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Heat flux determination based on the waterwall and gas–solid flow in a supercritical CFB boiler
Applied Thermal Engineering 99 (2016) 703–712
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Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g
Research Paper
Heat flux determination based on the waterwall and gas–solid flow in a supercritical CFB boiler Linjie Xu, Leming Cheng *, Yi Cai, Yuanquan Liu, Qinhui Wang, Zhongyang Luo, Mingjiang Ni State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou, Zhejiang 310027, China
H I G H L I G H T S
• • •
An HFW method was developed to predict the heat flux for a supercritical CFB boiler. The 3D distributions of fluid temperature and heat flux in a 1000 MW CFB furnace were presented. The effect of operating parameters on fluid temperature profile was studied.
A R T I C L E
I N F O
Article history: Received 13 October 2015 Accepted 18 January 2016 Available online 2 February 2016 Keywords: Supercritical CFB boiler Coupling thermal-hydraulic calculation Heat flux Working fluid temperature
A B S T R A C T
A heat flux determination method of combined thermal-hydraulics inside the waterwall tubes and thermal process on the furnace gas–solid side (HFW) is presented in this study, for the purpose of a detailed understanding of heat transfer characteristics on heating surface. The method consists of three main steps: 1. gas–solid hydrodynamic simulation by means of the Eulerian–Eulerian model; 2. bed-towall heat transfer coefficient calculation based on cluster renewal model; and 3. coupling thermalhydraulic calculation at supercritical condition. Due to the effect of metal temperature on bed to wall heat transfer coefficient, it will be computed iteratively in latter two steps. By this method, the threedimensional distributions of fluid temperature and heat flux in a 1000 MW supercritical circulating fluidized bed (CFB) boiler were presented. Results showed that fluid temperature increased with the increase of the furnace height, and the heat flux distributed uniformly along the width of furnace. In addition, the effect of operating parameters on fluid temperature profile was also studied. It turned out that fluid mass flux, inlet temperature and furnace temperature had a significant impact on temperature distribution along the tubes. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The supercritical CFB boiler has been developed rapidly in recent years due to the efficiency of its supercritical steam cycles and advantages as a CFB boiler, including fuel flexibility, high combustion efficiency and low emissions. On September 18, 2015, the world’s first 350 MWe supercritical CFB boiler has been passed its 168 hours operation smoothly with full load in Guojin Power Generation Plant at Shanxi Province, China. A principal concern in the design and operation of a supercritical CFB boiler is the heat transfer process occurring in the waterwall. When a boiler operates below supercritical parameters, the working fluid temperature is nearly constant since water is saturated boiling. In this case, the heat transfer process on the furnace
* Corresponding author. Tel.: +86 571 8795 2802; fax: +86 571 8795 1616. E-mail address: [email protected] (L. Cheng). http://dx.doi.org/10.1016/j.applthermaleng.2016.01.109 1359-4311/© 2016 Elsevier Ltd. All rights reserved.
side and the working fluid inside the tubes can usually be determined individually. Previous research results showed that bed-towall heat transfer coefficient (HTC) depends strongly on gas–solid suspension density and furnace temperature [1–3]. While the saturated flow boiling heat transfer coefficients inside tubes can be predicted from several well-known correlations summarized by Kandlikar [4]. However, heat transfer status inside tubes changes when a boiler operates at a supercritical condition. Thermo-physical properties of fluid including density and specific heat capacity are extremely sensitive to the temperature and pressure near the pseudo-critical point. Temperature of working fluid would increase with heat input along the furnace height. These will cause an uncertain increment in waterwall temperature, which would make a difference in the bedto-wall heat transfer coefficient. Thus the heat transfer on furnace side and inside tubes should be considered simultaneously. For this purpose, a thermal-hydraulic coupling analysis between the furnace and working fluid is required.
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
Value
Outer wall size/m Inner wall size/m Height/m Furnace temperature/°C Superficial gas velocity/m s−1 Secondary air ratio Bed inventory/m Inlet fluid temperature/°C Inlet fluid pressure/MPa Steam mass flux/kg m−2 s−1
33.6 × 19.9 22.1 × 8.4 51.9 900 4.5 0.5 1.8 330 27 800
Left Wall Rear Wall
The structure of the 1000 MW supercritical CFB boiler is shown in Fig. 1. The annular structure is the remarkable character of this boiler. This structure makes the depth of the furnace in a proper range for secondary air’s penetrating. Furthermore, bed inventory overturn easily occurring in the plant-leg structure boiler can be avoided. The waterwalll consists of inner and outer rings. The inner ring increase the evaporating heating surface area, and is more stable than the heating surface such as mid-partition and water-cooled panels because it is only one-sided heated and scoured by gas– solid flow. In this work, the boiler has 6 cyclones arranged at front left and right walls [9]. The outer side cross-section of the furnace is 33.6 m × 19.9 m and the inner is 22.1 m × 8.4 m. The boiler is 51.9 m high. Refractory is installed at the lower part of the furnace. Bed material has a diameter of 300 μm, particle density of 2340 kg/m3 and bulk density of 1440 kg/m3. Table 1 gives the main operation parameters in the computation. The hydraulic condition of the working fluid in tubes is determined according to water circulation loops. Only the outer ring waterwall was studied in this work. Fig. 2 shows the uniformly arranged loops in the outer ring waterwall that are simplified. There are 350 loops on the front wall and 600 loops on the right wall.
Name
Front Wall
2.1. Supercritical CFB boiler
Table 1 Basic operation parameters of the boiler.
1
2. Mathematical model
Fig. 1. The structure of 1000 MW supercritical CFB boiler.
2
A few research work considering thermal-hydraulic analysis has been carried in a supercritical CFB boilers. Yang and Gou [5] developed an integrated mathematical model of CFB boiler coupling steam and gas side. The method uses cell approach and ‘coreannular’ construction to simulate solid distribution in the bed, and computes HTC following the cluster renewal model. However, as CFB boilers scale up, the flow structure in the furnace will change due to the larger cross-section area and more suspended surfaces. The ‘core-annular’ flow model has limitation [6] and may not be suitable for gas–solid flow in large CFB boilers. Pan et al. [7] referred to the CE company’s heat flux curve for thermal-hydraulic analysis of a 600 MW supercritical CFB boiler. The assumed heat flux profile was still too simple to reflect the characteristics of heat flux distribution correctly in a certain boiler. Gas–solids flow is the cornerstone of heat flux on a heating surface. At present, the Eulerian–Eulerian approach is commonly used for the simulation of the fluid mechanics in large scale CFB boilers. Based on the 3D gas–solids hydrodynamics simulation results, Zhou et al. [8] obtained 3D HTC with the cluster renewal model in a large size CFB furnace. The heat flux distribution is more detailed, although only the furnace side is considered in his work. To improve the previous work, a thermal-hydraulics analysis method combined with the thermal process on the furnace side was presented in this paper. The method consists of three main steps: 1. gas–solids hydrodynamic simulation by means of the Eulerian– Eulerian model; 2. bed-to-wall heat transfer coefficient calculation based on cluster renewal model; and 3. coupling thermal-hydraulic calculation at supercritical condition. Based on the 3D gas–solids hydrodynamic simulation in furnace and thermal-hydraulics analysis inside waterwall, the heat flux determine method is defined as the HFW method, where ‘H’ represents heat flux, ‘F’ represents furnace, and ‘W’ represents waterwall. By this HWGS method, more fulfilled profiles of heat flux and fluid temperature were computed on the heating surface of a 1000 MW supercritical CFB boiler. The influence of mass flux, inlet parameters of working fluid and operation parameters on the thermal-hydraulic characteristics was also discussed.
350 349
704
Right Wall 351 352
949 950 Fig. 2. Platform of loops in water wall.
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
2.2. Gas–solid flow simulation Gas–solids suspension densities and velocities are the groundwork for furnace heat transfer coefficient calculation. The Eulerian– Eulerian model [10] with a drag coefficient based on the energy minimization multi scale (EMMS) model [11] was used to simulate the gas–solids flow on Fluent 6.3. The RNG k-epsilon model was applied to describe gas phase turbulence. The kinetic theory of granular flow was used to model the solid phase flow. The solid materials exiting from the outlets were returned via the solid return inlets by a user defined function (UDF). This process has been verified to produce better gas–solids flow field results than that without applying the EMMS model [8]. Fig. 3 displays the contour of solid volume fraction on waterwall surface. 2.3. Bed to wall HTC calculation Solids are known to accumulate near the wall, clustering, flowing, breaking and renewing along the wall in a CFB furnace. These solid clusters, together with and dilute gas–solids phase, would transfer heat from the furnace to the waterwall. Thus, the heat transfer coefficient is calculated based on cluster renewal model. The main formula is given as follows [12]:
htotal = hconv + hrad = f ⋅ (hc ,conv + hc ,rad ) + (1 − f ) ⋅ (hd ,conv + hd ,rad ) hc ,conv =
hd ,conv =
(1)
1 dp ⎛ tcπ ⎞ + nk g ⎜⎝ 4kc C c ρc ⎟⎠ k g C s ⎛ ρdis ⎞ d p c g ⎜⎝ ρs ⎟⎠
0.3
0.5
⎛ ut2 ⎞ ⎜⎝ gd ⎟⎠ p
(2)
0.21
Pr
(3)
705
hd ,conv =
σ 0 (t B4 − t w4 ) ⎛1 1 ⎞ − 1⎟ (t B − t w ) ⎜⎝ + ed ew ⎠
(4)
hc ,conv =
σ 0 (t B4 − t w4 ) ⎛1 1 ⎞ − 1⎟ (t B − t w ) ⎜⎝ + ec ew ⎠
(5)
In general, solid volume fraction, the velocity of gas and solid near the wall, and the temperature of wall and furnace are the major variables in cluster renewal model. Those gas–solid flow parameters were obtained from the 3D hydrodynamic simulation results. The temperature throughout the furnace is assumed to be homogeneous due to the limitation of gas–solid flow simulation. Wall temperature used in this step is first assumed to be a linear variation with the furnace height, then updated from the next thermalhydraulic calculation. The effect of fins between tubes on heat transfer was taken into account [13].
2.4. Thermal-hydraulic calculation At present, the vertical tube-platen technology has been successfully applied in the 350 MW and 600 MW supercritical CFB boilers in China [14,15]. The smooth tube is reportedly the main choice for the tube type in waterwall. Thus, all of the tubes used in this work are smooth tube with an outer diameter of 32 mm, pitch of 56 mm, and thickness of 7.5 mm. To simplify the calculation, pressure variations along the length of headers is neglected, and the mass flux is a constant. It means the statuses of loops in waterwall are independent. Each loop is divided into about 1000 units along the height. The outlet temperature of each unit is obtained on the basis of
Fig. 3. Contour of solid volume fraction on wall surface.
706
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conversation of energy. The outlet parameters of one unit would be used as the inlet parameters of the next one. The heat flux in each unit is calculated as follow:
q = k ⋅ (t B − t f )
Step 1
Operation parameters Furnace size
(6) Gas-solids flow simulation
where k is the overall HTC. It consists of the inside and outside heat transfer coefficient, and heat conduction through tube wall. The average thermodynamic parameters were adopted when the heat flux was calculated in a unit. The HTC of fluids at supercritical pressure is determined by equation (7) [16].
Nu = 0.015Re0.85 Pr m
(7)
Euler model EMMS model
Near wall parameters Vsolid, Vgas, solid
Step 2 Furnace temperature
Cluster-Renewal Model
where
m = 0.69 − (8100 qdht ) + fc q
(8)
qdht = 200 G1.2
(9)
⎧ 2.9 × 10−8 + 0.11 qdht ⎪ fc = ⎨−8.7 × 10−8 − 0.65 qdht ⎪−9.7 × 10−7 + 1.30 q dht ⎩
0 ≤ h ≤ 1500 kJ kg 1500 ≤ h ≤ 3300 kJ kg 3300 ≤ h ≤ 4000 kJ kg
Heat Flux Thermal-hydraulic analysis
Wall temperature
Step 3 NO
(10) YES
The total pressure gradient in each unit for one loop is a sum of friction pressure drop, gravitational pressure drop and acceleration pressure drop, obtained by equation (11):
Δp = Δpg + Δp f + Δpl
Bed to wall HTC
(11)
Heat flux distribution Temperature distribution
Fig. 4. Calculation scheme of the complete HFW method.
where
Δpg = ρ g Δl Δp f = λ
Δl G 2 2din ρ
Δpa = G 2 ( vout − vin )
(12)
(13)
(14)
After the calculations of 1000 units are completed, the thermalhydraulic calculation of one loop is finished. The outer temperature of tubes used in bed to wall HTC calculation is calculated by conventional correlations in reference [17]. The wall temperature obtained in this step should be equal to that used in the bed to wall HTC. If not, recalculations are done until the max relative deviation of the two wall temperatures is below the error 1%. The overall calculation scheme for a loop is given in Fig. 4. 3. Results and analysis Fig. 5 shows the computing result of fluid temperature contour on the waterwall surface. It increases along the furnace height and is horizontally uniform. Fig. 6 gives the heat flux distribution on the waterwall surface. The distribution and the heat flux magnitude agree with those obtained by Foster Wheeler (Fig. 7) [18]. The lower part of the furnace is featured by less heat flux in this study. This is mainly because the refractory installed here has much lower thermal conductivity than waterwall. 3.1. Temperature and heat flux distributions along the waterwall height Fig. 8 shows distribution profiles of fluid temperature, tube wall temperature, and heat flux along the furnace height. For illustration purposes, they are averaged along the furnace width.
In the upper furnace, the curves change with the furnace height. The variation rate of fluid temperature is dominated by both the heat flux and specific heat capacity. The fluid in regions near pseudocritical temperature (391.95 °C) has a large specific heat capacity, presenting small temperature gradient with respect to furnace height. For fluid in other regions, the temperature increases sharply with furnace height due to small heat specific capacity. While in the upper furnace, the fluid experiences small increase in temperature because of lower heat flux in the upper part. The simulated fluid temperature accords with that of Pan et al. [7]. In addition, the temperature difference between the fluid and outer tube wall ranges from 60 to 90 °C. Heat flux is in the range of 55–90 kw/m2 at the simulation condition. It decreases almost linearly as the furnace height increases. This is clearly because the temperature difference and HTC decreases along the furnace height. Few changes are seen in the working fluid temperatures and tube wall temperatures at the lower part of the furnace due to extremely low heat flux here. 3.2. Heat flux, outlet temperature and pressure drop distribution at horizontal direction Fig. 9 shows the distributions of outlet fluid temperatures and heat flux on front wall and right wall. These two quantities are closely associated with each other; larger heat flux leads to higher outlet fluid temperature. The outlet fluid temperatures vary from 438 to 455 °C among different loops. Heat flux values vary from 56 to 59 kW/m2. As a result of massive agglomerated particles, an increase in heat flux is observed near the corner zones (at loops 1, 350 and 950). Another peak in heat flux occurs in the middle of left wall. This agrees with the distribution of solid volume fraction in Fig. 3. On the right wall, the heat fluxes in the loop 740–890 are higher than those in the loop 410–680. This can be explained by the
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
Fig. 5. Contour of fluid temperature on wall surface (°C).
Fig. 6. Contour of heat flux on wall surface (kW/m2).
707
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
tout
Temperature (oC)
460
60
qf 58
450 56
440
54 Front wall
430
0
Heat flux (kw/m2)
708
Right wall
200
400
600
800
52 1000
Serial number of tubes Fig. 9. Water wall outlet temperature and heat flux distribution.
asymmetric arranged cyclones that results in significant flow nonuniformity in the riser outlets [19]. The asymmetric arrangement of exits may be the main reason for the uneven distribution of the heat flux in the right wall. Distribution of heat flux deviation coefficient on waterwall is important for understanding the heat flux change along the waterwall width. It may be 20–30% in a pulverized coal furnace [20]. But few data were published concerning CFB furnaces. Since the calculation is mainly based on the gas–solid flow, a more uniform distribution is acquired (Fig. 10). More accurate result shall be obtained if the distribution of furnace temperature along the furnace width is taken into account. Fig. 11 gives the percentage of the gravitational pressure drop, frictional pressure drop and acceleration pressure drop of the loop. The average pressure drop of loops in the waterwall is about 290 kPa ± 3 kPa. It can be seen that the gravitational and frictional pressure drops are the main contributors to pressure drop, while acceleration pressure drop is negligible.
Fig. 7. Foster Wheeler’s Heat flux distribution on furnace [17].
Temperature (oC) 320
60
400
440
480
520
qf
50
Furnace height (m)
360
tf tin
40
tw tf
30
Ref. [7] (Ref.[4])
20
10
0 0
20
40
60
80
100
2
Heat flux (kw/m ) Fig. 8. Average temperature and heat flux distribution on front wall.
3.3. Effect of inlet mass flux, fluid temperature and pressure Mass flux in tube is vital in the design of the heating surface. Due to the low heat flux and the homogeneous distribution of heat flux along the furnace width and depth, low and medium mass flux can be adopted in a supercritical CFB boiler [21]. Fig. 12 gives the average fluid temperature distribution on front wall at different mass fluxes. The fluid temperature falls as mass flux is enhanced. It can be noticed that the change of the working fluid temperature became less as the mass flux increases, and is similar to that of the outlet temperature. The fluid temperature difference between different mass fluxes changes with height, which is slight in the lower furnace and becomes larger in the upper furnace. When the fluid temperature is below pseudo-critical temperature, the higher temperature, the greater specific heat capacity. Thus it is a negative effect on temperature rising with the heat input. That results in a slight temperature difference in lower furnace. On the contrary, when the fluid temperature is above pseudo-critical temperature, the specific heat capacity decreases with temperature. Then it becomes a positive effect causing a larger temperature difference in upper furnace. In the vicinity of pseudo-critical point, the change of specific heat capacity becomes less pronounced with an increase in pressure [22]. Thus there is a higher outlet temperature for the higher pressure, as shown in Fig. 13.
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
709
Heat flux deviation coefficient
1.06 Front wall (Average value : 57.2 kw/m2) Right wall (Average value : 56.6 kw/m2) 1.04
1.02
1.00
0.98
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Dimensionless position Fig. 10. Distribution of heat flux deviation coefficient on water walls.
Pressure drop percentage (%)
75
Fig. 14 shows the influence of fluid inlet temperature on the average fluid temperature distribution on front wall. The temperature difference in outlet is almost the same with that in inlet. It is reduced near the pseudo-critical point as a result of high specific heat capacity.
60 45
3.4. Effect of superficial gas velocity, furnace temperature
30 15 0
Gravitational pressure drop
Frictional pressure drop
Acceleration pressure drop
50
50
40
40
Furnace height (m)
Furnace height (m)
Fig. 11. The percentage of three components of total pressure drop.
In general, operation parameters have strong impact on the gas– solid flow hydrodynamics in furnace. They will cause a change of heat transfer characteristic on heating surfaces. Fig. 15 presents the change of outlet temperature on walls with different superficial gas velocities. It is showed the outlet temperature does not change much as the superficial gas velocity changes, according to the little difference in the average heat flux on front wall (Fig. 16). It can be concluded that the superficial gas velocity has few impact on heat transfer to the waterwall within normal operation rang, while the furnace temperature is established.
30
20
G=700kg/m2s G=800kg/m2s G=900kg/m2s
10
0 300
330
360
390
420
450
30
20
P=26MPa P=27MPa P=28MPa
10
480
o
Fluid temperature ( C) Fig. 12. Average fluid temperature distribution on front wall at different mass flux.
0 300
330
360
390
420
450
480
o
Fluid temperature ( C) Fig. 13. Average fluid temperature distribution on front wall at different pressure.
710
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
90
Average Heat Flux (W/m2)
Furnace height (m)
50
40
30
20
tin=310oC tin=330oC
10
tin=350oC
60
0 0 300
330
360
390
420
450
U=4.5m/s U=4.8m/s U=5.0m/s
30
0
10
480
20
30
40
50
Furnace height (m)
o
Fluid temperature ( C)
Fig. 16. Average heat flux distribution on front wall under different superficial gas velocity.
Fig. 14. Average fluid temperature distribution on front wall at different inlet temperature.
Radiation plays an important role in heat transfer on heating surface. Thus the higher the furnace temperature is, the higher the heat flux is, as shown in Fig. 17. Fig. 18 gives the outlet temperature of waterwall at different furnace temperatures. The curves show similar trends but differs in value. Because heat flux differences among tubes are mainly determined by suspended density when the furnace temperature is fixed. While furnace temperature has a little effect on the distribution of solid volume fraction. The fluid temperature changing with furnace temperature is shown in Fig. 19. The energy conservation equation for each loop can be written as following:
⎛L ⎞ Δh = ⎜ ∫ ηqπ dw 2 ⋅ dl⎟ ⎝0 ⎠
(G ⋅ π din2 4) = 2ηdw L
din 2 ⋅ q G
(15)
When the structure of tubes is given, equation (16) can be derived.
d ( Δh) Δh = dq q − dG G
That is to say, the relative change in average heat flux is equivalent to that in mass flux. It is for this reason that the correlation of the curves in Fig. 19 is similar to that in Fig. 12. 4. Conclusions A HFW method was develop to predict the heat flux for a supercritical CFB boiler. Based on gas–solids flow distributions in large size CFB furnace computed by numerical simulation, heat transfer coefficient obtained by cluster renew model and thermal-hydraulic coupling analysis, heat flux is determined in a supercritical CFB boiler. This method was successfully applied to predict the heat flux of furnace to waterwall of a 1000 MW supercritical CFB boiler. As the example computation of the 1000 MW supercritical CFB boiler, heat flux on waterwall had a range of 55–90 kW/m2, and
Average Heat Flux (W/m2)
Outlet temperature (oC)
460
U=4.5m/s U=4.8m/s U=5.0m/s
455
450
445
440
435
0
200
400
600
800
1000
Serial number of tubes Fig. 15. Water wall outlet temperature distribution under different superficial gas velocity.
(16)
90
60
tb=880oC tb=900oC
30
tb=950oC 0
0
10
20
30
40
50
Furnace height (m) Fig. 17. Average heat flux distribution on front wall under different furnace temperature.
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
Acknowledgements
520
Outlet temperature (oC)
tb=880oC
This study was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDA07030100.
tb=900oC
500
tb=950oC 480
Nomenclature
460
440
420
0
200
400
600
800
1000
Serial number of tubes Fig. 18. Waterwall outlet temperature distribution at different furnace temperature.
distributes uniformly along the furnace depth except for tapered furnace. The outlet temperature was different in different loops and it is in the range of 438–455 °C. Effects of some operation parameters on heat transfer characteristics on waterwall were carried using the HFW method. Calculation results showed the mass flux and furnace temperature had significantly impacts on the fluid temperature profile, and the fluid temperature difference was slight in lower furnace and increases rapidly in the upper furnace. It is clear that a higher inlet fluid temperature would result in a higher outlet temperature. The inlet pressure increase brought a little rising in outlet temperature, due to a less pronounced change of specific heat capacity near pseudo-critical point. The superficial gas velocity made no difference to heat flux and temperature profiles under the simulation condition.
Furnace height (m)
50
40
30
20
tb=880oC tb=900oC
10
0 300
711
tb=950oC 330
360
390
420
450
480
o
Fluid temperature ( C) Fig. 19. Average fluid temperature distribution on front wall under different furnace temperature.
Symbols q Cc Cg Cs din dp dw ec ed ew f fc g G h hc,conv hc,rad hconv hd,conv hd,rad hrad k kc kg L m n Nu Pr q qdht qf Re tB tc tf tin tw ut vin vout Δh Δl Δp Δpa Δpf Δpg
Average heat flux for a loop [W/m2] Specific heat of cluster in the dilute section [J/(kg.K)] Specific heat of gas [J/(kg.K)] Specific heat of particle [J/(kg.K)] Inner diameter [m] Diameter of particle [m] Outer diameter [m] Cluster emissivity Dilute phase emissivity Wall emissivity Time average fraction of the wall covered by clusters Parameter Acceleration of gravity [m2/s] Mass flux [kg/(m2 s)] Specific enthalpy of bulk fluid [J/kg] Cluster convective heat transfer coefficient [W/(m2 K)] Cluster radiative heat transfer coefficient [W/(m2 K)] Convective heat transfer coefficient [W/(m2 K)] Dilute convective heat transfer coefficient [W/(m2 K)] Dilute radiative heat transfer coefficient [W/(m2 K)] Radiative heat transfer coefficient [W/(m2 K)] Overall HTC [W/(m2 K)] Thermal conductivity of cluster in the dilute section [W/(m.K)] Thermal conductivity of gas, gas film [W/(m.K)] Length of a loop [m] Parameter Non-dimensional gas layer thickness coefficient between wall and cluster Nusselt number Prandtl number Heat flux [W/m2] Deterioration heat flux [W/m2] Heat flux [W/m2] Reynolds number Furnace temperature [°C] Residence time of cluster with wall [s] Fluid temperature [°C] Inner tube wall temperature [°C] Outer tube wall temperature [°C] Terminal settling velocity [m/s] Inlet specific volume in a unit Outlet specific volume in a unit Specific enthalpy change of bulk fluid [J/kg] Length of each unit in a loop [m] Total pressure drop in a loop [MPa] Acceleration pressure drop [MPa] Frictional pressure drop [MPa] Gravitational pressure drop [MPa]
Greek symbols η Correction coefficient λ Friction coefficient ρ Average density in a unit Cluster density in the dilute section [kg/m3] ρc ρdis Density of dispersed phase [kg/m3] Density of gas [kg/m3] ρg
712
ρs σ0
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
Density of particle [kg/m3] Boltzmann constant
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[11] J. Li, M. Kwauk, Particle-Fluid Two-Phase Flow: The Energy-Minimization Multi-scale Method, Metallurgical Industry Press, Beijing, 1994. [12] L. Cheng, Z. Shi, Z. Luo, M. Ni, et al., A summary of the circulating fluidized bed heat transfer (mathematical model part), Power Eng. 18 (1) (1998) 24–33 (in Chinese). [13] J.K. Feng, Y.T. Shen, Theory and Calculation of Station Boiler, Science Press, Beijing, 1992. [14] H. Wang, X. Lu, Q. Wang, et al. The operating characteristic analysis of 600 MW supercritical CFB boiler. Chinese Society of Engineering Thermophysics – Combustion Branch. 2013. [15] H. Su, L. Nie, X. Yang, et al., The development and design of Dongfang 350 MW supercritical CFB boiler, Dongfang Boiler (1) (2010) 1–6. [16] K. Kitoh, S. Koshizuka, Y. Oka, Refinement of transient criteria and safety analysis for a high-temperature reactor cooled by supercritical water, Nucl. Technol. 135 (2001) 252–264. [17] Shanghai Power Equipment Packaged Design Research Institute, Shanghai. The National standard of the boiler hydrodynamics calculation (JB/Z201-83), 1983 (in Chinese). [18] I. Venäläinen, R. Psik, 460 MWe Supercritical CFB boiler design for Łagisza Power Plant, PowerGen Europe (2004) 25–27. [19] X. Zhou, L. Cheng, Q. Wang, et al., Non-uniform distribution of gas–solid flow through six parallel cyclones in a CFB system: an experimental study, Particuology 10 (2) (2012) 170–175. [20] V. Ganapathy, Industrial Boilers and Heat Recovery Steam Generators: Design, Applications, and Calculations, CRC Press, Boca Raton, 2002. [21] D. Yang, J. Pan, Q.C. Bi, et al. Research on the hydraulic characteristics of a 600 MW supercritical pressure CFB boiler. Proceedings of the 20th International Conference on Fluidized Bed Combustion. Springer Berlin Heidelberg, 2010: 180–185. [22] I. Pioro, S. Mokry Thermophysical properties at critical and supercritical conditions. Heat Transfer Theoretical Analysis, Experimental Investigations and Industrial Systems. InTech, Rijeka, 2011.
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Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g
Research Paper
Heat flux determination based on the waterwall and gas–solid flow in a supercritical CFB boiler Linjie Xu, Leming Cheng *, Yi Cai, Yuanquan Liu, Qinhui Wang, Zhongyang Luo, Mingjiang Ni State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou, Zhejiang 310027, China
H I G H L I G H T S
• • •
An HFW method was developed to predict the heat flux for a supercritical CFB boiler. The 3D distributions of fluid temperature and heat flux in a 1000 MW CFB furnace were presented. The effect of operating parameters on fluid temperature profile was studied.
A R T I C L E
I N F O
Article history: Received 13 October 2015 Accepted 18 January 2016 Available online 2 February 2016 Keywords: Supercritical CFB boiler Coupling thermal-hydraulic calculation Heat flux Working fluid temperature
A B S T R A C T
A heat flux determination method of combined thermal-hydraulics inside the waterwall tubes and thermal process on the furnace gas–solid side (HFW) is presented in this study, for the purpose of a detailed understanding of heat transfer characteristics on heating surface. The method consists of three main steps: 1. gas–solid hydrodynamic simulation by means of the Eulerian–Eulerian model; 2. bed-towall heat transfer coefficient calculation based on cluster renewal model; and 3. coupling thermalhydraulic calculation at supercritical condition. Due to the effect of metal temperature on bed to wall heat transfer coefficient, it will be computed iteratively in latter two steps. By this method, the threedimensional distributions of fluid temperature and heat flux in a 1000 MW supercritical circulating fluidized bed (CFB) boiler were presented. Results showed that fluid temperature increased with the increase of the furnace height, and the heat flux distributed uniformly along the width of furnace. In addition, the effect of operating parameters on fluid temperature profile was also studied. It turned out that fluid mass flux, inlet temperature and furnace temperature had a significant impact on temperature distribution along the tubes. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The supercritical CFB boiler has been developed rapidly in recent years due to the efficiency of its supercritical steam cycles and advantages as a CFB boiler, including fuel flexibility, high combustion efficiency and low emissions. On September 18, 2015, the world’s first 350 MWe supercritical CFB boiler has been passed its 168 hours operation smoothly with full load in Guojin Power Generation Plant at Shanxi Province, China. A principal concern in the design and operation of a supercritical CFB boiler is the heat transfer process occurring in the waterwall. When a boiler operates below supercritical parameters, the working fluid temperature is nearly constant since water is saturated boiling. In this case, the heat transfer process on the furnace
* Corresponding author. Tel.: +86 571 8795 2802; fax: +86 571 8795 1616. E-mail address: [email protected] (L. Cheng). http://dx.doi.org/10.1016/j.applthermaleng.2016.01.109 1359-4311/© 2016 Elsevier Ltd. All rights reserved.
side and the working fluid inside the tubes can usually be determined individually. Previous research results showed that bed-towall heat transfer coefficient (HTC) depends strongly on gas–solid suspension density and furnace temperature [1–3]. While the saturated flow boiling heat transfer coefficients inside tubes can be predicted from several well-known correlations summarized by Kandlikar [4]. However, heat transfer status inside tubes changes when a boiler operates at a supercritical condition. Thermo-physical properties of fluid including density and specific heat capacity are extremely sensitive to the temperature and pressure near the pseudo-critical point. Temperature of working fluid would increase with heat input along the furnace height. These will cause an uncertain increment in waterwall temperature, which would make a difference in the bedto-wall heat transfer coefficient. Thus the heat transfer on furnace side and inside tubes should be considered simultaneously. For this purpose, a thermal-hydraulic coupling analysis between the furnace and working fluid is required.
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
Value
Outer wall size/m Inner wall size/m Height/m Furnace temperature/°C Superficial gas velocity/m s−1 Secondary air ratio Bed inventory/m Inlet fluid temperature/°C Inlet fluid pressure/MPa Steam mass flux/kg m−2 s−1
33.6 × 19.9 22.1 × 8.4 51.9 900 4.5 0.5 1.8 330 27 800
Left Wall Rear Wall
The structure of the 1000 MW supercritical CFB boiler is shown in Fig. 1. The annular structure is the remarkable character of this boiler. This structure makes the depth of the furnace in a proper range for secondary air’s penetrating. Furthermore, bed inventory overturn easily occurring in the plant-leg structure boiler can be avoided. The waterwalll consists of inner and outer rings. The inner ring increase the evaporating heating surface area, and is more stable than the heating surface such as mid-partition and water-cooled panels because it is only one-sided heated and scoured by gas– solid flow. In this work, the boiler has 6 cyclones arranged at front left and right walls [9]. The outer side cross-section of the furnace is 33.6 m × 19.9 m and the inner is 22.1 m × 8.4 m. The boiler is 51.9 m high. Refractory is installed at the lower part of the furnace. Bed material has a diameter of 300 μm, particle density of 2340 kg/m3 and bulk density of 1440 kg/m3. Table 1 gives the main operation parameters in the computation. The hydraulic condition of the working fluid in tubes is determined according to water circulation loops. Only the outer ring waterwall was studied in this work. Fig. 2 shows the uniformly arranged loops in the outer ring waterwall that are simplified. There are 350 loops on the front wall and 600 loops on the right wall.
Name
Front Wall
2.1. Supercritical CFB boiler
Table 1 Basic operation parameters of the boiler.
1
2. Mathematical model
Fig. 1. The structure of 1000 MW supercritical CFB boiler.
2
A few research work considering thermal-hydraulic analysis has been carried in a supercritical CFB boilers. Yang and Gou [5] developed an integrated mathematical model of CFB boiler coupling steam and gas side. The method uses cell approach and ‘coreannular’ construction to simulate solid distribution in the bed, and computes HTC following the cluster renewal model. However, as CFB boilers scale up, the flow structure in the furnace will change due to the larger cross-section area and more suspended surfaces. The ‘core-annular’ flow model has limitation [6] and may not be suitable for gas–solid flow in large CFB boilers. Pan et al. [7] referred to the CE company’s heat flux curve for thermal-hydraulic analysis of a 600 MW supercritical CFB boiler. The assumed heat flux profile was still too simple to reflect the characteristics of heat flux distribution correctly in a certain boiler. Gas–solids flow is the cornerstone of heat flux on a heating surface. At present, the Eulerian–Eulerian approach is commonly used for the simulation of the fluid mechanics in large scale CFB boilers. Based on the 3D gas–solids hydrodynamics simulation results, Zhou et al. [8] obtained 3D HTC with the cluster renewal model in a large size CFB furnace. The heat flux distribution is more detailed, although only the furnace side is considered in his work. To improve the previous work, a thermal-hydraulics analysis method combined with the thermal process on the furnace side was presented in this paper. The method consists of three main steps: 1. gas–solids hydrodynamic simulation by means of the Eulerian– Eulerian model; 2. bed-to-wall heat transfer coefficient calculation based on cluster renewal model; and 3. coupling thermal-hydraulic calculation at supercritical condition. Based on the 3D gas–solids hydrodynamic simulation in furnace and thermal-hydraulics analysis inside waterwall, the heat flux determine method is defined as the HFW method, where ‘H’ represents heat flux, ‘F’ represents furnace, and ‘W’ represents waterwall. By this HWGS method, more fulfilled profiles of heat flux and fluid temperature were computed on the heating surface of a 1000 MW supercritical CFB boiler. The influence of mass flux, inlet parameters of working fluid and operation parameters on the thermal-hydraulic characteristics was also discussed.
350 349
704
Right Wall 351 352
949 950 Fig. 2. Platform of loops in water wall.
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
2.2. Gas–solid flow simulation Gas–solids suspension densities and velocities are the groundwork for furnace heat transfer coefficient calculation. The Eulerian– Eulerian model [10] with a drag coefficient based on the energy minimization multi scale (EMMS) model [11] was used to simulate the gas–solids flow on Fluent 6.3. The RNG k-epsilon model was applied to describe gas phase turbulence. The kinetic theory of granular flow was used to model the solid phase flow. The solid materials exiting from the outlets were returned via the solid return inlets by a user defined function (UDF). This process has been verified to produce better gas–solids flow field results than that without applying the EMMS model [8]. Fig. 3 displays the contour of solid volume fraction on waterwall surface. 2.3. Bed to wall HTC calculation Solids are known to accumulate near the wall, clustering, flowing, breaking and renewing along the wall in a CFB furnace. These solid clusters, together with and dilute gas–solids phase, would transfer heat from the furnace to the waterwall. Thus, the heat transfer coefficient is calculated based on cluster renewal model. The main formula is given as follows [12]:
htotal = hconv + hrad = f ⋅ (hc ,conv + hc ,rad ) + (1 − f ) ⋅ (hd ,conv + hd ,rad ) hc ,conv =
hd ,conv =
(1)
1 dp ⎛ tcπ ⎞ + nk g ⎜⎝ 4kc C c ρc ⎟⎠ k g C s ⎛ ρdis ⎞ d p c g ⎜⎝ ρs ⎟⎠
0.3
0.5
⎛ ut2 ⎞ ⎜⎝ gd ⎟⎠ p
(2)
0.21
Pr
(3)
705
hd ,conv =
σ 0 (t B4 − t w4 ) ⎛1 1 ⎞ − 1⎟ (t B − t w ) ⎜⎝ + ed ew ⎠
(4)
hc ,conv =
σ 0 (t B4 − t w4 ) ⎛1 1 ⎞ − 1⎟ (t B − t w ) ⎜⎝ + ec ew ⎠
(5)
In general, solid volume fraction, the velocity of gas and solid near the wall, and the temperature of wall and furnace are the major variables in cluster renewal model. Those gas–solid flow parameters were obtained from the 3D hydrodynamic simulation results. The temperature throughout the furnace is assumed to be homogeneous due to the limitation of gas–solid flow simulation. Wall temperature used in this step is first assumed to be a linear variation with the furnace height, then updated from the next thermalhydraulic calculation. The effect of fins between tubes on heat transfer was taken into account [13].
2.4. Thermal-hydraulic calculation At present, the vertical tube-platen technology has been successfully applied in the 350 MW and 600 MW supercritical CFB boilers in China [14,15]. The smooth tube is reportedly the main choice for the tube type in waterwall. Thus, all of the tubes used in this work are smooth tube with an outer diameter of 32 mm, pitch of 56 mm, and thickness of 7.5 mm. To simplify the calculation, pressure variations along the length of headers is neglected, and the mass flux is a constant. It means the statuses of loops in waterwall are independent. Each loop is divided into about 1000 units along the height. The outlet temperature of each unit is obtained on the basis of
Fig. 3. Contour of solid volume fraction on wall surface.
706
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conversation of energy. The outlet parameters of one unit would be used as the inlet parameters of the next one. The heat flux in each unit is calculated as follow:
q = k ⋅ (t B − t f )
Step 1
Operation parameters Furnace size
(6) Gas-solids flow simulation
where k is the overall HTC. It consists of the inside and outside heat transfer coefficient, and heat conduction through tube wall. The average thermodynamic parameters were adopted when the heat flux was calculated in a unit. The HTC of fluids at supercritical pressure is determined by equation (7) [16].
Nu = 0.015Re0.85 Pr m
(7)
Euler model EMMS model
Near wall parameters Vsolid, Vgas, solid
Step 2 Furnace temperature
Cluster-Renewal Model
where
m = 0.69 − (8100 qdht ) + fc q
(8)
qdht = 200 G1.2
(9)
⎧ 2.9 × 10−8 + 0.11 qdht ⎪ fc = ⎨−8.7 × 10−8 − 0.65 qdht ⎪−9.7 × 10−7 + 1.30 q dht ⎩
0 ≤ h ≤ 1500 kJ kg 1500 ≤ h ≤ 3300 kJ kg 3300 ≤ h ≤ 4000 kJ kg
Heat Flux Thermal-hydraulic analysis
Wall temperature
Step 3 NO
(10) YES
The total pressure gradient in each unit for one loop is a sum of friction pressure drop, gravitational pressure drop and acceleration pressure drop, obtained by equation (11):
Δp = Δpg + Δp f + Δpl
Bed to wall HTC
(11)
Heat flux distribution Temperature distribution
Fig. 4. Calculation scheme of the complete HFW method.
where
Δpg = ρ g Δl Δp f = λ
Δl G 2 2din ρ
Δpa = G 2 ( vout − vin )
(12)
(13)
(14)
After the calculations of 1000 units are completed, the thermalhydraulic calculation of one loop is finished. The outer temperature of tubes used in bed to wall HTC calculation is calculated by conventional correlations in reference [17]. The wall temperature obtained in this step should be equal to that used in the bed to wall HTC. If not, recalculations are done until the max relative deviation of the two wall temperatures is below the error 1%. The overall calculation scheme for a loop is given in Fig. 4. 3. Results and analysis Fig. 5 shows the computing result of fluid temperature contour on the waterwall surface. It increases along the furnace height and is horizontally uniform. Fig. 6 gives the heat flux distribution on the waterwall surface. The distribution and the heat flux magnitude agree with those obtained by Foster Wheeler (Fig. 7) [18]. The lower part of the furnace is featured by less heat flux in this study. This is mainly because the refractory installed here has much lower thermal conductivity than waterwall. 3.1. Temperature and heat flux distributions along the waterwall height Fig. 8 shows distribution profiles of fluid temperature, tube wall temperature, and heat flux along the furnace height. For illustration purposes, they are averaged along the furnace width.
In the upper furnace, the curves change with the furnace height. The variation rate of fluid temperature is dominated by both the heat flux and specific heat capacity. The fluid in regions near pseudocritical temperature (391.95 °C) has a large specific heat capacity, presenting small temperature gradient with respect to furnace height. For fluid in other regions, the temperature increases sharply with furnace height due to small heat specific capacity. While in the upper furnace, the fluid experiences small increase in temperature because of lower heat flux in the upper part. The simulated fluid temperature accords with that of Pan et al. [7]. In addition, the temperature difference between the fluid and outer tube wall ranges from 60 to 90 °C. Heat flux is in the range of 55–90 kw/m2 at the simulation condition. It decreases almost linearly as the furnace height increases. This is clearly because the temperature difference and HTC decreases along the furnace height. Few changes are seen in the working fluid temperatures and tube wall temperatures at the lower part of the furnace due to extremely low heat flux here. 3.2. Heat flux, outlet temperature and pressure drop distribution at horizontal direction Fig. 9 shows the distributions of outlet fluid temperatures and heat flux on front wall and right wall. These two quantities are closely associated with each other; larger heat flux leads to higher outlet fluid temperature. The outlet fluid temperatures vary from 438 to 455 °C among different loops. Heat flux values vary from 56 to 59 kW/m2. As a result of massive agglomerated particles, an increase in heat flux is observed near the corner zones (at loops 1, 350 and 950). Another peak in heat flux occurs in the middle of left wall. This agrees with the distribution of solid volume fraction in Fig. 3. On the right wall, the heat fluxes in the loop 740–890 are higher than those in the loop 410–680. This can be explained by the
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
Fig. 5. Contour of fluid temperature on wall surface (°C).
Fig. 6. Contour of heat flux on wall surface (kW/m2).
707
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tout
Temperature (oC)
460
60
qf 58
450 56
440
54 Front wall
430
0
Heat flux (kw/m2)
708
Right wall
200
400
600
800
52 1000
Serial number of tubes Fig. 9. Water wall outlet temperature and heat flux distribution.
asymmetric arranged cyclones that results in significant flow nonuniformity in the riser outlets [19]. The asymmetric arrangement of exits may be the main reason for the uneven distribution of the heat flux in the right wall. Distribution of heat flux deviation coefficient on waterwall is important for understanding the heat flux change along the waterwall width. It may be 20–30% in a pulverized coal furnace [20]. But few data were published concerning CFB furnaces. Since the calculation is mainly based on the gas–solid flow, a more uniform distribution is acquired (Fig. 10). More accurate result shall be obtained if the distribution of furnace temperature along the furnace width is taken into account. Fig. 11 gives the percentage of the gravitational pressure drop, frictional pressure drop and acceleration pressure drop of the loop. The average pressure drop of loops in the waterwall is about 290 kPa ± 3 kPa. It can be seen that the gravitational and frictional pressure drops are the main contributors to pressure drop, while acceleration pressure drop is negligible.
Fig. 7. Foster Wheeler’s Heat flux distribution on furnace [17].
Temperature (oC) 320
60
400
440
480
520
qf
50
Furnace height (m)
360
tf tin
40
tw tf
30
Ref. [7] (Ref.[4])
20
10
0 0
20
40
60
80
100
2
Heat flux (kw/m ) Fig. 8. Average temperature and heat flux distribution on front wall.
3.3. Effect of inlet mass flux, fluid temperature and pressure Mass flux in tube is vital in the design of the heating surface. Due to the low heat flux and the homogeneous distribution of heat flux along the furnace width and depth, low and medium mass flux can be adopted in a supercritical CFB boiler [21]. Fig. 12 gives the average fluid temperature distribution on front wall at different mass fluxes. The fluid temperature falls as mass flux is enhanced. It can be noticed that the change of the working fluid temperature became less as the mass flux increases, and is similar to that of the outlet temperature. The fluid temperature difference between different mass fluxes changes with height, which is slight in the lower furnace and becomes larger in the upper furnace. When the fluid temperature is below pseudo-critical temperature, the higher temperature, the greater specific heat capacity. Thus it is a negative effect on temperature rising with the heat input. That results in a slight temperature difference in lower furnace. On the contrary, when the fluid temperature is above pseudo-critical temperature, the specific heat capacity decreases with temperature. Then it becomes a positive effect causing a larger temperature difference in upper furnace. In the vicinity of pseudo-critical point, the change of specific heat capacity becomes less pronounced with an increase in pressure [22]. Thus there is a higher outlet temperature for the higher pressure, as shown in Fig. 13.
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
709
Heat flux deviation coefficient
1.06 Front wall (Average value : 57.2 kw/m2) Right wall (Average value : 56.6 kw/m2) 1.04
1.02
1.00
0.98
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Dimensionless position Fig. 10. Distribution of heat flux deviation coefficient on water walls.
Pressure drop percentage (%)
75
Fig. 14 shows the influence of fluid inlet temperature on the average fluid temperature distribution on front wall. The temperature difference in outlet is almost the same with that in inlet. It is reduced near the pseudo-critical point as a result of high specific heat capacity.
60 45
3.4. Effect of superficial gas velocity, furnace temperature
30 15 0
Gravitational pressure drop
Frictional pressure drop
Acceleration pressure drop
50
50
40
40
Furnace height (m)
Furnace height (m)
Fig. 11. The percentage of three components of total pressure drop.
In general, operation parameters have strong impact on the gas– solid flow hydrodynamics in furnace. They will cause a change of heat transfer characteristic on heating surfaces. Fig. 15 presents the change of outlet temperature on walls with different superficial gas velocities. It is showed the outlet temperature does not change much as the superficial gas velocity changes, according to the little difference in the average heat flux on front wall (Fig. 16). It can be concluded that the superficial gas velocity has few impact on heat transfer to the waterwall within normal operation rang, while the furnace temperature is established.
30
20
G=700kg/m2s G=800kg/m2s G=900kg/m2s
10
0 300
330
360
390
420
450
30
20
P=26MPa P=27MPa P=28MPa
10
480
o
Fluid temperature ( C) Fig. 12. Average fluid temperature distribution on front wall at different mass flux.
0 300
330
360
390
420
450
480
o
Fluid temperature ( C) Fig. 13. Average fluid temperature distribution on front wall at different pressure.
710
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
90
Average Heat Flux (W/m2)
Furnace height (m)
50
40
30
20
tin=310oC tin=330oC
10
tin=350oC
60
0 0 300
330
360
390
420
450
U=4.5m/s U=4.8m/s U=5.0m/s
30
0
10
480
20
30
40
50
Furnace height (m)
o
Fluid temperature ( C)
Fig. 16. Average heat flux distribution on front wall under different superficial gas velocity.
Fig. 14. Average fluid temperature distribution on front wall at different inlet temperature.
Radiation plays an important role in heat transfer on heating surface. Thus the higher the furnace temperature is, the higher the heat flux is, as shown in Fig. 17. Fig. 18 gives the outlet temperature of waterwall at different furnace temperatures. The curves show similar trends but differs in value. Because heat flux differences among tubes are mainly determined by suspended density when the furnace temperature is fixed. While furnace temperature has a little effect on the distribution of solid volume fraction. The fluid temperature changing with furnace temperature is shown in Fig. 19. The energy conservation equation for each loop can be written as following:
⎛L ⎞ Δh = ⎜ ∫ ηqπ dw 2 ⋅ dl⎟ ⎝0 ⎠
(G ⋅ π din2 4) = 2ηdw L
din 2 ⋅ q G
(15)
When the structure of tubes is given, equation (16) can be derived.
d ( Δh) Δh = dq q − dG G
That is to say, the relative change in average heat flux is equivalent to that in mass flux. It is for this reason that the correlation of the curves in Fig. 19 is similar to that in Fig. 12. 4. Conclusions A HFW method was develop to predict the heat flux for a supercritical CFB boiler. Based on gas–solids flow distributions in large size CFB furnace computed by numerical simulation, heat transfer coefficient obtained by cluster renew model and thermal-hydraulic coupling analysis, heat flux is determined in a supercritical CFB boiler. This method was successfully applied to predict the heat flux of furnace to waterwall of a 1000 MW supercritical CFB boiler. As the example computation of the 1000 MW supercritical CFB boiler, heat flux on waterwall had a range of 55–90 kW/m2, and
Average Heat Flux (W/m2)
Outlet temperature (oC)
460
U=4.5m/s U=4.8m/s U=5.0m/s
455
450
445
440
435
0
200
400
600
800
1000
Serial number of tubes Fig. 15. Water wall outlet temperature distribution under different superficial gas velocity.
(16)
90
60
tb=880oC tb=900oC
30
tb=950oC 0
0
10
20
30
40
50
Furnace height (m) Fig. 17. Average heat flux distribution on front wall under different furnace temperature.
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
Acknowledgements
520
Outlet temperature (oC)
tb=880oC
This study was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDA07030100.
tb=900oC
500
tb=950oC 480
Nomenclature
460
440
420
0
200
400
600
800
1000
Serial number of tubes Fig. 18. Waterwall outlet temperature distribution at different furnace temperature.
distributes uniformly along the furnace depth except for tapered furnace. The outlet temperature was different in different loops and it is in the range of 438–455 °C. Effects of some operation parameters on heat transfer characteristics on waterwall were carried using the HFW method. Calculation results showed the mass flux and furnace temperature had significantly impacts on the fluid temperature profile, and the fluid temperature difference was slight in lower furnace and increases rapidly in the upper furnace. It is clear that a higher inlet fluid temperature would result in a higher outlet temperature. The inlet pressure increase brought a little rising in outlet temperature, due to a less pronounced change of specific heat capacity near pseudo-critical point. The superficial gas velocity made no difference to heat flux and temperature profiles under the simulation condition.
Furnace height (m)
50
40
30
20
tb=880oC tb=900oC
10
0 300
711
tb=950oC 330
360
390
420
450
480
o
Fluid temperature ( C) Fig. 19. Average fluid temperature distribution on front wall under different furnace temperature.
Symbols q Cc Cg Cs din dp dw ec ed ew f fc g G h hc,conv hc,rad hconv hd,conv hd,rad hrad k kc kg L m n Nu Pr q qdht qf Re tB tc tf tin tw ut vin vout Δh Δl Δp Δpa Δpf Δpg
Average heat flux for a loop [W/m2] Specific heat of cluster in the dilute section [J/(kg.K)] Specific heat of gas [J/(kg.K)] Specific heat of particle [J/(kg.K)] Inner diameter [m] Diameter of particle [m] Outer diameter [m] Cluster emissivity Dilute phase emissivity Wall emissivity Time average fraction of the wall covered by clusters Parameter Acceleration of gravity [m2/s] Mass flux [kg/(m2 s)] Specific enthalpy of bulk fluid [J/kg] Cluster convective heat transfer coefficient [W/(m2 K)] Cluster radiative heat transfer coefficient [W/(m2 K)] Convective heat transfer coefficient [W/(m2 K)] Dilute convective heat transfer coefficient [W/(m2 K)] Dilute radiative heat transfer coefficient [W/(m2 K)] Radiative heat transfer coefficient [W/(m2 K)] Overall HTC [W/(m2 K)] Thermal conductivity of cluster in the dilute section [W/(m.K)] Thermal conductivity of gas, gas film [W/(m.K)] Length of a loop [m] Parameter Non-dimensional gas layer thickness coefficient between wall and cluster Nusselt number Prandtl number Heat flux [W/m2] Deterioration heat flux [W/m2] Heat flux [W/m2] Reynolds number Furnace temperature [°C] Residence time of cluster with wall [s] Fluid temperature [°C] Inner tube wall temperature [°C] Outer tube wall temperature [°C] Terminal settling velocity [m/s] Inlet specific volume in a unit Outlet specific volume in a unit Specific enthalpy change of bulk fluid [J/kg] Length of each unit in a loop [m] Total pressure drop in a loop [MPa] Acceleration pressure drop [MPa] Frictional pressure drop [MPa] Gravitational pressure drop [MPa]
Greek symbols η Correction coefficient λ Friction coefficient ρ Average density in a unit Cluster density in the dilute section [kg/m3] ρc ρdis Density of dispersed phase [kg/m3] Density of gas [kg/m3] ρg
712
ρs σ0
L. Xu et al./Applied Thermal Engineering 99 (2016) 703–712
Density of particle [kg/m3] Boltzmann constant
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