Dispersed flow film boiling in vertical narrow annular gaps

Applied Thermal Engineering 29 (2009) 1146–1152

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Dispersed flow film boiling in vertical narrow annular gaps Zhi-Hui Li a,*, Yu Wang b, Dou-Nan Jia b, Pei-Xue Jiang a a b

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

a r t i c l e

i n f o

Article history: Received 9 July 2007 Accepted 6 June 2008 Available online 17 June 2008 Keywords: Dispersed flow Low mass velocities Wall temperature Gap size

a b s t r a c t Dispersed flow film boiling heat transfer in vertical narrow annular gaps with gap sizes of 1.0, 1.5 and 2.0 mm was experimentally investigated with de-ionized water as the working fluid at low mass velocities. Comparisons of the experimental data with established correlations show that the correlations are not accurate for small gaps. The influences of the heating mode (only one tube heating or both tubes heated), the gap size and the tube diameter were analyzed. The data was correlated in the form of the Groeneveld equation with a modified wall temperature factor as use in the Polomik correlation and a modified gap size factor as use in the Yun and Muthu correlation. A new correlation was developed for dispersed flow film boiling heat transfer based on the experimental data for 1.0–2.0 mm gaps. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction Convective heat transfer across narrow gaps has become a widely used heat transfer techniques in recent years because of the small temperature differences and compact heat transfer surfaces. In addition, with smooth heat transfer surfaces, the flushing by the high velocity fluid reduces impurity deposition so that the heat transfer surface is not contaminated and the heat transfer is not reduced. The two classes of CHF mechanisms are departure from nucleate (DNB) and dry-out (DO). Dry-out is also called burnout or departure from forced convective boiling in flow boiling. At dryout location, the liquid film disappears and no liquid is in contact with the wall, consequently the heat transfer rate drops dramatically. The heat transfer from dry-out location to the location where vapor quality is less than 1.0 is called dispersed flow film boiling heat transfer (see Fig. 1). Dispersed flow film boiling heat transfer occurs in many engineering applications, such as once-through steam generators, spray coolers, nuclear reactors, refrigeration systems and engineering metallurgy processes. However, despite there many applications, there are few studies of dispersed flow heat transfer in narrow gaps, so more research is needed. There have been many studies of the heat transfer and dispersed flow film boiling in small gaps with numerous empirical correlations and mechanistic models developed. Aoki [1] studied boiling in narrow annular gaps with gap sizes of 0.2, 0.3, 0.4, 0.5, 1.0 and 1.5 mm with de-ionized water at atmospheric pressure. * Corresponding author. E-mail address: [email protected] (Z.-H. Li). 1359-4311/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2008.06.008

The test section had both closed and open bottoms of the annular gap. His experimental results showed that the heat transfer coefficient increased with decreasing gap size near the entrance of the open bottom annular gap, but was basically constant at the heating lengths of 40–100 mm. He also found that the heat transfer coefficient was not influenced by the gap size and the heating length with the closed bottom annular gap. Chernobylskii [2] studied the boiling heat transfer in a narrow annular gap of 1.25 mm in width and showed that the heat transfer coefficient was larger than for a common tube. Orozco [3] studied forced convection boiling in a small rectangle channel. As the flow velocity increased, the nucleate boiling was not influenced by the velocity but the heat transfer coefficient increased as the gap size decreased. Lee and Kim [4] studied dispersed flow film boiling in downward flow in which the film thickness increased with increasing length so the heat transfer coefficient decreased. Chen et al. [5] used a directly heated hot point technique with a measuring technique that gave better results than Goeneveld’s experiments. They did many experiments studying dispersed flow film boiling and analyzed the influence of many parameters on the film boiling heat transfer. Anglart and Persson [6] studied dispersed flow film boiling in a 10  22.1 mm annular test section with spacers. Their experimental results show a very strong influence of the spacers on the dispersed flow heat transfer. Jayanti and Valette [7] developed a model for dispersed film boiling at high pressures using a nondimensional three-fluid model for P/Per > 0.3. Their correlations were validated with literature data. For the flow and heat transfer in narrow gaps, when the gap size decreases below some limit, flow and heat transfer correlations for larger tubes will not be appropriate for the narrow gap size. However, the size limits between large tubes and micro scale sizes is

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Nomenclature A De Dh Nu k Pr Re h Ai Ao qi qo qav Hg Hl Hn x

flow area (m2) hydraulic equivalent diameter (m) heated equivalent diameter (m) Nusselt number (dimensionless) thermal conductivity (W/m °C) Prandtl number (dimensionless) Reynolds number (dimensionless) heat transfer coefficient (W/m2 °C) heated area of inside tube (m2) heated area of outside tube (m2) heat flux of inside tube (W/m2) heat flux of outside tube (W/m2) heat flux of average tube (W/m2) saturated gas enthalpy saturated liquid enthalpy cross sectional fluid enthalpy vapor quality (dimensionless)

l h

dynamic viscosity (N s/m2) correction factor

Subscripts f liquid g gas b both tubes o outside tube i inside tube w wall ii inner wall of inside tube oo outer wall of outside tube oi inner wall of outside tube io outer wall of inside tube s saturation i,a only inside tube heating o,a only outside tube heating av average (both tubes heated)

Greek symbols density (kg/m3)

q

still not well defined. Most previous works have focused on particular physical phenomena with the flow and heat transfer mechanisms, the size limits being uncertain. Also, these studies have mainly considered rectangular channels, circular channels, triangular tubes and rod bundles with high flow rates. Thus, there are well-developed theories on the heat transfer characteristic of the heat transfer in narrow annular gaps, especially for boiling heat transfer. Thus, additional research is needed on dispersed flow film boiling heat transfer in narrow annular gaps. This paper presents data for various gap sizes, tube diameters, and heating modes. Finally, an accurate, convenient heat transfer correlation is then presented to predict dispersed flow film boiling heat transfer rate in narrow annular gaps. 2. Experimental facility 2.1. Experimental system and test section The experimental system is shown schematically in Fig. 2. The working fluid, de-ionized water (specific resistively greater than 1.25 MX/cm) was driven by a pump through the S-type pre-heaters, the flow metering section and the U-type pre-heater in which the fluid temperature or vapor quality was raised to the desired level for each test. The water-vapor two phase flow then flowed through the vertical test section and the condenser and finally returned to the pump. The maximum system pressure of 16.0 MPa was controlled by the nitrogen pressurization system. The flow rate was regulated and maintained by a throttling valve and a needle regulator valve. The test section is shown in Fig. 3. The test section was composed of two straight stainless steel tubes (outside and inside tubes) with different diameters. The test section was 740 mm in length with an inner diameter of the outside tube of 10 mm, Doi, and outer diameters of the inside tube, Dio, of 6, 7 or 8 mm. The annular gap sizes were then 1.0, 1.5 and 2.0 mm. The inside and outside tubes of the annular channel were directly heated by AC current. Therefore, the tubes must be concentric and not contact each other. The two tubes were held in position by two sets of ceramic rods arranged near the inlet and outlet as shown in Fig. 4. Each set consisted of three small ceramic

Fig. 1. Region of dispersed film boiling.

rods, about 2.0 mm in diameter and 0.95 mm (for the 1.0 mm gap), 1.45 mm (for the 1.5 mm gap), and 1.95 mm (for the 2.0 mm gap) in length arranged at 120° intervals along the circumference of the inside tube in the upper and lower parts of the test section near the inlet and outlet sections. To reduce heat losses from the test section, the whole test section was first wrapped in a 120 mm thick layer of asbestos with a wire heater wound outside of this insulation layer and then with a 50 mm thick layer of asbestos outside of the wire heater. Two sets of thermocouples were arranged at different radial locations inside the first layer of asbestos. The heat loss was zero when the two temperatures were essentially equal. 2.2. Parameters measurement The temperatures were measured at 15 cross sections along the flow direction 25 mm apart as shown in Fig. 4. The outer wall tem-

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Z.-H. Li et al. / Applied Thermal Engineering 29 (2009) 1146–1152 P

P

P

P

P

Fig. 2. Schematic diagram of experimental system.

Fig. 5. Thermocouple locations in a horizontal cross section.

Fig. 3. Test section.

vertical levels as the thermocouples on the outer wall of the outside tube. Finally, the inside tube was filled with BN powder to form an adiabatic cavity. The temperatures measured by the thermocouples bundles were assumed to be equal to the inner wall temperatures of the inside tube after the experimental conditions had reached steady state. The test section inlet and outlet fluid temperatures were measured by K-type thermocouples. The pressure was measured by piezo capacitive type transducers. The mass flow rate was measured by low flow rate orifice or venture meters. All experimental data was acquired and recorded by a data acquisition system. 2.3. Experimental condition The ranges of experiment parameters are listed in Table 1. 2.4. Experimental procedure First, the system pressure and mass flow rate were adjusted to the desired values. Then, the heat input to the S-type and U-type

Fig. 4. Schematic of supports to hold the tubes in position.

peratures of the outside tube were measured by U 0.5 mm nickel– chromium and nickel–silicon thermocouples spot-welded on the outer wall of the outside tube. Four thermocouples were arranged symmetrically on each horizontal cross section as shown in Fig. 5. The inner wall temperatures of the inside tube were measured by 15 thermocouples (U 0.5 mm) wrapped in thin flexible mica sheets to electrically insulate them from the inside tube. Then, the thermocouple bundles were inserted into the inside tube at the same

Table 1 Experiment parameters Parameter

Variation range

Annular gap (mm) Pressure (MPa) Mass velocity (kg/m2 s) Outside tube thermal flux (kW/m2) Inside tube themal flux (kW/m2) Vapor quality

1.0, 1.5, 2.0 1.38–5.9 45.32–84.20 4.07–55.3 3.90–56.2 0.6–0.96

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pre-heaters was increased to increase the fluid temperature and quality so that saturated boiling existed before entering the test section. Finally, the heat fluxes on the inside and outside tubes were adjusted separately to control the wall temperature. Dryout occurred when the wall temperature of the inside or outside tube increased abruptly at some location along the test section. The region downstream of the dry-out point to the location where quality was less than 1.0 was the region of interest where dispersed flow film boiling heat transfer occurred. All the measured data was recorded after the system reached steady state at the chosen system pressure and mass flow rate. Then, the heat fluxes were varied at a given inlet fluid temperature. 3. Data analysis and results When only the inside or outside tube was heated, the heat transfer coefficient for each tube was calculated as:

hi;a ¼ qi =ðt io  t f Þ;

ho;a ¼ qo =ðtoi  t f Þ

xn ¼ ðHn  Hl Þ=ðHg  Hl Þ

Where Hn is the local fluid enthalpy obtained from the inlet fluid enthalpy and the local heat input. In the data reduction, the quality x is the average quality over all cross sections in the dispersed flow region. There are numerous empirical correlations for dispersed flow heat transfer, such as Groeneveld [8], Polomik [9], and Miropolskiy [10] which assume thermodynamic equilibrium with no temperature difference between the bulk vapor and the droplets. These correlations used experimental data obtained when only the inside or the outside tube was heated, so these are simple to use but have a limited range of validity. There are few results in the open literatures when both tubes are heated. In this study, the Groeneveld correlation [8]:

a

120

ð1Þ 100

The Nusselt number is then:

hi;a  De ; k

Nuo;a ¼

ho;a  De k

De ¼

4  p4 ðD2oi  D2io Þ ¼ Doi  Dio pðDoi  Dio Þ

20

ð3Þ

qo ¼ Q o =Ao

60 40

0 500

The heat fluxes on the inside tube and outside tube surfaces are calculated from their respective heat inputs:

qi ¼ Q i =Ai ;

b

100

Where the average heat flux, qav = (qiAi + qoAo)/(Ai + Ao). The average Nusselt number is then:

60

Nug

80

ð5Þ

40

The local inner wall temperature of the inside tube, tii,x, and the local outer wall temperature of the outside tube, too,x, were directly measured by the thermocouples. However, the experimental data reduction needed the local inner wall temperature of the outside tube, toi,x, and the local outer wall temperature of the inside tube, tio,x. toi,x and tio,x were calculated from the measured tii,x and too,x assuming one dimensional steady thermal conduction with uniform volumetric heat generation in the tube as:

20

t io;x

0 500

800

900

1000

Only outside tube heating (1.0 mm gap) Experimental data ( 33 points) Experimental data linear fit: Nug=0.0327X Groeneveld correlation, Nug=0.052X Mean error : 21%

600

700

800

900

1000

X

c

120 100 80

Both tubes heated (1.0 mm gap) Experimental data ( 51 points) Experimental data linear fit: Nug=0.0285X Groeneveld correlation: Nug=0.052X Mean error : 31%

ð6Þ

Nug

t oi;x

" #  2 qo Doi Doo 2 Doo Doi ð ¼ too;x  þ 1 Þ 2 ln kx ðD2oo  D2oi Þ 2 Doi Doo " #  2  2 qi Dio Dii Dio Dio ¼ tii;x  2 ln þ 1 kx ðD2io  D2ii Þ 2 Dii Dii

700

120

ð4Þ

Nuii ¼ ðhav  De Þ=k

600

X

When the inside and outside tubes were both heated, the average heat transfer coefficient was determined by

hav ¼ qav =ððtio þ t oi Þ=2  t f Þ

Nug=0.052X

Mean error: 23%

ð2Þ

Where De ¼ 4A is the hydraulic diameter, A is the cross sectional U flow area and U is the wetted perimeter

Thus

Only inside tube heating (1.0 mm gap) Experimental data ( 42 points) Experimental data linear fit: Nug=0.0236X Groeneveld Correlation:

80

Nug

Nui;a ¼

ð8Þ

ð7Þ

60 40 20

Where too and tii are the averages of all the wall temperatures measured in the dispersed film boiling region. In experiments, the fluid (mainly vapor) was not in thermodynamic equilibrium but was superheated and its temperature, tf, was not measured directly in the tests. Therefore, tf was assumed to be the saturation temperature, ts, at the given pressure. The vapor quality at each cross section was calculated as:

0 500

600

700

800

900

1000

X Fig. 6. Comparison of experimental data with the Groeneveld correlation for the 1.0 mm gap (a) only inside tube heating (b) only outside tube heating (c) both tubes heated.

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  0:688 qg 1:06 Nu ¼ 0:052 Reg x þ ð1  xÞ ðPrg Þ1:26 w Y

qf

Y ¼ 1  0:1

qf 1 qg

a

!0:4 ð1  xÞ0:4

120 100

ð9Þ

80

0:3 Nu ¼ 0:00115Re0:9 g Prg

 0:15 1:8T w þ 32 1 1:8T s þ 32

ð10Þ

Nug

and the Polomik correlation [9]:

20 0 2500

b

As can been seen in Fig. 6, the original correlation coefficient of 0.052 is larger than the correlation coefficient for the experimental data. The smallest coefficient for the 1.0 mm gap was 0.0236 with a mean error of 23% for only inside tube heating because the Groeneveld correlation is mainly for high mass flux conditions. At low mass fluxes and far from the dry-out location where the droplets are larger in diameter, the interfacial heat transfer is inefficient so the vapor is highly superheated and the effect of the thermodynamic non-equilibrium is more obvious. Also, the estimated wall temperature with Groeneveld correlation may be too low, which would lead to somewhat bigger Nusselt numbers. Thus, the Groeneveld correlation can not accurately predict the experimental data at low mass flow rates. Similar results were obtained for the 1.5 and 2.0 mm gaps as shown in Table 2. Fig. 7 compares the experimental data for the various heating modes with the Polomik correlation for a 1.0 mm annular gap. 0:3 Here, the ordinate is Nug and the abscissa is Re0:9 g Prg  0:15 1:8T w þ32 1 . The mean error which is related to the linear 1:8T s þ32

fit of the data is also given in the figure. The results show that the original correlation coefficient of 0.00115 is smaller than the correlation coefficients for the experimental data. The smallest coefficient for the 1.0 mm gap is 0.0046 with a mean error of 17% for only inside tube heating. Unlike the Groeneveld correlation, the Polomik correlation induced a factor for the ratio of the wall temperature and the saturation temperature, which reduces the mean error. Similar results were also obtained for the 1.5 and 2.0 mm gaps. However, the Polomik correlation does not include the effect of the vapor quality, which

Table 2 Correlation coefficients for Groeneveld correlation Gap size (mm)

Groeneveld coefficient

Obtained coefficient (mean error) Inside tube

Outside tube

Both tubes

1.0 1.5 2.0

0.052 0.052 0.052

0.0236 (23%) 0.0182 (25%) 0.0152 (21%)

0.0327 (25%) 0.0188 (25%) 0.0169 (21%)

0.0285 (31%) 0.0165 (30%) 0.015 (24%)

Nug

ð11Þ

n

80

4000

4500

5000

Only outside tube heating (1.0 mm gap) Experimental data ( 33 points) :Experimental data linear fit: Nug=0.0060X :Polomik correlation: Nu g=0.00115X Mean error : 18%

60 40 20 0 2800

3200

3600

4000

4400

4800

X

c

120 100 80

Both tubes heated (1.0 mm gap) Experimental data ( 51 points) Experimental data linear fit: Nug=0.0052X Polomik correlation:

Nug=0.00115X

Mean error: 24%

Nug

Nug; exp

3500

120 100

the figure is related to the linear fit of the data shown in the figure where:

n  P Nug; exp Nug;cal

3000

X

f

Mean error ¼

60 40

are used for data comparison and analysis. The experiments used three heating modes with only the inside tube heating, only the outside tube heating, and both the inside and outside tubes simultaneously heated at the same or different heat fluxes with narrow annular gap sizes of 1.0, 1.5 and 2.0 mm. The experimental data for the various heating modes is compared with the Groeneveld correlation for the 1.0 mm gap in Fig. 6 where the ordinate represents Nug and the abscissa repren h io0:688 q 1:06 Pr1:26 . The mean error given in sents Reg x þ qg ð1  xÞ w Y

1

Only inside tube heating (1.0 mm gap) Experimental data ( 42 points) Experimental data linear fit: Nug=0.0046X Polomik correlation: Nu g=0.00115X Mean error: 17%

60 40 20 0 2500

3000

3500

4000

4500

5000

X Fig. 7. Comparison of experimental data with the Polomik correlation for the 1.0 mm gap only inside tube heating (b) only outside tube heating (c) both tubes heated.

would lead to large deviations from the experiment data as summarized in Table 3. In dispersed flow film boiling heat transfer, the real wall temperature is a very important parameter which results from the heat transfer between the inside tube and the outside tube, the heat transfer between superheated vapor and the droplets, and the radiation heat transfer between the droplets and the heated walls. As can be seen from Tables 2 and 3, the correlation coefficients for only outside tube heating are larger than for only inside tube heating for all three gap sizes. The coefficients for both tubes heated is smaller than only inside tube heating and only outside tube heating for the 1.5 and 2.0 mm gaps, and falls between only inside heating and only outside tube heating for the 1.0 mm gap. This is probably due to the average heat fluxes for both tubes heated for the 1.0 mm gap are different from the heat fluxes for

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Z.-H. Li et al. / Applied Thermal Engineering 29 (2009) 1146–1152 Table 3 Correlation coefficients for Polomik correlation Polomik Coefficient

1.0 1.5 2.0

0.00115 0.00115 0.00115

1.0 mm experimental data (126 points) 1.5 mm experimental data (129 points) 2.0 mm experimental data (235 points)

40

Obtained coefficient (mean error) Inside tube

Outside tube

Both tubes

0.0046 (17%) 0.00385 (17%) 0.00358 (19%)

0.006 (18%) 0.0039 (16%) 0.00384 (18%)

0.0052 (24%) 0.0033 (23%) 0.00328 (22%)

+18%

35 -18%

30

Nue

Gap size (mm)

45

25 20 15

only single side heating in our experiment and basically equal to the heat fluxes for only single side heating for the 1.5 and 2.0 mm gap sizes which result in the problem of the fitted equation coefficient. When the tubes are heated, the heat fluxes of the inside tube affect the inside wall temperature of the outside tube and the heat fluxes of the outside tube affect the outside wall temperature of the inside tube. The average wall temperatures for both tubes heating are larger than that of only single tube heating when the average heat fluxes of both sides are basically equal to the heat fluxes of single side which result in the reduced heat transfer for the 1.5 and 2.0 mm gap sizes. Thus, the heating mode has a more significant effect on dispersed flow film boiling heat transfer in annular channels than in round tubes. When only the inside or outside tube is heated, some of the droplets deposit on the unheated wall, so there is less liquid on the heated wall and dry-out occurs easier. Also the data showed that the dry-out location on the inside and outside tubes for the similar conditions were obviously different when both sides of the channel were heated. The larger deposition rate and the thicker liquid film on the outside tube caused by larger shear stresses than on the inside tube resulted in larger heat transfer coefficients on the outside tube than on the inside tube. The critical heat flux on the outside tube was also larger than on the inside tube for dry-out at the same axial position. The heated equivalent diameter, Dh, was re-defined to study the influence of heating mode on the heat transfer. The thermal equilibrium correlation for the entire annular channel was defined as:

T out

qF ¼ T in þ WC p

ð12Þ

where qF = p(Doiqo + Dioqi)L, W ¼ GpðD2oi  D2io Þ=4

q ¼ qo þ qi Rearranging Eq. (12) yields:

pðDoi qo þ Dio qi ÞL pDh ðqo þ qi ÞL ¼ GpðD2oi  D2io Þ=4 GpD2h =4

ð13Þ

Therefore, the heated equivalent diameter correlation for heating of both tubes is:

Dh;b ¼

ðD2oi

D2io Þ

 ðq þ qi Þ Doi qo þ Dio qi o

ð14Þ

Thus, the heated equivalent diameter correlation for only inside tube heating is:

Dh;i ¼

ðD2oi  D2io Þ Dio

ð15Þ

and the heated equivalent diameter correlation for only outside tube heating is:

Dh;o ¼

ðD2oi  D2io Þ Doi

ð16Þ

As can be seen from Tables 2 and 3, the gap size has a strong effect on the dispersed flow film boiling. As the gap size decreases, the

10 5 5

10

15

20

25

30

35

40

45

Nu p Fig. 8. Comparison of Nup from Eq. (17) with experimental data.

heat transfer increases for all three types of heating as the vapor velocity increases in channel. The Yun and Muthu [11] correlation accounts for the influence of gap size on the heat transfer using io which was also used here to the dimensionless factor h ¼ ddoi d þd oi

io

introduced to describe the effect of gap size and the inside and outside tube diameters on the heat transfer. The factors Tw/Ts and h were introduced into the Groeneveld correlation to obtain a more comprehensive mode. The experimental data for three gap sizes and all three heating modes was then fit to obtain a new correlation for dispersed flow film boiling heat transfer:

Nu ¼

h  Dh kg

¼ 2:14  hð4:065h0:2624Þ fReg ½x þ qg f1  xÞ=qf g1:27 Pr0:909 Y 1:06 ðT w =T s  1Þ0:67

ð17Þ

Where Dh is calculated according to Eqs. (14)–(16). Fig. 8 compares the experimental Nusselt number, Nue, with the Nusselt number, Nup, predicted by Eq. (17). The abscissa represents the predicted Nup while the ordinate represents the experimental Nue. The range of the experimental parameters is: P = 1.38– 5.90 MPa, G = 45.32–84.20 kg/m2 s and x = 0.6–0.96. Within this range, the predicted values show good agreement with the experimental data with an average relative error of ±19.2%. 4. Conclusions

(1) Dispersed flow film boiling heat transfer in narrow annular gaps with gap sizes of 1.0, 1.5 and 2.0 mm was investigated at low mass flow rate. Comparison of the experimental data with empirical correlation such as those of Groeneveld and Polomik showed that none of the correlations gives good agreement with the experimental data. (2) The heating mode and the gap size were both found to influence the dispersed flow film boiling heat transfer. (3) At low mass flow rate, the droplets are larger in diameter, hence, the interfacial heat transfer is less efficient and the vapor is highly superheated. Thermodynamic non-equilibrium then becomes more significant, which makes the dispersed flow heat transfer more difficult to accurately predict. (4) The Groeneveld correlation was modified to include a factor for the ratio of the wall temperature to the saturation temperature, Tw/Ts, used in the Polomik correlation and the facio from the Yun and Muthu correlation to include the tor DDoi D þD oi

io

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effect of gap size and the inside and outside tube diameters. A new correlation was then presented based on the 1.0– 2.0 mm gap size data at low velocities for dispersed flow film boiling heat transfer.

References [1] S. Aoki, Experimental study on the boiling phenomena with in a narrow gap, Int. J. Heat Mass Tran. 25 (1982) 985–990. [2] L.I. Chernobylskii, Heat exchange during boiling of liquid in narrow annular tubes, Soviet Tech. Phys. 3 (1956) 1244–1249. [3] J.A. Orozco, Study of mixed convection boiling heat transfer in narrow gaps, 28th national heat transfer conference and exhibition, ASME HTD 206 (2) (1992) 81–85.

[4] Y. Lee, K.H. Kim, Inverted annular flow boiling, Int. J. Multiphase Flow 13 (1987) 345–355. [5] J.C. Chen, F.T. Ozkaynak, R.K. Sundaram, Vapor heat transfer in post CHF region including the effect of thermodynamic non equilibrium, Nucl. Eng. Des. 51 (1979) 143–155. [6] H. Anglart, P. Persson, Experimental investigation of post-dryout heat transfer in annulus with spacers, Int. J. Multiphase Flow 33 (2007) 809–821. [7] S. Jayanti, M. Valette, Prediction of dryout and post dryout heat transfer at high pressures using a one-dimensional three-fluid model, Int. J. Heat Mass Tran. 47 (2004) 4895–4910. [8] D.C. Groeneveld, Post Dryout Heat Transfer at Reactor Operating Conditions, AECL Report, AECL-4513, 1973. [9] E.F. Polomik, Transition Boiling Heat Transfer Program Final Summary Report on Program for February/63–October/67, 1967, GEAP-5563. [10] Z.L. Miropolskiy, Heat transfer in film boiling of steam water mixture in steam generating tubes, Teploenerg 10 (5) (1963) 49–53. [11] C. Yun, S. Muthu, Convective heat transfer in vertical asymmetrically heated narrow channels, J. Heat Transf. 124 (2002) 1019–1025.