- Email: [email protected]
Thermal–hydraulic calculation and analysis of a 600 MW supercritical circulating fluidized bed boiler with annular furnace
Accepted Manuscript Title: Thermal-hydraulic calculation and analysis of a 600 MW supercritical circulating fluidized bed boiler with annular furnace Author: Long Wang, Dong Yang, Zhi Shen, Kaiyuan Mao, Jun Long PII: DOI: Reference:
S1359-4311(15)01249-1 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.11.014 ATE 7294
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
27-7-2015 6-11-2015
Please cite this article as: Long Wang, Dong Yang, Zhi Shen, Kaiyuan Mao, Jun Long, Thermalhydraulic calculation and analysis of a 600 MW supercritical circulating fluidized bed boiler with annular furnace, Applied Thermal Engineering (2015), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.11.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
Thermal-hydraulic calculation and analysis of a 600 MW supercritical circulating
2
fluidized bed boiler with annular furnace
3
Long Wang, Dong Yang*, Zhi Shen, Kaiyuan Mao, Jun Long
4
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong
5
University,No.28, Xianning West Road, Xi’an, Shaanxi 710049, China
6 7
Highlights
8
1.Non-linear model of supercritical CFB boiler with annular furnace is developed.
9
2.Many empirical correlations are used to solve the model.
10
3.The thermal-hydraulic characteristics of boiler are analyzed.
11
4.The results show the design of the annular furnace is reasonable.
12 13
Abstract
14
The development of supercritical Circulating Fluidized Bed (CFB) boiler has great
15
economic and environmental value. An entirely new annular furnace structure with
16
outer and inner ring sidewalls for supercritical CFB boiler has been put forward by
17
Institute of Engineering Thermophysics (IET), Chinese Academy of Sciences and
18
Dongfang Boiler Group Co., Ltd. (DBC). Its outer and inner ring furnace structure
19
makes more water walls arranged and reduces furnace height availably. In addition,
20
compared with other additional evaporating heating surface structures such as
*
Corresponding author. Tel.: +86 029 82668393 E-mail address: [email protected] (D. Yang) 1
Page 1 of 29
21
mid-partition and water-cooled panels, the integrative structure can effectively avoid
22
the bed-inventory overturn and improve the penetrability of secondary air. The
23
conditions of the 600 MW supercritical CFB boiler including capability, pressure and
24
mass flux are harsh. In order to insure the safety of boiler operation, it’s very necessary
25
to analyze the thermal-hydraulic characteristics of water-wall system. The water-wall
26
system with complicated pipe arrangement is regarded as a network consisting of
27
series-parallel circuits, pressure nodes and linking circuits, which represent vertical
28
water-wall tubes, different headers and linking tubes, respectively. Based on the mass,
29
momentum and energy conservation, a mathematical model is built, which consists of
30
some simultaneous nonlinear equations. The mass flux in circuits, pressure drop
31
between headers, outer vapor temperature of water-wall system and metal temperature
32
data of tubes at the boiler maximum continuous rating (BMCR), 75% BMCR and 30%
33
BMCR load are obtained by solving the mathematical model. The results show that the
34
vertical water wall design with smooth tubes in the 600 MW supercritical CFB boiler is
35
applicable.
36
Keywords: supercritical CFB boiler, annular furnace, thermal-hydraulic characteristic,
37
vertical water wall
38
1. Introduction
39
Because of good fuel flexibility, high combustion efficiency, efficient sulfur
40
removal, low NO2 emission, good load following capability and other technical
41
advantages, supercritical CFB technology has recently developed rapidly [1-2]. 2
Page 2 of 29
42
According to thermodynamic theories, the key to obtain higher boiler efficiency is large
43
capacity CFB boiler with higher steam parameters. As the unit capacity increases,
44
more heating surfaces are needed. And some additional evaporating heating surface
45
structures, such as mid-partition and water-cooled panels, correspondingly leads to a
46
series of problems such as non-uniform fluidization, penetrability of secondary air,
47
bed-inventory overturn and layout of several cyclones. In purpose of solving the
48
problems related to the heating surface arrangement, an entirely new annular furnace
49
structure for 600 MW supercritical CFB boiler is put forward by IET, Chinese
50
Academy of Sciences and DBC. The 600 MW supercritical CFB boiler has inner ring
51
and outer ring sidewalls and its operating conditions are harsh. In order to keep the
52
metal temperature of water wall not over reliable range and choose the operating
53
pressure head of feed pump matching the pressure drop of water wall flow system,
54
setting up mathematical model to analyze thermal-hydraulic characteristics of the new
55
supercritical CFB boiler is essential.
56
In the past, due to limitations of working equipment, relevant staffs used complex
57
but not accurate graphic method to model thermal-hydraulic calculation. The graphic
58
method has large errors and it cannot be easily applied on computer to analyze complex
59
water-wall system. In recent years, various calculation models for thermal-hydraulic
60
analysis have been put forward and developed by scholars from different countries.
61
Base on two non-linear models which are for the phase separation in the steam drum
62
and the evaporation process of heated working fluid in vertical water wall, Adam and 3
Page 3 of 29
63
Marchetti [3] presented a dynamic simulator and verified it in boilers with natural
64
recirculation. Kim and Choi [4] assumed the superficial velocity of water was zero and
65
average size of steam bubbles was an arbitrary value. Then they applied constitutional
66
equations into a hydraulic model for drum-type boilers. Tucakovic et al. [5] established
67
a method to investigate operating characteristics of a forced circulation steam boiler in
68
which rifled tubes were installed to increase the turbulivity of steam-water mixture.
69
Dong et al. [6] proposed hydrodynamic circuit analysis method and calculated
70
hydrodynamic characteristic of a boiler with natural circulation. Zhao [7] presented a
71
universal hydraulic calculation model for drum boiler. Pan et al. [8] put forward a
72
non-linear mathematical model for supercritical coal-fired boiler, in which mass
73
conservation equations, momentum conservations equation and energy conservation
74
equation of simplified water-wall system were included. Pan et al. [9-10] applied
75
non-linear mathematical model on hydraulic calculation of conceptual 600MW CFB
76
boiler with mid-partition wall which was proposed by Harbin Boiler Company.
77
Compared with Harbin Boiler Company’s conceptual CFB boiler, the more complex
78
furnace configuration of 600MW CFB boiler with inner and outer ring water-wall
79
system presented higher requirement for boiler operation.
80
The water wall is composed of vertical smooth tubes and rectangular fin in the 600
81
MW supercritical CFB boiler with annular furnace. At different operation condition,
82
the computing methods of the heat transfer and frictional characteristics are studied and
83
corresponding calculation formulas can be found in Ref. [11-15]. A non-linear model is 4
Page 4 of 29
84
developed in this paper by combining these correlations and three conservation laws
85
(mass, momentum and energy conservation). The mass flux distribution of circuits,
86
pressure drop of water-wall system, outlet vapor temperatures of furnace hearth and
87
metal temperatures data at three different loads (BMCR, 75% BMCR and 30% BMCR
88
load) are obtained by directly solving non-linear model with quasi-Newton iterative
89
method. The results show the design of the water wall can guarantee the operating
90
safety.
91 92
Nomenclature
93
di
internal pipe diameter, m
94
dw
external pipe diameter, m
95
f
friction coefficient
96
G
mass flux, kg/(m2s)
97
Gcr
critical mass flux, kg/(m2s)
98
h
specific enthalpy, J/kg
99
hw
enthalpy of tube wall surface fluid, J/kg
100
hf
average enthalpy of fluid, J/kg
101
J
current sharing coefficient of heat flux
102
Jn
current sharing coefficient of internal pipe wall heat flux
103
l
pipe length, m
104
Nu
nusselt number
5
Page 5 of 29
105
Rew
reynolds number of tube wall surface fluid
106
p
pressure, MPa
107
p(i)
pressure in circuit i, MPa
108
△p(i) total pressure loss in circuit i, MPa
109
△pf
frictional pressure loss, MPa
110
△pg
gravitational pressure loss, MPa
111
△pl
local resistance pressure loss, MPa
112
q
heat flux, W/m2
113
qcr
crcritical heat flux, W/m2
114
qw
outer wall heat flux, W/m2
115
qin
inner wall heat flux, W/m2
116
s
pitch between adjacent tubes, m
117
t
temperature, ℃
118
tf
bulk fluid temperature, ℃
119
ti
tube inner-wall temperature, ℃
120
tm
metal temperature in the middle of tube wall, ℃
121
tw
tube outer-wall temperature, ℃
122
tqd
metal temperature in the tip of fin, ℃
123
tqg
metal temperature in the root of fin, ℃
124
w
total mass flow rate in water wall, kg/s
125
w(i)
mass flow rate in circuit i, kg/s 6
Page 6 of 29
126
x
vapor quality of working fluid, kg/kg
127
xcr
critical vapor quality, kg/kg
128
Greek symbols
129
α
heat transfer coefficient, W/(m2 ℃)
130
δ
thickness of fin, m
131
density, kg/m3
132
l
density of water, kg/m3
133
g
density of saturated vapor, kg/m3
134
average density of fluid, kg/m3
135
λ
thermal conductivity of tube, W/(m﹒k)
136
w
thermal conductivity of tube wall surface fluid, N﹒s/m2
137
w
dynamic viscosity of tube wall surface fluid, N﹒s/m2
138
ηqd
balance coefficient of heat flux in the tip of fin
139
ηqg
balance coefficient of heat flux in the root of fin
140
correction coefficient
f
141
2. Water wall structure and circuits division
142
2.1. Water wall structure
143
The structure diagram of the 600 MW supercritical CFB boiler with annular furnace
144
is displayed in Fig. 1. The perimeter of annular furnace consists of outer ring and inner
145
ring sidewalls, whose sizes are 33600×19900 mm and 8400×22099.41 mm. The
146
vertical water wall with simple smooth tubes is applied. 6 cyclones are divided into two 7
Page 7 of 29
147
groups and symmetrically installed at outer front wall and outer rear wall. The
148
integrative structure can effectively avoid the bed-inventory overturn, improve the
149
penetrability of secondary air and reduce the flow resistance. In addition, more water
150
walls can be arranged on the inner ring sidewalls to ensure adequate heat absorption,
151
which is a key factor to ensure the operation safety of the boiler. Besides, the design of
152
water wall reduces the furnace height availably and the cost of boiler is economized.
153
The boiler design parameters at BMCR, 75% BMCR and 30% BMCR load are shown
154
in Table 1.
155
2.2. Flow circuit division and furnace-side heat flux distribution
156
The vertical water wall tubes, linking tubes and headers in water-wall system of the
157
600 supercritical CFB boiler with annular furnace, can be regarded as heated
158
series-parallel circuits, unheated linking circuits and pressure nodes. Then the
159
water-wall system processing becomes a flowing network which is shown in Fig. 2
160
and includes 70 heated circuits, 17 unheated linking circuits and 18 pressure nodes. In
161
Fig. 2, the numbers of heated circuits in outer front wall, outer right wall, outer rear
162
wall, outer left wall, inner front wall, inner right wall, inner rear wall and inner left wall
163
are 1-12, 13-21, 22-33, 34-42, 43-51, 53-55, 57-65 and 67-69, respectively. The serial
164
numbers of circuits 52, 56, 66, 70 refer to water wall in the corner of inner ring
165
sidewalls. The linking tubes, lower distribution headers, inlet headers, upper outlet
166
headers and steam-water separator are represented by serial numbers 71-87, 88, 89-96,
167
97-104 and 105, respectively. The top view of heated circuits in inner and outer ring 8
Page 8 of 29
168
vertical water wall is shown in Fig.3.
169
Because the CFB boiler with annular furnace, which is put forward by IET, Chinese
170
Academy of Sciences and DBC, has the entirely new annular furnace structure and
171
hasn’t been in operation, furnace-side heat flux curve is estimated according to furnace
172
heat equilibrium [11]. Fig. 4 gives heat flux distribution at different loads along height.
173
Heat flux will increase with the load increasing can be reflected, which is reasonable.
174
The non-uniformity of heat flux at level direction also has influence on the flow
175
distribution of circuits. The deviation factor of heat flux along furnace width is
176
factitiously supposed to be among 80% to 120% of the average furnace-side heat flux.
177
Because the size of outer ring sidewalls is larger than the size of inner ring sidewalls,
178
the heat flux deviation in outer ring sidewalls is larger. With this assumption, the heat
179
flux deviation in the new 600 MW supercritical CFB boiler can be well simulated and
180
the heat flux deviation among all the circuits in water wall is shown in Fig. 3.
181
3. Mathematical model
182
3.1. Analysis model of mass flux and pressure drop
183
Water-wall system is simplified as flowing network. Based on energy conservation
184
between working fluid absorption heat and furnace effective radiation, working fluid
185
enthalpy in reference section of water wall can be obtained. According to the fluid
186
flowing network, 87 nonlinear momentum conservation equations of 87 circuits (70
187
heated circuits and 17 unheated linking circuits) and 18 nonlinear mass conservation
188
equations of 18 nodes is presented. The pressure of nodes and the circuit mass flux can 9
Page 9 of 29
189
be obtained by using Chord secant method to solving the nonlinear mathematical
190
model[16].
191
The momentum conservation equation means pressure difference between import
192
node and export node equals pressure drop which causes by working flow. For 70
193
heated circuits in outer front wall, outer right wall, outer rear wall, outer left wall, inner
194
front wall, inner right wall, inner rear wall and inner left wall, momentum conservation
195
equations are given by: 0 p (89) p (97) p ( i )
i 1 12
(1)
0 p (90) p (98) p ( i )
i 13 21
(2)
198
0 p (91) p (99) p ( i )
i 22 33
(3)
199
0 p (92) p (100) p ( i )
i 34 42
(4)
200
0 p (93) p (101) p ( i )
i 43 52
(5)
201
0 p (94) p (102) p ( i )
i 53 56
(6)
202
0 p (95) p (103) p ( i )
i 5 7 6 6
(7)
203
0 p (96) p (104) p ( i )
i 67 70
(8)
204
The momentum conservation equations of unheated linking circuits 71-87 are given
196 197
205
by:
206
0 p cs p (88) p (71)
207
0 p (88) p ( i 17) p ( i )
i 72 79
(10)
0 p ( i 17) p (105) p ( i )
i 80 87
(11)
208 209
(9)
The friction between working fluid and inner wall of tubes, the height difference 10
Page 10 of 29
210
at vertical direction between inlet position and outlet position, local resistance and
211
acceleration give rise to the pressure drop p (i) . With the fact that acceleration
212
pressure drops are relatively little, the pressure drops in circuit i are calculated by:
213
p (i ) p f (i ) p g (i ) p l (i )
214
The gravitational pressure drop
(12) pg
can be given with the average density of
215
working fluid and height difference at vertical direction between inlet position and
216
outlet position known. The average density of working fluid can be obtained
217
through calculation of property of fluid.
218
pg g h
219
The single-phase water, single-phase vapor and supercritical water all can be
(13)
220
treated as single-phase fluid and flow frictional pressure drop
221
fluid is given as:
222
p f f
223
In smooth tube, the frictional pressure drop
224
l G
p f
of single-phase
2
(14)
di 2 p f
of two-phase steam-water is
calculated as [11]: l G
2
l
225
p f f
226
In the above formula, the correction factors is obtained by:
227
=1+
228
1
di 2l
[1 x (
g
1)]
1000 x 1 x 1 l G g 1 x l 1 g
(15)
G 1 0 0 0k g
/ m s 2
G 1 0 0 0k g /m 2
(16)
s
(17)
11
Page 11 of 29
229
=1+
1000 x 1 x 1 l G g 1 (1 x ) l 1 g
G 1 0 0 0k g /m 2
(18)
s
230
For flow under different states, the friction coefficient f is associated with tube
231
inner wall roughness k and the value of k for carbon steel tube is 6 10 -5 , which
232
is used in the calculation of flow frictional pressure drop
233
coefficient f can be achieved by[11]:
234
235 236
f
p f
. The friction
1 3 .7 d i 4 lg ( ) k
(19)
2
The mass conservation equations of nodes 88-105, which are used to calculate the mass flow flux of heated circuits and unheated linking circuits, are presented as:
237
0 w w (71)
238
0 w (7 1)
(20)
79
w (i )
(21)
i 72
12
239
0 w (7 2 )
w (i )
(22)
i 1
21
240
0 w (7 3)
w (i )
(23)
i 1 3
33
241
0 w (7 4 )
w (i )
(24)
w (i )
(25)
i 22
42
242
0 w (7 5)
i 34
52
243
0 w (7 6 )
w (i )
(26)
i 43
12
Page 12 of 29
56
244
0 w (7 7 )
w (i )
(27)
i 53
66
245
0 w (7 8)
w (i )
(28)
i 57
70
246
0 w (7 9 )
w (i )
(29)
w ( i ) w (8 0 )
(30)
i 67
12
247
0
i 1
21
248
0
w ( i ) w (8 1)
(31)
i 1 3
33
249
0
w ( i ) w (8 2 )
(32)
w ( i ) w (8 3)
(33)
i 22
42
250
0
i 34
52
251
0
w ( i ) w (8 4 )
(34)
i 43
56
252
0
w ( i ) w (8 5)
(35)
i 53
66
253
0
w ( i ) w (8 6 )
(36)
i 57
70
254
0
w ( i ) w (8 7 )
(37)
i 67
87
255
0
w (i ) w
(38)
i 80
256
Energy conservation equation, in which the thermodynamic parameters used are
257
reckoned with furnace-sided heat flux curve along height and heat flux deviation along
258
width, is given by: 13
Page 13 of 29
qsl
259
hout hin
260
The local pressure drop p l which is mainly caused by elbows, inlet structure and
261
outlet structure, is taken into account in this paper and is calculated by correlation
262
formulas in Ref. [11].
263
3.2. Analysis model of metal temperature
(39)
w
264
The metal temperature of water-wall system can be predicted with the mass flux of
265
circuits and the pressure of nodes known. The heat transfer coefficient of working fluid
266
is a key factor for metal temperatures calculation of water wall and affected by four
267
elements, which are pressure parameter, fluid state, tube structure and the fireside heat
268
flux. A lot of heat transfer coefficient empirical formulas and calculation models have
269
been summarized in Ref. [11-15].
270 271
When the pressure is higher than 22.1 MPa, the flow is in supercritical pressure region and the heat transfer correlations in smooth tube are given as follows[14]:
272
(1) In low enthalpy region
273
N u 1.9855 R e
274
(2) In high enthalpy region
275
N u 1.5803 R e
276
When the pressure is higher than 19 MPa and lower than 22.1 MPa, the critical
277
conditions of heat transfer deteriorations are very important in the process of
278
calculating heat transfer coefficient. Heat transfer deteriorations include departure
0.44307 w
0.50143 w
（ h w h f ） w （ t t ） f w w
（ h w h f ） w （ t t ） f w w
0.93953
1.06098
w f
w f
0.54295
(40)
2.19757
(41)
14
Page 14 of 29
279
from nucleate boiling (DNB) and dry-out, which are related to critical heat flux and
280
critical vapor quality, respectively. The critical heat flux are researched by Sun et al.
281
[15] and the correlation are obtained by: G G cr
(42)
G G cr
(43)
q cr 3343.92(22.115 p )
283
q cr 2 .2 6 6 5( 2 2 .1 1 5 p )
284
In the above formula, the critical mass flux is calculated as:
285
G cr 800.44 223.85 ln(22.115 p )
286
under the pressure 19MPa~22.1MPa, before the DNB occurs the heat transfer
287
coefficients are calculated by the national standard of the boiler hydrodynamics
288
calculation (China) [11]. After the DNB occurs, the heat transfer correlation is given
289
by [15]:
290
0.4091
0 .1 0 0 7
G
（ 1-x ）
282
G
-0.3835
0.6792
（ 1-x ）
0 .7 3 8 5
N u 0.1864 R e G x (1 x ) g l
0 .1 8 8 8
(44)
0.0545
P rG w
3.4313
q
1.0738
(
G cr
)
0.5928
p p cr
2.8319
(45)
291 292 293
When the pressure is lower than 19MPa, the heat transfer correlations in the literature [11] are used into the analysis model.
294
The calculation of inner and outer wall temperatures of tube is related to inner and
295
outer diameter, fluid temperature, heat transfer coefficient, current sharing coefficient
296
heat flux and thermal conductivity of tube, and they are confirmed by [11]:
297
ti t f J n
qw d w
298
tw t f J n
qw d w
(46)
di
di
Jq w
2d w (d w d i )
(47)
(d w d i )
15
Page 15 of 29
299
The temperatures of the middle of tube walls are given by:
300
tm
301
The temperature in the root of fins [17] and the tip of fins [9] are calculated as:
302
t q g t f q w q g
303
t qd t qg
ti t w
(48)
2
q qd 2
dw
[ln (
di
(
dw di
s dw
)
)
di 2
1
(49)
]
2
(50)
2
304
4. Results and discussions
305
4.1. Pressure drop
306
Table 2 summarizes the pressure drops of 8 pieces of vertical water walls in
307
supercritical CFB boiler with annular furnace at three different loads (BMCR, 75%
308
BMCR and 30% BMCR). The pressure drops in right wall and left wall are higher than
309
those in front wall and rear wall. At BMCR load, the differences between minimum
310
pressure drop and maximum pressure drop in outer ring and inner ring water walls are
311
reasonable, which are 1.83% and 0.26%, respectively. What’s more, the pressure drop
312
differences among different water walls decrease as the load decreases in the ultra
313
supercritical tower boiler with annular furnace.
314
Table 3 summarizes the total pressure drops of two 600 MW supercritical CFB
315
boilers (the one is with annular furnace in this paper and another boiler is proposed by
316
HB (Harbin Boiler) company [9]). It makes clear that the total pressure drop of
317
supercritical CFB boiler with annular furnace is lower than that in HB company’s
318
supercritical CFB boiler. In supercritical CFB boiler with annular furnace, more water 16
Page 16 of 29
319
walls are arranged on the inner ring sidewalls and the design of water wall reduces the
320
furnace height, so the gravitational pressure drop is minished. Besides, the friction
321
resistance is directly proportional to the square of the flow speed. Compared with HB
322
company’s supercritical CFB boiler, lower mass flux are applied and the operating
323
conditions of supercritical CFB boiler with annular furnace are harsher. So the friction
324
pressure drop also can be reduced. Therefore, the energy cost of feed pump will be
325
reduced efficiently.
326
4.2 .Flow distribution
327
Fig. 5 shows the mass flux distribution at three different loads (BMCR, 75%
328
BMCR and 30% BMCR). At BMCR load, the fluctuation range of mass flux in inner
329
ring sidewalls is 579.0-713.5 kg/(m2s) and that in outer sidewalls is 647.8-726.7
330
kg/(m2s). The relative difference of flow distribution in outer ring water walls, which is
331
18.8%, is higher than that in outer ring water walls, which is 10.8%. The difference of
332
flow distribution in the vertical water wall is mainly caused by the heat absorption
333
deviation in the width direction of the furnace. Moreover, the mass flux have a positive
334
response to heat flux, namely, when less heat is absorbed by a tube, less flow of the
335
tube is drawn. It implies the gravitational pressure drop becomes chief flow resistance
336
with smooth tubes installed in vertical water wall and the average fluid density
337
increases with decreasing heat flux, which enhances gravitational drag in relevant
338
circuits. For instance, in outer right wall the mass flux in circuit 17 with the highest heat
339
flux is the highest, which is 713.5 kg/(m2s) and that in circuit 13 with lowest heat flux is 17
Page 17 of 29
340
the lowest, which is 624.4 kg/(m2s). Except for the heat absorption deviation, the length
341
of pipes also has effect on the flow distribution. Because the pipes in circuits 7, 8, 28
342
and 29 through the cyclone separator region are longer than others, the mass fluxes in
343
these circuits are low.
344
With the observation of the calculation data in Fig.5, it can be concluded that the
345
flow distribution situations at low loads (70% BMCR and 30% BMCR) are similar
346
with that at BMCR load. The reason is that the same heat absorption deviation
347
coefficients have been assumed along furnace width and the similar heat flux curves
348
along at vertical direction are applied at three different loads, which is consistent with
349
actual boiler operation. The decrease of the boiler load results in decrease of the mass
350
flux deviation. At 75% BMCR load, the fluctuation range of the mass flux in inner ring
351
sidewalls is 436.3-561.8 kg/(m2s) and that in outer sidewalls is 489.4-559.8 kg/(m2s).
352
At 30% BMCR load, the mass flux range in inner ring sidewalls is 177.4-234.2 kg/(m2s)
353
and that in outer sidewalls is 198.9-228.0 kg/(m2s). Generally, with the good positive
354
flow characteristics in 600 MW supercritical boiler with annular furnace, restriction
355
orifices can be spared for flow regulation, which makes water wall design easier.
356
4.3. Temperature distribution of outlet vapor
357
Fig. 6 shows the temperature distribution of outlet vapor in vertical water wall at
358
three different loads (BMCR, 75% BMCR and 30% BMCR). With large heat
359
absorption deviation, the maximum difference value of outlet fluid temperature
360
happens in outer front sidewall and outer rear sidewall among 8 pieces of walls. On 18
Page 18 of 29
361
account of symmetrical heat flux distribution, outlet vapor temperature distributions of
362
circuits in outer front sidewalls and outer rear sidewalls are symmetrical. At BMCR
363
load, in outer front sidewall the maximum outlet vapor temperature is 438.9 ℃ and
364
minimum outlet vapor temperature is 405.8 ℃, whose temperature difference is
365
33.1 ℃. At 75% BMCR load, in outer front sidewall the maximum outlet vapor
366
temperature is 403.8 ℃ and the minimum outlet vapor temperature is 375.6 ℃,
367
whose temperature difference is 28.2 ℃. At 30% BMCR load, in outer front sidewall
368
the maximum outlet vapor temperature is 401.3.6 ℃ and the minimum outlet vapor
369
temperature is 312.6 ℃, whose temperature difference is 88.7 ℃. It is seen that outlet
370
fluid temperature deviation of different circuits in inner sidewalls at 30% BMCR load is
371
higher than that at BMCR and 75% BMCR load. It is because the influence of furnace
372
heat flux on outlet vapor temperature is strengthened under low mass flux operation of
373
boiler. At 30% BMCR load, in outer front sidewall, maximum outlet fluid temperature
374
appears in circuit 6, and minimum outlet fluid temperature appears in circuit 1, whose
375
relative temperature difference is 22.1%.
376
Heat absorption deviation coefficients of circuits 7, 8, 28 and 29 are higher than that
377
of circuits 9, 10, 30 and 31, but the tubes sections in circuits 7, 8, 28 and 29 through
378
cyclone separator region are not heated. Taken the two factors into consideration, the
379
total heat absorbed by tube in circuits 7, 8, 28 and 29 is low. So the outlet fluid
380
temperature in circuits 9, 10, 30 and 31 is higher than that in circuits 7, 8, 28 and 29.
381
4.4. Metal temperature calculation results 19
Page 19 of 29
382
In outer right wall, inner front wall and the corners of inner ring sidewalls, most
383
dangerous circuits 17, 47 and 52, are selected as representative to shown metal
384
temperature. Figs. 7-9 shows fluid temperature and the temperatures of tube outer-wall,
385
middle part of tube wall, tube inner-wall and the tip of fin at BMCR load in circuits 17,
386
47 and 52. Operating at supercritical pressures, the internal fluid is in single-phase
387
region and temperature increases with heat absorbing process. Meanwhile, the
388
temperatures of tube and fin increase with increasing fluid temperature. In outer ring
389
sidewalls, tube outer-wall temperature and the tip temperature of fins simultaneously
390
reach the maximum value at the outlet of water wall, which are 499.9 ℃ and 512.4 ℃.
391
The maximum tube outer-wall temperature in circuits 47 and 52 are 487.5 ℃ and
392
477 ℃. The maximum tip temperature of fins in circuits 47 and 52 are 501.6 ℃ and
393
492.7 ℃. At BMCR, the temperature values of tube and fin are highest and the result
394
shows they are less than 520 ℃, which can ensure the safety of water wall. On account
395
of abrupt change of furnace heat flux, the metal temperature has a speedy increase at the
396
height 15.77 m of furnace. Due to physical properties of fluid varying with temperature
397
sharply in large specific heat region, a heat transfer enhancement occurs at about the
398
furnace height of 35 m, which can be inferred from the decreasing of the temperature
399
difference between tube inner-wall and fluid. At the height 45.6 m of furnace, the
400
temperatures of tube and fin have the same value with fluid temperature and the data of
401
the mental temperature show a large fluctuation. The reason is that 0 m length of tube
402
has been defined at local sites, which is necessary while the mathematical model is 20
Page 20 of 29
403
implemented on a computer. In fact, this type of temperature fluctuation has no
404
meaning for the boiler operation.
405
Figs. 10-12 show the fluid temperature and the temperatures of tube outer-wall,
406
middle part of tube wall, tube inner-wall and the tip of fin at 75% BMCR load in
407
circuits 17, 47 and 52. The operating pressure at 75% BMCR load is slightly lower than
408
the critical pressure. At the furnace height of less than 3.2 m, the value of heat flux is 0.
409
The metal temperatures are same with single-phase liquid temperature. At the height
410
3.2-28 m of furnace, affected by heat flux the metal temperature is higher than the
411
single-phase liquid temperature and it increases monotonously with the rise of the
412
furnace height in circuit 3. At the height 28-40 m of furnace, the fluid turns into
413
two-phase region and the fluid temperature remains the same. Because heat transfer
414
mechanism of single-phase fluid is different from that of two-phase fluid, the heat
415
transfer coefficient increases rapidly while working fluid enters two-phase area.
416
Meanwhile, the intense heat transfer enhancement causes the temperatures of tube and
417
fin decrease. The flow completely becomes the vapour and vapour temperature rises
418
with the increase with heat absorbing process at furnace height of more than 40 m. The
419
maximum temperature of tube and fin in circuits 17, 47 and 52 are 466.8 ℃, 458.5 ℃
420
and 451.4 ℃, which all occur at outlet of water wall.
421
Figs.13-15 show the fluid temperature and the temperatures of tube outer-wall,
422
middle part of tube wall, tube inner-wall and the tip of fin at 30% BMCR load in
423
circuits 17, 47 and 52. At the furnace height of less than 15 m, the flow is in 21
Page 21 of 29
424
single-phase water region and the temperature variation curves at 30% BMCR load are
425
similar with that at 75% BMCR load. Along with the fluid into two-phase region, a
426
distinct heat transfer enhancement occurs in circuit 17 at the height 15-33 m of furnace.
427
The temperatures of tube and fin are related to fluid temperature and heat flux. Under
428
the condition of constant temperature of the fluid in two-phase region, metal
429
temperatures keep constant at the furnace height with same heat flux. At the height 33
430
m of furnace, the heat transfer coefficient suddenly becomes low in two phases area of
431
fluid and the temperatures of tube and fin rise quickly, which suggests that dry-out
432
occurs in the vertical smooth tubes. Whereas, the temperatures of tube and fin in
433
circuits 17, 47 and 52 are always lower than 460 ℃ and the vertical water wall can work
434
safely. At the furnace height of more than 44 m, temperatures rise with heat absorbing
435
process in single phase area of vapour. Duo to the low flow flux at 30% BMCR load,
436
the heat transfer coefficient is lower than that at 75% BMCR load. In circuits 17, 47 and
437
52, the maximum metal temperature are 458.3 ℃, 439.9.5 ℃ and 420.5 ℃ at outlet
438
of water wall.
439
5. Conclusion
440
The water-wall system of a 600 MW supercritical CFB boiler with annular furnace
441
is regarded as a flowing network. The vertical water wall tubes, linking tubes and
442
headers in water-wall system are simplified as heated parallel circuits, unheated
443
linking circuits and pressure nodes. Based on conservation of energy, mass and
444
momentum, the flow distribution, pressure drop, outer working fluid temperature and 22
Page 22 of 29
445
the temperature of tube and fin are gotten through solving a nonlinear mathematical
446
model.
447
Duo to inner and outer annular furnace structure design, the results show that the
448
total pressure drops in annular water wall in this paper at three different loads (BMCR,
449
75% BMCR and 30% BMCR) is lower than that in HB company’s 600 MW
450
supercritical CFB boiler. Affected by heat flux non-uniformity, the relative difference
451
of flow distribution in outer ring water walls is higher than that in outer ring water walls.
452
The mass flux range in inner ring sidewalls is 177.4-234.2 kg/(m2s) and that in outer
453
sidewalls is 198.9-228.0 kg/(m2s) at 30% BMCR load. With the large heat absorption
454
deviation, the biggest outlet fluid temperature difference happens in outer front
455
sidewall, which is 88.7 ℃ at 30% BMCR load. The highest metal temperature is
456
512.4 ℃, which appears in circuit 17 at BMCR load. At 30% BMCR load, the dry-out
457
occurs in the vertical tube but the metal temperatures in the most dangerous circuits 3,
458
25 and 77 are always lower than 460 ℃, which is applicable in the boiler operation. In
459
conclusion, thermal-hydraulic characteristics of the CFB boiler with annular furnace
460
are good, and the water wall structure is appropriate.
461
Acknowledgement
462
This work was supported by the “Strategic Priority Research Program” of the
463
Chinese Academy of Sciences, Grant No. XDA07030100.
464
References
465
[1] D. Yang, J. Pan, Chenn Q. Zhou, et al., Experimental investigation on heat transfer 23
Page 23 of 29
466
and frictional characteristics of vertical upward rifled tube in supercritical CFB
467
boiler, Experimental Thermal and Fluid Science 35 (2) (2011) 291-300.
468
[2] R.Q. Zhang, H.R. Yang, N. Hu, et al., Experimental investigation and model
469
validation of the heat flux profile in a 300 MW CFB boiler, Powder Technology 246
470
(2013) 31-40.
471
[3] E.J. Adam, J.L. Marchetti, Dynamic simulation of large boilers with natural
472
recirculation, Computers and Chemical Engineering 23 (8) (1999) 1031一1040.
473
[4] H. Kim, S. Choi, A model on water level dynamics in natural circulation drum-type
474
boilers, International Communications in Heat and Mass Transfer 32 (6) (2005)
475
786-796.
476
[5] D.R. Tucakovic, V.D. Stevanovic, T. Zivanovic, et al., Thermal-hydraulic analysis
477
of a steam boiler with rifled evaporating tubes, Applied Thermal Engineering 27 (3)
478
(2007) 509-519.
479
[6] F. Dong, Y.Y. Xu, R.H. Lan, Loop analysis method for the numerical calculation of
480
hydrodynamic characteristic of boiler with natural circulation, Journal of Harbin
481
Institute of Technology 39 (3) (2007) 462-466 (in Chinese).
482 483
[7] Z.N. Zhao, Universal model for hydrodynamic calculation, North China Electric Power 12 (2004) 1-4 (in Chinese).
484
[8] J. Pan, D. Yang, H. Yu, et al., Mathematical modeling and thermal-hydraulic
485
analysis of vertical water wall in an ultra supercritical boiler, Applied Thermal
486
Engineering 29 (2009) 2500-2507. 24
Page 24 of 29
487
[9] J. Pan, D. Yang, G.M. Chen, et al. Thermal-hydraulic analysis of a 600 MW
488
supercritical CFB boiler with low mass flux, Applied Thermal Engineering 32
489
(2012) 41-48.
490
[10] J. Pan, G. Wu, D. Yang, Thermal-hydraulic calculation and analysis on water wall
491
system of 600MW supercritical CFB boiler, Applied Thermal Engineering 82(2015)
492
225-236.
493
[11] The National Standard of the Boiler Hydrodynamics Calculation (JB/Z201-83)
494
Shanghai Power Equipment Packaged Design Research Institute, Shanghai, 1983
495
(in Chinese).
496
[12] W.W. Chen, X.D. Fang, A new heat transfer correlation for supercritical water
497
flowing in vertical tubes, International Journal of Heat and Mass Transfer 78 (2014)
498
156-160.
499
[13] J.Y. Yu, B.S. Jia, D. Wu, et al., Optimization of heat transfer coefficient correlation
500
at supercritical pressure using genetic algorithms, Heat Mass Transfer 45 (2009)
501
757-766.
502
[14] J.Pan, D.Yang, Z.C.Dong, et al., Experimental investigation on heat transfer
503
characteristics of water in vertical upward tube under supercritical pressure,
504
Nuclear Power Engineering 01(2011)75-80 (in Chinese).
505
[15] Dan Sun, T.K. Chen, Y.S. Luo, et al., Research on the heat transfer performance of
506
water in vertical upward smooth tube under near critical pressure. Journal of xi'an
507
jiaotong university01(2001) 10-14 (in Chinese). 25
Page 25 of 29
508 509 510 511
[16] K. David, C. Ward, Numerical Analysis: Mathematics of Scientific Computing. Brooks Publishing Company, CA, 2003. [17] S. Kakas, Y. Yener, Heat Conduction, second ed. Hemisphere Publishing Corporation, Washington, USA, 1986.
512
Figure captions
513
Fig. 1. Structure diagram of the 600 MW supercritical CFB boiler with annular furnace.
514
Fig. 2. Flowing network system of water wall.
515
Fig. 3. Top view of heated loops in inner and outer ring vertical water wall.
516
Fig. 4. Average heat flux along furnace height
517
Fig. 5. Flow distribution at BMCR, 75% BMCR and 30% BMCR load.
518
Fig. 6. Temperature distribution of water wall outlet vapor at BMCR, 75% BMCR and
519 520 521 522 523 524 525 526 527 528
30% BMCR load. Fig. 7. Temperature distribution of fluid, tube and fin along the height in loop 17 at BMCR load. Fig. 8. Temperature distribution of fluid, tube and fin along the height in loop 47 at BMCR load. Fig. 9. Temperature distribution of fluid, tube and fin along the height in loop 52 at BMCR load. Fig. 10. Temperature distribution of fluid, tube and fin along the height in loop 17 at 75% BMCR load. Fig. 11. Temperature distribution of fluid, tube and fin along the height in loop 47 at 26
Page 26 of 29
529 530 531 532 533 534 535 536 537
75% BMCR load. Fig. 12. Temperature distribution of fluid, tube and fin along the height in loop 52 at 75% BMCR load. Fig. 13. Temperature distribution of fluid, tube and fin along the height in loop 17 at 30% BMCR load. Fig. 14. Temperature distribution of fluid, tube and fin along the height in loop 47 at 30% BMCR load. Fig. 15. Temperature distribution of fluid, tube and fin along the height in loop 52 at 30% BMCR load.
538
27
Page 27 of 29
539 Parameter
540
RMCR
75%RMCR 30%RMCR
Unit
Mass flow rate
1995
1530
628
t/h
Outlet pressure of economizer
28.45
21.8
10
MPa
Outlet temperature of economizer
329.6
314
100
℃
Vapor temperature in outlet header
415.2
389
360
MPa
Table 1 Design parameters of supercritical CFB boiler with annular furnace.
541 542 Pressure drop (kPa) Item BMCR
543
75% BMCR 30% BMCR
Outer front wall
312.085
290.710
201.777
Outer right wall
312.888
291.272
202.156
Outer rear wall
312.085
290.710
201.777
Outer left wall
312.888
291.272
202.156
Inner front wall
311.713
290.378
201.696
Inner right wall
317.533
294.844
204.007
Inner rear wall
311.713
290.378
201.696
Inner left wall
317.533
294.844
204.007
Total pressure drop 319.145
296.060
204.847
Table 2 The pressure drops of water walls in different walls. 28
Page 28 of 29
544 Total pressure drop (kPa) Item BMCR
75% BMCR 30% BMCR
HB company’ 600 MW 426.060
373.968
246.799
319.145
296.060
204.847
supercritical CFB boiler 600 MW supercritical CFB boiler with annular furnace 545
Table 3 The total pressure drops in vertical water wall at different operating
546
conditions.
29
Page 29 of 29
S1359-4311(15)01249-1 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.11.014 ATE 7294
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
27-7-2015 6-11-2015
Please cite this article as: Long Wang, Dong Yang, Zhi Shen, Kaiyuan Mao, Jun Long, Thermalhydraulic calculation and analysis of a 600 MW supercritical circulating fluidized bed boiler with annular furnace, Applied Thermal Engineering (2015), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.11.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
Thermal-hydraulic calculation and analysis of a 600 MW supercritical circulating
2
fluidized bed boiler with annular furnace
3
Long Wang, Dong Yang*, Zhi Shen, Kaiyuan Mao, Jun Long
4
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong
5
University,No.28, Xianning West Road, Xi’an, Shaanxi 710049, China
6 7
Highlights
8
1.Non-linear model of supercritical CFB boiler with annular furnace is developed.
9
2.Many empirical correlations are used to solve the model.
10
3.The thermal-hydraulic characteristics of boiler are analyzed.
11
4.The results show the design of the annular furnace is reasonable.
12 13
Abstract
14
The development of supercritical Circulating Fluidized Bed (CFB) boiler has great
15
economic and environmental value. An entirely new annular furnace structure with
16
outer and inner ring sidewalls for supercritical CFB boiler has been put forward by
17
Institute of Engineering Thermophysics (IET), Chinese Academy of Sciences and
18
Dongfang Boiler Group Co., Ltd. (DBC). Its outer and inner ring furnace structure
19
makes more water walls arranged and reduces furnace height availably. In addition,
20
compared with other additional evaporating heating surface structures such as
*
Corresponding author. Tel.: +86 029 82668393 E-mail address: [email protected] (D. Yang) 1
Page 1 of 29
21
mid-partition and water-cooled panels, the integrative structure can effectively avoid
22
the bed-inventory overturn and improve the penetrability of secondary air. The
23
conditions of the 600 MW supercritical CFB boiler including capability, pressure and
24
mass flux are harsh. In order to insure the safety of boiler operation, it’s very necessary
25
to analyze the thermal-hydraulic characteristics of water-wall system. The water-wall
26
system with complicated pipe arrangement is regarded as a network consisting of
27
series-parallel circuits, pressure nodes and linking circuits, which represent vertical
28
water-wall tubes, different headers and linking tubes, respectively. Based on the mass,
29
momentum and energy conservation, a mathematical model is built, which consists of
30
some simultaneous nonlinear equations. The mass flux in circuits, pressure drop
31
between headers, outer vapor temperature of water-wall system and metal temperature
32
data of tubes at the boiler maximum continuous rating (BMCR), 75% BMCR and 30%
33
BMCR load are obtained by solving the mathematical model. The results show that the
34
vertical water wall design with smooth tubes in the 600 MW supercritical CFB boiler is
35
applicable.
36
Keywords: supercritical CFB boiler, annular furnace, thermal-hydraulic characteristic,
37
vertical water wall
38
1. Introduction
39
Because of good fuel flexibility, high combustion efficiency, efficient sulfur
40
removal, low NO2 emission, good load following capability and other technical
41
advantages, supercritical CFB technology has recently developed rapidly [1-2]. 2
Page 2 of 29
42
According to thermodynamic theories, the key to obtain higher boiler efficiency is large
43
capacity CFB boiler with higher steam parameters. As the unit capacity increases,
44
more heating surfaces are needed. And some additional evaporating heating surface
45
structures, such as mid-partition and water-cooled panels, correspondingly leads to a
46
series of problems such as non-uniform fluidization, penetrability of secondary air,
47
bed-inventory overturn and layout of several cyclones. In purpose of solving the
48
problems related to the heating surface arrangement, an entirely new annular furnace
49
structure for 600 MW supercritical CFB boiler is put forward by IET, Chinese
50
Academy of Sciences and DBC. The 600 MW supercritical CFB boiler has inner ring
51
and outer ring sidewalls and its operating conditions are harsh. In order to keep the
52
metal temperature of water wall not over reliable range and choose the operating
53
pressure head of feed pump matching the pressure drop of water wall flow system,
54
setting up mathematical model to analyze thermal-hydraulic characteristics of the new
55
supercritical CFB boiler is essential.
56
In the past, due to limitations of working equipment, relevant staffs used complex
57
but not accurate graphic method to model thermal-hydraulic calculation. The graphic
58
method has large errors and it cannot be easily applied on computer to analyze complex
59
water-wall system. In recent years, various calculation models for thermal-hydraulic
60
analysis have been put forward and developed by scholars from different countries.
61
Base on two non-linear models which are for the phase separation in the steam drum
62
and the evaporation process of heated working fluid in vertical water wall, Adam and 3
Page 3 of 29
63
Marchetti [3] presented a dynamic simulator and verified it in boilers with natural
64
recirculation. Kim and Choi [4] assumed the superficial velocity of water was zero and
65
average size of steam bubbles was an arbitrary value. Then they applied constitutional
66
equations into a hydraulic model for drum-type boilers. Tucakovic et al. [5] established
67
a method to investigate operating characteristics of a forced circulation steam boiler in
68
which rifled tubes were installed to increase the turbulivity of steam-water mixture.
69
Dong et al. [6] proposed hydrodynamic circuit analysis method and calculated
70
hydrodynamic characteristic of a boiler with natural circulation. Zhao [7] presented a
71
universal hydraulic calculation model for drum boiler. Pan et al. [8] put forward a
72
non-linear mathematical model for supercritical coal-fired boiler, in which mass
73
conservation equations, momentum conservations equation and energy conservation
74
equation of simplified water-wall system were included. Pan et al. [9-10] applied
75
non-linear mathematical model on hydraulic calculation of conceptual 600MW CFB
76
boiler with mid-partition wall which was proposed by Harbin Boiler Company.
77
Compared with Harbin Boiler Company’s conceptual CFB boiler, the more complex
78
furnace configuration of 600MW CFB boiler with inner and outer ring water-wall
79
system presented higher requirement for boiler operation.
80
The water wall is composed of vertical smooth tubes and rectangular fin in the 600
81
MW supercritical CFB boiler with annular furnace. At different operation condition,
82
the computing methods of the heat transfer and frictional characteristics are studied and
83
corresponding calculation formulas can be found in Ref. [11-15]. A non-linear model is 4
Page 4 of 29
84
developed in this paper by combining these correlations and three conservation laws
85
(mass, momentum and energy conservation). The mass flux distribution of circuits,
86
pressure drop of water-wall system, outlet vapor temperatures of furnace hearth and
87
metal temperatures data at three different loads (BMCR, 75% BMCR and 30% BMCR
88
load) are obtained by directly solving non-linear model with quasi-Newton iterative
89
method. The results show the design of the water wall can guarantee the operating
90
safety.
91 92
Nomenclature
93
di
internal pipe diameter, m
94
dw
external pipe diameter, m
95
f
friction coefficient
96
G
mass flux, kg/(m2s)
97
Gcr
critical mass flux, kg/(m2s)
98
h
specific enthalpy, J/kg
99
hw
enthalpy of tube wall surface fluid, J/kg
100
hf
average enthalpy of fluid, J/kg
101
J
current sharing coefficient of heat flux
102
Jn
current sharing coefficient of internal pipe wall heat flux
103
l
pipe length, m
104
Nu
nusselt number
5
Page 5 of 29
105
Rew
reynolds number of tube wall surface fluid
106
p
pressure, MPa
107
p(i)
pressure in circuit i, MPa
108
△p(i) total pressure loss in circuit i, MPa
109
△pf
frictional pressure loss, MPa
110
△pg
gravitational pressure loss, MPa
111
△pl
local resistance pressure loss, MPa
112
q
heat flux, W/m2
113
qcr
crcritical heat flux, W/m2
114
qw
outer wall heat flux, W/m2
115
qin
inner wall heat flux, W/m2
116
s
pitch between adjacent tubes, m
117
t
temperature, ℃
118
tf
bulk fluid temperature, ℃
119
ti
tube inner-wall temperature, ℃
120
tm
metal temperature in the middle of tube wall, ℃
121
tw
tube outer-wall temperature, ℃
122
tqd
metal temperature in the tip of fin, ℃
123
tqg
metal temperature in the root of fin, ℃
124
w
total mass flow rate in water wall, kg/s
125
w(i)
mass flow rate in circuit i, kg/s 6
Page 6 of 29
126
x
vapor quality of working fluid, kg/kg
127
xcr
critical vapor quality, kg/kg
128
Greek symbols
129
α
heat transfer coefficient, W/(m2 ℃)
130
δ
thickness of fin, m
131
density, kg/m3
132
l
density of water, kg/m3
133
g
density of saturated vapor, kg/m3
134
average density of fluid, kg/m3
135
λ
thermal conductivity of tube, W/(m﹒k)
136
w
thermal conductivity of tube wall surface fluid, N﹒s/m2
137
w
dynamic viscosity of tube wall surface fluid, N﹒s/m2
138
ηqd
balance coefficient of heat flux in the tip of fin
139
ηqg
balance coefficient of heat flux in the root of fin
140
correction coefficient
f
141
2. Water wall structure and circuits division
142
2.1. Water wall structure
143
The structure diagram of the 600 MW supercritical CFB boiler with annular furnace
144
is displayed in Fig. 1. The perimeter of annular furnace consists of outer ring and inner
145
ring sidewalls, whose sizes are 33600×19900 mm and 8400×22099.41 mm. The
146
vertical water wall with simple smooth tubes is applied. 6 cyclones are divided into two 7
Page 7 of 29
147
groups and symmetrically installed at outer front wall and outer rear wall. The
148
integrative structure can effectively avoid the bed-inventory overturn, improve the
149
penetrability of secondary air and reduce the flow resistance. In addition, more water
150
walls can be arranged on the inner ring sidewalls to ensure adequate heat absorption,
151
which is a key factor to ensure the operation safety of the boiler. Besides, the design of
152
water wall reduces the furnace height availably and the cost of boiler is economized.
153
The boiler design parameters at BMCR, 75% BMCR and 30% BMCR load are shown
154
in Table 1.
155
2.2. Flow circuit division and furnace-side heat flux distribution
156
The vertical water wall tubes, linking tubes and headers in water-wall system of the
157
600 supercritical CFB boiler with annular furnace, can be regarded as heated
158
series-parallel circuits, unheated linking circuits and pressure nodes. Then the
159
water-wall system processing becomes a flowing network which is shown in Fig. 2
160
and includes 70 heated circuits, 17 unheated linking circuits and 18 pressure nodes. In
161
Fig. 2, the numbers of heated circuits in outer front wall, outer right wall, outer rear
162
wall, outer left wall, inner front wall, inner right wall, inner rear wall and inner left wall
163
are 1-12, 13-21, 22-33, 34-42, 43-51, 53-55, 57-65 and 67-69, respectively. The serial
164
numbers of circuits 52, 56, 66, 70 refer to water wall in the corner of inner ring
165
sidewalls. The linking tubes, lower distribution headers, inlet headers, upper outlet
166
headers and steam-water separator are represented by serial numbers 71-87, 88, 89-96,
167
97-104 and 105, respectively. The top view of heated circuits in inner and outer ring 8
Page 8 of 29
168
vertical water wall is shown in Fig.3.
169
Because the CFB boiler with annular furnace, which is put forward by IET, Chinese
170
Academy of Sciences and DBC, has the entirely new annular furnace structure and
171
hasn’t been in operation, furnace-side heat flux curve is estimated according to furnace
172
heat equilibrium [11]. Fig. 4 gives heat flux distribution at different loads along height.
173
Heat flux will increase with the load increasing can be reflected, which is reasonable.
174
The non-uniformity of heat flux at level direction also has influence on the flow
175
distribution of circuits. The deviation factor of heat flux along furnace width is
176
factitiously supposed to be among 80% to 120% of the average furnace-side heat flux.
177
Because the size of outer ring sidewalls is larger than the size of inner ring sidewalls,
178
the heat flux deviation in outer ring sidewalls is larger. With this assumption, the heat
179
flux deviation in the new 600 MW supercritical CFB boiler can be well simulated and
180
the heat flux deviation among all the circuits in water wall is shown in Fig. 3.
181
3. Mathematical model
182
3.1. Analysis model of mass flux and pressure drop
183
Water-wall system is simplified as flowing network. Based on energy conservation
184
between working fluid absorption heat and furnace effective radiation, working fluid
185
enthalpy in reference section of water wall can be obtained. According to the fluid
186
flowing network, 87 nonlinear momentum conservation equations of 87 circuits (70
187
heated circuits and 17 unheated linking circuits) and 18 nonlinear mass conservation
188
equations of 18 nodes is presented. The pressure of nodes and the circuit mass flux can 9
Page 9 of 29
189
be obtained by using Chord secant method to solving the nonlinear mathematical
190
model[16].
191
The momentum conservation equation means pressure difference between import
192
node and export node equals pressure drop which causes by working flow. For 70
193
heated circuits in outer front wall, outer right wall, outer rear wall, outer left wall, inner
194
front wall, inner right wall, inner rear wall and inner left wall, momentum conservation
195
equations are given by: 0 p (89) p (97) p ( i )
i 1 12
(1)
0 p (90) p (98) p ( i )
i 13 21
(2)
198
0 p (91) p (99) p ( i )
i 22 33
(3)
199
0 p (92) p (100) p ( i )
i 34 42
(4)
200
0 p (93) p (101) p ( i )
i 43 52
(5)
201
0 p (94) p (102) p ( i )
i 53 56
(6)
202
0 p (95) p (103) p ( i )
i 5 7 6 6
(7)
203
0 p (96) p (104) p ( i )
i 67 70
(8)
204
The momentum conservation equations of unheated linking circuits 71-87 are given
196 197
205
by:
206
0 p cs p (88) p (71)
207
0 p (88) p ( i 17) p ( i )
i 72 79
(10)
0 p ( i 17) p (105) p ( i )
i 80 87
(11)
208 209
(9)
The friction between working fluid and inner wall of tubes, the height difference 10
Page 10 of 29
210
at vertical direction between inlet position and outlet position, local resistance and
211
acceleration give rise to the pressure drop p (i) . With the fact that acceleration
212
pressure drops are relatively little, the pressure drops in circuit i are calculated by:
213
p (i ) p f (i ) p g (i ) p l (i )
214
The gravitational pressure drop
(12) pg
can be given with the average density of
215
working fluid and height difference at vertical direction between inlet position and
216
outlet position known. The average density of working fluid can be obtained
217
through calculation of property of fluid.
218
pg g h
219
The single-phase water, single-phase vapor and supercritical water all can be
(13)
220
treated as single-phase fluid and flow frictional pressure drop
221
fluid is given as:
222
p f f
223
In smooth tube, the frictional pressure drop
224
l G
p f
of single-phase
2
(14)
di 2 p f
of two-phase steam-water is
calculated as [11]: l G
2
l
225
p f f
226
In the above formula, the correction factors is obtained by:
227
=1+
228
1
di 2l
[1 x (
g
1)]
1000 x 1 x 1 l G g 1 x l 1 g
(15)
G 1 0 0 0k g
/ m s 2
G 1 0 0 0k g /m 2
(16)
s
(17)
11
Page 11 of 29
229
=1+
1000 x 1 x 1 l G g 1 (1 x ) l 1 g
G 1 0 0 0k g /m 2
(18)
s
230
For flow under different states, the friction coefficient f is associated with tube
231
inner wall roughness k and the value of k for carbon steel tube is 6 10 -5 , which
232
is used in the calculation of flow frictional pressure drop
233
coefficient f can be achieved by[11]:
234
235 236
f
p f
. The friction
1 3 .7 d i 4 lg ( ) k
(19)
2
The mass conservation equations of nodes 88-105, which are used to calculate the mass flow flux of heated circuits and unheated linking circuits, are presented as:
237
0 w w (71)
238
0 w (7 1)
(20)
79
w (i )
(21)
i 72
12
239
0 w (7 2 )
w (i )
(22)
i 1
21
240
0 w (7 3)
w (i )
(23)
i 1 3
33
241
0 w (7 4 )
w (i )
(24)
w (i )
(25)
i 22
42
242
0 w (7 5)
i 34
52
243
0 w (7 6 )
w (i )
(26)
i 43
12
Page 12 of 29
56
244
0 w (7 7 )
w (i )
(27)
i 53
66
245
0 w (7 8)
w (i )
(28)
i 57
70
246
0 w (7 9 )
w (i )
(29)
w ( i ) w (8 0 )
(30)
i 67
12
247
0
i 1
21
248
0
w ( i ) w (8 1)
(31)
i 1 3
33
249
0
w ( i ) w (8 2 )
(32)
w ( i ) w (8 3)
(33)
i 22
42
250
0
i 34
52
251
0
w ( i ) w (8 4 )
(34)
i 43
56
252
0
w ( i ) w (8 5)
(35)
i 53
66
253
0
w ( i ) w (8 6 )
(36)
i 57
70
254
0
w ( i ) w (8 7 )
(37)
i 67
87
255
0
w (i ) w
(38)
i 80
256
Energy conservation equation, in which the thermodynamic parameters used are
257
reckoned with furnace-sided heat flux curve along height and heat flux deviation along
258
width, is given by: 13
Page 13 of 29
qsl
259
hout hin
260
The local pressure drop p l which is mainly caused by elbows, inlet structure and
261
outlet structure, is taken into account in this paper and is calculated by correlation
262
formulas in Ref. [11].
263
3.2. Analysis model of metal temperature
(39)
w
264
The metal temperature of water-wall system can be predicted with the mass flux of
265
circuits and the pressure of nodes known. The heat transfer coefficient of working fluid
266
is a key factor for metal temperatures calculation of water wall and affected by four
267
elements, which are pressure parameter, fluid state, tube structure and the fireside heat
268
flux. A lot of heat transfer coefficient empirical formulas and calculation models have
269
been summarized in Ref. [11-15].
270 271
When the pressure is higher than 22.1 MPa, the flow is in supercritical pressure region and the heat transfer correlations in smooth tube are given as follows[14]:
272
(1) In low enthalpy region
273
N u 1.9855 R e
274
(2) In high enthalpy region
275
N u 1.5803 R e
276
When the pressure is higher than 19 MPa and lower than 22.1 MPa, the critical
277
conditions of heat transfer deteriorations are very important in the process of
278
calculating heat transfer coefficient. Heat transfer deteriorations include departure
0.44307 w
0.50143 w
（ h w h f ） w （ t t ） f w w
（ h w h f ） w （ t t ） f w w
0.93953
1.06098
w f
w f
0.54295
(40)
2.19757
(41)
14
Page 14 of 29
279
from nucleate boiling (DNB) and dry-out, which are related to critical heat flux and
280
critical vapor quality, respectively. The critical heat flux are researched by Sun et al.
281
[15] and the correlation are obtained by: G G cr
(42)
G G cr
(43)
q cr 3343.92(22.115 p )
283
q cr 2 .2 6 6 5( 2 2 .1 1 5 p )
284
In the above formula, the critical mass flux is calculated as:
285
G cr 800.44 223.85 ln(22.115 p )
286
under the pressure 19MPa~22.1MPa, before the DNB occurs the heat transfer
287
coefficients are calculated by the national standard of the boiler hydrodynamics
288
calculation (China) [11]. After the DNB occurs, the heat transfer correlation is given
289
by [15]:
290
0.4091
0 .1 0 0 7
G
（ 1-x ）
282
G
-0.3835
0.6792
（ 1-x ）
0 .7 3 8 5
N u 0.1864 R e G x (1 x ) g l
0 .1 8 8 8
(44)
0.0545
P rG w
3.4313
q
1.0738
(
G cr
)
0.5928
p p cr
2.8319
(45)
291 292 293
When the pressure is lower than 19MPa, the heat transfer correlations in the literature [11] are used into the analysis model.
294
The calculation of inner and outer wall temperatures of tube is related to inner and
295
outer diameter, fluid temperature, heat transfer coefficient, current sharing coefficient
296
heat flux and thermal conductivity of tube, and they are confirmed by [11]:
297
ti t f J n
qw d w
298
tw t f J n
qw d w
(46)
di
di
Jq w
2d w (d w d i )
(47)
(d w d i )
15
Page 15 of 29
299
The temperatures of the middle of tube walls are given by:
300
tm
301
The temperature in the root of fins [17] and the tip of fins [9] are calculated as:
302
t q g t f q w q g
303
t qd t qg
ti t w
(48)
2
q qd 2
dw
[ln (
di
(
dw di
s dw
)
)
di 2
1
(49)
]
2
(50)
2
304
4. Results and discussions
305
4.1. Pressure drop
306
Table 2 summarizes the pressure drops of 8 pieces of vertical water walls in
307
supercritical CFB boiler with annular furnace at three different loads (BMCR, 75%
308
BMCR and 30% BMCR). The pressure drops in right wall and left wall are higher than
309
those in front wall and rear wall. At BMCR load, the differences between minimum
310
pressure drop and maximum pressure drop in outer ring and inner ring water walls are
311
reasonable, which are 1.83% and 0.26%, respectively. What’s more, the pressure drop
312
differences among different water walls decrease as the load decreases in the ultra
313
supercritical tower boiler with annular furnace.
314
Table 3 summarizes the total pressure drops of two 600 MW supercritical CFB
315
boilers (the one is with annular furnace in this paper and another boiler is proposed by
316
HB (Harbin Boiler) company [9]). It makes clear that the total pressure drop of
317
supercritical CFB boiler with annular furnace is lower than that in HB company’s
318
supercritical CFB boiler. In supercritical CFB boiler with annular furnace, more water 16
Page 16 of 29
319
walls are arranged on the inner ring sidewalls and the design of water wall reduces the
320
furnace height, so the gravitational pressure drop is minished. Besides, the friction
321
resistance is directly proportional to the square of the flow speed. Compared with HB
322
company’s supercritical CFB boiler, lower mass flux are applied and the operating
323
conditions of supercritical CFB boiler with annular furnace are harsher. So the friction
324
pressure drop also can be reduced. Therefore, the energy cost of feed pump will be
325
reduced efficiently.
326
4.2 .Flow distribution
327
Fig. 5 shows the mass flux distribution at three different loads (BMCR, 75%
328
BMCR and 30% BMCR). At BMCR load, the fluctuation range of mass flux in inner
329
ring sidewalls is 579.0-713.5 kg/(m2s) and that in outer sidewalls is 647.8-726.7
330
kg/(m2s). The relative difference of flow distribution in outer ring water walls, which is
331
18.8%, is higher than that in outer ring water walls, which is 10.8%. The difference of
332
flow distribution in the vertical water wall is mainly caused by the heat absorption
333
deviation in the width direction of the furnace. Moreover, the mass flux have a positive
334
response to heat flux, namely, when less heat is absorbed by a tube, less flow of the
335
tube is drawn. It implies the gravitational pressure drop becomes chief flow resistance
336
with smooth tubes installed in vertical water wall and the average fluid density
337
increases with decreasing heat flux, which enhances gravitational drag in relevant
338
circuits. For instance, in outer right wall the mass flux in circuit 17 with the highest heat
339
flux is the highest, which is 713.5 kg/(m2s) and that in circuit 13 with lowest heat flux is 17
Page 17 of 29
340
the lowest, which is 624.4 kg/(m2s). Except for the heat absorption deviation, the length
341
of pipes also has effect on the flow distribution. Because the pipes in circuits 7, 8, 28
342
and 29 through the cyclone separator region are longer than others, the mass fluxes in
343
these circuits are low.
344
With the observation of the calculation data in Fig.5, it can be concluded that the
345
flow distribution situations at low loads (70% BMCR and 30% BMCR) are similar
346
with that at BMCR load. The reason is that the same heat absorption deviation
347
coefficients have been assumed along furnace width and the similar heat flux curves
348
along at vertical direction are applied at three different loads, which is consistent with
349
actual boiler operation. The decrease of the boiler load results in decrease of the mass
350
flux deviation. At 75% BMCR load, the fluctuation range of the mass flux in inner ring
351
sidewalls is 436.3-561.8 kg/(m2s) and that in outer sidewalls is 489.4-559.8 kg/(m2s).
352
At 30% BMCR load, the mass flux range in inner ring sidewalls is 177.4-234.2 kg/(m2s)
353
and that in outer sidewalls is 198.9-228.0 kg/(m2s). Generally, with the good positive
354
flow characteristics in 600 MW supercritical boiler with annular furnace, restriction
355
orifices can be spared for flow regulation, which makes water wall design easier.
356
4.3. Temperature distribution of outlet vapor
357
Fig. 6 shows the temperature distribution of outlet vapor in vertical water wall at
358
three different loads (BMCR, 75% BMCR and 30% BMCR). With large heat
359
absorption deviation, the maximum difference value of outlet fluid temperature
360
happens in outer front sidewall and outer rear sidewall among 8 pieces of walls. On 18
Page 18 of 29
361
account of symmetrical heat flux distribution, outlet vapor temperature distributions of
362
circuits in outer front sidewalls and outer rear sidewalls are symmetrical. At BMCR
363
load, in outer front sidewall the maximum outlet vapor temperature is 438.9 ℃ and
364
minimum outlet vapor temperature is 405.8 ℃, whose temperature difference is
365
33.1 ℃. At 75% BMCR load, in outer front sidewall the maximum outlet vapor
366
temperature is 403.8 ℃ and the minimum outlet vapor temperature is 375.6 ℃,
367
whose temperature difference is 28.2 ℃. At 30% BMCR load, in outer front sidewall
368
the maximum outlet vapor temperature is 401.3.6 ℃ and the minimum outlet vapor
369
temperature is 312.6 ℃, whose temperature difference is 88.7 ℃. It is seen that outlet
370
fluid temperature deviation of different circuits in inner sidewalls at 30% BMCR load is
371
higher than that at BMCR and 75% BMCR load. It is because the influence of furnace
372
heat flux on outlet vapor temperature is strengthened under low mass flux operation of
373
boiler. At 30% BMCR load, in outer front sidewall, maximum outlet fluid temperature
374
appears in circuit 6, and minimum outlet fluid temperature appears in circuit 1, whose
375
relative temperature difference is 22.1%.
376
Heat absorption deviation coefficients of circuits 7, 8, 28 and 29 are higher than that
377
of circuits 9, 10, 30 and 31, but the tubes sections in circuits 7, 8, 28 and 29 through
378
cyclone separator region are not heated. Taken the two factors into consideration, the
379
total heat absorbed by tube in circuits 7, 8, 28 and 29 is low. So the outlet fluid
380
temperature in circuits 9, 10, 30 and 31 is higher than that in circuits 7, 8, 28 and 29.
381
4.4. Metal temperature calculation results 19
Page 19 of 29
382
In outer right wall, inner front wall and the corners of inner ring sidewalls, most
383
dangerous circuits 17, 47 and 52, are selected as representative to shown metal
384
temperature. Figs. 7-9 shows fluid temperature and the temperatures of tube outer-wall,
385
middle part of tube wall, tube inner-wall and the tip of fin at BMCR load in circuits 17,
386
47 and 52. Operating at supercritical pressures, the internal fluid is in single-phase
387
region and temperature increases with heat absorbing process. Meanwhile, the
388
temperatures of tube and fin increase with increasing fluid temperature. In outer ring
389
sidewalls, tube outer-wall temperature and the tip temperature of fins simultaneously
390
reach the maximum value at the outlet of water wall, which are 499.9 ℃ and 512.4 ℃.
391
The maximum tube outer-wall temperature in circuits 47 and 52 are 487.5 ℃ and
392
477 ℃. The maximum tip temperature of fins in circuits 47 and 52 are 501.6 ℃ and
393
492.7 ℃. At BMCR, the temperature values of tube and fin are highest and the result
394
shows they are less than 520 ℃, which can ensure the safety of water wall. On account
395
of abrupt change of furnace heat flux, the metal temperature has a speedy increase at the
396
height 15.77 m of furnace. Due to physical properties of fluid varying with temperature
397
sharply in large specific heat region, a heat transfer enhancement occurs at about the
398
furnace height of 35 m, which can be inferred from the decreasing of the temperature
399
difference between tube inner-wall and fluid. At the height 45.6 m of furnace, the
400
temperatures of tube and fin have the same value with fluid temperature and the data of
401
the mental temperature show a large fluctuation. The reason is that 0 m length of tube
402
has been defined at local sites, which is necessary while the mathematical model is 20
Page 20 of 29
403
implemented on a computer. In fact, this type of temperature fluctuation has no
404
meaning for the boiler operation.
405
Figs. 10-12 show the fluid temperature and the temperatures of tube outer-wall,
406
middle part of tube wall, tube inner-wall and the tip of fin at 75% BMCR load in
407
circuits 17, 47 and 52. The operating pressure at 75% BMCR load is slightly lower than
408
the critical pressure. At the furnace height of less than 3.2 m, the value of heat flux is 0.
409
The metal temperatures are same with single-phase liquid temperature. At the height
410
3.2-28 m of furnace, affected by heat flux the metal temperature is higher than the
411
single-phase liquid temperature and it increases monotonously with the rise of the
412
furnace height in circuit 3. At the height 28-40 m of furnace, the fluid turns into
413
two-phase region and the fluid temperature remains the same. Because heat transfer
414
mechanism of single-phase fluid is different from that of two-phase fluid, the heat
415
transfer coefficient increases rapidly while working fluid enters two-phase area.
416
Meanwhile, the intense heat transfer enhancement causes the temperatures of tube and
417
fin decrease. The flow completely becomes the vapour and vapour temperature rises
418
with the increase with heat absorbing process at furnace height of more than 40 m. The
419
maximum temperature of tube and fin in circuits 17, 47 and 52 are 466.8 ℃, 458.5 ℃
420
and 451.4 ℃, which all occur at outlet of water wall.
421
Figs.13-15 show the fluid temperature and the temperatures of tube outer-wall,
422
middle part of tube wall, tube inner-wall and the tip of fin at 30% BMCR load in
423
circuits 17, 47 and 52. At the furnace height of less than 15 m, the flow is in 21
Page 21 of 29
424
single-phase water region and the temperature variation curves at 30% BMCR load are
425
similar with that at 75% BMCR load. Along with the fluid into two-phase region, a
426
distinct heat transfer enhancement occurs in circuit 17 at the height 15-33 m of furnace.
427
The temperatures of tube and fin are related to fluid temperature and heat flux. Under
428
the condition of constant temperature of the fluid in two-phase region, metal
429
temperatures keep constant at the furnace height with same heat flux. At the height 33
430
m of furnace, the heat transfer coefficient suddenly becomes low in two phases area of
431
fluid and the temperatures of tube and fin rise quickly, which suggests that dry-out
432
occurs in the vertical smooth tubes. Whereas, the temperatures of tube and fin in
433
circuits 17, 47 and 52 are always lower than 460 ℃ and the vertical water wall can work
434
safely. At the furnace height of more than 44 m, temperatures rise with heat absorbing
435
process in single phase area of vapour. Duo to the low flow flux at 30% BMCR load,
436
the heat transfer coefficient is lower than that at 75% BMCR load. In circuits 17, 47 and
437
52, the maximum metal temperature are 458.3 ℃, 439.9.5 ℃ and 420.5 ℃ at outlet
438
of water wall.
439
5. Conclusion
440
The water-wall system of a 600 MW supercritical CFB boiler with annular furnace
441
is regarded as a flowing network. The vertical water wall tubes, linking tubes and
442
headers in water-wall system are simplified as heated parallel circuits, unheated
443
linking circuits and pressure nodes. Based on conservation of energy, mass and
444
momentum, the flow distribution, pressure drop, outer working fluid temperature and 22
Page 22 of 29
445
the temperature of tube and fin are gotten through solving a nonlinear mathematical
446
model.
447
Duo to inner and outer annular furnace structure design, the results show that the
448
total pressure drops in annular water wall in this paper at three different loads (BMCR,
449
75% BMCR and 30% BMCR) is lower than that in HB company’s 600 MW
450
supercritical CFB boiler. Affected by heat flux non-uniformity, the relative difference
451
of flow distribution in outer ring water walls is higher than that in outer ring water walls.
452
The mass flux range in inner ring sidewalls is 177.4-234.2 kg/(m2s) and that in outer
453
sidewalls is 198.9-228.0 kg/(m2s) at 30% BMCR load. With the large heat absorption
454
deviation, the biggest outlet fluid temperature difference happens in outer front
455
sidewall, which is 88.7 ℃ at 30% BMCR load. The highest metal temperature is
456
512.4 ℃, which appears in circuit 17 at BMCR load. At 30% BMCR load, the dry-out
457
occurs in the vertical tube but the metal temperatures in the most dangerous circuits 3,
458
25 and 77 are always lower than 460 ℃, which is applicable in the boiler operation. In
459
conclusion, thermal-hydraulic characteristics of the CFB boiler with annular furnace
460
are good, and the water wall structure is appropriate.
461
Acknowledgement
462
This work was supported by the “Strategic Priority Research Program” of the
463
Chinese Academy of Sciences, Grant No. XDA07030100.
464
References
465
[1] D. Yang, J. Pan, Chenn Q. Zhou, et al., Experimental investigation on heat transfer 23
Page 23 of 29
466
and frictional characteristics of vertical upward rifled tube in supercritical CFB
467
boiler, Experimental Thermal and Fluid Science 35 (2) (2011) 291-300.
468
[2] R.Q. Zhang, H.R. Yang, N. Hu, et al., Experimental investigation and model
469
validation of the heat flux profile in a 300 MW CFB boiler, Powder Technology 246
470
(2013) 31-40.
471
[3] E.J. Adam, J.L. Marchetti, Dynamic simulation of large boilers with natural
472
recirculation, Computers and Chemical Engineering 23 (8) (1999) 1031一1040.
473
[4] H. Kim, S. Choi, A model on water level dynamics in natural circulation drum-type
474
boilers, International Communications in Heat and Mass Transfer 32 (6) (2005)
475
786-796.
476
[5] D.R. Tucakovic, V.D. Stevanovic, T. Zivanovic, et al., Thermal-hydraulic analysis
477
of a steam boiler with rifled evaporating tubes, Applied Thermal Engineering 27 (3)
478
(2007) 509-519.
479
[6] F. Dong, Y.Y. Xu, R.H. Lan, Loop analysis method for the numerical calculation of
480
hydrodynamic characteristic of boiler with natural circulation, Journal of Harbin
481
Institute of Technology 39 (3) (2007) 462-466 (in Chinese).
482 483
[7] Z.N. Zhao, Universal model for hydrodynamic calculation, North China Electric Power 12 (2004) 1-4 (in Chinese).
484
[8] J. Pan, D. Yang, H. Yu, et al., Mathematical modeling and thermal-hydraulic
485
analysis of vertical water wall in an ultra supercritical boiler, Applied Thermal
486
Engineering 29 (2009) 2500-2507. 24
Page 24 of 29
487
[9] J. Pan, D. Yang, G.M. Chen, et al. Thermal-hydraulic analysis of a 600 MW
488
supercritical CFB boiler with low mass flux, Applied Thermal Engineering 32
489
(2012) 41-48.
490
[10] J. Pan, G. Wu, D. Yang, Thermal-hydraulic calculation and analysis on water wall
491
system of 600MW supercritical CFB boiler, Applied Thermal Engineering 82(2015)
492
225-236.
493
[11] The National Standard of the Boiler Hydrodynamics Calculation (JB/Z201-83)
494
Shanghai Power Equipment Packaged Design Research Institute, Shanghai, 1983
495
(in Chinese).
496
[12] W.W. Chen, X.D. Fang, A new heat transfer correlation for supercritical water
497
flowing in vertical tubes, International Journal of Heat and Mass Transfer 78 (2014)
498
156-160.
499
[13] J.Y. Yu, B.S. Jia, D. Wu, et al., Optimization of heat transfer coefficient correlation
500
at supercritical pressure using genetic algorithms, Heat Mass Transfer 45 (2009)
501
757-766.
502
[14] J.Pan, D.Yang, Z.C.Dong, et al., Experimental investigation on heat transfer
503
characteristics of water in vertical upward tube under supercritical pressure,
504
Nuclear Power Engineering 01(2011)75-80 (in Chinese).
505
[15] Dan Sun, T.K. Chen, Y.S. Luo, et al., Research on the heat transfer performance of
506
water in vertical upward smooth tube under near critical pressure. Journal of xi'an
507
jiaotong university01(2001) 10-14 (in Chinese). 25
Page 25 of 29
508 509 510 511
[16] K. David, C. Ward, Numerical Analysis: Mathematics of Scientific Computing. Brooks Publishing Company, CA, 2003. [17] S. Kakas, Y. Yener, Heat Conduction, second ed. Hemisphere Publishing Corporation, Washington, USA, 1986.
512
Figure captions
513
Fig. 1. Structure diagram of the 600 MW supercritical CFB boiler with annular furnace.
514
Fig. 2. Flowing network system of water wall.
515
Fig. 3. Top view of heated loops in inner and outer ring vertical water wall.
516
Fig. 4. Average heat flux along furnace height
517
Fig. 5. Flow distribution at BMCR, 75% BMCR and 30% BMCR load.
518
Fig. 6. Temperature distribution of water wall outlet vapor at BMCR, 75% BMCR and
519 520 521 522 523 524 525 526 527 528
30% BMCR load. Fig. 7. Temperature distribution of fluid, tube and fin along the height in loop 17 at BMCR load. Fig. 8. Temperature distribution of fluid, tube and fin along the height in loop 47 at BMCR load. Fig. 9. Temperature distribution of fluid, tube and fin along the height in loop 52 at BMCR load. Fig. 10. Temperature distribution of fluid, tube and fin along the height in loop 17 at 75% BMCR load. Fig. 11. Temperature distribution of fluid, tube and fin along the height in loop 47 at 26
Page 26 of 29
529 530 531 532 533 534 535 536 537
75% BMCR load. Fig. 12. Temperature distribution of fluid, tube and fin along the height in loop 52 at 75% BMCR load. Fig. 13. Temperature distribution of fluid, tube and fin along the height in loop 17 at 30% BMCR load. Fig. 14. Temperature distribution of fluid, tube and fin along the height in loop 47 at 30% BMCR load. Fig. 15. Temperature distribution of fluid, tube and fin along the height in loop 52 at 30% BMCR load.
538
27
Page 27 of 29
539 Parameter
540
RMCR
75%RMCR 30%RMCR
Unit
Mass flow rate
1995
1530
628
t/h
Outlet pressure of economizer
28.45
21.8
10
MPa
Outlet temperature of economizer
329.6
314
100
℃
Vapor temperature in outlet header
415.2
389
360
MPa
Table 1 Design parameters of supercritical CFB boiler with annular furnace.
541 542 Pressure drop (kPa) Item BMCR
543
75% BMCR 30% BMCR
Outer front wall
312.085
290.710
201.777
Outer right wall
312.888
291.272
202.156
Outer rear wall
312.085
290.710
201.777
Outer left wall
312.888
291.272
202.156
Inner front wall
311.713
290.378
201.696
Inner right wall
317.533
294.844
204.007
Inner rear wall
311.713
290.378
201.696
Inner left wall
317.533
294.844
204.007
Total pressure drop 319.145
296.060
204.847
Table 2 The pressure drops of water walls in different walls. 28
Page 28 of 29
544 Total pressure drop (kPa) Item BMCR
75% BMCR 30% BMCR
HB company’ 600 MW 426.060
373.968
246.799
319.145
296.060
204.847
supercritical CFB boiler 600 MW supercritical CFB boiler with annular furnace 545
Table 3 The total pressure drops in vertical water wall at different operating
546
conditions.
29
Page 29 of 29