Experimental investigation on heat transfer and ...

Experimental Thermal and Fluid Science 35 (2011) 291–300

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Experimental investigation on heat transfer and frictional characteristics of vertical upward rifled tube in supercritical CFB boiler Dong Yang a,⇑, Jie Pan a, Chenn Q. Zhou b, Xiaojing Zhu a, Qincheng Bi a, Tingkuan Chen a a b

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China Department of Mechanical Engineering, Purdue University Calumet, Hammond, IN 46323, USA

a r t i c l e

i n f o

Article history: Received 9 February 2010 Received in revised form 15 September 2010 Accepted 26 September 2010

Keywords: Supercritical CFB boiler Rifled tube Wall temperature Heat transfer Frictional resistance Empirical correlation

a b s t r a c t Water wall design is a key issue for supercritical Circulating Fluidized Bed (CFB) boiler. On account of the good heat transfer performance, rifled tube is applied in the water wall design of a 600 MW supercritical CFB boiler in China. In order to investigate the heat transfer and frictional characteristics of the rifled tube with vertical upward flow, an in-depth experiment was conducted in the range of pressure from 12 to 30 MPa, mass flux from 230 to 1200 kg/(m2 s), and inner wall heat flux from 130 to 720 kW/m2. The wall temperature distribution and pressure drop in the rifled tube were obtained in the experiment. The normal, enhanced and deteriorated heat transfer characteristics were also captured. In this paper, the effects of pressure, inner wall heat flux and mass flux on heat transfer characteristics are analyzed, the heat transfer mechanism and the frictional resistance performance are discussed, and the corresponding empirical correlations are presented. The experimental results show that the rifled tube can effectively prevent the occurrence of Departure from Nucleate Boiling (DNB) and keep the tube wall temperature in a permissible range under the operating condition of supercritical CFB boiler. Ó 2010 Elsevier Inc. All rights reserved.

1. Introduction In the 1980s, CFB combustion technology began to be developed in the world. On account of the good performances including good fuel flexibility, high combustion efficiency and efficient pollution control, CFB boiler is successfully commercialized for coal-fired power generation. As a clean coal technology with bright prospect, supercritical CFB boiler technology can further improve the boiler efficiency and reduce the pollution emission [1], so it becomes a very important development trend for coal-fired power plants in China [2]. At present, a 460 MWe supercritical CFB boiler at Lagisza power plant in Poland, which is the first supercritical CFB boiler and the largest CFB boiler in the world, has been put into operation at March, 2009 [3]. Foster Wheeler and Alstom Power all present different conceptual designs of supercritical CFB boiler with larger scale and higher parameter now. With the aim to meet the operating requirement of high efficiency, low pollution emission and variable load, high operating parameters, low mass flux and sliding pressure mode are often applied in the design of supercritical CFB boiler. Additionally, breeches-legs structure and additional evaporating heating surface may be adopted in supercritical CFB boiler. So the water wall structure and the boiler operating condition is very complex. Therefore, it is a key technology in the water wall design to ensure all water ⇑ Corresponding author. Tel.: +86 29 82668393; fax: +86 29 82669033. E-mail address: [email protected] (D. Yang). 0894-1777/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2010.09.011

wall tubes can be cooled effectively and to keep the tube wall temperature in a permissible range [4]. Due to the good heat transfer performance, rifled tube is often applied in boiler water wall to enhance turbulization and to prevent the burnout of tubes walls. Many scholars experimentally investigated the heat transfer characteristics of rifled tubes at subcritical pressure. Swenson et al. [5] studied the effects of nucleate boiling versus film boiling on heat transfer in power boiling tubes and the experimental results shows that nucleate boiling could be maintained to higher vapor qualities with rifled tube than with smooth tube. Watson et al. [6] found that the rotational flow in ribbed tube can greatly raise CHF and critical vapor quality. Nishikawa et al. [7] found that rifled tubes with different geometrical structures have different heat transfer enhancement performances. Iwabuchi et al. [8] detected that in near-critical pressure region the heat transfer enhanced by rotational flow in rifled tube disappeared and heat transfer deterioration even occurs in subcooling region. Kolher and Kastner [9] experimentally ascertained that rifled tube can effectively delay heat transfer deterioration and improve heat transfer in postdryout region. Due to the special thermophysical properties, great importance was attached to the heat transfer characteristics of supercritical water. Shitsman [10] studied the heat transfer deterioration near pseudo-critical point. Swenson et al. [11] detected that pressure and heat flux has important influence on the heat transfer of supercritical water. Virkrev et al. [12] discovered two kinds of heat transfer deterioration. One occurs in the inlet region at high heat

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Nomenclature cp C(x) din dout E f g G Gmax h hw DH I kw L Nu p pcr Pr Prg,w Prw

Dp Dpa Dpf Dpg Dplo Dptp q QE Re Reg

specific heat at constant pressure, J/(kg °C) fitting coefficient inner diameter, m outer diameter, m input voltage, V frictional coefficient acceleration of gravity, m/s2 mass flux, kg/(m2 s) maximum mass flux, kg/(m2 s) specific enthalpy of core fluid, J/kg specific enthalpy of tube wall surface fluid, J/kg added enthalpy, J/s input current, A thermal conductivity of test section, W/(m K) length of test section, m Nusselt number pressure, MPa critical pressure, MPa Prandtl number Prandtl number of gas phase while the qualitative temperature is inner tube wall temperature Prandtl number while the qualitative temperature is inner tube wall temperature pressure drop, MPa acceleration pressure drop, MPa frictional pressure drop, MPa gravitational pressure drop, MPa frictional pressure drop in single-phase zone, MPa frictional pressure drop in two-phase zone, MPa furnace heat flux, W/m2 input electric power, W Reynolds number Reynolds number of gas phase

flux and low mass flux while the bulk temperature is far lower than pseudo-critical temperature, the other appears near pseudocritical point, which was considered to result from the tremendous changes in thermophysical properties of supercritical water. Yamagata et al. [13] found the maximum heat transfer coefficient appears at the local section where the bulk temperature is lower than the pseudo-critical temperature slightly and wall temperature is higher than the pseudo-critical temperature. In his opinion, the ratio of heat flux and mass flux decides weather heat transfer deterioration appears. Goldman [14] found that the heat transfer deterioration occurs at high heat flux near pseudo-critical point. Ackerman [15] indicated that the critical heat flux rises with increasing pressure and mass flux and decreasing diameter. Gospodinov et al. [16] studied the normal, deteriorated and enhanced heat transfer characteristics of supercritical water in vertical upward smooth tube, and contrastively studied Dittus–Boelter and Bishop formulas. Jackson [17] summarized the previous research findings and present improved heat transfer coefficient formula. Cheng and Schulenberg [18] and Pioro et al. [19,20] respectively summarized the flow and heat transfer characteristics of supercritical water, and compared the heat transfer coefficient formulas. For abnormal heat transfer at supercritical pressure, Goldman [14] and Ackerman [15] present two-phase pseudo-boiling heat transfer theory. They considered that the heat transfer enhancement at supercritical pressure is similar to two-phase boiling at subcritical pressure, and the heat transfer mode change from pseudo-nucleate boiling to pseudo-film boiling can result in heat transfer deterioration. On the contrary, many scholars supported the single-phase forced convection heat transfer theory and believed the heat

Rew t tf tin tout twi two V

vf vw x xcr xe xi Xtt

Reynolds number while the qualitative temperature is inner tube wall temperature temperature, °C core fluid temperature, °C inlet fluid temperature, °C outlet fluid temperature, °C inner tube wall temperature, °C outer tube wall temperature, °C measured water volume in test section, m3 specific volume while the qualitative temperature is core fluid temperature specific volume while the qualitative temperature is inner wall temperature vapor quality, kg/kg critical quality, kg/kg outlet vapor quality, kg/kg inlet vapor quality, kg/kg Martinelli number

Greek symbols a heat transfer coefficient, W/(m2 K) alo single-phase heat transfer coefficient for the entire as liquid, W/(m2 K) atp two-phase heat transfer coefficient, W/(m2 K) g thermal efficiency kcr critical thermal conductivity, W/(m K) kg thermal conductivity of gas phase, W/(m K) lg dynamic viscosity of gas phase, N s/m2 ll dynamic viscosity of liquid phase, N s/m2 qg density of gas phase, kg/m3 ql density of liquid phase, kg/m3 2 /lo two-phase frictional multiplier, MPa

transfer abnormity results from the drastic change in thermophysical properties of supercritical water. Ackerman [15] experimentally found that the tube with rough wall surface can increase turbulent shear stress and prevent heat transfer deterioration. The experimental results indicate rifled tube can enhance heat transfer compared with smooth tube. Generally speaking, frictional pressure drop in rifled tube is far higher than that in smooth tube. Ackerman [15] found that the frictional resistance in adiabatic rifled tube is 25% higher than that in smooth tube. Kolher and Kastner [9] presented calculated formulas for single-phase and two-phase frictional coefficient, and found the frictional resistance difference between rifled tube and smooth tube rises with increasing mass flux. Zdaniuk et al. [21] studied the frictional resistance characteristics of rifled tube and obtained empirical formulas about frictional coefficient. In China, a research team led by Chen [22–32] has devised a high pressure water experimental system in Xi’an Jiaotong University, and has done a lot of work to investigate the heat transfer and resistance characteristics in smooth and rifled tube at subcritical and supercritical pressure. The experiment investigations regarding rifled tubes are numerous and lots of empirical correlations were obtained. But the most of the works in this literature were done under the operating condition of pulverized coal-fired boiler. At the same time, different opinions on the flow and heat transfer mechanism in rifled tube is still existed, and there is no corresponding correlation to accurately predict the heat transfer characteristics and frictional pressure drop. Hence, it is very necessary to conduct more experiments to analyze the heat transfer and friction characteristics of

D. Yang et al. / Experimental Thermal and Fluid Science 35 (2011) 291–300

rifled tube. In this paper, an in-depth experiment was carried out at the operating condition of a 600 MW supercritical CFB boiler. The main purpose is to improve our understanding on the flow and heat transfer mechanism of rifled tube and provide important references to supercritical CFB boiler design.

2. Experimental apparatus and procedure 2.1. Experimental loop The experimental loop, schematically shown in Fig. 1, is established to investigate the heat transfer and friction characteristics of rifled tube. It consists of a deionized water tank, a high-pressure piston pump, a filter, an orifice plate, a heat exchanger, a preheater, a vertical test section, a horizontal test section, a condenser, a rotameter and a number of valves. The heat exchanger is designed for heat recovery and the rotameter is used to visually monitor the flow rate in experimental system. The preheater and vertical test sections are directly heated by AC power supplies with high current and low voltage. The heating powers are continuously regulated by transformers and the maximums can reach 760 and 180 kW, respectively. The mass flux and pressure in experimental loop are precisely controlled by adjusting valves. The orifice plate is used to measure mass flux in test section and the maximum uncertainty is 2.6%. The fluid pressure and temperature are measured at different locations by pressure transmitters and NiCr–NiSi armored thermocouples respectively, which are indicated by P and T, respectively, in Fig. 1. The maximum uncertainties are 0.84% and 0.16% respectively.

293

2.2. Test section Fig. 2 shows a schematic diagram of the vertical test section, which is a £33  6.35 mm four-head rifled tube and the material is carbon steel (SA-213T12). The geometric dimensions of rifled tube are summarized in Table 1. The heated length of test section is 2 m. The wall temperature is measured by £0.3 mm NiCr–NiSi K-type thermocouples which are jointed on the outer tube wall and the maximum uncertainty is 0.13%. The thermocouples arrangement in test section is also shown in Fig. 2. The NiCr–NiSi armored thermocouples are protruded into rifled tube to measure fluid temperature. The heat flux is estimated from the imposed electric power and thermal efficiency and the maximum uncertainty is 6.15%. The horizontal test section is constructed for the friction characteristics investigation at adiabatic condition and it is also the rifled tube with the length of 2 m. The pressure drops in vertical and horizontal test sections are all measured by differential pressure transmitters and the maximum uncertainties are 1.25% and 2.51% respectively. The steady flow tubes are installed at the inlet and outlet of the two test sections with the aim to avoid influence of elbow. The heat insulator was put on the outer tube wall to minimize the heat loss.

2.3. Data acquisition The data acquisition system mainly consists of a personal computer, a 24 V power supply and 4 Solarton IMP3595 distributed data acquisition boards and peripheral sensors. An assembly language driver was used to communicate the information of data acquisition board to user program. A code including calibration

Fig. 1. Flow and heat transfer experimental system.

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Fig. 2. Schematic diagram of vertical test section.

Table 1 The geometric dimensions of rifled tube. Outer tube diameter Maximum inner diameter Minimum inner diameter Hydraulic diameter Number of ribs Rib height Rib width (circumferential direction) Rib width (longitudinal direction) Helical angle Pitch

dout = 0.033 m dmax = 0.021 m dmin = 0.0193 m din = 0.0203 mm N=4 H = 0.00085 m b1 = 0.0053 m b2 = 0.0068 m a = 54° s = 0.0227 m

The heat efficiency in test section is estimated by enthalpy change of single-phase water and input electric power, which is given by:

g¼

DH QE

ð2Þ

where DH and QE are calculated as below:

DH ¼

1 2 pd Gcp ðtout  tin Þ 4 in

ð3Þ

Q E ¼ EI

ð4Þ

The inner wall heat flux q is calculated as: formulas and unit conversions was written to visually monitor the transient signals from sensors and pertinent operating parameters such as input power, mass flux, pressure, pressure drop, fluid temperature, wall temperature and outlet vapor quality. 2.4. Test procedure Within the range of pressure from 12 to 30 MPa, mass flux from 230 to 1200 kg/(m2 s), and inner wall heat flux from 130 to 720 kW/m2. The experiment was conducted to investigate the heat transfer and frictional characteristics in rifled tube under the operating conditions of a 600 MW supercritical CFB boiler. In the experiment, the electric power in vertical test section was set to a certain level to keep the wall heat flux at the predetermined operating condition. The pressure and mass flux in the experimental system is also controlled at predetermined value by adjusting valves. When steady state was achieved, a determination was made to save 30 sets of all transient data and a set of averaged data by data acquisition system. Then, the heating power in preheater is augmented progressively by regulating transformers to increase the inlet fluid enthalpy until the abrupt wall temperature rise occurs or the vapor in test section is superheated. At different inlet fluid enthalpy, the steady experimental data is saved. 3. Data reduction The hydraulic diameter din is obtained by water-filled method, which is defined as:

rffiffiffiffiffiffiffi 4V din ¼ pL

q¼

Q Eg pdin L

ð5Þ

The heat transfer coefficient a is defined as:

a¼

q twi  t f

ð6Þ

where the inner wall temperature twi was determined from a onedimensional (radial) heat conduction model, which is calculated as follows [33]: 2

twi ¼ two 

qdin 1 din dout  ln 2kw 2 d2out  d2in din

! ð7Þ

The single-phase frictional pressure drop in vertical rifled tube was calculated by:

Dpf ¼ Dp  qm gL

ð8Þ

The two-phase frictional pressure drop in vertical rifled tube was calculated as follows:

Dpf ¼ Dp  Dpg  Dpa

ð9Þ

where the two-phase gravitational and acceleration pressure drop were computed based on homogeneous flow model [25], which are given by:

"

#

1 þ xe ðql =qg  1Þ ql gL Dpg ¼ ln 1 þ xi ðql =qg  1Þ ðxe  xi Þðql =qg  1Þ

ð10Þ

Dpa ¼ G2 ðxe  xi Þð1=qg  1=ql Þ

ð11Þ

The single-phase and two-phase frictional pressure drops in horizontal rifled tube were calculated by:

ð1Þ

Dpf ¼ Dp

ð12Þ

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4. Experimental results and analysis 4.1. heat transfer in subcritical region Fig. 3 shows the inner wall temperature change with the fluid enthalpy under the pressure of 12 and 16 MPa, the inner wall heat flux of 380 kW/m2 and the mass flux of 520 kg/(m2 s). As shown in Fig. 3, at the pressure of 12 MPa, the inner wall temperature at low to moderate vapor quality is about 335 °C and the fluid saturation temperature is 324.7 °C. The temperature difference between the wall and bulk fluid is about 10 °C. At the pressure of 16 MPa, the inner wall temperature at low to moderate vapor quality is about 360 °C and the fluid saturation temperature is 347.4 °C. The temperature difference between the wall and core fluid is about 12 °C. It indicates that the rifled tube has good heat transfer performance and the heat transfer coefficient has a little decrease with increasing pressure. Fig. 3 also illustrates that the heat transfer deterioration occurs ahead with the increase of pressure. When the vapor quality increases from 0 to 1, the flow in tube undergoes transitions from bubbly to slug, slug to churn, churn to annular flow, and annular to mist flow [34]. With increasing void fraction, the flow pattern changes to annular flow, whereupon evaporation from the water–vapor interface becomes increasingly important and replace nucleate boiling to be the dominant vaporization mechanism at high vapor quality [34]. According to the boiling regime map presented by Collier [35], DNB only occurs at low vapor quality even in subcooling region at high heat flux condition. As indicates in Fig. 3, dryout occurs in rifled tube at high vapor quality. Fig. 4 shows the inner wall temperature change with fluid enthalpy in vertical rifled tube at different mass flux under the pressure of 16 MPa and the inner wall heat flux of 380 kW/m2. It can be seen that the wall temperature is slightly higher than the saturation temperature in a wide quality range and the temperature difference is about 14 °C, which indicates the rifled tube can enhance heat transfer effectively. Because the critical quality is larger than 0.8, it is not DNB but dryout that occurs in rifled tube. It illuminates the rifled tube prevents the occurrence of DNB at low vapor quality. Because rifled tube increases the fluid turbulence intensity, the bubble carrying capability of core fluid is improved and it cannot form continuous bubble layer in inner tube wall. As shown in Fig. 4, the wall temperature and heat transfer coefficient at low and moderate quality hardly rise with increasing mass flux, which shows the nucleate boiling is unaffected. While the mass flux increases from 310 to 690 kg/(m2 s), the critical vapor quality increases obviously. The reason is that the increase in rotational

Fig. 6 shows the comparison of heat transfer characteristics between rifled tube and £22  2.5 mm smooth tube in near-critical region at similar mass flux and the inner wall heat flux under the pressure of 21 MPa. As can be seen in Fig. 6, abrupt wall temperature rise occurs in smooth tube at vapor quality of 0.24, which implies DNB occurs. The maximum wall temperature at DNB condition is 495 °C. As shown in Fig. 6, the heat transfer

Fig. 3. Inner wall temperature change with fluid enthalpy at different pressure in subcritical region.

Fig. 5. Inner wall temperature change with fluid enthalpy at different heat flux in subcritical region.

Fig. 4. Inner wall temperature change with fluid enthalpy at different mass flux in subcritical region.

flow velocity in rifled tube results in more liquid is thrown into the wall and remarkably delays the occurrence of dryout. Fig. 5 shows the inner wall temperature change with the fluid enthalpy at different inner wall heat flux under the pressure of 16 MPa and the mass flux of 520 kg/(m2 s). As can be seen in Fig. 5, with increasing heat flux, the critical vapor quality obviously decreases. The high critical quality also shows that it is not DNB occurs in rifled tube. At high vapor quality, the flow pattern in rifled tube is annular flow. As the bulk fluid enthalpy increases, liquid film in the wall is evaporated and is entrained by core vapor continuously. At last, core vapor tears the liquid film in inner tube wall and local dryout occurs in rifled tube and dominates the heat transfer deterioration eventually. As the heat flux rises, the liquid film is torn more easily, which produces dryout occurs ahead. The boiling regime map presented by Collier [35] also indicates the critical quality decreases with the increasing heat flux. 4.2. Heat transfer in near-critical region

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Fig. 6. Comparison of heat transfer characteristics between rifled tube and smooth tube in near-critical region.

Fig. 8. Heat transfer coefficient change with fluid enthalpy at different pressure in supercritical region.

performance in rifled tube is good in a wide quality range, the occurrence of DNB is successfully prevented and the critical vapor quality is delayed to 0.94. Compared with smooth tube, the wall temperature rise in rifled tube is also very slow in post-dryout region. The experimental result in Fig. 6 fully proves the good heat transfer performance of rifled tube. It was generally acknowledged that rifled tube maintains nucleate boiling in a wide quality range because of the following advantages: (1) enlarging the surface area of convection heat transfer; (2) increasing the turbulent intensity in boundary layer; (3) increasing the relative velocity between wall and core fluid by rotational flow, and improving the mass transfer between boundary layer and core fluid due to centrifugal force.

While the fluid temperature at supercritical pressure approach pseudo-critical temperature, the fluid thermophysical properties, which includes specific heat, density, viscosity, thermal conductivity, all have tremendous changes coupled with the change of turbulent structure [36]. Due to the special thermophysics properties in pseudo-critical enthalpy region, the heat transfer characteristics of water at supercritical pressure are different with that at subcritical and near-critical pressure. Figs. 7 and 8 show the variations of inner wall temperature and heat transfer coefficient with the fluid enthalpy in vertical rifled tube at different pressures under the mass flux of 600 kg/(m2 s) and the inner wall heat flux of

470 kW/m2. Fig. 7 indicates low wall temperature gradients near pseudo-critical point. Moreover, in Fig. 8 the maximum heat transfer coefficients are located in pseudo-critical enthalpy region. It means that the heat transfer of supercritical water in pseudo-critical enthalpy range is effectively enhanced. The reason is that the peak value of specific heat appears at pseudo-critical temperature. Due to the large specific heat in pseudo-critical enthalpy range, the wall temperature increases slowly with the increase of fluid enthalpy. As shown in Fig. 7, the wall temperature in rifled tube increases with the increasing pressure, especially near pseudocritical point. It also can be seen in Fig. 8 that the peak value of heat transfer coefficient in pseudo-critical enthalpy region decreases with the increasing of pressure, which illustrates that the heat transfer enhancement is weakened. It is because the heat transfer enhanced by thermophysics properties change of supercritical water is not dominant when fluid pressure is much higher than critical pressure. As can be seen in Figs. 7 and 8, because the heat transfer of supercritical water is better than that of supercritical steam, the wall temperature rises rapidly and the heat transfer coefficient is very low while the fluid enthalpy is much larger than pseudo-critical enthalpy. Figs. 9 and 10 show the variations of inner wall temperature and heat transfer coefficient with the fluid enthalpy at different mass flux under the pressure of 25 MPa and the inner wall heat flux of 470 kW/m2. It is seen in Fig. 9 that the wall temperature in rifled tube decreases with the increasing mass flux, especially

Fig. 7. Inner wall temperature change with fluid enthalpy at different pressure in supercritical region.

Fig. 9. Inner wall temperature change with fluid enthalpy at different mass flux in supercritical region.

4.3. Heat transfer in supercritical region

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Fig. 10. Heat transfer coefficient change with fluid enthalpy at different mass flux in supercritical region.

Fig. 12. Heat transfer coefficient change with fluid enthalpy at different heat flux in supercritical region.

near pseudo-critical point. At the same time, as shown in Fig. 10, the peak value of heat transfer coefficient rises obviously with the increase of mass flux. Because the turbulent and rotational flow in rifled tube is improved with increasing mass flux, the heat transfer enhancement in pseudo-critical enthalpy region gets more evident. Therefore, homogeneous mass flux distribution in water wall is very important for the safe operation of supercritical CFB boiler. Figs. 11 and 12 show the variations of inner wall temperature and heat transfer coefficient with the fluid enthalpy at different inner wall heat flux under the mass flux of 25 MPa and the mass flux of 600 kg/(m2 s). As can be seen in Fig. 11, the wall temperature in rifled tube rises with increasing heat flux. As shown in Fig. 12, the maximum heat transfer coefficient decreases obviously with increasing heat flux, which means the heat transfer enhancement in pseudo-critical enthalpy region in rifled tube is weakened effectively. It also can be seen that the maximum heat transfer coefficient appears ahead with increasing heat flux. Especially at the inner wall heat flux of 660 kW/m2, the heat transfer is even deteriorated near pseudo-critical point. According to the view of pseudo-boiling theory, the heat transfer mode changes from pseudonucleate boiling to pseudo-film boiling with increasing heat flux, which results in the heat transfer enhancement in pseudo-critical enthalpy region is weakened, even heat transfer deterioration occurs. Therefore, it is an efficacious method to decrease wall temperature and improve heat transfer by reducing heat flux.

4.4. Empirical correlation 4.4.1. subcritical and near-critical pressure region In the experiment, the normal and deteriorated heat transfer characteristics in rifled tube are captured. Through the experimental data processing, in this paper, corresponding empirical correlations on the heat transfer and critical quality in rifled tube are obtained. The Nusselt number in single-phase region based on Dittus– Boelter formula [37] is given by:

Nu ¼ 0:0499Re0:74752 Pr0:47426

ð13Þ

Based on Lockhart–Martinelli formula [38], the empirical correlation for two-phase normal heat transfer is written as below:



atp 1 ¼ 1:37999 X tt al

0:24786 

p pcr

1:24494 

G

0:64401

Gmax

ð14Þ

where Xtt is defined as:

 0:9  0:5 qg 1x X tt ¼ x ql

ll lg

!0:1 ð15Þ

and

Gmax ¼ 1200 kg=ðm2 sÞ According to Slaughterback empirical relation [39], the Nusselt number in post-dryout region is calculated as:

  0:78075 qg Nu ¼ 0:00001238 Reg x þ ð1  xÞ  Pr2:11935 q0:94741 gw



ql

kg kcr

1:29486 ð16Þ

where kcr = 0.914 The empirical correlation on critical quality in rifled tube is given by:

xcr ¼ 2:27533q0:10489 G0:00386 e0:58229ðp=22:115Þ

Fig. 11. Inner wall temperature change with fluid enthalpy at different heat flux in supercritical region.

ð17Þ

The average relative absolute value errors of correlation (13), (14), (16), and (17) are 6.20%, 6.91%, 6.75% and 3.89% respectively. The scope of application is pressure range from 12 to 21 MPa, mass flux range from 230 to 770 kg/(m2 s), inner wall heat flux range from 130 to 660 kW/m2.

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4.4.2. Supercritical pressure region Based on the experimental data, Dittus–Boelter formula [37] is used to induce the empirical correlation of supercritical water heat transfer. The specific volume ratio between core fluid and tube wall surface fluid, and the average specific heat are adopted to correct the empirical correlations of heat transfer coefficient. The empirical correlation of Nusselt number in low enthalpy region is given by:

Nuw ¼ 3:3374Re0:40483 w

 0:96138  0:49053 mf ðhw  hÞlw ðt w  tf Þkw mw

ð18Þ

The empirical correlation of Nusselt number in high enthalpy region is given by:

Nuw ¼ 7:41976Re0:34764 w

 1:39002  1:12257 mf ðhw  hÞlw ðt w  tf Þkw mw

ð19Þ

The average relative absolute value errors of correlation (18) and (19) are 4.96% and 4.13% respectively. The scope of application is pressure range from 22.5 to 30 MPa, mass flux range from 430 to 1200 kg/(m2 s), inner wall heat flux range from 280 to 720 kW/m2. 4.5. Frictional resistance 4.5.1. Single-phase region Single-phase pressure drop in heat-insulated and heating rifled tube was measured in the experiment. The experimental results indicate that flow exists in self-stimulated domain (Re > 105) and the single-phase frictional coefficient hardly varies with Reynolds number. previous studies shows that in self-stimulated domain the viscous sublayer thins, accordingly the frictional coefficient is mainly decided by wall roughness and the single-phase frictional resistance only is proportionate to flow velocity squared. The experimental data also imply that the single-phase frictional coefficient in heat-insulated rifled tube is higher than that in heating rifled tube because the qualitative temperature is not liquid film but fluid temperature. Building on the Blasius formula, the following relation for single-phase frictional coefficient in heat-insulated rifled tube is proposed:

f ¼

4:99572 Re0:5864

þ 0:03857

ð20Þ

A similar correlation for heating rifled tube is given below:

f ¼

1:97912 Re0:5479

þ 0:03822

ð21Þ

The average relative absolute value errors of correlation (20) and (21) are 8.03% and 6.29% respectively. The scope of application is pressure range from 12 to 30 MPa, mass flux range from 230 to 1200 kg/(m2 s), inner wall heat flux range from 130 to 720 kW/m2.

Fig. 13. Two-phase frictional multiplier in rifled tube at different pressure and mass flux.

value. Because centrifugal force induced by rotational flow exists in rifled tube, the wall surface is covered by water film at low to moderate quality, which results in the increase of two-phase multiplier. In high quality region, the high-speed vapor in heating rifled tube can tear the liquid film in inner wall and the flow pattern is changed into mist flow with low frictional pressure drop. Therefore, the two-phase multiplier at high fluid quality is low. The effect of pressure is to decrease two-phase multiplier, as clearly displayed in Fig. 13. It shows that due to the variation of thermophysical properties, the vapor-phase and liquid-phase frictional pressure drop decreases quickly with increasing pressure. Otherwise, the two-phase multiplier rises with increasing mass flux, although the effect of mass flux is so little that it can be neglected. According to the concept ‘‘actual dynamic head” presented by Chisholm [41], the two-phase multiplier is expressed as:

/2lo ¼ 1 þ ðql =qg  1Þ½CðxÞ þ x2 

ð23Þ

Through the multiple regression analysis on experimental data, the fitting coefficients for heat-insulated and heating rifled tube are obtained respectively, which are given by:

CðxÞ ¼ 1:498044x0:94402 ð1  xÞ0:08624

ð24Þ

CðxÞ ¼ 1:447691x0:70569 ð1  xÞ0:0396

ð25Þ

The average relative absolute value errors of correlation (24) and (25) are 9.21% and 14.44% respectively. The scope of application is pressure range from 12 to 21 MPa, mass flux range from 230 to 770 kg/(m2 s), inner wall heat flux range from 130 to 660 kW/m2. 5. Conclusions

4.5.2. Two-phase region In order to simplify calculation for engineering application, the two-phase frictional pressure drop data were analyzed by using the concept of two-phase multiplier, which is expressed as [40]:

/2lo ¼ Dptp =Dplo

ð22Þ

Fig. 13 shows the two-phase frictional multiplier in heating rifled tube at different pressure and mass flux. As can be seen in Fig. 13, at low to moderate vapor quality, as more vapor is generated in the flow the two-phase multiplier increases rapidly, which indicates the frictional pressure drop of vapor-phase is higher than that of liquid-phase. At high quality, whereas, the two-phase multiplier rises slowly with increasing quality, even begins to decrease while the vapor quality reaches a certain

An experiment on heat transfer and friction characteristics of £33  6.35 mm four-head rifled tube with vertical upward flow was conducted. The wall temperature and pressure drop in rifled tube under the operating condition of supercritical CFB boiler is obtained in the experiment. The following conclusions are the findings of this investigation. 1. At subcritical pressure, rifled tube can effectively prevent the occurrence of DNB and delay the onset of dryout. With increasing pressure and inner wall heat flux and decreasing mass flux, dryout occurred ahead, the wall temperature increased obviously and in post-dryout region the wall temperature rises more rapidly.

D. Yang et al. / Experimental Thermal and Fluid Science 35 (2011) 291–300

2. At near-critical pressure, the heat transfer in rifled tube gets worse. Whereas, compared with smooth tube, rifled tube can still prevent the occurrence of DNB and delay critical vapor quality effectively. 3. At supercritical pressure, the heat transfer in high enthalpy region is far better than that in low enthalpy region. The wall temperature near pseudo-critical point increases slowly with increasing fluid enthalpy due to the intense changes in thermophysical properties of supercritical water. The heat transfer coefficient in rifled tube increases with increasing enthalpy and reaches a peak value in pseudo-critical enthalpy region. With increasing pressure and inner wall heat flux and decreasing mass flux, the wall temperature increased obviously and the heat transfer enhancement in pseudo-critical enthalpy region is weakened. At high heat flux, the maximum heat transfer coefficient appears ahead and the heat transfer enhanced by thermophysics properties change of supercritical water is not dominant, even heat transfer deterioration occurs near pseudo-critical point. 4. The single-phase frictional coefficient in heat-insulated rifled tube is higher than that in heating rifled tube because the qualitative temperature is not liquid film but fluid temperature. The single-phase frictional coefficients in the two tubes hardly vary with Reynolds number because the flow exists in self-stimulated domain (Re > 105). 5. At low to moderate vapor quality, as more vapor is generated in the flow, the two-phase frictional multiplier increases rapidly. At high quality, whereas, the two-phase multiplier rises slowly with increasing quality, even begins to decrease while the vapor quality reaches a certain value. 6. The experimental result shows that the rifled tube has good heat transfer characteristics. Based on the experimental data, the corresponding empirical correlations on heat transfer, critical quality, and frictional resistance of rifled tube are obtained. These correlations can be applied in predicting the thermal– hydraulic characteristics of the 600 MW supercritical CFB boiler, which include mass flux distribution, metal and vapor temperature in water wall. Acknowledgement This work was supported by the National Key Technology R&D Program of China during the 11th Five-Year Plan Period (Grant No. 2006BAA03B02-03). References [1] Y. Li, L. Nie, X.K. Hu, et al., Structure and performance of a 600 MWe supercritical CFB boiler with water cooled panels, in: Proceedings of 20th International Conference on Fluidized Bed Combustion, Xi’an, China, 2009. [2] J. Xin, J.F. Lu, G.X. Yue, et al., A discussion concerning the development of supercritical circulating fluidized beds, Journal of Engineering for Thermal Energy and Power 17 (101) (2002) 439–442 (in Chinese). [3] A. Hotta, Foster Wheeler’s solutions for large scale CFB boiler technology: features and operational performance of Lagisza 460 MWe CFB boiler, in: Proceedings of 20th International Conference on Fluidized Bed Combustion, Xi’an, China, 2009, pp. 59–70. [4] G.N. Stamatelopoulds, Advancement in CFB technology: A combination of excellent environmental performance and high efficiency, in: Proceedings of 18th International Conference on Fluidized Bed Combustion, Toronto, Canada, 2005, pp. 85–93. [5] H.S. Swenson et al., The effects of nucleate boiling versus film boiling on heat transfer in power boiling tubes, Transactions of the ASME. Series A, Journal of Engineering for Power 84 (1962) 365–371. [6] G.B. Watson et al., Critical heat flux in inclined and vertical smooth and ribbed tubes, Heat Transfer 4 (1974) 275–279. [7] K. Nishikawa, T. Fujii, S. Yoshida, Flow boiling crisis in grooved boiler-tubes, in: Proceedings of 5th International Heat Transfer Conference, Tokyo, Japan, 1974, pp. 270–274. [8] M. Iwabuchi, M. Tateiwa, H. Haneda, Heat transfer characteristics of rifled tubes in the near critical pressure region, in: Proceedings of the 7th

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