Two-phase PTS

### 3.1. Free Liquid Jet

The cold liquid jet injected into
the horizontal cold leg pipe interacts first with the surrounding hot steam
environment. These interactions are strongly dependent on the position and
shape of the interface between the cold water and the hot gaseous environment.
Interface tracking methods (ITM) are needed for a detailed description of these
interactions. Depending on various characteristics of both the liquid and the
gas, such as the relative velocity between the two phases or turbulence
properties, instabilities at the surface of the jet can occur. Instabilities
can also be directly generated by the condensation process [20]. They
affect the heat and mass transfer. Models for DCC at the jet surface have to be
applied. The instabilities also influence the gas entrainment at the jet
impingement point on the liquid surface by capturing gas. Adequate modelling of
the interface, in connection with a suitable coupling of the turbulence fields
of the single phases and local mass and heat transfer, is needed.Numerous theories relating to
mechanisms on generation and growth of jet instabilities exist. Several
numerical approaches have been used, such as DNS or large-eddy simulation (LES) for the prediction of their behaviour using
various conditions [21, 22]. Even if
the individual effects of some parameters, such as gravity or nozzle internal
flow, have been separately studied, no computations exist taking into account
all these effects simultaneously. Actually, some models for the treatment of
these instabilities are based on restrictive assumptions, which limit strongly
their applicability. The LES approach seems the most suitable for the modelling
of this specific flow situation, not presuming what would be the best choice for
the simulation of the whole PTS.DCC at the jet surface resulting
from the temperature difference between the two phases is responsible for a non-negligible
part of the total condensation in the considered flow domain of the cold leg
[19]. For the condensation rate at the jet surface,
correlations exist [19], but no representative experimental
data are available to confirm this model. No special models were developed for
DCC at the jet surface. The variations of the condensation rate along the jet
and the effects of the noncondensable gases have been qualitatively reproduced
[23], but the quantitative prediction was not fully mature.


### 3.2. Zone of the Impinging Jet

Appropriate modelling of the
turbulence production below the jet is highly important, since turbulence is
responsible for the mixing of the fluid. Gas entrainment caused by the jet
impingement influences the characteristics of the turbulence below the free
surface. The properties of the entrained gas (e.g., bubble size, penetration
depth, horizontal migration, and total amount of entrained gas) are dependent
on various properties of both phases and jet. The jet velocity is one of the
most critical parameters. Depending on it, several scenarios for the gas
entrainment below the free surface have already been experimentally identified
[24, 25]. Most of the attempts for the
development of theories able to reproduce the properties of the entrained gas
below the free liquid surface have resulted in global correlations, which are
limited to the corresponding operating conditions and geometric configuration.
Several studies have highlighted the absence of theoretical approach and of
valid correlations for the prediction of the minimal jet velocity at which the
gas entrainment occurs. The modelling of the impinging jet zone requires
simultaneous consideration of separated (surface) and dispersed (bubbles) flow
within one flow domain.Two issues have to be considered
regarding turbulence production: the turbulence generated by the impingement of
the jet itself and the influence of the bubbles on the turbulence. In the
NURESIM project, investigations are done on the turbulence production below the
jet by CEA and University of Pisa which simulated [8] tests of a plunging jet [26]. Together with Neptune_CFD standard models, a CEA/Grenoble
modified k-ε model was tested. Quite good agreement
with experimental data was achieved with best performing models: numerical predictions of the mean velocity
field were always good, and turbulence was generally not bad but with
significant underestimation far from the jet axis region.In most simulations, the effect of
the liquid turbulence on the bubbles is modelled, but the opposite effect
(corresponding to the influence of the bubbles on the liquid turbulence field)
is only considered in regards to the turbulent viscosity, for example, using
the Sato model [27], despite this effect being important in the dense bubble region (near the
impingement point). Some studies have thus to be conducted to improve
understanding and modelling of the coupling between these various processes.Both LES and RANS models can be used for the simulation of the zone of the
impinging jet. A more general investigation on the applicability of RANS and
LES models for bubbly flow, including bubble plumes, was undertaken in the
frame of the NURESIM project by PSI.In the impinging jet zone, four
different interface struc-
tures have to be considered:
(1) the surface of the jet, (2) the free surface of the pool (i.e., liquid level in the cold leg), (3) the entrained bubbles, and (4) the complicated surface structure in the region
where the jet impacts the surface. Separated (jet surface and pool surface) as
well as dispersed (bubbles) flow regions exist simultaneously in one flow
domain. The most difficult thing
is to model the transitions between the two types of interfaces (i.e., bubble
entrainment and de-entrainment). For the different interfacial structures,
different closure models are needed, for example, for drag. The identification
of the interfaces for separated flows is thus of crucial importance.Some computations of the whole
plunging jet process (starting from the jet, to the bubble de-entrainment,
considering the impingement zone, the bubble migration below the free liquid
surface and the free surface) have been performed with some success in the past
[28]. These were able to reproduce the global behaviour for the free
liquid surface (small waves at the free surface and shape at the impingement
point), the gas entrainment, the bubble migration below the free surface, and
the bubble de-entrainment at the free surface. Even if the entrainment process
has been more or less well reproduced numerically (generation of entrained
bubbles at the impingement point), the total volume flow rate of entrained gas
has been largely overestimated. One of the most critical problems pointed out
during these computations is the treatment of the liquid/gas interfaces. To
overcome the discrepancies, the two kinds of interface mentioned above have to
be modelled using two different models (or at least the same model with
different values for the parameters). In the frame of the NURESIM project,
investigations are done by FZD regarding these problems. This resulted in the
suggestion to use so-called algebraic interfacial area density (AIAD)
models which allow to apply two different drag coefficients for free surface
and for bubbly flow. A blending function based on the gas void fraction is used
to apply the adequate drag coefficient depending on the flow regime.The behaviour of the entrained gas
bubbles below the free liquid surface is determined by several forces acting on
individual bubbles. The most important of these forces are buoyancy, drag,
virtual mass force, lift force, and turbulent dispersion force. All these
forces are strongly dependent on the bubble size (see, e.g., [29]).
For bubbly flow in vertical pipes, a combination of Tomiyama lift- and wall
force together with the Favre-averaged drag force [30] was found to reflect
the experimental findings in poly-dispersed flows [31]. In the case of developing flows, some differences have
been pointed out between calculations and experimental data [32]. In the frame of the NURESIM project, the influence of the
bubble forces on bubble migration is investigated by FZD for an impinging jet
configuration.In most computations, the bubble
diameters are assumed to be constant. In principle, CFD models which allow
consideration of a number of bubbles classes already exist [33], but calculations are
then very time consuming. The bubbles size distribution is strongly influenced
by bubble coalescence and breakup, for which various models exist in the
literature (e.g., [34–36]). The models for
bubble forces, as well as the models for bubble coalescence and breakup, have
consequently to be validated for the plunging jet configuration.There are also some attempts on a direct
tracking of interfaces at zone of the jet impingement. Interface tracking
techniques have indeed been applied, in combination with LES of the fields in
each phase, to interfacial, sheared, two-phase flow [37, 38]. These authors incorporated the VOF approach to an LES simulation and
applied it to the case of air/steam injection into a water pool, as
investigated previously by Meier [39]. It is obvious that the available computational
resources will not allow this approach to be used to capture the details of a
dispersed bubbly flow; the routinely used two-fluid formulation remains much
less demanding. Nevertheless, the LES/VOF combination may be a candidate future
technique for tackling flows involving large interfacial inclusions. Novel
analytical developments to the method have now been made by Liovic and Lakehal [38],  namely, in the treatment of turbulence near sheared deformable
interfaces.


### 3.3. Zone of Stratified Flow in the Cold Leg

In the horizontal cold leg pipe, a
stratified flow has to be considered. In the context of PTS, the interface is characterised
by intense heat, mass, momentum, and turbulence transfer. Heat transfer between
the fluids and the wall of the cold leg pipe has also to be considered.


#### 3.3.1. Momentum and Turbulence Transfer

Depending on the relative velocities
of the gas and the liquid phases, the liquid/gas interface is strongly or
mildly perturbed. For low relative velocities, the interface is quasistatic.
For higher relative velocities, the interface is perturbed, and small waves are
generated. Depending on the actual conditions, these waves can be amplified
during their propagation in the horizontal pipe. The so-calledKelvin-Helmholtz
instability can occur when a velocity shear is present within a continuous
fluid or when there is sufficient velocity difference across the interface
between two fluids. The CFD modelling of this instability was investigated in
the frame of the NURESIM project by UCL. The classical theory can be used to
predict the onset of instability in fluids of slightly different densities
moving at various speeds. In the absence of surface tension, all wavelengths
are unstable. The existence of surface tension stabilises the short wavelength
condition; the theory then predicts stability until a velocity threshold is
reached. For this reason, interface tracking methods or any method which
includes surface tension effects have to be used [40, 41]. For cases with high-density differences, such as steam and water
in the case of PTS, the situation is much more complicated (see [42]). It was found that either a single-fluid approach with VOF (FLUENT) or a
two-fluid model with a large interface recognition (Neptune)
could predict reasonably wave generation and growing and that condensation-induced instability could also be qualitatively predicted by Neptune and CFX.In cases with high relative
velocities in horizontal pipes, the waves are strongly amplified, and aslug flow with a complex system of
interactions (presence of gas bubbles and liquid droplets) between the two
phases can occur. The generated waves can, in certain cases of high relative
velocity, entirely block the cold leg pipe. The slug flow regime is usually characterised
by an acceleration of the gaseous phase and by the transition of fast liquid
slugs carrying a significant amount of liquid with high-kinetic energy. The
two-phase flow regimes in horizontal pipes are not only dependent on the local
conditions but depend also on the characteristics of the free falling jet which
may itself generate waves.A systematic study of numerical
simulation of slug flow in horizontal pipes using ANSYS CFX was carried out by
Frank [9] and Vallée et al. [43]. It was shown that the formation of the slug flow regime strongly
depends on the wall friction of the liquid phase. In simulations using
inlet/outlet boundary conditions, it was found that the formation of slug flow
regimes strongly depends on the agitation or perturbation of the inlet boundary
conditions. Furthermore, Frank showed that the length of the computational
domain also plays an important role in slug formation. Similar experimental
data are being used in NURESIM for benchmarking the Neptune_CFD code by UCL,
while University of Pisa
and CEA do
simulations of Fabre et al. [10]. A new modelling approach of
large interfaces is developed considering an interfacial layer of 3 cells
[44].Momentum transfer is closely
connected with turbulent transfer. In the case of the turbulence predicted by
thek-ε model, the interfacial momentum can be modelled using several closure
laws. The interfacial sublayer model (ISM, [14]) in the gas phase supposes, due to the significant
difference between the gas and liquid densities, that the interface can be
treated as a “moving solid wall” with a velocity equal to the liquid velocity.
The gas region close to the interface is modelled with the two sublayer models, which is similar
to the wall function concept. It is also possible to use the average viscosity
assumption (AVM, [14]).
This model is based on the simplified momentum equation in the case of a thin
layer near a smooth interface without phase change, which permits the
interfacial friction and velocity to be evaluated. Morel [45] has proposed a
modification of the Taitel and Dukler model (TDM, [46])
for multidimensional calculations.


#### 3.3.2. Turbulence Modelling

The mixing of hot and cold water is
mainly determined by turbulence. The turbulence fields for both the liquid and
the gas phases and the coupling between them play also important roles on the
interfacial transfer and on the two-phase flow regime in the cold leg, and for
the transition between different regimes (i.e., smooth surface, wavy flow, slug
flow). Close to the interface, three turbulence sources have been identified:
turbulence diffused from wall boundaries, turbulence production by the
interfacial friction, and turbulence induced by interfacial waves. Close to the
interface, the anisotropy of the turbulence has to be considered. It is not
reproduced by any classic model. In most of the cases, the turbulence is modelled
using thek-ω or the k-ε (classic or modified) models, together with a specific hypothesis at
the interface [47, 48]. Without any special treatment of the free surface, the high-velocity
gradients at the free surface generate too high turbulence when using eddy
viscosity models like the k-ε or the k-ω model.
Therefore, a symmetric damping procedure for the solid wall-like damping of
turbulence in both gas and liquid phases has been proposed by Egorov [28]. A
numerical database obtained by DNS simulation of the interface was generated in
the frame of NURESIM by ASCOMP [49, 50].Vallée et al. [51] employed the shear stress transport
(SST) turbulence model for each phase. The k-ω based SST model [52] accounts for the transport of the turbulent shear stress and gives good
predictions of the onset and the amount of flow separation under adverse
pressure gradients. The qualitative slug formation in the
simulations (ANSYS-CFX) was in good agreement with the experiment.


#### 3.3.3.
Modelling of the Free Surface

According to Zwart [53], numerical
models for free surface flow may be divided into three categories: surface
adaptive methods, interface-capturing methods, and interface-tracking methods.Surface-adaptive methods are typically single-phase approaches in which the kinematic condition
is used to update the location of the free surface interface, and the mesh
boundary conforms to this interface at all times. These methods inherently
involve mesh motion. While these methods are successful for certain classes of
flows, they are typically restricted to modest degrees of interface deformation.
Methods of working around these limitations have been devised, including
periodic remeshing and interpolation, characteristic streamline diffusion
finite element methods [54], and the integrated space-time finite
volume method [55]. Despite these advances in tracking significant interface deformation, it
remains the case that surface adaptive methods are useful primarily when the
interface topology is straightforward. Effects such as splashing, breaking, and
colliding of waves remain difficult challenges. Moreover, the geometries
themselves must be simple in order to calculate how to move the mesh at interface-wall
intersections.These limitations may be overcome by
having a fixed mesh, which spans the interface location. Theinterface is captured within the mesh
by specific algorithms. Most commonly, the algorithm makes use of the
continuity equation for one of the phases, in which the dependent variable is
the volume fraction of that phase; these methods are called volume-of-fluid (VOF)
methods. They differ widely in their detailed implementation. Many of them are
interface-capturing and solve the VOF equation using a continuum advection
scheme. If standard techniques are used for the advection operator, numerical
diffusion will lead to significant smearing of the interface. A variety of
compressive advection schemes have been devised to minimize this diffusion. The
compressivness is often obtained by using a controlled downwinding of the
fluxes, as with the donor-acceptor [56] and CICSAM
[57] schemes. Controlled down-winding schemes have
compressive characteristics which depend upon the time-step and therefore
require small time steps to retain sharp interfaces, even for steady-state free
surface flows. More recently, a new scheme having compressive characteristics
independent of the time step size has been developed [58].Other VOF methods areinterface-tracking and explicitly track
the free surface interface. For a particular volume fraction field, the
interface is reconstructed using a piecewise representation (constant, linear,
or parabolic) in each cell. The volume fluxes may be calculated either
geometrically or using an advection operator as described above. Further
details of these algorithms can be found in [59, 60]. Another fixed grid
strategy for free surface flow problems involves the use of level set method
[61]. The level
set strategy formulates and solves an equation representing the signed distance
to the free surface interface; the interface itself is extracted as the
zero-distance isosurface. This method has the advantage that the level set variable
is smooth, rather than discontinuous across the interface, and is therefore
easier to solve. Its disadvantage is that the level set needs to be reset
periodically, and this process is not strictly mass-conservative.Surface tension effects are important
in many free surface flows as well, as mentioned above. The continuum surface
force method [62] formulates the surface tension force as a volumetric force. A key
ingredient of this method is eval-
uating the interface curvature; it is
challenging because it in effect requires second derivatives of the
discontinuous volume fraction field. Care must be used in order to avoid errors
in this calculation. Further details are discussed by Kothe et al. [60].In addition
to the surface adaptive,
interface-capturing, and interface-tracking methods, Coste has developed a
method of large interface recognition in a two-fluid model [44]. This method allows to define the
position of large interfaces (the characteristic length scale being larger than
the mesh size) like a free surface or a surface of the jet in order to being
able to model interfacial transfers by an extension of the wall function
approach. The objective is to combine the merits of the two-fluid model which
models statistically “small interfaces” (e.g., for bubbles and droplets) with
the specific treatment of large interfaces required for PTS simulations.


#### 3.3.4.
Direct Contact Condensation

In the context of PTS, the gas-liquid
interface is characterised by intense heat and mass transfer in addition to the
effects discussed in the previous section. Some simulations exist on the safety
analysis of a nuclear reactor in which rapid contact condensation of vapour
occurs during the emergency injection of cold water [63–67]. The
following condensation models were tested by Yao et al. [14] in a turbulent stratified
steam-water flow of Lim's experiment [12].
(i)
Interfacial
sublayer concept (ISM), using “wall function” approach to model
the sublayer that exists at a gas-liquid interface. The modelling
of the interfacial heat transfer is based on approaches similar to the
interfacial friction transfer. Schiestel [68] and Jayatilleke [69] have proposed relations for the temperature profile and the Prandtl number,
using a formulation similar to the interfacial sublayer model.(ii)
A model based on asymptotic behaviour of the eddy viscosity model (EVM)
[70–72] describes the turbulent viscosity in the boundary
layer with a Gaussian function.(iii)
A
model based on surface renewal
concept [63, 64, 73, 74] with small eddies
(HDM) was proposed by Banerjee [75]. He has proposed a relation for the
heat transfer, that was modified by Hughes and Duffey [64] by
introducing the Kolmogorov time scale for the small eddies. The use of
these models with the steam-water flow is theoretically questionable as
discussed by Yao et al. [14].An alternative
model was then proposed [23] in order to avoid this question. The time
scale in this model is built with the Kolmogorov length scale and the turbulent
velocity (velocity
fluctuations due to turbulence) which gives in
the theoretical framework of surface renewal an acceptable domain of validity
compatible with steam water flows. This model has been validated with SIMMER
and Neptune_CFD codes calculations of eighteen COSI tests and a LAOKOON test
[76]. It is being tested and used within the 3D
two-fluid models for the stratified flow condensation during the PTS related transients.Various experiments
are being used to test these condensation models in the stratified flow with
two-fluid models of various 3D CFD codes.(i)
Condensation
of hot steam in the stratified flow of the LAOKOON test facility [77] at
Technical University of Munich is being modelled in the frame of the NURESIM
project by GRS, CEA, and University of Pisa with two-fluid models of the
computer codes Neptune_CFD and CFX.(ii)
Condensation-induced water hammer experiment, where a cold liquid is slowly flooding a
horizontal pipe filled with hot steam, has been performed at KFKI, Budapest [78, 79]. The
first phase of the transient is another example of condensation of hot
steam on a stratified cold liquid, that can lead to the slug formation and
severe pressure peaks due to the condensation-induced slug acceleration.
CFD simulations of this experiment for benchmarking Neptune_CFD and CFX
are done in NURESIM project by JSI. The development and implementation of
new models are planned.(iii)
Test
STB-31 at the POOLEX experimental facility is the test case for the
condensation modes in a different geometry of a stratified flow: steam is
being introduced into the cold water pool through a vertical pipe, and the
selected test case exhibits a condensation over a flat and stable
gas-liquid interface in the vertical pipe. The experiment was done by LUT
in the frame of the national SAFIR programme for the NURESIM project.
Simulations of the experiment are done by LUT and VTT using Neptune_CFD.The KFKI
water hammer experiment and the POOLEX experiment of LUT might require
conjugate heat transfer calculations that take into account heat transfer in
the structure walls and thus present a test case also for that physical
phenomenon relevant for the integral PTS simulations.In the frame of the NURESIM project, a database
generated by DNS simulations of a stratified air/steam water flow is used by
ASCOMP to obtain new scaling laws for the normalized heat transfer coefficient
for both the steam and liquid phases. The database has been initially developed to
infer modelling approaches to turbulence transport at interfacial two-phase
flows without phase change. In a second step, a thermal DNS database for the
steam-water stratified
flow has been exploited in order to understand the importance of the relative
driving mechanisms for the condensation heat transfer in both phases [50]. New
scaling laws for the normalized heat transfer coefficient have been derived for
both the steam and liquid phases. On
the gas side of the interface, condensation heat transfer was found to scale
with the interfacial friction velocity and Prandtl number like in the passive
heat transfer case studied by Lakehal et al. [49]. In the liquid phase, the
DNS results produced a condensation heat transfer coefficient that remains
roughly constant at a given total shear velocity. However, an augmentation of
heat transfer due to the combined effects of mass exchange and interfacial
waviness has been observed. The surface divergence model of Banerjee et al. [80] is found to apply in the liquid phase, with an excellent agreement in
the low-to-mild interfacial shear regime in particular. Regarding the
interfacial friction, the DNS data confirm that in the presence of
condensation, the interfacial shear stress is influenced by the mass exchange,
and a correction factor based on the rate of condensation is needed to
correctly predict the variation of the friction coefficient.


### 3.4. Flow in the Downcomer and Wall Heat Transfer

In the case of
a partially filled cold leg, the flow in the downcomer can be assumed to be single
phase, and the temperature distribution of the fluid cooling the pressure
vessel wall is mainly influenced by ECC injections, local mixing phenomena, and
geometrical constraints. On the other hand, if the water level in the downcomer
is below the nozzle of the cold leg, a complex two-phase flow regime occurs.
Because of the low liquid level in the downcomer, another impingement region
has to be considered. The same modelling approaches have to be applied as
discussed for the impinging jet. Depending on the water velocity when entering
the downcomer, a detachment of the flow from the walls is possible. If this
detachment occurs, the heat transfer between the water and the walls is
decreased. Because of the variations in the flow regime and the presence of
waves in the cold leg pipe, the velocity is not constant when the liquid enters
the downcomer. The presence of the walls modifies the liquid flow behaviour by
changing the turbulence properties, the liquid temperature, and the velocity
field. Some calculations of the flow in the downcomer have been performed
[81] and have been able to reproduce the water temperature
oscillations in the downcomer.The prediction of the transient and
local heat transfer to the RPV wall is the final aim of the thermal fluid
dynamic simulation of the PTS situation. However, the heat transfer to the cold
leg wall has also to be considered, since there is a feedback from the wall
temperatures on the flow. The various flow regimes taking place in the
different regions influence the heat transfer at the walls. The numerical
prediction of the transfer with the walls is strongly dependent on the accuracy
with which the other phenomena are represented. The variations of the
temperature fields for both the liquid and the gas phases are strongly
dependent on the mixing between the phases, which results in the local
phenomena. Conversely, the heat transfer at the walls influences the behaviour
of the other phenomena by changing the temperature fields of the fluids.As far as the simulation of the wall
heat transfer is con-
cerned, models valid for single phase should be sufficient.
Various models exist and have been extensively studied. In most of the CFD
codes, some heat transfer models with a solid wall are available. These
models require the definition of the wall properties, depending on their
composition. These models have
already been used successfully in various configurations but not for the jet
impingement where the local Nusselt number is not properly predicted [82].


### 3.5.
Integral Simulation

The
thermal-hydraulic phenomena at the origin of the two-phase PTS event have been
split into several parts or subphenomena in the sections above. Each of those subphenomena,
that is, Sections3.1 to 3.4, actually implies the presence of inherent:
(a) transient conditions, (b) thermo-dynamic non equilibrium, (c) mechanical nonequilibrium, (d) three-dimensional situation, and (e) nonfully-developed
flow condition. Starting from this premise, any attempt to perform an integral
simulation (i.e., considering all together the listed phenomena and the related
interactions) of the PTS thermal-hydraulics phenomena are at worst meaningless,
or more positively tainted by unreliable results, as also pointed out in the
text before (e.g., attempts to consider together some of the identified
subphenomena).Three
calculation types can be identified:(A)
licensing
analysis accepted or acceptable by regulatory authorities;(B)
support
(i.e., to licensing) calculations performed by “advanced” methods;(C)
scoping
calculations by “advanced” methods to un-
derstand the phenomena or the use of
the computational tools.Advanced
methods mean two-phase CFD in this case. Analyses of type (A) are performed by
system thermal-hydraulic codes and typically based on conservative assumptions
and do not fit with the content of the present paper (however, see below):
there is no or limited consideration for phenomena, and the calculations are
addressed to the estimate of the safety margins rather than to the prediction
of the physical system transient evolution. At the basis of those analyses,
there is the experience of safety technologists, including the consideration of
experimental data and of deficiencies of the available computational tools. At
the bottom end, comparison of expected conservative results from analyses of
type (A), and results from methods discussed in this paper, when these will be
available, will definitely prove the quality of the adequacy of the adopted
conservatism. Analyses of type (B) are not accepted by licensing authorities
nowadays. Therefore, only analyses of type (C) can be carried out. The analyses
of type (C) suffer from all the limitations and the problems discussed in Sections3.1 to 3.4.In the frame
of the NURESIM project, simulations are done by CEA for the COSI experiments
(see Section2) using the Neptune_CFD code. They found that some results are generally within a
reasonable range, namely the water level, the liquid heat up in the cold water
injection region, and the global condensation rate. Some other results are not
satisfactory, for example, water temperature profiles upstream of the
injection, and even in the downstream region in some cases. Simulations of UPTF
TRAM experiments were done by EDF and GRS.Further code improvements are required to
allow reliable simulations of the two-phase PTS situation considering all the
involved phenomena.In the near term, one may envisage a
simplified treatment of two-phase PTS transients by neglecting some effects
which are not yet controlled like the bubble entrainment and the possible
effects of waves on the free surface. A better modelling of interfacial
transfers of heat and mass at the free surface allowing convergence with a
reasonable coarse mesh is still required to be able to predict the minimum
liquid temperature entering the downcomer. It is very likely that neglecting
entrained bubbles and interfacial waves leads to conservative predictions since
both phenomena may increase condensation and mixing.


### 4. Conclusions

A comprehensive overview of the
thermal-hydraulic phenomena (and subphenomena) connected with PTS in
pressurized water reactors has been provided, with emphasis given to two-phase
conditions.The outline given in relation to
single-phase phenomena shows that coupling techniques involving system
thermal-hydraulics and CFD codes are mature enough to be used for technological
purposes, with main reference to the evaluation of safety margins, though
improvements are still needed (as expected when nuclear safety is part of the
game) in the area of convection heat transfer.The detailed analysis performed in
relation to the two-phase flow phenomena shows the complexity of those
phenomena. Computation techniques are capable to reproduce qualitatively the
individual aspects (also called subphenomena) but fail, so far, in the
prediction of the interaction among the subphenomena and of the overall system
behaviour.The NURESIM EC project, that
constitutes the key source of information for this paper, gave a unique
possibility to a dozen EU institutions to cooperate and create a synergy for
better understanding and modelling the overall thermal-hydraulic phenomena at
the basis of PTS, and a continuation of the project is envisaged to address the
open issues listed in Sections3.1 to 3.5. Best practice guidelines [52] have to be applied for the integral simulations.


## 3.1. Free Liquid Jet

The cold liquid jet injected into
the horizontal cold leg pipe interacts first with the surrounding hot steam
environment. These interactions are strongly dependent on the position and
shape of the interface between the cold water and the hot gaseous environment.
Interface tracking methods (ITM) are needed for a detailed description of these
interactions. Depending on various characteristics of both the liquid and the
gas, such as the relative velocity between the two phases or turbulence
properties, instabilities at the surface of the jet can occur. Instabilities
can also be directly generated by the condensation process [20]. They
affect the heat and mass transfer. Models for DCC at the jet surface have to be
applied. The instabilities also influence the gas entrainment at the jet
impingement point on the liquid surface by capturing gas. Adequate modelling of
the interface, in connection with a suitable coupling of the turbulence fields
of the single phases and local mass and heat transfer, is needed.Numerous theories relating to
mechanisms on generation and growth of jet instabilities exist. Several
numerical approaches have been used, such as DNS or large-eddy simulation (LES) for the prediction of their behaviour using
various conditions [21, 22]. Even if
the individual effects of some parameters, such as gravity or nozzle internal
flow, have been separately studied, no computations exist taking into account
all these effects simultaneously. Actually, some models for the treatment of
these instabilities are based on restrictive assumptions, which limit strongly
their applicability. The LES approach seems the most suitable for the modelling
of this specific flow situation, not presuming what would be the best choice for
the simulation of the whole PTS.DCC at the jet surface resulting
from the temperature difference between the two phases is responsible for a non-negligible
part of the total condensation in the considered flow domain of the cold leg
[19]. For the condensation rate at the jet surface,
correlations exist [19], but no representative experimental
data are available to confirm this model. No special models were developed for
DCC at the jet surface. The variations of the condensation rate along the jet
and the effects of the noncondensable gases have been qualitatively reproduced
[23], but the quantitative prediction was not fully mature.


## 3.2. Zone of the Impinging Jet

Appropriate modelling of the
turbulence production below the jet is highly important, since turbulence is
responsible for the mixing of the fluid. Gas entrainment caused by the jet
impingement influences the characteristics of the turbulence below the free
surface. The properties of the entrained gas (e.g., bubble size, penetration
depth, horizontal migration, and total amount of entrained gas) are dependent
on various properties of both phases and jet. The jet velocity is one of the
most critical parameters. Depending on it, several scenarios for the gas
entrainment below the free surface have already been experimentally identified
[24, 25]. Most of the attempts for the
development of theories able to reproduce the properties of the entrained gas
below the free liquid surface have resulted in global correlations, which are
limited to the corresponding operating conditions and geometric configuration.
Several studies have highlighted the absence of theoretical approach and of
valid correlations for the prediction of the minimal jet velocity at which the
gas entrainment occurs. The modelling of the impinging jet zone requires
simultaneous consideration of separated (surface) and dispersed (bubbles) flow
within one flow domain.Two issues have to be considered
regarding turbulence production: the turbulence generated by the impingement of
the jet itself and the influence of the bubbles on the turbulence. In the
NURESIM project, investigations are done on the turbulence production below the
jet by CEA and University of Pisa which simulated [8] tests of a plunging jet [26]. Together with Neptune_CFD standard models, a CEA/Grenoble
modified k-ε model was tested. Quite good agreement
with experimental data was achieved with best performing models: numerical predictions of the mean velocity
field were always good, and turbulence was generally not bad but with
significant underestimation far from the jet axis region.In most simulations, the effect of
the liquid turbulence on the bubbles is modelled, but the opposite effect
(corresponding to the influence of the bubbles on the liquid turbulence field)
is only considered in regards to the turbulent viscosity, for example, using
the Sato model [27], despite this effect being important in the dense bubble region (near the
impingement point). Some studies have thus to be conducted to improve
understanding and modelling of the coupling between these various processes.Both LES and RANS models can be used for the simulation of the zone of the
impinging jet. A more general investigation on the applicability of RANS and
LES models for bubbly flow, including bubble plumes, was undertaken in the
frame of the NURESIM project by PSI.In the impinging jet zone, four
different interface struc-
tures have to be considered:
(1) the surface of the jet, (2) the free surface of the pool (i.e., liquid level in the cold leg), (3) the entrained bubbles, and (4) the complicated surface structure in the region
where the jet impacts the surface. Separated (jet surface and pool surface) as
well as dispersed (bubbles) flow regions exist simultaneously in one flow
domain. The most difficult thing
is to model the transitions between the two types of interfaces (i.e., bubble
entrainment and de-entrainment). For the different interfacial structures,
different closure models are needed, for example, for drag. The identification
of the interfaces for separated flows is thus of crucial importance.Some computations of the whole
plunging jet process (starting from the jet, to the bubble de-entrainment,
considering the impingement zone, the bubble migration below the free liquid
surface and the free surface) have been performed with some success in the past
[28]. These were able to reproduce the global behaviour for the free
liquid surface (small waves at the free surface and shape at the impingement
point), the gas entrainment, the bubble migration below the free surface, and
the bubble de-entrainment at the free surface. Even if the entrainment process
has been more or less well reproduced numerically (generation of entrained
bubbles at the impingement point), the total volume flow rate of entrained gas
has been largely overestimated. One of the most critical problems pointed out
during these computations is the treatment of the liquid/gas interfaces. To
overcome the discrepancies, the two kinds of interface mentioned above have to
be modelled using two different models (or at least the same model with
different values for the parameters). In the frame of the NURESIM project,
investigations are done by FZD regarding these problems. This resulted in the
suggestion to use so-called algebraic interfacial area density (AIAD)
models which allow to apply two different drag coefficients for free surface
and for bubbly flow. A blending function based on the gas void fraction is used
to apply the adequate drag coefficient depending on the flow regime.The behaviour of the entrained gas
bubbles below the free liquid surface is determined by several forces acting on
individual bubbles. The most important of these forces are buoyancy, drag,
virtual mass force, lift force, and turbulent dispersion force. All these
forces are strongly dependent on the bubble size (see, e.g., [29]).
For bubbly flow in vertical pipes, a combination of Tomiyama lift- and wall
force together with the Favre-averaged drag force [30] was found to reflect
the experimental findings in poly-dispersed flows [31]. In the case of developing flows, some differences have
been pointed out between calculations and experimental data [32]. In the frame of the NURESIM project, the influence of the
bubble forces on bubble migration is investigated by FZD for an impinging jet
configuration.In most computations, the bubble
diameters are assumed to be constant. In principle, CFD models which allow
consideration of a number of bubbles classes already exist [33], but calculations are
then very time consuming. The bubbles size distribution is strongly influenced
by bubble coalescence and breakup, for which various models exist in the
literature (e.g., [34–36]). The models for
bubble forces, as well as the models for bubble coalescence and breakup, have
consequently to be validated for the plunging jet configuration.There are also some attempts on a direct
tracking of interfaces at zone of the jet impingement. Interface tracking
techniques have indeed been applied, in combination with LES of the fields in
each phase, to interfacial, sheared, two-phase flow [37, 38]. These authors incorporated the VOF approach to an LES simulation and
applied it to the case of air/steam injection into a water pool, as
investigated previously by Meier [39]. It is obvious that the available computational
resources will not allow this approach to be used to capture the details of a
dispersed bubbly flow; the routinely used two-fluid formulation remains much
less demanding. Nevertheless, the LES/VOF combination may be a candidate future
technique for tackling flows involving large interfacial inclusions. Novel
analytical developments to the method have now been made by Liovic and Lakehal [38],  namely, in the treatment of turbulence near sheared deformable
interfaces.


## 3.3. Zone of Stratified Flow in the Cold Leg

In the horizontal cold leg pipe, a
stratified flow has to be considered. In the context of PTS, the interface is characterised
by intense heat, mass, momentum, and turbulence transfer. Heat transfer between
the fluids and the wall of the cold leg pipe has also to be considered.


### 3.3.1. Momentum and Turbulence Transfer

Depending on the relative velocities
of the gas and the liquid phases, the liquid/gas interface is strongly or
mildly perturbed. For low relative velocities, the interface is quasistatic.
For higher relative velocities, the interface is perturbed, and small waves are
generated. Depending on the actual conditions, these waves can be amplified
during their propagation in the horizontal pipe. The so-calledKelvin-Helmholtz
instability can occur when a velocity shear is present within a continuous
fluid or when there is sufficient velocity difference across the interface
between two fluids. The CFD modelling of this instability was investigated in
the frame of the NURESIM project by UCL. The classical theory can be used to
predict the onset of instability in fluids of slightly different densities
moving at various speeds. In the absence of surface tension, all wavelengths
are unstable. The existence of surface tension stabilises the short wavelength
condition; the theory then predicts stability until a velocity threshold is
reached. For this reason, interface tracking methods or any method which
includes surface tension effects have to be used [40, 41]. For cases with high-density differences, such as steam and water
in the case of PTS, the situation is much more complicated (see [42]). It was found that either a single-fluid approach with VOF (FLUENT) or a
two-fluid model with a large interface recognition (Neptune)
could predict reasonably wave generation and growing and that condensation-induced instability could also be qualitatively predicted by Neptune and CFX.In cases with high relative
velocities in horizontal pipes, the waves are strongly amplified, and aslug flow with a complex system of
interactions (presence of gas bubbles and liquid droplets) between the two
phases can occur. The generated waves can, in certain cases of high relative
velocity, entirely block the cold leg pipe. The slug flow regime is usually characterised
by an acceleration of the gaseous phase and by the transition of fast liquid
slugs carrying a significant amount of liquid with high-kinetic energy. The
two-phase flow regimes in horizontal pipes are not only dependent on the local
conditions but depend also on the characteristics of the free falling jet which
may itself generate waves.A systematic study of numerical
simulation of slug flow in horizontal pipes using ANSYS CFX was carried out by
Frank [9] and Vallée et al. [43]. It was shown that the formation of the slug flow regime strongly
depends on the wall friction of the liquid phase. In simulations using
inlet/outlet boundary conditions, it was found that the formation of slug flow
regimes strongly depends on the agitation or perturbation of the inlet boundary
conditions. Furthermore, Frank showed that the length of the computational
domain also plays an important role in slug formation. Similar experimental
data are being used in NURESIM for benchmarking the Neptune_CFD code by UCL,
while University of Pisa
and CEA do
simulations of Fabre et al. [10]. A new modelling approach of
large interfaces is developed considering an interfacial layer of 3 cells
[44].Momentum transfer is closely
connected with turbulent transfer. In the case of the turbulence predicted by
thek-ε model, the interfacial momentum can be modelled using several closure
laws. The interfacial sublayer model (ISM, [14]) in the gas phase supposes, due to the significant
difference between the gas and liquid densities, that the interface can be
treated as a “moving solid wall” with a velocity equal to the liquid velocity.
The gas region close to the interface is modelled with the two sublayer models, which is similar
to the wall function concept. It is also possible to use the average viscosity
assumption (AVM, [14]).
This model is based on the simplified momentum equation in the case of a thin
layer near a smooth interface without phase change, which permits the
interfacial friction and velocity to be evaluated. Morel [45] has proposed a
modification of the Taitel and Dukler model (TDM, [46])
for multidimensional calculations.


### 3.3.2. Turbulence Modelling

The mixing of hot and cold water is
mainly determined by turbulence. The turbulence fields for both the liquid and
the gas phases and the coupling between them play also important roles on the
interfacial transfer and on the two-phase flow regime in the cold leg, and for
the transition between different regimes (i.e., smooth surface, wavy flow, slug
flow). Close to the interface, three turbulence sources have been identified:
turbulence diffused from wall boundaries, turbulence production by the
interfacial friction, and turbulence induced by interfacial waves. Close to the
interface, the anisotropy of the turbulence has to be considered. It is not
reproduced by any classic model. In most of the cases, the turbulence is modelled
using thek-ω or the k-ε (classic or modified) models, together with a specific hypothesis at
the interface [47, 48]. Without any special treatment of the free surface, the high-velocity
gradients at the free surface generate too high turbulence when using eddy
viscosity models like the k-ε or the k-ω model.
Therefore, a symmetric damping procedure for the solid wall-like damping of
turbulence in both gas and liquid phases has been proposed by Egorov [28]. A
numerical database obtained by DNS simulation of the interface was generated in
the frame of NURESIM by ASCOMP [49, 50].Vallée et al. [51] employed the shear stress transport
(SST) turbulence model for each phase. The k-ω based SST model [52] accounts for the transport of the turbulent shear stress and gives good
predictions of the onset and the amount of flow separation under adverse
pressure gradients. The qualitative slug formation in the
simulations (ANSYS-CFX) was in good agreement with the experiment.


### 3.3.3.
Modelling of the Free Surface

According to Zwart [53], numerical
models for free surface flow may be divided into three categories: surface
adaptive methods, interface-capturing methods, and interface-tracking methods.Surface-adaptive methods are typically single-phase approaches in which the kinematic condition
is used to update the location of the free surface interface, and the mesh
boundary conforms to this interface at all times. These methods inherently
involve mesh motion. While these methods are successful for certain classes of
flows, they are typically restricted to modest degrees of interface deformation.
Methods of working around these limitations have been devised, including
periodic remeshing and interpolation, characteristic streamline diffusion
finite element methods [54], and the integrated space-time finite
volume method [55]. Despite these advances in tracking significant interface deformation, it
remains the case that surface adaptive methods are useful primarily when the
interface topology is straightforward. Effects such as splashing, breaking, and
colliding of waves remain difficult challenges. Moreover, the geometries
themselves must be simple in order to calculate how to move the mesh at interface-wall
intersections.These limitations may be overcome by
having a fixed mesh, which spans the interface location. Theinterface is captured within the mesh
by specific algorithms. Most commonly, the algorithm makes use of the
continuity equation for one of the phases, in which the dependent variable is
the volume fraction of that phase; these methods are called volume-of-fluid (VOF)
methods. They differ widely in their detailed implementation. Many of them are
interface-capturing and solve the VOF equation using a continuum advection
scheme. If standard techniques are used for the advection operator, numerical
diffusion will lead to significant smearing of the interface. A variety of
compressive advection schemes have been devised to minimize this diffusion. The
compressivness is often obtained by using a controlled downwinding of the
fluxes, as with the donor-acceptor [56] and CICSAM
[57] schemes. Controlled down-winding schemes have
compressive characteristics which depend upon the time-step and therefore
require small time steps to retain sharp interfaces, even for steady-state free
surface flows. More recently, a new scheme having compressive characteristics
independent of the time step size has been developed [58].Other VOF methods areinterface-tracking and explicitly track
the free surface interface. For a particular volume fraction field, the
interface is reconstructed using a piecewise representation (constant, linear,
or parabolic) in each cell. The volume fluxes may be calculated either
geometrically or using an advection operator as described above. Further
details of these algorithms can be found in [59, 60]. Another fixed grid
strategy for free surface flow problems involves the use of level set method
[61]. The level
set strategy formulates and solves an equation representing the signed distance
to the free surface interface; the interface itself is extracted as the
zero-distance isosurface. This method has the advantage that the level set variable
is smooth, rather than discontinuous across the interface, and is therefore
easier to solve. Its disadvantage is that the level set needs to be reset
periodically, and this process is not strictly mass-conservative.Surface tension effects are important
in many free surface flows as well, as mentioned above. The continuum surface
force method [62] formulates the surface tension force as a volumetric force. A key
ingredient of this method is eval-
uating the interface curvature; it is
challenging because it in effect requires second derivatives of the
discontinuous volume fraction field. Care must be used in order to avoid errors
in this calculation. Further details are discussed by Kothe et al. [60].In addition
to the surface adaptive,
interface-capturing, and interface-tracking methods, Coste has developed a
method of large interface recognition in a two-fluid model [44]. This method allows to define the
position of large interfaces (the characteristic length scale being larger than
the mesh size) like a free surface or a surface of the jet in order to being
able to model interfacial transfers by an extension of the wall function
approach. The objective is to combine the merits of the two-fluid model which
models statistically “small interfaces” (e.g., for bubbles and droplets) with
the specific treatment of large interfaces required for PTS simulations.


### 3.3.4.
Direct Contact Condensation

In the context of PTS, the gas-liquid
interface is characterised by intense heat and mass transfer in addition to the
effects discussed in the previous section. Some simulations exist on the safety
analysis of a nuclear reactor in which rapid contact condensation of vapour
occurs during the emergency injection of cold water [63–67]. The
following condensation models were tested by Yao et al. [14] in a turbulent stratified
steam-water flow of Lim's experiment [12].
(i)
Interfacial
sublayer concept (ISM), using “wall function” approach to model
the sublayer that exists at a gas-liquid interface. The modelling
of the interfacial heat transfer is based on approaches similar to the
interfacial friction transfer. Schiestel [68] and Jayatilleke [69] have proposed relations for the temperature profile and the Prandtl number,
using a formulation similar to the interfacial sublayer model.(ii)
A model based on asymptotic behaviour of the eddy viscosity model (EVM)
[70–72] describes the turbulent viscosity in the boundary
layer with a Gaussian function.(iii)
A
model based on surface renewal
concept [63, 64, 73, 74] with small eddies
(HDM) was proposed by Banerjee [75]. He has proposed a relation for the
heat transfer, that was modified by Hughes and Duffey [64] by
introducing the Kolmogorov time scale for the small eddies. The use of
these models with the steam-water flow is theoretically questionable as
discussed by Yao et al. [14].An alternative
model was then proposed [23] in order to avoid this question. The time
scale in this model is built with the Kolmogorov length scale and the turbulent
velocity (velocity
fluctuations due to turbulence) which gives in
the theoretical framework of surface renewal an acceptable domain of validity
compatible with steam water flows. This model has been validated with SIMMER
and Neptune_CFD codes calculations of eighteen COSI tests and a LAOKOON test
[76]. It is being tested and used within the 3D
two-fluid models for the stratified flow condensation during the PTS related transients.Various experiments
are being used to test these condensation models in the stratified flow with
two-fluid models of various 3D CFD codes.(i)
Condensation
of hot steam in the stratified flow of the LAOKOON test facility [77] at
Technical University of Munich is being modelled in the frame of the NURESIM
project by GRS, CEA, and University of Pisa with two-fluid models of the
computer codes Neptune_CFD and CFX.(ii)
Condensation-induced water hammer experiment, where a cold liquid is slowly flooding a
horizontal pipe filled with hot steam, has been performed at KFKI, Budapest [78, 79]. The
first phase of the transient is another example of condensation of hot
steam on a stratified cold liquid, that can lead to the slug formation and
severe pressure peaks due to the condensation-induced slug acceleration.
CFD simulations of this experiment for benchmarking Neptune_CFD and CFX
are done in NURESIM project by JSI. The development and implementation of
new models are planned.(iii)
Test
STB-31 at the POOLEX experimental facility is the test case for the
condensation modes in a different geometry of a stratified flow: steam is
being introduced into the cold water pool through a vertical pipe, and the
selected test case exhibits a condensation over a flat and stable
gas-liquid interface in the vertical pipe. The experiment was done by LUT
in the frame of the national SAFIR programme for the NURESIM project.
Simulations of the experiment are done by LUT and VTT using Neptune_CFD.The KFKI
water hammer experiment and the POOLEX experiment of LUT might require
conjugate heat transfer calculations that take into account heat transfer in
the structure walls and thus present a test case also for that physical
phenomenon relevant for the integral PTS simulations.In the frame of the NURESIM project, a database
generated by DNS simulations of a stratified air/steam water flow is used by
ASCOMP to obtain new scaling laws for the normalized heat transfer coefficient
for both the steam and liquid phases. The database has been initially developed to
infer modelling approaches to turbulence transport at interfacial two-phase
flows without phase change. In a second step, a thermal DNS database for the
steam-water stratified
flow has been exploited in order to understand the importance of the relative
driving mechanisms for the condensation heat transfer in both phases [50]. New
scaling laws for the normalized heat transfer coefficient have been derived for
both the steam and liquid phases. On
the gas side of the interface, condensation heat transfer was found to scale
with the interfacial friction velocity and Prandtl number like in the passive
heat transfer case studied by Lakehal et al. [49]. In the liquid phase, the
DNS results produced a condensation heat transfer coefficient that remains
roughly constant at a given total shear velocity. However, an augmentation of
heat transfer due to the combined effects of mass exchange and interfacial
waviness has been observed. The surface divergence model of Banerjee et al. [80] is found to apply in the liquid phase, with an excellent agreement in
the low-to-mild interfacial shear regime in particular. Regarding the
interfacial friction, the DNS data confirm that in the presence of
condensation, the interfacial shear stress is influenced by the mass exchange,
and a correction factor based on the rate of condensation is needed to
correctly predict the variation of the friction coefficient.


## 3.3.1. Momentum and Turbulence Transfer

Depending on the relative velocities
of the gas and the liquid phases, the liquid/gas interface is strongly or
mildly perturbed. For low relative velocities, the interface is quasistatic.
For higher relative velocities, the interface is perturbed, and small waves are
generated. Depending on the actual conditions, these waves can be amplified
during their propagation in the horizontal pipe. The so-calledKelvin-Helmholtz
instability can occur when a velocity shear is present within a continuous
fluid or when there is sufficient velocity difference across the interface
between two fluids. The CFD modelling of this instability was investigated in
the frame of the NURESIM project by UCL. The classical theory can be used to
predict the onset of instability in fluids of slightly different densities
moving at various speeds. In the absence of surface tension, all wavelengths
are unstable. The existence of surface tension stabilises the short wavelength
condition; the theory then predicts stability until a velocity threshold is
reached. For this reason, interface tracking methods or any method which
includes surface tension effects have to be used [40, 41]. For cases with high-density differences, such as steam and water
in the case of PTS, the situation is much more complicated (see [42]). It was found that either a single-fluid approach with VOF (FLUENT) or a
two-fluid model with a large interface recognition (Neptune)
could predict reasonably wave generation and growing and that condensation-induced instability could also be qualitatively predicted by Neptune and CFX.In cases with high relative
velocities in horizontal pipes, the waves are strongly amplified, and aslug flow with a complex system of
interactions (presence of gas bubbles and liquid droplets) between the two
phases can occur. The generated waves can, in certain cases of high relative
velocity, entirely block the cold leg pipe. The slug flow regime is usually characterised
by an acceleration of the gaseous phase and by the transition of fast liquid
slugs carrying a significant amount of liquid with high-kinetic energy. The
two-phase flow regimes in horizontal pipes are not only dependent on the local
conditions but depend also on the characteristics of the free falling jet which
may itself generate waves.A systematic study of numerical
simulation of slug flow in horizontal pipes using ANSYS CFX was carried out by
Frank [9] and Vallée et al. [43]. It was shown that the formation of the slug flow regime strongly
depends on the wall friction of the liquid phase. In simulations using
inlet/outlet boundary conditions, it was found that the formation of slug flow
regimes strongly depends on the agitation or perturbation of the inlet boundary
conditions. Furthermore, Frank showed that the length of the computational
domain also plays an important role in slug formation. Similar experimental
data are being used in NURESIM for benchmarking the Neptune_CFD code by UCL,
while University of Pisa
and CEA do
simulations of Fabre et al. [10]. A new modelling approach of
large interfaces is developed considering an interfacial layer of 3 cells
[44].Momentum transfer is closely
connected with turbulent transfer. In the case of the turbulence predicted by
thek-ε model, the interfacial momentum can be modelled using several closure
laws. The interfacial sublayer model (ISM, [14]) in the gas phase supposes, due to the significant
difference between the gas and liquid densities, that the interface can be
treated as a “moving solid wall” with a velocity equal to the liquid velocity.
The gas region close to the interface is modelled with the two sublayer models, which is similar
to the wall function concept. It is also possible to use the average viscosity
assumption (AVM, [14]).
This model is based on the simplified momentum equation in the case of a thin
layer near a smooth interface without phase change, which permits the
interfacial friction and velocity to be evaluated. Morel [45] has proposed a
modification of the Taitel and Dukler model (TDM, [46])
for multidimensional calculations.


## 3.3.2. Turbulence Modelling

The mixing of hot and cold water is
mainly determined by turbulence. The turbulence fields for both the liquid and
the gas phases and the coupling between them play also important roles on the
interfacial transfer and on the two-phase flow regime in the cold leg, and for
the transition between different regimes (i.e., smooth surface, wavy flow, slug
flow). Close to the interface, three turbulence sources have been identified:
turbulence diffused from wall boundaries, turbulence production by the
interfacial friction, and turbulence induced by interfacial waves. Close to the
interface, the anisotropy of the turbulence has to be considered. It is not
reproduced by any classic model. In most of the cases, the turbulence is modelled
using thek-ω or the k-ε (classic or modified) models, together with a specific hypothesis at
the interface [47, 48]. Without any special treatment of the free surface, the high-velocity
gradients at the free surface generate too high turbulence when using eddy
viscosity models like the k-ε or the k-ω model.
Therefore, a symmetric damping procedure for the solid wall-like damping of
turbulence in both gas and liquid phases has been proposed by Egorov [28]. A
numerical database obtained by DNS simulation of the interface was generated in
the frame of NURESIM by ASCOMP [49, 50].Vallée et al. [51] employed the shear stress transport
(SST) turbulence model for each phase. The k-ω based SST model [52] accounts for the transport of the turbulent shear stress and gives good
predictions of the onset and the amount of flow separation under adverse
pressure gradients. The qualitative slug formation in the
simulations (ANSYS-CFX) was in good agreement with the experiment.


## 3.3.3.
Modelling of the Free Surface

According to Zwart [53], numerical
models for free surface flow may be divided into three categories: surface
adaptive methods, interface-capturing methods, and interface-tracking methods.Surface-adaptive methods are typically single-phase approaches in which the kinematic condition
is used to update the location of the free surface interface, and the mesh
boundary conforms to this interface at all times. These methods inherently
involve mesh motion. While these methods are successful for certain classes of
flows, they are typically restricted to modest degrees of interface deformation.
Methods of working around these limitations have been devised, including
periodic remeshing and interpolation, characteristic streamline diffusion
finite element methods [54], and the integrated space-time finite
volume method [55]. Despite these advances in tracking significant interface deformation, it
remains the case that surface adaptive methods are useful primarily when the
interface topology is straightforward. Effects such as splashing, breaking, and
colliding of waves remain difficult challenges. Moreover, the geometries
themselves must be simple in order to calculate how to move the mesh at interface-wall
intersections.These limitations may be overcome by
having a fixed mesh, which spans the interface location. Theinterface is captured within the mesh
by specific algorithms. Most commonly, the algorithm makes use of the
continuity equation for one of the phases, in which the dependent variable is
the volume fraction of that phase; these methods are called volume-of-fluid (VOF)
methods. They differ widely in their detailed implementation. Many of them are
interface-capturing and solve the VOF equation using a continuum advection
scheme. If standard techniques are used for the advection operator, numerical
diffusion will lead to significant smearing of the interface. A variety of
compressive advection schemes have been devised to minimize this diffusion. The
compressivness is often obtained by using a controlled downwinding of the
fluxes, as with the donor-acceptor [56] and CICSAM
[57] schemes. Controlled down-winding schemes have
compressive characteristics which depend upon the time-step and therefore
require small time steps to retain sharp interfaces, even for steady-state free
surface flows. More recently, a new scheme having compressive characteristics
independent of the time step size has been developed [58].Other VOF methods areinterface-tracking and explicitly track
the free surface interface. For a particular volume fraction field, the
interface is reconstructed using a piecewise representation (constant, linear,
or parabolic) in each cell. The volume fluxes may be calculated either
geometrically or using an advection operator as described above. Further
details of these algorithms can be found in [59, 60]. Another fixed grid
strategy for free surface flow problems involves the use of level set method
[61]. The level
set strategy formulates and solves an equation representing the signed distance
to the free surface interface; the interface itself is extracted as the
zero-distance isosurface. This method has the advantage that the level set variable
is smooth, rather than discontinuous across the interface, and is therefore
easier to solve. Its disadvantage is that the level set needs to be reset
periodically, and this process is not strictly mass-conservative.Surface tension effects are important
in many free surface flows as well, as mentioned above. The continuum surface
force method [62] formulates the surface tension force as a volumetric force. A key
ingredient of this method is eval-
uating the interface curvature; it is
challenging because it in effect requires second derivatives of the
discontinuous volume fraction field. Care must be used in order to avoid errors
in this calculation. Further details are discussed by Kothe et al. [60].In addition
to the surface adaptive,
interface-capturing, and interface-tracking methods, Coste has developed a
method of large interface recognition in a two-fluid model [44]. This method allows to define the
position of large interfaces (the characteristic length scale being larger than
the mesh size) like a free surface or a surface of the jet in order to being
able to model interfacial transfers by an extension of the wall function
approach. The objective is to combine the merits of the two-fluid model which
models statistically “small interfaces” (e.g., for bubbles and droplets) with
the specific treatment of large interfaces required for PTS simulations.


## 3.3.4.
Direct Contact Condensation

In the context of PTS, the gas-liquid
interface is characterised by intense heat and mass transfer in addition to the
effects discussed in the previous section. Some simulations exist on the safety
analysis of a nuclear reactor in which rapid contact condensation of vapour
occurs during the emergency injection of cold water [63–67]. The
following condensation models were tested by Yao et al. [14] in a turbulent stratified
steam-water flow of Lim's experiment [12].
(i)
Interfacial
sublayer concept (ISM), using “wall function” approach to model
the sublayer that exists at a gas-liquid interface. The modelling
of the interfacial heat transfer is based on approaches similar to the
interfacial friction transfer. Schiestel [68] and Jayatilleke [69] have proposed relations for the temperature profile and the Prandtl number,
using a formulation similar to the interfacial sublayer model.(ii)
A model based on asymptotic behaviour of the eddy viscosity model (EVM)
[70–72] describes the turbulent viscosity in the boundary
layer with a Gaussian function.(iii)
A
model based on surface renewal
concept [63, 64, 73, 74] with small eddies
(HDM) was proposed by Banerjee [75]. He has proposed a relation for the
heat transfer, that was modified by Hughes and Duffey [64] by
introducing the Kolmogorov time scale for the small eddies. The use of
these models with the steam-water flow is theoretically questionable as
discussed by Yao et al. [14].An alternative
model was then proposed [23] in order to avoid this question. The time
scale in this model is built with the Kolmogorov length scale and the turbulent
velocity (velocity
fluctuations due to turbulence) which gives in
the theoretical framework of surface renewal an acceptable domain of validity
compatible with steam water flows. This model has been validated with SIMMER
and Neptune_CFD codes calculations of eighteen COSI tests and a LAOKOON test
[76]. It is being tested and used within the 3D
two-fluid models for the stratified flow condensation during the PTS related transients.Various experiments
are being used to test these condensation models in the stratified flow with
two-fluid models of various 3D CFD codes.(i)
Condensation
of hot steam in the stratified flow of the LAOKOON test facility [77] at
Technical University of Munich is being modelled in the frame of the NURESIM
project by GRS, CEA, and University of Pisa with two-fluid models of the
computer codes Neptune_CFD and CFX.(ii)
Condensation-induced water hammer experiment, where a cold liquid is slowly flooding a
horizontal pipe filled with hot steam, has been performed at KFKI, Budapest [78, 79]. The
first phase of the transient is another example of condensation of hot
steam on a stratified cold liquid, that can lead to the slug formation and
severe pressure peaks due to the condensation-induced slug acceleration.
CFD simulations of this experiment for benchmarking Neptune_CFD and CFX
are done in NURESIM project by JSI. The development and implementation of
new models are planned.(iii)
Test
STB-31 at the POOLEX experimental facility is the test case for the
condensation modes in a different geometry of a stratified flow: steam is
being introduced into the cold water pool through a vertical pipe, and the
selected test case exhibits a condensation over a flat and stable
gas-liquid interface in the vertical pipe. The experiment was done by LUT
in the frame of the national SAFIR programme for the NURESIM project.
Simulations of the experiment are done by LUT and VTT using Neptune_CFD.The KFKI
water hammer experiment and the POOLEX experiment of LUT might require
conjugate heat transfer calculations that take into account heat transfer in
the structure walls and thus present a test case also for that physical
phenomenon relevant for the integral PTS simulations.In the frame of the NURESIM project, a database
generated by DNS simulations of a stratified air/steam water flow is used by
ASCOMP to obtain new scaling laws for the normalized heat transfer coefficient
for both the steam and liquid phases. The database has been initially developed to
infer modelling approaches to turbulence transport at interfacial two-phase
flows without phase change. In a second step, a thermal DNS database for the
steam-water stratified
flow has been exploited in order to understand the importance of the relative
driving mechanisms for the condensation heat transfer in both phases [50]. New
scaling laws for the normalized heat transfer coefficient have been derived for
both the steam and liquid phases. On
the gas side of the interface, condensation heat transfer was found to scale
with the interfacial friction velocity and Prandtl number like in the passive
heat transfer case studied by Lakehal et al. [49]. In the liquid phase, the
DNS results produced a condensation heat transfer coefficient that remains
roughly constant at a given total shear velocity. However, an augmentation of
heat transfer due to the combined effects of mass exchange and interfacial
waviness has been observed. The surface divergence model of Banerjee et al. [80] is found to apply in the liquid phase, with an excellent agreement in
the low-to-mild interfacial shear regime in particular. Regarding the
interfacial friction, the DNS data confirm that in the presence of
condensation, the interfacial shear stress is influenced by the mass exchange,
and a correction factor based on the rate of condensation is needed to
correctly predict the variation of the friction coefficient.


## 3.4. Flow in the Downcomer and Wall Heat Transfer

In the case of
a partially filled cold leg, the flow in the downcomer can be assumed to be single
phase, and the temperature distribution of the fluid cooling the pressure
vessel wall is mainly influenced by ECC injections, local mixing phenomena, and
geometrical constraints. On the other hand, if the water level in the downcomer
is below the nozzle of the cold leg, a complex two-phase flow regime occurs.
Because of the low liquid level in the downcomer, another impingement region
has to be considered. The same modelling approaches have to be applied as
discussed for the impinging jet. Depending on the water velocity when entering
the downcomer, a detachment of the flow from the walls is possible. If this
detachment occurs, the heat transfer between the water and the walls is
decreased. Because of the variations in the flow regime and the presence of
waves in the cold leg pipe, the velocity is not constant when the liquid enters
the downcomer. The presence of the walls modifies the liquid flow behaviour by
changing the turbulence properties, the liquid temperature, and the velocity
field. Some calculations of the flow in the downcomer have been performed
[81] and have been able to reproduce the water temperature
oscillations in the downcomer.The prediction of the transient and
local heat transfer to the RPV wall is the final aim of the thermal fluid
dynamic simulation of the PTS situation. However, the heat transfer to the cold
leg wall has also to be considered, since there is a feedback from the wall
temperatures on the flow. The various flow regimes taking place in the
different regions influence the heat transfer at the walls. The numerical
prediction of the transfer with the walls is strongly dependent on the accuracy
with which the other phenomena are represented. The variations of the
temperature fields for both the liquid and the gas phases are strongly
dependent on the mixing between the phases, which results in the local
phenomena. Conversely, the heat transfer at the walls influences the behaviour
of the other phenomena by changing the temperature fields of the fluids.As far as the simulation of the wall
heat transfer is con-
cerned, models valid for single phase should be sufficient.
Various models exist and have been extensively studied. In most of the CFD
codes, some heat transfer models with a solid wall are available. These
models require the definition of the wall properties, depending on their
composition. These models have
already been used successfully in various configurations but not for the jet
impingement where the local Nusselt number is not properly predicted [82].


## 3.5.
Integral Simulation

The
thermal-hydraulic phenomena at the origin of the two-phase PTS event have been
split into several parts or subphenomena in the sections above. Each of those subphenomena,
that is, Sections3.1 to 3.4, actually implies the presence of inherent:
(a) transient conditions, (b) thermo-dynamic non equilibrium, (c) mechanical nonequilibrium, (d) three-dimensional situation, and (e) nonfully-developed
flow condition. Starting from this premise, any attempt to perform an integral
simulation (i.e., considering all together the listed phenomena and the related
interactions) of the PTS thermal-hydraulics phenomena are at worst meaningless,
or more positively tainted by unreliable results, as also pointed out in the
text before (e.g., attempts to consider together some of the identified
subphenomena).Three
calculation types can be identified:(A)
licensing
analysis accepted or acceptable by regulatory authorities;(B)
support
(i.e., to licensing) calculations performed by “advanced” methods;(C)
scoping
calculations by “advanced” methods to un-
derstand the phenomena or the use of
the computational tools.Advanced
methods mean two-phase CFD in this case. Analyses of type (A) are performed by
system thermal-hydraulic codes and typically based on conservative assumptions
and do not fit with the content of the present paper (however, see below):
there is no or limited consideration for phenomena, and the calculations are
addressed to the estimate of the safety margins rather than to the prediction
of the physical system transient evolution. At the basis of those analyses,
there is the experience of safety technologists, including the consideration of
experimental data and of deficiencies of the available computational tools. At
the bottom end, comparison of expected conservative results from analyses of
type (A), and results from methods discussed in this paper, when these will be
available, will definitely prove the quality of the adequacy of the adopted
conservatism. Analyses of type (B) are not accepted by licensing authorities
nowadays. Therefore, only analyses of type (C) can be carried out. The analyses
of type (C) suffer from all the limitations and the problems discussed in Sections3.1 to 3.4.In the frame
of the NURESIM project, simulations are done by CEA for the COSI experiments
(see Section2) using the Neptune_CFD code. They found that some results are generally within a
reasonable range, namely the water level, the liquid heat up in the cold water
injection region, and the global condensation rate. Some other results are not
satisfactory, for example, water temperature profiles upstream of the
injection, and even in the downstream region in some cases. Simulations of UPTF
TRAM experiments were done by EDF and GRS.Further code improvements are required to
allow reliable simulations of the two-phase PTS situation considering all the
involved phenomena.In the near term, one may envisage a
simplified treatment of two-phase PTS transients by neglecting some effects
which are not yet controlled like the bubble entrainment and the possible
effects of waves on the free surface. A better modelling of interfacial
transfers of heat and mass at the free surface allowing convergence with a
reasonable coarse mesh is still required to be able to predict the minimum
liquid temperature entering the downcomer. It is very likely that neglecting
entrained bubbles and interfacial waves leads to conservative predictions since
both phenomena may increase condensation and mixing.


## 4. Conclusions

A comprehensive overview of the
thermal-hydraulic phenomena (and subphenomena) connected with PTS in
pressurized water reactors has been provided, with emphasis given to two-phase
conditions.The outline given in relation to
single-phase phenomena shows that coupling techniques involving system
thermal-hydraulics and CFD codes are mature enough to be used for technological
purposes, with main reference to the evaluation of safety margins, though
improvements are still needed (as expected when nuclear safety is part of the
game) in the area of convection heat transfer.The detailed analysis performed in
relation to the two-phase flow phenomena shows the complexity of those
phenomena. Computation techniques are capable to reproduce qualitatively the
individual aspects (also called subphenomena) but fail, so far, in the
prediction of the interaction among the subphenomena and of the overall system
behaviour.The NURESIM EC project, that
constitutes the key source of information for this paper, gave a unique
possibility to a dozen EU institutions to cooperate and create a synergy for
better understanding and modelling the overall thermal-hydraulic phenomena at
the basis of PTS, and a continuation of the project is envisaged to address the
open issues listed in Sections3.1 to 3.5. Best practice guidelines [52] have to be applied for the integral simulations.



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*Source: 583259-2008-10-14.xml*