Methodology and results of thermal calculation of one-through steam generators for NPP of small power
Due to the invaluable interest in small-scale nuclear power plants around the world, it has been proposed to pay sufficient attention to the design of appropriate equipment, which can make Ukraine with its great potential as a producer a supplier of such nuclear power plants. The work considers the...
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irk-123456789-1943682023-11-23T16:16:20Z Methodology and results of thermal calculation of one-through steam generators for NPP of small power Kravchenko, V.P. Xiaolong Zhou Problems of modern nuclear power engineering Due to the invaluable interest in small-scale nuclear power plants around the world, it has been proposed to pay sufficient attention to the design of appropriate equipment, which can make Ukraine with its great potential as a producer a supplier of such nuclear power plants. The work considers the method of thermal calculation of a oncethrough steam generator with a coil heating surface and superheating of steam. As a result of analysis and comparison of the results, formulas were selected for calculating six different conditions of heat transfer: lumbar flow around the coil package with coolant and five heat transfer sections during the movement of the working fluid in the tube. The results of calculating the heat transfer surface for a steam generator with a capacity of 45 MW are presented. The obtained results correlate well with the calculation data by the ASPEN-TECH computer code. В связи с большим интересом во всем мире к АЭС малой мощности предложено уделять достаточное внимание проектированию соответствующего оборудования, что может сделать Украину с ее мощным потенциалом производителя поставщиком таких АЭС. В работе рассмотрена методика теплового расчета прямоточного парогенератора со змеевиковой поверхностью нагрева и перегревом пара. В результате анализа и сопоставления результатов были выбраны формулы для расчета шести различных условий теплообмена: поперечного обтекания пакета змеевиков теплоносителем и пяти участков теплообмена при движении рабочего тела в трубке. Приведены результаты расчета поверхности теплообмена для парогенератора мощностью 45 МВт. Полученные результаты хорошо коррелируют с данными расчета компьютерным кодом ASPEN-TECH. У зв’язку з великим інтересом у всьому світі до АЕС малої потужності запропоновано приділяти достатню увагу проектуванню відповідного устаткування, що може зробити Україну з її великим потенціалом виробника постачальником таких АЕС. В роботі розглянуто методику теплового розрахунку прямоточного парогенератора зі змієвиковою поверхнею нагріву та перегрівом пара. В результаті аналізу та співставлення результатів було вибрано формули для розрахунку шести різних умов теплообміну: поперекового обтікання пакету змієвиків теплоносієм та п’яти ділянок теплообміну при русі робочого тіла в трубці. Наведено результати розрахунку поверхні теплообміну для парогенератору потужністю 45 МВт. Отримані результати добре корелюються з даними розрахунку комп’ютерним кодом ASPEN-TECH. 2020 Article Methodology and results of thermal calculation of one-through steam generators for NPP of small power / V.P. Kravchenko, Xiaolong Zhou // Problems of atomic science and tecnology. — 2020. — № 2. — С. 85-88. — Бібліогр.: 10 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/194368 621.181.6 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Problems of modern nuclear power engineering Problems of modern nuclear power engineering |
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Problems of modern nuclear power engineering Problems of modern nuclear power engineering Kravchenko, V.P. Xiaolong Zhou Methodology and results of thermal calculation of one-through steam generators for NPP of small power Вопросы атомной науки и техники |
| description |
Due to the invaluable interest in small-scale nuclear power plants around the world, it has been proposed to pay sufficient attention to the design of appropriate equipment, which can make Ukraine with its great potential as a producer a supplier of such nuclear power plants. The work considers the method of thermal calculation of a oncethrough steam generator with a coil heating surface and superheating of steam. As a result of analysis and comparison of the results, formulas were selected for calculating six different conditions of heat transfer: lumbar flow around the coil package with coolant and five heat transfer sections during the movement of the working fluid in the tube. The results of calculating the heat transfer surface for a steam generator with a capacity of 45 MW are presented. The obtained results correlate well with the calculation data by the ASPEN-TECH computer code. |
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Article |
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Kravchenko, V.P. Xiaolong Zhou |
| author_facet |
Kravchenko, V.P. Xiaolong Zhou |
| author_sort |
Kravchenko, V.P. |
| title |
Methodology and results of thermal calculation of one-through steam generators for NPP of small power |
| title_short |
Methodology and results of thermal calculation of one-through steam generators for NPP of small power |
| title_full |
Methodology and results of thermal calculation of one-through steam generators for NPP of small power |
| title_fullStr |
Methodology and results of thermal calculation of one-through steam generators for NPP of small power |
| title_full_unstemmed |
Methodology and results of thermal calculation of one-through steam generators for NPP of small power |
| title_sort |
methodology and results of thermal calculation of one-through steam generators for npp of small power |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2020 |
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Problems of modern nuclear power engineering |
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http://dspace.nbuv.gov.ua/handle/123456789/194368 |
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Methodology and results of thermal calculation of one-through steam generators for NPP of small power / V.P. Kravchenko, Xiaolong Zhou // Problems of atomic science and tecnology. — 2020. — № 2. — С. 85-88. — Бібліогр.: 10 назв. — англ. |
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Вопросы атомной науки и техники |
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2025-07-16T21:37:26Z |
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2025-07-16T21:37:26Z |
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| fulltext |
ISSN 1562-6016. PASТ. 2020. №2(126), p. 85-88.
UDC 621.181.6
METHODOLOGY AND RESULTS OF THERMAL CALCULATION OF
ONE-THROUGH STEAM GENERATORS FOR NPP
OF SMALL POWER
V.P. Kravchenko, Xiaolong Zhou
Odessa National Polytechnic University, Odessa, Ukraine
E-mail: kravchenko@opu.ua; tel. +38-050-390-17-92
Due to the invaluable interest in small-scale nuclear power plants around the world, it has been proposed to pay
sufficient attention to the design of appropriate equipment, which can make Ukraine with its great potential as a
producer a supplier of such nuclear power plants. The work considers the method of thermal calculation of a once-
through steam generator with a coil heating surface and superheating of steam. As a result of analysis and compari-
son of the results, formulas were selected for calculating six different conditions of heat transfer: lumbar flow
around the coil package with coolant and five heat transfer sections during the movement of the working fluid in the
tube. The results of calculating the heat transfer surface for a steam generator with a capacity of 45 MW are present-
ed. The obtained results correlate well with the calculation data by the ASPEN-TECH computer code.
INTRODUCTION
The relevance of the technology of small modular
reactors (SMR) is already evidenced by the fact that
only 2020 holds several international conferences of
world level [1, 2]. This indicates a great interest in SMR
technology and its broad prospects. The most ready-to-
use for today is NuScale technology, which is described
in the IAEA report [3].
Extensive experience in the design, manufacture and
operation of low-power nuclear power plants (NPP)
accumulated in the icebreaking and submarine fleet.
Reactor installation (RI) KLT-40 (ship icebreaking
type) with a capacity of 150 MW (therm.) installed on
modern lighter carriers “Sevmorput”, icebreakers “Tai-
myr”, and “Vaigach”, as well as on the floating NPP
“Akademik Lomonosov” [4].
Today's prospects of nuclear energy in Ukraine are
associated with RI SMR-160, which is being designed
by the American company Holtec International [5].
Ukraine with its powerful production potential of power
engineering could take its rightful place in the world in
the production of appropriate equipment for SMR, nec-
essary for use both in our country and for export abroad.
One of the main elements of NPP equipment is a
steam generator, the calculation of which is the object of
consideration in this article. It should be noted that in
the mentioned projects, options with natural and forced
circulation are considered. Regardless of the possible
design options, a mandatory section in the design of the
steam generator is its thermal calculation.
The aim of the article is to refine the methods of
thermal calculation and calculation of a 45 MW steam
generator.
For further consideration, a NPP with a thermal ca-
pacity of 180 MW was adopted, the prototype of which
is the KLT-40S NPP [6].
1. DESCRIPTION OF THE DESIGN
OF THE STEAM GENERATOR
One-through type steam generator: feed water enters
in the heat exchange tubes (HET) (coils), on the output
of which is superheated steam. The main characteristics
of the steam generator:
• fluids movement – counter flow;
• the coolant of the 1st circuit (water under pressure)
moves from top to bottom in the annulus. That is, there
is a lumbar flow around the tubes at an angle;
• coolant of the 2nd circuit (feed water – steam water
mixture – superheated steam) moves inside the pipes
from the bottom up along a curved path.
Heat transfer surface consists of cylindrical rows of
coils. Each row (layer) has a different number of tubes.
The number of tubes in the layer is determined from the
condition of equal length of tubes in different rows. The
main parameters of the coolants are given in the table.
The main parameters of the coolants
in the steam generator
Thermal power, MW 45
Mass flow of steam, t/h 62.1
Steam parameters: Р, МW
t, °C
3
275
Feed water temperature, °C 65
Coolant temperature, °C: Entrance
Exit
297. 8
270
Coolant pressure at the inlet, МPa 15
Heat transfer tubes made of titanium alloy ПТ-7М.
2. METHODOLOGY OF THERMAL
CALCULATION OF ONE-THROUGH
STEAM GENERATOR [7–10]
Constructive calculation with given (accepted) char-
acteristics determines the amount of HET, external
dimensions. The required characteristics are usually: the
diameter and steps between the HET, as well as the
speed at the entrance to the tubes. When using a coil
surface of cylindrical layers this is not enough. The
number of layers is determined by the velocity of the
coolant in the annulus or, conversely, given the number
of rows of cylindrical coils, it is possible to obtain the
velocity of the coolant in the annulus. Thus, the coil
heating area, for definiteness, requires one more inde-
pendent parameter than conventional heat exchangers
[6].
mailto:kravchenko@opu.ua
The heat exchange area is calculated for five sec-
tions in which different heat transfer conditions for the
working fluid:
Economizer (ECS): 1 – Convective heat transfer;
2 – Surface boiling.
Evaporator (EVS): 3 – Developed boiling EVS;
4 – poor heat transfer EVS.
Superheater (SUS): 5 – Overheating steam.
The first stage of the thermal calculation is the con-
struction of t, Q – SG diagrams, determining the power,
transmitted on the ECS, EVS, and SUS (Figure).
t, Q – steam generator diagram
The boundary between the first and second zones of
the economizer section is determined from the condi-
tion: the temperature of the inner surface of the wall is
equal to the boiling point
. To determine the
fraction of heat transferred to ECS1, it is necessary to
calculate the temperatures on the inner surface of the
wall at the inlet and outlet of the economizer section
and
. To do this, at these points it is necessary to
calculate the heat transfer coefficient from the coolant to
the wall, the heat transfer coefficient from the wall to
the working fluid, the heat transfer coefficient at an
average wall temperature, the heat transfer coefficient,
and heat flux. Hence, the thermal power of the first
economizing section is defined as:
where – thermal power economizer section.
The heat transfer coefficient (HTC) from the wall to
the feed water which moves in the pipes, is determined
by the formula [8]:
αfw.ECS1 = 0.023∙(𝜆/din)∙Re
0.8
∙ Pr
0.4
(μf/μw )
0.11
. (1)
where 𝜆 – thermal conductivity of water, W/(m∙K);
din – inner diameter HET, m; Re, Pr – Reynolds and
Prandtl numbers; μf, μw – dynamic viscosity coeffi-
cients of water at an average temperature at ECS1 and at
a temperature of the inner wall surface.
The movement in the coil increases HTC, which is
taken into account by the coefficient:
К = 1+3.5 din/Dcoil, (2)
where Dcoil – coil diameter.
As you can see, to determine HTC, you should first
take the temperature of the inner surface of the wall.
The heat transfer from the coolant to the wall during the
transverse flow around the coils for all sections is de-
termined identically [9]:
αC = 0.02 𝜆/dout ∙Re
0.84
∙Pr
0.36
. (3)
where dout – outside diameter of HET.
Attack angle φ, which differs from 90º is taken into
account by multiplying by a coefficient:
К = 1–0.54cos
2
φ. (4)
The coolant velocity in the annulus is defined as the
highest at the smallest intersection.
Next, you should take the average wall temperature,
determine from it the thermal conductivity of the wall
(for ПТ-7М), W/(m∙К):
𝜆w = 0.002∙tw+14.873, (5)
determine heat transfer coefficient:
(
)
(6)
Rf is fouling resistance inside the tube,
Rf = 8.8∙10
-6
(m
2
∙K)/W.
As a result determine the heat flux, W/(m
2
∙К):
(7)
where
– logarithmic temperature difference.
Using the known heat flux and HTC from the wall to
the working fluid and from the coolant to the wall, the
wall temperatures on the internal and external surfaces
are specified:
(8)
. (9)
With a large difference between the previously ac-
cepted and received values, the wall temperatures are
restarted and the calculation is repeated.
After calculating the thermal power of the first and
second economizer sections, the first economizer sec-
tion ECS1 is calculated similarly to the previous calcu-
lation. Heat transfer area (HTA):
. (10)
When determining the height of the HTA, it must be
taken into account that the thermal conductivity coeffi-
cient is determined by the average diameter of the tube.
Water underheated to saturation temperature boils
on ED2 [8]:
{ [ (
)]
}
, (11)
where
(12)
q – specific heat flux, W/m
2
; – is determined by
expression (1); ) – underheating of liquid to
saturation temperature.
The calculation algorithm in the second economizer
section ECS2 is similar to the previous one except that it
is necessary to accept the heat flux q. To determine the
thermal conductivity of the wall in this area, one also
has to take the average wall temperature. After that,
HTC from the coolant, HTC k, heat flux and wall tem-
perature on both surfaces of the HET are calculated. The
calculation is considered complete if the accepted and
received values of the heat flux and wall temperatures
are close enough.
The boundary between the third and fourth sections
is determined by the formula for calculating xb (vapor
content) in the evaporation region. At the point of xb the
zone of developed boiling passes into the zone of im-
paired heat transfer [8]:
√
(
)
(13)
where Р – pressure, bap; – saturated water density,
kg/m
3
; – the speed of the water in the pipe, provided
that it is saturated, m/s; – tube inner diameter, m.
On EVS1 is developed boiling in channels [8]:
= 0 :
{ [(
)]
}
(14)
=
(
)
(15)
= :
√ (
)
,
(16)
√
,
, (17)
where – HTC during a single-phase fluid flow, de-
termined by the circulation rate 0:
√
; (18)
; (19)
(20)
Ct = (μf/μw )
0.11
, (21)
is determined by (12),
[ (
)] (22)
x – average steam content in the area.
The HTC in this area was determined as the arithme-
tic mean at the input and output of the section.
On the EVS2 is reduced boiling zone. It was calcu-
lated in accordance with [9]:
√[
]
[
]
[
]
(23)
· · (
)
; (24)
· · ·(
)
·k; (25)
(
) (
)
(26)
. (27)
Superheater section (SUS). During the flow of gases
in curved channels, it is proposed [8]:
(
)
{
[ (
)
]
} (30)
3. CALCULATION RESULTS
According to the presented methodology, a direct-
low steam generator was calculated with the initial data
given earlier (Table).
From the above data it is seen that when the coolant
moves with a decrease in its temperature, the HTC
gradually decreases. The HTC of the working fluid is
significantly less than the HTC from the coolant in all
areas of heat transfer.
The main results of the calculation of a once-through
steam generator with a coil heat area surface
Indicators ECS1 ECS2 EVS1 EVS2 SUS
Q, kW 11272 2328 18274 5641 2129
q, kW/m
2
31.2 178.3 180.3 102.3 69.74
αc,
kW/(m
2
∙К)
40.84 41.09 41.59 42.15 42.31
αwf,
kW/(m
2
∙К)
6.34 39.44 92.99 7.7 3.045
, °C 228.6 255.8 264.6 272.5 287.5
Flow rate of
coolant, m/s
4.02 4.06 4.207 4.23 4.25
Flow rate of
working
fluid, m/s
0.604 0.68 26.98 33.83 38.5
k, kW/(m
2
∙К) 2.676 4.158 4.249 1.838 1.846
Δtlog, С 116.6 42.9 40.7 55.5 37.8
HTA, m
2
36.12 13.05 186.7 55.3 30.5
Height, m 0.349 0.126 1.8 0.534 0.29
As a result, the wall temperature is close to the tem-
perature of the coolant. The thermal resistance of the
wall is essential. At the economizer site, it is even more
than the thermal resistance of heat transfer of the work-
ing fluid. This indicates the feasibility of searching for
material for heat transfer tubes with a high coefficient of
thermal conductivity and better strength characteristics.
The overall dimensions of the steam generator re-
sulting from the calculation coincide with the calcula-
tion data using the ASPEN-TECH computer code.
CONCLUSIONS
1. An algorithm and a program for calculating a one
through steam generator for low power NPP with a coil
heating area have been developed. This program can be
used to optimize parameters when designing steam
generators of a similar design.
2. The calculation showed good coincidence be-
tween the obtained values of the overall dimensions of
the steam generator and the calculation data of the AS-
PEN-TECH computer code.
REFERENCES
1. Annual International SMR and Advanced Re-
actor Summit
https://www.nuclearenergyinsider.com/international-
smr-advanced-reactor/brochure-thank-you.php (Date of
the application 21.02.2020).
2. International Conference on Generation IV and
Small Reactor http://g4sr.org/ (Date of the application
21.02.2020).
3. Advances in Small Modular Reactor Technology
Developments. https://aris.iaea.org/Publications/SMR-
Book_2018.pdf (Date of the application 21.02.2020).
4. Реакторная установка КЛТ-40
https://ru.wikipedia.org/wiki/%D0%9A%D0%9B%D0
%A2-40 (Date of the application 21.02.2020).
5. Уникальные возможности Украины для внед-
рения технологий SMR-160
http://www.energoatom.com.ua/files/file/smr_160_for_
naek_industry_forum_rus.pdf (Date of the application
21.02.2020).
6. V.P. Kravchenko , R.M. Sereda , Zhou Xiaolong,
Yu.I. Visotskii, А.Н. Rybakov. Choice of basic con-
struction parameters of steam generators for NPP of low
power // Problems of Atomic Science and Technology.
2019, N 5(125), p. 62-68.
7. Д.Ф. Романов, М.А. Лебедев, С.С. Саварен-
ский, Н.П. Шаманов. Судовые ядерные паропроиз-
водящие установки. Л.: «Судостроение», 1967,
404 с.
8. П.Л. Кириллов, Ю.С. Юрьев, В.П. Бобков.
Справочник по теплогидравлическим расчетам
(ядерные реакторы, теплообменники, парогенера-
торы). М.: «Энергоатомиздат», 1990, 360 с.
9. РД 24.035.05-89. Методические указания.
Тепловой и гидравлический расчет теплообменного
оборудования АЭС.
http://docs.cntd.ru/document/1200085786 (Date of the
application 21.02.2020).
10. М.А. Михеев, И.М. Михеева. Краткий курс
теплопередачи. М.-Л.: «Госэнергоиздат», 1960,
208 с.
Article received 02.03.2020
МЕТОДИКА И РЕЗУЛЬТАТЫ ТЕПЛОВОГО РАСЧЕТА ПРЯМОТОЧНОГО
ПАРОГЕНЕРАТОРА ДЛЯ АЭС МАЛОЙ МОЩНОСТИ
В.П. Кравченко, Сяолун Чжоу
В связи с большим интересом во всем мире к АЭС малой мощности предложено уделять достаточное
внимание проектированию соответствующего оборудования, что может сделать Украину с ее мощным по-
тенциалом производителя поставщиком таких АЭС. В работе рассмотрена методика теплового расчета пря-
моточного парогенератора со змеевиковой поверхностью нагрева и перегревом пара. В результате анализа и
сопоставления результатов были выбраны формулы для расчета шести различных условий теплообмена:
поперечного обтекания пакета змеевиков теплоносителем и пяти участков теплообмена при движении рабо-
чего тела в трубке. Приведены результаты расчета поверхности теплообмена для парогенератора мощно-
стью 45 МВт. Полученные результаты хорошо коррелируют с данными расчета компьютерным кодом
ASPEN-TECH.
МЕТОДИКА ТА РЕЗУЛЬТАТИ ТЕПЛОВОГО РОЗРАХУНКУ ПРЯМОТОЧНОГО
ПАРОГЕНЕРАТОРА ДЛЯ АЕС МАЛОЇ ПОТУЖНОСТІ
В.П. Кравченко, Сяолун Чжоу
У зв’язку з великим інтересом у всьому світі до АЕС малої потужності запропоновано приділяти достат-
ню увагу проектуванню відповідного устаткування, що може зробити Україну з її великим потенціалом
виробника постачальником таких АЕС. В роботі розглянуто методику теплового розрахунку прямоточного
парогенератора зі змієвиковою поверхнею нагріву та перегрівом пара. В результаті аналізу та співставлення
результатів було вибрано формули для розрахунку шести різних умов теплообміну: поперекового обтікання
пакету змієвиків теплоносієм та п’яти ділянок теплообміну при русі робочого тіла в трубці. Наведено ре-
зультати розрахунку поверхні теплообміну для парогенератору потужністю 45 МВт. Отримані результати
добре корелюються з даними розрахунку комп’ютерним кодом ASPEN-TECH.
https://www.nuclearenergyinsider.com/international-smr-advanced-reactor/brochure-thank-you.php
https://www.nuclearenergyinsider.com/international-smr-advanced-reactor/brochure-thank-you.php
http://g4sr.org/
https://aris.iaea.org/Publications/SMR-Book_2018.pdf
https://aris.iaea.org/Publications/SMR-Book_2018.pdf
https://ru.wikipedia.org/wiki/%D0%9A%D0%9B%D0%A2-40
https://ru.wikipedia.org/wiki/%D0%9A%D0%9B%D0%A2-40
http://www.energoatom.com.ua/files/file/smr_160_for_naek_industry_forum_rus.pdf
http://www.energoatom.com.ua/files/file/smr_160_for_naek_industry_forum_rus.pdf
http://docs.cntd.ru/document/1200085786
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