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The finite volume method for evaluating the wall temperature profiles of the superheater and reheater tubes in power plant
Accepted Manuscript Research Paper The finite volume method for evaluating the wall temperature profiles of the superheater and reheater tubes in power plant Hong Xu, Bo Deng, Dongfang Jiang, Yongzhong Ni, Naiqiang Zhang PII: DOI: Reference:
S1359-4311(16)32397-3 http://dx.doi.org/10.1016/j.applthermaleng.2016.10.091 ATE 9293
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
17 May 2016 15 August 2016 13 October 2016
Please cite this article as: H. Xu, B. Deng, D. Jiang, Y. Ni, N. Zhang, The finite volume method for evaluating the wall temperature profiles of the superheater and reheater tubes in power plant, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.10.091
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The finite volume method for evaluating the wall temperature profiles of the superheater and reheater tubes in power plant Hong Xu, Bo Deng, Dongfang Jiang, Yongzhong Ni, Naiqiang Zhang* MOE’s Key Lab of Condition Monitoring and Control for Power Plant Equipment, School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China *Corresponding author: N. Zhang. Email: mailto:[email protected]. Tel. +86(10)13810137811;
Abstract: A single tube model based on the finite volume method and measured temperature of inlet and outlet steam is proposed to evaluate the wall temperature profiles of the high temperature surface tubes in power plant. The model permits the consideration of oxide scales in the inner wall, which can leading to the overheating of material. With the increasing of outer oxide scale thickness under the same condition, the temperature of the outer wall will be rapidly increasing more than inner wall. In the same condition without oxide scale, steam is more easily leading to the increased of the wall temperature than flue gas. The higher mass flow rate will increase the convection coefficient and decrease the heat flux from the tube metal to the steam. Keywords: High temperature surface; Finite volume method; Wall temperature profiles; Power plant 1. Introduction With the vigorous development of industrialization and increasing demand for power, traditional thermal power plant in order to achieve higher thermal efficiency and lower pollutant emission, the temperature and pressure of the steam have been constantly improved. 1 / 24
At present, the overheating of high temperature surface in coal-fired thermal power plant is still serious. According to statistics, approximately 40% of the forced power station outages was caused by boiler tube failures due to the overheating of the material[1]. During the operating of boiler, the steam-side oxidation corrosion of the boiler tubes will be obvious deteriorate with the increasing of tube metal temperature. Owing to the lower thermal conductivity, the oxide scales will reduce the heat transfer from the metal to the steam and the metal temperature has increased. Moreover, in the process of start-up of the boiler from a cold state, too quickly increasing of the tube temperature can brought more thermal stress and lead to the exfoliation and deposition of steam-side oxide scales. Therefore, it is significance to monitor the tube wall temperature of superheater and reheater in power plant. However, superheater and reheater tubes have to operate under an extremely environment. It is very difficult to install the wall temperature measuring instrument on the superheater and reheater tubes of boiler due to excessive high temperature flue gas of the tube external. Therefore, the tube wall temperature measuring instrument is mainly installed at the tube exit outside of the furnace as shown in Fig 1, where
and
stand for the inlet and
outlet steam temperature obtained by measuring instruments respectively. What’s more, for the most dangerous place, the wall temperature cannot be obtained directly. It is critical to avoid overheating of the superheater material if the detailed tube wall temperature is known over the entire length of the superheater[2]. It is well known that the standard method for thermal calculations of superheater and reheater is presented in[3]. This method is used to design or performance calculation of superheater and reheater assuming constant fluid properties. And a lot of studies have been 2 / 24
conducted over the past decades to improve the method. The thermal deviation theory was proposed for the calculation of the heat transfer in the external surface of the superheater and reheater tube by Wang and Chen[4,5] and was developed by Xu et al.[6]. A nonlinear mathematical model is developed to determine the flow rate distribution in the parallel tubes of superheater and reheater by Yang et al.[7]. Another model is described in 3-D and the solution algorithm fully couples the flow and heat transfer by Prieto et al. [8,9,10]. They obtained the temperature of combustion gases by means of experiment measurement at the inlet section of reheater and the model can be applied to the tube bundle of boiler components placed in the convective-radiative zone. Commercial software based on the finite element method was used to analyze the gas thermal deviation and uneven wall temperature in[11,12,13]. The combustion chamber and the convective section of the boiler can be simulated by three-dimension fire side models, but the modeling of thermal and hydraulic processes in steam superheater and reheater are very simplifying so that the tube wall temperature field are not certainly. Ghasemi et al. [14,15] established the multi-objective optimization system for oil-fired furnaces. They used the Sprint CFD code to predict the exit temperature and emissions of the furnace. The NOx and soot were minimized simultaneously by changing the air inlet axial velcocity, air inlet tangential velocity, diameter of droplets and air inlet preheating. A numerical method was proposed for determining the local heat flux in boiler furnace from the distribution of temperature in instrumental tube sections by Taylor et al. in[16]. And the superheater modeling taking into account the flow and heat transfer processes in cross-flow tube heat exchanges with complicated flow arrangements would developed in[17]. 3 / 24
In this paper, the single tube model based on the finite volume method and measurements wall temperatures is proposed to evaluate the wall temperature profiles of the superheater and reheater tubes in the power plant. This model taking into account the temperature distributions both of the steam side and the flue gas side are used to determine the wall temperature with a variety of combinations include different steam flow rate and heat transfer coefficient. And the model makes it possible to calculate the effect of oxide scales on the heat transfer from the flue gas to the steam. Moreover, the calculated results for the wall temperature of the tubes are analyzed. 2. Mathematical model 2.1. Assumption conditions To simplify the model, the general assumption conditions of tube are made as follow: 1） The steam along the fluid flow direction is one dimension linear mass flow. 2） The pressure along the steam flow is not change. 3） Circumferential heat conduction in the tube wall is negligible. 4） The change of diameter and material of one single tube is negligible. 2.2. Heat transfer model The high temperature surfaces of the utility boiler are schematically shown in Fig. 1. It mainly consists of a suspended platen superheater placed above the combustion chamber, at the front part of the exit from the furnace cross-section, and the secondary superheater placed above the furnace nose. The two-dimensional heat conduction governing equation can be written as
4 / 24
（1） Where m and n denote the node numbers of the z and r axis respectively; and
is density;
are specific heat and thermal conductivity respectively. The subscript x can
denote the tube wall metal substrate or oxide scale by being rewritten as ox or met respectively. The initial conditions are （2）
, The symbol
denotes the temperature of the metal or oxide scale; the subscript 0 means
the initial time. And the boundary conditions at steam-side and gas-side can be respectively described as
（3）
Here,
and
denote the steam-side convection heat transfer coefficient and the
gas-side heat transfer coefficient, where subscripts s and g stand for the steam-side and gas-side respectively. The finite volume method is used to solve the differential equations for the temperature of the tube wall[18]. The tube walls are divided into (m-1) uniform layers along the z axis and (n-1) uniform layers along the r axis respectively, as there are shown in Fig 2. Each node represents a core of the control volume. The temperature at each node is denoted by symbol
and
; the
stand for the measuring temperature of the inlet tube wall and the
outlet tube wall respectively;
and
denote the cell length of the control volume
along the r and z axis respectively. The median line
is the interface of the metal control
volumes and the oxide scale control volumes. And the thermal conductivity 5 / 24
between the
oxide scale and the tube wall metal can be described by [18] （4） Multiplying the equation (1) on both sides by r, we can obtain the discretization equation by integrating the governing equation over the control volume and over the time interval to
, as follows （5） The symbol a stands for the coefficient of the temperature of the node. And the
expression of the coefficient
in different kinds of control volume can be observed in
Appendix, such as one control volume, half of one control volume and quarter of one control volume. The upper index 0 denotes the last moment. The heat transfer between the inner wall of the tube and the steam is usually considered as a forced convection heat transfer due to the relatively faster steam in the tube. The steam side heat transfer coefficient heat is calculated using [19] （6） where the Reynolds number
and Prandtl number
is based on the inner diameter of
the tube and calculated at the film temperature with the following conditions: 1) ; 2)
; 3)
,
is the tube length. （7） （8）
The symbol
is mass flow rate of the steam in a single tube;
is dynamic viscosity
of the steam. And the value of the thermo-physical properties of the steam can be calculate using the equations of IAPWS-IF97 as suggested by[20]. The gas side heat transfer 6 / 24
coefficient accounts for the simultaneous convection and radiation mechanisms as follow[21,22] （9） where
is the coefficient of the non-uniform sleeping of the boiler components by gases, for
a cross-current flow,
. The surface heat transfer coefficient due to convection
is
expressed as suggested by [3] （10） where
(Reynolds number) and
(Prandtl number) are defined as: （11） （12）
in which and
is gas velocity;
is the kinematic viscosity;
is the dynamic viscosity.
denote the correction factors for the arrangement and the effect of a number of tube
rows in the array respectively. The value of the coefficient (when relative transversal pitch ,
is calculated to be
and relative longitudinal pitch
) ; the value of the coefficient
is calculated to be
=1 ,
(when
, mean number of rows in the tube group). The radiation heat transfer coefficient
may be expressed by [3] （13）
The coefficient A is assumed to be A=0.3 for fuel oil and gas, A=0.4 for bitumite and A=0.5 for lignite;
is the flue gas mean temperature over the tube section;
and
are
the depth of the gas space before the tube row and the calculated tube bundle, respectively. The symbol
is the radiation heat transfer coefficient of the combustion products for 7 / 24
pulverized coal boiler. 3 Operating parameters and boundary conditions The FVM model can be applied to a secondary superheater of a pulverized coal boiler working under the turbine heat acceptance (THA) load. The boiler’s type is B&WB-2028/17.5-M, and the superheater has a capacity of 1754.8 t/h at the design pressure of 17.28 MPa and the design temperature of 541℃. The secondary superheater arranged in the horizontal flue, there are 33 serpentines made up of 20 tubes each, and the primary material of the tube metal is SA-213T91. As it is shown in Fig 3, in which D is the outer diameter; d is the inner diameter;
is the thickness of the tube;
tube;
is the longitudinal pitch;
is the transversal pitch;
is the length of a Single is the number of tube wide;
The geometries of the secondary superheater and the thermo-physical properties of metal are shown in Table 1 and 2, respectively. To solve the temperature profiles of the tube wall, the grid independency check was performed by a series of grid numbers and the 100×10=1000 cells was chosen. The discretization equation is solved sequentially with the line-by-line tridiagnoal-matrix algorithm [23,24]. 3.1 The steam-side conditions It is well known that the steam is heated by the high temperature flue gas when passing through the tube due to the larger temperature difference between the steam and the flue gas. So we can take into account the temperature of the steam along the fluid flow path is one dimension and increased monotonically. In the operation, the most dangerous point in the tube may occur in the tube elbow or the outlet position. The measuring in-line data of
and
in serpentine 1, 7, and 16 of the 8 / 24
secondary superheater were obtained for a power plant working under stable conditions at nominal load as showed in Table3, which subsequently introduced into the model as boundary conditions for the inlet and outlet sections. Fig. 3 shows the tube arrangement of the secondary superheater. The serpentine 1, 7 and 16 are located at the left side of the boiler. Due to the effect of thermal gas deviation, the highest temperatures maybe placed more toward the side walls, as it verified by [8]. From the Table 3, the measurements steam temperature differences between the inlet section and outlet tube in serpentine 7 are about 19K and 34K than serpentine 1 and serpentine 16 respectively. The steam-side heat transfer coefficient and the gas-side heat transfer coefficient under the nominal load in a single tube of the serpentine 1 are presented in Table 4. 3.2 The gas-side conditions We shall analyze the model solution for uniform flow and temperature for the combustion gases under the normal load: .
and
,
and
are the mean temperature at the inlet and outlet cross-section of the
secondary superheater by thermal calculation. For the sake of simplified calculation, Combustion simulation calculation was carried out based on the numerical simulation software FLUENT. Fig.4 shows the gas temperature distribution along the length direction of a single tube in serpentine 1. From the picture, the higher flue gas temperature region is concentrated in the lower part of the tube. The flue gas temperature at the inlet and outlet are of 115K and 96K lower than the temperature of the flue gas at the lower part of the tube. The simulation results are consistent with the experimental results in [8, 13]. The values of the radiation heat transfer coefficient and the thermo-physical 9 / 24
properties of the flue gas are shown in Table 5[25]. 4 Results and discussion Results of the tube wall temperature along the length direction of a single tube obtained using the calculation procedures with Tables 1-5 and Fig 4. Detailed discussions on the calculation results as follows: 4.1 Effects of oxide scales of the tube inner surface on the wall temperature In order to calculate the effect of oxide scales of the tube inner surface, the oxide scales are considered to be single layered scale of uniform thickness. The superheater tubes are running in the same steam and gas condition with the following data is adopted: and
. From the Fig. 5, it is can be seen that the wall
temperature is as a monotonic function increased with the increasing of the oxide scales thickness. Under the same steam condition, the inner wall temperatures do almost not change but the wall temperatures with
are about 40K than
times temperature increasing larger than
. It is nearly 2
with 2.5 times increased of the outer
oxide scales thickness. This is because that the oxidation film added the thermal resistance between the tube metal and steam, thereby the heat transfer performance will be reduced. In a long time’s results collection and calculation, we can find the influence to the oxide scale thickness by differences of the wall temperature. And we can help to forecast the growth conditions of oxide scales. 4.2 Effects of steam temperature distribution on the tube wall temperature In this case, the steam heated by the flue gas flows from the inlet headers to the outlet headers under the normal load:
, 10 / 24
and
. It can be seen
,
from Fig. 6(a) and 6(b) that the steam temperature distributions have a large impact on the tube wall temperature. The calculated wall temperature show monotonic growth under the measurements steam temperatures for serpentine 1, 7 and 16 in Table 3. With the increasing of steam temperature along the single tube, the tube wall temperature is simultaneous increasing. Furthermore, Fig. 6(a) indicates the temperature of all the inner tube walls are linear distribution along the direction of the steam flow, the same as in Fig. 6(b). The temperature of outer wall in Serpentine 7 is the highest in the calculated results, when the temperature difference reaches about 51K from the inlet to the outlet section and the outer wall temperature is larger 44K than the temperature of Serpentine 1..Therefore, the uneven flue gas temperature has a great influence to the heat absorption from flue gas to the steam. 4.3 Effects of gas temperature distribution on the tube wall temperature As shown in Fig. 7 under the steam conditions of serpentine 1 without oxide scales on the inner wall, the effect of different flue gas loads on the wall temperature of a single tube is calculated with
,
and
. It can be seen that the
higher flue gas temperature lead to a larger increase of the wall temperature in the tube metal as mentioned in [26,27]. Both in the Fig. 7(a) and 7(b), the increasing of the tube wall temperatures are only about 5K while the increasing of the flue gas temperature are about 60K. And due to the effect of the ash deposit coefficient, the wall temperature in Fig. 7(b) is 2K higher than 7(a). For the same Node 51 under the same condition without oxide scale, the outer wall temperature is increasing of 7.4% with the steam temperature increased by 5.8%. But the gas temperature is nearly increasing of 7% induced only 0.7% increasing of the outer wall temperature. It means that the out wall temperature increased about 1% induced by flue 11 / 24
gas is more 12.8 times than steam. So according to measuring temperature of the outlet section wall to judge the tube wall temperature in the boiler is feasible without consideration of oxide scales and steam mass flow. Actually, the steam in each single tube when heated by the flue gas from the inlet to the outlet section is not uniform due to the uneven gas temperature profile. To compare the effect of the gas temperature and the heat transfer coefficient, the calculation of the wall temperature distributions along the steam flow path under the mean gas temperature and the simulated gas (see Fig. 4) are shown in Fig. 8. It can be seen clearly from this figure that the wall temperature difference are larger in the inlet and the outlet of the tube. The maximum wall temperature difference in the inlet of tube is
. And there is almost no
temperature difference in the tube elbow as can be seen from the Fig. 9. According to the results of the tube wall temperature under the simulated gas condition and even gas condition, we can used to guide the operation and adjust working load of the boiler. 4.4 Effects of Steam Mass flow on the tube wall temperature For the calculation, the following data is adopted:
,
and
; the steam temperature is adopted in accordance with the serpentine 1; the average steam mass flow rate through the single tube is
. Due to the tee joint
distributions of the headers affect the steam mass flow rate deviation as mentioned in [6], we adopted two types flow rate deviation to analysis, and
(dropped by 20%)
(dropped by 50%). The influence of different steam flow rate on the
wall temperature of the tube is shown in the Fig. 10 under the normal load. It can be seen from the picture, the wall temperature increases with the decrease of the 12 / 24
steam mass flow rate. When the flow deviation reaches from 20% to 50%, the maximum wall temperature difference is increased by about 3.6 times. Because of the convection coefficient for the steam in the tube is decided by the steam mass flow rate. The higher mass flow rate will increase the convection coefficient and decrease the heat flux from the tube metal to the steam. Therefore, The lower steam mass flow rate maybe lead to the overheating of material. In general, the steam flow deviation maybe caused by the oxide scales 5 Conclusion This paper presents a numerical modeling of the superheaters that can be used for detailed descriptions of a heat transfer process in power plant. The model allow to use in the on-line thermal monitoring and simulation of the tube wall and applied to provide overheating alarm. The model employs the finite volume method to discretize the system of two-dimension heat conduction governing equation. The model include the variable thermo-physical properties (i.e. density, specific heat capacity, dynamic viscosity, heat conductivity, heat transfer coefficient) of flue gas and steam, the working load, measuring data’s, geometries of the superheaters and related parameters.
The model is a good tool to extend the temperature distribution of the whole serpentines and use to help for the future design of the wall temperature distribution in the presence of the oxide scale. Acknowledgement This paper was supported by the National Natural Science Foundation of China (51134016, 51471069 and 51201064), Natural Science Foundation of Beijing (2152029) and 13 / 24
the Fundamental Research Funds for the Central Universities. Appendix 1） For the one control volume (
,
2）
)
Near the gas-side (
While
When
, for the quarter of one control volume
14 / 24
)
When
, for the quarter of one control volume
3） Near the steam-side ( While
When
)
, for
, for the quarter of one control volume
15 / 24
When
, for the quarter of one control volume
4） In the inlet side, for the half of one control volume (
5） In the outlet side, for the half of one control volume (
16 / 24
)
)
References
[1] French DN, Metallurgical failures in fossil fired boilers, 2nd Ed. New York, USA: John Wiley & Sons, (1993). [2] Z. Y. Zhao, H. Xu, A study on the residual life of high-temperature boiler tube for inner wall oxidation thickness, International Conference on Electrical and Control Engineering, 285-287(2010). [3] N. W.,Kuznetsov, W.W. Mitor, I.E. Dubovski, E. S. Karasina, Thermal calculations of steam boilers (standard method), Moscow, Russia: Energia(1973). [4] M. H. Wang, The calculation of thermal deviation for plate superheater, Power Engineering, 2 (1986):7-14. [5] Z.H. Chen. The calculation and analysis of the flow distribution and the thermal variation of the single-phase fluid flowing through the manifold systems in boilers, Journal of University of Shanghai for Science and Technology, 19(1997): 160-178. [6] L. J. Xu, J. A. Khan, Z.H. Chen, Thermal load deviation model for superheater and reheater of a utility boiler, Applied Thermal Engineering, 20(2000): 545-558. [7] D. Yang, T. k. Chen, H. X. Li, L. Z. Liu, X. L, Ji, Nonlinear mathematical model for flow rate distribution in the parallel tubes of boiler superheater/reheater and the calculation method of tube surface temperature, Proceeding of CSEE, 21(2001)38-42 [8] M.M. Prieto, F.J. Fernandez, I. Suarez, H. Sa′nchez, Experimental thermal behavior of a power plant reheater, Energy, 31(2006)665-676.
17 / 24
[9] M.M. Prieto, I Suarez, F.J. Fernandez, H. Sa′nchez, M. Mateos, Application of a thermal model to a power plant reheater with irregular tube temperatures, Applied Thermal Engineering, 27(2007)185-193. [10] M.M. Prieto, I. Suarez, F.J. Fernandez, H. Sa′nchez, M. Mateos, Theoretical development of a thermal model for the reheater of a power plant boiler, Applied Thermal Engineering, 27(2007)619-626. [11] C.G. Yin, S. Caillat, J. L. Harion, B. Baudoin, E. Perez, Investigation of the flow, combustion, heat-transfer and emission from a 609MW utility tangentially fired pulverized-coal boiler, Fuel, 81(2002)997-1006. [12]C.G. Yin, L. Rosendahl, T. J. Condra, Further study of the gas temperature deviation in large-scale tangentially coal-fired boilers, Fuel, 82(2003)1127-1137 [13] H. Y. Park , S. H. Baek , Y. J. Kim , T. H. Kim , D. S. Kang , D. W. Kim, Numerical and experimental investigations on the gas temperature deviation in a large scale, advanced low NOx, tangentially fired pulverized coal boiler, Fuel, 104(2013)641-646. [14] A.M. Ghasemi, A. Saeedi, M. Moghiman, Application of Multi-Objective Optimization for Pollutants Emission Control in an Oil-Fired Furnace, Journal of the Chinese Society of Mechanical Engineers, 32(2011):303-312. [15] M. Javadi , A. Golshani , A. M. Ghasemi et al, Improving Power Plant Efficiency using Water Droplet Injection in Air Condensers, In World Academy of Science, Engineering and Technology, (2010) [ 16 ] J. Taler, A method of determining local heat flux in boiler furnaces, Heat Mass Transfer, 35(1992)1625-1634. [17] M. Trojan, D. Taler, Thermal simulation of superheaters taking into account the processes occurring on the side of the steam and flue gas, Fuel, 150(2015)75-87.
18 / 24
[18] Patankar, Numerical heat transfer and fluid flow, New York, USA: McGRAW-HILL Book Company, (1980). [19] F.P. Incropera, D.P. DeWitt, Introduction to Heat Transfer, third ed., John Wiley, (1996). [20] J. L. Huang, K.Y. Zhou, J.Q. Xu, C. X. Bian, On the failure of steam-side oxide scales in high temperature components of boilers during unsteady thermal processes, Journal of Loss Prevention in the Process Industries, 26(2013)22-31. [21] Z.H. Lin, Thermohydraulic design of fossil-fuel-fire boiler components, in: S. Kakac (Ed.), Evaporators and Condensers, John Wiley & Sons, Inc, Canada, (1991). [22] Q. T. Zhou, K. Y. Zhou, W. Leng, Fundamentals of boilers in thermal power plants, Beijing, China: Electric Power Press, (2009). [23] A. Ghasemi, M. Moghiman, S. M. Javadi, N. Hosseini, Effects of droplet size and air preheating on soot formation in turbulent combustion of liquid fuel, Proceedings of the ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Turkey, (2010) [24] M. M. Gholizadeh, R. Nikbakhti, A Ghasemi, Numerical study of double diffusive buoyancy forces induced natural convection in a trapezoidal enclosure partially heated from the right sidewall, Alexandria Engineering Journal, 55(2016):779-795. [25] R. K. Mobley, Plant engineer’s handbook, Woburn, USA: Butterworth-Heinemann Press, 23/392 Industrial Boilers, (2001). [26] J. Purbolaksono, A. Khinani, A.Z. Rashid, A.A. Ali, J. Ahmad, N.F. Nordin, A new method for estimating heat flux in superheater and reheater tubes, Nuclear Engineering and Design, (239)2009:1879-1884.
19 / 24
[27] J.Purbolaksono, A. Khinani, A.Z. Rashid, A.A. Ali, N.F. Nordin, Prediction of oxide scale growth in superheater and reheater tubes, Corrosion Science, 51(2009):1022-1029.
Table and figure captions Table 1 Geometries of the secondary superheater Table 2 Thermo-physical properties of the tube wall metal and the oxide scale Table 3 Measurements steam temperatures in the inlet and outlet sections of serpentine 1, 7 and 16 Table 4 Thermo-physical properties of steam and heat transfer coefficient Table 5 Thermo-physical properties of the flue gas and the convection heat transfer coefficient
Figures Fig. 1. Utility boiler diagram Fig. 2. The discretization model of the single tube: (a) m uniform layers along the z axis; (b) n uniform layers along the r axis;
- one control volume;
- half of one control volume;
- the interface of two adjacent control volume;
-quarter of one control volume;
-the interface of the oxide scales and metal; ND (1,
1),…, ND (i, j) - the core of the control volume at the node Fig. 3. Arrangement and geometry of secondary superheater tubes Fig. 4. The distributions of simulated and even gas temperatures along the single tube. Fig. 5. The tube wall temperature distribution along the single tube with three kinds of oxide scale Fig. 6. The tube wall temperature distribution in three Serpentines: (a) inner wall temperature; (b) outer wall temperature Fig. 7. The tube wall temperature distribution in the three gas temperature conditions: (a) (b)
20 / 24
;
Fig. 8. The wall temperature distribution along the steam flow path with the mean gas temperature and the simulated gas temperature Fig. 9. The heat transfer coefficient distribution in the gas side along the steam flow path with the mean gas temperature and the simulated gas temperature Fig. 10. The wall temperature distribution with the different steam flow rate
Nomenclature
coefficient changed with the kinds of fuel a, b
coefficients of the node temperature specific heat, correction factors for the arrangement of a number of tube rows correction factors for the effect of a number of tube rows original inner diameter of tube, m outer diameter, m steam-side convection heat transfer coefficient, gas-side heat transfer coefficient, convection heat transfer coefficient, radiation heat transfer coefficient, 21 / 24
k
median line of the control volume tube length, m cell length, m ,
m
depth of the gas space before the tube row and the calculated tube bundle, m node numbers of the z axis mass flow rate, numbers of tube wide
n
node numbers of the r axis Prandtl number
r
coordinate r Reynolds number transversal pitch, m longitudinal pitch, m temperature of the metal substrate or oxide scale, o C ,
steam temperatures at the inlet and outlet of secondary superheater， o C kinematic viscosity， gas velocity， m/s
z
coordinate z radiation heat transfer coefficient of the combustion products duration，s density,
22 / 24
thermal conductivity cell thickness, m dynamic viscosity， coefficient of the non-uniform sleeping of the boiler components by gases relative transversal pitch, m relative longitudinal pitch, m
Subscripts g
gas-side
in
inlet of the tube
met
metal substrate of tube
ox
oxide scale
out
the outlet of the tube
s
steam-side
x
denote ox or met
0
initial
Upper 0
last moment
‘
inlet section
“
outlet cetion
23 / 24
24 / 24
Fig. 1. Utility boiler diagram
Fig. 2. The discretization model of the single tube: (a) m uniform layers along the z axis; (b) n uniform layers along the r axis; control volume;
- one control volume;
- half of one control volume;
- the interface of two adjacent control volume;
-quarter of one
-the interface of the oxide
scales and metal; ND (1, 1),…, ND (i, j) - the core of the control volume at the node.
Fig. 3. Arrangement and geometry of secondary superheater tubes
1000
o
Temperature, C
900
800
700 The simulated gas temperature of Serpentine 33 The even gas temperature of whole secondary supheater
600 0
20
40
60
80
100
Node Number
Fig. 4. The distributions of simulated and even gas temperatures along the single tube.
580 560
Wall Temperature,
℃
540 520 500 inner wall with 0mm oxide scale outer wall with 0mm oxide scale inner wall with 0.2mm oxide scale outer wall with 0.2mm oxide scale inner wall with 0.5mm oxide scale outer wall with 0.5mm oxide scale
480 460 0
20
40
60
80
100
Node Number
Fig. 5. The tube wall temperature distribution along the single tube with different thickness oxide scale
(a)
580
Wall Temperature,
℃
560
℃
560 Wall Temperature,
(b)
580
540
520
500
Serptine 1 , inner wall Serptine 14 , inner wall Serptine 32 , inner wall
480 0
20
40
60
80
100
540
520
500
Serptine 1 , outer wall Serptine 14 , outer wall Serptine 32 , outer wall
480 0
Node Number
20
40
60
80
100
Node Number
Fig. 6. The tube wall temperature distribution in three Serpentines: (a) inner wall temperature; (b) outer wall temperature
(a)
(b)
520
o
inner wall, Tg'=855 C o outer wall, Tg'=855 C o inner wall, Tg'=924 C o outer wall, Tg'=924 C o inner wall, Tg'=924 C o outer wall, Tg'=986 C
500
480
Wall Temperature,
Wall Temperature,
℃
540
℃
540
520
o
inner wall, Tg'=855 C o outer wall, Tg'=855 C o inner wall, Tg'=855 C o outer wall, Tg'=855 C o inner wall, Tg'=855 C o outer wall, Tg'=855 C
500
480 0
20
40
60
80
100
Node Number
0
20
40
60
80
Node Number
Fig. 7. The tube wall temperature distribution in the three gas temperature conditions: (a) ; (b)
100
540
Wall Temperature,
℃
520
500
480
the inner wall temperature in uneven gas temperature the outer wall temperature in uneven gas temperature the inner wall temperature in mean gas temperature the outer wall temperature in mean gas temperature
460 0
20
40
60
80
100
Node Number
Fig. 8. The wall temperature distribution along the steam flow path with the mean gas temperature and the simulated gas temperature
140
Wall Temperature,
℃
120
100
80
hg in the uneven gas temperature profile with clear surface hg in the uneven gas temperature profile with ash deposit hg in the mean gas temperature profile with clear surface hg in the mean gas temperature profile with ash deposit
60 0
20
40
60
80
100
Node Number
Fig. 9. The heat transfer coefficient distribution in the gas side along the steam flow path with the mean gas temperature and the simulated gas temperature
Wall Temperature,
℃
540
520
500
the inner wall temperature with ms=0.74kg/s the outer wall temperature with ms=0.74kg/s the inner wall temperature with ms=0.59kg/s
480
the outer wall temperature with ms=0.59kg/s the inner wall temperature with ms=0.37kg/s the outer wall temperature with ms=0.37kg/s
460 0
20
40
60
80
100
Node Number
Fig. 10. The wall temperature distribution with the different steam flow rate
Table 1 Geometries of the secondary superheater (m)
(m)
(m)
(m)
0.051
0.039
0.006
24.000
(m) 0.300
, (m) 0.070
(m) 0.75
(m) 1.33
33
Table 2 Thermo-physical properties of the tube wall metal and the oxide scale Material
,
,
,
T91
7760
622
33
Oxide scale[18]
5010
833
0.851
Table 3 Measurements steam temperatures in the inlet and outlet sections of serpentine 1, 7 and 16 Inlet section, Date
31/3/ 2013
Time
20:00
Outlet section,
Serpentine Point 1
Point 2
Mean
Point 1
Point 2
Point 3
Mean
1
466.8
469.6
468.2
509.9
509.5
508.0
509.1
7
498.1
496.3
497.2
556.1
558.5
556.4
557.0
16
485.6
483.4
484.5
508.2
512.1
511.0
510.4
Table 4 Thermo-physical properties of steam and heat transfer coefficient （MPa）
（℃）
（
）
（℃）
（
）
17.28
468.2
2867.71
924
45.20
17.28
473.1
2858.20
924
45.48
17.28
478.0
2833.07
924
45.76
17.28
482.9
2808.18
916
46.04
17.28
487.8
2798.46
916
46.37
17.28
489.0
2798.46
909
45.98
17.28
494.7
2771.30
909
45.52
17.28
499.6
2756.86
909
45.80
17.28
504.5
2741.54
909
46.09
17.28
509.1
2738.02
909
46.31
Table 5 Thermo-physical properties of the flue gas and the convection heat transfer coefficient （℃）
（
）
（
）
（
）
（
）
800
1.222
42.83
69.93
63.57
900
1.242
45.24
74.68
61.93
1000
1.259
47.55
79.11
60.33
1100
1.275
49.75
83.23
58.81
Highlights
A single tube model is proposed to evaluate the wall temperature profiles
Effect of excessive higher gas temperature and steam temperature
Oxide scales on the inner tube can cause the overheating of the tube wall
Higher mass flow rate will decrease the heat flux from the tube metal to the steam
S1359-4311(16)32397-3 http://dx.doi.org/10.1016/j.applthermaleng.2016.10.091 ATE 9293
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
17 May 2016 15 August 2016 13 October 2016
Please cite this article as: H. Xu, B. Deng, D. Jiang, Y. Ni, N. Zhang, The finite volume method for evaluating the wall temperature profiles of the superheater and reheater tubes in power plant, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.10.091
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The finite volume method for evaluating the wall temperature profiles of the superheater and reheater tubes in power plant Hong Xu, Bo Deng, Dongfang Jiang, Yongzhong Ni, Naiqiang Zhang* MOE’s Key Lab of Condition Monitoring and Control for Power Plant Equipment, School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China *Corresponding author: N. Zhang. Email: mailto:[email protected]. Tel. +86(10)13810137811;
Abstract: A single tube model based on the finite volume method and measured temperature of inlet and outlet steam is proposed to evaluate the wall temperature profiles of the high temperature surface tubes in power plant. The model permits the consideration of oxide scales in the inner wall, which can leading to the overheating of material. With the increasing of outer oxide scale thickness under the same condition, the temperature of the outer wall will be rapidly increasing more than inner wall. In the same condition without oxide scale, steam is more easily leading to the increased of the wall temperature than flue gas. The higher mass flow rate will increase the convection coefficient and decrease the heat flux from the tube metal to the steam. Keywords: High temperature surface; Finite volume method; Wall temperature profiles; Power plant 1. Introduction With the vigorous development of industrialization and increasing demand for power, traditional thermal power plant in order to achieve higher thermal efficiency and lower pollutant emission, the temperature and pressure of the steam have been constantly improved. 1 / 24
At present, the overheating of high temperature surface in coal-fired thermal power plant is still serious. According to statistics, approximately 40% of the forced power station outages was caused by boiler tube failures due to the overheating of the material[1]. During the operating of boiler, the steam-side oxidation corrosion of the boiler tubes will be obvious deteriorate with the increasing of tube metal temperature. Owing to the lower thermal conductivity, the oxide scales will reduce the heat transfer from the metal to the steam and the metal temperature has increased. Moreover, in the process of start-up of the boiler from a cold state, too quickly increasing of the tube temperature can brought more thermal stress and lead to the exfoliation and deposition of steam-side oxide scales. Therefore, it is significance to monitor the tube wall temperature of superheater and reheater in power plant. However, superheater and reheater tubes have to operate under an extremely environment. It is very difficult to install the wall temperature measuring instrument on the superheater and reheater tubes of boiler due to excessive high temperature flue gas of the tube external. Therefore, the tube wall temperature measuring instrument is mainly installed at the tube exit outside of the furnace as shown in Fig 1, where
and
stand for the inlet and
outlet steam temperature obtained by measuring instruments respectively. What’s more, for the most dangerous place, the wall temperature cannot be obtained directly. It is critical to avoid overheating of the superheater material if the detailed tube wall temperature is known over the entire length of the superheater[2]. It is well known that the standard method for thermal calculations of superheater and reheater is presented in[3]. This method is used to design or performance calculation of superheater and reheater assuming constant fluid properties. And a lot of studies have been 2 / 24
conducted over the past decades to improve the method. The thermal deviation theory was proposed for the calculation of the heat transfer in the external surface of the superheater and reheater tube by Wang and Chen[4,5] and was developed by Xu et al.[6]. A nonlinear mathematical model is developed to determine the flow rate distribution in the parallel tubes of superheater and reheater by Yang et al.[7]. Another model is described in 3-D and the solution algorithm fully couples the flow and heat transfer by Prieto et al. [8,9,10]. They obtained the temperature of combustion gases by means of experiment measurement at the inlet section of reheater and the model can be applied to the tube bundle of boiler components placed in the convective-radiative zone. Commercial software based on the finite element method was used to analyze the gas thermal deviation and uneven wall temperature in[11,12,13]. The combustion chamber and the convective section of the boiler can be simulated by three-dimension fire side models, but the modeling of thermal and hydraulic processes in steam superheater and reheater are very simplifying so that the tube wall temperature field are not certainly. Ghasemi et al. [14,15] established the multi-objective optimization system for oil-fired furnaces. They used the Sprint CFD code to predict the exit temperature and emissions of the furnace. The NOx and soot were minimized simultaneously by changing the air inlet axial velcocity, air inlet tangential velocity, diameter of droplets and air inlet preheating. A numerical method was proposed for determining the local heat flux in boiler furnace from the distribution of temperature in instrumental tube sections by Taylor et al. in[16]. And the superheater modeling taking into account the flow and heat transfer processes in cross-flow tube heat exchanges with complicated flow arrangements would developed in[17]. 3 / 24
In this paper, the single tube model based on the finite volume method and measurements wall temperatures is proposed to evaluate the wall temperature profiles of the superheater and reheater tubes in the power plant. This model taking into account the temperature distributions both of the steam side and the flue gas side are used to determine the wall temperature with a variety of combinations include different steam flow rate and heat transfer coefficient. And the model makes it possible to calculate the effect of oxide scales on the heat transfer from the flue gas to the steam. Moreover, the calculated results for the wall temperature of the tubes are analyzed. 2. Mathematical model 2.1. Assumption conditions To simplify the model, the general assumption conditions of tube are made as follow: 1） The steam along the fluid flow direction is one dimension linear mass flow. 2） The pressure along the steam flow is not change. 3） Circumferential heat conduction in the tube wall is negligible. 4） The change of diameter and material of one single tube is negligible. 2.2. Heat transfer model The high temperature surfaces of the utility boiler are schematically shown in Fig. 1. It mainly consists of a suspended platen superheater placed above the combustion chamber, at the front part of the exit from the furnace cross-section, and the secondary superheater placed above the furnace nose. The two-dimensional heat conduction governing equation can be written as
4 / 24
（1） Where m and n denote the node numbers of the z and r axis respectively; and
is density;
are specific heat and thermal conductivity respectively. The subscript x can
denote the tube wall metal substrate or oxide scale by being rewritten as ox or met respectively. The initial conditions are （2）
, The symbol
denotes the temperature of the metal or oxide scale; the subscript 0 means
the initial time. And the boundary conditions at steam-side and gas-side can be respectively described as
（3）
Here,
and
denote the steam-side convection heat transfer coefficient and the
gas-side heat transfer coefficient, where subscripts s and g stand for the steam-side and gas-side respectively. The finite volume method is used to solve the differential equations for the temperature of the tube wall[18]. The tube walls are divided into (m-1) uniform layers along the z axis and (n-1) uniform layers along the r axis respectively, as there are shown in Fig 2. Each node represents a core of the control volume. The temperature at each node is denoted by symbol
and
; the
stand for the measuring temperature of the inlet tube wall and the
outlet tube wall respectively;
and
denote the cell length of the control volume
along the r and z axis respectively. The median line
is the interface of the metal control
volumes and the oxide scale control volumes. And the thermal conductivity 5 / 24
between the
oxide scale and the tube wall metal can be described by [18] （4） Multiplying the equation (1) on both sides by r, we can obtain the discretization equation by integrating the governing equation over the control volume and over the time interval to
, as follows （5） The symbol a stands for the coefficient of the temperature of the node. And the
expression of the coefficient
in different kinds of control volume can be observed in
Appendix, such as one control volume, half of one control volume and quarter of one control volume. The upper index 0 denotes the last moment. The heat transfer between the inner wall of the tube and the steam is usually considered as a forced convection heat transfer due to the relatively faster steam in the tube. The steam side heat transfer coefficient heat is calculated using [19] （6） where the Reynolds number
and Prandtl number
is based on the inner diameter of
the tube and calculated at the film temperature with the following conditions: 1) ; 2)
; 3)
,
is the tube length. （7） （8）
The symbol
is mass flow rate of the steam in a single tube;
is dynamic viscosity
of the steam. And the value of the thermo-physical properties of the steam can be calculate using the equations of IAPWS-IF97 as suggested by[20]. The gas side heat transfer 6 / 24
coefficient accounts for the simultaneous convection and radiation mechanisms as follow[21,22] （9） where
is the coefficient of the non-uniform sleeping of the boiler components by gases, for
a cross-current flow,
. The surface heat transfer coefficient due to convection
is
expressed as suggested by [3] （10） where
(Reynolds number) and
(Prandtl number) are defined as: （11） （12）
in which and
is gas velocity;
is the kinematic viscosity;
is the dynamic viscosity.
denote the correction factors for the arrangement and the effect of a number of tube
rows in the array respectively. The value of the coefficient (when relative transversal pitch ,
is calculated to be
and relative longitudinal pitch
) ; the value of the coefficient
is calculated to be
=1 ,
(when
, mean number of rows in the tube group). The radiation heat transfer coefficient
may be expressed by [3] （13）
The coefficient A is assumed to be A=0.3 for fuel oil and gas, A=0.4 for bitumite and A=0.5 for lignite;
is the flue gas mean temperature over the tube section;
and
are
the depth of the gas space before the tube row and the calculated tube bundle, respectively. The symbol
is the radiation heat transfer coefficient of the combustion products for 7 / 24
pulverized coal boiler. 3 Operating parameters and boundary conditions The FVM model can be applied to a secondary superheater of a pulverized coal boiler working under the turbine heat acceptance (THA) load. The boiler’s type is B&WB-2028/17.5-M, and the superheater has a capacity of 1754.8 t/h at the design pressure of 17.28 MPa and the design temperature of 541℃. The secondary superheater arranged in the horizontal flue, there are 33 serpentines made up of 20 tubes each, and the primary material of the tube metal is SA-213T91. As it is shown in Fig 3, in which D is the outer diameter; d is the inner diameter;
is the thickness of the tube;
tube;
is the longitudinal pitch;
is the transversal pitch;
is the length of a Single is the number of tube wide;
The geometries of the secondary superheater and the thermo-physical properties of metal are shown in Table 1 and 2, respectively. To solve the temperature profiles of the tube wall, the grid independency check was performed by a series of grid numbers and the 100×10=1000 cells was chosen. The discretization equation is solved sequentially with the line-by-line tridiagnoal-matrix algorithm [23,24]. 3.1 The steam-side conditions It is well known that the steam is heated by the high temperature flue gas when passing through the tube due to the larger temperature difference between the steam and the flue gas. So we can take into account the temperature of the steam along the fluid flow path is one dimension and increased monotonically. In the operation, the most dangerous point in the tube may occur in the tube elbow or the outlet position. The measuring in-line data of
and
in serpentine 1, 7, and 16 of the 8 / 24
secondary superheater were obtained for a power plant working under stable conditions at nominal load as showed in Table3, which subsequently introduced into the model as boundary conditions for the inlet and outlet sections. Fig. 3 shows the tube arrangement of the secondary superheater. The serpentine 1, 7 and 16 are located at the left side of the boiler. Due to the effect of thermal gas deviation, the highest temperatures maybe placed more toward the side walls, as it verified by [8]. From the Table 3, the measurements steam temperature differences between the inlet section and outlet tube in serpentine 7 are about 19K and 34K than serpentine 1 and serpentine 16 respectively. The steam-side heat transfer coefficient and the gas-side heat transfer coefficient under the nominal load in a single tube of the serpentine 1 are presented in Table 4. 3.2 The gas-side conditions We shall analyze the model solution for uniform flow and temperature for the combustion gases under the normal load: .
and
,
and
are the mean temperature at the inlet and outlet cross-section of the
secondary superheater by thermal calculation. For the sake of simplified calculation, Combustion simulation calculation was carried out based on the numerical simulation software FLUENT. Fig.4 shows the gas temperature distribution along the length direction of a single tube in serpentine 1. From the picture, the higher flue gas temperature region is concentrated in the lower part of the tube. The flue gas temperature at the inlet and outlet are of 115K and 96K lower than the temperature of the flue gas at the lower part of the tube. The simulation results are consistent with the experimental results in [8, 13]. The values of the radiation heat transfer coefficient and the thermo-physical 9 / 24
properties of the flue gas are shown in Table 5[25]. 4 Results and discussion Results of the tube wall temperature along the length direction of a single tube obtained using the calculation procedures with Tables 1-5 and Fig 4. Detailed discussions on the calculation results as follows: 4.1 Effects of oxide scales of the tube inner surface on the wall temperature In order to calculate the effect of oxide scales of the tube inner surface, the oxide scales are considered to be single layered scale of uniform thickness. The superheater tubes are running in the same steam and gas condition with the following data is adopted: and
. From the Fig. 5, it is can be seen that the wall
temperature is as a monotonic function increased with the increasing of the oxide scales thickness. Under the same steam condition, the inner wall temperatures do almost not change but the wall temperatures with
are about 40K than
times temperature increasing larger than
. It is nearly 2
with 2.5 times increased of the outer
oxide scales thickness. This is because that the oxidation film added the thermal resistance between the tube metal and steam, thereby the heat transfer performance will be reduced. In a long time’s results collection and calculation, we can find the influence to the oxide scale thickness by differences of the wall temperature. And we can help to forecast the growth conditions of oxide scales. 4.2 Effects of steam temperature distribution on the tube wall temperature In this case, the steam heated by the flue gas flows from the inlet headers to the outlet headers under the normal load:
, 10 / 24
and
. It can be seen
,
from Fig. 6(a) and 6(b) that the steam temperature distributions have a large impact on the tube wall temperature. The calculated wall temperature show monotonic growth under the measurements steam temperatures for serpentine 1, 7 and 16 in Table 3. With the increasing of steam temperature along the single tube, the tube wall temperature is simultaneous increasing. Furthermore, Fig. 6(a) indicates the temperature of all the inner tube walls are linear distribution along the direction of the steam flow, the same as in Fig. 6(b). The temperature of outer wall in Serpentine 7 is the highest in the calculated results, when the temperature difference reaches about 51K from the inlet to the outlet section and the outer wall temperature is larger 44K than the temperature of Serpentine 1..Therefore, the uneven flue gas temperature has a great influence to the heat absorption from flue gas to the steam. 4.3 Effects of gas temperature distribution on the tube wall temperature As shown in Fig. 7 under the steam conditions of serpentine 1 without oxide scales on the inner wall, the effect of different flue gas loads on the wall temperature of a single tube is calculated with
,
and
. It can be seen that the
higher flue gas temperature lead to a larger increase of the wall temperature in the tube metal as mentioned in [26,27]. Both in the Fig. 7(a) and 7(b), the increasing of the tube wall temperatures are only about 5K while the increasing of the flue gas temperature are about 60K. And due to the effect of the ash deposit coefficient, the wall temperature in Fig. 7(b) is 2K higher than 7(a). For the same Node 51 under the same condition without oxide scale, the outer wall temperature is increasing of 7.4% with the steam temperature increased by 5.8%. But the gas temperature is nearly increasing of 7% induced only 0.7% increasing of the outer wall temperature. It means that the out wall temperature increased about 1% induced by flue 11 / 24
gas is more 12.8 times than steam. So according to measuring temperature of the outlet section wall to judge the tube wall temperature in the boiler is feasible without consideration of oxide scales and steam mass flow. Actually, the steam in each single tube when heated by the flue gas from the inlet to the outlet section is not uniform due to the uneven gas temperature profile. To compare the effect of the gas temperature and the heat transfer coefficient, the calculation of the wall temperature distributions along the steam flow path under the mean gas temperature and the simulated gas (see Fig. 4) are shown in Fig. 8. It can be seen clearly from this figure that the wall temperature difference are larger in the inlet and the outlet of the tube. The maximum wall temperature difference in the inlet of tube is
. And there is almost no
temperature difference in the tube elbow as can be seen from the Fig. 9. According to the results of the tube wall temperature under the simulated gas condition and even gas condition, we can used to guide the operation and adjust working load of the boiler. 4.4 Effects of Steam Mass flow on the tube wall temperature For the calculation, the following data is adopted:
,
and
; the steam temperature is adopted in accordance with the serpentine 1; the average steam mass flow rate through the single tube is
. Due to the tee joint
distributions of the headers affect the steam mass flow rate deviation as mentioned in [6], we adopted two types flow rate deviation to analysis, and
(dropped by 20%)
(dropped by 50%). The influence of different steam flow rate on the
wall temperature of the tube is shown in the Fig. 10 under the normal load. It can be seen from the picture, the wall temperature increases with the decrease of the 12 / 24
steam mass flow rate. When the flow deviation reaches from 20% to 50%, the maximum wall temperature difference is increased by about 3.6 times. Because of the convection coefficient for the steam in the tube is decided by the steam mass flow rate. The higher mass flow rate will increase the convection coefficient and decrease the heat flux from the tube metal to the steam. Therefore, The lower steam mass flow rate maybe lead to the overheating of material. In general, the steam flow deviation maybe caused by the oxide scales 5 Conclusion This paper presents a numerical modeling of the superheaters that can be used for detailed descriptions of a heat transfer process in power plant. The model allow to use in the on-line thermal monitoring and simulation of the tube wall and applied to provide overheating alarm. The model employs the finite volume method to discretize the system of two-dimension heat conduction governing equation. The model include the variable thermo-physical properties (i.e. density, specific heat capacity, dynamic viscosity, heat conductivity, heat transfer coefficient) of flue gas and steam, the working load, measuring data’s, geometries of the superheaters and related parameters.
The model is a good tool to extend the temperature distribution of the whole serpentines and use to help for the future design of the wall temperature distribution in the presence of the oxide scale. Acknowledgement This paper was supported by the National Natural Science Foundation of China (51134016, 51471069 and 51201064), Natural Science Foundation of Beijing (2152029) and 13 / 24
the Fundamental Research Funds for the Central Universities. Appendix 1） For the one control volume (
,
2）
)
Near the gas-side (
While
When
, for the quarter of one control volume
14 / 24
)
When
, for the quarter of one control volume
3） Near the steam-side ( While
When
)
, for
, for the quarter of one control volume
15 / 24
When
, for the quarter of one control volume
4） In the inlet side, for the half of one control volume (
5） In the outlet side, for the half of one control volume (
16 / 24
)
)
References
[1] French DN, Metallurgical failures in fossil fired boilers, 2nd Ed. New York, USA: John Wiley & Sons, (1993). [2] Z. Y. Zhao, H. Xu, A study on the residual life of high-temperature boiler tube for inner wall oxidation thickness, International Conference on Electrical and Control Engineering, 285-287(2010). [3] N. W.,Kuznetsov, W.W. Mitor, I.E. Dubovski, E. S. Karasina, Thermal calculations of steam boilers (standard method), Moscow, Russia: Energia(1973). [4] M. H. Wang, The calculation of thermal deviation for plate superheater, Power Engineering, 2 (1986):7-14. [5] Z.H. Chen. The calculation and analysis of the flow distribution and the thermal variation of the single-phase fluid flowing through the manifold systems in boilers, Journal of University of Shanghai for Science and Technology, 19(1997): 160-178. [6] L. J. Xu, J. A. Khan, Z.H. Chen, Thermal load deviation model for superheater and reheater of a utility boiler, Applied Thermal Engineering, 20(2000): 545-558. [7] D. Yang, T. k. Chen, H. X. Li, L. Z. Liu, X. L, Ji, Nonlinear mathematical model for flow rate distribution in the parallel tubes of boiler superheater/reheater and the calculation method of tube surface temperature, Proceeding of CSEE, 21(2001)38-42 [8] M.M. Prieto, F.J. Fernandez, I. Suarez, H. Sa′nchez, Experimental thermal behavior of a power plant reheater, Energy, 31(2006)665-676.
17 / 24
[9] M.M. Prieto, I Suarez, F.J. Fernandez, H. Sa′nchez, M. Mateos, Application of a thermal model to a power plant reheater with irregular tube temperatures, Applied Thermal Engineering, 27(2007)185-193. [10] M.M. Prieto, I. Suarez, F.J. Fernandez, H. Sa′nchez, M. Mateos, Theoretical development of a thermal model for the reheater of a power plant boiler, Applied Thermal Engineering, 27(2007)619-626. [11] C.G. Yin, S. Caillat, J. L. Harion, B. Baudoin, E. Perez, Investigation of the flow, combustion, heat-transfer and emission from a 609MW utility tangentially fired pulverized-coal boiler, Fuel, 81(2002)997-1006. [12]C.G. Yin, L. Rosendahl, T. J. Condra, Further study of the gas temperature deviation in large-scale tangentially coal-fired boilers, Fuel, 82(2003)1127-1137 [13] H. Y. Park , S. H. Baek , Y. J. Kim , T. H. Kim , D. S. Kang , D. W. Kim, Numerical and experimental investigations on the gas temperature deviation in a large scale, advanced low NOx, tangentially fired pulverized coal boiler, Fuel, 104(2013)641-646. [14] A.M. Ghasemi, A. Saeedi, M. Moghiman, Application of Multi-Objective Optimization for Pollutants Emission Control in an Oil-Fired Furnace, Journal of the Chinese Society of Mechanical Engineers, 32(2011):303-312. [15] M. Javadi , A. Golshani , A. M. Ghasemi et al, Improving Power Plant Efficiency using Water Droplet Injection in Air Condensers, In World Academy of Science, Engineering and Technology, (2010) [ 16 ] J. Taler, A method of determining local heat flux in boiler furnaces, Heat Mass Transfer, 35(1992)1625-1634. [17] M. Trojan, D. Taler, Thermal simulation of superheaters taking into account the processes occurring on the side of the steam and flue gas, Fuel, 150(2015)75-87.
18 / 24
[18] Patankar, Numerical heat transfer and fluid flow, New York, USA: McGRAW-HILL Book Company, (1980). [19] F.P. Incropera, D.P. DeWitt, Introduction to Heat Transfer, third ed., John Wiley, (1996). [20] J. L. Huang, K.Y. Zhou, J.Q. Xu, C. X. Bian, On the failure of steam-side oxide scales in high temperature components of boilers during unsteady thermal processes, Journal of Loss Prevention in the Process Industries, 26(2013)22-31. [21] Z.H. Lin, Thermohydraulic design of fossil-fuel-fire boiler components, in: S. Kakac (Ed.), Evaporators and Condensers, John Wiley & Sons, Inc, Canada, (1991). [22] Q. T. Zhou, K. Y. Zhou, W. Leng, Fundamentals of boilers in thermal power plants, Beijing, China: Electric Power Press, (2009). [23] A. Ghasemi, M. Moghiman, S. M. Javadi, N. Hosseini, Effects of droplet size and air preheating on soot formation in turbulent combustion of liquid fuel, Proceedings of the ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Turkey, (2010) [24] M. M. Gholizadeh, R. Nikbakhti, A Ghasemi, Numerical study of double diffusive buoyancy forces induced natural convection in a trapezoidal enclosure partially heated from the right sidewall, Alexandria Engineering Journal, 55(2016):779-795. [25] R. K. Mobley, Plant engineer’s handbook, Woburn, USA: Butterworth-Heinemann Press, 23/392 Industrial Boilers, (2001). [26] J. Purbolaksono, A. Khinani, A.Z. Rashid, A.A. Ali, J. Ahmad, N.F. Nordin, A new method for estimating heat flux in superheater and reheater tubes, Nuclear Engineering and Design, (239)2009:1879-1884.
19 / 24
[27] J.Purbolaksono, A. Khinani, A.Z. Rashid, A.A. Ali, N.F. Nordin, Prediction of oxide scale growth in superheater and reheater tubes, Corrosion Science, 51(2009):1022-1029.
Table and figure captions Table 1 Geometries of the secondary superheater Table 2 Thermo-physical properties of the tube wall metal and the oxide scale Table 3 Measurements steam temperatures in the inlet and outlet sections of serpentine 1, 7 and 16 Table 4 Thermo-physical properties of steam and heat transfer coefficient Table 5 Thermo-physical properties of the flue gas and the convection heat transfer coefficient
Figures Fig. 1. Utility boiler diagram Fig. 2. The discretization model of the single tube: (a) m uniform layers along the z axis; (b) n uniform layers along the r axis;
- one control volume;
- half of one control volume;
- the interface of two adjacent control volume;
-quarter of one control volume;
-the interface of the oxide scales and metal; ND (1,
1),…, ND (i, j) - the core of the control volume at the node Fig. 3. Arrangement and geometry of secondary superheater tubes Fig. 4. The distributions of simulated and even gas temperatures along the single tube. Fig. 5. The tube wall temperature distribution along the single tube with three kinds of oxide scale Fig. 6. The tube wall temperature distribution in three Serpentines: (a) inner wall temperature; (b) outer wall temperature Fig. 7. The tube wall temperature distribution in the three gas temperature conditions: (a) (b)
20 / 24
;
Fig. 8. The wall temperature distribution along the steam flow path with the mean gas temperature and the simulated gas temperature Fig. 9. The heat transfer coefficient distribution in the gas side along the steam flow path with the mean gas temperature and the simulated gas temperature Fig. 10. The wall temperature distribution with the different steam flow rate
Nomenclature
coefficient changed with the kinds of fuel a, b
coefficients of the node temperature specific heat, correction factors for the arrangement of a number of tube rows correction factors for the effect of a number of tube rows original inner diameter of tube, m outer diameter, m steam-side convection heat transfer coefficient, gas-side heat transfer coefficient, convection heat transfer coefficient, radiation heat transfer coefficient, 21 / 24
k
median line of the control volume tube length, m cell length, m ,
m
depth of the gas space before the tube row and the calculated tube bundle, m node numbers of the z axis mass flow rate, numbers of tube wide
n
node numbers of the r axis Prandtl number
r
coordinate r Reynolds number transversal pitch, m longitudinal pitch, m temperature of the metal substrate or oxide scale, o C ,
steam temperatures at the inlet and outlet of secondary superheater， o C kinematic viscosity， gas velocity， m/s
z
coordinate z radiation heat transfer coefficient of the combustion products duration，s density,
22 / 24
thermal conductivity cell thickness, m dynamic viscosity， coefficient of the non-uniform sleeping of the boiler components by gases relative transversal pitch, m relative longitudinal pitch, m
Subscripts g
gas-side
in
inlet of the tube
met
metal substrate of tube
ox
oxide scale
out
the outlet of the tube
s
steam-side
x
denote ox or met
0
initial
Upper 0
last moment
‘
inlet section
“
outlet cetion
23 / 24
24 / 24
Fig. 1. Utility boiler diagram
Fig. 2. The discretization model of the single tube: (a) m uniform layers along the z axis; (b) n uniform layers along the r axis; control volume;
- one control volume;
- half of one control volume;
- the interface of two adjacent control volume;
-quarter of one
-the interface of the oxide
scales and metal; ND (1, 1),…, ND (i, j) - the core of the control volume at the node.
Fig. 3. Arrangement and geometry of secondary superheater tubes
1000
o
Temperature, C
900
800
700 The simulated gas temperature of Serpentine 33 The even gas temperature of whole secondary supheater
600 0
20
40
60
80
100
Node Number
Fig. 4. The distributions of simulated and even gas temperatures along the single tube.
580 560
Wall Temperature,
℃
540 520 500 inner wall with 0mm oxide scale outer wall with 0mm oxide scale inner wall with 0.2mm oxide scale outer wall with 0.2mm oxide scale inner wall with 0.5mm oxide scale outer wall with 0.5mm oxide scale
480 460 0
20
40
60
80
100
Node Number
Fig. 5. The tube wall temperature distribution along the single tube with different thickness oxide scale
(a)
580
Wall Temperature,
℃
560
℃
560 Wall Temperature,
(b)
580
540
520
500
Serptine 1 , inner wall Serptine 14 , inner wall Serptine 32 , inner wall
480 0
20
40
60
80
100
540
520
500
Serptine 1 , outer wall Serptine 14 , outer wall Serptine 32 , outer wall
480 0
Node Number
20
40
60
80
100
Node Number
Fig. 6. The tube wall temperature distribution in three Serpentines: (a) inner wall temperature; (b) outer wall temperature
(a)
(b)
520
o
inner wall, Tg'=855 C o outer wall, Tg'=855 C o inner wall, Tg'=924 C o outer wall, Tg'=924 C o inner wall, Tg'=924 C o outer wall, Tg'=986 C
500
480
Wall Temperature,
Wall Temperature,
℃
540
℃
540
520
o
inner wall, Tg'=855 C o outer wall, Tg'=855 C o inner wall, Tg'=855 C o outer wall, Tg'=855 C o inner wall, Tg'=855 C o outer wall, Tg'=855 C
500
480 0
20
40
60
80
100
Node Number
0
20
40
60
80
Node Number
Fig. 7. The tube wall temperature distribution in the three gas temperature conditions: (a) ; (b)
100
540
Wall Temperature,
℃
520
500
480
the inner wall temperature in uneven gas temperature the outer wall temperature in uneven gas temperature the inner wall temperature in mean gas temperature the outer wall temperature in mean gas temperature
460 0
20
40
60
80
100
Node Number
Fig. 8. The wall temperature distribution along the steam flow path with the mean gas temperature and the simulated gas temperature
140
Wall Temperature,
℃
120
100
80
hg in the uneven gas temperature profile with clear surface hg in the uneven gas temperature profile with ash deposit hg in the mean gas temperature profile with clear surface hg in the mean gas temperature profile with ash deposit
60 0
20
40
60
80
100
Node Number
Fig. 9. The heat transfer coefficient distribution in the gas side along the steam flow path with the mean gas temperature and the simulated gas temperature
Wall Temperature,
℃
540
520
500
the inner wall temperature with ms=0.74kg/s the outer wall temperature with ms=0.74kg/s the inner wall temperature with ms=0.59kg/s
480
the outer wall temperature with ms=0.59kg/s the inner wall temperature with ms=0.37kg/s the outer wall temperature with ms=0.37kg/s
460 0
20
40
60
80
100
Node Number
Fig. 10. The wall temperature distribution with the different steam flow rate
Table 1 Geometries of the secondary superheater (m)
(m)
(m)
(m)
0.051
0.039
0.006
24.000
(m) 0.300
, (m) 0.070
(m) 0.75
(m) 1.33
33
Table 2 Thermo-physical properties of the tube wall metal and the oxide scale Material
,
,
,
T91
7760
622
33
Oxide scale[18]
5010
833
0.851
Table 3 Measurements steam temperatures in the inlet and outlet sections of serpentine 1, 7 and 16 Inlet section, Date
31/3/ 2013
Time
20:00
Outlet section,
Serpentine Point 1
Point 2
Mean
Point 1
Point 2
Point 3
Mean
1
466.8
469.6
468.2
509.9
509.5
508.0
509.1
7
498.1
496.3
497.2
556.1
558.5
556.4
557.0
16
485.6
483.4
484.5
508.2
512.1
511.0
510.4
Table 4 Thermo-physical properties of steam and heat transfer coefficient （MPa）
（℃）
（
）
（℃）
（
）
17.28
468.2
2867.71
924
45.20
17.28
473.1
2858.20
924
45.48
17.28
478.0
2833.07
924
45.76
17.28
482.9
2808.18
916
46.04
17.28
487.8
2798.46
916
46.37
17.28
489.0
2798.46
909
45.98
17.28
494.7
2771.30
909
45.52
17.28
499.6
2756.86
909
45.80
17.28
504.5
2741.54
909
46.09
17.28
509.1
2738.02
909
46.31
Table 5 Thermo-physical properties of the flue gas and the convection heat transfer coefficient （℃）
（
）
（
）
（
）
（
）
800
1.222
42.83
69.93
63.57
900
1.242
45.24
74.68
61.93
1000
1.259
47.55
79.11
60.33
1100
1.275
49.75
83.23
58.81
Highlights
A single tube model is proposed to evaluate the wall temperature profiles
Effect of excessive higher gas temperature and steam temperature
Oxide scales on the inner tube can cause the overheating of the tube wall
Higher mass flow rate will decrease the heat flux from the tube metal to the steam