Local boiling heat transfer characteristics of ammonia in a vertical plate evaporator

international journal of refrigeration 33 (2010) 359–370

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Local boiling heat transfer characteristics of ammonia in a vertical plate evaporator H. Arima*, J.H. Kim, A. Okamoto, Y. Ikegami Institute of Ocean Energy, Saga University, 1-48, Hirao, Kubara-aza, Yamashiro-machi, Imari, Saga, 849-4256 Japan

article info

abstract

Article history:

Ocean thermal energy conversion systems are expected to be the next-generation energy

Received 27 December 2008

production systems. In these systems, a plate heat exchanger is used for improving the

Received in revised form

power generation efficiency, and ammonia or an ammonia/water mixture is used as

19 September 2009

a working fluid.

Accepted 26 September 2009 Available online 8 October 2009

In this study, boiling heat transfer coefficients of pure ammonia are measured on a vertical flat PHE (a plate heat exchanger), for elucidating and characterizing the behavior of ammonia on a compact plate evaporator, a type of PHE

Keywords:

The measurement results show that local boiling heat transfer coefficients increase with

Heat exchanger

increasing vapor quality. Further, the effects of saturation pressure, mass flow rate, and

Plate exchanger

average heat flux on the boiling heat transfer coefficient are elucidated. An empirical

Heat transfer

correlation for the local boiling heat transfer coefficient is derived using the Lockhart-Mar-

Boiling

tinelli parameter. Further, a visualization experiment of boiling phenomena of ammonia is

Ammonia

performed to elucidate the relation between boiling behavior and heat transfer.

Measurement

ª 2009 Elsevier Ltd and IIR. All rights reserved.

Heat transfer coefficient Visualization

Caracte´ristiques de transfert de chaleur lors de l’e´bullition locale d’ammoniac dans un e´vaporateur a` plaque verticale Mots cle´s : E´changeur de chaleur ; E´changeur a` plaque ; Transfert de chaleur ; E´bullition ; Ammoniac ; Mesure ; Coefficient de transfert de chaleur ; Imagerie

1.

Introduction

It is well known that greenhouse gases such as CO2 contribute to global warming. Further, abnormal weather conditions continue to be observed worldwide due to global warming.

Therefore, the reduction of CO2 emissions has become an important issue worldwide. The best method for the reduction of CO2 emissions is to reduce the use of fossil fuels such as petroleum and coal. Furthermore, it is important to employ renewable energy sources. Recently, ocean thermal energy

* Corresponding author. Institute of Ocean Energy, Saga University, 849-4256 Japan (IOES). Tel.: þ81 955 20 2190; fax: þ81 955 20 2191. E-mail address: [email protected] (H. Arima). 0140-7007/$ – see front matter ª 2009 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2009.09.017

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international journal of refrigeration 33 (2010) 359–370

Nomenclature A b C C1wC5 Cp Dh F Ffl G h hLZ

n ifg ipre,in ipre,out isat,l itest,n j k li m Psat q Q T Twall DTsat w x

constant [–] constant [–] proportionality factor [(W/m2)(1-n)/K] constant specific heat [J/(kg K)] hydraulic diameter [m] ¼ 2wd /(w þ d) constant [–] fluid-dependent parameter [–] mass flux [kg/(m2 s)] boiling heat transfer coefficient [W/(m2 K)] heat transfer coefficient for two-phase flow and for flow of only a liquid phase in a channel [W/(m2 K)] constant [–] latent heat of vaporization [J/kg] specific enthalpy of preheater inlet [J/kg] specific enthalpy of preheater outlet [J/kg] specific enthalpy of saturated liquid [J/kg] local specific enthalpy of test plate [J/kg] superficial velocity [m/s] thermal conductivity [W/(m K)] distance between two thermocouples [m] mass flow rate [kg/s] saturation pressure (absolute) [Pa] heat flux [W/m2] heat flow [W] temperature [ C] plate wall temperature [ C] wall superheat [K] width of test plate channel [m] vapor quality [–]

conversion (OTEC) systems or hot spring thermal energy conversion (STEC) systems have attracted considerable attention as sources of renewable energy. One of the drawbacks of the OTEC system is that it generates less electricity than conventional power plants such as nuclear and thermal power generation plants do. This is because in an OTEC plant, a small temperature difference between heat sources on surface and in deep ocean water is used; therefore, the thermal efficiency of the OTEC system is very low. Hence, for improving the power generation efficiency, plate heat exchangers (PHEs) such as evaporators and condensers are employed in OTEC plants. PHEs facilitate temperature control and provide a large heat transfer area per unit volume Temperatures of both heat sources of the OTEC system are very small; therefore, the use of a low boiling point refrigerant as a working fluid is required in the OTEC system. In these systems, pure ammonia or ammonia/water binary mixtures are commonly used as the working fluid. Since the ozone depletion potential (ODP) and global warming potential (GWP) of ammonia are zero, it is a very good refrigerant from the viewpoint of preserving the quality of the earth’s environment. Further, for improving the performance of PHEs, it is important to improve the heat transfer coefficient of the working fluid. However, the boiling heat transfer performance of ammonia has not yet been elucidated. Some studies

Dy

distance between two neighboring thermocouple wells [m]

Greek symbols d height of test plate channel [m] m viscosity [Pa s] r density [kg/m3] Subscripts av average g vapor i position of measuring point in inlet l liquid loc local n number of measuring point out outlet pre preheater sat saturation sus SUS304 test test section wall wall Dimensionless number Bo boiling number [–] ¼ ðGHq fg Þ 0:8 rg 0:5 Co convection number [–] ¼ ð1x x Þ ð rl Þ 2 Fr Froude number with all flow [–] ¼ ðr2GgD Þ h l l Prandtl number of the liquid phase [–] ¼ ðmlkCp Þ Prl l Reynolds number of the vapor phase [–] Reg ¼ (GxDh/mg) Reynolds number of the liquid phase [–] Rel ¼ (G(1-x)Dh/ml) Lockhart-Martinelli parameter for turbulent liquid Xtt and vapor phases [–]

(Kushibe et al., 2005) determined forced convective boiling heat transfer coefficients of ammonia on the plate evaporator of an experimental OTEC plant. However, in these studies, local boiling heat transfers on the working fluid side of the plate evaporator were not determined, because the overall heat transfers coefficients which include boiling heat transfers on the working fluid and heat source side, were calculated. Furthermore, few studies (Nishikawa and Fujita, 1977; Inoue et al., 2002; Arima et al., 2003) were conducted for measuring the pool boiling heat transfer of ammonia. In these studies, data on different saturation pressure, average heat flux, and mass fraction were obtained. In addition, some studies (Zurcher et al., 2002; Zamfirescu and Chiriac, 2002) were conducted for measuring the local boiling heat transfer coefficient of ammonia on a horizontal or vertical tube type evaporator. However, thus far, no studies have been conducted for measuring the local forced convective boiling heat transfer coefficient of ammonia on a vertical plate evaporator. Therefore, in the present study, the local convective boiling heat transfer coefficient of ammonia on a plate evaporator (used as a test plate) is measured. Using the results of this study, suitable design criteria for improving the power generation efficiency of thermal conversion systems with small temperature differences can be established. Further, effects of mass flux, heat flux, and saturation pressure on the boiling heat

international journal of refrigeration 33 (2010) 359–370

361

2.

Experiment

accuracy of less than  0.15  C); the mass flow rate is measured using a Coriolis mass flowmeter (Endress þ Hauser, accuracy of  1% of F.S.); pressure is measured using a gauge pressure transducer (Toshiba, 3051CG, range 0w2070 kPa, accuracy of  0.25% of F.S.); and flow rates of hot and cold water are measured using magnetic flowmeters (Toshiba, LF410, accuracy of  0.5% of F.S.). All measured data were recorded using a programmable logic controller (PLC; Mitsubishi Electric, MELSEC Q series) connected to a personal computer (PC).

2.1.

Experimental apparatus and procedure

2.2.

transfer coefficients of ammonia are examined. In addition, an empirical correlation for the local forced convective boiling heat transfer coefficient of ammonia is derived. Moreover, in order to elucidate the effect of the local boiling heat transfer performance of ammonia on its boiling phenomenon, an experiment for the visualization of the interiors of the plate is performed.

Fig. 1 shows a schematic of the experimental apparatus consisting of a plate evaporator (test plate), condenser, and three flow circuitsda warm water circuit, cold water circuit, and working fluid circuit. A subcooled working fluid (ammonia, approximately 8 K) is pumped up to a preheater using working fluid pump (Teikoku Electric Mfg. Co., Ltd., reverse circulation type canned motor pump, head 12 m, power 1.1 kW). The working fluid is heated by the preheater (brazed plate heat exchanger Tokyo Braze Co., Ltd.) to achieve the recommended vapor quality at the test plate inlet. Then, the working fluid is flown into the test plate, and the fluid exchanges heat with hot water. As a result, the state of the working fluid changes from liquid to a two-phase fluid. The two-phase fluid is transported to an after-condenser and plate condenser, and then, it is condensed into liquid using cold water. The condensed working fluid is stored in a working fluid tank and transported to the working fluid pump. Further, the hot and cold water are generated by a gas boiler and refrigerator and stored in hot and cold water tanks, respectively. The working fluid temperature is measured using resistance thermometers (Hayashi Denko Co., Ltd., ER6, JIS A-class,

Test plate

Fig. 2 shows a schematic diagram of the test plate evaporator. The test plate consists of a main plate, two flames, and two spacers. The test plate has dimensions of 380 nm (width)  850 nm (length)  40 nm (thickness). Further, the two flames have dimensions of 380 mm (width)  850 mm (height)  30 nm (thickness). Spacers on the working fluid side and heat source side have thicknesses of 2 mm and 10 mm, respectively. The area of heat exchanger above the main plate is 250 mm  650 mm; the main plate is polished using #2000 sandpaper. The main plate, flames, and spacer on the working fluid side are made of SUS304, and the spacer on the heat source side is made of rubber. The rubber spacer is also used for thermal insulator. The channels of the working fluid and hot source consist of the main plate, one spacer, and one flame. Then, the cross-sectional areas of the flow channels are 2 mm  250 mm (working fluid side) and 10 mm  250 mm (hot source side). Inside the main plate, there are six thermocouple (TC) wells in which thermocouple sheaths (Fig. 3) are inserted for measuring local temperatures. Each TC well is 3 mm in diameter and 38 mm in length. The thermocouple sheaths consist of a urethane tube and two fixed K-type thermocouples (0.1 mm

Fig. 1 – Schematic diagram of experimental apparatus.

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international journal of refrigeration 33 (2010) 359–370

Fig. 2 – Schematic diagram of test plate.

in diameter). The thermocouples are mounted on the surfaces of the sheaths. In order to increase the temperature measurement accuracy, the distance l1 between the thermocouples is maintained to be sufficiently large (average distance of 33.5 mm). All data measured using the thermocouples are recorded using a multimeter (Keithley, model 2701) connected to the PC. In addition, temperature proofreading is carried out in a constant temperature bath by using thermocouples. Therefore, the temperature measurement is highly accurate (less than  0.1  C accuracy). In order to visualize the boiling phenomena occurring inside the flow channels, three sight glasses were placed on the working fluid side.

2.3.

Visualization experiment

Fig. 4 show a cross section of the sight glass used for visualization. The sight glass is 45 mm in diameter. Visualized images of the dotted square (having an area of 2500 mm2) are shown in subsequent figures. Boiling phenomena occurring inside the flow channels are observed using images captured using a digital still camera (Pentax *istD); these images are captured from outside the flow channels, as shown in Fig. 5. The camera shutter speed is 1/4000 s. The light source is a 250 W cold lamp.

2.4.

Local heat flux

The six TC wells, located along the center line of the test plate, are used to measure the local heat flux.

Assuming that local heat fluxes (q) can be estimated from one-dimensional, steady-state heat conduction, q can be expressed by Eq. (1): q ¼ ksus

T1  T2 l1

(1)

where ksus is the thermal conductivity of SUS304 and T1 and T2 are local temperatures. The wall temperature of the working fluid side (Twall) is calculated by Eq. (2): Twall ¼ T2 

q$l2 ksus

(2)

where l2 is the distance between the thermocouple and the wall surface.

A: Working fluid

T2 Twall

Hot water

Urethan tube

l2

Plate l1

T1

Fig. 3 – Position of local thermocouple inside the test plate (enlarged view of area A shown in Fig. 2).

international journal of refrigeration 33 (2010) 359–370

φ 45

View area

Fig. 4 – Cross section of sight glass.

The local heat transfer coefficient (h) is calculated by Eq. (3): h¼

q q ¼ ðTwall  Tsat Þ DTsat

(3)

Qpre m

pipe connecting the preheater and evaporator is sufficiently insulated. Next, the local specific enthalpy (itest,n) in each TC well at point n is calculated by adding the increase in stock of the specific enthalpy from a plate entrance. Here, the increase in stock of specific enthalpy between neighboring TC wells is calculated using the heat flow (Qn) between two neighboring TC wells and the mass flow rate (m), similar to the calculation shown in Eq. (1). Here, Qn is obtained from the local heat flux (qn) and the heat transfer area. However, since the heat flux of each TC well is different, the heat flow of each area Q0 n is calculated using the area of each plate part An ¼ yn  w, as shown in Fig. 6. Finally, Qn is calculated from the average value of the heat flow Q0 n and Q0 n-1 Further, itest,n is expressed as follows: (a) in the case that n ¼ 1

where DTsat is the wall superheat and Tsat is the bulk temperature of the working fluid side, derived using the saturation pressure at the plate inlet. By the way, since the inside of a plate has pressure drop, it along the flow should be considered in deriving the local saturation pressure and local saturation temperature. However, since change of the saturation temperature by pressure drop was about 0.04  C, it was assumed that a saturation temperature was fixed. The local specific enthalpy (itest,n) on the test plate is derived using the following method. First, the subcooled working fluid is flown into the preheater inlet. Then, the preheater inlet specific enthalpy (ipre,in) is calculated from the fluid temperature and pressure by using the P-Propath computer program package (PROPATH Group, 2006). The outlet specific enthalpy (ipre,out) at the preheater is obtained from the heat transport rate (Qpre) and mass flow rate (m ¼ G  d  w) for the preheater: ipre;out ¼ ipre;in þ

363

itest;1 ¼ itest;in þ

Q1 ; m

Q1 ¼ q1 A1

(b) in the case that n ¼ 2w6 0 Qn Q 0 þ Qn1 ; Qn ¼ n ; Qn0 ¼ qn An ðn ¼ 2w6Þ m 2 The local vapor quality (xn) is defined as follows:

itest;n ¼ itest;n1 þ

(5)

(4)

The specific enthalpy of the plate inlet (itest,in) is defined as being equal to that of the preheater outlet (ipre,out), because the

Fig. 5 – Setup for visualization.

Fig. 6 – Schematic diagram of effective heat transfer surface for calculating local enthalpies.

364

xn ¼

international journal of refrigeration 33 (2010) 359–370

itest;n  isat;liq ifg

ðn ¼ 1w6Þ

(6)

where isat,liq is the specific enthalpy of the saturated liquid at the saturation pressure of the plate inlet (Psat) and ifg is the latent heat, which can be calculated using P-Propath. The experimental conditions are shown in Table 1.

3.

Experimental results

3.1.

Boiling curve

Fig. 7 shows the boiling curve (at Psat ¼ 0.7 MPa) with changes in the mass flux and average heat flux. The local heat flux increases linearly with increasing DTsat. This tendency was observed in the pool boiling curve of ammonia (Arima et al., 2003). However, change of the wall superheat temperature is only 2 K against change of heat flux being 10 kW/m2. Therefore, the effect of the wall superheat temperature is very small on the heat flux. Furthermore, the local heat flux was not affected by the mass flux in present study. Because each mass flux differences is small in itself and the result is close to the pool boiling condition due to the very small mass flux for forced convection experiment. The solid line and diamond plots in Fig. 7 show that the experimental data of the boiling curve for the pool boiling of ammonia by Arima et al. (2003). And the short and long dashed line shows a pool boiling prediction, which is obtained by Eqs. (1) and (3). Eq. (7) has been proposed by Stephan and Abdelsalam (1980) and Nishikawa and Fujita (1977). h ¼ Cqn

(7)

where C ¼ 1.05, n ¼ 0.745 (Stephan and Abdelsalam, 1980) and C ¼ 4.41, n ¼ 2/3 (Nishikawa, 2000) at Psat ¼ 0.7 MPa for ammonia. It is found that DTsat for forced convective boiling and the result of pool boiling by Arima et al. (2003) are mostly in agreement. On the other hand, DTsat for forced convective boiling is 8 K or 3 K lower than each prediction. According to Arima et al. (2003) or Inoue et al. (2002), the boiling pool boiling correlation of Nishikawa and Fujita (1977) is more agreement compared with that of Stephan and Abdelsalam (1980). Therefore, even if it compares with the prediction of Nishikawa and Fujita (1977), it was found out that the present result indicates near pool boiling condition. The reason why the local heat flux as not affected by the mass fluxes that the result is close to the pool boiling condition.

3.2.

Local boiling heat transfer

3.2.1.

Influence of mass flux

Fig. 8(a) and (b) show that plots of the measured local boiling heat transfer coefficient hloc versus vapor quality x at various

Table 1 – Experimental conditions. Working fluid

Ammonia 2

Mass flux G [kg/(m s)] Average heat flux qav [kW/m2] Saturation pressure Psat [MPa] Saturation temperature Tsat [ C] Vapor quality of test plate inlet xtest,in[–]

7.5, 10, 15 15, 20, 25 0.7, 0.8, 0.9 13.9, 17.9, 21.6 0.1w0.4

Fig. 7 – Boiling curve at Psat [ 0.7 MPa.

mass fluxes; the average heat fluxes in these cases are 15 kW/ m2 and 20 kW/m2, respectively, and the saturation pressure in both these cases remains constant at 0.70 MPa. In case of x < 0.3, the local heat transfer coefficients remain almost constant with increasing x. However, in case of 0.3 < x < 0.7, that tend to increase with increasing x. In general, at the forced convective boiling in a vertical tube, it is known that in case of nucleate boiling region, wall superheat is constant with increasing x and in case of forced convective heat transfer through liquid film region (forced convective region), the wall superheat is little decrease with increasing x (Tong and Tang, 1997). Since change of the gradient of heat transfer was observed bordering on x ¼ 0.3 as shown in Fig. 8. However, regardless of the amount of mass flux, the local boiling heat transfer coefficient remains almost constant for a given vapor quality. Therefore, this tendency shows that an increase in mass flux has almost no effect on the boiling heat transfer coefficient. At the nucleate boiling region, it is considered that the bubble which is generated in the heating surface tends to stagnate into the narrow channel, although heat transfer by the forced convection is performed. Because these mass fluxes are small different and mass fluxes of present study are lower than that of previous study. Therefore, it is considered that it depends for heat transfer on the amount of bubbles emergence and heat transfer is not influenced by the mass flux. In addition, the boiling heat transfer coefficient decreases rapidly with increasing x for x > 0.7 on Fig. 8 (b). The range x > 0.7 implies the occurrence of a dry-out. The same tendency is observed in Fig. 9(a).

3.2.2.

Influence of heat flux

Fig. 9(a) and (b) show the plot of measured local boiling heat transfer coefficient hloc versus vapor quality x at various average heat fluxes; the mass fluxes in these cases are 7.5 kg/(m2 s) and 10 kg/(m2 s), respectively, and the saturation pressure in both these cases remains constant at 0.70 MPa.

365

international journal of refrigeration 33 (2010) 359–370

a

b qav = 15 kW/m2 Pabs = 0.70 MPa

9

2

G = 7.4 kg/(m . s) 2

G = 10 kg/(m . s)

8

7

6

5 0.0

0.2

0.4

0.6

0.8

10

Local heat transfer coefficient 2 hloc kW/(m . K)

Local heat transfer coefficient 2 hloc kW/(m . K)

10

qav = 20 kW/m2 Pabs = 0.70 MPa

9

8

7

6

5 0.0

1.0

G = 7.5 kg/(m2 . s) G = 10 kg/(m2 . s)

0.2

0.4

0.6

Quality x [-]

Quality x [-]

qav = 15 kW/m2

qav = 20 kW/m2

0.8

1.0

Fig. 8 – Plot of local boiling heat transfer coefficient versus vapor quality at various mass fluxes.

All local boiling heat transfer coefficients tend to increase with decreasing average heat flux and increasing quality. However, as shown in Fig. 9(a), at qav ¼ 20.0 and 24.5 kW/m2, boiling heat transfer decreases for x > 0.85, thereby causing a dry-out. Under the same saturation pressure and mass flux, the boiling heat transfer coefficient decreases with increasing average heat flux. This tendency is different from that observed by Kido et al. (1992) and Hsieh et al. (2002): they reported that the boiling heat transfer coefficient increases with increasing average heat flux. The reason for this tendency is considered to be the fact that in their experiments, heating was carried out using a fluid and not a heater. In the former case, heat flux is determined by the balance between heat transfers of the working fluid and warm water, whereas in the latter case, even when the operating fluid has an irregular flow with air bubbles, fixed heating is carried out. Therefore, it is considered that fluid heating is difficult to heat uniformly. The investigation of this phenomenon is the subject of a future study.

G = 7.5 kg/(m2 . s) Pabs = 0.70 MPa

2

qav = 20.0 kW/m

2

qav = 24.5 kW/m

8

7

6

0.2

Comparisons of previous correlation

Comparisons between the existing correlations and present data which are shown in Fig. 8 are performed. Nishikawa and

10 G = 7.5 kg/(m2 . s) Pabs = 0.70 MPa

qav = 15.4 kW/m2

9

5 0.0

3.2.4.

b

10

Influence of saturation pressure

Fig. 10(a) and (b) show variations in the local boiling heat transfer coefficient hloc with vapor quality x at a given saturation pressure. The local boiling heat transfer coefficient tends to increase with increasing quality, as is the case whose plot is shown in Fig. 9. In addition, the boiling heat transfer coefficient decreases with increasing saturation pressure. This is the cause of the increase in the wall superheat with increasing saturation pressure. However, the local boiling heat transfer coefficient decreases with increasing saturation pressure at Psat ¼ 0.8 and 0.9 MPa at G ¼ 10.0 kg/m2 s, despite the wall superheat being almost constant. This result is the same as that obtained by Ishibashi and Nishikawa (1969): under a slug and annular flow, the boiling heat transfer coefficient decreases with increasing saturation pressure at a constant heat flux.

Local heat transfer coefficient hloc kW/(m2 . K)

Local heat transfer coefficient hloc kW/(m2 . K)

a

3.2.3.

0.4

0.6

0.8

1.0

qav = 15.4 kW/m2 qav = 20.0 kW/m2

9

qav = 24.5 kW/m2

8

7

6

5 0.0

0.2

0.4

0.6

Quality x [-]

Quality x [-]

G = 7.5 kg/m2s

G = 10.0 kg/m2s

Fig. 9 – Plot of local boiling heat transfer coefficient versus quality at various heat fluxes.

0.8

1.0

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international journal of refrigeration 33 (2010) 359–370

b

10

9

G = 7.5 kg/(m2 . s) qav = 20 kW/m2

Pabs = 0.70 MPa

Local heat transfer coefficient hloc kW/(m2 . K)

Local heat transfer coefficient hloc kW/(m2 . K)

a

Pabs = 0.80 MPa Pabs = 0.90 MPa

8

7

6

5

0.0

0.2

0.4

0.6

0.8

10

9

Pabs = 0.8 MPa Pabs = 0.9 MPa

8

7

6

5 0.0

1.0

Pabs = 0.7 MPa

G = 10.0 kg/(m2 . s) qav = 20 kW/m2

0.2

0.4

0.6

Quality x [-]

Quality x [-]

G = 7.5 kg/m2s

G = 10.0 kg/m2s

0.8

1.0

Fig. 10 – Variations in local boiling heat transfer coefficient with quality at various saturation pressures.

Fujita (1977) and Stephan and Abdelsalam (1980) are proposed correlation Eq. (7) for pure ammonia on pool boiling. The correlation of Arima et al. (2003) is derived by their pool boiling data. Kandlikar (1990) proposed correlation Eq. (8) for local boiling heat transfer on vertical tube using convection number Co. hloc ¼ Cl CoC2 þ C3 BoC4 Ffl hLZ

(a) Case convective region (at Co < 0.65); (10)

(b) Case nucleate boiling region (at Co > 0.65); C1 ¼ 0:6683; C2 ¼ 0:2; C3 ¼ 1058:0; C4 ¼ 0:7

(11)

Incidentally, fluid-dependent parameter Ffl for ammonia was not given by Kandlikar. Therefore, Zamfirescu and Chiriac, 2002 proposed Ffl ¼ 0.7 for ammonia. On the other hand, Shah (1982) proposed correlation Eq. (12) for local boiling heat transfer on vertical tube. hloc ¼j hLZ

(12)

The value of j is given by following Eqs. (13) to (17) with the value of convection number Co. jcb ¼ 1:8=Co0:8

(13)

(a) Case 0.1 < Co  1.0   jbs ¼ FBo0:5 exp 2:74Co0:1 (b) Case Co  0.1

F ¼ 14:7; F ¼ 15:43;

where Prl is the Prandtl number of the liquid phase. The parameters C1wC4 are as follows on different Co numbers;

(14)

(15)

when j > jbs and jcb, Thus if jbs > jcb, j ¼ jbs. If jcb > jbs, j ¼ jcb where, constant F in Eqs. (14) and (15) is defined by Eqs. (16) and (17).

(8)

where, hLZ is the heat transfer coefficient for a two-phase flow and for the flow of just the liquid phase in the channel. hLZ is expressed using the Dittus-Boelter equation as follows:  0:8 kl Gð1  xÞDh Pr0:4 (9) hLZ ¼ 0:023 l Dh ml

C1 ¼ 1:1360; C2 ¼ 0:9; C3 ¼ 667:2; C4 ¼ 0:7

  jbs ¼ FBo0:5 exp 2:47Co0:15

Bo > 11  104 Bo < 11  104

(16) (17)

The values of both correlations are plotted into Fig. 11. Fig. 11 shows that the predicted heat transfer coefficients by Shah (1982) and Kandlikar (1990) correlations are very smaller than present study data. It is found that both correlations cannot predict present data on vertical plate. It is considered that the reason for disagreement is the magnitude of the present mass fluxes is very smaller than that of assumed in the tube experiment. Generally the correlation in tube experiment is made on the conditions of a high mass flux. Since the effect of heat transfer by forced convection is quite large, the effect of nucleate boiling will be underestimated. On the other hand, in present study, since a mass flux is very small and the effect by nucleate boiling is large, the large heat transfer is shown compared with the correlation. Furthermore, the correlation of pool boiling heat transfer by Nishikawa and Fujita (1977) and Stephan and Abdelsalam (1980) are also very smaller than present study data. On the other hand, Arima’s correlation is more close to present study data. Therefore, it was found that the present data was able to be well expressed with the correlation of the pool boiling which derived from Arima’s et al.(2003) experiment.

3.3.

Nondimensional correlation

The nondimensional correlations for forced convective heat transfer on different refrigerants were proposed by many researchers (Mandrusiak and Carey, 1989; Wen and Ho, 2005; Kushibe et al., 2005). Eq. (18) is the general correlation for boiling heat transfer. The correlation is expressed using the Lockhart-Martinelli parameter X. In their studies, X was defined as Xtt where the liquid was turbulent and vapor was turbulent flow, which can be expressed as Eq. (19).

367

international journal of refrigeration 33 (2010) 359–370

G = 7.4 G = 10 G = 7.4 (Kandlikar) G = 10 (Kandlikar) G = 7.4 (Shah) G = 10 (Shah)

Local heat transfer coefficient hloc kW/(m2 . K)

10 qav = 15 kW/m2 Pabs = 0.70 MPa

8

Pool boiling (Stephan) Pool boiling (Nishikawa) Pool boiling (Arima)

6 Arima

4

Shah

2 Kandlikar

b Local heat transfer coefficient hloc kW/(m2 . K)

a

Stephan

0 0.0

0.2

0.4

0.6

0.8

2

qav = 20 kW/m Pabs = 0.70 MPa

8

Arima

Pool boiling (Stephan) Pool boiling (Nishikawa) Pool boiling (Arima)

6 Nishikawa

Shah

4

2 Kandlikar Stephan

0 0.0

1.0

G = 7.5 G = 10 G = 7.5 (Kandlikar) G = 10 (Kandlikar) G = 7.5 (Shah) G = 10 (Shah)

10

0.2

0.4

0.6

Quality x [-]

Quality x [-]

qav = 15 kW/m2

qav = 20 kW/m2

0.8

1.0

Fig. 11 – Comparisons of local boiling heat transfer coefficient between present and predicted data.

However, in the present study, both of the liquid and vapor phases are laminar conditions, because Rel ¼ 40 – 300 (Liquid phase Re number) and Reg ¼ 780 – 3600 (Vapor phase Re number). Then, X is defined as Xvv which is expressed as Eq. (20).  b hloc 1 ¼A (18) hLZ X where A and b are constants.  Xtt ¼

Xvv ¼

!0:1 0:9  0:5 rg ml ðturbulent-turbulentÞ rl mg

1x x

!0:5  0:5  0:5 rg 1x ml ðlaminar  laminarÞ rl mg x

(19)

(20)

The relationship between the ratio hloc/hLZ and X1 vv is shown in Fig. 12. It is found that hloc/hLZ increases with increasing 1 X1 vv . However, the gradient for Xvv < 2 differs from that for 1 Xvv > 2. This difference in gradients is considered to be due to the difference in flow patterns. We considered that in the case of low gradient region, the two-phase flow became slug flow, whereas in the case of high gradient region, the flow became annular flow when a thin liquid film covered the entire flow channel. The flow pattern in this study is examined in the next Section 3.4.

The solid line in Fig. 12 shows the correlation obtained in the present study. This correlation is obtained by the leastsquares method using all data obtained here. 1:08  hloc 1 ¼ 16:4 (21) hLZ Xvv The empirical correlation expressed in Eq. (21) can predict experimental results within 25% accuracy for X1 vv > 2. On the other hand, the measured local heat transfer coefficients are predicted using the correlation Eq. (21). Fig. 13 shows that the comparison of predicted by Eq. (21) against measured the ratio hloc/hLZ. It is found that almost data can be predicted by Eq. (21) within 25% accuracy. However, in case of hloc/hLZ < 30 of G ¼ 7.5, the value is larger than 25%.The range of hloc/hLZ < 30 is indicated X1 vv < 1.7 which is low vapor quality. Then, the correlation cannot predict the measured data.

3.4.

Visualization

Visualization of the boiling phenomena of ammonia is carried out under various mass fluxes, heat fluxes, saturation pressures, and vapor qualities. 100

+25%

G=7.5 G=10 Experimental hloc /hLZ [-]

80

-25% 60

40

20

0 0

20

40

60

80

100

Predicted hloc /hLZ [-]

Fig. 12 – hloc/hLZ as a function of 1/Xvv.

Fig. 13 – Comparison of predicted against experimental hloc/hLZ.

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Fig. 14 – Boiling flow patterns of ammonia at two different vapor qualities (G [ 10 kg/m2 s, Psat [ 0.7 MPa, qav [ 20 kW/m2)

3.4.1.

Effect of vapor quality

Fig. 14(a) and (b) show visualization results of boiling of ammonia at various vapor qualities and constant mass flux, heat flux, and saturation pressure. The vapor quality x considered for visualization whose results are shown in Fig. 14(a) and (b) is determined by a polynomial interpolation of the vapor quality values measured in the flow direction. Fig. 14(a) shows that some small bubbles appear on the plate surface at x ¼ 0.28. It is found that the flow pattern consists of bubble flow. On the other hand, Fig. 14(b) shows that instead of bubbles, a liquid film covers the entire visualized area. It is considered that this flow pattern is annular flow corresponding to flow inside the tube. In section 3.3, we stated that in the case of X1 vv < 2 and 1 Xvv > 2, the flow pattern becomes slug flow and annular flow, respectively. Since the visualization results in shown Fig. 14(a) (x ¼ 0.28 and Xvv ¼ 1.68) demonstrate that the flow is a bubble flow and those shown in Fig. 14(b) (x ¼ 0.63 and Xvv ¼ 3.51) demonstrate that the flow is liquid flow, we can conclude that the classification of the flow pattern according to Xvv is accurate

3.4.2.

Effect of mass flux

Fig. 15(a) and (b) show visualization results at various mass fluxes at a constant vapor quality, heat flux, and saturation pressure.

In the case of a low mass flux (Fig. 15(a)), some intermediate-size bubbles are observed over the entire area. On the other hand, in the case of a high mass flux (Fig. 15(b)), the liquid film that covers the entire visualized area is observed, similar to the results shown in Fig. 15(b). The flow patterns shown in Figs. 15(a) and (b) are different; however, the boiling heat transfer coefficient for these patterns is almost the same. Therefore, we conclude that the flow pattern does not contribute to boiling heat transfer. As mentioned in Section 3.2, forced convection is dominant in the boiling heat transfer under these conditions. This behavior is also confirmed in the visualization experiment.

3.5.

Flow pattern map

In order to consider the flow pattern obtained by visualization, comparison with the existing flow map was performed. The flow pattern maps for horizontal flow were proposed in some papers. However, the map for vertical upflow in tube has at least the diagram of Hewitt–Roberts map (Hewitt and Roberts, 1969) and there is no map for vertical upflow in plate. Therefore, the all data were plotted into the Hewitt–Roberts map as shown in Fig. 16. The map shows that plots of superficial liquid momentum flux rlj2l versus superficial vapor momentum flux

Fig. 15 – Boiling flow patterns at different mass fluxes (Psat [ 0.8 MPa, qav [ 20 kW/m2, x [ 0.4)

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(5) The results of visualization confirm that the relation between the flow pattern and Xvv is correct. Moreover, the relation between boiling heat transfer and the flow pattern clearly indicates that boiling heat transfer is dominated by forced convection.

Superficial vapor momentum flux g j g2 [kg/ms2]

105 104

G=7.5 G=10 Annular

103

369

Whispy annular

102 Bubbly

100 10

Acknowledgement

Churn

101

We thank the Ministry of Education, Culture, Sports, Science and Technology, Japan, for financial support in the form of a grant under their 21st Century COE Program ‘‘Advanced Science and Technology for Utilization of Ocean Energy.’’

Bubbly-slug

-1

10-3 10-2 10-1 100 101 102 103 104 105 106 Superficial liquid momentum flux l jl2 [kg/ms2]

references

Fig. 16 – Hewitt–Roberts flow pattern map (Hewitt and Roberts, 1969) rgj2g. Where, superficial liquid velocity jl and vapor velocity jg are defined by as follows; jl ¼ Gð1  xÞ=rl

(22)

jg ¼ Gx=rg

(23)

Fig. 14(a) and (b) show that the flow patterns were bubble and annular flow, respectively. However, Fig. 16 shows that all data are in churn flow, because both momentum fluxes of present data are very lower than that of general study in tube. It is found that the vertical flow on plate could not be expressed on this map for vertical tube. In the future, it is necessary to examine the map of the vertical plate flow.

4.

Conclusion

The experimental results of the boiling heat transfer coefficients of pure ammonia under forced convective boiling in a vertical flat plate are summarized as follows. (1) The boiling curve in the case of a forced convective boiling heat transfer shows that in such a heat transfer, the surface wall superheat is 8 K less than that for a pool boiling heat transfer. Therefore, it is concluded that in the boiling heat transfer under the present experimental conditions, forced convection is dominant. (2) The forced convective boiling heat transfer coefficient of ammonia increases with increasing vapor quality x at a constant mass flux, saturation pressure, and average heat flux. However, in the case of x > 0.7, a dry-out occurs occasionally, and therefore, boiling heat transfer decreases. (3) An increase in mass flux has almost no effect on boiling heat transfer. On the other hand, an increase in the heat flux and saturation pressure cause a decrease in boiling heat transfer. (4) An empirical correlation for the forced convective boiling heat transfer coefficient is derived using the Lockhart-Martinelli parameter. The boiling heat transfer coefficient estimated by this correlation in the range of Xvv > 2 is in good agreement with the measured boiling heat transfer coefficient.

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