Simulation of two-phase flow on shell side of VVER-440 secondary boilers
Shell side flow in VVER-440 steam generators has been simulated by using twodimensional and three-dimensional geometrical approach. A number of operating states have been analyzed: nominal and increased power load with the original feed water injection (within the tube bank) and with presently used...
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Інститут проблем міцності ім. Г.С. Писаренка НАН України
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irk-123456789-369072012-08-05T12:09:19Z Simulation of two-phase flow on shell side of VVER-440 secondary boilers Gergely, K. Gabor, S. Tamas, R. Shell side flow in VVER-440 steam generators has been simulated by using twodimensional and three-dimensional geometrical approach. A number of operating states have been analyzed: nominal and increased power load with the original feed water injection (within the tube bank) and with presently used water injection (above the tube bank). The mathematical model involves physical effects such as: thermal expansion of water phase, local condensation in the region of feed water injection (mixed pre/heater tank), variable slip velocity of the bubbly phase depending on local volume fraction of steam, spatial variation of the water level above the tube bank settling of disperse corrosion product under the tube bank. Micro-models have been developed for calculation of anisotropic resistance of the tube bank and pipe supports, local heat flux over the tube surfaces and the spatial variation of water injection intensity. Water surface elevation and disperse phase deposition patterns are in line with measured data published in scientific literature. С помощью двумерного и трехмерного геометрических подходов был смоделирован поток теплоносителей в парогенераторах энергоблока ВВЭР-440. Проанализированы следующие рабочие состояния: номинальная и повышенная нагрузки при первоначальной подаче водного питания (внутри трубного пучка) и использование текущего водного питания (над трубным пучком). Математическая модель включает в себя следующие физические явления: тепловое расширение водной фазы, местная конденсация в месте впуска водяного питания, переменная скорость скольжения пузырьковой фазы в зависимости от локальной объемной доли пара, пространственное изменение С помощью двумерного и трехмерного геометрических подходов был смоделирован поток теплоносителей в парогенераторах энергоблока ВВЭР-440. Проанализированы следующие рабочие состояния: номинальная и повышенная нагрузки при первоначальной подаче водного питания (внутри трубного пучка) и использование текущего водного питания (над трубным пучком). Математическая модель включает в себя следующие физические явления: тепловое расширение водной фазы, местная конденсация в месте впуска водяного питания, переменная скорость скольжения пузырьковой фазы в зависимости от локальной объемной доли пара, пространственное изменение уровня воды над трубным пучком и оседание дисперсных продуктов коррозии под трубным пучком. Разработаны микро модели для расчета анизотропного сопротивления пучка труб и опор трубопроводов, локального теплового потока по поверхности труб и пространственные изменения интенсивности подачи воды. Уровень воды и осаждение дисперсной фазы в соответствии с данными измерений опубликованы в научной литературе. З допомогою двомірного и трьохмірного геометричних підходів змодельовано потік теплоносіїв в парогенераторах енергоблока ВВЕР-440. Проаналізовано наступні рабочі стани: номінальне і підвищене навантаження при первинній подачі водяного живлення (всередині трубного пучка) і використання поточного водяного живлення (над трубним пучком). Математична модель містить в собі наступні фізичні явища: теплове розширення водяної фази, місцеву конденсацію в місці впуску водяного живлення, змінна швидкість ковзання бульбашкової фази в залежності від локальної об’ємної частки пари, просторова зміна рівня води над трубним пучком і осідання дисперсних продуктів корозії під трубним пучком. Розроблено мікро моделі для розрахунку анізотропного опору пучка труб і опор трубопроводів, локального теплового потоку по поверхні труб і просторові зміни інтенсивності подачі води. Рівень води і осад дисперсної фази у відповідності з даними вимірювань опубліковані в науковій літературі. 2009 Article Simulation of two-phase flow on shell side of VVER-440 secondary boilers / K. Gergely, S. Gabor, R. Tamas // Надійність і довговічність машин і споруд. — 2009. — Вип. 32. — С. 5-17. — Бібліогр.: 5 назв. — англ. 0206-3131 http://dspace.nbuv.gov.ua/handle/123456789/36907 539.4 en Надійність і довговічність машин і споруд Інститут проблем міцності ім. Г.С. Писаренка НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Shell side flow in VVER-440 steam generators has been simulated by using twodimensional and three-dimensional geometrical approach. A number of operating states have been analyzed: nominal and increased power load with the original feed water injection (within the tube bank) and with presently used water injection (above the tube bank). The mathematical model involves physical effects such as: thermal expansion of water phase, local condensation in the region of feed water injection (mixed pre/heater tank), variable slip velocity of the bubbly phase depending on local volume fraction of steam, spatial variation of the water level above the tube bank settling of disperse corrosion product under the tube bank. Micro-models have been developed for calculation of anisotropic resistance of the tube bank and pipe supports, local heat flux over the tube surfaces and the spatial variation of water injection intensity. Water surface elevation and disperse phase deposition patterns are in line with measured data published in scientific literature. |
| format |
Article |
| author |
Gergely, K. Gabor, S. Tamas, R. |
| spellingShingle |
Gergely, K. Gabor, S. Tamas, R. Simulation of two-phase flow on shell side of VVER-440 secondary boilers Надійність і довговічність машин і споруд |
| author_facet |
Gergely, K. Gabor, S. Tamas, R. |
| author_sort |
Gergely, K. |
| title |
Simulation of two-phase flow on shell side of VVER-440 secondary boilers |
| title_short |
Simulation of two-phase flow on shell side of VVER-440 secondary boilers |
| title_full |
Simulation of two-phase flow on shell side of VVER-440 secondary boilers |
| title_fullStr |
Simulation of two-phase flow on shell side of VVER-440 secondary boilers |
| title_full_unstemmed |
Simulation of two-phase flow on shell side of VVER-440 secondary boilers |
| title_sort |
simulation of two-phase flow on shell side of vver-440 secondary boilers |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренка НАН України |
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2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/36907 |
| citation_txt |
Simulation of two-phase flow on shell side of VVER-440 secondary boilers / K. Gergely, S. Gabor, R. Tamas // Надійність і довговічність машин і споруд. — 2009. — Вип. 32. — С. 5-17. — Бібліогр.: 5 назв. — англ. |
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Надійність і довговічність машин і споруд |
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2025-07-03T18:38:44Z |
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2025-07-03T18:38:44Z |
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| fulltext |
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 5
УДК 539.4
2009 K. Gergely, S. Gabor, R. Tamas
CFD.HU Ltd., Budapest, Hungary
SIMULATION OF TWO-PHASE FLOW ON SHELL SIDE OF
VVER-440 SECONDARY BOILERS
Shell side flow in VVER-440 steam generators has been simulated by using two-
dimensional and three-dimensional geometrical approach. A number of operating states
have been analyzed: nominal and increased power load with the original feed water
injection (within the tube bank) and with presently used water injection (above the tube
bank). The mathematical model involves physical effects such as: thermal expansion of
water phase, local condensation in the region of feed water injection (mixed pre/heater
tank), variable slip velocity of the bubbly phase depending on local volume fraction of
steam, spatial variation of the water level above the tube bank settling of disperse
corrosion product under the tube bank. Micro-models have been developed for calculation
of anisotropic resistance of the tube bank and pipe supports, local heat flux over the tube
surfaces and the spatial variation of water injection intensity. Water surface elevation and
disperse phase deposition patterns are in line with measured data published in scientific
literature [3], [4].
Keywords: simulation, two-phase flow, VVER-440, steam generator.
1. Introduction. Inefficient blow down is one of the known design problems
of VVER-440 type secondary boilers. Since secondary boilers are critical parts
from the point of view of the prolongation of life cycle, the improvement of mud
extraction efficiency has been issued by NPP Paks. The blow down system is
aimed at the extraction of ionic and disperse contaminants from the steam
generator vessel. In order to achieve high blow down efficiency, the extraction
outlet need to be placed at the point of highest contaminant concentration [5]. LG
Energy Ltd. has been contracted by NPP Paks for the improvement of blow down
efficiency, analyses of shell side flow and transport processes has been carried out
by CFD.HU Ltd. as a subcontractor.
The most important effect concerning the shell side flow in a secondary
boiler is the unevenness of heating. Every steam generator contains 5536 pipes of
16 mm external diameter bended in horizontal planes. With the help of the enthalpy
of the primary circuit coolant delivered by the pipes secondary circuit water is
heated up to saturation temperature and evaporated on the shell side of the pipes. In
the vicinity of the hot leg (inlet collector) temperature of the primary circuit water
and the consequential heat flux is higher then those at the cold leg (outlet
collector). Unevenness of steam production due to the spatial variation of heat flux
is the driver of the shell side circulation. Pipe supports placed in planes
perpendicular to the axis of the vessel has a significant resistance against the axial
flow component thus the circulation is forced into cross-sectional planes (nearly
2D flow). Really three-dimensional flow takes place only at the end walls of the
vessel, in the vicinity of the collector. Circulation intensity is limited by the shell
side resistance of the tube bank and by the admittance of the relatively large gap
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 6
between the tube bank and the vessel wall. Spatial distribution of the heat flux has
been obtained from pipe wise coupled 1D thermo-hydraulic model. Anisotropic
shell side resistance of the tube bank and the resistance of pipe supports have been
calculated by using 2D and 3D micro-models.
Due to the overheating of water phase the bubbles are growing while rising
towards the surface. In regions characterized by high local void fraction the bubble
agglomeration process can occur as well further increasing the bubble size. Owing
to these effects the difference between bubbly phase and liquid phase velocities
(slip velocity) varies. In order to obtain accurate representation of surface shape
and vapor distribution, the local value of slip velocity has been obtained from a
mathematical model based on measured correlations.
Feed water injection has a large impact on shall side circulation as well.
9.3% of the heat power is spent on pre-heating of feed water to saturation
temperature. This is mostly covered by latent heat released by the bubbly vapor
phase during local condensation processes. Since the energy demand of feed water
decreases the vapor content and the specific volume, feed water drops downwards
from the injection point. For the accurate representation of pre-heating and steam
generation processes a special multi-phase flow model fulfilling local mass and
energy balances has been developed and implemented in ANSYS-FLUENT
simulation system in the form of User Defined Functions (UDF-s).
Numerical simulation of the multiphase flow provides complete image about
the spatial distributions of velocity and void fraction, thus allowing detailed
analysis of the sedimentation of disperse corrosion products and providing data
essential for improvement of blow down efficiency. Numerous further application
of the Computational Fluid Dynamic (CFD) model is foreseeable.
2. Geometrical model, mesh and boundary conditions. Three-dimensional
meshes of two different resolution and a two-dimensional (cross-section) mesh
have been developed. The latter has been found very useful in the work phase of
simulation model development. Time dependent (unsteady) simulation has been
carried out in every case with sufficient number of time steps for achieving
converged solution.
Our most detailed 3D model is illustrated in Fig. 1. The number of
computational cells is 1.2 million. The geometrical model contains both the new
and the old feed water supply collectors. The simplified 3D model consist of 0,5
million cells. In order to reduce the number of cells the feed water collectors, some
inclined rows of pipe supports at the vessel ends, together with some details of
minor importance have been omitted from the model. By using the converged
results of the simplified model as initial condition for the finely resolved model 5
fold reduction of the computation time could be achieved.
Number of cells in the 2D model was 4100, therefore the computing time is
about 100 times shorter relative to the simplified 3D model, which has been found
very helpful when developing the mathematical description of slip velocity and
phase changes, moreover, the 2D simulation gave meaningful results in the
investigated cross-section due to the nearly two-dimensional nature of then flow.
The uppermost part of vessel together with the droplet separator has been
omitted from the model. The upper boundary condition has been placed well above
the water surface, therefore the liquid water content of the flow was nearly zero at
the outlet. Water surface elevation has been locally obtained from dynamics of
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 7
phase separation. Rigid, adiabatic wall boundary conditions have been used for
modeling the remaining part of the vessel wall. Further mass, momentum and
energy exchange processes have been described with spatially distributed volume
sources. Specification of the source terms will discussed in the next chapter.
Fig. 1. The geometrical model (left) and the numerical mesh (right).
3. Mathematical model.
3.1. Heating. Shell side water circulation in the steam generator vessel is
driven by heat flux received from the heat exchanger tubes and the consequential
increase in the specific volume of the fluid, which is 6.7% in the case of feed water
pre-heating and a factor of 33.8 in the case of evaporation.
Heating intensity can be computed on the basis of coupled modeling of
primary and secondary circuit processes. Pressure drop between the hot and cold
collector uniformly effects every heat exchanger pipes, therefore the tubes can be
regarded as different hydraulic resistances in parallel connection. Diameter and
wall thickness is identical for every pipe but pipe lengths vary between 8.3 m
(inner pipes) and 12.5 m (outer pipes). The shorter pipes deliver more water with
smaller temperature drop along the pipe. In view of the mass flow-rate values, the
cooling curves and heat flux distribution could be calculated for each individual
pipes. Constant value of the shell side surface heat transfer coefficient has been
assumed. Outlet temperature of the primary circuit water has been calculated as the
mass weighted average of the pipe outlet temperatures.
Potentially the exact locations of inactive (plugged) pipes can be taken into
account in the model. Presently a power density distribution for randomly
distributed plugged pipes (58 pipes out of 5478) has been taken into account (see
Fig. 2.).
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 8
Fig. 2. Power density distribution in Wm-3.
3.2. Hydraulic resistance of the tube bank and pipe supports. ANSYS-
FLUENT simulation system provides anisotropic model for porous media flows.
Pressure gradient is calculated by means of Eq. 1.:
vCvvDF ?
2
1? ,
(1)
velocity vv
in Eq. 1 is the physical velocity in porous medium of blocking
ratio, D? and C? are symmetric tensors of resistance coefficients specified on the
basis of characteristic directions (symmetries) of the medium.
Tube banks of the steam generators has been modeled as a porous zone of
variable resistance matrices obtained from zone by zone 2D micro modeling of the
flow. Pipe supports have been taken into account as porous surfaces (pressure
jumps). Resistance coefficient has been identified via 3D micro modeling by
assuming periodicity both horizontal and vertical direction.
3.3 Pre-heating and evaporation. Feed water injection has been modeled by
volume sources active in the vicinity of injection nozzles. Intensity of the volume
source has been approximated by a linear function of axial coordinate
parameterized on the basis of hydraulic assumptions concerning the feed water
collectors. Both the original and the new (see Fig. 3) feed water injection systems
can be activated in the simulation model.
The feed water, characterized by a temperature range 223–225°C, mixes
with the boiling water (characterized by the saturation temperature 258.7°C and by
variable fraction of vapor bubbles) when injected into the vessel.
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 9
Fig. 3. Feed water injection (new design).
When relatively small portion of feed water is mixed with boiling water of
high vapor content, the liquid temperature in the resulting mixture reaches the
saturation temperature. When volume fraction of the initial feed water is larger, the
vapor content can condense perfectly and the temperature of the resulting mixture
can be lower than the saturation temperature. The mixing process can take place
within the tube bank too. In this latter case, the additional heat received from the
heat exchanger pipes must be taken into account.
This coupled process of pre-heating, condensation and heat exchange with
the solid surface has been described by the introduction of a fictive third phase –
the feed water phase –to the mathematical model. In every computational cell a
mixture of the following phases are present:
Phase 1: saturated vapor – primary phase,
Phase 2: saturated water – secondary phase,
Phase 3: feed water – secondary phase.
Portion of the k-th phase is described by its volume fraction αk, which is the
volume occupied by the k-th phase over the cell volume. Obviously the following
implicit condition has to be fulfilled:
1
3
1k
k
.
(2)
Mixture density and velocity can be calculated from the following formulae:
3
1k
kk ,
(3)
k
3
1k
kk v1v
,
(4)
in which ρk and kv are the density and velocity of the k-th phase.
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 10
Simulation has been carried out in ANSYS-FLUENT system, by using
multiphase mixture flow model based on the following conservation equations:
Continuity:
3
1
,
k
kmSv
t
,
(5)
in which Sm,k is a volume source of mass in kg m-3 s-1 for the k-th phase. Volume
sources can be evaluated in user defined functions written in C programming
language. Source terms can be functions of spatial coordinate, time and any field
variables used in the mathematical model, which makes the mathematical
description of phase change process possible.
In addition to the continuity equation of the mixture the continuity equation
must be solved for every secondary phase:
pmpdrppmpppp Svv
t ,, )()()(
,
(6)
in which mpp,dr vvv is the drift velocity for the k-th phase. Volume fraction
of primary phase can be evaluated from Eq. 2, therefore the solution of an
additional continuity equation is not required.
The momentum equation for the mixture reads:
.
)()()(
3
1
,,
k
kdrkdrkk
T
vvFg
vvpvvv
t
(7)
Number of phases in Eq. 7 is 3. F
denotes the volume forces (out of the gravitation
force), which is the hydraulic resistance of the tube bank in our case. ? is the
dynamical viscosity of the mixture including turbulent viscosity. ? is calculated on
the following way:
m
1k
kk .
(8)
Eq. 5 expression of the continuity equation, Eq. 6 for two secondary phases
and the three components of Eq. 7 constitute a system of 6 transport equations for 6
primary scalar unknowns: pressure )r,t(p
, volume fraction of two secondary
phases )r,t(p
and 3 components of the mixture velocity )r,t(v
.
In thermodynamic equilibrium state, feed water and vapor cannot be present
together in the same computational cell. Phase changes have to guide the system
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 11
towards the local thermodynamic equilibrium and fulfill the local energy balance.
The local thermodynamic equilibrium is quickly restored in the real system due to
the intensive mixing, therefore the relaxation time necessary for achieving the
thermodynamic equilibrium is estimated by the t time step of the simulation.
(Processes shorter than one time step can be regarded as sudden changes.)
Condensation of the local vapor content leads to the release of the following
amount of heat:
tru /1111 , (9)
in which r1 is the latent heat of water vapor.
For heating the local feed water content to saturation temperature we need to
provide u3 amount of energy:
tru /3333 , (10)
)( 323,3 TTcr p is the enthalpy difference and cp,3 is the specific heat of feed
water on constant pressure, T2 and T3 are the temperatures of saturated water and
feed water.
q denotes the power released by the heat exchanger tubes in unit volume.
Conditions on local evaporation and pre-heating can be expressed in the following
terms:
A. Evaporation: 0uuq 31 , (11)
B. Pre-hating: 0uuq 31 . (12)
A. In the case of local evaporation the feed water phase need to be completely
transformed into saturated water by pre-heating:
333, / ruSm , (13)
the remaining energy is used for steam production:
131, /)( ruqSm . (14)
B. When local pre-heating takes place, we remove the local steam phase (by
perfect condensation):
111, / ruSm , (15)
and the remaining energy can be used for pre-heating:
313, /)( ruqSm . (16)
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 12
Formation rate of saturated water can be calculated from the local mass
conservation:
3,m1,m2,m SSS . (17)
Application of mass sources Eqs. 13–17 in transport equations 5–6 enforces
local mass and energy balances during the phase change process. By the
application of the 3 phase model together with the above sources the solution of
energy equation for temperature can be avoided.
3.4. Slip velocity. Slip velocity of water vapor relative to the liquid phases is
calculated from measured correlation [1, 2] depending on local vapor content and
the vector sum of gravity and inertial accelerations. Slip velocity in homogenous
steady flow for the operating conditions specific to NPP Paks is plotted in Fig. 4
against the local vapor concentration.
Fig. 4. Slip velocity (difference between velocity of gas and liquid phases) as a function of
the volume fraction of gas phase (steam) for homogenous flow with zero inertial forces.
In the flow field of the steam generator large inertial forces occur due to the
flow inhomogeneous flow. The resulting slip velocity is plotted in Fig. 5.
The slip velocity formula, employed in this study, provide at least
qualitatively correct description of the water droplet sedimentation above the
surface. This modeling feature is necessary for realistic formation of water surface
which is actually the upper boundary condition for the shell side water circulation
in the steam generator vessel.
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 13
Fig. 5. Distribution of slip velocity [m s-1] in the cross-section of the steam generator.
3.5. Numerical control of water level. Water level is controlled by signals of
real time water level measurements in the real technological process. Output signal
of the water level probes is proportional to the hydrostatic pressure difference
between the higher and the lower taping points of the probe. If the lower taping
point is positioned to a height other than the bottom of the tank, which is usually
the case, the total mass of liquid water contained by the vessel depends on the
steam content under the lower tapping point. The applied mathematical model of
multiphase flow ensures mass conservation for the saturated water phase, but the
initial mass is unknown due to its dependence on the steam concentration,
therefore, a kind of level control must be employed in the numerical simulation as
well.
Role of numerical level control is the fastest possible adjustment of the
instantaneous water level to a given target level, for that reason, time constant of
level control in the numerical system has been chosen to 1 sec, which is much
shorter than that in the reality. By the application of an evenly distributed mass
source of saturated water the numerical level control has managed to stabilize the
instantaneous water level within an error bound of 1 mm after 10 seconds of
simulation time.
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 14
4. Simulation results. Simulation of the shell side flow in a VVER type
steam generator has been carried out for the power load of the original design (224
MW) and for an increased power operation (251 MW) assuming a randomly
distributed plugging of heat exchanger tubes. From the simulation results the
following conclusions could be drawn:
1. Maximum volume fraction of water vapor in the liquid mixture is about
55%. A well defined surface is formed, above of which, the volume fraction of
vapor approaches 100% (see Fig. 8).
2. Highest point of the water surface is located in the vicinity of the hot leg
(see Fig. 7), the lowest point (40 cm-s below the highest level) is close those end
wall that is at maximum distant from the hot leg. Water surface at the lowest level
point approaches (or reaches) the heat exchanger tube bank. Surface shape obtained
from the simulation model is in good correlation with earlier experimental
observations [3].
3. As can be speculated, the shell side flow is directed upwards on the hot
side and downwards on the cold side of the vessel, forming the main circulation
pattern in the cross-section of the vessel, visualized in Fig. 6. Moreover an
extensive local circulation is present on the cold side as a consequence of large
difference between arch lengths and heating intensities of the heat exchanger tubes
of inner and outer positions. Similar, but narrower, circulation can be observed on
the hot side due to the low hydraulic resistance of the clearance between the vessel
wall and the tube bank.
4. Strong circulations take place at both end walls of the vessel (see Fig. 6)
caused by the relatively large gap between the wall and the tube bank.
5. The way of feed water injection has a substantial effect on the shell side
flow. Fluid characterized by steam content strongly reduced by the feed water
injection has a tendency for fast drop down motion. This cold plume can reach the
bottom of the vessel even in the case of upper feed water injection. Higher steam
content and more intensive circulation has been predicted by the simulation model
for high level feed water injection.
6. Results obtained from simulations with two different approximations for
the turbulent transport, i.e. constant turbulent viscosity ( 100t ) and realizable
k–ε model, could be compared for the detailed geometrical model. Only minor
differences could be observed in the results, underlining the dominance of
multiphase flow effects.
7. Model results from coarse and fine spatial resolutions were very similar
too. Surface pattern obtained from the highly resolved model showed better
correlation with the measured data.
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 15
Fig. 6: Stream lines (colored by velocity magnitude) and the main flow features highlighted
by heavy arrows.
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 16
Fig. 7: Water surface elevation [m] defined by the 70% iso-surface of the volume fraction
of water vapor.
Fig. 8: Volume fraction of gas phase (water vapor) in the cross section 1.5 m away from the
symmetry plane with lower (lower) and upper (right) feed water supply.
Резюме
С помощью двумерного и трехмерного геометрических подходов был
смоделирован поток теплоносителей в парогенераторах энергоблока ВВЭР-440.
Проанализированы следующие рабочие состояния: номинальная и повышенная
нагрузки при первоначальной подаче водного питания (внутри трубного пучка)
и использование текущего водного питания (над трубным пучком).
Математическая модель включает в себя следующие физические явления:
тепловое расширение водной фазы, местная конденсация в месте впуска
водяного питания, переменная скорость скольжения пузырьковой фазы в
зависимости от локальной объемной доли пара, пространственное изменение
ISSN 0206-3131. Надійність і довговічність машин і споруд, 2009. Вип. 32 17
уровня воды над трубным пучком и оседание дисперсных продуктов коррозии
под трубным пучком. Разработаны микро модели для расчета анизотропного
сопротивления пучка труб и опор трубопроводов, локального теплового потока
по поверхности труб и пространственные изменения интенсивности подачи
воды. Уровень воды и осаждение дисперсной фазы в соответствии с данными
измерений опубликованы в научной литературе [3] и [4].
Ключевые слова: моделирование, двухфазный поток, парогенератор, ВВЭР-440.
Резюме
З допомогою двомірного и трьохмірного геометричних підходів
змодельовано потік теплоносіїв в парогенераторах енергоблока ВВЕР-440.
Проаналізовано наступні рабочі стани: номінальне і підвищене навантаження
при первинній подачі водяного живлення (всередині трубного пучка) і
використання поточного водяного живлення (над трубним пучком).
Математична модель містить в собі наступні фізичні явища: теплове
розширення водяної фази, місцеву конденсацію в місці впуску водяного
живлення, змінна швидкість ковзання бульбашкової фази в залежності від
локальної об’ємної частки пари, просторова зміна рівня води над трубним
пучком і осідання дисперсних продуктів корозії під трубним пучком.
Розроблено мікро моделі для розрахунку анізотропного опору пучка труб і
опор трубопроводів, локального теплового потоку по поверхні труб і
просторові зміни інтенсивності подачі води. Рівень води і осад дисперсної
фази у відповідності з даними вимірювань опубліковані в науковій літературі
[3] і [4].
Ключові слова: моделювання, двохфазний потік, парогенератор, ВВЕР-440.
1. Stosic Z., Stevanovic V. Advanced three-dimensional two-fluid porose media
method for transient two-phase flow thermal-hydraulics in complex
geometries // Numer. Heat Transfer. – 2002. – A 41. – P. 263 – 289.
2. Pezo M., Stevanovic V. D., Stevanovic Z. A two-dimensional model of the
kettle reboiler shell side thermal-hydraulics // Int. J. Heat Mass Transfer. –
2006. – 49. – P. 1214 – 1224.
3. Dmitrijev A. I., Kozlov Ju. V. et. al. Opyt ispolzovaniya zhalyuznyh
separatorov v sisteme AES // Teploenergetika. – 1989. – 12. – P. 11 – 14.
4. Beljakov V. A., Szmirnov Sz. V. Analiz i ocenka dannyh VTK teploobmennyh
trub parogeneratorov Kolskoj AES. – Proceedings of the 7-th International
Seminar on Horizontal Steam Generators, 3-5 October, 2006, Podolsk, Section
1: Operational experience, inspection and life management.
5. Ősz J., Tajti T., Kaszás Cs: A VVER-440 gőzfejlesztők megbízhatósága és
hatekonyabb leiszapolasa a PA-ben. Magyar Energetika 2008 / (megjelenes
alatt).
Поступила 20.05.2009
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