Effects of the outflow area on saturated pool boiling in a vertical annulus

International Journal of Heat and Mass Transfer 55 (2012) 7341–7345

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Technical Note

Effects of the outflow area on saturated pool boiling in a vertical annulus Myeong-Gie Kang ⇑ Department of Mechanical Engineering Education, Andong National University, 388 Songchun-dong, Andong-city, Kyungbuk 760-749, South Korea

a r t i c l e

i n f o

Article history: Received 12 March 2012 Received in revised form 18 June 2012 Accepted 20 June 2012 Available online 13 July 2012 Keywords: Heat transfer Pool boiling Annulus Vertical tube Outflow area

a b s t r a c t The outflow area has been varied to investigate its effect on pool boiling heat transfer in a vertical annular space. For the test, a smooth stainless steel tube of 19.1 mm diameter and the water at atmospheric pressure have been used. The ratio of areas of the outflow and the gap space has been changed from 0.04 to 1.13. As the area ratio decreases a clear change in heat transfer is observed. Throughout the area ratios the heat transfer coefficient is increased or decreased depending on the main mechanisms of heat transfer. The major cause for the tendency is attributed to the formation of a lumped bubble around the upper regions of the annulus and the reduced flow rate. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction For the past several decades the mechanisms of pool boiling heat transfer have been studied extensively to design efficient heat transfer devices or to assure the integrity of safety related systems [1,2]. Although many researchers have investigated effects of heater geometries on pool boiling heat transfer by assuming several different geometric parameters, knowledge on pool boiling heat transfer in a confined space is still quite limited [3]. It is well known from the literature that the confined nucleate boiling is an effective technique to enhance heat transfer [4,5]. Improved heat transfer characteristics with the restriction might be attributed to an increase in the heat transfer coefficient due to vaporization from the thin liquid film on the heating surface or increased bubble activity [5,6]. Since the major heat transfer resistance is the heat conduction across the liquid film, the reduced film thickness increases the heat transfer coefficient [6]. According to Cornwell and Houston, the bubbles sliding on the heated surface agitate environmental liquid [7]. In a confined space a kind of pulsating flow due to the bubbles is created and, as a result very active liquid agitation is generated [8]. The increase in the intensity of liquid agitation results in heat transfer enhancement. Sometimes a deterioration of heat transfer appears at high heat fluxes for confined than for unrestricted boiling [6,9]. The cause of the deterioration is suggested as active bubble coalescence at the upper part of the annulus [8]. When too many coalesced bubbles are generated at high heat fluxes, the heating surface is almost ⇑ Tel.: +82 54 820 5483; fax: +82 54 823 1766. E-mail address: [email protected] 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.06.057

covered with a single mass of vapor [5]. If the outflow of bubbles were interrupted, the bubbles coming from the lower regions would coalesce into much bigger bubbles while fluctuating up and down in the annular space [3]. Recently, Kang [3] published inflow effects on pool boiling heat transfer in a vertical annulus with closed bottoms. Kang [3] regulated the gap size at the upper regions of the annulus and identified that effects of the reduced gaps on heat transfer become evident as the heat flux increases. This kind of geometry is found in an in-pile test section [10] that is important to identify nuclear fuel irradiation behavior at the operating condition of a commercial power plant. Since the characteristics of pool boiling due to the reduced flow area in the upper regions of a vertical annulus is very important for the analysis and design of a nuclear power plants, more detailed analysis is necessary. Therefore, effects of the outflow area on nucleate pool boiling heat transfer are investigated in this study. Up to the author’s knowledge, no previous results concerning to this effect have been published yet. The results of this study could provide a clue to the thermal design of this type of facility.

2. Experiments A schematic view of the present experimental apparatus and a test section is shown in Fig. 1. The water tank (Fig. 1(a)) is made of stainless steel and has a rectangular cross section (950  1300 mm) and a height of 1400 mm. The sizes of the inner tank are 800  1000  1100 mm (depth  width  height). Four auxiliary heaters (5 kW/heater) are installed at the space between the inside and the outside tank bottoms. The heat exchanging tube is a resistance heater (Fig. 1(b)) made of a very smooth stainless

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M.-G. Kang / International Journal of Heat and Mass Transfer 55 (2012) 7341–7345

Nomenclature cross sectional area of the annular space, m2 outflow area, m2 area ratio (=Aout/Agap) data acquisition error, °C diameter of the heating tube, m inside diameter of the glass tube, m inside diameter of the outflow restrictor, m boiling heat transfer coefficient, W/m2 °C supplied current, A heated tube length, m

Agap Aout Ar AT D Di d hb I L

PT q00 s Tsat TW V DTsat

precision limit, °C heat flux, W/m2 gap size (=(Di  D)/2), m saturation temperature, °C tube wall temperature, °C supplied voltage, V tube wall superheat (=TW  Tsat), °C

Unit: mm Outer tank

unit: mm

Inner tank

1300

0

Spacer

50

95

d

Outflow restrictor

Tc1

Water supply line

100

Resistance wire Wire supporter Tc2

100

Thermocouple Tc3

100

T/C lines

L=500

1400

Power supply

600

Flow holes

Insulation powder

Test section Glass tube

Tc4

Tc5

30

50

Heaters

Inflow holes

30

100

D=19.1

Water drain Reinforced glass

Tube supporter

Test section and supporter

Power supply lines

Filter

(a) water tank

(b) assembled test section

Fig. 1. Schematic diagram of experimental apparatus.

steel tube (L = 0.5 m and D = 19.1 mm). The surface of the tube is finished through a buffing process to have a smooth surface. Electric power of 220 V AC is supplied through the bottom side of the tube. The tube outside is instrumented with five T-type sheathed thermocouples (diameter is 1.5 mm). The thermocouple tip (about 10 mm) is brazed on the tube wall. The brazing metal is a kind of brass and the averaged brazing thickness is less than 0.1 mm. The temperature decrease along the brazing metal is calibrated by the one dimensional conduction equation. Since the thermal conductivity of the brass is nearby 130 W/m °C at 110 °C [11], the maximum temperature decrease through the brazing metal is 0.12 °C at 160 kW/m2. The value was calculated by the product of the heat transfer rate and the thermal resistance. The measured temperatures were calibrated considering the above error. The water temperatures are measured with six sheathed T-type thermocouples brazed on a stainless steel tube that placed vertically at a corner of the inside tank. All thermocouples are calibrated at a saturation value (100 °C since all tests are done at atmospheric

pressure). To measure and/or control the supplied voltage and current, two power supply systems are used. For the tests, the heat exchanging tube is assembled vertically at the supporter (Fig. 1(a)) and an auxiliary supporter is used to fix a glass tube (Fig. 1(b)). To make the annular condition, a glass tube of 55.4 mm inner diameter (Di) and 600 mm length are situated around the heated tube. The gap size (s = (Di  D)/2) of the main body of the annulus is 18.2 mm. To maintain the gap size between the heated tube and the glass tube a spacer has been installed at the upper region of the test section. The upper outflow from the annular space is controlled by the flow restrictor (Fig. 1(b)) as listed in Table 1. The area ratio (Ar) is defined as the outflow area (Aout) divided by the cross sectional area (Agap ¼ pðD2i  D2 Þ=4) of the annular space. The ratio of the areas varies from 0.04 to 1.13 as shown in Table 1. Among the values Ar = 1.13 represents the annulus without the outflow restrictor. After the water tank is filled with water until the initial water level gets 1100 mm, the water is then heated using four pre-heaters at constant power. When the water temperature is reached at

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M.-G. Kang / International Journal of Heat and Mass Transfer 55 (2012) 7341–7345 Table 1 Values of the area ratios.

180 5.2

d, mm

Aout, mm2

Ar = Aout /Agap

10 15 20 25 30 38 55.4

78.5 176.6 314.0 490.6 706.5 1133.5 2409.3

0.04 0.08 0.15 0.23 0.33 0.53 1.13

140

q'', kW/m2

120 100 80

40

30

20

0

2

4

ð1Þ

where V and I are the supplied voltage and current, and D and L are the outside diameter and the length of the heated tube, respectively. TW and Tsat represent the measured temperatures of the tube surface and the saturated water, respectively. Every temperature used in Eq. (1) is the arithmetic average value of the temperatures measured by the thermocouples. The uncertainties of the experimental data are calculated from the law of error propagation [12]. The data acquisition error (AT, ±0.05 °C) and the precision limit (PT, ±0.1 °C) have been counted for the uncertainty analysis of the temperature. The 95% confidence uncertainty of the measured temperature is calculated from ðA2T þ P 2T Þ1=2 and has the value of ±0.11 °C. The error bound of the voltage and current meters used for the test is ±0.5% of the measured value. Therefore, the uncertainty of the calculated power (voltage  current) has been obtained as ±0.7%. Since the heat flux has the same error bound as the power, the uncertainty in the heat flux is estimated to be ±0.7%. When evaluating the uncertainty of the heat flux, the error of the heat transfer area is not counted since the uncertainty of the tube diameter and the length is ±0.1 mm and its effect on the area is negligible. To determine the uncertainty of the heat transfer coefficient the uncertainty propagation equation has been applied on the Eq. (1). Since values of the heat transfer coefficient are resulted from the calculation of q00 =DT sat a statistical analysis on the results has been performed. After calculation and taking the mean of the uncertainties of the propagation errors the uncertainty of the heat transfer coefficient can be decided as ±6%.

6.5

4.1

0 6

8

10

o

ΔTsat, C Fig. 2. Plot of q00 versus DTsat data.

30

25 2

q''=150kW/m

20

hb, kW/m2-oC

VI ¼ hb DT sat ¼ hb ðT W  T sat Þ pDL

90

60

the saturation value, the water is then boiled for 30 min to remove the dissolved air. The temperatures of the tube surfaces (TW) are measured when they are at steady state while controlling the heat flux on the tube surface with input power. The heat flux from the electrically heated tube surface is calculated from the measured values of the input power as follows:

q00 ¼

7.6

Ar=0.04 Ar=0.08 Ar=0.15 Ar=0.23 Ar=0.33 Ar=0.53 Ar=1.13

160

2

15

q''=100kW/m

10 2

q''=50kW/m

5

0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

A r=Aout /A gap Fig. 3. Variations in heat transfer coefficients as Ar changes.

3. Results and discussion Fig. 2 shows variations in heat transfer as the area ratio decreases from 1.13 to 0.04. Because of the outflow restrictor the heat transfer gets deteriorated comparing to the annulus without the restrictor. Although heat transfer change is not consistent for the area ratio variation, the decrease in Ar ultimately leads to the decrease in heat transfer. For example, DTsat increases 46.2% (from 5.2 to 7.6 °C) when Ar is decreased from 1.13 to 0.04 at q00 ¼ 90 kW/m2. At low heat fluxes the tendency is more clearly observed. For the same change in the area ratio, DTsat increases 58.5% (from 4.1 to 6.5 °C) at q00 ¼ 30 kW/m2. The slope of q00 versus DTsat curve becomes steeper as the area ratio decreases from Ar = 1.13 to Ar = 0.04. However, the tendency in heat transfer is changed through the area ratio variation. This suggests the changes in the main heat transfer mechanisms. Fig. 3 shows heat transfer coefficients for the heat fluxes of 50, 100, and 150 kW/m2 as Ar changes. Throughout the heat fluxes

three obvious tendencies are observed for the area ratio variation. For 0.04 6 Ar 6 0.15, hb increases. As the area ratio increases from 0.15 to 0.33, a gradual decrease in the heat transfer coefficients is observed. More increase in Ar greater than 0.33 increases in hb. As the gap ratio is more than 0.53, however, no clear change in the heat transfer coefficient is observed. Those tendencies are same regardless of the heat flux. The possible mechanisms affecting on heat transfer in an annulus can be counted as convective flow, liquid agitation, bubble coalescence, and the nucleation site density. The increase in the heat flux also results in the increase in the nucleation sites which increase heat transfer. The convective flow enhances heat transfer and is important for the heat transfer analysis around the lower region of a vertical annulus, especially, at low heat fluxes. The liquid agitation also enhances heat transfer. The intensity of the liquid agitation depends on the amount of bubbles and the active movement of the bubbles. The bubble coalescence enhances or

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M.-G. Kang / International Journal of Heat and Mass Transfer 55 (2012) 7341–7345

2.0 Ar=0.53 Ar=0.23 Ar=0.08

Ar=0.33 Ar=0.15 Ar=0.04

r

hr=hb/hb,A =1.13

1.5

1.0

0.5 (a) upper regions(T/C1)

0.0 2.0 Ar=0.53 Ar=0.23 Ar=0.08

Ar=0.33 Ar=0.15 Ar=0.04

r

hr=hb/hb,A =1.13

1.5

1.0

0.5 (b) middle regions(T/C3)

0.0 2.0 Ar=0.53 Ar=0.23 Ar=0.08

Ar=0.33 Ar=0.15 Ar=0.04

r

hr=hb/hb,A=1.13

1.5

1.0

0.5 (c) lower regions(T/C5)

0.0

0

20

40

60

80 100 120 140 160 180 2

q'', kW/m

Fig. 4. Changes in local heat transfer coefficients.

deteriorates heat transfer depending on the bubble size and its movement in the annular space. As the area ratio decreases from 1.13 to 0.33 the flow rate in the annular space decreases. The amount of convective heat transfer (especially, at the lowermost regions) and the intensity of liquid agitation along the space gets decreased due to the reduced fluid velocity. The change in the ratio of heat transfer coefficients at the local positions shown in Fig. 4 explains effects of the reduced velocity on heat transfer. In the figure, hr is defined as the heat transfer coefficient for a given Ar divided by the heat transfer coefficient for the annulus without the flow restrictor (i.e., Ar = 1.13). The heat transfer coefficient for Ar = 1.13 is the local value. For Ar = 0.33, hr has the values lower than 1 throughout the heat fluxes. At the lower regions, hr is around 0.5. The heat transfer coefficients are very sensitive to the convective flow around the lower regions. At the upper regions, hr converges to 1 as the heat flux increases because of the increased liquid agitation generated by the bubbles coming from the lower side. The photo shown in Fig. 5 shows the reduced flow velocity. The bubbles for Ar = 0.33, shows much clear boundary than the bubbles for Ar = 1.13 due to the reduced velocity. More decrease in Ar from 0.33 to 0.15 reduces the flow velocity and accelerates the rate of bubble coalescence as shown in Fig. 5. The small outflow area obstructs the outward bubble flow from

the annulus. Then, the detached bubbles coming from the lower part of the tube get stagnant for a while and accumulate at the upper region of the annulus. During the stay the bubbles are coalescing together and are growing to a big lump of bubble. Thereafter, the upward rising velocity of the fluid gets decreased because of the lump. The size of the bubble lump is increasing until the amount of the buoyancy is enough to escape from the gap space. If the lump flows out a vacancy is created in the gap space. Then, a sudden rush of the liquid is occurred. During the process the inside fluid is accelerated to move up and downward, generating a pulsating flow, in the gap space. As a result very active liquid agitation is observed visually. The high rate of heat transfer by boiling in the gap space has been ascribed to the intense agitation of the liquid at the heating surface by the bubbles and this is the major cause of heat transfer enhancement. As shown in Figs. 2 and 3, the result for Ar = 0.15 is very unique comparing to the other results. The curve for the area ratio shows a kind of transition from enhanced to deteriorated heat transfer. When the heat fluxes are lower than 80 kW/m2, the tube wall superheat has relatively low value. As the heat flux increases, the curve for q00 versus DTsat shift right side and the deterioration of heat transfer is observed. As the outflow area gets small, the size of the coalesced bubble becomes increased. This results in active liquid agitation at low heat fluxes. The local heat transfer coefficient at the upper regions gives some clue. The increase in heat flux also increases the bubble size in the annular space. As a result, hr for the upper and middle regions gradually decreases lower than 1. Therefore, the decrease of Ar from 0.15 to 0.08 results in sudden decrease in heat transfer. There seems to be two competing effects on the nucleate boiling heat transfer. One is the effect of liquid agitation by bubbles generated on the surface which increases heat transfer rate and the other is the effect of bubble coalescence and the formation of large vapor slugs in the high heat flux region in particular which reduces heat transfer from the tube surface. The results for Ar =0.15 shows that this value is just the transition point of the major heat transfer mechanism from the liquid agitation to the formation of big size bubbles. As Kang [3] explained the major causes of the deterioration are the formation of large bubble slugs around the upper region of the annulus. As the area ratio gets decreased lower than 0.15 the creation of the bigger bubbles is accelerated even at a low heat fluxes (see Fig. 5). If big size bubble lumps were generated, the intensity of the liquid agitation should be decreased since the length for the flow acceleration is shorten. Moreover, the lumps prevent the smooth supply of liquid into the gap space. Thereafter the decrease in the heat transfer rate is caused. If there is an enough flow area around the upper region of the annulus, the lumped bubbles agitate inside fluid while flowing outward without suffering a notable interference between the bubbles and the liquid. But, if the upper outflow area is not enough like the present study, the flow friction increases. The decrease in the heat transfer rate is accelerated as the value of the gap ratio decreases. A total of 111 data points have been obtained for the heat flux versus wall superheat for various area ratios. Through the statistical analysis on the experimental data with the help of a computer program (which uses the least square method as a regression technique) a simple equation was determined as follows.

hb ¼ 0:356q000:808 lnðAr þ 2:48Þ

ð2Þ

In the above equation, the dimensions for hb and q00 are kW/m2 °C and kW/m2. Fig. 6 shows a comparison of the measured heat transfer coefficient from experiments and the calculated heat transfer coefficient by Eq. (2). The suggested empirical correlation well predicts the experimental data within ±10% error band, with some exceptions from the fitted data of Eq. (2). The scatter of the present

M.-G. Kang / International Journal of Heat and Mass Transfer 55 (2012) 7341–7345

7345

Fig. 5. Photos of pool boiling in annuler space.

0.33 results in the increase in hb. As the gap ratio is more than 0.53, no clear change in the heat transfer coefficient is observed. Those tendencies are same regardless of the heat flux. (2) Throughout the area ratios the heat transfer coefficient is increased or decreased depending on the main mechanisms of heat transfer. The major cause for the tendency is attributed to the formation of a lumped bubble around the upper regions of the annulus and the reduced flow velocity.

40

2o

hb,calculated, kW/m - C

+10%

30 -10%

20

Acknowledgment

10

This work was supported by a grant from 2012 Research Fund of Andong National University.

0.808

hb=0.356q''

0

ln(Ar+2.48)

References

0

10

20

30

40

2 o

hb, experimental, kW/m - C Fig. 6. Comparison of experimental data to calculated heat transfer coefficients.

data is of similar size to that found in other existing pool boiling data. 4. Conclusions To investigate effects of the upside outflow area on pool boiling heat transfer in a vertical annulus, the ratio of areas of the outflow and the gap space has been changed from 0.04 to 1.13. For the test, a heated tube of 19.1 mm diameter and the water at atmospheric pressure have been used. Major conclusions of the study are as follows: (1) For 0.04 6 Ar 6 0.15, hb increases. As the area ratio increases from 0.15 to 0.33, a gradual decrease in the heat transfer coefficients is observed. More increase in Ar larger than

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