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Distributed parameters modeling for evaporation system in a once-through coal-fired twin-furnace boiler
International Journal of Thermal Sciences 50 (2011) 2496e2505
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Distributed parameters modeling for evaporation system in a once-through coal-fired twin-furnace boiler Shu Zheng, Zixue Luo*, Xiangyu Zhang, Huaichun Zhou State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, 1037, Luoyu Road, Hongshan District, Wuhan, Hubei 430074, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 December 2010 Received in revised form 19 May 2011 Accepted 19 July 2011 Available online 23 August 2011
In this paper, a distributed parameter model for the evaporation system of a subcritical once-through, coal-fired, twin-furnace boiler based on 3-D temperature field reconstruction is developed. The imaginary wall surface was put forward to simplify the twin-furnace problem. The mathematical model was formulated for predicting the transient distributions of parameters, such as the heat flux, the metalsurface temperature and the steam quality; while considering the non-uniform distributions of the surface heat transfer coefficient and frictional resistance coefficient. The model was based on the 3-D temperature distribution got by a flame image processing technique. The model was validated by some measurable parameters of the evaporation system at three typical loads. The results show that the heat flux and the temperature which are located at the overlapping region of the two tangential flames are higher than those in other corners. This distributed parameter model on evaporation system reflects the in-situ operating status of the power plant boiler, which may lead to the subsequent research on a supercritical boiler. Ó 2011 Elsevier Masson SAS. All rights reserved.
Keywords: Distributed parameter modeling Evaporation system 3-D temperature distribution Once-through boiler
1. Introduction The analysis and modeling of the evaporation system of a oncethrough boiler are crucial for the safe operation, which is related to the combustion behavior in the furnace and the pressure of the working substance. The evaporation system of the boiler absorbs the heat from the flame in the furnace, and the study of the boiler performance and the design of an appropriate control strategy are necessary for analyzing its dynamic characteristic. The prediction of transient behavior of the evaporation system requires dynamic models. There are two kinds of dynamic models for the evaporation system simulation. One is the fine mesh model, and the other is the lumped parameter model which focuses on the fast simulation and the control system design [1]. Considering the complexity of combustion and the heat transfer process in the furnace, many researchers are using a lumped parameter to establish a model of the evaporation system. Li H-P et al. [2] developed a lumped parameter mathematical model to analyze the helical coiled once-
Abbreviations: BMCR, boiler maximum continuous rating; DCS, distributed control systems; DNB, departure from nucleate boiling. * Corresponding author. E-mail address: [email protected] (Z. Luo). 1290-0729/$ e see front matter Ó 2011 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2011.07.010
through steam generator. Wang et al. [3] also proposed a new lumped parameter method for modeling the evaporation zone of a once-through boiler. These lumped parameter models only considered the total heat flow rate, but neglected the non-uniform heat flux distribution. With the development of a distributed parameter model, some scholars [4,5] considered the characteristic of non-uniform heat flux distribution to build the model. Zhu and Zhang [4] put forward a real-time mathematical distributed parameter model for the heat transfer in the furnace. Pan et al. [5] calculated the thermal-hydraulic characteristics of the water wall in an ultra supercritical coal-fired boiler which adopted a mathematical distributed parameter model. However, all the models in these references are based on a reduced one-dimensional heat flux distribution model. The model for the evaporation system will become more accurate and valuable by considering a 2-D, nonuniform distribution of radiation heat flux on the water wall. Due to the lack of on-line, 3-D combustion monitoring systems, this kind of model has seldom been reported. Li Z-Q. et al. [6,7] introduced an optical pyrometer, with a measurement range from 500 to 2000 C, to measure furnace temperature. Zhou et al. [8e10] developed a flame image processing technique on visualization of 3-D temperature distributions in pulverized-coal (pc) fired boilers. Chu et al. [11] proposed an accurate, 2-D, distributed parameter model for the evaporation system of a controlled natural circulation boiler based on the 3-D temperature distribution and the emissivity
S. Zheng et al. / International Journal of Thermal Sciences 50 (2011) 2496e2505
Nomenclature
D 3
c C d D F g G h H M Nu p Pr q Q Rd Re S T u V x Xtt
specific heat capacity [J kg1 K1] fitting coefficient diameter [m] mass flow rate [kg s1] flow area [m2] acceleration of gravity [m s2] mass velocity [kg m2 s1] specific enthalpy [J kg] height [m] mass [kg] Nusselt number pressure [Pa] Prandtl number heat flux [W m2] heat flow rate [W] READ number Reynolds number surface area [m2] absolute temperature [K] specific internal energy [J kg1] volume [m3] steam quality Martinelli number
Greek symbols a heat transfer coefficient [W m2 K1] b frictional resistance coefficient
of the particle phase. However, their model can not be applied in a once-through boiler because of the large difference in the evaporation surfaces. The evaporation system is divided into subcooled region, boiling region and super heated region according to the secondary water/steam status. The boundaries of these regions are movable, and the steam-water separation takes place at the location of dryout in evaporating tubes. Swenson et al. [12] studied the effects of nucleate boiling versus film boiling on heat transfer in power boiling tubes and the experimental results show that nucleate boiling could be maintained to higher vapor qualities with rifled tubes than with smooth tubes. Pan et al. [5] proposed that not only DNB (saturated boiling zone), but dryout (film boiling range) occur in the vertical rifled tube under subcritical pressure. More refined models of the two-phase flow, such as the steam boiler evaporating tubes based on the multi-fluid models of two-phase flow are presented in the work of Delhye et al. [13], Stevanovic and Studovic [14], and Stosic and Stevanovic [15]. It is of extreme importance to determine whether heat transfer deterioration will be generated for the evaporation system, and when or where it occurs. Therefore, a dynamic, accurate, 2-D, distributed parameter model for the evaporation system of a once-through boiler is very meaningful for the development of power plant boilers. Yao Meng power plant is a 300 MW twin-furnace subcritical once-through boiler in China, it was designed and manufactured by Shanghai Boiler Works Ltd, and a 3-D temperature field reconstruction system has been installed in this boiler. Vertical ribbed bore tubes were applied in the water wall; and rifled tubes with good heat transfer performance were adopted. The restriction orifices are mounted to meet the matching requirement between heat flux and mass flux. In this paper, a distributed parameter model for the evaporation system based on 3-D combustion monitoring in the furnace is developed and the imaginary wall surface is put forward to simplify
h k l m x r s f u
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difference in any quantity emissivity absorptance of the imaginary wall surface absorption coefficient [m1] thermal conductivity [W m1 K1] dynamic viscosity [N m1 s1] resistance coefficient density [kg m3] StefaneBoltzmann constant [W m2 K4] two-phase frictional multiplier velocity [m s1]
Subscripts A, B number of furnace cr critical point f flue gas i, j number of element in inner l liquid max maximum value out outer w water wall 1 inlet 2 outlet Superscripts saturated liquid state 00 saturated vapor state e average value 0
the twin-furnace problem. A mathematical model was formulated for predicting the transient distributions of parameters, such as the heat flux, the metal-surface temperature and the steam quality; while considering the non-uniform distributions of the surface heat transfer coefficient and frictional resistance coefficient. Based on the 3-D temperature distribution, the heat flux, mass fraction of steam, and metal temperature distribution in the water wall at three typical loads are obtained by directly solving non-linear equations. The results show that the heat flux and temperature near the overlapping region of two tangential flames is larger than the edge. The predicted increase of the outlet steam quality and the decrease of the two-phase flow zone, caused by the load increase, are in agreement with measured data. This model strategy is helpful for fine distributed parameter research in upper-critical once-through boiler. 2. Distributed mathematical model The evaporation system is divided into three sub-models: flue gas model, tube wall model and water/steam model. These models are connected with some coupling thermodynamic parameters, as shown in Fig.1. In the flue gas model, the non-uniform distribution of radiation heat flux on the water walls is got from the 3-D temperature distribution of flue gas; and the average emissivity of the particle phase is obtained through the monitoring system for the 3-D combustion in the furnace. In the tube wall model, the temperatures inside/outside the water wall are taken into account. For the water/steam model, its function is to obtain the dynamics of steam quality and mass velocity. To reduce the complexity of boiler modeling, some assumptions are made: (1) The furnace is assumed to be filled by a gray emitting, absorbing, and isotropically scattering medium and surrounded by gray water walls.
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Monitoring system for 3-D combustion a
b
c
Flue gas model
d
e Tube wall model f Water/steam model
a: 3-D temperature distribution of flue gas; b: average emissivity of the particle phase; c: 2-D temperature distribution of tube wall; d: heat transfer coefficient and fluid temperature of riser; e: 2-D heat flux distribution of water wall; f: heat flux of tube wall; g: 2-D steam quality and mass velocity distribution of tube wall
g Fig. 1. Model structure of evaporation system.
hA ¼ qA/B =qA
(1)
(2) Heat transfer between the water walls and the flue gases is mainly due to radiation. (3) The mass velocity of water/steam mixture is constant in steady-state conditions along an evaporating tube. (4) Water and steam are mixed evenly in the cross section of the riser. (5) The pressure is equivalent in the same distribution header/ collection header. (6) There is no heat conduction in the axial direction of the tube wall of the riser.
If the imaginary wall surface is assumed to be a gray body, then the emissivity of furnace A can be set equal to hA. So as to furnace B. By using a fast algorithm based on the Monte Carlo method [16,17], the emissivity of this twin-furnace boiler is found to be 0.96. The radiative heat flux absorbed by the imaginary wall surface of furnace A which was emitted from the mediums of furnace B is obtained on the basis of the radiative transfer equation:
2.1. Flue gas model
qB/A;i ¼ 1=DSwi @
0
m1 X j¼0
The cross-section of the 300 MW coal-fired tangential boiler is 17.0 m 8.475 m. The boiler was divided into two furnaces by the double-sided water wall, as shown in Fig. 2. There are 8 corners (#1w#8) at the two furnaces. The flue gas of furnace A has clockwise rotation, and furnace B has counter-clockwise rotation. The fumes mixed at corners 4 and 5. There is a gap existing in the double-sided water wall and its width is 1/3 of the furnace depth; and the two furnaces’ exchange heat through the imaginary wall surface. qA in furnace A is absorbed and scattered by the mediums from furnace B, and part of the energy returns back to furnace B (energy qA absorbed by furnace B is qA/B). For furnace A, the absorptance of the imaginary wall surface is:
þ
n1 X j¼0
Rdfw ðj/iÞ4ksTfj4 DVfj 1
4 DSwj A Rdww ðj/iÞ3 wj sTwj
(2)
Where Rdfw(j / i) and Rdww(j / i) represent the ratios of the radiative energy absorbed by the ith wall element to the energy emitted from the jth volume element of the flue gases and the jth surface element of the water walls, respectively. These are determined by the system’s structure and radiation parameters can be calculated by the READ method proposed by Yang et al. [18]. Chu et al. [11] has introduced a new and accurate method to calculate k the absorption coefficient of the combustion medium. In this paper, this method was also used in our model.
Fig. 2. Schematic plan of twin-furnace boiler.
S. Zheng et al. / International Journal of Thermal Sciences 50 (2011) 2496e2505
Therefore, the ith element temperature of the imaginary wall surface of furnace A can be obtained as:
TA;i ¼
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 qA/B =ð3 sÞ
(3)
So, the parameters of a single furnace can be calculated when the emissivities and temperatures of the imaginary wall surface are obtained on the basis of the imaginary wall surface assumption method. The furnace is assumed to be filled by a gray emitting, absorbing, and isotropically scattering medium and surrounded by gray water walls [11]. Then the energy equation for a surface element can be expressed as:
qwi DSwi ¼
m1 X j¼0
þ
j¼0
Where
Pn1
i¼0
4 4 DSwj 3 wi sTwi DSwi Rdww ðj/iÞ3 wj sTwj
For the once-through boiler, the rifled tubes are used to enhance heat transfer. When the vapor quality increases from 0 to 1, the flow in the tube undergoes transitions from bubbly to slug, slug to churn, churn to annular flow, and annular to mist flow [19]. By the flow and heat transfer conditions under the subcritical pressure shown in Fig. 3 [20], the heat transfer coefficients in forced convection of single phase fluid, subcooled boiling, saturated boiling and post dryout, are required to determine the tube wall temperature. The surface heat transfer coefficient a in the single-phase water region can be calculated by the DittuseBoelter correlation [21]:
l a ¼ 0:023 Re0:8 Pr0:4
(10)
d
Rdfw ðj/iÞ4ksTfj4 DVfj
n1 X
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The computational formula of saturated boiling heat transfer coefficient based on LockharteMartinelli formular [22] is given by:
(4)
qwi DSwi ¼ Qout
atp 1 ¼ 1:38 al Xtt
0:25
p pcr
1:25
G
0:64 (11)
Gmax
Where Xtt is defined as:
2.2. Tube wall model Compared with the double-sided water wall, at the other three water walls only the water side is heated and the other side can be considered as a thermal insulation surface. The process of heat conduction can be ignored in the axial direction of the tube wall of the riser because the tube wall is so thin compared with the length of riser. Therefore, the process of heat conduction in the tube wall can be expressed by the 2-D steady-state heat conduction model [11]:
v vT 1 v2 T r þ ¼ 0 vr vr r v42
(5)
The flue gas model takes the temperature outside the tube wall which faces towards the fire as the input for the calculation of the heat flux outside the water walls. The water/steam model takes the temperature inside the tube wall as the input for the calculation of working fluid enthalpy value. The temperature outside the tube wall which faces away from the fire is needed to validate the model. Considering the computation time, the authors combined the lump-parameter model with the 2-D steady-state heat conduction model. The lump-parameter model is:
dT Mc in ¼ Qout Qin ds
Xtt
!0:1 1 x 0:9 rf 0:5 ml ¼ rl mf x
(12)
The critical quality xcr (which characterizes the heat transfer deterioration of the second kind) is given by [3]:
xcr ¼ 0:3664q0:128 G0:1552 e0:2983ðp=pcr Þ
(13)
The computational formula of post-dryout region heat transfer coefficient is given by [20]:
Nu ¼
ad
l00
¼ 0:023Prb0:8
rud r00 x þ 0 ð1 xÞ m00 r
0:8
(6)
2.3. Water/steam model The mathematical model for predicting the dynamics in the risers is put forward based on the mass, energy and momentum conservation equations:
D1 D2 ¼ V
dr2 ds
(7)
Qin þ D1 ðh1 h2 Þ ¼ V r2
p1 p2 r1 Hg ¼ x
ðruÞ22 2r 2
du2 ds
(8)
(9) Fig. 3. Simplified flow boiling in a vertical tube.
y
(14)
2500
S. Zheng et al. / International Journal of Thermal Sciences 50 (2011) 2496e2505 Left wall
Temperature data DCS system Measurement points in-situ
30.0m
3-D temperature reconstruction computer
Membrane wall
27.6m
ISA Slot Card PCL-727
Singal Cable
Main Operation Parameters
Front wall
LAYER 5 23.9m
LAYER 4 20.4m
LAYER 3 Real-time 3-D temperature distribution
15.9m
LAYER 2 12.0m
LAYER 1
B A
TCP/IP
Distributed parameters modeling Simulation computer
Video signals Monitoring computer Flame image Frame-maker
Fig. 4. Monitoring system for 3-D temperature reconstruction in twin-furnace once-through boiler.
The surface heat transfer coefficient a in the single-phase vapor region can be calculated by the following correlation [20]:
Table 1 The operational data of the simulated system. Case
Load (MW)
Mainsteam pressure (MPa)
Feedwater quantity (t/h)
Temperature of feedwater ( C)
1 2 3
150 240 300
11.26 15.15 16.74
459.54 723.11 900.82
292.24 294.35 303.55
0 0:4 r y ¼ 1 0:1 00 1 ð1 xÞ0:4
r
dn
(15)
(16)
(17)
The frictional resistance coefficients under the subcritical pressure are as expressed by Yang et al. [23]. For the single-phase under the subcritical pressure, the frictional resistance coefficient b can be calculated by:
b¼
Where x is defined as:
00
x ¼ h h0 h h0
l a ¼ 0:0133 Re0:84 Pr1=3
1
4 lg3:7
din
2
l
Fig. 5. Comparison of temperature in front wall: case 1 and case 3.
(18)
S. Zheng et al. / International Journal of Thermal Sciences 50 (2011) 2496e2505
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Fig. 6. The wall temperature measuring points in-situ at 100% BMCR load.
Fig. 7. Comparison of mass velocity in front wall : case 1 and case 3.
is 300 MW, the steam mass flow rate is 1025 t/h, the main steam pressure is 17.4 MPa, the temperature of feedwater is 277 C. The horizontal-cross dimension of each furnace is 8.5 m wide 8.475 m deep. As shown in Fig. 4, 16 flame image detectors were mounted in four layers at different heights and different corners, two CCD cameras are in one layer of each furnace. By use of a frame-maker, the 16 video signals captured by the detectors were combined into one entire video signal and transmitted to the visualization computer through the image capture card. A visualization computer and a data computer are used to reconstruct realtime the 3-D temperature distribution in twin-furnace. The evaporation zone between the ash hopper (12.0 m) and the arch nose (27.6 m) was divided into 16 layers. The horizontal crosssection of the areas is uniformly divided into 20 10 ¼ 200 meshes, the corresponding areas in each furnace are uniformly divided into 10 10 ¼ 100 meshes. So, in total, there were 3200 cubic meshes, 1600 in each furnace, and there were 960 the surface meshes. The dimensions of each cubic mesh are 1 m 0.85 m 0.847 m. The
The computational formula of two-phase region frictional resistance coefficient b0 is given by:
b0 ¼ fb f ¼ 1þ
(19)
r0 1 C þ x2 00 r
(20)
CðxÞ ¼ 1:182x0:697 ð1 xÞ0:308
p ¼ 12w17 MPa
(21)
CðxÞ ¼ 0:890x0:567 ð1 xÞ0:215
p ¼ 19w21 MPa
(22)
3. 3-D temperature distribution and model validation In this paper, a twin-furnace, four-cornered, single-reheat, tangentially coal-fired boiler was adopted for this study. The unit
Table 2 Comparison of temperatures in front wall in case 3.
Furnace A
Furnace B
Mesh No.
1
2
3
4
5
6
7
8
9
10
Measured Temp. ( C) Calculated Temp. ( C) Error (%)
361.2 360.0 0.33
364.5 362.6 0.52
364 362.5 0.41
364.1 361.9 0.61
362.9 360.7 0.61
362.5 358.3 1.16
362.9 359.5 0.94
362.5 357.7 1.32
361.8 357.2 1.27
362.9 359.8 0.85
Mesh No. Measured Temp. ( C) Calculated Temp. ( C) Error (%)
11 363.1 357.4 1.60
12 363 360.7 0.63
13 362.9 362.5 0.11
14 363.4 363.5 0.03
15 363.7 363.2 0.14
16 364 363 0.27
17 363.9 361.3 0.71
18 362.5 359.6 0.80
19 361.9 356.8 1.41
20 361.4 356.3 1.41
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Fig. 8. The measured values of mass flow rate in-situ at 50% BMCR load in furnace B.
Fig. 9. Distributions of heat flux on the front wall (kW/m2): (a) case 1; (b) case 2; (c) case 3; (d) tendency of the 3 cases at the width of 12 m.
S. Zheng et al. / International Journal of Thermal Sciences 50 (2011) 2496e2505
absorptivity of the water wall surface was assumed to be 0.8, and numerical calculation cases are listed in Table 1. A simulation was carried out to capture the dynamics of temperature and the distribution of mass velocity at the height of 30 m. The comparisons of two measurable parameters in the evaporation system obtained by the proposed model and measured values are shown in Fig. 5 and Fig. 7. The measured outside wall temperature and calculated value gotten theoretically at the height of 30 m are given in Fig. 5. Fig. 6 expressed the measured values of metal temperature in-situ at 100% BMCR load captured in DCS screen. The values of case 3 are listed in Table 2. The maximum relative difference is 1.6%, which appears at the width of 8.5 m. The temperatures of the front water wall in furnace B and furnace A are symmetrical. In addition, temperatures in corners 4 and 5 are higher than corners 3 and 6 at the high load and high combustion zone, because of the residual flue gas rotating and mixing in corners 4 and 5. The results are consistent with the two-tangential firing manner. Fig. 7 shows the mass velocity in the front wall in case 1 and case 3. The maximum relative difference between the current results and the plant data is 5%. The mass velocity in front wall presents an M-type curve. The mass velocity of the center riser is larger than that of the edge riser. The mass velocity distribution can match the operating requirement of the vertical water wall under the various pressure conditions by the use of restriction orifice. Fig. 8 shows the measured values of mass flow rate in-situ at 50% BMCR load in furnace B captured in DCS screen. There is an even distribution of
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30 measuring points in furnace B. For instance, the front wall has a uniform distribution of 10 points. So, the measured values of mass velocity is expressed by:
ðruÞi ¼ Di
npd2 4
(23)
Where i ¼ 1, 2,.10 Fig. 7 indicates that the heat flux deviation plays an important role in the mass velocity distribution. So, combustion process optimization and reduction of heat flux non-uniform distribution are the effective approaches to decrease the mass velocity deviation. The results show the mathematical model for predicting the mass velocity distribution and metal temperatures of tubes are fit for in-situ operation. Furthermore, the reconstructed 3-D temperature distribution got by the flame image processing technique can reflect the actual heat transfer process in the furnace. 4. Results and discussion Distributions of the heat flux, steam quality and metal temperature can be obtained based on the above simulation. In view of the general situation, three kinds of cases were illustrated in thermodynamic parameter distributions on the front water wall. Fig. 9 shows heat flux distributions on the front water wall in the three different cases. It can be seen that the heat flux in the furnace
Fig. 10. Distributions of steam quality on the front wall: (a) case 1; (b) case 2; (c) case 3; (d) tendency of the 3 cases at the width of 12 m.
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center is much larger than the boundary region. The heat flux reaches the maximum of 504 kW/m2 at a height of 25 m. The corners 4 and 5 are located at the overlapping region of two tangential flames and the residual flue gas rotates in the zone. So, the heat flux is higher than in other regions. These results are consistent with the two-tangential firing manner. Fig. 9 (d) shows the heat flux variation curves at the furnace width of 12 m at the three typical loads. It can be seen the heat flux rises with the increment of load. For case 3, the heat flux reaches the maximum of 475 kW/m2 at the furnace height of 22 m, and the heat flux decreases with further increase in height. Fig. 10 shows the steam quality distributions on the front water wall in these cases. It can be seen that the steam quality decreases from the center to the edge along the width of water wall for a given elevation. This is due to the heat flux of single furnace on the center region is much higher than on the boundary region. With the absorption of the heat inside the furnace, the steam quality increases along the elevation for the same riser. It can also be seen that the two-phase flow zone becomes small with the inceasing boiler load. Fig. 10 (d) shows the steam quality variation curves at the furnace width of 12 m. It can be seen the appearance of two-phase flow zone is delayed with the increase of the load. The reason is that the increase in mass velocity in rifled tubes results in more liquid thrown into the wall, and the phase-transition point temperature increases with enhanced pressure. Also the outlet steam quality increases with increasing load.
Fig. 11 shows the metal temperature distribution on the front water wall in these operating cases. The temperature increases with the furnace height monotonously because the fluid temperature at 0e15 m is in single-phase zone. The metal temperature rises to the maximum of 405 C at a height of 25 m. Meanwhile, the heat flux reaches 504 kW/m2. The metal temperature reduces with the decrease of the heat flux at higher positions, due to the difference of heat exchange coefficient calculation models. The maximum deviation of metal temperature on the front wall is 20 C in case 2, and is 50 C in case 3. The temperature of corners 4 and 5 is also higher than of corners 3 and 6. Fig. 11 (d) shows the metal temperature variation curves at the given width of the furnace. The fluid begins to vaporize and to be in a saturated boiling zone at the height of 16 m. The heat exchange coefficient of fluid obviously increases and the fluid temperature is at the saturated temperature all the time. So the metal temperature increases slowly. However, the metal temperature increases rapidly with the decreasing heat exchange coefficient of fluid in the postdryout region. At greater furnace height, the heat flux decreases with increased height. So the metal temperature begins to decrease at the height of 24 m. According to the figures described above, it can be seen that the non-uniform distribution of heat flux and steam quality play an essential role in the metal temperature deviation. In order to reduce the deviation of heat flux and delay the vapor generation, the optimal ribbed bore tubes and restriction orifice should be applied in the water wall. Then, the tube wall overheating can be avoided and the secure operation of boiler is ensured.
Fig. 11. Distributions of metal temperature ( C) on the front wall: (a) case 1; (b) case 2; (c) case 3; (d) tendency of the 3 cases at the width of 12 m.
S. Zheng et al. / International Journal of Thermal Sciences 50 (2011) 2496e2505
5. Conclusions A distributed parameter model for the evaporation system in a twin-furnace once-through boiler was established. An imaginary wall surface was put forward to simplify the twin-furnace problem. The model for predicting the transient distributions of parameters, such as the heat flux, the metal-surface temperature and the steam quality in the evaporation system was proposed based on 3-D temperature distribution. The heat flux, steam quality and metal temperature distribution in the water wall were obtained by directly solving non-linear equations; and the in-situ measured data is consistent with the computerized values. The simulation results show that the metal temperature of corners 4 and 5 is higher than other corners at the high load and high combustion zone. The heat flux reaches a maximum value at rated load in furnace. At greater furnace height, the heat flux decreases with the increase of the furnace height. The steam quality increases along the elevation for the same riser with the absorption of the heat inside the furnace. It can be seen that the two-phase flow zone becomes shorter with increased load. The metal temperature may reach to the maximum at a certain height in the furnace, while the deviation of metal temperature is nearly 50 C at different load. The model can promote the transient, distributed parameters of the evaporation system, which has a great value for safe, economic operation in a once-through boiler. It is a new supported method for research on supercritical once-through boiler based on flame image processing technique. Acknowledgments This work is sponsored by the National Natural Science Foundation of China (Contract Nos.: 51076049, 51025622 and 50721005). References [1] A. Ray, H.F. Bowman, A nonlinear dynamic model of a once-through subcritical steam generator, J. Dyn. Syst. Meas. Control. Trans. ASME 98 (1976) 332e339. [2] H.P. Li, X.J. Huang, L.J. Zhang, A lumped parameter dynamic model of the helical coiled once-through steam generator with movable boundaries, Nucl. Eng. Des. 238 (2008) 1657e1663. [3] W. Wang, T.J. Ren, Q.R. Gao, X.C. Liu, Mathematical model and simulation of the evaporating surface in a once-through boiler, Qinghua Daxue Xuebao/J. Tsinghua Univ. 41 (2001) 105e108 (in Chinese). [4] J.R. Zhu, C.Y. Zhang, Real-time mathematical model for the heat transfer in the furnace and the evaporating condition of an once-through boiler, Zhongguo Dianji Gongcheng Xueb 11 (1991) 63e72 (in Chinese).
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[5] J. Pan, D. Yang, H. Yu, Q.C. Bi, H.Y. Hua, F. Gao, Z.M. Yang, Mathematical modeling and thermal-hydraulic analysis of vertical water wall in an ultra supercritical boiler, Appl. Therm. Eng. 29 (2009) 2500e2507. [6] Z.Q. Li, J.P. Jing, G.K. Liu, Z.C. Chen, C.L. Liu, Measurement of gas species, temperatures, char burnout, and wall heat fluxes in a 200-MW00 e lignite-fired boiler at different loads, Appl. Energ. 87 (2010) 1217e1230. [7] Z.Q. Li, M. Kuang, J. Zhang, Y.F. Han, Q.Y. Zhu, L.J. Yang, W.G. Kong, Influence of staged-air on airflow, combustion characteristics and NOx emissions of a down-fired pulverized-coal 300 MWe utility boiler with direct flow split burners, Environ. Sci. Technol. 44 (2010) 1130e1136. [8] Z.X. Luo, H.C. Zhou, A combustion-monitoring system with 3-D temperature reconstruction based on flame-image processing technique, IEEE T. Instrum. Meas. 56 (2007) 1877e1882. [9] H.C. Zhou, C. Lou, Q. Cheng, Z.W. Jiang, J. He, B.Y. Huang, Z.L. Pei, C.X. Lu, Experimental investigations on visualization of three-dimensional temperature distributions in a large-scale pulverized-coal-fired boiler furnace, Proc. Combust. Inst. 30 (2005) 1699e1706. [10] H.C. Zhou, S.D. Han, F. Sheng, C.G. Zheng, Visualization of three-dimensional temperature distributions in a large-scale furnace via regularized reconstruction from radiative energy images: numerical studies, J. Quant. Spectrosc. Radiat. Transfer. 72 (2002) 361e383. [11] Y.T. Chu, C. Lou, Q. Cheng, H.C. Zhou, Distributed parameter modeling and simulation for the evaporation system of a controlled circulation boiler based on 3-D combustion monitoring, Appl. Therm. Eng. 28 (2008) 164e177. [12] H.S. Swenson, J.R. Carver, G. Szoeke, The effects of nucleate boiling versus film boiling on heat transfer in power boiling tubes, J. Eng. Power Trans. ASME 84 (1962) 365e371. [13] J.M. Delhaye, M. Giot, M.L. Riethmuller, Thermohydraulics of Two-Phase Systems for Industrial Design and Nuclear Engineering. Hemisphere, Washington, DC, 1981, 353e403. [14] V. Stevanovic, M. Studovic, A simple model for vertical annular and horizontal stratified two-phase flows with liquid entrainment and phase transitions: one-dimensional steady state conditions, Nucl. Eng. Des. 154 (1995) 357e379. [15] Z. Stosic, V. Stevanovic, Numerical prediction of pipe CHF data with multifluid modeling approach, in: Pro. 11th. Int. Conf. Nucl. Eng. e ICONE 11, Tokyo, Japan (2003) Paper ICONE11e36382. [16] K. Kudo, A. Kuroda, A. Eid, Radiative load problem using the single value decomposition technique, JSME, Series B 39 (1996) 808e814. [17] H.C. Zhou, Q. Cheng, The DRESOR method for the solution of the radiative transfer equation in gray plane-parallel media, in: Proc. 4th. Int. Symp. Rad. Transf. Begell House, New York, 2004, pp. 184e190. [18] W.J. Yang, H. Taniguchi, K. Kudo, Radiation heat transfer by the Monte Carlo method. in: J.P. Hartnett, T.F. Irvine (Eds.), Advances in Heat Transfer, vol. 24. Academic Press, San Diego, 1995, pp. 1e215. [19] V.P. Carey, Liquid-Vapor Phase-Change PhenomenaeAn Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment, second ed. Taylor & Francis Group, New York, USA, 2008. [20] D.F. Che, Boilers-Theory, Design and Operation. Xi’an Jiaotong University Press, Xi’an, China, 2008. [21] F.W. Dittus, L.M.K. Boelter, Heat transfer in automobile radiators of the tubular type, Int. Commun. Heat Mass. 12 (1985) 3e22. [22] J.C. Chen, Correlation for boiling heat transfer to saturated fluids in convective flow, Ind. Eng. Chem. Process Des. 5 (1966) 322e329. [23] D. Yang, J. Pan, C.Q. Zhou, X.J. Zhu, Q.C. Bi, T.K. Chen, Experimental investigation on heat transfer and frictional characteristics of vertical upward rifled tube in supercritical CFB boiler, Exp. Therm. Fluid Sci. 35 (2011) 291e300.
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Distributed parameters modeling for evaporation system in a once-through coal-fired twin-furnace boiler Shu Zheng, Zixue Luo*, Xiangyu Zhang, Huaichun Zhou State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, 1037, Luoyu Road, Hongshan District, Wuhan, Hubei 430074, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 December 2010 Received in revised form 19 May 2011 Accepted 19 July 2011 Available online 23 August 2011
In this paper, a distributed parameter model for the evaporation system of a subcritical once-through, coal-fired, twin-furnace boiler based on 3-D temperature field reconstruction is developed. The imaginary wall surface was put forward to simplify the twin-furnace problem. The mathematical model was formulated for predicting the transient distributions of parameters, such as the heat flux, the metalsurface temperature and the steam quality; while considering the non-uniform distributions of the surface heat transfer coefficient and frictional resistance coefficient. The model was based on the 3-D temperature distribution got by a flame image processing technique. The model was validated by some measurable parameters of the evaporation system at three typical loads. The results show that the heat flux and the temperature which are located at the overlapping region of the two tangential flames are higher than those in other corners. This distributed parameter model on evaporation system reflects the in-situ operating status of the power plant boiler, which may lead to the subsequent research on a supercritical boiler. Ó 2011 Elsevier Masson SAS. All rights reserved.
Keywords: Distributed parameter modeling Evaporation system 3-D temperature distribution Once-through boiler
1. Introduction The analysis and modeling of the evaporation system of a oncethrough boiler are crucial for the safe operation, which is related to the combustion behavior in the furnace and the pressure of the working substance. The evaporation system of the boiler absorbs the heat from the flame in the furnace, and the study of the boiler performance and the design of an appropriate control strategy are necessary for analyzing its dynamic characteristic. The prediction of transient behavior of the evaporation system requires dynamic models. There are two kinds of dynamic models for the evaporation system simulation. One is the fine mesh model, and the other is the lumped parameter model which focuses on the fast simulation and the control system design [1]. Considering the complexity of combustion and the heat transfer process in the furnace, many researchers are using a lumped parameter to establish a model of the evaporation system. Li H-P et al. [2] developed a lumped parameter mathematical model to analyze the helical coiled once-
Abbreviations: BMCR, boiler maximum continuous rating; DCS, distributed control systems; DNB, departure from nucleate boiling. * Corresponding author. E-mail address: [email protected] (Z. Luo). 1290-0729/$ e see front matter Ó 2011 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2011.07.010
through steam generator. Wang et al. [3] also proposed a new lumped parameter method for modeling the evaporation zone of a once-through boiler. These lumped parameter models only considered the total heat flow rate, but neglected the non-uniform heat flux distribution. With the development of a distributed parameter model, some scholars [4,5] considered the characteristic of non-uniform heat flux distribution to build the model. Zhu and Zhang [4] put forward a real-time mathematical distributed parameter model for the heat transfer in the furnace. Pan et al. [5] calculated the thermal-hydraulic characteristics of the water wall in an ultra supercritical coal-fired boiler which adopted a mathematical distributed parameter model. However, all the models in these references are based on a reduced one-dimensional heat flux distribution model. The model for the evaporation system will become more accurate and valuable by considering a 2-D, nonuniform distribution of radiation heat flux on the water wall. Due to the lack of on-line, 3-D combustion monitoring systems, this kind of model has seldom been reported. Li Z-Q. et al. [6,7] introduced an optical pyrometer, with a measurement range from 500 to 2000 C, to measure furnace temperature. Zhou et al. [8e10] developed a flame image processing technique on visualization of 3-D temperature distributions in pulverized-coal (pc) fired boilers. Chu et al. [11] proposed an accurate, 2-D, distributed parameter model for the evaporation system of a controlled natural circulation boiler based on the 3-D temperature distribution and the emissivity
S. Zheng et al. / International Journal of Thermal Sciences 50 (2011) 2496e2505
Nomenclature
D 3
c C d D F g G h H M Nu p Pr q Q Rd Re S T u V x Xtt
specific heat capacity [J kg1 K1] fitting coefficient diameter [m] mass flow rate [kg s1] flow area [m2] acceleration of gravity [m s2] mass velocity [kg m2 s1] specific enthalpy [J kg] height [m] mass [kg] Nusselt number pressure [Pa] Prandtl number heat flux [W m2] heat flow rate [W] READ number Reynolds number surface area [m2] absolute temperature [K] specific internal energy [J kg1] volume [m3] steam quality Martinelli number
Greek symbols a heat transfer coefficient [W m2 K1] b frictional resistance coefficient
of the particle phase. However, their model can not be applied in a once-through boiler because of the large difference in the evaporation surfaces. The evaporation system is divided into subcooled region, boiling region and super heated region according to the secondary water/steam status. The boundaries of these regions are movable, and the steam-water separation takes place at the location of dryout in evaporating tubes. Swenson et al. [12] studied the effects of nucleate boiling versus film boiling on heat transfer in power boiling tubes and the experimental results show that nucleate boiling could be maintained to higher vapor qualities with rifled tubes than with smooth tubes. Pan et al. [5] proposed that not only DNB (saturated boiling zone), but dryout (film boiling range) occur in the vertical rifled tube under subcritical pressure. More refined models of the two-phase flow, such as the steam boiler evaporating tubes based on the multi-fluid models of two-phase flow are presented in the work of Delhye et al. [13], Stevanovic and Studovic [14], and Stosic and Stevanovic [15]. It is of extreme importance to determine whether heat transfer deterioration will be generated for the evaporation system, and when or where it occurs. Therefore, a dynamic, accurate, 2-D, distributed parameter model for the evaporation system of a once-through boiler is very meaningful for the development of power plant boilers. Yao Meng power plant is a 300 MW twin-furnace subcritical once-through boiler in China, it was designed and manufactured by Shanghai Boiler Works Ltd, and a 3-D temperature field reconstruction system has been installed in this boiler. Vertical ribbed bore tubes were applied in the water wall; and rifled tubes with good heat transfer performance were adopted. The restriction orifices are mounted to meet the matching requirement between heat flux and mass flux. In this paper, a distributed parameter model for the evaporation system based on 3-D combustion monitoring in the furnace is developed and the imaginary wall surface is put forward to simplify
h k l m x r s f u
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difference in any quantity emissivity absorptance of the imaginary wall surface absorption coefficient [m1] thermal conductivity [W m1 K1] dynamic viscosity [N m1 s1] resistance coefficient density [kg m3] StefaneBoltzmann constant [W m2 K4] two-phase frictional multiplier velocity [m s1]
Subscripts A, B number of furnace cr critical point f flue gas i, j number of element in inner l liquid max maximum value out outer w water wall 1 inlet 2 outlet Superscripts saturated liquid state 00 saturated vapor state e average value 0
the twin-furnace problem. A mathematical model was formulated for predicting the transient distributions of parameters, such as the heat flux, the metal-surface temperature and the steam quality; while considering the non-uniform distributions of the surface heat transfer coefficient and frictional resistance coefficient. Based on the 3-D temperature distribution, the heat flux, mass fraction of steam, and metal temperature distribution in the water wall at three typical loads are obtained by directly solving non-linear equations. The results show that the heat flux and temperature near the overlapping region of two tangential flames is larger than the edge. The predicted increase of the outlet steam quality and the decrease of the two-phase flow zone, caused by the load increase, are in agreement with measured data. This model strategy is helpful for fine distributed parameter research in upper-critical once-through boiler. 2. Distributed mathematical model The evaporation system is divided into three sub-models: flue gas model, tube wall model and water/steam model. These models are connected with some coupling thermodynamic parameters, as shown in Fig.1. In the flue gas model, the non-uniform distribution of radiation heat flux on the water walls is got from the 3-D temperature distribution of flue gas; and the average emissivity of the particle phase is obtained through the monitoring system for the 3-D combustion in the furnace. In the tube wall model, the temperatures inside/outside the water wall are taken into account. For the water/steam model, its function is to obtain the dynamics of steam quality and mass velocity. To reduce the complexity of boiler modeling, some assumptions are made: (1) The furnace is assumed to be filled by a gray emitting, absorbing, and isotropically scattering medium and surrounded by gray water walls.
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Monitoring system for 3-D combustion a
b
c
Flue gas model
d
e Tube wall model f Water/steam model
a: 3-D temperature distribution of flue gas; b: average emissivity of the particle phase; c: 2-D temperature distribution of tube wall; d: heat transfer coefficient and fluid temperature of riser; e: 2-D heat flux distribution of water wall; f: heat flux of tube wall; g: 2-D steam quality and mass velocity distribution of tube wall
g Fig. 1. Model structure of evaporation system.
hA ¼ qA/B =qA
(1)
(2) Heat transfer between the water walls and the flue gases is mainly due to radiation. (3) The mass velocity of water/steam mixture is constant in steady-state conditions along an evaporating tube. (4) Water and steam are mixed evenly in the cross section of the riser. (5) The pressure is equivalent in the same distribution header/ collection header. (6) There is no heat conduction in the axial direction of the tube wall of the riser.
If the imaginary wall surface is assumed to be a gray body, then the emissivity of furnace A can be set equal to hA. So as to furnace B. By using a fast algorithm based on the Monte Carlo method [16,17], the emissivity of this twin-furnace boiler is found to be 0.96. The radiative heat flux absorbed by the imaginary wall surface of furnace A which was emitted from the mediums of furnace B is obtained on the basis of the radiative transfer equation:
2.1. Flue gas model
qB/A;i ¼ 1=DSwi @
0
m1 X j¼0
The cross-section of the 300 MW coal-fired tangential boiler is 17.0 m 8.475 m. The boiler was divided into two furnaces by the double-sided water wall, as shown in Fig. 2. There are 8 corners (#1w#8) at the two furnaces. The flue gas of furnace A has clockwise rotation, and furnace B has counter-clockwise rotation. The fumes mixed at corners 4 and 5. There is a gap existing in the double-sided water wall and its width is 1/3 of the furnace depth; and the two furnaces’ exchange heat through the imaginary wall surface. qA in furnace A is absorbed and scattered by the mediums from furnace B, and part of the energy returns back to furnace B (energy qA absorbed by furnace B is qA/B). For furnace A, the absorptance of the imaginary wall surface is:
þ
n1 X j¼0
Rdfw ðj/iÞ4ksTfj4 DVfj 1
4 DSwj A Rdww ðj/iÞ3 wj sTwj
(2)
Where Rdfw(j / i) and Rdww(j / i) represent the ratios of the radiative energy absorbed by the ith wall element to the energy emitted from the jth volume element of the flue gases and the jth surface element of the water walls, respectively. These are determined by the system’s structure and radiation parameters can be calculated by the READ method proposed by Yang et al. [18]. Chu et al. [11] has introduced a new and accurate method to calculate k the absorption coefficient of the combustion medium. In this paper, this method was also used in our model.
Fig. 2. Schematic plan of twin-furnace boiler.
S. Zheng et al. / International Journal of Thermal Sciences 50 (2011) 2496e2505
Therefore, the ith element temperature of the imaginary wall surface of furnace A can be obtained as:
TA;i ¼
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 qA/B =ð3 sÞ
(3)
So, the parameters of a single furnace can be calculated when the emissivities and temperatures of the imaginary wall surface are obtained on the basis of the imaginary wall surface assumption method. The furnace is assumed to be filled by a gray emitting, absorbing, and isotropically scattering medium and surrounded by gray water walls [11]. Then the energy equation for a surface element can be expressed as:
qwi DSwi ¼
m1 X j¼0
þ
j¼0
Where
Pn1
i¼0
4 4 DSwj 3 wi sTwi DSwi Rdww ðj/iÞ3 wj sTwj
For the once-through boiler, the rifled tubes are used to enhance heat transfer. When the vapor quality increases from 0 to 1, the flow in the tube undergoes transitions from bubbly to slug, slug to churn, churn to annular flow, and annular to mist flow [19]. By the flow and heat transfer conditions under the subcritical pressure shown in Fig. 3 [20], the heat transfer coefficients in forced convection of single phase fluid, subcooled boiling, saturated boiling and post dryout, are required to determine the tube wall temperature. The surface heat transfer coefficient a in the single-phase water region can be calculated by the DittuseBoelter correlation [21]:
l a ¼ 0:023 Re0:8 Pr0:4
(10)
d
Rdfw ðj/iÞ4ksTfj4 DVfj
n1 X
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The computational formula of saturated boiling heat transfer coefficient based on LockharteMartinelli formular [22] is given by:
(4)
qwi DSwi ¼ Qout
atp 1 ¼ 1:38 al Xtt
0:25
p pcr
1:25
G
0:64 (11)
Gmax
Where Xtt is defined as:
2.2. Tube wall model Compared with the double-sided water wall, at the other three water walls only the water side is heated and the other side can be considered as a thermal insulation surface. The process of heat conduction can be ignored in the axial direction of the tube wall of the riser because the tube wall is so thin compared with the length of riser. Therefore, the process of heat conduction in the tube wall can be expressed by the 2-D steady-state heat conduction model [11]:
v vT 1 v2 T r þ ¼ 0 vr vr r v42
(5)
The flue gas model takes the temperature outside the tube wall which faces towards the fire as the input for the calculation of the heat flux outside the water walls. The water/steam model takes the temperature inside the tube wall as the input for the calculation of working fluid enthalpy value. The temperature outside the tube wall which faces away from the fire is needed to validate the model. Considering the computation time, the authors combined the lump-parameter model with the 2-D steady-state heat conduction model. The lump-parameter model is:
dT Mc in ¼ Qout Qin ds
Xtt
!0:1 1 x 0:9 rf 0:5 ml ¼ rl mf x
(12)
The critical quality xcr (which characterizes the heat transfer deterioration of the second kind) is given by [3]:
xcr ¼ 0:3664q0:128 G0:1552 e0:2983ðp=pcr Þ
(13)
The computational formula of post-dryout region heat transfer coefficient is given by [20]:
Nu ¼
ad
l00
¼ 0:023Prb0:8
rud r00 x þ 0 ð1 xÞ m00 r
0:8
(6)
2.3. Water/steam model The mathematical model for predicting the dynamics in the risers is put forward based on the mass, energy and momentum conservation equations:
D1 D2 ¼ V
dr2 ds
(7)
Qin þ D1 ðh1 h2 Þ ¼ V r2
p1 p2 r1 Hg ¼ x
ðruÞ22 2r 2
du2 ds
(8)
(9) Fig. 3. Simplified flow boiling in a vertical tube.
y
(14)
2500
S. Zheng et al. / International Journal of Thermal Sciences 50 (2011) 2496e2505 Left wall
Temperature data DCS system Measurement points in-situ
30.0m
3-D temperature reconstruction computer
Membrane wall
27.6m
ISA Slot Card PCL-727
Singal Cable
Main Operation Parameters
Front wall
LAYER 5 23.9m
LAYER 4 20.4m
LAYER 3 Real-time 3-D temperature distribution
15.9m
LAYER 2 12.0m
LAYER 1
B A
TCP/IP
Distributed parameters modeling Simulation computer
Video signals Monitoring computer Flame image Frame-maker
Fig. 4. Monitoring system for 3-D temperature reconstruction in twin-furnace once-through boiler.
The surface heat transfer coefficient a in the single-phase vapor region can be calculated by the following correlation [20]:
Table 1 The operational data of the simulated system. Case
Load (MW)
Mainsteam pressure (MPa)
Feedwater quantity (t/h)
Temperature of feedwater ( C)
1 2 3
150 240 300
11.26 15.15 16.74
459.54 723.11 900.82
292.24 294.35 303.55
0 0:4 r y ¼ 1 0:1 00 1 ð1 xÞ0:4
r
dn
(15)
(16)
(17)
The frictional resistance coefficients under the subcritical pressure are as expressed by Yang et al. [23]. For the single-phase under the subcritical pressure, the frictional resistance coefficient b can be calculated by:
b¼
Where x is defined as:
00
x ¼ h h0 h h0
l a ¼ 0:0133 Re0:84 Pr1=3
1
4 lg3:7
din
2
l
Fig. 5. Comparison of temperature in front wall: case 1 and case 3.
(18)
S. Zheng et al. / International Journal of Thermal Sciences 50 (2011) 2496e2505
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Fig. 6. The wall temperature measuring points in-situ at 100% BMCR load.
Fig. 7. Comparison of mass velocity in front wall : case 1 and case 3.
is 300 MW, the steam mass flow rate is 1025 t/h, the main steam pressure is 17.4 MPa, the temperature of feedwater is 277 C. The horizontal-cross dimension of each furnace is 8.5 m wide 8.475 m deep. As shown in Fig. 4, 16 flame image detectors were mounted in four layers at different heights and different corners, two CCD cameras are in one layer of each furnace. By use of a frame-maker, the 16 video signals captured by the detectors were combined into one entire video signal and transmitted to the visualization computer through the image capture card. A visualization computer and a data computer are used to reconstruct realtime the 3-D temperature distribution in twin-furnace. The evaporation zone between the ash hopper (12.0 m) and the arch nose (27.6 m) was divided into 16 layers. The horizontal crosssection of the areas is uniformly divided into 20 10 ¼ 200 meshes, the corresponding areas in each furnace are uniformly divided into 10 10 ¼ 100 meshes. So, in total, there were 3200 cubic meshes, 1600 in each furnace, and there were 960 the surface meshes. The dimensions of each cubic mesh are 1 m 0.85 m 0.847 m. The
The computational formula of two-phase region frictional resistance coefficient b0 is given by:
b0 ¼ fb f ¼ 1þ
(19)
r0 1 C þ x2 00 r
(20)
CðxÞ ¼ 1:182x0:697 ð1 xÞ0:308
p ¼ 12w17 MPa
(21)
CðxÞ ¼ 0:890x0:567 ð1 xÞ0:215
p ¼ 19w21 MPa
(22)
3. 3-D temperature distribution and model validation In this paper, a twin-furnace, four-cornered, single-reheat, tangentially coal-fired boiler was adopted for this study. The unit
Table 2 Comparison of temperatures in front wall in case 3.
Furnace A
Furnace B
Mesh No.
1
2
3
4
5
6
7
8
9
10
Measured Temp. ( C) Calculated Temp. ( C) Error (%)
361.2 360.0 0.33
364.5 362.6 0.52
364 362.5 0.41
364.1 361.9 0.61
362.9 360.7 0.61
362.5 358.3 1.16
362.9 359.5 0.94
362.5 357.7 1.32
361.8 357.2 1.27
362.9 359.8 0.85
Mesh No. Measured Temp. ( C) Calculated Temp. ( C) Error (%)
11 363.1 357.4 1.60
12 363 360.7 0.63
13 362.9 362.5 0.11
14 363.4 363.5 0.03
15 363.7 363.2 0.14
16 364 363 0.27
17 363.9 361.3 0.71
18 362.5 359.6 0.80
19 361.9 356.8 1.41
20 361.4 356.3 1.41
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Fig. 8. The measured values of mass flow rate in-situ at 50% BMCR load in furnace B.
Fig. 9. Distributions of heat flux on the front wall (kW/m2): (a) case 1; (b) case 2; (c) case 3; (d) tendency of the 3 cases at the width of 12 m.
S. Zheng et al. / International Journal of Thermal Sciences 50 (2011) 2496e2505
absorptivity of the water wall surface was assumed to be 0.8, and numerical calculation cases are listed in Table 1. A simulation was carried out to capture the dynamics of temperature and the distribution of mass velocity at the height of 30 m. The comparisons of two measurable parameters in the evaporation system obtained by the proposed model and measured values are shown in Fig. 5 and Fig. 7. The measured outside wall temperature and calculated value gotten theoretically at the height of 30 m are given in Fig. 5. Fig. 6 expressed the measured values of metal temperature in-situ at 100% BMCR load captured in DCS screen. The values of case 3 are listed in Table 2. The maximum relative difference is 1.6%, which appears at the width of 8.5 m. The temperatures of the front water wall in furnace B and furnace A are symmetrical. In addition, temperatures in corners 4 and 5 are higher than corners 3 and 6 at the high load and high combustion zone, because of the residual flue gas rotating and mixing in corners 4 and 5. The results are consistent with the two-tangential firing manner. Fig. 7 shows the mass velocity in the front wall in case 1 and case 3. The maximum relative difference between the current results and the plant data is 5%. The mass velocity in front wall presents an M-type curve. The mass velocity of the center riser is larger than that of the edge riser. The mass velocity distribution can match the operating requirement of the vertical water wall under the various pressure conditions by the use of restriction orifice. Fig. 8 shows the measured values of mass flow rate in-situ at 50% BMCR load in furnace B captured in DCS screen. There is an even distribution of
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30 measuring points in furnace B. For instance, the front wall has a uniform distribution of 10 points. So, the measured values of mass velocity is expressed by:
ðruÞi ¼ Di
npd2 4
(23)
Where i ¼ 1, 2,.10 Fig. 7 indicates that the heat flux deviation plays an important role in the mass velocity distribution. So, combustion process optimization and reduction of heat flux non-uniform distribution are the effective approaches to decrease the mass velocity deviation. The results show the mathematical model for predicting the mass velocity distribution and metal temperatures of tubes are fit for in-situ operation. Furthermore, the reconstructed 3-D temperature distribution got by the flame image processing technique can reflect the actual heat transfer process in the furnace. 4. Results and discussion Distributions of the heat flux, steam quality and metal temperature can be obtained based on the above simulation. In view of the general situation, three kinds of cases were illustrated in thermodynamic parameter distributions on the front water wall. Fig. 9 shows heat flux distributions on the front water wall in the three different cases. It can be seen that the heat flux in the furnace
Fig. 10. Distributions of steam quality on the front wall: (a) case 1; (b) case 2; (c) case 3; (d) tendency of the 3 cases at the width of 12 m.
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center is much larger than the boundary region. The heat flux reaches the maximum of 504 kW/m2 at a height of 25 m. The corners 4 and 5 are located at the overlapping region of two tangential flames and the residual flue gas rotates in the zone. So, the heat flux is higher than in other regions. These results are consistent with the two-tangential firing manner. Fig. 9 (d) shows the heat flux variation curves at the furnace width of 12 m at the three typical loads. It can be seen the heat flux rises with the increment of load. For case 3, the heat flux reaches the maximum of 475 kW/m2 at the furnace height of 22 m, and the heat flux decreases with further increase in height. Fig. 10 shows the steam quality distributions on the front water wall in these cases. It can be seen that the steam quality decreases from the center to the edge along the width of water wall for a given elevation. This is due to the heat flux of single furnace on the center region is much higher than on the boundary region. With the absorption of the heat inside the furnace, the steam quality increases along the elevation for the same riser. It can also be seen that the two-phase flow zone becomes small with the inceasing boiler load. Fig. 10 (d) shows the steam quality variation curves at the furnace width of 12 m. It can be seen the appearance of two-phase flow zone is delayed with the increase of the load. The reason is that the increase in mass velocity in rifled tubes results in more liquid thrown into the wall, and the phase-transition point temperature increases with enhanced pressure. Also the outlet steam quality increases with increasing load.
Fig. 11 shows the metal temperature distribution on the front water wall in these operating cases. The temperature increases with the furnace height monotonously because the fluid temperature at 0e15 m is in single-phase zone. The metal temperature rises to the maximum of 405 C at a height of 25 m. Meanwhile, the heat flux reaches 504 kW/m2. The metal temperature reduces with the decrease of the heat flux at higher positions, due to the difference of heat exchange coefficient calculation models. The maximum deviation of metal temperature on the front wall is 20 C in case 2, and is 50 C in case 3. The temperature of corners 4 and 5 is also higher than of corners 3 and 6. Fig. 11 (d) shows the metal temperature variation curves at the given width of the furnace. The fluid begins to vaporize and to be in a saturated boiling zone at the height of 16 m. The heat exchange coefficient of fluid obviously increases and the fluid temperature is at the saturated temperature all the time. So the metal temperature increases slowly. However, the metal temperature increases rapidly with the decreasing heat exchange coefficient of fluid in the postdryout region. At greater furnace height, the heat flux decreases with increased height. So the metal temperature begins to decrease at the height of 24 m. According to the figures described above, it can be seen that the non-uniform distribution of heat flux and steam quality play an essential role in the metal temperature deviation. In order to reduce the deviation of heat flux and delay the vapor generation, the optimal ribbed bore tubes and restriction orifice should be applied in the water wall. Then, the tube wall overheating can be avoided and the secure operation of boiler is ensured.
Fig. 11. Distributions of metal temperature ( C) on the front wall: (a) case 1; (b) case 2; (c) case 3; (d) tendency of the 3 cases at the width of 12 m.
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5. Conclusions A distributed parameter model for the evaporation system in a twin-furnace once-through boiler was established. An imaginary wall surface was put forward to simplify the twin-furnace problem. The model for predicting the transient distributions of parameters, such as the heat flux, the metal-surface temperature and the steam quality in the evaporation system was proposed based on 3-D temperature distribution. The heat flux, steam quality and metal temperature distribution in the water wall were obtained by directly solving non-linear equations; and the in-situ measured data is consistent with the computerized values. The simulation results show that the metal temperature of corners 4 and 5 is higher than other corners at the high load and high combustion zone. The heat flux reaches a maximum value at rated load in furnace. At greater furnace height, the heat flux decreases with the increase of the furnace height. The steam quality increases along the elevation for the same riser with the absorption of the heat inside the furnace. It can be seen that the two-phase flow zone becomes shorter with increased load. The metal temperature may reach to the maximum at a certain height in the furnace, while the deviation of metal temperature is nearly 50 C at different load. The model can promote the transient, distributed parameters of the evaporation system, which has a great value for safe, economic operation in a once-through boiler. It is a new supported method for research on supercritical once-through boiler based on flame image processing technique. Acknowledgments This work is sponsored by the National Natural Science Foundation of China (Contract Nos.: 51076049, 51025622 and 50721005). References [1] A. Ray, H.F. Bowman, A nonlinear dynamic model of a once-through subcritical steam generator, J. Dyn. Syst. Meas. Control. Trans. ASME 98 (1976) 332e339. [2] H.P. Li, X.J. Huang, L.J. Zhang, A lumped parameter dynamic model of the helical coiled once-through steam generator with movable boundaries, Nucl. Eng. Des. 238 (2008) 1657e1663. [3] W. Wang, T.J. Ren, Q.R. Gao, X.C. Liu, Mathematical model and simulation of the evaporating surface in a once-through boiler, Qinghua Daxue Xuebao/J. Tsinghua Univ. 41 (2001) 105e108 (in Chinese). [4] J.R. Zhu, C.Y. Zhang, Real-time mathematical model for the heat transfer in the furnace and the evaporating condition of an once-through boiler, Zhongguo Dianji Gongcheng Xueb 11 (1991) 63e72 (in Chinese).
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