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Dryout study of a helical coil once-through steam generator integrated in a thermal storage prototype
Journal Pre-proofs Dryout study of a helical coil once-through steam generator integrated in a thermal storage prototype E. Rivas, J. Muñoz-Antón PII: DOI: Reference:
S1359-4311(19)37115-7 https://doi.org/10.1016/j.applthermaleng.2020.115013 ATE 115013
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
14 October 2019 9 January 2020 25 January 2020
Please cite this article as: E. Rivas, J. Muñoz-Antón, Dryout study of a helical coil once-through steam generator integrated in a thermal storage prototype, Applied Thermal Engineering (2020), doi: https://doi.org/10.1016/ j.applthermaleng.2020.115013
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© 2020 Published by Elsevier Ltd.
DRYOUT STUDY OF A HELICAL COIL ONCE-THROUGH STEAM GENERATOR INTEGRATED IN A THERMAL STORAGE PROTOTYPE E. Rivasa,∗, J. Mu˜ noz-Ant´ona a Escuela
T´ ecnica Superior de Ingenieros Industriales Universidad Polit´ ecnica de Madrid (ETSII-UPM) C/ Jos´ e Guti´ errez Abascal, 2, 28006 Madrid, Spain
Abstract In this work, it is studied several dryout parameters (the dryout onset, first and total dryout, its associated azimuthal position and local steam qualities) in a triple helical coil once-through steam generator under quasi-steady working conditions (inlet pressure, PIN ∈ [37.9, 39.2] bar, inlet subcooling, ∆Tsub ≈ 0 ◦
C and total mass flow rate, m ˙ ws ≈ 0.082 kg·s-1 ) which exchanges heat with
a molten salts counterflow under quasi-steady pressure and temperature conditions (atmospheric pressure and inlet temperature, TIN ∈ [472, 477] ◦ C) but transient mass flow rate, m ˙ ms , depending on the helical coil diameter, D. For this purpose, a CFD model (Computational Fluid Dynamics model) has been used which has been evaluated with the experimental data obtained during a discharge test of the 300 kWth thermal storage prototype with integrated steam generator of the Casaccia Research Center (ENEA, Italy), previous benchmarking of two phase flow model. Results show, within the working conditions range and considering the particular steam generator characteristics, the two-phase flow behavior is uniform. This information has not been reported yet on available literature. In addition, numerical local steam qualities are compared with those calculated by using forced convective boiling correlations suitable for this ∗ Corresponding
author Email address: [email protected] (E. Rivas)
Preprint submitted to Applied Thermal Engineering
January 31, 2020
type of steam generator geometry, concluding that: 270◦ Ruffel’s and Santini’s correlations are the most appropriate during first dryout, and to assume a local steam quality value of 0.97 during total dryout the most suitable approximation. This work can be useful for those who pretend to scale-up such a steam generator for industrial applications requiring process heat and/or power generation. Keywords: scale-up, once-through steam generator, helical coil, dryout, steam quality, Computational Fluid Dynamics (CFD). elsarticle.cls, LATEX, Elsevier, template 2010 MSC: 00-01, 99-00
1
1. Introduction
2
Currently, there are a large number of industrial applications where process
3
steam is required (desalination, sterilization, building or district heating and
4
cooling, etc.). Other clear examples are the CSP plants (Concentrating Solar
5
Power plants), which generate electricity from the transformation of concen-
6
trating solar radiation. In them, the presence of thermal storage systems is
7
very common because it allows to manage its electrical production even in the
8
absence of solar radiation.
9
In general, the thermal storages for commercial CSP plants are based on the
10
double tank system with molten salts. Although the efficiency of these systems
11
is very high (> 93 %) [1], it is necessary to research and develop new thermal
12
storage designs more profitable in order to demonstrate that this technologies
13
have enough potential to replace the more conventional ones, such as those based
14
on the use of fossil fuels.
15
With this aim, the ENEA Research Center (Italy) [2] and the company
16
ANSALDO Nucleare S.p.A. (Italy) [3] have patented the layout of a molten
17
salts thermal storage system based on a single tank with an integrated helical
18
coil steam generator [4], inspired by the SFR technology (Sodium-cooled Fast
19
Reactors) [5]. The patent bases its competitiveness in the simplification of the
20
plant configuration [6]. Subsequently, its technical feasibility has been demon-
2
21
strated on a prototype scale (300 KWth) in ENEA [7, 8, 9]. The next step in
22
its development would be to scale-up it at commercial CSP plant level (> 10
23
MWe).
24
One of the key points in the thermohydraulic design of the system is the
25
calculus of local steam qualities associated to the onset of the dryout because it
26
implies a worsening of the local heat transfer coefficients in the water-steam side
27
(in some cases until one and two orders of magnitude [10]). The difficulty is due
28
to, from the experimental point of view, the ENEA prototype instrumentation
29
is not enough: there are no measurements of local heat fluxes and there are only
30
temperature measurements of a single coil. Also, from the theoretical point of
31
view, the found correlations in the literature for forced convective boiling flows
32
in this type of geometries are not 100 % suitable: either by the heat transfer
33
fluid, the helical coil/tube characteristics or the working conditions.
34
Therefore, the objectives of this work are:
35
• to study the dryout onset in the covered working conditions range depend-
36
ing on the helical coil diameter,
37
• and from this information, to assess the adaptability of the literature
38
correlations, both during the first and the total dryout, to this system.
39
For this purpose, the employed methodology has been the numerical analysis
40
by CFD modeling (software: STAR-CCM+ 9.04.011 [11]), which results has
41
been evaluated, first, against experimental data from the state-of-the-art, and
42
second, against those obtained during a discharge test of the thermal storage
43
prototype with integrated steam generator belonging to ENEA.
44
This work is structured as follows: first of all, it is summarized the state-
45
of-the-art correlations for calculating local steam qualities associated with the
46
dryout onset in forced convective boiling, particularly in vertical helical coils.
47
Then, the ENEA thermal storage prototype and its operating mode during
48
discharge tests is described. Secondly, the CFD pre and post processing are
49
presented, and the model evaluation (both numerical and experimental) is made
50
up. And finally, the dryout study as function of the helical coil diameter and 3
51
the comparison with the found correlations, are carried out. The most relevant
52
conclusions are set out.
53
2. State-of-the-art of the correlations for calculating local steam qual-
54
ities associated with the dryout onset in forced convective boiling
55
flows in vertical helical coils
56
One of the main differences in forced convective boiling flows between vertical
57
straight tubes and vertical helical coils is the dryout onset. While in the first
58
case it happens simultaneously in all tubes at equal height, in the second one,
59
it starts at certain surface points and spreads until all surface points dryout
60
completely at a particular height (Figure 1), i.e., there is a height range where
61
the coils are partially dry and partially wet.
Figure 1: Visualization of dryout onset in a helical coil (Source: CFD research findings).
62
This difference is due to the joint action of frictional, centrifugal and vis-
63
cous forces. These forces induce the two-phase flow undergoes a secondary flow
64
perpendicular to the principal flow [12]. The secondary flow promotes the extra-
65
dos surface wetting until higher steam qualities than in case of straight tubes.
66
Comparative studies carried out by Cumo et al. [13] and Styrikovich et al. [14]
67
between vertical straight tubes and vertical helical coils show such difference.
4
68
The characteristics of employed samples and the working conditions ranges of
69
these studies are shown in Table 1.
70
In Table 1 it can be seen that the main involved factors on found correlations
71
for calculating steam qualities for dryout onset in forced convective boiling flows
72
are pressure (P ), mass flux (G) and heat flux (Q).
73
The pressure and mass flux effects were analyzed by Styrikovich et al. [14].
74
This work analyses that increasing pressure and mass flux, steam quality de-
75
creases accordingly during the total dryout, evidencing its dependency. Among
76
the revised correlations, only Naitoh et al. correlation [15] is mass flux indepen-
77
dent, see Table 1.
78
Berthoud and Jayanti propose three different correlations to determine the
79
steam quality during the first dryout depending on the type of annular flow
80
regime [16] (Table 1). This work is based on the experimental data of Roumy
81
¨ [17], Styrikovich et al. [14], Unal et al. [18, 19], Breus and Belyakov [20] and
82
Carver et al. [21]. To identify the regime type, Berthoud and Jayanti employed
83
a 2D map (Figure 2) in which, on the x-axis, it is represented the dimensionless
84
number x0 given by the expression:
x0 =
G √ ρv gD
(1)
85
where ρv is the steam density, g the gravity and D the helical coil diame-
86
ter. This parameter is a measure of the centrifugal force acting on the vapor
87
phase and the drag force acting on the droplets, which shows up the droplets
88
redeposition process. And, on the y-axis, it is represented the dimensionless
89
number y0 (equivalent to the Reynolds number of the liquid phase) given by the
90
expression:
y0 = 91
G · d∗ µl
where d∗ is a geometric factor given by di ·
(2) q
di ( 0.02 ) (di is the inner tube
92
diameter) and µl the water dynamic viscosity. This parameter shows up the
93
droplets entrainment process through the vapor core. 5
Figure 2: Processes controlling the first dryout in helical coils, 2D map [16].
94
95
On this map, depending on working conditions and samples characteristics, three different zones can be distinguished:
96
• Gravity zone: characterized by high D, low G and high P , where dryout
97
onset happens at low steam qualities. In this case, flows are often very
98
stratified.
99
• Redeposition zone: characterized by low D, high G and low P , where
100
dryout onset happens at high steam qualities. In this case, flows tend to
101
be slightly stratified and the extrados surface remains often well chilled.
102
• Entrainment zone: characterized by very high D and G and standard P ,
103
where dryout onset happens at medium steam qualities. In this case, flows
104
tend to be slightly stratified and the intrados surface remains often well
105
chilled.
106
In this work, the authors also propose a correlation during total dryout, 6
107
noting that it also depends only on the type of annular flow regime [16] (Table 1).
108
Although, in contrast to the previous correlations, it is heat flux independent.
109
110
Therefore, to clarify this issue (heat flux dependence/independence) it is necessary to draw upon other works.
111
¨ While in correlations proposed by Duchatelle et al. [22], Unal et al. [18, 19],
112
Jensen et al. [23, 24, 25, 26] and Ruffell [27] heat flux appears explicitly, in that
113
proposed by Santini et al. [28] heat flux does not appear (see Table 1). First
114
three correlations were obtained from non-uniform wall heatings and fourth and
115
fifth ones were obtained at lab scale with electrical heat (uniform heating):
116
117
118
119
120
121
• 1st : Duchatelle et al. used the data of a real steam generator exchanging heat with a liquid sodium at counterflow ¨ • 2nd : Unal et al. used the data of three concentric helical coils heated by means of an external liquid sodium at counterflow • 3rd : Jensen et al. used the data of three helical coils electrically heated applying a higher flux on the top surface than on the bottom surface.
122
I.e., the employed wall heating methodologies (uniform or non-uniform) are
123
different and, therefore, it is difficult to distinguish the potential heat flux de-
124
pendence/independence.
125
On the other hand, the Jensen’s correlation is not applicable here because its
126
working pressure is far from those of the ENEA prototype (since he employed
127
¨ R113 as working fluid). And, neither the Duchatelle’s and Unal’s correlations
128
are applicable here because they have been derived from very different working
129
conditions ranges. In particular, the first, for large heat and mass fluxes and
130
the second, for very high pressures and inlet subcoolings.
131
Even though in most of the works where it was employed few helical coils par-
132
allel arranged, two-phase flow instabilities were observed, hardly ever included
133
specific studies about their influence on the dryout (in many cases, two-phase
134
flow instabilities were inhibited by using calibrated orifices at the tubes in-
135
¨ lets). About this regard, highlighting the Chapter 7 of Unal [18], where a study
7
136
about the DWOs (Density Wave Oscillations) observed during the operation of
137
a full-scale steam generator is presented, and the Naitoh et al. study [26], who
138
investigated the dryout coupled by DWOs. Naitoh deduced the dryout fluctua-
139
tions had periods between 3 s and 20 s, result consistent with the experimental
140
data of the ENEA prototype. Here it has shown, without inhibiting two-phase
141
flow instabilities experimentally, they do not influence the dryout by using a
142
simulation methodology which takes into account this period.
143
Finally, there are very few authors who have analyzed the effect of the geo-
144
metric characteristics of the samples. According to Ruffell [27], the helix angle,
145
¨ ϕ, strongly influences the first dryout and according to Unal et al. [18, 19],
146
if D/di ≥ 38.9, the geometry effect on the necessary power (Q˙ nec ) to achieve
147
the first dryout is negligible, but not the necessary power to achieve the total
148
dryout. Here it has analyzed both of them: ϕ ∈ [1.61, 2.36]◦ and D/di ∈ [15,
149
22] under different working conditions.
150
Considering this review, the objectives of this study are justified based on
151
the following ideas: it is difficult to distinguish which correlation/s among those
152
found in the literature are applicable to the ENEA prototype working conditions
153
for calculating local steam qualities associated with the dryout onset since not all
154
of them depend on the same factors (Naitoh’s, Berthoud and Jayanti’s, Ruffell’s,
155
and Santini’s. correlations, see expressions and applicability ranges in Table 1).
156
Perhaps, due to the fact that the employed wall heating methodologies are very
157
different. Limitation which, besides, was also detected by Santini et al. [28],
158
¨ Jensen et al. [23, 24, 25, 26], Unal et al. [18, 19] and Ruffell [27] in their works.
8
9
L = 1.709 m; di = 0.010 m; D = 0.136 m; pitch = 0.055 m
(upward or downward)
1984) [14]
Water/R12 (upward)
Water (upward)
Jayanti 1990) [16]
(Santini et al.
2014) [28]
do = 0.00635 m;
(upward)
(Berthoud &
L = 2 m; di = 0.00475 m;
1972) [13]
G ∈ [199, 810] kg·s-1 ·m-2
D = 1 m; pitch = 0.79 m
do = 0.01723 m;
P ∈ [10.7, 60.7] bar
Q ∈ [43.6, 209.3] kW·m-2
1 Helical coil L = 32m; di = 0.01253 m;
P ∈ [11, 200] bar
Q ∈ [10, 1800] kW·m
-2
G ∈ [100, 1900] kg·s-1 ·m-2
P ∈ [65, 240] bar
Q = 120 kW·m-2
G ∈ [500, 1800] kg·s-1 ·m-2
P ∈ [98.1, 176] bar
Q ∈ [100, 1500] kW·m-2
G ∈ [500, 1500] kg·s-1 ·m-2
xT ot
x1 = 103.235 ·
ρl ρv
v
v
Gravity zone −2.378 −1.712 · Gµldi · ρ
v
G √ g D
0.967 −0.740 · GQ ∆H
Redeposition zone 0.098 ! 0.067 −0.430 0.101 −0.785 q G di G · µl · ρ √ · GQ · µl Q∆H · g·(ρlσ−ρv ) ∆H g D
ρv ρl
x1 = 0.44 − 0.0006 · P · 10−5 · G0.114
v
G √ g D
0.08
Entrainment zone 0.119 −0.267 −0.984 0.950 −0.428 q G · Gµldi · ρ √ · GQ · µl Q∆H · g·(ρlσ−ρv ) ∆H g D
ρl ρv
—
—
CORRELATION
Total dryout 1.722 −0.494 2 −0.381 −1.61 ρl = log10 · µµvl · Gµldi · Gσ µdli · ρ ρv
x1 = 3.223 + log10
x1 = 107.068 ·
DRYOUT STEAM QUALITY CONDITIONS
D = [0.08-3.3] m
di = [0.008-0.02] m;
1 Helical coil
D = 0.09 m; pitch = 0.07 m
Straight tube vs. helical coil R12
(Cumo et al.
Straight tube vs. helical coil
Water
(Styrikovich et al.
GEOMETRY
FLUID
AUTHOR
vertical helical coils.
Table 1: Correlations for calculating local steam qualities associated with the dryout onset (first and total) in forced convective boiling flows in
10 Water (upward)
¨ ¨ Unal 1981, Unal
et al. 1981) [18, 19]
R113 (upward)
Jensen & Bergles 1981,
FLUID
1982, 1983) [23, 24, 25, 26]
(Jensen 1980,
AUTHOR
GEOMETRY
xT ot ∈ [0.55, 0.94]
0.1175 m; di /D = 0.0182,
ϕ = 7.77◦ , 8.83◦
pitch = 0.79 m;
D= 1.5 m, 0.7 m, 0.7 m;
xT ot ∈ [0.08, 1.00]
∆Tsub ∈ [35.6, 156.8] ◦ C
P ∈ [147, 202] bar
Q ∈ [41,731] kW·m-2
L = 40.13 m, 35.50 m, 26.67 m; di = 0.018 m;
G ∈ [112, 1829] kg·s-1 ·m-2
4 Helical coils
0.01270 m
pitch = 0.0254 m, 0.01588 m,
ϕ = 1.78◦ , 1.68◦ , 3.87◦ ;
0.0353, 0.0649;
∆Tsub ∈ [0,110] ◦ C
P = 9.4 bar
Q ∈ [54, 800] kW·m-2
G ∈ [570,5470] kg·s-1 ·m-2
CONDITIONS
D = 0.4096 m, 0.2159 m,
do =0.00777 m, 0.00769 m;
di =0.00762 m, 0.00744 m;
heating length);
1.295 m, 1.257 m (wall
L = 0.635 m, 1.27 m,
3 Helical coils
, if G > 950 kg· m-2 · s-1
, if G ≤ 950 kg· m-2 · s-1 di 0.31 D
di 0.17 D
PIN IN a1 = 1 + 3.8 · 1 − HHSAT ; a2 = 0.114 − 0.041 · log 1 − P cri −1/2 L a3 = 1 + 4.59 · deq ; Leq = πAdGQ · (HSAT − HIN + ∆H · x) i n o n o a41 = 1 + 0.44 · exp −0.056 · dDi − exp − 3dD , 1st dryout i n o n o a42 = 1 + 0.56 · exp −0.011 · dDi − exp − 3dD , Total dryout i 0.32 Leq 2 (d0 −di ) 0.22 a5 = , a6 = di + 28 · F r , a7 = 1 di
3 ·a41 ·a5 Q = G · ∆H · 0.97 · a1 ·a2a·a6 ·a , 1st dryout 7· a1 ·a2 ·a3 ·a42 ·a5 Q = G · ∆H · 0.97 · , Total dryout a6 ·a7 ·
Q = G · ∆H · 1.7126 · 105 · Re−1.143 · x−0.436 · T ot
Q = G · ∆H · 4.09 · 10−6 · Re0.50 · x−0.460 · T ot
CORRELATION
11
Water (upward)
Water (upward)
Water (upward)
(Naitoh et al.
1974) [15]
(Duchatelle et al.
1975) [22]
(Ruffel et al.
1974) [27]
G ∈ [300, 1800] kg·s-1 ·m-2
3 Helical coils
D = 0.58 m, 1.32 m, 2.36 m
length); di = 0.0125 m;
P up to 180 bar*
Q/G ∈ [0.06, 0.34] J·G-1
P ∈ [45, 175] bar
0.011, 0.007
L = 8.2 m (wall heating
Q ∈ [310, 1500] kW·m-2
G ∈ [375, 3500] kg·s-1 ·m-2
P up to 175 bar
CONDITIONS
di /D = 0.032, 0.025,
4 Helical coils
di /D=0.0165
GEOMETRY
*Although it was also validated for other working conditions by means of modeling.
FLUID
AUTHOR
0.13·(D/(100·di )) (G/103 )1.5
·
Q 100
x1,270◦ = 1 − 0.0004 · Q − 0.0109 ·
x1,0◦ = 1 −
G 2 103
·
D di
0.5
0.75·(G/103 )0.5
xT ot = 1.39 · 10−4 · Q0.732 · G−0.209 · exp 2.46 · 10−3 · P · 10−5
xT ot = 1 + (0.139 − 0.071 · (P · 10−5 )0.186 ) · (Q · 0.85986 · 10−5 )
CORRELATION
159
3. ENEA experimental setup
160
ENEA prototype is a 2 m diameter and 2.8 m height thermal storage tank
161
whereby the hot molten salts enter through the upper side of the tank. Inside it,
162
there are 12 tons mixture of inorganic molten salts, commonly known as “solar
163
salt”: NaNO3 and KNO3 (60/40 % by weight), under atmospheric pressure. The
164
integrated steam generator is vertically and non-symmetrically arranged within
165
the tank. It consists of two concentric cylindrical shells, called “downcomer”
166
and “shell”, and three in-line helical coils, referred as #1, #2 and #3 (coil/tube
167
characteristics: see Table 2) comprised in the space between shells (Figure 3).
168
For additional information about the prototype setup consult [29] and [30].
Figure 3: ENEA experimental setup
169
During discharge tests, the pressurized water flowing within the tubes changes
12
170
phase due to the heat transfer with the molten salts at counterflow circulation
171
through the space between shells and tubes. Therefore, the highest thermal
172
hydraulic gradients within the prototype happen here and thus, the involved
173
phenomenology intrinsically depends on the steam generator geometry. Table 2: Design characteristics of the integrated steam generator (Source: ENEA).
GEOMETRIC FEATURE
VALUE (Unit)
External tube diameter, do
0.0127 m
Internal tube diameter, di
0.0094 m
Horizontal pich, Xhor
0.0162 m
Vertical pich, Xver
0.0180 m
Helical coil diameters, D1
0.2038 m
Helical coil diameters: D2
0.1714 m
Helical coil diameters: D3
0.1390 m
174
The shells have a thermal insulating function: the downcomer allows the
175
water to arrive the lower part of the generator without directly exchanging heat
176
with the molten salts (thus, water-steam phase change happens upwards) and
177
the shell separates the molten salts circulating though the generator from the
178
molten salts tank bulk. Finally, it has a window at the top, through which the
179
hot molten salts go into the generator, and a diffuser at the bottom, through
180
which the cold molten salts depart the generator.
181
Its operating mode during discharge tests is as follows: the water flow is
182
established by a pump belonging to an external loop; that is the reason to talk
183
about forced convective boiling in the water-steam side. With this operating
184
mode, the coming out fluid is superheated steam, saturated steam or subcooled
185
water, depending on the thermal conditions of the tank. Molten salts circulate
186
through the existing gaps in the tubes matrix by gravity. Their driving force is
187
gravity when go through the generator, since they increase their density while
188
they cool down because heat exchange with the tubes matrix where the pres-
189
sured water flows at a lower temperature than molten salts. This process causes 13
190
the molten salts tank stratification, i.e., it promotes the development of a cold
191
zone at the tank lower part, coming from the salts that have gone through the
192
generator, a hot zone at the tank upper part, and an intermediate zone, which
193
thickness depends on the tank thermal conditions (see Figure 4). In summary,
194
during discharge tests, there is a continuous natural circulation of molten salts
195
which transports heat from the source (molten salts) to the sink (water-steam).
196
Such molten salts natural circulation will slow down as the discharge evolves
197
due to the gradual decrease of the buoyancy forces. This is the reason to talk
198
about molten salts transient mass flow rate. This gradual decrease is the result
199
of the progressive difference height decreasing between the respective hot molten
200
salts columns from the source and the sink, ∆L, during discharge, i.e, in Figure
201
4, ∆L7050s > ∆L10650s .
Figure 4: Simplified temperature field at two times, t7050s (left) and t10650s (right) during a discharge test [29]. Arrows indicate the molten salts inlet/outlet.
202
The heat transfer between molten salts and water-steam is less efficient as
203
discharge evolves. Consequently, as the discharge evolves, the two-phase flow
204
length on the steam generator increases (in Figure 4, z7050s < z10650s although
205
this two-phase flow length may be different on each helical coil). This fact can
206
affect the dryout onset depending on the helical coil diameter. In order to check
207
this influence, a CFD model has been developed and validated with the different 14
208
variables measured in the prototype at ENEA. This analysis has not yet been
209
reported on the available bibliography and could be of interest for developers of
210
this type of steam generator technology.
211
4. CFD modelling
212
4.1. Geometry and mesh models
213
CFD model is focused on the steam generator. Geometrically is a 3D full-
214
R scale model made by means Autodesk Inventor Professional 2016 (helical coils
215
R design) [31] and STAR-CCM+9.04.011 CAD module (downcomer, shell, win-
216
dow and diffuser design) [11], see Figure 5.
Figure 5: Steam generator geometric model, perspective views: outer view: shell, window and diffuser (top); intermediate view: helical coils (center) and inner view: downcomer (bottom).
15
217
Downcomer, shell, window and diffuser have been assumed un-thickness and,
218
in addition, adiabatic elements. Although window and diffuser are metal ele-
219
ments (with high thermal conductivity), their influence on the water-steam be-
220
haviour in the helical tubes has been considered negligible because they are far
221
enough.
222
The geometric domain is divided into three subdomains: the water-steam
223
side, the molten salts side, and the helical coils walls, which separate both media.
224
Therefore, the model allows to study the thermohydraulic behavior of molten
225
salts circulating by the space existing between helical coils and shells and water-
226
steam flowing within the tubes simultaneously.
227
They have been discretized by means of a polyhedral cells meshing (see
228
Figure 6). The maximum characteristic sizes in molten salts and water-steam
229
sides are 0.0050 m and 0.0025 m respectively, although meshing includes some
230
refinements in the narrower zones with, at least, two polyhedral cells by gap.
231
Both subdomains take account with a prismatic layer, single in the first
232
case and double in the second, on their respective boundaries (i.e. shell and
233
tubes, in molten salts side; and tubes, in water-steam side), which maximum
234
characteristic sizes are 0.00250 m and 0.00125 m respectively (see Figure 6).
235
The transition between prismatic layers (smaller cells) and polyhedral bulks
236
(larger cells) has been carried out gradually (by a 1.5 factor). Also, a double
237
uniform prismatic layer has been included filling the helical coils walls thickness
238
(see Figure 6).
239
The mesh has been made using the automatic tool of STAR-CCM+ 9.04.-
240
R 011 . The total number of cells is around 7.2·106 ; from which 32 % belong to
241
molten salts side, 45 % belong to water-steam side and 23 % belong to helical
242
coils walls.
16
Figure 6: Mesh model detailed view: molten salts side in yellow, helical coils walls in grey and water-steam side in blue.
243
In order to ensure numerical results are mesh model independent, a test
244
varying the maximum characteristic size only in water-steam side has been car-
245
ried out (the molten salts mesh model was already evaluated by Rivas and Rojas
246
[29]). The results are summarized in the following table (Table 3) and they are
247
satisfactory for “coarse” and “medium” mesh models. Table 3: Mesh model test: some numerical results at t¯7050s .
Total number of cells Characteristic size (m)
COARSE
MEDIUM
FINE
Reference Value
≈ 6.9·106 (97 %)
≈ 7.2·106 (100 %)
≈ 8.5·106 (119 %)
—
0.00375
0.00250
0.00150
—
PIN,1 (bar)
39.0
39.0
38.5
39.2
PIN,2 (bar)
39.0
39.0
38.7
39.2
PIN,3 (bar)
39.1
39.1
39.0
39.2
zx1 ,3 Y+ water-steam side
1.16
1.16
1.13
—
50-500
50-300
10-60
Recommended: < 1 or > 30
248
As can be seen, the finest mesh (referred in Table 3 as “fine”) presents
17
249
the worst numerical results of some variables of interest to this work as the
250
inlet pressure to each helical coil, {PIN,# }#=1,2,3 . It is due to the used wall
251
treatment “All Y+”. For this mesh model, the wall treatment dependency
252
with the prismatic layer size on boundaries implies unsuitable values of the Y+
253
in water-steam side (values between 1 and 30, [32, 33]) to assess adequately
254
the turbulent variables (shear stress, turbulence kinetic energy and turbulent
255
dissipation rate), on such boundaries. Since, to make a finer mesh to solve
256
this problem and thus, to obtain suitable values of the Y+ (values less than
257
1, [32, 33]), would be a very time consuming task from the computational cost
258
point of view and coarser meshes present equally suitable inlet pressure results
259
(absolute errors between 0.1 bar and 0.2 bar), they have been selected. Besides,
260
with these coarser meshes (“medium” and “coarse”), similar values of the first
261
dryout z-location in helical coil 3, zx1 ,3 , have been obtained. Therefore, the finer
262
mesh of both (“medium”) has been chosen because its computational cost did
263
not differ too much from the “coarse” mesh (3 %). Colombo [34] drew similar
264
conclusions regarding finer meshes when this type of wall treatment is used.
265
266
In addition, the available experimental data allow to evaluate the chosen mesh model making needless a more exhaustive test.
267
Finally, a mesh topological diagnosis has been conducted using the statistical
268
parameters (volume change, cell quality, face validity y cell and boundary skew-
269
ness angle) established by the software developer [33]. The results are shown in
270
the following table (Table 4). Table 4: Topological diagnosis of “medium” mesh.
MINIMUM VALUE
MAXIMUM VALUE
Cell and boundary skewness angles
0◦
89◦
Face validity
1
1
Cell quality
0.01
1
0.0004
1
Volume change
271
All obtained values are within the ranges which ensure the good quality of
18
272
the mesh, according to the information provided by the software developer [33].
273
All the above following the standards established in Best Practice Guidelines
274
for a suitable use of CFD codes in the industrial field, [35].
275
4.2. Physical models
276
To study the thermohydraulic behavior of the system, a conjugated steady-
277
state heat transfer model has been employed. This model takes into account
278
natural circulation in molten salts, conduction through helical coils walls and
279
forced convective boiling in water-steam.
280
Both external molten salts and internal water-steam flows are considered
281
turbulent flows. Although salts circulate by natural convection through the
282
generator and, therefore, they move slowly, the generator geometry strongly
283
disturbs their motion, generating complex circulations around helical coils which
284
do not allow simulating a laminar flow. However, water-steam flows by forced
285
convective boiling within the tubes, so, during the phase change turbulent is
286
promoted and upstream the flow is fully developed.
287
Both of them are simulated using a “RANS model” (Reynolds-Average
288
NavierStokes) whose closure is made using the “Realizable κ − Two Layer
289
model” [32, 33], considering the approximations of Xu for molten salts (suitable
290
for buoyancy driven flows, [36, 33]) and Wolfstein for water-steam (suitable for
291
shear driven flows, [37, 33]), together with the hybrid wall treatment “All Y+”.
292
For the turbulent model, constants pre-established by the software developer
293
have been assumed. The flow is solved in a segregated way, and the nexus
294
between mass and momentum equations is made via the “SIMPLE algorithm”
295
with the Rhie-Chow interpolation [32, 33]. To solve the energy equation a segre-
296
gated model has been assumed (for the variables: temperature, in molten salts
297
and enthalpy, in water-steam).
298
Boussinesq approximation has been assumed in molten salts side [29]. The
299
rest of molten salts thermophysical properties have been considered temperature-
300
dependent [38].
301
The helical coils walls properties were considered constant and uniform, and 19
302
the pre-established values by the software developer for a stainless-steel type
303
UNSS316 [33] have been assumed.
304
4.2.1. Two-phase flow model description
305
To simulate the two-phase flow, a homogeneous model is employed. It solves
306
a single set of transport equations assuming the two-phase flow as a single-
307
phase flow with equivalent or mixture thermophysical properties. These ones
308
are calculated from the thermophysical properties of each phase and their corre-
309
sponding volume fractions, based on a homogeneity hypothesis. This two-phase
310
flow treatment is commonly used in industrial applications such as steam gener-
311
ators [33]. Its main advantage versus other models, which simulate each phase
312
separately, is its computational efficiency. The principal assumptions of this
313
model are: a) both phases flow at the same velocity (the slip between phases is
314
negligible) and b) both phases are in thermal equilibrium.
315
316
Two phase flow mass, momentum and energy equations, in integral form, are: ∂ ∂t
Z
Z
Z ρm vm · dS =
ρm dV + V
S
Sm dV
(3)
V
317
∂ ∂t
Z
Z ρm vm dV +
V
S
Z ρm vm ⊗ vm · dS = − P I · dS S Z Z + Tm · dS + (fg + sm ) dV S
(4)
V
318
∂ ∂t
Z
Z
Z (ρm Hm vm + P ) · dS = − Q · dS S ZS Z + Tm · vm · dS + (fg · vm + Sh ) dV
ρm Em dV + V
S
(5)
V
319
where mixture density and mixture velocity, ρm and vm , are defined as
320
function of densities and velocities of liquid phase and vapor phase respectively
321
(ρl , ρv , vl , vv ) as:
ρm = (α ρl + (1 − α) ρl ); vm = 20
(α ρl vl + (1 − α) ρv vv ) ρm
(6)
322
323
being: Sm , sm and Sh mass, momentum and energy sources, fg the gravity force, I the unitary tensor and Tm viscous stress tensor, calculated as: 2 T (∇vm + ∇vm ) − (∇ · vm ) I 3
Tm = µef f 324
where µef f is the mixture effective viscosity, given by:
µef f = µt + µm 325
326
being µt the turbulent viscosity, computed as ρm 0.09
(8) κ2
and µm the mixture
viscosity, which is defined as:
µm = (α µl + (1 − α) µv ) 327
329
P |vm |2 ; Hm = hm − ρm 2
phase and vapor phase enthalpies respectively (hl , hv ): 1 (α ρl hl + (1 − α) ρv hv ) ρm
332
334
(12)
where kef f,l and kef f,v are the effective thermal conductivities of the liquid phase and vapor phase respectively, given by:
kef f = k − 333
(11)
And the heat flux vector Q is calculated as:
Q = − [α kef f,l + (1 − α)kef f,v ] · ∇T 331
(10)
where hm is the mixture static enthalpy determined as function of liquid
hm = 330
(9)
The mixture energy Em and the mixture enthalpy Hm are defined as:
Em = Hm − 328
(7)
µt CP P rt
(13)
being, k the thermal conductivity, CP the specific heat and P rt the turbulent Prandtl number of such phases.
335
The distribution of phases, that is, the volume fraction, α, is not obtained
336
by solving a transport equation, but from the distribution of static enthalpy 21
337
under the assumption of thermodynamic equilibrium. In this case, the steam
338
quality, x, is given by the next function:
hm − hl,sat x = max 0, min 1, hv,sat − hl,sat 339
340
341
342
phase, respectively, at the saturation temperature Tsat . And finally, considering the above approaches, the steam volume fraction α can be defined as: x x + (1 − x)
344
(14)
where hl,sat and hv,sat are the static enthalpies of liquid phase and vapor
α=
343
ρv,sat ρl,sat
(15)
where ρl,sat and ρv,sat are the densities of liquid phase and vapor phase, respectively, at the saturation temperature Tsat .
345
The Rohsenow model [39, 33] is used to simulate the heat transfer through
346
the helical coils walls. This model is based on the following hypothesis: during
347
the phase change heat transfer through the walls takes place, either by nucleated
348
boiling or by film boiling.
349
Nucleated boiling occurs when walls temperature is slightly above the satu-
350
rated liquid temperature and involves the bubble nucleation at walls.
351
Here it is assumed nucleated boiling is present even within the annular liquid film
352
regime (this assumption is appropriate at relative low flow rates and sufficient
353
wall superheats, [40]). The bubbles nucleation depends on the walls roughness.
354
In this case, smoothed walls have been assumed. A wall finish type 2B (EN
355
10088-2, [41]) has been considered and, in the working conditions range (3 ·
356
104 < Re < 2 · 105 ), we have checked the flow behavior is hydraulically smooth
357
(although this check is outside of the scope of this work).
358
However, film boiling involves the creation of a continuous vapor film cover-
359
ing the helical coils walls when the critical heat flux is exceeded. Vapor film has
360
a low thermal conductivity, which isolates the walls decreasing the heat transfer
361
process considerably.
22
362
363
To calculate the heat flux during nucleated boiling, the model employs the Rohsenow correlation [39, 33]: r Q = µl hlat
g(ρl − ρv ) σ
CP,l (Tw − Tsat ) n Cqw hlat P rl p
3.03 (16)
364
In equation: µl , hlat , CP,l , ρl , y P rl are the viscosity, boiling enthalpy,
365
specific heat, density and Prandtl number of liquid phase respectively, np is a
366
model coefficient which depends on the working fluid (in this case, it is assumed
367
1, [42]), g is the gravity, ρv the vapor phase density, σ the surface tension on
368
water-steam interface, Tw the walls temperature, Tsat the saturation tempera-
369
ture and Cqw is a model coefficient which depends on the combination working
370
fluid-helical coils walls (it is assumed 0.013, [42]).
371
This correlation is applicable to any type of geometry since it does not
372
depend on it (neither on its orientation). It is based on the hypothesis the
373
agitation of the bubbles is the heat transfer mechanism controlling the nucleated
374
boiling, and it is formulated as a single-phase flow in forced convection.
375
To calculate the heat flux during film boiling, the model uses the same
376
equations as in the case of a single-phase flow of superheated steam. The model
377
coefficient which controls the transition between both regions is αf ilmBoiling .
378
If it is not possible to have a fine enough mesh to solve the steam film thick-
379
ness (as happens in this case), αf ilmBoiling should be explicitly given. Here,
380
a αf ilmBoiling = 1 has been assumed because, by means a sensibility analy-
381
sis (comparing the obtained results for αf ilmBoiling = 0.8, 0.95, 0.99, 1), we
382
have checked this value provided the best numerical results of some variables of
383
interest to this work.
384
Finally, for calculating water-steam thermophysical properties, the IAPWS-
385
IF97 models [43] have been used. These ones provide the fundamental equation
386
for the specific Gibbs free energy from which, using appropriate combinations
387
and their derivatives, it is possible to deduce the specific volume, internal energy,
388
entropy, enthalpy, specific heat and the sound velocity of water-steam.
23
389
4.2.2. Two-phase flow model justification
390
Currently, the two -phase flow mechanistic approaches (those which first
391
determine the existing two-phase flow pattern for certain given conditions and
392
then formulate separate hydrodynamic models for each of them) are the most
393
commonly used approaches according to the CFD codes state-of-the-art, but
394
some limitations and shortcomings have been found for its applicability to this
395
work as:
396
• they need a minimal number of coefficients which require calibration against
397
experimental data [44]. For example, in StarCCM+ it is possible imple-
398
ment different models, but all of them depend on specific submodels to
399
correctly capture: the nucleation site density, bubble departure frequency,
400
bubble departure diameter, quenching heat transfer coefficient, etc. [33].
401
Furthermore, solving this set of equations entails assuming higher compu-
402
tational costs and,
403
• they have an intrinsic dependence on the near-wall mesh [45, 46]. This
404
is due to these submodels were originally formulated for one-dimensional
405
thermo-hydraulic models in terms of the mean-flow variables. The imple-
406
mentation of these submodels as CFD wall boundary conditions assumes
407
replacing the non-local flow quantities by the near-wall local flow quanti-
408
ties. And, it can only be done for extremely coarse meshes, with the first
409
near-wall cell covering the whole boundary layer thickness. With a near-
410
wall mesh, which is adequate for the CFD turbulent wall treatment, such
411
approximation can significantly overestimate the vapor generation [47].
412
For these reasons and because:
413
• from the experimental point of view, the Roshenow correlation has been
414
tested for a wide range of working fluids on cylindrical surfaces and ma-
415
terials [48] and,
416
• from the numerical point of view, the homogeneous boiling model together
417
with the Roshenow correlation implemented in StarCCM+, have been 24
418
already successfully used in other cases to predict the forced convection
419
boiling flows behavior, for example [49], [50], and [51],
420
in this work, this semi-empiric approach has been chosen to simulate the two
421
-phase flow.
422
4.2.3. Two-phase flow model benchmarking
423
Since the experimental setup does not have other direct measurements in
424
water-steam side than inlet water and and outlet steam temperatures to each
425
helical coil ({TI 8 20#}#=1,2,3 and {TI 8 21#}#=1,2,3 respectively, Figure 3),
426
and no adequate experiments have been found in the literature about vertical
427
helical tubes to assess the two-phase flow model performance along the coils,
428
reference experiments on vertical straight tubes have been used here, as some
429
authors have already done in their works about vertical helical tubes (for exam-
430
ple [52]).
431
The experiments are those carried out by Bartolomei et al. [53], explained
432
and analyzed in [54], and Bartolomei and Chanturiya [55]. These tests, classified
433
in the literature as “surface boiling experiments”, are commonly used for boiling
434
models benchmarking [56].
435
Bartolomei et al. measured the average void fractions at different heights
436
along vertical straight tubes, in which the water-steam phase change happened
437
upwards. The test sections walls were uniformly heated and all the experiments
438
were carried out with subcooled water at the tube inlets.
439
Here, two test sections have been considered: the first one with tube diameter
440
of 12.03 mm and total tube length of 1.4 m (heated length of 1 m) and the second
441
one with diameter of 24 mm and total tube length of 2.4 m (heated length of 2
442
m). And two experiments in each of them.
443
The working conditions of these experiments are summarized in Table 5.
25
Table 5: Bartolomei et al. experiments working conditions.
Ref.
Experiment
Q (MW·m-2 )
m ˙ ws (kg·s-1 )
∆Tsub (K)
POU T (bar)
1
1.2
0.1705
63
68.9
2
0.8
0.1705
39
68.9
3
7.9
0.4026
48
45
4
7.9
0.4026
50
30
[53, 54]
[56]
444
As can be seen, they combine different values of boundary heat flux (Q),
445
mass flow rate (m ˙ ws ), inlet subcooling (∆Tsub ) and the outlet pressure (POU T ).
446
Using the mesh model described in section 4.1, a sensitivity study has been
447
carried out once again in order to ensure numerical results are mesh model
448
independent.
449
First, a benchmarking between the two-phase flow model and a mechanis-
450
tic type model implemented in STAR-CCM+, [56], is carries out. Results of
451
experiments 1 and 2 are employed for it.
452
453
The comparison between observed and simulated average void fractions along the first test section are shown in Figure 7.
Figure 7: Average void fraction as function of distance along the first test section.
454
The benchmarking is calculated by means of the statistical parameters: cor-
455
relation coefficient (R), normalized mean square error (N M SE), fractional bias
456
(F B) and fraction of prediction within a factor of two of observations (F AC2) 26
457
(see Appendix for definitions). A perfect model would have R, F AC2 = 1 and
458
N M SE, F B = 0.
459
460
In Table 6, these parameters for the average void fractions along test sections are shown. Table 6: Statistical parameters comparing the average void fractions models results with the measured data by Bartolomei et al. All of them are dimensionless.
EXPERIMENT 1
EXPERIMENT 2
NMSE
FB
FAC2
R
NMSE
FB
FAC2
R
SIMULATION
0.063
-0.041
0.750
0.931
0.149
-0.217
0.917
0.952
MECH.MODEL
0.075
0.027
0.750
0.960
0.092
0.122
0.917
0,974
461
In general, there is a good agreement for both cases. The N M SE and F B
462
have the same order of magnitude (note that the negative F B values indicate
463
a general model overestimation), the F AC2 are similar and the R are high for
464
both cases. Although the mechanistic model shows slightly better results.
465
466
Hence, it could be assumed that the approximations made on the watersteam side are a good compromise for this case.
467
Second, a comparison between the Bartolomei et al. experimental results,
468
which working pressures are closer to those of the ENEA prototype, and the nu-
469
merical results obtained with the two-phase flow model is is addressed. Results
470
of experiments 3 and 4 are used for it.
471
472
In Figure 8, observed and simulated average void fractions along the second test section are shown.
27
Figure 8: Average void fraction as function of distance along the second test section.
473
As can be appreciated, the two-phase flow model:
474
• has reasonably captured the boiling beginning in both cases,
475
• has correctly reproduced the average void fraction profiles: during experi-
476
ment 3 with an average relative error (RE) of 33 % and during experiment
477
4 with an average RE of 22 %, comparable to those showed by some mech-
478
anistic models for the average void fraction calculus, for example [52], [56]
479
and [57].
480
Finally, by means CFD simulations the dryout z-location on test sections
481
can be directly determined from steam quality azimuthal distributions on their
482
walls. Here, the simulated dryout z-location along the second test section has
483
been observed, during experiment 3, on zx = 1.8 m and, during experiment 4,
484
on zx = 2 m.
485
Therefore, considering all the above and given the objectives of this work, it
486
is concluded that this model seems suitable to describe the two-phase flow up
487
to the dryout.
488
4.3. Boundary conditions and simulation methodology
489
The model boundary conditions are established:
490
• firstly, from direct and indirect measurements obtained during a discharge
491
test of the thermal storage prototype; 28
492
• secondly, from the obtained results by means of a pressure drop model in
493
water-steam side. The main pressure drop model hypothesis is that the
494
thermohydraulic instabilities strongly evidenced in the mass flow rates
495
during discharge did not affect the dryout and, therefore, an average be-
496
havior of them can be assumed.
497
The discharge test of October 29th , 2012 has been used. This test was devised
498
and carried out by researchers and technicians from ENEA and provided to the
499
OPTS project partners to development different tasks. Briefly, it takes 10400
500
s and comprises three intervals (see Figures 9 and 10): the first one, from the
501
1650 s to 5250 s (left red area), is a transient interval to achieve the test nominal
502
conditions (PIN ≈ 39 bar, ∆Tsub ≈ 0 y m ˙ ws ≈ 0.082 kg/s), the second one, from
503
the 5250 s to 11350 s (central green area), is a quasi-stationary interval, and
504
the third one, from the 11350 s to 12050 s (right red area), is also a transient
505
interval to get the safe shutdown conditions (PIN ≈ 0 bar, ∆Tsub ≈ 0 y m ˙ ws ≈
506
0 kg/s). Figures 9 and 10 show some measurements during the test.
Figure 9: Temperatures (on both sides) and mass flow rate of molten salts during the test of October 29th , 2012 (in red, transient intervals and in green quasi-stationary interval).
29
Figure 10: Individual pressures and total mass flow rate of water-steam during the test of October 29th , 2012 (in red, transient intervals and in green, quasi-stationary interval).
507
In particular, in Figure 9 direct measurements are: inlet water temperature
508
to each helical coil, {TI 8 20#}#=1,2,3 , and molten salts temperature at steam
509
generator inlet, TI 8 111.
510
511
And indirect measures are: molten salts mass flow rate through steam generator, m ˙ ms , which is calculated by the following energy balance: ¯ OU T − H ¯ IN ) m ˙ ws (H m ˙ ms = ¯ CP,ms (TI 8 111 − TI 8 110)
(17)
512
¯ IN and H ¯ OU T , the where m ˙ ws is the total water-steam mass flow rate; H
513
average enthalpies of inlet water and outlet steam respectively and C¯P,ms the
514
molten salts average specific heat in the temperature range.
515
Inlet water average turbulent kinetic energy and inlet water average turbu-
516
lence dissipation rate to each helical coil, {k¯IN# }#=1,2,3 and {¯ εIN# }#=1,2,3 , are
30
517
given by the expressions [32]: 3 k¯IN# = 2
v¯IN#
I¯IN#
2
; ε¯IN# =
Cµ3/4
3/2 k¯IN#
di
(18)
518
where {¯ vIN# }#=1,2,3 is the inlet water average velocity and {I¯IN# }#=1,2,3
519
the inlet water average turbulence intensity to each helical coil. Cµ a turbulence
520
model constant pre-established by the software developer [33]. In this case, an
521
inlet fully developed flow has been assumed to each helical coil, so: ¯ −1/8 I¯IN# = 0.16 Re IN#
522
523
(19)
¯ IN }#=1,2,3 the inlet water average Reynolds number to each hebeing {Re # lical coil, based on di [32].
524
Molten salts average turbulent kinetic energy and molten salts average tur-
525
bulence dissipation rate at steam generator inlet have been considered negligible
526
because they are far enough from the studied area.
527
Finally, obtained measurements from pressure drop model are the outlet
528
steam pressures to each helical coil, {POU T# }#=1,2,3 (Figure 10). Since, the
529
simulation computational cost of the entire discharge interval is very high, the
530
following methodology has been adopted.
531
• Firstly, two times within the quasi-stationary interval has been select,
532
denoted by t7050s and t10650s (see Figures 9 and 10). These, have been se-
533
lected because, on the one hand, they are far enough from the startup/shutdown
534
intervals to assume negligible their transient effects and, on the other hand,
535
from t7050s to t10650s , molten salts mass flow rate decreases up to a 12 %,
536
which allows to study its influence on the dryout. Each selected time
537
belongs to a two-phase flow instability cycle. These instabilities can be
538
seen within the time evolution of inlet water temperatures and pressures,
539
{TI 8 20#}#=1,2,3 and {PIN# }#=1,2,3 and in outlet steam temperatures
540
and pressures, {TI 8 21#}#=1,2,3 and {POU T# }#=1,2,3 (see Figures 9 and
541
10).
31
542
• Secondly, the representative cycles of each selected time, denote by t¯7050s
543
and t¯10650s , have been made and simulated. Taking into account the
544
measured instabilities period is 20 s (compatible with Naitoh et al. results
545
[26]), for example, t¯7050s is made by averaging the measurements between
546
(t7050s − 10 s) and (t7050s + 10 s), and the associated uncertainties have
547
been assumed as the standard deviations in such interval.
548
Finally, the numerical approach provides a second order precision in the
549
spatial resolution of main conservation equations. These have been carried out
550
R R in 12 nodes DELL M630 of 20 cores Intel Xeon [email protected] by
551
node, with processing times about 26 hours by simulation.
552
5. Model evaluation
553
The model evaluation conditions are established from direct and indirect
554
measurements during the test and pressure drop model results, taking into ac-
555
count the methodology described above.
556
In particular, direct measurements are: outlet steam temperature to each
557
helical coil, {TI 8 21#}#=1,2,3 , molten salts temperature at steam generator
558
outlet, TI 8 110 (see Figure 9) and local wall temperatures along helical coil
559
3, {TI 8 3n1}n=0,1,...,9 , corresponding to heights {zn }n=0,1,...,9 (see Figure 11).
560
These last, considering a local reference system in polar coordinates centered in
561
such helical coil, {r3 , θ3 }, are always in the same position: r3 = do and θ3 = 0.
562
˙ is the And, the exchanged power between molten salts and water-steam, Q,
563
indirect magnitude, calculated using the following expression: ¯ OU T − H ¯ IN ) Q˙ = m ˙ ws (H
564
565
566
567
(20)
¯ IN and H ¯ OU T , the where m ˙ ws is the total water-steam mass flow rate; H average enthalpies of inlet water and outlet steam respectively. The obtained magnitudes from pressure drop model are inlet water pressures to each helical coil, {PIN# }#=1,2,3 (Figure 10).
32
Figure 11: Wall thermocouples distribution along the internal helical tube (left) and zoom of the n-th (right)
568
In Table 7, simulated and observed outlet steam temperature to each heli-
569
cal coil, {TI 8 21#}#=1,2,3 , and molten salts temperature at steam generator
570
outlet, TI 8 110, are shown at t¯7050s and t¯10650s , as well as, the corresponding
571
uncertainties. Table 7: Comparison between simulated and observed temperatures.
t¯7050s
t¯10650s
Simulated
Observed
Simulated
Observed
476
475 ± 2
470
469 ± 2
TI 8 212 ( C)
476
470 ± 2
468
459 ± 2
TI 8 213 (◦ C)
475
474 ± 2
466
467 ± 2
305
305 ± 2
277
278 ± 2
TI 8 211 (◦ C) ◦
◦
TI 8 110 ( C)
33
572
As can be seen, simulated temperatures fit well with observed at both times.
573
Nevertheless, there is a slight overestimation in helical coil 2 (possibly, due to a
574
thermocouple placement error). Therefore, it could be said the model correctly
575
captures the global thermal behavior, both the molten salts and the water-
576
steam, within the quasi-stationary interval.
577
In Table 8, simulated and observed exchanged power between molten salts
578
and water-steam are shown at t¯7050s and t¯10650s . In this table, the corresponding
579
uncertainties are not presented due to its calculation difficulty. Table 8: Comparison between simulated and observed exchanged powers.
t¯7050s Q˙ (W)
t¯10650s
Simulated
Observed
Simulated
Observed
189834
192114
189023
189663
580
As can be observed, there is a good agreement between numerical and ex-
581
perimental results at both times, with differences of 2280 W in the first time
582
(equivalent to 1.2 % of percent error) and of 640 W in the second one (equivalent
583
to 0.3 % of percent error). Thus, it could be also claimed the model correctly
584
captures the total heat transfer between molten salts and the water-steam within
585
the quasi-stationary interval.
586
Simulated and observed inlet water pressures to each helical coil, {PIN# }#=1,2,3 ,
587
at t¯7050s and t¯10650s , as well as, the corresponding uncertainties are shown in
588
Table 9. Table 9: Comparison between simulated and observed pressures.
t¯7050s
t¯10650s
Simulated
Observed
Simulated
Observed
PIN1 (bar)
39.0
39.2 ± 0.6
37.3
37.9 ± 0.6
PIN2 (bar)
39.0
39.2 ± 0.6
37.5
37.9 ± 0.6
PIN3 (bar)
39.1
39.2 ± 0.6
37.6
37.9 ± 0.6
34
589
As can be appreciated, simulated pressures fit well with observed ones at
590
both times. So, the model properly captures the water-steam global hydraulic
591
behavior within the quasi-stationary interval.
592
In Figure 12, local wall temperatures along helical coil 3, {TI 8 3n1}n=0,1,...,9 ,
593
observed measurements (filled dots) and simulated values (empty dots) at t¯7050s
594
(in red) and t¯10650s (in blue) are shown, as well as, the corresponding uncer-
595
tainties.
Figure 12: Observed and simulated local wall temperatures (helical coil 3).
596
597
It is shown, simulated local wall temperatures fit well with observed up to heights: z5 at t¯7050s and z3 at t¯10650s .
598
From it, the model overestimates the wall heating. It is probably due to this
599
model is not suitable to completely describe the water-steam phase change in
600
this case, as it had been advanced during the benchmarking when average void
601
fractions were high.
602
As has been mentioned before, the experimental setup does not have other
603
direct measurements in water-steam side than those already used for validation. 35
604
In this case, it is logical because, on the one hand, “traditional” measure-
605
ments generally are invasive techniques (such as the use of thermocouples, etc.)
606
and, given the coils dimensions, they would strongly disturb the two-phase flow
607
masking its local phenomenology and, on the other hand, more “sophisticated”
608
measurements, generally non-invasive techniques (such as the use of X-rays,
609
etc.), would not be techno-economically viable.
610
At the dryout onset, the cooling of the walls drastically modifies because
611
they change from being: liquid wetted walls to steam wetted walls. This causes
612
a sharp decrease of local heat transfer coefficients causing a poor fluid-structure
613
thermal response. It implies a local increase of walls temperature regarding to
614
the downstream walls temperature [10].
615
Thus, using a wall thermocouples distribution along the tubes can be con-
616
sidered a non-invasive technique for indirect measure the dryout z-localization
617
(as it is stated, for example, in [58]).
618
619
Here, from the helical coil 3 wall thermocouples distribution, the dryout onset in such helical coil has been experimentally determined.
620
As can be observed in Figure 9, the first increase of walls temperature is
621
between heights: z6 y z5 (TI 8 361 − TI 8 351 = 71 ◦ C) at t¯7050s and, z4 y z3
622
(TI 8 341 − TI 8 331 = 69 ◦ C) at t¯10650s .
623
However, by means CFD simulations the dryout z-location, both first dryout,
624
zx1 ,3 , and total dryout, zxT ot ,3 , on such helical coil can be directly determined
625
from steam quality azimuthal distributions on walls.
626
627
In Table 10, the simulated and observed dryout z-location along helical coil 3, are shown at t¯7050s and t¯10650s , as well as, the corresponding uncertainties. Table 10: Comparison between simulated and observed dryout z-location in helical coil 3.
t¯7050s
zx1 ,3 /zxT ot ,3 (m)
628
t¯10650s
Simulated
Observed
Simulated
Observed
1.16/1.17
1.13 ± 0.063
1.35/1.36
1.38 ± 0.063
Taking into account the problem uncertainties, these results reveal, simu36
629
lated dryout z-locations along helical coil 3 fit well the observations at both
630
times.
631
Hence, it can be assumed the model performance is good enough to capture
632
the two-phase flow local behavior, at least up to the dryout onset, within the
633
quasi-stationary interval. As it had been stated before during the benchmarking.
634
In summary, this model is considered appropriate to deal with the work
635
objectives.
636
6. Dryout study
637
Hereafter, the dryout onset (first and total dryout) is studied in the covered
638
working conditions range, i.e. it is associated azimuthal position and local steam
639
qualities, depending on the helical coil diameter. And finally, the comparison
640
with the found literature correlations is carried out.
641
6.1. Azimuthal position and local steam qualities
642
From numerical results, dryout z-location, both first and total, on each he-
643
lical coil tube are obtained. Results at t¯7050s and t¯10650s are shown in Table
644
11. Table 11: Dryout z-location: first/total.
zx1 ,3 /zxT ot ,3 (m)
zx1 ,2 /zxT ot ,2 (m)
zx1 ,1 /zxT ot ,1 (m)
t¯7050s
1.16 / 1.17
1.14 / 1.15
1.11 / 1.12
t¯10650s
1.35 / 1.36
1.33 / 1.34
1.30 / 1.31
645
From them it follows that under practically the same working conditions of
646
in water-steam side (PIN ∈ [37.9, 39.2] bar, ∆Tsub ≈ 0 and m ˙ ws ≈ 0.082 kg·s-1 )
647
and molten salts side (atmospheric pressure and TIN ∈ [472, 477] ◦ C) but a 12
648
% mass flow rate decrease, both first and total dryout:
649
650
• shift along the steam generator almost 11 turns upwards (0.19 m), i.e., regardless on the helical coil diameter, D,
37
651
• happen primarily on helical coil 1, almost 2 turns upwards on helical coil
652
2 and almost 3 turns upwards on helical coil 3, regardless on molten salts
653
mass flow rate, m ˙ ms .
654
These results quantify that it was already knew: as discharge evolves, heat
655
transfer is increasingly less effective, so a greater heat transfer area along the
656
steam generator is needed to achieve the dryout, being the outer tube (helical
657
coil 1), in which, dryout, first and total, primarily happens. This, at equal z-
658
location height, has a greater heat transfer area than the others (helical coils 2
659
and 3).
660
Once determined dryout z-locations on each tube, the respective steam qual-
661
ity azimuthal distributions on walls during first dryout, {x1,# }#=1,2,3 , as well
662
as the steam quality bulk values both during first and total dryout, x1,bulk and
663
xT ot,bulk respectively, are plotted on the cross sections to the flow containing
664
such z-locations at t¯7050s and t¯10650s . The obtained results are presented in
665
Figure 13.
Figure 13: Steam quality azimuthal distributions on walls and bulk values, during first and total dryout at t¯7050s (left) and t¯10650s (right).
666
From them, it follows that:
667
• The first dryout azimuthal positions, {θx1 ,# }#=1,2,3 , remain constant re38
668
gardless on D and m ˙ ms (θx1 ≈ 170◦ , on the intrados). This is also true
669
for the lowest steam quality azimuthal positions on walls (θx1 ≈ 350◦ , on
670
the extrados). This result can be explained due to the secondary flow
671
presence.
672
On a two-phase flow in a helical coil, the centrifugal and gravity forces act
673
trying to separate the flow due to the density differences between both phases.
674
In addition, there is a secondary flow, superimposed to the primary flow, which
675
also acts on the two-phase flow. This is perpendicular to the main flow and
676
follows lines forming loops, dragging the fluid from the extrados to the intrados,
677
counteracting the separation effects between both phases [12]. The separation
678
effects depend on m ˙ ws since the buoyancy forces have higher influence at low
679
m ˙ ws due to the existing lower turbulence.
680
To visualize the secondary flow presence in this case, in Figure 14 two-phase
681
flow distribution obtained by means the line integral convolution of the vector
682
velocity field (removing the normal component and projecting the tangential
683
component on the cross section to the flow) at z6 and t¯7050s is shown as example.
Figure 14: Line integral convolution of tangential vector velocity field in helical coils at z6 and t¯7050s field (steam generator axis placed on the left side of the figure).
684
As can be seen, the streamlines shape two vortices coincident with first
685
dryout and lowest steam quality on walls azimuthal positions, which represent
686
the loops dragging the fluid from the extrados to the intrados. They go through
687
the walls perimeters and then close through the bulks, as it is shown in Figure
688
15. 39
Figure 15: Tangential vector velocity field in helical coils at z6 and t¯7050s (steam generator axis placed on the left side of the figure).
689
This phenomenology agree with that described by other authors as Pointer
690
et al. [59], Colombo [34], Jo et al. [52] and Cioncolini et al. [60], who also
691
employed CFD techniques to describe forced convective boiling flows in heli-
692
cal coils but using different working conditions, wall heating methodologies or
693
geometric characteristics than here.
694
By other hand, from steam quality azimuthal distributions on walls, the
695
best/worst chilled surface points during the first dryout can be deducted. In
696
Figure 16, temperature azimuthal distributions on walls during the first dryout,
697
{Tx1 ,# }#=1,2,3 , as well as the respective bulk values, Tx1 ,bulk , are plotted on the
698
cross sections to the flow at t¯7050s and t¯10650s .
40
Figure 16: Temperature azimuthal distributions on walls and bulk values during 1st dryout at t¯7050s (left) and t¯10650s (right).
699
It is observed the temperature difference between first dryout and lowest
700
steam quality on walls azimuthal position is ≈ 20 ◦ C. This lack uniformity on
701
the walls thermal behavior at equal z-location (even promoted by the two-phase
702
flow instabilities) could affect the steam generator safety. Although it is outside
703
the scope of this work, it is recommended the steam generator thermomechanical
704
behaviour will be also analyzed by those who pretend to scale-up this system.
705
706
• Both x1,bulk and xT ot,bulk remain constant regardless on D and m ˙ ms (x1,bulk ≈ 0.94 and xT ot,bulk ≈ 0.97).
707
These values can be understood by means the 2D map of Berthoud and
708
Jayanti, which helps to identify the process controlling the first dryout in helical
709
coils. In Figure 17, dimensionless numbers x0 and y0 of each helical coil are
710
represented, both at t¯7050s and t¯10650s .
41
Figure 17: B&J 2D map during the first dryout at t¯7050s and t¯10650s .
711
As can be observed, the study case belongs to the “Redeposition zone”, char-
712
acterized by high steam qualities during the first dryout. In addition, according
713
to the obtained vales of x0 and y0 (very close to each other), it can be deduced
714
the steam quality distributions within the helical coils follow the same pattern,
715
as it is shown in Figure 18.
Figure 18: Two-phase flow patterns at z6 and t¯7050s (steam generator axis placed on the left side of the figure).
716
This pattern is typical from the “Redeposition zone” and has been also ob-
42
717
served in the experiments conducted by Murai et al. [61] using a computed
718
tomography technique, so this model reproduces available experiments in bibli-
719
ography.
720
In summary, it can be said that, in the covered working conditions range
721
and considering this steam generator geometry, although D1 > D2 > D3 , the
722
two-phase flow behavior is uniform. Besides, that what happens at t¯7050s is
723
reproduced, without loss of generality, at t¯10650s , except a certain heights dif-
724
ference. And, therefore, the prototype operation seems not to influence on the
725
dryout.
726
6.2. Simulation results and literature correlations comparison
727
Once defined local steam qualities as {¯ x1,# }#=1,2,3 or {¯ xT ot,# }#=1,2,3 , it is
728
proceed to compare simulated values, {¯ x1,sim,# }#=1,2,3 or {¯ xT ot,sim,# }#=1,2,3 ,
729
with those calculated by using literature correlations applicable to the ENEA
730
prototype working condition for both first dryout, {¯ x1,correlac,# }#=1,2,3 (cor-
731
relations of: Berthoud and Jayanti, Ruffell and Santini et al., see expressions
732
and applicability ranges in Table 1) and total dryout, {¯ xT ot,correlac,# }#=1,2,3
733
(correlations of: Naitoh et al. and Berthoud and Jayanti, see expressions and
734
applicability ranges in Table 1), where simulated values have been calculated as
735
follows:
x ¯1orT ot,sim,# 736
737
738
1 = S
Z x1orT ot,# (r# , θ# ) dS
(21)
S
being {x1orT ot,# }#=1,2,3 the steam quality distributions on the cross sections to the flow during first or total dryout respectively. Note that one of the main handicaps assessing {¯ x1,# }#=1,2,3 or {¯ xT ot,# }#=1,2,3
739
by means experimental correlations is the boundary heat flux calculus (Q). This
740
happens mainly in those cases in which the wall heating is not uniform, as in this
741
case. Nevertheless, in correlations where Q is taken into account (correlation
742
of Berthoud and Jayanti for first dryout, and correlations of Ruffell and Naitoh
743
et al. for total dryout), the necessary power, Q˙ nec , to achieve the dryout, here
43
744
is uniformly distributed on the walls. Considering this hypothesis, obtained
745
results for {¯ x1,# }#=1,2,3 are shown in Figure 19.
Figure 19: Comparison between simulated and calculated results for first dryout.
746
As can be seen, obtained results using Ruffel0 s correlation fit well simulated
747
results, while those obtained using Santini et al. correlation underestimate
748
slightly (around 20 %) local steam qualities during first dryout. Finally, those
749
obtained using Berthoud and Jayanti correlation overestimate them up to 60
750
%. This is due to, in the first case, the correlation (considering 270◦ Ruffel0 s
751
correlation, which corresponds to 180◦ in the local polar reference systems used
752
here) was validated for water as working fluid in a set of helical coils whose
753
working conditions and characteristics were not far away from that established
754
in this work.
755
Regarding Santini et al. correlation, although the considered working fluid
756
is water and the covered working conditions range is supported here, the helical
757
coils characteristics are different: greater vertical pich, Xver , and diameters of
758
helical coil, D, and tube, di .
44
759
To a better understanding of Santini et al. results, it can be used the
760
Berthoud and Jayanti 2D map [16]. If dimensionless numbers x0 and y0 for
761
a helical coil with Santini et al. characteristics but ENEA prototype work-
762
ing conditions are represented on this map, obtained points during first dryout
763
would be shifted to the “Gravity zone”, characterized by lower steam qualities
764
than the “Redeposition Zone”. Taking into account Santini et al. helical coil
765
diameter is between 5 and 7 times larger than those of the ENEA prototype, is
766
clear the effect of centrifugal forces decreases against the gravity force.
767
In the Berthoud and Jayanti correlation case, notwithstanding working con-
768
ditions and helical coils characteristics comprise those of this case, obtained
769
results does not fit adequately, probably because this correlation was based on
770
the experimental data of five researchers (Breus and Belyakov [20], Carver et
771
¨ al. [21], Roumy [17], Styrikovich et al. [14] and Unal [18, 19]), who employed
772
different working fluids (and therefore, working conditions).
773
Figure 20 shows obtained results for {¯ xT ot,# }#=1,2,3 .
Figure 20: Comparison between simulated and calculated results for total dryout.
45
774
As can be observed, obtained results using Naitoh et al. correlation fits
775
quite well simulated results, while those obtained using Berthoud and Jayanti
776
correlation overestimate them up to 60 % the local steam qualities during total
777
dryout as it was expected. Despite the good fit in the first case, the explicit
778
independence of this correlation with the mass flux allows to question it. Be-
779
sides, there are big differences between Naitoh at al. helical coils and ENEA
780
prototype characteristics.
781
7. Conclusions
782
• In this work, the dryout onset (first and total dryout) in a triple helical
783
coil once-through steam generator has been experimentally and numeri-
784
cally studied. For this purpose, a CFD modelling based on steady-state
785
simulations and a conjugate heat transfer model has been carried out.
786
Besides, a numerical methodology based on the two-phase flow average
787
behavior in each thermohydraulic instability cycle has been employed.
788
• From a benchmarking between the two-phase flow model and a mechanis-
789
tic model, it is deduced that the used semi-empiric model can be applied
790
to the simulation of the forced convection boiling flow in the helical coils.
791
• Numerical results have been evaluated, first, against experimental data
792
from the state-of-the-art, and second, against acquired measurements dur-
793
ing a discharge test of the thermal energy storage prototype with inte-
794
grated steam generator belonging to ENEA and the obtained results with
795
a pressure drop model developed ad hoc for this case, getting good fits up
796
to the dryout.
797
• By means two phase flow tangential vector velocity field on cross section
798
to the flow has been possible to show the secondary flow presence in the
799
helical coils. And, by means steam quality distributions has been possible
800
to characterize the dryout onset, azimuthal position and associated local
801
steam qualities, as function of helical coil diameter. In this case, within the 46
802
working conditions range and considering these particular steam generator
803
characteristics, the two-phase flow behavior is uniform. And, therefore,
804
the prototype operation seems not to influence on the dryout. This phys-
805
ical phenomenology and analysis have not been reported yet on available
806
literature.
807
• Besides, the derived two-phase flow pattern is typical of “Redeposition
808
Zone” within the 2D map of Berthoud and Jayanti [16] and it is like
809
those observed in other works using, both experimental and numerical
810
methodologies, to describe forced convective boiling flows in helical coils
811
at high steam qualities.
812
• Finally, the numerical local steam qualities have been compared with those
813
calculated by using appropriate experimental correlations. From the ob-
814
tained scatter-plots it is concluded, the 270◦ Ruffel0 s correlation is the
815
most adequate expression to determine the local steam quality value dur-
816
ing the first dryout.
817
• Also, assuming a 0.97 value during the total dryout is a good approxi-
818
mation, since although it is the most conservative choice, it matches the
819
value recommended by Mazufri [62] for the thermohydraulic design of a
820
helical steam generator. On the other hand, the Santini et al. correlation
821
offers suitable results (within a 20 % error) being this one, moreover, sim-
822
pler than others because it does not depend on walls heat flux. So, the
823
obtained steam quality macro values are validated, and it is justified the
824
interest of a comprehensive study of them.
825
ACKNOWLEDGEMENTS
826
The authors would like to acknowledge the EU through the 7th Framework
827
Program for the financial support of this work under the OPTS project with
828
contract number: 283138, the UTRINN-STD from Casaccia Research Center
829
(ENEA) for providing the experimental data and the information concerning 47
830
to the experimental setup and the Extremadura Research Centre for Advances
831
Technologies (CETA-CIEMAT) for providing the necessary computing resources
832
for simulations. Technical discussions with members of ATYCOS-CIEMAT were
833
essential for this work.
834
Appendix A. Statistical parameters The relative error (RE) is defined as: RE[%] =
|Cp − Co | Co
The correlation coefficient (R), the normalized mean square error (N M SE), the fractional bias (F B) and the fraction of prediction within a factor of two of observations (F AC2), are given by: R=
(Co − Co )(Cp − Cp ) (Co − Cp )2 (Co − Cp ) ; N M SE = ; FB = σCp · σCp Co · Cp 0.5(Co + Cp ) F AC2 = fraction of data that satisfy 0.5 ≤
Cp ≤ 2.0 Co
835
where: Cp are model predictions; Co observations; and C and σC the corre-
836
sponding average and standard deviation, respectively, over the data-set.
837
Note that since F B measures only the systematic bias of a model, it is
838
possible for a model to have predictions completely out of phase of observations
839
and still have F B = 0.0 because of cancelling errors.
48
NOMENCLATURE Tube diameter (m)
Q
Heat flux (W·m-2 )
f
Force (N)
Q˙
Power (W)
g
Gravity (9.806 65 m·s-2 )
Re
Reynolds number
h
Static enthalpy (J·kg-1 )
S
Surface (m2 )
d
-1
-1
k
Thermal conductivity (W·m ·K )
T
Temperature (K)
m ˙
Mass flow rate (kg·s-1 )
V
Volume (m3 )
t
Time (s)
X
Pitch (m)
{x, y, z}
Cartesian coordinates (m)
α
Vapor volume fraction
-1
v
Velocity (m·s )
x
Steam quality
x ¯
Local steam quality
{x0 , y0 }
Dimensionless numbers (B&J 2D Map)
Turbulent dissipation rate (m2 ·s-3 )
-1
CP
Specific heat (J·kg ·K )
κ
Turbulent kinetic energy (J·s-1 )
D
Helical coil diameter (m)
µ
Dynamic viscosity (Pa·s)
E
Energy (J)
ρ
Density (kg·m-3 )
-1
-1
-2
G
Mass flux (kg·s ·m )
σ
Surface tension (N·m-1 )
H
Enthalpy (J·kg-1 )
ϕ
Helix angle (◦ )
L
Length (m)
∆
Increment
P
Pressure (bar)
{r, θ}
Polar coordinates
Pr
Prandtl number
{r, θ, z}
Cylindrical coordinates
SUBSCRIPTS 1
First
l
Liquid
sat
Saturated
bulk
Bulk
lat
Latent
simu
Simulated
correlac
Correlated
m
Mixture
sub
Subcooled
cri
Critic
max
Maximum
t
Turbulent
ef f
Effective
min
Minimum
T ot
Total
g
Gravity
ms
Molten salts
v
Vapor
hor
Horizontal
nec
Necessary
ver
Vertical
i
Inner
o
Outer
w
Wall
IN
Inlet
OU T
Outlet
ws
Water-steam
49
ACRONYMS CFD
Computational Fluid Dynamics
RANS
Reynolds Averaged Navier-Stokes
CSP
Concentrating Solar Power
SFR
Sodium-cooled Fast Reactor
DWO
Density Wave Oscillations
[1] E. Zarza, Principales retos de I+D y potencial contribuci´on a un mercado sostenible, in: Gu´ıa T´ecnica de La Energ´ıa Solar Termoel´ectrica, Fundaci´on de la Energ´ıa de la Comunidad de Madrid (FENERCOM), 2012, Ch. 3, pp. 71–122. [2] ENEA. URL http://www.enea.it/it [3] ANSALDO Nucleare S.p.A. URL https://www.ansaldoenergia.com/ansaldo-nucleare/home [4] L. Rinaldi, F. Fabrizi, A. Alemberti, W. Gaggioli, S. Aliotta, A. Barbensi, P. Tarquini, Thermal Energy Storage Tank With Integrated Steam Generator, EP 2652272 B1 (2015-10-28). [5] F. Fabrizi, W. Gaggioli, L. Rinaldi, C. Rocca, R. Surace, Progettazione e realizzazione di uno scambiatore di calore prototipico per reattori refrigerati a sodio con circuito intermedio a sali fusi, Tech. Rep. NNFISS LP3 - 027, ENEA (2011). [6] F. Fabrizi, Trough Molten Salt HTF Field Test Experience, in: NREL Parabolic Trough Technology Workshop, 2007, p. 59. [7] W. Gaggioli, P. Di Ascenzi, L. Rinaldi, P. Tarquini, F. Fabrizi, Effects assessment of 10 functioning years on the main components of the molten salt PCS experimental facility of ENEA, in: AIP Conference Proceedings, Vol. 1734, AIP Publishing, 2016, p. 070009. doi:10.1063/1.4949156. [8] W. Gaggioli, F. Fabrizi, P. Tarquini, L. Rinaldi, Experimental validation of the innovative thermal energy storage based on an integrated system 50
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57
Highlights
•
CFD modelling of dryout onset in a triple helical coil once-through steam generator.
•
Benchmarking of two-phase flow model against experimental data from the state-ofthe-art.
•
Evaluation of numerical results with experimental data of a thermal energy storage prototype with integrated steam generator during a discharge test.
•
Azimuthal distributions analysis of the two-phase flow as function of helical coils characteristics and working conditions.
•
Comparison of numerical results with those obtained from adequate correlations for forced convective boiling flows in vertical helical coils.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S1359-4311(19)37115-7 https://doi.org/10.1016/j.applthermaleng.2020.115013 ATE 115013
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
14 October 2019 9 January 2020 25 January 2020
Please cite this article as: E. Rivas, J. Muñoz-Antón, Dryout study of a helical coil once-through steam generator integrated in a thermal storage prototype, Applied Thermal Engineering (2020), doi: https://doi.org/10.1016/ j.applthermaleng.2020.115013
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© 2020 Published by Elsevier Ltd.
DRYOUT STUDY OF A HELICAL COIL ONCE-THROUGH STEAM GENERATOR INTEGRATED IN A THERMAL STORAGE PROTOTYPE E. Rivasa,∗, J. Mu˜ noz-Ant´ona a Escuela
T´ ecnica Superior de Ingenieros Industriales Universidad Polit´ ecnica de Madrid (ETSII-UPM) C/ Jos´ e Guti´ errez Abascal, 2, 28006 Madrid, Spain
Abstract In this work, it is studied several dryout parameters (the dryout onset, first and total dryout, its associated azimuthal position and local steam qualities) in a triple helical coil once-through steam generator under quasi-steady working conditions (inlet pressure, PIN ∈ [37.9, 39.2] bar, inlet subcooling, ∆Tsub ≈ 0 ◦
C and total mass flow rate, m ˙ ws ≈ 0.082 kg·s-1 ) which exchanges heat with
a molten salts counterflow under quasi-steady pressure and temperature conditions (atmospheric pressure and inlet temperature, TIN ∈ [472, 477] ◦ C) but transient mass flow rate, m ˙ ms , depending on the helical coil diameter, D. For this purpose, a CFD model (Computational Fluid Dynamics model) has been used which has been evaluated with the experimental data obtained during a discharge test of the 300 kWth thermal storage prototype with integrated steam generator of the Casaccia Research Center (ENEA, Italy), previous benchmarking of two phase flow model. Results show, within the working conditions range and considering the particular steam generator characteristics, the two-phase flow behavior is uniform. This information has not been reported yet on available literature. In addition, numerical local steam qualities are compared with those calculated by using forced convective boiling correlations suitable for this ∗ Corresponding
author Email address: [email protected] (E. Rivas)
Preprint submitted to Applied Thermal Engineering
January 31, 2020
type of steam generator geometry, concluding that: 270◦ Ruffel’s and Santini’s correlations are the most appropriate during first dryout, and to assume a local steam quality value of 0.97 during total dryout the most suitable approximation. This work can be useful for those who pretend to scale-up such a steam generator for industrial applications requiring process heat and/or power generation. Keywords: scale-up, once-through steam generator, helical coil, dryout, steam quality, Computational Fluid Dynamics (CFD). elsarticle.cls, LATEX, Elsevier, template 2010 MSC: 00-01, 99-00
1
1. Introduction
2
Currently, there are a large number of industrial applications where process
3
steam is required (desalination, sterilization, building or district heating and
4
cooling, etc.). Other clear examples are the CSP plants (Concentrating Solar
5
Power plants), which generate electricity from the transformation of concen-
6
trating solar radiation. In them, the presence of thermal storage systems is
7
very common because it allows to manage its electrical production even in the
8
absence of solar radiation.
9
In general, the thermal storages for commercial CSP plants are based on the
10
double tank system with molten salts. Although the efficiency of these systems
11
is very high (> 93 %) [1], it is necessary to research and develop new thermal
12
storage designs more profitable in order to demonstrate that this technologies
13
have enough potential to replace the more conventional ones, such as those based
14
on the use of fossil fuels.
15
With this aim, the ENEA Research Center (Italy) [2] and the company
16
ANSALDO Nucleare S.p.A. (Italy) [3] have patented the layout of a molten
17
salts thermal storage system based on a single tank with an integrated helical
18
coil steam generator [4], inspired by the SFR technology (Sodium-cooled Fast
19
Reactors) [5]. The patent bases its competitiveness in the simplification of the
20
plant configuration [6]. Subsequently, its technical feasibility has been demon-
2
21
strated on a prototype scale (300 KWth) in ENEA [7, 8, 9]. The next step in
22
its development would be to scale-up it at commercial CSP plant level (> 10
23
MWe).
24
One of the key points in the thermohydraulic design of the system is the
25
calculus of local steam qualities associated to the onset of the dryout because it
26
implies a worsening of the local heat transfer coefficients in the water-steam side
27
(in some cases until one and two orders of magnitude [10]). The difficulty is due
28
to, from the experimental point of view, the ENEA prototype instrumentation
29
is not enough: there are no measurements of local heat fluxes and there are only
30
temperature measurements of a single coil. Also, from the theoretical point of
31
view, the found correlations in the literature for forced convective boiling flows
32
in this type of geometries are not 100 % suitable: either by the heat transfer
33
fluid, the helical coil/tube characteristics or the working conditions.
34
Therefore, the objectives of this work are:
35
• to study the dryout onset in the covered working conditions range depend-
36
ing on the helical coil diameter,
37
• and from this information, to assess the adaptability of the literature
38
correlations, both during the first and the total dryout, to this system.
39
For this purpose, the employed methodology has been the numerical analysis
40
by CFD modeling (software: STAR-CCM+ 9.04.011 [11]), which results has
41
been evaluated, first, against experimental data from the state-of-the-art, and
42
second, against those obtained during a discharge test of the thermal storage
43
prototype with integrated steam generator belonging to ENEA.
44
This work is structured as follows: first of all, it is summarized the state-
45
of-the-art correlations for calculating local steam qualities associated with the
46
dryout onset in forced convective boiling, particularly in vertical helical coils.
47
Then, the ENEA thermal storage prototype and its operating mode during
48
discharge tests is described. Secondly, the CFD pre and post processing are
49
presented, and the model evaluation (both numerical and experimental) is made
50
up. And finally, the dryout study as function of the helical coil diameter and 3
51
the comparison with the found correlations, are carried out. The most relevant
52
conclusions are set out.
53
2. State-of-the-art of the correlations for calculating local steam qual-
54
ities associated with the dryout onset in forced convective boiling
55
flows in vertical helical coils
56
One of the main differences in forced convective boiling flows between vertical
57
straight tubes and vertical helical coils is the dryout onset. While in the first
58
case it happens simultaneously in all tubes at equal height, in the second one,
59
it starts at certain surface points and spreads until all surface points dryout
60
completely at a particular height (Figure 1), i.e., there is a height range where
61
the coils are partially dry and partially wet.
Figure 1: Visualization of dryout onset in a helical coil (Source: CFD research findings).
62
This difference is due to the joint action of frictional, centrifugal and vis-
63
cous forces. These forces induce the two-phase flow undergoes a secondary flow
64
perpendicular to the principal flow [12]. The secondary flow promotes the extra-
65
dos surface wetting until higher steam qualities than in case of straight tubes.
66
Comparative studies carried out by Cumo et al. [13] and Styrikovich et al. [14]
67
between vertical straight tubes and vertical helical coils show such difference.
4
68
The characteristics of employed samples and the working conditions ranges of
69
these studies are shown in Table 1.
70
In Table 1 it can be seen that the main involved factors on found correlations
71
for calculating steam qualities for dryout onset in forced convective boiling flows
72
are pressure (P ), mass flux (G) and heat flux (Q).
73
The pressure and mass flux effects were analyzed by Styrikovich et al. [14].
74
This work analyses that increasing pressure and mass flux, steam quality de-
75
creases accordingly during the total dryout, evidencing its dependency. Among
76
the revised correlations, only Naitoh et al. correlation [15] is mass flux indepen-
77
dent, see Table 1.
78
Berthoud and Jayanti propose three different correlations to determine the
79
steam quality during the first dryout depending on the type of annular flow
80
regime [16] (Table 1). This work is based on the experimental data of Roumy
81
¨ [17], Styrikovich et al. [14], Unal et al. [18, 19], Breus and Belyakov [20] and
82
Carver et al. [21]. To identify the regime type, Berthoud and Jayanti employed
83
a 2D map (Figure 2) in which, on the x-axis, it is represented the dimensionless
84
number x0 given by the expression:
x0 =
G √ ρv gD
(1)
85
where ρv is the steam density, g the gravity and D the helical coil diame-
86
ter. This parameter is a measure of the centrifugal force acting on the vapor
87
phase and the drag force acting on the droplets, which shows up the droplets
88
redeposition process. And, on the y-axis, it is represented the dimensionless
89
number y0 (equivalent to the Reynolds number of the liquid phase) given by the
90
expression:
y0 = 91
G · d∗ µl
where d∗ is a geometric factor given by di ·
(2) q
di ( 0.02 ) (di is the inner tube
92
diameter) and µl the water dynamic viscosity. This parameter shows up the
93
droplets entrainment process through the vapor core. 5
Figure 2: Processes controlling the first dryout in helical coils, 2D map [16].
94
95
On this map, depending on working conditions and samples characteristics, three different zones can be distinguished:
96
• Gravity zone: characterized by high D, low G and high P , where dryout
97
onset happens at low steam qualities. In this case, flows are often very
98
stratified.
99
• Redeposition zone: characterized by low D, high G and low P , where
100
dryout onset happens at high steam qualities. In this case, flows tend to
101
be slightly stratified and the extrados surface remains often well chilled.
102
• Entrainment zone: characterized by very high D and G and standard P ,
103
where dryout onset happens at medium steam qualities. In this case, flows
104
tend to be slightly stratified and the intrados surface remains often well
105
chilled.
106
In this work, the authors also propose a correlation during total dryout, 6
107
noting that it also depends only on the type of annular flow regime [16] (Table 1).
108
Although, in contrast to the previous correlations, it is heat flux independent.
109
110
Therefore, to clarify this issue (heat flux dependence/independence) it is necessary to draw upon other works.
111
¨ While in correlations proposed by Duchatelle et al. [22], Unal et al. [18, 19],
112
Jensen et al. [23, 24, 25, 26] and Ruffell [27] heat flux appears explicitly, in that
113
proposed by Santini et al. [28] heat flux does not appear (see Table 1). First
114
three correlations were obtained from non-uniform wall heatings and fourth and
115
fifth ones were obtained at lab scale with electrical heat (uniform heating):
116
117
118
119
120
121
• 1st : Duchatelle et al. used the data of a real steam generator exchanging heat with a liquid sodium at counterflow ¨ • 2nd : Unal et al. used the data of three concentric helical coils heated by means of an external liquid sodium at counterflow • 3rd : Jensen et al. used the data of three helical coils electrically heated applying a higher flux on the top surface than on the bottom surface.
122
I.e., the employed wall heating methodologies (uniform or non-uniform) are
123
different and, therefore, it is difficult to distinguish the potential heat flux de-
124
pendence/independence.
125
On the other hand, the Jensen’s correlation is not applicable here because its
126
working pressure is far from those of the ENEA prototype (since he employed
127
¨ R113 as working fluid). And, neither the Duchatelle’s and Unal’s correlations
128
are applicable here because they have been derived from very different working
129
conditions ranges. In particular, the first, for large heat and mass fluxes and
130
the second, for very high pressures and inlet subcoolings.
131
Even though in most of the works where it was employed few helical coils par-
132
allel arranged, two-phase flow instabilities were observed, hardly ever included
133
specific studies about their influence on the dryout (in many cases, two-phase
134
flow instabilities were inhibited by using calibrated orifices at the tubes in-
135
¨ lets). About this regard, highlighting the Chapter 7 of Unal [18], where a study
7
136
about the DWOs (Density Wave Oscillations) observed during the operation of
137
a full-scale steam generator is presented, and the Naitoh et al. study [26], who
138
investigated the dryout coupled by DWOs. Naitoh deduced the dryout fluctua-
139
tions had periods between 3 s and 20 s, result consistent with the experimental
140
data of the ENEA prototype. Here it has shown, without inhibiting two-phase
141
flow instabilities experimentally, they do not influence the dryout by using a
142
simulation methodology which takes into account this period.
143
Finally, there are very few authors who have analyzed the effect of the geo-
144
metric characteristics of the samples. According to Ruffell [27], the helix angle,
145
¨ ϕ, strongly influences the first dryout and according to Unal et al. [18, 19],
146
if D/di ≥ 38.9, the geometry effect on the necessary power (Q˙ nec ) to achieve
147
the first dryout is negligible, but not the necessary power to achieve the total
148
dryout. Here it has analyzed both of them: ϕ ∈ [1.61, 2.36]◦ and D/di ∈ [15,
149
22] under different working conditions.
150
Considering this review, the objectives of this study are justified based on
151
the following ideas: it is difficult to distinguish which correlation/s among those
152
found in the literature are applicable to the ENEA prototype working conditions
153
for calculating local steam qualities associated with the dryout onset since not all
154
of them depend on the same factors (Naitoh’s, Berthoud and Jayanti’s, Ruffell’s,
155
and Santini’s. correlations, see expressions and applicability ranges in Table 1).
156
Perhaps, due to the fact that the employed wall heating methodologies are very
157
different. Limitation which, besides, was also detected by Santini et al. [28],
158
¨ Jensen et al. [23, 24, 25, 26], Unal et al. [18, 19] and Ruffell [27] in their works.
8
9
L = 1.709 m; di = 0.010 m; D = 0.136 m; pitch = 0.055 m
(upward or downward)
1984) [14]
Water/R12 (upward)
Water (upward)
Jayanti 1990) [16]
(Santini et al.
2014) [28]
do = 0.00635 m;
(upward)
(Berthoud &
L = 2 m; di = 0.00475 m;
1972) [13]
G ∈ [199, 810] kg·s-1 ·m-2
D = 1 m; pitch = 0.79 m
do = 0.01723 m;
P ∈ [10.7, 60.7] bar
Q ∈ [43.6, 209.3] kW·m-2
1 Helical coil L = 32m; di = 0.01253 m;
P ∈ [11, 200] bar
Q ∈ [10, 1800] kW·m
-2
G ∈ [100, 1900] kg·s-1 ·m-2
P ∈ [65, 240] bar
Q = 120 kW·m-2
G ∈ [500, 1800] kg·s-1 ·m-2
P ∈ [98.1, 176] bar
Q ∈ [100, 1500] kW·m-2
G ∈ [500, 1500] kg·s-1 ·m-2
xT ot
x1 = 103.235 ·
ρl ρv
v
v
Gravity zone −2.378 −1.712 · Gµldi · ρ
v
G √ g D
0.967 −0.740 · GQ ∆H
Redeposition zone 0.098 ! 0.067 −0.430 0.101 −0.785 q G di G · µl · ρ √ · GQ · µl Q∆H · g·(ρlσ−ρv ) ∆H g D
ρv ρl
x1 = 0.44 − 0.0006 · P · 10−5 · G0.114
v
G √ g D
0.08
Entrainment zone 0.119 −0.267 −0.984 0.950 −0.428 q G · Gµldi · ρ √ · GQ · µl Q∆H · g·(ρlσ−ρv ) ∆H g D
ρl ρv
—
—
CORRELATION
Total dryout 1.722 −0.494 2 −0.381 −1.61 ρl = log10 · µµvl · Gµldi · Gσ µdli · ρ ρv
x1 = 3.223 + log10
x1 = 107.068 ·
DRYOUT STEAM QUALITY CONDITIONS
D = [0.08-3.3] m
di = [0.008-0.02] m;
1 Helical coil
D = 0.09 m; pitch = 0.07 m
Straight tube vs. helical coil R12
(Cumo et al.
Straight tube vs. helical coil
Water
(Styrikovich et al.
GEOMETRY
FLUID
AUTHOR
vertical helical coils.
Table 1: Correlations for calculating local steam qualities associated with the dryout onset (first and total) in forced convective boiling flows in
10 Water (upward)
¨ ¨ Unal 1981, Unal
et al. 1981) [18, 19]
R113 (upward)
Jensen & Bergles 1981,
FLUID
1982, 1983) [23, 24, 25, 26]
(Jensen 1980,
AUTHOR
GEOMETRY
xT ot ∈ [0.55, 0.94]
0.1175 m; di /D = 0.0182,
ϕ = 7.77◦ , 8.83◦
pitch = 0.79 m;
D= 1.5 m, 0.7 m, 0.7 m;
xT ot ∈ [0.08, 1.00]
∆Tsub ∈ [35.6, 156.8] ◦ C
P ∈ [147, 202] bar
Q ∈ [41,731] kW·m-2
L = 40.13 m, 35.50 m, 26.67 m; di = 0.018 m;
G ∈ [112, 1829] kg·s-1 ·m-2
4 Helical coils
0.01270 m
pitch = 0.0254 m, 0.01588 m,
ϕ = 1.78◦ , 1.68◦ , 3.87◦ ;
0.0353, 0.0649;
∆Tsub ∈ [0,110] ◦ C
P = 9.4 bar
Q ∈ [54, 800] kW·m-2
G ∈ [570,5470] kg·s-1 ·m-2
CONDITIONS
D = 0.4096 m, 0.2159 m,
do =0.00777 m, 0.00769 m;
di =0.00762 m, 0.00744 m;
heating length);
1.295 m, 1.257 m (wall
L = 0.635 m, 1.27 m,
3 Helical coils
, if G > 950 kg· m-2 · s-1
, if G ≤ 950 kg· m-2 · s-1 di 0.31 D
di 0.17 D
PIN IN a1 = 1 + 3.8 · 1 − HHSAT ; a2 = 0.114 − 0.041 · log 1 − P cri −1/2 L a3 = 1 + 4.59 · deq ; Leq = πAdGQ · (HSAT − HIN + ∆H · x) i n o n o a41 = 1 + 0.44 · exp −0.056 · dDi − exp − 3dD , 1st dryout i n o n o a42 = 1 + 0.56 · exp −0.011 · dDi − exp − 3dD , Total dryout i 0.32 Leq 2 (d0 −di ) 0.22 a5 = , a6 = di + 28 · F r , a7 = 1 di
3 ·a41 ·a5 Q = G · ∆H · 0.97 · a1 ·a2a·a6 ·a , 1st dryout 7· a1 ·a2 ·a3 ·a42 ·a5 Q = G · ∆H · 0.97 · , Total dryout a6 ·a7 ·
Q = G · ∆H · 1.7126 · 105 · Re−1.143 · x−0.436 · T ot
Q = G · ∆H · 4.09 · 10−6 · Re0.50 · x−0.460 · T ot
CORRELATION
11
Water (upward)
Water (upward)
Water (upward)
(Naitoh et al.
1974) [15]
(Duchatelle et al.
1975) [22]
(Ruffel et al.
1974) [27]
G ∈ [300, 1800] kg·s-1 ·m-2
3 Helical coils
D = 0.58 m, 1.32 m, 2.36 m
length); di = 0.0125 m;
P up to 180 bar*
Q/G ∈ [0.06, 0.34] J·G-1
P ∈ [45, 175] bar
0.011, 0.007
L = 8.2 m (wall heating
Q ∈ [310, 1500] kW·m-2
G ∈ [375, 3500] kg·s-1 ·m-2
P up to 175 bar
CONDITIONS
di /D = 0.032, 0.025,
4 Helical coils
di /D=0.0165
GEOMETRY
*Although it was also validated for other working conditions by means of modeling.
FLUID
AUTHOR
0.13·(D/(100·di )) (G/103 )1.5
·
Q 100
x1,270◦ = 1 − 0.0004 · Q − 0.0109 ·
x1,0◦ = 1 −
G 2 103
·
D di
0.5
0.75·(G/103 )0.5
xT ot = 1.39 · 10−4 · Q0.732 · G−0.209 · exp 2.46 · 10−3 · P · 10−5
xT ot = 1 + (0.139 − 0.071 · (P · 10−5 )0.186 ) · (Q · 0.85986 · 10−5 )
CORRELATION
159
3. ENEA experimental setup
160
ENEA prototype is a 2 m diameter and 2.8 m height thermal storage tank
161
whereby the hot molten salts enter through the upper side of the tank. Inside it,
162
there are 12 tons mixture of inorganic molten salts, commonly known as “solar
163
salt”: NaNO3 and KNO3 (60/40 % by weight), under atmospheric pressure. The
164
integrated steam generator is vertically and non-symmetrically arranged within
165
the tank. It consists of two concentric cylindrical shells, called “downcomer”
166
and “shell”, and three in-line helical coils, referred as #1, #2 and #3 (coil/tube
167
characteristics: see Table 2) comprised in the space between shells (Figure 3).
168
For additional information about the prototype setup consult [29] and [30].
Figure 3: ENEA experimental setup
169
During discharge tests, the pressurized water flowing within the tubes changes
12
170
phase due to the heat transfer with the molten salts at counterflow circulation
171
through the space between shells and tubes. Therefore, the highest thermal
172
hydraulic gradients within the prototype happen here and thus, the involved
173
phenomenology intrinsically depends on the steam generator geometry. Table 2: Design characteristics of the integrated steam generator (Source: ENEA).
GEOMETRIC FEATURE
VALUE (Unit)
External tube diameter, do
0.0127 m
Internal tube diameter, di
0.0094 m
Horizontal pich, Xhor
0.0162 m
Vertical pich, Xver
0.0180 m
Helical coil diameters, D1
0.2038 m
Helical coil diameters: D2
0.1714 m
Helical coil diameters: D3
0.1390 m
174
The shells have a thermal insulating function: the downcomer allows the
175
water to arrive the lower part of the generator without directly exchanging heat
176
with the molten salts (thus, water-steam phase change happens upwards) and
177
the shell separates the molten salts circulating though the generator from the
178
molten salts tank bulk. Finally, it has a window at the top, through which the
179
hot molten salts go into the generator, and a diffuser at the bottom, through
180
which the cold molten salts depart the generator.
181
Its operating mode during discharge tests is as follows: the water flow is
182
established by a pump belonging to an external loop; that is the reason to talk
183
about forced convective boiling in the water-steam side. With this operating
184
mode, the coming out fluid is superheated steam, saturated steam or subcooled
185
water, depending on the thermal conditions of the tank. Molten salts circulate
186
through the existing gaps in the tubes matrix by gravity. Their driving force is
187
gravity when go through the generator, since they increase their density while
188
they cool down because heat exchange with the tubes matrix where the pres-
189
sured water flows at a lower temperature than molten salts. This process causes 13
190
the molten salts tank stratification, i.e., it promotes the development of a cold
191
zone at the tank lower part, coming from the salts that have gone through the
192
generator, a hot zone at the tank upper part, and an intermediate zone, which
193
thickness depends on the tank thermal conditions (see Figure 4). In summary,
194
during discharge tests, there is a continuous natural circulation of molten salts
195
which transports heat from the source (molten salts) to the sink (water-steam).
196
Such molten salts natural circulation will slow down as the discharge evolves
197
due to the gradual decrease of the buoyancy forces. This is the reason to talk
198
about molten salts transient mass flow rate. This gradual decrease is the result
199
of the progressive difference height decreasing between the respective hot molten
200
salts columns from the source and the sink, ∆L, during discharge, i.e, in Figure
201
4, ∆L7050s > ∆L10650s .
Figure 4: Simplified temperature field at two times, t7050s (left) and t10650s (right) during a discharge test [29]. Arrows indicate the molten salts inlet/outlet.
202
The heat transfer between molten salts and water-steam is less efficient as
203
discharge evolves. Consequently, as the discharge evolves, the two-phase flow
204
length on the steam generator increases (in Figure 4, z7050s < z10650s although
205
this two-phase flow length may be different on each helical coil). This fact can
206
affect the dryout onset depending on the helical coil diameter. In order to check
207
this influence, a CFD model has been developed and validated with the different 14
208
variables measured in the prototype at ENEA. This analysis has not yet been
209
reported on the available bibliography and could be of interest for developers of
210
this type of steam generator technology.
211
4. CFD modelling
212
4.1. Geometry and mesh models
213
CFD model is focused on the steam generator. Geometrically is a 3D full-
214
R scale model made by means Autodesk Inventor Professional 2016 (helical coils
215
R design) [31] and STAR-CCM+9.04.011 CAD module (downcomer, shell, win-
216
dow and diffuser design) [11], see Figure 5.
Figure 5: Steam generator geometric model, perspective views: outer view: shell, window and diffuser (top); intermediate view: helical coils (center) and inner view: downcomer (bottom).
15
217
Downcomer, shell, window and diffuser have been assumed un-thickness and,
218
in addition, adiabatic elements. Although window and diffuser are metal ele-
219
ments (with high thermal conductivity), their influence on the water-steam be-
220
haviour in the helical tubes has been considered negligible because they are far
221
enough.
222
The geometric domain is divided into three subdomains: the water-steam
223
side, the molten salts side, and the helical coils walls, which separate both media.
224
Therefore, the model allows to study the thermohydraulic behavior of molten
225
salts circulating by the space existing between helical coils and shells and water-
226
steam flowing within the tubes simultaneously.
227
They have been discretized by means of a polyhedral cells meshing (see
228
Figure 6). The maximum characteristic sizes in molten salts and water-steam
229
sides are 0.0050 m and 0.0025 m respectively, although meshing includes some
230
refinements in the narrower zones with, at least, two polyhedral cells by gap.
231
Both subdomains take account with a prismatic layer, single in the first
232
case and double in the second, on their respective boundaries (i.e. shell and
233
tubes, in molten salts side; and tubes, in water-steam side), which maximum
234
characteristic sizes are 0.00250 m and 0.00125 m respectively (see Figure 6).
235
The transition between prismatic layers (smaller cells) and polyhedral bulks
236
(larger cells) has been carried out gradually (by a 1.5 factor). Also, a double
237
uniform prismatic layer has been included filling the helical coils walls thickness
238
(see Figure 6).
239
The mesh has been made using the automatic tool of STAR-CCM+ 9.04.-
240
R 011 . The total number of cells is around 7.2·106 ; from which 32 % belong to
241
molten salts side, 45 % belong to water-steam side and 23 % belong to helical
242
coils walls.
16
Figure 6: Mesh model detailed view: molten salts side in yellow, helical coils walls in grey and water-steam side in blue.
243
In order to ensure numerical results are mesh model independent, a test
244
varying the maximum characteristic size only in water-steam side has been car-
245
ried out (the molten salts mesh model was already evaluated by Rivas and Rojas
246
[29]). The results are summarized in the following table (Table 3) and they are
247
satisfactory for “coarse” and “medium” mesh models. Table 3: Mesh model test: some numerical results at t¯7050s .
Total number of cells Characteristic size (m)
COARSE
MEDIUM
FINE
Reference Value
≈ 6.9·106 (97 %)
≈ 7.2·106 (100 %)
≈ 8.5·106 (119 %)
—
0.00375
0.00250
0.00150
—
PIN,1 (bar)
39.0
39.0
38.5
39.2
PIN,2 (bar)
39.0
39.0
38.7
39.2
PIN,3 (bar)
39.1
39.1
39.0
39.2
zx1 ,3 Y+ water-steam side
1.16
1.16
1.13
—
50-500
50-300
10-60
Recommended: < 1 or > 30
248
As can be seen, the finest mesh (referred in Table 3 as “fine”) presents
17
249
the worst numerical results of some variables of interest to this work as the
250
inlet pressure to each helical coil, {PIN,# }#=1,2,3 . It is due to the used wall
251
treatment “All Y+”. For this mesh model, the wall treatment dependency
252
with the prismatic layer size on boundaries implies unsuitable values of the Y+
253
in water-steam side (values between 1 and 30, [32, 33]) to assess adequately
254
the turbulent variables (shear stress, turbulence kinetic energy and turbulent
255
dissipation rate), on such boundaries. Since, to make a finer mesh to solve
256
this problem and thus, to obtain suitable values of the Y+ (values less than
257
1, [32, 33]), would be a very time consuming task from the computational cost
258
point of view and coarser meshes present equally suitable inlet pressure results
259
(absolute errors between 0.1 bar and 0.2 bar), they have been selected. Besides,
260
with these coarser meshes (“medium” and “coarse”), similar values of the first
261
dryout z-location in helical coil 3, zx1 ,3 , have been obtained. Therefore, the finer
262
mesh of both (“medium”) has been chosen because its computational cost did
263
not differ too much from the “coarse” mesh (3 %). Colombo [34] drew similar
264
conclusions regarding finer meshes when this type of wall treatment is used.
265
266
In addition, the available experimental data allow to evaluate the chosen mesh model making needless a more exhaustive test.
267
Finally, a mesh topological diagnosis has been conducted using the statistical
268
parameters (volume change, cell quality, face validity y cell and boundary skew-
269
ness angle) established by the software developer [33]. The results are shown in
270
the following table (Table 4). Table 4: Topological diagnosis of “medium” mesh.
MINIMUM VALUE
MAXIMUM VALUE
Cell and boundary skewness angles
0◦
89◦
Face validity
1
1
Cell quality
0.01
1
0.0004
1
Volume change
271
All obtained values are within the ranges which ensure the good quality of
18
272
the mesh, according to the information provided by the software developer [33].
273
All the above following the standards established in Best Practice Guidelines
274
for a suitable use of CFD codes in the industrial field, [35].
275
4.2. Physical models
276
To study the thermohydraulic behavior of the system, a conjugated steady-
277
state heat transfer model has been employed. This model takes into account
278
natural circulation in molten salts, conduction through helical coils walls and
279
forced convective boiling in water-steam.
280
Both external molten salts and internal water-steam flows are considered
281
turbulent flows. Although salts circulate by natural convection through the
282
generator and, therefore, they move slowly, the generator geometry strongly
283
disturbs their motion, generating complex circulations around helical coils which
284
do not allow simulating a laminar flow. However, water-steam flows by forced
285
convective boiling within the tubes, so, during the phase change turbulent is
286
promoted and upstream the flow is fully developed.
287
Both of them are simulated using a “RANS model” (Reynolds-Average
288
NavierStokes) whose closure is made using the “Realizable κ − Two Layer
289
model” [32, 33], considering the approximations of Xu for molten salts (suitable
290
for buoyancy driven flows, [36, 33]) and Wolfstein for water-steam (suitable for
291
shear driven flows, [37, 33]), together with the hybrid wall treatment “All Y+”.
292
For the turbulent model, constants pre-established by the software developer
293
have been assumed. The flow is solved in a segregated way, and the nexus
294
between mass and momentum equations is made via the “SIMPLE algorithm”
295
with the Rhie-Chow interpolation [32, 33]. To solve the energy equation a segre-
296
gated model has been assumed (for the variables: temperature, in molten salts
297
and enthalpy, in water-steam).
298
Boussinesq approximation has been assumed in molten salts side [29]. The
299
rest of molten salts thermophysical properties have been considered temperature-
300
dependent [38].
301
The helical coils walls properties were considered constant and uniform, and 19
302
the pre-established values by the software developer for a stainless-steel type
303
UNSS316 [33] have been assumed.
304
4.2.1. Two-phase flow model description
305
To simulate the two-phase flow, a homogeneous model is employed. It solves
306
a single set of transport equations assuming the two-phase flow as a single-
307
phase flow with equivalent or mixture thermophysical properties. These ones
308
are calculated from the thermophysical properties of each phase and their corre-
309
sponding volume fractions, based on a homogeneity hypothesis. This two-phase
310
flow treatment is commonly used in industrial applications such as steam gener-
311
ators [33]. Its main advantage versus other models, which simulate each phase
312
separately, is its computational efficiency. The principal assumptions of this
313
model are: a) both phases flow at the same velocity (the slip between phases is
314
negligible) and b) both phases are in thermal equilibrium.
315
316
Two phase flow mass, momentum and energy equations, in integral form, are: ∂ ∂t
Z
Z
Z ρm vm · dS =
ρm dV + V
S
Sm dV
(3)
V
317
∂ ∂t
Z
Z ρm vm dV +
V
S
Z ρm vm ⊗ vm · dS = − P I · dS S Z Z + Tm · dS + (fg + sm ) dV S
(4)
V
318
∂ ∂t
Z
Z
Z (ρm Hm vm + P ) · dS = − Q · dS S ZS Z + Tm · vm · dS + (fg · vm + Sh ) dV
ρm Em dV + V
S
(5)
V
319
where mixture density and mixture velocity, ρm and vm , are defined as
320
function of densities and velocities of liquid phase and vapor phase respectively
321
(ρl , ρv , vl , vv ) as:
ρm = (α ρl + (1 − α) ρl ); vm = 20
(α ρl vl + (1 − α) ρv vv ) ρm
(6)
322
323
being: Sm , sm and Sh mass, momentum and energy sources, fg the gravity force, I the unitary tensor and Tm viscous stress tensor, calculated as: 2 T (∇vm + ∇vm ) − (∇ · vm ) I 3
Tm = µef f 324
where µef f is the mixture effective viscosity, given by:
µef f = µt + µm 325
326
being µt the turbulent viscosity, computed as ρm 0.09
(8) κ2
and µm the mixture
viscosity, which is defined as:
µm = (α µl + (1 − α) µv ) 327
329
P |vm |2 ; Hm = hm − ρm 2
phase and vapor phase enthalpies respectively (hl , hv ): 1 (α ρl hl + (1 − α) ρv hv ) ρm
332
334
(12)
where kef f,l and kef f,v are the effective thermal conductivities of the liquid phase and vapor phase respectively, given by:
kef f = k − 333
(11)
And the heat flux vector Q is calculated as:
Q = − [α kef f,l + (1 − α)kef f,v ] · ∇T 331
(10)
where hm is the mixture static enthalpy determined as function of liquid
hm = 330
(9)
The mixture energy Em and the mixture enthalpy Hm are defined as:
Em = Hm − 328
(7)
µt CP P rt
(13)
being, k the thermal conductivity, CP the specific heat and P rt the turbulent Prandtl number of such phases.
335
The distribution of phases, that is, the volume fraction, α, is not obtained
336
by solving a transport equation, but from the distribution of static enthalpy 21
337
under the assumption of thermodynamic equilibrium. In this case, the steam
338
quality, x, is given by the next function:
hm − hl,sat x = max 0, min 1, hv,sat − hl,sat 339
340
341
342
phase, respectively, at the saturation temperature Tsat . And finally, considering the above approaches, the steam volume fraction α can be defined as: x x + (1 − x)
344
(14)
where hl,sat and hv,sat are the static enthalpies of liquid phase and vapor
α=
343
ρv,sat ρl,sat
(15)
where ρl,sat and ρv,sat are the densities of liquid phase and vapor phase, respectively, at the saturation temperature Tsat .
345
The Rohsenow model [39, 33] is used to simulate the heat transfer through
346
the helical coils walls. This model is based on the following hypothesis: during
347
the phase change heat transfer through the walls takes place, either by nucleated
348
boiling or by film boiling.
349
Nucleated boiling occurs when walls temperature is slightly above the satu-
350
rated liquid temperature and involves the bubble nucleation at walls.
351
Here it is assumed nucleated boiling is present even within the annular liquid film
352
regime (this assumption is appropriate at relative low flow rates and sufficient
353
wall superheats, [40]). The bubbles nucleation depends on the walls roughness.
354
In this case, smoothed walls have been assumed. A wall finish type 2B (EN
355
10088-2, [41]) has been considered and, in the working conditions range (3 ·
356
104 < Re < 2 · 105 ), we have checked the flow behavior is hydraulically smooth
357
(although this check is outside of the scope of this work).
358
However, film boiling involves the creation of a continuous vapor film cover-
359
ing the helical coils walls when the critical heat flux is exceeded. Vapor film has
360
a low thermal conductivity, which isolates the walls decreasing the heat transfer
361
process considerably.
22
362
363
To calculate the heat flux during nucleated boiling, the model employs the Rohsenow correlation [39, 33]: r Q = µl hlat
g(ρl − ρv ) σ
CP,l (Tw − Tsat ) n Cqw hlat P rl p
3.03 (16)
364
In equation: µl , hlat , CP,l , ρl , y P rl are the viscosity, boiling enthalpy,
365
specific heat, density and Prandtl number of liquid phase respectively, np is a
366
model coefficient which depends on the working fluid (in this case, it is assumed
367
1, [42]), g is the gravity, ρv the vapor phase density, σ the surface tension on
368
water-steam interface, Tw the walls temperature, Tsat the saturation tempera-
369
ture and Cqw is a model coefficient which depends on the combination working
370
fluid-helical coils walls (it is assumed 0.013, [42]).
371
This correlation is applicable to any type of geometry since it does not
372
depend on it (neither on its orientation). It is based on the hypothesis the
373
agitation of the bubbles is the heat transfer mechanism controlling the nucleated
374
boiling, and it is formulated as a single-phase flow in forced convection.
375
To calculate the heat flux during film boiling, the model uses the same
376
equations as in the case of a single-phase flow of superheated steam. The model
377
coefficient which controls the transition between both regions is αf ilmBoiling .
378
If it is not possible to have a fine enough mesh to solve the steam film thick-
379
ness (as happens in this case), αf ilmBoiling should be explicitly given. Here,
380
a αf ilmBoiling = 1 has been assumed because, by means a sensibility analy-
381
sis (comparing the obtained results for αf ilmBoiling = 0.8, 0.95, 0.99, 1), we
382
have checked this value provided the best numerical results of some variables of
383
interest to this work.
384
Finally, for calculating water-steam thermophysical properties, the IAPWS-
385
IF97 models [43] have been used. These ones provide the fundamental equation
386
for the specific Gibbs free energy from which, using appropriate combinations
387
and their derivatives, it is possible to deduce the specific volume, internal energy,
388
entropy, enthalpy, specific heat and the sound velocity of water-steam.
23
389
4.2.2. Two-phase flow model justification
390
Currently, the two -phase flow mechanistic approaches (those which first
391
determine the existing two-phase flow pattern for certain given conditions and
392
then formulate separate hydrodynamic models for each of them) are the most
393
commonly used approaches according to the CFD codes state-of-the-art, but
394
some limitations and shortcomings have been found for its applicability to this
395
work as:
396
• they need a minimal number of coefficients which require calibration against
397
experimental data [44]. For example, in StarCCM+ it is possible imple-
398
ment different models, but all of them depend on specific submodels to
399
correctly capture: the nucleation site density, bubble departure frequency,
400
bubble departure diameter, quenching heat transfer coefficient, etc. [33].
401
Furthermore, solving this set of equations entails assuming higher compu-
402
tational costs and,
403
• they have an intrinsic dependence on the near-wall mesh [45, 46]. This
404
is due to these submodels were originally formulated for one-dimensional
405
thermo-hydraulic models in terms of the mean-flow variables. The imple-
406
mentation of these submodels as CFD wall boundary conditions assumes
407
replacing the non-local flow quantities by the near-wall local flow quanti-
408
ties. And, it can only be done for extremely coarse meshes, with the first
409
near-wall cell covering the whole boundary layer thickness. With a near-
410
wall mesh, which is adequate for the CFD turbulent wall treatment, such
411
approximation can significantly overestimate the vapor generation [47].
412
For these reasons and because:
413
• from the experimental point of view, the Roshenow correlation has been
414
tested for a wide range of working fluids on cylindrical surfaces and ma-
415
terials [48] and,
416
• from the numerical point of view, the homogeneous boiling model together
417
with the Roshenow correlation implemented in StarCCM+, have been 24
418
already successfully used in other cases to predict the forced convection
419
boiling flows behavior, for example [49], [50], and [51],
420
in this work, this semi-empiric approach has been chosen to simulate the two
421
-phase flow.
422
4.2.3. Two-phase flow model benchmarking
423
Since the experimental setup does not have other direct measurements in
424
water-steam side than inlet water and and outlet steam temperatures to each
425
helical coil ({TI 8 20#}#=1,2,3 and {TI 8 21#}#=1,2,3 respectively, Figure 3),
426
and no adequate experiments have been found in the literature about vertical
427
helical tubes to assess the two-phase flow model performance along the coils,
428
reference experiments on vertical straight tubes have been used here, as some
429
authors have already done in their works about vertical helical tubes (for exam-
430
ple [52]).
431
The experiments are those carried out by Bartolomei et al. [53], explained
432
and analyzed in [54], and Bartolomei and Chanturiya [55]. These tests, classified
433
in the literature as “surface boiling experiments”, are commonly used for boiling
434
models benchmarking [56].
435
Bartolomei et al. measured the average void fractions at different heights
436
along vertical straight tubes, in which the water-steam phase change happened
437
upwards. The test sections walls were uniformly heated and all the experiments
438
were carried out with subcooled water at the tube inlets.
439
Here, two test sections have been considered: the first one with tube diameter
440
of 12.03 mm and total tube length of 1.4 m (heated length of 1 m) and the second
441
one with diameter of 24 mm and total tube length of 2.4 m (heated length of 2
442
m). And two experiments in each of them.
443
The working conditions of these experiments are summarized in Table 5.
25
Table 5: Bartolomei et al. experiments working conditions.
Ref.
Experiment
Q (MW·m-2 )
m ˙ ws (kg·s-1 )
∆Tsub (K)
POU T (bar)
1
1.2
0.1705
63
68.9
2
0.8
0.1705
39
68.9
3
7.9
0.4026
48
45
4
7.9
0.4026
50
30
[53, 54]
[56]
444
As can be seen, they combine different values of boundary heat flux (Q),
445
mass flow rate (m ˙ ws ), inlet subcooling (∆Tsub ) and the outlet pressure (POU T ).
446
Using the mesh model described in section 4.1, a sensitivity study has been
447
carried out once again in order to ensure numerical results are mesh model
448
independent.
449
First, a benchmarking between the two-phase flow model and a mechanis-
450
tic type model implemented in STAR-CCM+, [56], is carries out. Results of
451
experiments 1 and 2 are employed for it.
452
453
The comparison between observed and simulated average void fractions along the first test section are shown in Figure 7.
Figure 7: Average void fraction as function of distance along the first test section.
454
The benchmarking is calculated by means of the statistical parameters: cor-
455
relation coefficient (R), normalized mean square error (N M SE), fractional bias
456
(F B) and fraction of prediction within a factor of two of observations (F AC2) 26
457
(see Appendix for definitions). A perfect model would have R, F AC2 = 1 and
458
N M SE, F B = 0.
459
460
In Table 6, these parameters for the average void fractions along test sections are shown. Table 6: Statistical parameters comparing the average void fractions models results with the measured data by Bartolomei et al. All of them are dimensionless.
EXPERIMENT 1
EXPERIMENT 2
NMSE
FB
FAC2
R
NMSE
FB
FAC2
R
SIMULATION
0.063
-0.041
0.750
0.931
0.149
-0.217
0.917
0.952
MECH.MODEL
0.075
0.027
0.750
0.960
0.092
0.122
0.917
0,974
461
In general, there is a good agreement for both cases. The N M SE and F B
462
have the same order of magnitude (note that the negative F B values indicate
463
a general model overestimation), the F AC2 are similar and the R are high for
464
both cases. Although the mechanistic model shows slightly better results.
465
466
Hence, it could be assumed that the approximations made on the watersteam side are a good compromise for this case.
467
Second, a comparison between the Bartolomei et al. experimental results,
468
which working pressures are closer to those of the ENEA prototype, and the nu-
469
merical results obtained with the two-phase flow model is is addressed. Results
470
of experiments 3 and 4 are used for it.
471
472
In Figure 8, observed and simulated average void fractions along the second test section are shown.
27
Figure 8: Average void fraction as function of distance along the second test section.
473
As can be appreciated, the two-phase flow model:
474
• has reasonably captured the boiling beginning in both cases,
475
• has correctly reproduced the average void fraction profiles: during experi-
476
ment 3 with an average relative error (RE) of 33 % and during experiment
477
4 with an average RE of 22 %, comparable to those showed by some mech-
478
anistic models for the average void fraction calculus, for example [52], [56]
479
and [57].
480
Finally, by means CFD simulations the dryout z-location on test sections
481
can be directly determined from steam quality azimuthal distributions on their
482
walls. Here, the simulated dryout z-location along the second test section has
483
been observed, during experiment 3, on zx = 1.8 m and, during experiment 4,
484
on zx = 2 m.
485
Therefore, considering all the above and given the objectives of this work, it
486
is concluded that this model seems suitable to describe the two-phase flow up
487
to the dryout.
488
4.3. Boundary conditions and simulation methodology
489
The model boundary conditions are established:
490
• firstly, from direct and indirect measurements obtained during a discharge
491
test of the thermal storage prototype; 28
492
• secondly, from the obtained results by means of a pressure drop model in
493
water-steam side. The main pressure drop model hypothesis is that the
494
thermohydraulic instabilities strongly evidenced in the mass flow rates
495
during discharge did not affect the dryout and, therefore, an average be-
496
havior of them can be assumed.
497
The discharge test of October 29th , 2012 has been used. This test was devised
498
and carried out by researchers and technicians from ENEA and provided to the
499
OPTS project partners to development different tasks. Briefly, it takes 10400
500
s and comprises three intervals (see Figures 9 and 10): the first one, from the
501
1650 s to 5250 s (left red area), is a transient interval to achieve the test nominal
502
conditions (PIN ≈ 39 bar, ∆Tsub ≈ 0 y m ˙ ws ≈ 0.082 kg/s), the second one, from
503
the 5250 s to 11350 s (central green area), is a quasi-stationary interval, and
504
the third one, from the 11350 s to 12050 s (right red area), is also a transient
505
interval to get the safe shutdown conditions (PIN ≈ 0 bar, ∆Tsub ≈ 0 y m ˙ ws ≈
506
0 kg/s). Figures 9 and 10 show some measurements during the test.
Figure 9: Temperatures (on both sides) and mass flow rate of molten salts during the test of October 29th , 2012 (in red, transient intervals and in green quasi-stationary interval).
29
Figure 10: Individual pressures and total mass flow rate of water-steam during the test of October 29th , 2012 (in red, transient intervals and in green, quasi-stationary interval).
507
In particular, in Figure 9 direct measurements are: inlet water temperature
508
to each helical coil, {TI 8 20#}#=1,2,3 , and molten salts temperature at steam
509
generator inlet, TI 8 111.
510
511
And indirect measures are: molten salts mass flow rate through steam generator, m ˙ ms , which is calculated by the following energy balance: ¯ OU T − H ¯ IN ) m ˙ ws (H m ˙ ms = ¯ CP,ms (TI 8 111 − TI 8 110)
(17)
512
¯ IN and H ¯ OU T , the where m ˙ ws is the total water-steam mass flow rate; H
513
average enthalpies of inlet water and outlet steam respectively and C¯P,ms the
514
molten salts average specific heat in the temperature range.
515
Inlet water average turbulent kinetic energy and inlet water average turbu-
516
lence dissipation rate to each helical coil, {k¯IN# }#=1,2,3 and {¯ εIN# }#=1,2,3 , are
30
517
given by the expressions [32]: 3 k¯IN# = 2
v¯IN#
I¯IN#
2
; ε¯IN# =
Cµ3/4
3/2 k¯IN#
di
(18)
518
where {¯ vIN# }#=1,2,3 is the inlet water average velocity and {I¯IN# }#=1,2,3
519
the inlet water average turbulence intensity to each helical coil. Cµ a turbulence
520
model constant pre-established by the software developer [33]. In this case, an
521
inlet fully developed flow has been assumed to each helical coil, so: ¯ −1/8 I¯IN# = 0.16 Re IN#
522
523
(19)
¯ IN }#=1,2,3 the inlet water average Reynolds number to each hebeing {Re # lical coil, based on di [32].
524
Molten salts average turbulent kinetic energy and molten salts average tur-
525
bulence dissipation rate at steam generator inlet have been considered negligible
526
because they are far enough from the studied area.
527
Finally, obtained measurements from pressure drop model are the outlet
528
steam pressures to each helical coil, {POU T# }#=1,2,3 (Figure 10). Since, the
529
simulation computational cost of the entire discharge interval is very high, the
530
following methodology has been adopted.
531
• Firstly, two times within the quasi-stationary interval has been select,
532
denoted by t7050s and t10650s (see Figures 9 and 10). These, have been se-
533
lected because, on the one hand, they are far enough from the startup/shutdown
534
intervals to assume negligible their transient effects and, on the other hand,
535
from t7050s to t10650s , molten salts mass flow rate decreases up to a 12 %,
536
which allows to study its influence on the dryout. Each selected time
537
belongs to a two-phase flow instability cycle. These instabilities can be
538
seen within the time evolution of inlet water temperatures and pressures,
539
{TI 8 20#}#=1,2,3 and {PIN# }#=1,2,3 and in outlet steam temperatures
540
and pressures, {TI 8 21#}#=1,2,3 and {POU T# }#=1,2,3 (see Figures 9 and
541
10).
31
542
• Secondly, the representative cycles of each selected time, denote by t¯7050s
543
and t¯10650s , have been made and simulated. Taking into account the
544
measured instabilities period is 20 s (compatible with Naitoh et al. results
545
[26]), for example, t¯7050s is made by averaging the measurements between
546
(t7050s − 10 s) and (t7050s + 10 s), and the associated uncertainties have
547
been assumed as the standard deviations in such interval.
548
Finally, the numerical approach provides a second order precision in the
549
spatial resolution of main conservation equations. These have been carried out
550
R R in 12 nodes DELL M630 of 20 cores Intel Xeon [email protected] by
551
node, with processing times about 26 hours by simulation.
552
5. Model evaluation
553
The model evaluation conditions are established from direct and indirect
554
measurements during the test and pressure drop model results, taking into ac-
555
count the methodology described above.
556
In particular, direct measurements are: outlet steam temperature to each
557
helical coil, {TI 8 21#}#=1,2,3 , molten salts temperature at steam generator
558
outlet, TI 8 110 (see Figure 9) and local wall temperatures along helical coil
559
3, {TI 8 3n1}n=0,1,...,9 , corresponding to heights {zn }n=0,1,...,9 (see Figure 11).
560
These last, considering a local reference system in polar coordinates centered in
561
such helical coil, {r3 , θ3 }, are always in the same position: r3 = do and θ3 = 0.
562
˙ is the And, the exchanged power between molten salts and water-steam, Q,
563
indirect magnitude, calculated using the following expression: ¯ OU T − H ¯ IN ) Q˙ = m ˙ ws (H
564
565
566
567
(20)
¯ IN and H ¯ OU T , the where m ˙ ws is the total water-steam mass flow rate; H average enthalpies of inlet water and outlet steam respectively. The obtained magnitudes from pressure drop model are inlet water pressures to each helical coil, {PIN# }#=1,2,3 (Figure 10).
32
Figure 11: Wall thermocouples distribution along the internal helical tube (left) and zoom of the n-th (right)
568
In Table 7, simulated and observed outlet steam temperature to each heli-
569
cal coil, {TI 8 21#}#=1,2,3 , and molten salts temperature at steam generator
570
outlet, TI 8 110, are shown at t¯7050s and t¯10650s , as well as, the corresponding
571
uncertainties. Table 7: Comparison between simulated and observed temperatures.
t¯7050s
t¯10650s
Simulated
Observed
Simulated
Observed
476
475 ± 2
470
469 ± 2
TI 8 212 ( C)
476
470 ± 2
468
459 ± 2
TI 8 213 (◦ C)
475
474 ± 2
466
467 ± 2
305
305 ± 2
277
278 ± 2
TI 8 211 (◦ C) ◦
◦
TI 8 110 ( C)
33
572
As can be seen, simulated temperatures fit well with observed at both times.
573
Nevertheless, there is a slight overestimation in helical coil 2 (possibly, due to a
574
thermocouple placement error). Therefore, it could be said the model correctly
575
captures the global thermal behavior, both the molten salts and the water-
576
steam, within the quasi-stationary interval.
577
In Table 8, simulated and observed exchanged power between molten salts
578
and water-steam are shown at t¯7050s and t¯10650s . In this table, the corresponding
579
uncertainties are not presented due to its calculation difficulty. Table 8: Comparison between simulated and observed exchanged powers.
t¯7050s Q˙ (W)
t¯10650s
Simulated
Observed
Simulated
Observed
189834
192114
189023
189663
580
As can be observed, there is a good agreement between numerical and ex-
581
perimental results at both times, with differences of 2280 W in the first time
582
(equivalent to 1.2 % of percent error) and of 640 W in the second one (equivalent
583
to 0.3 % of percent error). Thus, it could be also claimed the model correctly
584
captures the total heat transfer between molten salts and the water-steam within
585
the quasi-stationary interval.
586
Simulated and observed inlet water pressures to each helical coil, {PIN# }#=1,2,3 ,
587
at t¯7050s and t¯10650s , as well as, the corresponding uncertainties are shown in
588
Table 9. Table 9: Comparison between simulated and observed pressures.
t¯7050s
t¯10650s
Simulated
Observed
Simulated
Observed
PIN1 (bar)
39.0
39.2 ± 0.6
37.3
37.9 ± 0.6
PIN2 (bar)
39.0
39.2 ± 0.6
37.5
37.9 ± 0.6
PIN3 (bar)
39.1
39.2 ± 0.6
37.6
37.9 ± 0.6
34
589
As can be appreciated, simulated pressures fit well with observed ones at
590
both times. So, the model properly captures the water-steam global hydraulic
591
behavior within the quasi-stationary interval.
592
In Figure 12, local wall temperatures along helical coil 3, {TI 8 3n1}n=0,1,...,9 ,
593
observed measurements (filled dots) and simulated values (empty dots) at t¯7050s
594
(in red) and t¯10650s (in blue) are shown, as well as, the corresponding uncer-
595
tainties.
Figure 12: Observed and simulated local wall temperatures (helical coil 3).
596
597
It is shown, simulated local wall temperatures fit well with observed up to heights: z5 at t¯7050s and z3 at t¯10650s .
598
From it, the model overestimates the wall heating. It is probably due to this
599
model is not suitable to completely describe the water-steam phase change in
600
this case, as it had been advanced during the benchmarking when average void
601
fractions were high.
602
As has been mentioned before, the experimental setup does not have other
603
direct measurements in water-steam side than those already used for validation. 35
604
In this case, it is logical because, on the one hand, “traditional” measure-
605
ments generally are invasive techniques (such as the use of thermocouples, etc.)
606
and, given the coils dimensions, they would strongly disturb the two-phase flow
607
masking its local phenomenology and, on the other hand, more “sophisticated”
608
measurements, generally non-invasive techniques (such as the use of X-rays,
609
etc.), would not be techno-economically viable.
610
At the dryout onset, the cooling of the walls drastically modifies because
611
they change from being: liquid wetted walls to steam wetted walls. This causes
612
a sharp decrease of local heat transfer coefficients causing a poor fluid-structure
613
thermal response. It implies a local increase of walls temperature regarding to
614
the downstream walls temperature [10].
615
Thus, using a wall thermocouples distribution along the tubes can be con-
616
sidered a non-invasive technique for indirect measure the dryout z-localization
617
(as it is stated, for example, in [58]).
618
619
Here, from the helical coil 3 wall thermocouples distribution, the dryout onset in such helical coil has been experimentally determined.
620
As can be observed in Figure 9, the first increase of walls temperature is
621
between heights: z6 y z5 (TI 8 361 − TI 8 351 = 71 ◦ C) at t¯7050s and, z4 y z3
622
(TI 8 341 − TI 8 331 = 69 ◦ C) at t¯10650s .
623
However, by means CFD simulations the dryout z-location, both first dryout,
624
zx1 ,3 , and total dryout, zxT ot ,3 , on such helical coil can be directly determined
625
from steam quality azimuthal distributions on walls.
626
627
In Table 10, the simulated and observed dryout z-location along helical coil 3, are shown at t¯7050s and t¯10650s , as well as, the corresponding uncertainties. Table 10: Comparison between simulated and observed dryout z-location in helical coil 3.
t¯7050s
zx1 ,3 /zxT ot ,3 (m)
628
t¯10650s
Simulated
Observed
Simulated
Observed
1.16/1.17
1.13 ± 0.063
1.35/1.36
1.38 ± 0.063
Taking into account the problem uncertainties, these results reveal, simu36
629
lated dryout z-locations along helical coil 3 fit well the observations at both
630
times.
631
Hence, it can be assumed the model performance is good enough to capture
632
the two-phase flow local behavior, at least up to the dryout onset, within the
633
quasi-stationary interval. As it had been stated before during the benchmarking.
634
In summary, this model is considered appropriate to deal with the work
635
objectives.
636
6. Dryout study
637
Hereafter, the dryout onset (first and total dryout) is studied in the covered
638
working conditions range, i.e. it is associated azimuthal position and local steam
639
qualities, depending on the helical coil diameter. And finally, the comparison
640
with the found literature correlations is carried out.
641
6.1. Azimuthal position and local steam qualities
642
From numerical results, dryout z-location, both first and total, on each he-
643
lical coil tube are obtained. Results at t¯7050s and t¯10650s are shown in Table
644
11. Table 11: Dryout z-location: first/total.
zx1 ,3 /zxT ot ,3 (m)
zx1 ,2 /zxT ot ,2 (m)
zx1 ,1 /zxT ot ,1 (m)
t¯7050s
1.16 / 1.17
1.14 / 1.15
1.11 / 1.12
t¯10650s
1.35 / 1.36
1.33 / 1.34
1.30 / 1.31
645
From them it follows that under practically the same working conditions of
646
in water-steam side (PIN ∈ [37.9, 39.2] bar, ∆Tsub ≈ 0 and m ˙ ws ≈ 0.082 kg·s-1 )
647
and molten salts side (atmospheric pressure and TIN ∈ [472, 477] ◦ C) but a 12
648
% mass flow rate decrease, both first and total dryout:
649
650
• shift along the steam generator almost 11 turns upwards (0.19 m), i.e., regardless on the helical coil diameter, D,
37
651
• happen primarily on helical coil 1, almost 2 turns upwards on helical coil
652
2 and almost 3 turns upwards on helical coil 3, regardless on molten salts
653
mass flow rate, m ˙ ms .
654
These results quantify that it was already knew: as discharge evolves, heat
655
transfer is increasingly less effective, so a greater heat transfer area along the
656
steam generator is needed to achieve the dryout, being the outer tube (helical
657
coil 1), in which, dryout, first and total, primarily happens. This, at equal z-
658
location height, has a greater heat transfer area than the others (helical coils 2
659
and 3).
660
Once determined dryout z-locations on each tube, the respective steam qual-
661
ity azimuthal distributions on walls during first dryout, {x1,# }#=1,2,3 , as well
662
as the steam quality bulk values both during first and total dryout, x1,bulk and
663
xT ot,bulk respectively, are plotted on the cross sections to the flow containing
664
such z-locations at t¯7050s and t¯10650s . The obtained results are presented in
665
Figure 13.
Figure 13: Steam quality azimuthal distributions on walls and bulk values, during first and total dryout at t¯7050s (left) and t¯10650s (right).
666
From them, it follows that:
667
• The first dryout azimuthal positions, {θx1 ,# }#=1,2,3 , remain constant re38
668
gardless on D and m ˙ ms (θx1 ≈ 170◦ , on the intrados). This is also true
669
for the lowest steam quality azimuthal positions on walls (θx1 ≈ 350◦ , on
670
the extrados). This result can be explained due to the secondary flow
671
presence.
672
On a two-phase flow in a helical coil, the centrifugal and gravity forces act
673
trying to separate the flow due to the density differences between both phases.
674
In addition, there is a secondary flow, superimposed to the primary flow, which
675
also acts on the two-phase flow. This is perpendicular to the main flow and
676
follows lines forming loops, dragging the fluid from the extrados to the intrados,
677
counteracting the separation effects between both phases [12]. The separation
678
effects depend on m ˙ ws since the buoyancy forces have higher influence at low
679
m ˙ ws due to the existing lower turbulence.
680
To visualize the secondary flow presence in this case, in Figure 14 two-phase
681
flow distribution obtained by means the line integral convolution of the vector
682
velocity field (removing the normal component and projecting the tangential
683
component on the cross section to the flow) at z6 and t¯7050s is shown as example.
Figure 14: Line integral convolution of tangential vector velocity field in helical coils at z6 and t¯7050s field (steam generator axis placed on the left side of the figure).
684
As can be seen, the streamlines shape two vortices coincident with first
685
dryout and lowest steam quality on walls azimuthal positions, which represent
686
the loops dragging the fluid from the extrados to the intrados. They go through
687
the walls perimeters and then close through the bulks, as it is shown in Figure
688
15. 39
Figure 15: Tangential vector velocity field in helical coils at z6 and t¯7050s (steam generator axis placed on the left side of the figure).
689
This phenomenology agree with that described by other authors as Pointer
690
et al. [59], Colombo [34], Jo et al. [52] and Cioncolini et al. [60], who also
691
employed CFD techniques to describe forced convective boiling flows in heli-
692
cal coils but using different working conditions, wall heating methodologies or
693
geometric characteristics than here.
694
By other hand, from steam quality azimuthal distributions on walls, the
695
best/worst chilled surface points during the first dryout can be deducted. In
696
Figure 16, temperature azimuthal distributions on walls during the first dryout,
697
{Tx1 ,# }#=1,2,3 , as well as the respective bulk values, Tx1 ,bulk , are plotted on the
698
cross sections to the flow at t¯7050s and t¯10650s .
40
Figure 16: Temperature azimuthal distributions on walls and bulk values during 1st dryout at t¯7050s (left) and t¯10650s (right).
699
It is observed the temperature difference between first dryout and lowest
700
steam quality on walls azimuthal position is ≈ 20 ◦ C. This lack uniformity on
701
the walls thermal behavior at equal z-location (even promoted by the two-phase
702
flow instabilities) could affect the steam generator safety. Although it is outside
703
the scope of this work, it is recommended the steam generator thermomechanical
704
behaviour will be also analyzed by those who pretend to scale-up this system.
705
706
• Both x1,bulk and xT ot,bulk remain constant regardless on D and m ˙ ms (x1,bulk ≈ 0.94 and xT ot,bulk ≈ 0.97).
707
These values can be understood by means the 2D map of Berthoud and
708
Jayanti, which helps to identify the process controlling the first dryout in helical
709
coils. In Figure 17, dimensionless numbers x0 and y0 of each helical coil are
710
represented, both at t¯7050s and t¯10650s .
41
Figure 17: B&J 2D map during the first dryout at t¯7050s and t¯10650s .
711
As can be observed, the study case belongs to the “Redeposition zone”, char-
712
acterized by high steam qualities during the first dryout. In addition, according
713
to the obtained vales of x0 and y0 (very close to each other), it can be deduced
714
the steam quality distributions within the helical coils follow the same pattern,
715
as it is shown in Figure 18.
Figure 18: Two-phase flow patterns at z6 and t¯7050s (steam generator axis placed on the left side of the figure).
716
This pattern is typical from the “Redeposition zone” and has been also ob-
42
717
served in the experiments conducted by Murai et al. [61] using a computed
718
tomography technique, so this model reproduces available experiments in bibli-
719
ography.
720
In summary, it can be said that, in the covered working conditions range
721
and considering this steam generator geometry, although D1 > D2 > D3 , the
722
two-phase flow behavior is uniform. Besides, that what happens at t¯7050s is
723
reproduced, without loss of generality, at t¯10650s , except a certain heights dif-
724
ference. And, therefore, the prototype operation seems not to influence on the
725
dryout.
726
6.2. Simulation results and literature correlations comparison
727
Once defined local steam qualities as {¯ x1,# }#=1,2,3 or {¯ xT ot,# }#=1,2,3 , it is
728
proceed to compare simulated values, {¯ x1,sim,# }#=1,2,3 or {¯ xT ot,sim,# }#=1,2,3 ,
729
with those calculated by using literature correlations applicable to the ENEA
730
prototype working condition for both first dryout, {¯ x1,correlac,# }#=1,2,3 (cor-
731
relations of: Berthoud and Jayanti, Ruffell and Santini et al., see expressions
732
and applicability ranges in Table 1) and total dryout, {¯ xT ot,correlac,# }#=1,2,3
733
(correlations of: Naitoh et al. and Berthoud and Jayanti, see expressions and
734
applicability ranges in Table 1), where simulated values have been calculated as
735
follows:
x ¯1orT ot,sim,# 736
737
738
1 = S
Z x1orT ot,# (r# , θ# ) dS
(21)
S
being {x1orT ot,# }#=1,2,3 the steam quality distributions on the cross sections to the flow during first or total dryout respectively. Note that one of the main handicaps assessing {¯ x1,# }#=1,2,3 or {¯ xT ot,# }#=1,2,3
739
by means experimental correlations is the boundary heat flux calculus (Q). This
740
happens mainly in those cases in which the wall heating is not uniform, as in this
741
case. Nevertheless, in correlations where Q is taken into account (correlation
742
of Berthoud and Jayanti for first dryout, and correlations of Ruffell and Naitoh
743
et al. for total dryout), the necessary power, Q˙ nec , to achieve the dryout, here
43
744
is uniformly distributed on the walls. Considering this hypothesis, obtained
745
results for {¯ x1,# }#=1,2,3 are shown in Figure 19.
Figure 19: Comparison between simulated and calculated results for first dryout.
746
As can be seen, obtained results using Ruffel0 s correlation fit well simulated
747
results, while those obtained using Santini et al. correlation underestimate
748
slightly (around 20 %) local steam qualities during first dryout. Finally, those
749
obtained using Berthoud and Jayanti correlation overestimate them up to 60
750
%. This is due to, in the first case, the correlation (considering 270◦ Ruffel0 s
751
correlation, which corresponds to 180◦ in the local polar reference systems used
752
here) was validated for water as working fluid in a set of helical coils whose
753
working conditions and characteristics were not far away from that established
754
in this work.
755
Regarding Santini et al. correlation, although the considered working fluid
756
is water and the covered working conditions range is supported here, the helical
757
coils characteristics are different: greater vertical pich, Xver , and diameters of
758
helical coil, D, and tube, di .
44
759
To a better understanding of Santini et al. results, it can be used the
760
Berthoud and Jayanti 2D map [16]. If dimensionless numbers x0 and y0 for
761
a helical coil with Santini et al. characteristics but ENEA prototype work-
762
ing conditions are represented on this map, obtained points during first dryout
763
would be shifted to the “Gravity zone”, characterized by lower steam qualities
764
than the “Redeposition Zone”. Taking into account Santini et al. helical coil
765
diameter is between 5 and 7 times larger than those of the ENEA prototype, is
766
clear the effect of centrifugal forces decreases against the gravity force.
767
In the Berthoud and Jayanti correlation case, notwithstanding working con-
768
ditions and helical coils characteristics comprise those of this case, obtained
769
results does not fit adequately, probably because this correlation was based on
770
the experimental data of five researchers (Breus and Belyakov [20], Carver et
771
¨ al. [21], Roumy [17], Styrikovich et al. [14] and Unal [18, 19]), who employed
772
different working fluids (and therefore, working conditions).
773
Figure 20 shows obtained results for {¯ xT ot,# }#=1,2,3 .
Figure 20: Comparison between simulated and calculated results for total dryout.
45
774
As can be observed, obtained results using Naitoh et al. correlation fits
775
quite well simulated results, while those obtained using Berthoud and Jayanti
776
correlation overestimate them up to 60 % the local steam qualities during total
777
dryout as it was expected. Despite the good fit in the first case, the explicit
778
independence of this correlation with the mass flux allows to question it. Be-
779
sides, there are big differences between Naitoh at al. helical coils and ENEA
780
prototype characteristics.
781
7. Conclusions
782
• In this work, the dryout onset (first and total dryout) in a triple helical
783
coil once-through steam generator has been experimentally and numeri-
784
cally studied. For this purpose, a CFD modelling based on steady-state
785
simulations and a conjugate heat transfer model has been carried out.
786
Besides, a numerical methodology based on the two-phase flow average
787
behavior in each thermohydraulic instability cycle has been employed.
788
• From a benchmarking between the two-phase flow model and a mechanis-
789
tic model, it is deduced that the used semi-empiric model can be applied
790
to the simulation of the forced convection boiling flow in the helical coils.
791
• Numerical results have been evaluated, first, against experimental data
792
from the state-of-the-art, and second, against acquired measurements dur-
793
ing a discharge test of the thermal energy storage prototype with inte-
794
grated steam generator belonging to ENEA and the obtained results with
795
a pressure drop model developed ad hoc for this case, getting good fits up
796
to the dryout.
797
• By means two phase flow tangential vector velocity field on cross section
798
to the flow has been possible to show the secondary flow presence in the
799
helical coils. And, by means steam quality distributions has been possible
800
to characterize the dryout onset, azimuthal position and associated local
801
steam qualities, as function of helical coil diameter. In this case, within the 46
802
working conditions range and considering these particular steam generator
803
characteristics, the two-phase flow behavior is uniform. And, therefore,
804
the prototype operation seems not to influence on the dryout. This phys-
805
ical phenomenology and analysis have not been reported yet on available
806
literature.
807
• Besides, the derived two-phase flow pattern is typical of “Redeposition
808
Zone” within the 2D map of Berthoud and Jayanti [16] and it is like
809
those observed in other works using, both experimental and numerical
810
methodologies, to describe forced convective boiling flows in helical coils
811
at high steam qualities.
812
• Finally, the numerical local steam qualities have been compared with those
813
calculated by using appropriate experimental correlations. From the ob-
814
tained scatter-plots it is concluded, the 270◦ Ruffel0 s correlation is the
815
most adequate expression to determine the local steam quality value dur-
816
ing the first dryout.
817
• Also, assuming a 0.97 value during the total dryout is a good approxi-
818
mation, since although it is the most conservative choice, it matches the
819
value recommended by Mazufri [62] for the thermohydraulic design of a
820
helical steam generator. On the other hand, the Santini et al. correlation
821
offers suitable results (within a 20 % error) being this one, moreover, sim-
822
pler than others because it does not depend on walls heat flux. So, the
823
obtained steam quality macro values are validated, and it is justified the
824
interest of a comprehensive study of them.
825
ACKNOWLEDGEMENTS
826
The authors would like to acknowledge the EU through the 7th Framework
827
Program for the financial support of this work under the OPTS project with
828
contract number: 283138, the UTRINN-STD from Casaccia Research Center
829
(ENEA) for providing the experimental data and the information concerning 47
830
to the experimental setup and the Extremadura Research Centre for Advances
831
Technologies (CETA-CIEMAT) for providing the necessary computing resources
832
for simulations. Technical discussions with members of ATYCOS-CIEMAT were
833
essential for this work.
834
Appendix A. Statistical parameters The relative error (RE) is defined as: RE[%] =
|Cp − Co | Co
The correlation coefficient (R), the normalized mean square error (N M SE), the fractional bias (F B) and the fraction of prediction within a factor of two of observations (F AC2), are given by: R=
(Co − Co )(Cp − Cp ) (Co − Cp )2 (Co − Cp ) ; N M SE = ; FB = σCp · σCp Co · Cp 0.5(Co + Cp ) F AC2 = fraction of data that satisfy 0.5 ≤
Cp ≤ 2.0 Co
835
where: Cp are model predictions; Co observations; and C and σC the corre-
836
sponding average and standard deviation, respectively, over the data-set.
837
Note that since F B measures only the systematic bias of a model, it is
838
possible for a model to have predictions completely out of phase of observations
839
and still have F B = 0.0 because of cancelling errors.
48
NOMENCLATURE Tube diameter (m)
Q
Heat flux (W·m-2 )
f
Force (N)
Q˙
Power (W)
g
Gravity (9.806 65 m·s-2 )
Re
Reynolds number
h
Static enthalpy (J·kg-1 )
S
Surface (m2 )
d
-1
-1
k
Thermal conductivity (W·m ·K )
T
Temperature (K)
m ˙
Mass flow rate (kg·s-1 )
V
Volume (m3 )
t
Time (s)
X
Pitch (m)
{x, y, z}
Cartesian coordinates (m)
α
Vapor volume fraction
-1
v
Velocity (m·s )
x
Steam quality
x ¯
Local steam quality
{x0 , y0 }
Dimensionless numbers (B&J 2D Map)
Turbulent dissipation rate (m2 ·s-3 )
-1
CP
Specific heat (J·kg ·K )
κ
Turbulent kinetic energy (J·s-1 )
D
Helical coil diameter (m)
µ
Dynamic viscosity (Pa·s)
E
Energy (J)
ρ
Density (kg·m-3 )
-1
-1
-2
G
Mass flux (kg·s ·m )
σ
Surface tension (N·m-1 )
H
Enthalpy (J·kg-1 )
ϕ
Helix angle (◦ )
L
Length (m)
∆
Increment
P
Pressure (bar)
{r, θ}
Polar coordinates
Pr
Prandtl number
{r, θ, z}
Cylindrical coordinates
SUBSCRIPTS 1
First
l
Liquid
sat
Saturated
bulk
Bulk
lat
Latent
simu
Simulated
correlac
Correlated
m
Mixture
sub
Subcooled
cri
Critic
max
Maximum
t
Turbulent
ef f
Effective
min
Minimum
T ot
Total
g
Gravity
ms
Molten salts
v
Vapor
hor
Horizontal
nec
Necessary
ver
Vertical
i
Inner
o
Outer
w
Wall
IN
Inlet
OU T
Outlet
ws
Water-steam
49
ACRONYMS CFD
Computational Fluid Dynamics
RANS
Reynolds Averaged Navier-Stokes
CSP
Concentrating Solar Power
SFR
Sodium-cooled Fast Reactor
DWO
Density Wave Oscillations
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57
Highlights
•
CFD modelling of dryout onset in a triple helical coil once-through steam generator.
•
Benchmarking of two-phase flow model against experimental data from the state-ofthe-art.
•
Evaluation of numerical results with experimental data of a thermal energy storage prototype with integrated steam generator during a discharge test.
•
Azimuthal distributions analysis of the two-phase flow as function of helical coils characteristics and working conditions.
•
Comparison of numerical results with those obtained from adequate correlations for forced convective boiling flows in vertical helical coils.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: