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Development and preliminary
verification of a 1D–3D coupled
flow and heat transfer model
of OTSG
Xianghui Lu, Xin Wang*, Xiong Zheng, Xiting Chen, Shuqi Meng,
Tianming Ruan, Jun Chen, Yulong Mao, Yisong Hu and
Chaohao Shang
China Nuclear Power Technology Research Institute Co., Ltd., Shenzhen, China
Introduction: A simulation model was developed by coupling a one-dimensional
(1D) system code and 3D CFD software, to analyze the three-dimensional (3D) flow
and heat transfer characteristics of the once-through steam generator (OTSG).
Methods: The shell side of the OTSG was simulated by FLUENT, and the tube side
was simulated by the system code LOCUST. Through spatial mapping, the 1D and
3D simulations were coupled along the outer wall of the OTSG’s helically
coiled tubes.
Results and Discussion: This coupling method enabled the acquisition of high-
resolution flow and heat transfer characteristics of the OTSG, and the error of heat flux
calculation result by the coupled model is within 15%. Through coupling simulation
analysis of the prototype OTSG, it was found that the inlet and outlet temperature
difference reached as high as 150°C. The unevenness of the radial temperature
distribution increased along the flow direction, and the wake swing effect caused by
the sweeping flow of the tube bundle at the exit position was evident. The results of
this study provide reference and a coupled simulation method for the engineering
design and thermal-hydraulic characteristics analysis of OTSG.
KEYWORDS
once-through steam generator (OTSG, ), coupling model, three-dimensional flow and
heat transfer, shell and tube side coupling, parallel multi-channel
1 Introduction
The Once-Through Steam Generator (OTSG) boasts superior heat transfer efficiency, and the
capability to produce steam at higher pressures and temperatures compared to traditional
pressurized water reactor steam generators. Additionally, OTSG enables more flexible operational
strategies to accommodate variations in the reactor loop power and the grid load. Its compact
structure makes it suitable for modular reactor designs. During operation, the OTSG helically
coiled tubes experience complex two-phase flow heat transfer phenomena, with centrifugal forces
impacting pressure and temperature within the tubes. Issues such as flow instability may occur,
leading to degradation in heat transfer performance, power reduction, or tube rupture, adversely
affecting reactor operation. Therefore, the prediction and analysis of the flow and heat transfer
characteristics of OTSG are crucial.
Presently, OTSG finds extensive applications in small and medium-sized advanced
reactors, including sodium-cooled fast reactors, small water reactors, high-temperature
OPEN ACCESS
EDITED BY
Yuze Sun,
Northwestern Polytechnical University, China
REVIEWED BY
Taiyang Zhang,
University of Illinois at Urbana-Champaign,
United States
Bo Kuang,
Shanghai Jiao Tong University, China
*CORRESPONDENCE
Xin Wang,
kasim56@163.com
RECEIVED 10 January 2024
ACCEPTED 26 January 2024
PUBLISHED 16 February 2024
CITATION
Lu X, Wang X, Zheng X, Chen X, Meng S, Ruan T,
Chen J, Mao Y, Hu Y and Shang C (2024),
Development and preliminary verification of a
1D–3D coupled flow and heat transfer model
of OTSG.
Front. Energy Res. 12:1368303.
doi: 10.3389/fenrg.2024.1368303
COPYRIGHT
© 2024 Lu, Wang, Zheng, Chen, Meng, Ruan,
Chen, Mao, Hu and Shang. This is an open-
access article distributed under the terms of the
Creative Commons Attribution License (CC BY).
The use, distribution or reproduction in other
forums is permitted, provided the original
author(s) and the copyright owner(s) are
credited and that the original publication in this
journal is cited, in accordance with accepted
academic practice. No use, distribution or
reproduction is permitted which does not
comply with these terms.
Frontiers in Energy Research frontiersin.org01
TYPE Original Research
PUBLISHED 16 February 2024
DOI 10.3389/fenrg.2024.1368303
gas-cooled reactors, and lead-cooled fast reactors. As the
development of small modular reactors progresses rapidly,
numerous studies have focused on simulating and predicting
the flow and heat transfer characteristics of OTSG.
Xu et al. (2021) evaluated the applicability of heat transfer and
friction coefficient models for helically coiled tubes and successfully
applied well-suited models to the RELAP5 code, simulating the steady-
state flow and heat transfer behavior of helically coiled tubes. Their
results aligned well with experimental data and captured flow
instability phenomena using a modified model. Huang et al. (2020)
developed the NUSOL-SG program, incorporating a two-fluid two-
phase flow model considering thermal non-equilibrium for thermal-
hydraulic analysis of the helically coiled tubes steam generator. The
program embedded heat transfer and pressure-drop relationships, and
the results demonstrated good agreement with RELAP5 calculation.
Chen et al. (2019) developed the THOSG code for thermal-hydraulic
analysis, simulating the thermal-hydraulic behavior of OTSG by
coupling flow and heat transfer on the primary and tube sides. Yao
et al. (2021) developed the code TACS, utilizing a homogeneous flow
model for simulating two-phase flow in helically coiled tubes. TACS
performed thermal-hydraulic characteristic analysis on OTSGs with
varying thermal and geometric parameters. Niu et al. (2016)
conducted numerical simulations of uniform single-side heating in
pipes using the commercial CFD software FLUENT, based on the
VOF and the Realizable k-εturbulence model. The study explored the
thermohydraulic characteristics of flow in helically coiled tubes under
different heating conditions. Sun et al. (2018) numerically simulated
nucleate boiling heat transfer in helically coiled tubes using the
Eulerian two-fluid model with commercial CFD software FLUENT.
Jo et al. (2009),Prattipati et al. (2021),andSun et al. (2018) used the
Eulerian two-fluid model for boiling heat transfer calculations in
helically coiled tubes. However, due to the complex two-phase flow
patterns in helically coiled tubes transitioning from bubbly to churn,
slug, annular, and dispersed flows, with different models for interface
concentration and interphase mass, momentum, and energy transfer,
there is no universal sub-model between phases. Heydari et al. (2021)
employed the Taguchi optimization method to analyze the heat
transfer performance of helically coiled corrugated tube heat
exchangers of different geometric parameters and operational
conditions. Etghani and Baboli (2017) also used the Taguchi
method to conduct heat transfer and friction loss analyses on
helically coiled tube heat exchangers, focusing on the influence of
pitch, tube diameter, and shell-side flow rate. Xu et al. (2022)
investigated the effects of groove shapes and depths on the heat
transfer of helically coiled tube heat exchangers using software
such as SolidWorks and ANSYS FLUENT. Mirgolbabaei (2018)
evaluated the heat transfer performance of helically coiled tube
heat exchangers under different mass flow rates, coil diameters,
and pitches using CFD simulations. Kim et al. (2016) studied heat
exchangers with bumps and depressions on helically coiled tubes,
analyzing heat transfer performance under different flow rates and
inlet temperatures. Mansour et al. (2019) simulated upward air-water
two-phase flow in vertical helically coiled tubes under adiabatic
conditions using the commercial CFD software Star-CCM + based
on the VOF model. The study revealed that the realizable k-εmodel
predicted velocity distribution on the vertical centerline more
accurately, while the SST k-ωmodel predicted velocity distribution
on the horizontal centerline more accurately.
In contrast to the analysis methods mentioned above, this paper
proposes a one-dimensional (1D) and three-dimensional (3D) coupling
simulation method for the flow and heat transfer characteristics of
OTSG. For 1D two-phase flow heat transfer inside the tubes (the tube
side of OTSG), considering the complexity of two-phase flow heat
transfer, a system analysis program is used to establish a parallel multi-
channel model. For 3D single-phase flow heat transfer outside the tubes
(the shell side of OTSG), FLUENT is employed to establish a 3D
analysis model. By mapping the spatial domain, a coupled heat transfer
model is established for both inside and outside the tubes, providing a
3D distribution of flow and heat transfer characteristics for OTSG. This
approach supports the fine design and analysis of OTSG.
2 Numerical approach
2.1 OTSG flow and heat transfer model
An Once-Through Steam Generators (OTSGs) consist of the
helically coiled tubes and the outer shell. Tube sideshell sideSteam
is generated by heating the water inside the helically coiled tube (tube
side) by the high-temperature fluid of the shell side. Inthe tube side, a
complex convective heat transfer phenomenon involving the
transition from single-phase to two-phase fluid, while the external
flow consists of a single-phase fluid with non-uniform axial and radial
temperature distributions. To simulate the flow and heat transfer of
OTSG more accurately, this study employs a coupled calculation
method using 1D system programs and 3D Computational Fluid
Dynamics (CFD) programs for a comprehensive high-resolution
analysis of the overall flow and heat transfer characteristics of
OTSG. For the complex phase-change heat transfer within the
helical tubes, a heat transfer model with higher applicability and
accuracy is used, simulated through 1D system programs. For the
external single-phase fluid, CFD calculations are utilized to capture
the 3D effects of axial and radial flow heat transfer in the shell side
flow passage more accurately during the heat exchange process of
OTSG. Therefore, different heat transfer models are applied in the
simulation for the internal and external sections of OTSG.
2.1.1 Heat transfer model of shell side
The flow and heat transfer in the OTSG shell side, where a
single-phase fluid is present, are simulated using commercial CFD
software. The fundamental governing equations Eqs. 1–3for the
simulation of flow and heat transfer include the continuity,
momentum, and energy equations, respectively (De Schepper
et al., 2008;Yang et al., 2008;Xie et al., 2015;Jiaqiang et al., 2016):
∂ρ
∂t+∇ρ
u
S(1)
∂ρ
u
∂t+∇ρ
u
u
−∇p+∇μ∇
u+∇
uT
+ρg(2)
∂ρE
∂t+∇
uρE+p
∇k∇T
()
+Q(3)
Among the turbulence calculation models, the Reynolds time-
averaged model RANS (Reynolds Average Navier-Stokes) is more
widespread, reliable, and practical in numerical simulation studies
and engineering design due to its high computational efficiency and
accuracy. Therefore, in this study, the SST k-ωturbulence model
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with the RANS method is adopted in the CFD calculations with the
following turbulence transport equations Eq. 4:
∂
∂tρk
+∂
∂xi
ρk
ui
∂
∂xj
μ+μt
σk
∂k
∂xj
+Gk−Yk
∂
∂tρω
+∂
∂xi
ρω
ui
∂
∂xj
μ+μt
σω
∂ω
∂xj
+Gω−Yω+Dω
⎧
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎩(4)
where ρis the density; kis the turbulent kinetic energy; ωis the
dissipation rate; uis the velocity; μis the molecular viscosity
coefficient; μ
t
is the turbulent molecular viscosity coefficient; σ
k
and σ
ω
are the diffusion coefficients of the turbulent kinetic energy
for kand ω, respectively; G
k
and G
ω
are the turbulent kinetic energy
generated by the mean velocity gradient and the generation of ω;Y
k
and Y
ω
are the dissipation of kand ωunder turbulence; and D
ω
is the
source term of definition.
In this study, the SST k-ωmodel in FLUENT using the enhanced
wall function is used to reduce the mesh requirements for solving the
turbulent model in the near-wall region so that it can be applied to
different y + meshes, and can achieve simulation of the flow heat
transfer characteristics of the shell side.
2.1.2 Flow and heat transfer model of tube side
For the complex boiling two-phase flow heat transfer
phenomena in tube side of OTSG, a 1D system code with two
fluid model named LOCUST is used for analysis. The flow and heat
transfer models modified for helically coiled tubes are used in
LOCUST to ensure the accuracy of the simulation.
1) Flow model of tube side
The Eq. 5for the friction pressure drop under single-phase
conditions is as follows:
Δpλ·l
D·ρv2
2(5)
where λis the frictional resistance coefficient; vis the velocity; Dis
the diameter of the tube; lis the length of the tube. The frictional
resistance coefficient Eq. 6is corrected by experimental data, which
considered the Re, coil diameter Di, tube diameter D, and helical lift
angle α(Zheng et al., 2023):
λL0.0791
Re0.25 +81858
Re1.54
d
Dc
0.48
DcDi1+tan α
()
⎧
⎪
⎪
⎨
⎪
⎪
⎩(6)
The two-phase wall drag coefficient Eq. 7are selected from the most
validated literature correlations taking into account the effects of
secondary flowinsidethetubesideofOTSG(Colombo et al., 2015):
Φ2
f00.12Φ2
FRDe0.21
l
ρmix
ρf
⎛
⎝⎞
⎠−0.26
DelG1−x
()
Di
μf
Di
D
(7)
where Φ2
f0is the two-phase multiplier, Φ2
FR is the Friedel correlation
based on the liquid-only approach (Friedel, 1979), Gis the flowrate,
xis the quality, μis the dynamic viscosity of liquid, mix and f
represent the mixture and liquid phase respectively.
2) Heat transfer model
In the 1D system code, the heat transfer model of helically coiled
tubes are modeled as inclined straight tubes. which are as follows.
1) Single-phase heat transfer section is calculated by the Dittus-
Boelter equation, and a correction coefficient cris
incorporated in the model to take into account improved
heat transfer effects as observed in helical coils. (McAdams,
1954;Griffith and Wallis, 1961;Saha et al., 2022):
hcr
k
Di
0.023Re0.8Pr0.4
cr1+bDi
D
p(8)
where band pare the correction parameters obtained from
experimental data.
2) Nucleate boiling and transition boiling are calculated by the
modified Chen equation (Seban and McLaughlin, 1963;Chen,
1966;Bjornard and Griffith, 1977) in Eq. 9:
hS·hb+F·hc(9)
where Fand Srepresent the Reynolds number factor and
suppression factor, respectively, Eqs. 10–12
F
1,1
Xtt
<0.1
2.35 0.213 +1
Xtt
0.736
,1
Xtt
≥0.1
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩(10)
S
11+0.12Re1.14
,Re′<32.5
11+0.42Re0.78
,32.5≤Re′<70
0.0797,70 <Re′
⎧
⎪
⎪
⎨
⎪
⎪
⎩(11)
Re′RefF1.25 ×10
−4(12)
where his the heat transfer coefficient, kis the thermal conductivity;
X
tt
is the Matineli parameter.
3) The film boiling section is calculated by the Bromley equation
(Radovcich, 1962;Hewitt, 1977;Choe et al., 1978) in Eq. 13:
h0.62 k2ρgρf−ρg
gγ′cp
Δt·D·Pr
⎛
⎝⎞
⎠0.25
(13)
where γ′is the latent heat of vaporization; Δtis the temperature
difference between the heated wall and the boiling temperature of
the fluid.
2.2 Coupling methodology
In this study, the OTSG flow and heat transfer characteristics are
calculated using a coupled simulation method. The shell side of the
OTSG (outside of the helically coiled tubes) is simulated by
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LOCUST, a 1D system code developed by China General Nuclear
Power Group (CGN). The tube side (inside the helically coiled
tubes) is simulated by CFD software FLUENT. Use CORBA add-ons
for FLUENT to establish an coupling face between FLUENT and
system code, so that it is possible to manage the FLUENT session
through Text User Interface (TUI) specific commands. Scripts were
developed with Python to process the results of the calculations of
the two programs and to transfer data between the coupling
interface. The whole framework of the coupling procedure and
the calculation flow are shown in Figure 1.
The script program drives the system code through CMD
commands, reads the data on the coupling boundary at the end
of the computation, and records the results in the UDF (User
Defined Function), thus redefining the boundary conditions used
in the FLUENT computation. After that, use the script to establish
a connection with FLUENT by CORBA, and at the same time
enable FLUENT’s aaS (as a Server) mode, so that it can drive
FLUENT’s calculations by sending TUI (Text User Interface)
commands to FLUENT. Finally, the convergence of the results
of the coupled computation is checked to determine whether to
continue the coupling iteration. If the results do not converge, the
script program writes the results of the above calculations to the
input card of the system code calculations and drives the system
code calculations again, thus starting a new round of coupling
iterations.
For the CFD computational domain of the shell side of the
OTSG, an approximate division of the area is performed in the same
way as the node division of the tube side by the system code. As
shown in Figure 2, in the radial direction, the CFD computational
domain is divided into five blocks, with a layer of helically coiled
tube bundles wrapped in each region, corresponding to the five pipe
components of the system code; in the axial direction, the tube side
computational domain is divided into 80 blocks, with the height of
each block being the same as the height of the corresponding node of
the tube side by system code.
In addition, the UDF macros used in the FLUENT coupling
calculations are shown in Table 1, and these macros are used to
define the boundary conditions on the coupling boundary, modify
the fluid physical properties, and approximate the region of the shell
side computational domain in the same way as the node partitioning
of the tube side by system code.
The delivery of data in the coupling iteration process between
CFD and 1D-system code is shown in Figure 3, in which the system
code uses the first kind thermal boundary condition for calculation,
and FLUENT uses the second kind. The specific solution processes
are as follows:
1) Given a set of temperature distributions on the outer wall of
the helically coiled tubes, and initialize calculations with the
system code to calculate the flow heat transfer process inside
the tubes;
2) After the system code analysis procedure is completed, the heat
flux distribution on the outer wall of the tubes is transferred
to FLUENT;
3) FLUENT uses this heat flux as the boundary condition to start
calculating the convection process of the shell side of OTSG;
4) In FLUENT’s calculation process, after the temperature
distribution in the fluid domain is relatively stable, it starts
to read and record the temperature result data of the outer wall
of the tubes in a certain time step;
5) After the FLUENT calculation, the recorded temperature data
are arithmetically averaged to obtain the mean value of the
temperature distribution;
6) Determine the convergence of the temperature distribution. If
it converges, stop the coupling iteration; if there is no
convergence, relax the temperature distribution and the
temperature distribution result input to the system code in
FIGURE 1
Schematic diagram of coupling calculation process controlled by
batch program.
FIGURE 2
Schematic Diagram of Fluid Division on the Shell side.
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this iteration and use it as the system input data in the next
calculation, and start the next coupling iteration;
7) Repeat the process from step 2) to step 6) until convergence
is reached.
It should be added that during the coupled model development and
calculations it was found that before the coupling process starts, an
initial set of temperature distributions will be reasonably given based on
the OTSG design conditions. And, when the initial temperature
distribution is lower than the actual temperature distribution, it is
helpful to ensure the stability of FLUENT in the subsequent calculation
process; on the contrary, if the initial temperature distributionishigher
than the actual temperature distribution, it will cause a high wall heat
flux data delivery to FLUENT by the system code. This may cause
unreasonable temperature values to appear in the shell side calculation
domain during FLUENT’s calculations, causing the calculation to
terminate. In addition, after the FLUENT calculation process is
completed, if the wall temperature is not relaxed and directly
transferred to the system code for calculation, the heat transfer
power on the tube side will oscillate back and forth around the final
value, causing the iteration to fail to converge; while using a small
relaxation factor can ensure the stability of convergence during the
iteration process, it will reduce the iteration convergence speed and
cause a waste of computing resources. Therefore, it is necessary to select
a relaxation factor that can not only ensure iterative convergence but
also ensure a certain convergence rate during the coupling calculation
process. In addition, the type of thermodynamic boundary conditions
at the coupled boundary also affects the convergence efficiency of the
calculation process. It is found in the calculations that the convergence
efficiency of the boundary conditions on the outer wall surface of the
helically coiled tube on the primary and tube sides of the OTSG is
higher when the thermodynamic boundary conditions are taken as the
second kind and the third kind respectively than other boundary
conditions.
3 Preliminary validation of the
coupling model
In this article, the coupling program calculation results are
compared with the experimental results to preliminarily verify
the correctness of the coupling program calculation results.
3.1 OTSG geometric modeling and mesh
generation
The experimental object is a small helically coiled tube OTSG, as
shown in Figure 4. The experiment is carried out to study the overall
heat transfer characteristics of the OTSG by measuring the inlet/
outlet fluid temperatures and pressure drops, under different inlet
temperatures and flow rates of the fluid of the primary and tube
sides. The range of test conditions are shown in Table 2.
The fluid in the primary and tube side of the OTSG are both
water, and the outlet of the tube side is saturated steam. The
diameter of the OTSG heat exchanger is about 30 cm, and the
inlet and outlet pipe flange inner diameter of the OTSG is about
9 cm. There are five layers of the helically coiled tubes in the OTSG.
The average length of the tube is 65 m, the diameter range of the
helix is 120–200 mm, and the helix rising angle is 8.2°. In the
experiments, the primary and tube side fluids are both water and
the tube side outlet is saturated steam.
In the establishment of the CFD model of the OTSG, the
experimental device was reasonably simplified to increase the
computational efficiency, and the elliptical head at the inlet and
outlet of the tube side of the OTSG was replaced by a cylindrical
cylinder. In terms of meshing, a polyhedral mesh is used to fill the
TABLE 1 Macros and functions of UDF.
Name Function
DEFINE_ADJUST Divide the fluid domain and output the simulation data in each part
DEFINE_PROFILE Define the boundary conditions for the outer wall of the helically coiled tubes
DEFINE_PRANDTL_T Define the turbulence Prandtl number
DEFINE_SPECIFIC_HEAT Define the specific heat of the fluid
DEFINE_PROPERTY Define fluid density, thermal conductivity, and dynamic viscosity
FIGURE 3
Data Transmission Flowchart using First and Second Type
Boundary Conditions.
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fluid domain, and a prismatic layer mesh is used in the near-wall
position. The total number of meshes in the final computational
model is 14 million after verification of mesh-independence. The
simplified geometrical and mesh model of the OTSG are shown
in Figure 5.
Figure 6 shows the system code nodalization of the tube side of
the OTSG. Since the system code cannot directly simulate the helical
tubes, the helical heat exchanger tubes were equivalent to inclined
straight tubes in this study (Cioncolini et al., 2003). Each layer of the
helically coiled tubes is equivalent to 1 inclined straight pipe for
calculation, and the angle of inclination is the helix rising angle. To
give more accurate boundary conditions for the coupling interface in
FIGURE 4
Schematic diagram of a small OTSG heat exchanger.
TABLE 2 Test conditions for OTSG.
Test conditions Ranges
Pressure of the shell side, (MPa) 15.5
Mass flow rate of the shell side, (t/h) 3–4
Inlet temperature of the shell side, (°C) 280–320
Pressure of the tube side, (MPa) 6.0
Mass flow rate of the tube side, (t/h) 0.5–1.5
Inlet temperature of the tube side, (°C) 100–200
FIGURE 5
Geometric and mesh modeling of water-water steam generator.
FIGURE 6
Tube side node diagram of water reactor heat exchanger.
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the coupling calculation with CFD, the node division of the axial
direction of the model is encrypted. Each tube contains 80 nodes, of
which the inlet straight section and outlet straight section both
contain 5 nodes, and the helically coiled tube section
contains 70 nodes.
3.2 Validation analysis
The OTSG 1D and 3D coupled heat transfer calculation model
developed in this study is preliminarily validated using experimental
data. In the test, four test conditions were selected, respectively, with
different primary and tube side inlet and outlet water pressures, flow
rates, and temperatures, and the OTSG heat transfer power obtained
from the test was compared with the results obtained from the
calculation. As shown in Figure 7, it can be seen that the coupled
calculated values are small relative to the experimental values, but
the overall error is not large, all within 15%. Test conditions of each
case of OTSG tests are shown in Table 3. And the uncertainty of the
heating power in the test is 1.4%.
Figures 8,9show the wall temperature input data and heat flux
output data of system code for the first-fifth and fifth-10th coupling
iteration steps, respectively, of one coupling case. It can be seen that
after five coupling iterations, the input values of wall temperature
have basically converged, and the corresponding wall heat flux is
also basically stable. Therefore, it can be preliminarily judged that, in
the case of choosing a reasonable initial tube wall temperature, after
FIGURE 7
Comparison of coupling calculation results and
experimental values.
TABLE 3 Parameters of specific cases.
Case
no.
Mass flow rate of the
shell side, (t/h)
Inlet temperature of the
shell side, (°C)
Mass flow rate of the
tube side, (t/h)
Inlet temperature of the
tube side, (°C)
1 4 315 1 180
2 4 320 0.8 180
3 4 320 0.66 180
4 3.5 330 0.7 180
FIGURE 8
Wall temperature input and heat flux output of LOCUST during iteration step 1-5. (A) wall temperature. (B) heat flux.
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a certain number of coupling calculations, relatively reliable OTSG
heat transfer characteristics can be obtained, and the deviation of the
calculated OTSG power from the experimental value is
less than 15%.
4 Coupled simulations of a
prototype OTSG
A prototype designed OTSG with liquid lead-bismuth
eutectic alloy on the shell side and water on the tube side is
simulated using the 1D and 3D coupling method developed
above. The inner and outer diameters of the annular flow
channel of the OTSG are 376 and 596 mm, respectively, and
it includes a total of 37 helically coiled heat transfer tubes in five
layers, with a tube outer diameter of 16 mm and a tube wall
thickness of 2 mm. The helix diameters, the number of tubes,
and the helix rising angle are shown in Table 4.Theshellsideof
the OTSG is simulated using FLUENT and the tube side is
simulated using the system code, and the boundary
conditions of the primary and tube sides are shown in
Table 5. The coupling procedure is used to calculate the
TABLE 4 Geometric parameters of the prototype OTSG helically coiled tubes.
Layer no. Helix diameter Number of tubes Helix rising angle Height Pitch of helix Axial distance
1 574 9 5.44 2000 171 19
2 530 8 5.23 2000 152 19
3 486 7 4.99 2000 133 19
4 442 7 5.49 2000 133 19
5 398 6 5.23 2000 114 19
FIGURE 9
Wall temperature input and heat flux output of LOCUST during iteration step 5–10. (A) wall temperature. (B) heat flux.
TABLE 5 Boundary conditions of the primary and tube sides.
Calculation domain Boundary type Boundary conditions Boundary parameters
Shell side Inlet Mass flowrate_inlet Mass flowrate:200.6 kg/s Temperature:450°C
Outlet Pressure_outlet Pressure: 0 MPa(gauge pressure)
Tube wall Heat flux Provided by calculation results of the tube side
Tube side and tube wall Inlet Mass flowrate_inlet Mass flowrate:1.924 kg/s Temperature:280°C
Outlet Pressure_outlet Pressure: 0 MPa(gauge pressure)
Tube wall Temperature Provided by calculation results of the shell side
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steady state of the OTSG, and the results of the overall
temperature and flow fields of the primary and tube sides
are obtained.
4.1 Heat transfer characteristics of OTSG
shell side
The distribution of temperature and velocity on the vertical
section of the shell side of OTSG is shown in Figure 10. The shell side
fluid temperature gradually decreases along the process (from top to
bottom, and the bottom Z = 0), and the radial distribution is
relatively uniform, but the non-uniformity of the radial
distribution increases. Regarding the velocity distribution, due to
the influence of the swept flow of the tube bundle, local maximum
and minimum points of velocity appear on the side of the tube, but
the velocity distribution of the four internal tube bundle gaps is
relatively uniform. It can be seen from the velocity vector diagram in
Figure 11 that the wake swing effect caused by the tube bundle cross-
flow is obvious. Especially at the outlet position of the tube bundle
area, the velocity vector shows obvious asymmetry.
The temperature distribution diagrams on different height planes
are shown in Figure 12. It can be seen that the unevenness of the
temperature distribution in each height plane gradually increases
along the shell side fluid flow direction. The cross-section velocity
distribution cloud diagram shown in Figure 13 is relatively uniform.
4.2 OTSG tube side flow and heat transfer
characteristics
This type of OTSG prototype contains a total of five layers of
heat transfer tubes. Due to the internal resistance of the tube
bundle and the different heat transfer boundaries between the
inside and outside of the tubes, the power of the heat transfer
FIGURE 10
Distribution of temperature and velocity on the vertical section of the shell side of OTSG. (A) Temperature. (B) Velocity.
FIGURE 11
Velocity vector on the vertical section of the shell side of OTSG.
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FIGURE 12
Temperature on the vertical section of the shell side of OTSG. (A) Z=0.58 m. (B) Z=0.86 m. (C) Z=1.34 m. (D) Z=1.72 m. (E) Z=2.1 m.
FIGURE 13
Velocity on the vertical section of the shell side of OTSG. (A) Z=0.58 m. (B) Z=0.86 m. (C) Z=1.34 m. (D) Z=1.72 m. (E) Z=2.1 m.
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tubesineachlayermaybedifferent.Theflow rate, outlet steam
temperature, and total heat transfer power of each layer of heat
transfer tubes are calculated, as shown in Table 4.Theoutlet
steam temperature of each layer of heat transfer tubes is the same,
but because the number of heat transfer tubes in the outermost
layer is greater than that in the inner layer, the total power of the
outer layer tubes is greater than that of the innermost layer.
However, on average for each heat transfer tube, there is little
difference in flow rate and heat transfer power between the inner
tube and the outer tube.
Figures 14–16 show the axial distribution of the average
temperature of the outer wall of the heat transfer tubes, the heat
flux of the outer wall of the tube, and the quality in the tubes. The
heat flux density changes significantly with the flow phase change in
the tube side. It can be seen from the figure that the difference in the
average temperature of the outer wall of the heat transfer tubes of
different layers is small, there is a significant difference in heat flux
between heights of about 0.5–1.7 m, but this difference in heat flux
has little impact on the outlet gas content.
5 Conclusion
In this paper, a flow heat transfer model was developed that
couples a 1D system code and a 3D CFD software by building a
coupling surface to transfer heat flux density on the outer wall of the
OTSG helically coiled tubes. The overall flow heat transfer
characteristics of a prototype OTSG are analyzed. The main
conclusions are as follows:
Layer
no.
Total steam mass
flow rate (kg/s)
Steam mass flow rate
of each tube (kg/s)
Steam
temperature (K)
Total heat transfer
power (MW)
Heat transfer power
of each tube (MW)
1 0.4747 0.0527 721.5 0.97 0.1078
2 0.4143 0.0518 722.0 0.85 0.1063
3 0.3551 0.0507 722.3 0.73 0.1043
4 0.3698 0.0528 721.6 0.76 0.1086
5 0.3118 0.0520 721.8 0.64 0.1067
FIGURE 14
Average temperature of the outer wall of the heat transfer tubes.
FIGURE 15
Heat flux of the outer wall of the tube.
FIGURE 16
Quality in the tubes.
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1) For the fluid inside the OTSG helically coiled tubes, use LOCUST
to establish a 1D parallel multi-channel model to simulate its
complex two-phase flow heat transfer. For the single-phase flow
and heat transfer characteristic outside the tubes, use FLUENT to
analyze by 3D simulation. A coupled heat transfer model inside
and outside the tube is built through spatial mapping, and the wall
heat flux calculated by LOCUST is transferred to FLUENT for 3D
simulation, thereby obtaining the 3D distribution characteristics
of the flow and heat transfer characteristics inside and outside the
OTSG helically coiled tubes. This coupling method can obtain a
high-resolution single-phase fluid flow field and temperature field
outside the tubes while ensuring accurate simulation of complex
two-phase flow heat transfer in the tubes. After comparing with
the experimental data, the error of the heat flux calculated by the
coupled model is within 15%.
2) During the steady-state calculation process, if the given initial
wall temperature is lower than the actual value, the program
calculation convergence will be accelerated, otherwise, the
program will be more likely to diverge. Therefore, it is
necessary to relax the outer wall temperature of the
helically coiled tubes to avoid failure to converge due to
temperature and heat flow data oscillation in the coupled
calculation. The selection of the convergence factor and the
type of boundary conditions at the primary and tube side
coupling boundaries will all have an impact on the
convergence efficiency of the coupling program.
3) In the coupling simulation of the OTSG prototype, the shell
side temperature field gradually decreases along the flow
direction, the inlet-outlet temperature difference is as high
as 150°C, and the unevenness of the radial temperature
distribution increases along the flow direction. In addition,
the wake swing effect caused by the sweeping flow of the tube
bundle at the exit position is obvious. What needs to be noted
in the design of OTSG is that large fluid temperature
differences and possible temperature fluctuations will cause
stress on the OTSG structural materials.
This research can provide support for the refined design and
analysis of OTSG and has good application prospects in the analysis
of heat transfer characteristics of OTSG.
Data availability statement
The original contributions presented in the study are included in
the article/supplementary material, further inquiries can be directed
to the corresponding author.
Author contributions
WX: Writing–original draft, Writing–review and editing. LX:
Supervision, Writing–review and editing. ZX: Formal analysis. CX:
Validation. MS: Writing–review and editing. RT: Data curation,
Writing–review and editing. CJ: Writing–review and editing. MY:
Writing–review and editing. HY: Writing–review and editing. SC:
Writing–review and editing.
Funding
The author(s) declare financial support was received for the
research, authorship, and/or publication of this article. National
Natural Science Foundation of China Joint Fund
Project (U20B2011).
Conflict of interest
Authors WX, LX, ZX, CX, MS, RT, CJ, MY, HY, and SC were
employed by China Nuclear Power Technology Research
Institute Co., Ltd.
Publisher’s note
All claims expressed in this article are solely those of the authors
and do not necessarily represent those of their affiliated
organizations, or those of the publisher, the editors and the
reviewers. Any product that may be evaluated in this article, or
claim that may be made by its manufacturer, is not guaranteed or
endorsed by the publisher.
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