Effects of tube inclination angle on nucleate pool boiling heat transfer of water at atmospheric pressure have been obtained experimentally. Experiments were performed for seven angles (0 deg, 15 deg, 30 deg, 45 deg, 60 deg, 75 deg, and 90 deg) with a tube of 540 mm in length. It is found that the nucleate boiling heat transfer on the outside of a tube is strongly dependent on the tube angle of inclination. The maximum and minimum heat transfer coefficients occur at 30 deg and 75 deg, respectively. The major reason for the enhanced heat transfer is thought to be the increase in liquid agitation on the tube surface.

The mechanisms of pool boiling heat transfer have been studied for a long time since it is closely related with the designs of more efficient heat exchangers. Recently, it has been widely investigated in nuclear power plants for application to the design of new passive heat removal systems employed in the advanced light water reactors design [1,2]. To determine the required heat transfer area as well as to evaluate the system performance during postulated accidents, detailed analysis on pool boiling heat transfer applicable to the systems are needed. Through the review of the published results it can be concluded that one of the efficient ways to increase the heat transfer rate is to incline the heated surface.

Summarizing the works, it can be said that effects of the inclination angle on pool boiling heat transfer closely depend on the heating surface geometry (i.e., wire, plate, or tube). As Cornwell and Houston [12] suggested, nucleate boiling on a tube differs considerably from that on a flat plate and a wire. Since Kang [11] performed experiments for the three inclination angles only, more detailed study on the tube inclination angles is necessary. As such, the present study is aimed at the determination of effects of the tube inclination angle on pool boiling heat transfer (1) to improve Kang’s result [11] and (2) to investigate the potential areas for improvement of the thermal design of passive heat exchangers.

For the tests, the heat exchanging tube is placed on the tube supporter. The tube supporter can rotate freely to adjust the inclination angle. After the water storage tank is filled with water until the initial water level is at 1200 mm from the outer tank bottom, the water is heated using four pre-heaters at constant power (5 kW/heater). When the water temperature reaches the saturation value (100 °C since all the tests are run at atmospheric pressure), the water is then boiled for 30 minutes at saturation temperature to remove the dissolved air. The temperatures of the water and tube surfaces are measured when they are at steady state while controlling the heat flux on the tube surface with input power. In this manner a series of experiments has been performed for various tube inclination angles.

The uncertainty in theheat flux is estimated to be 1.0%. The uncertainty of the measured temperatures are originated from thermocoupl probe itself, thermocouple brazing, and translation of the measured electric signal to digital values and the value is ±0.3 K.

The heat flux from the electrically heated tube surface is calculated from the measured values of the AC power input as follows:

where and are the supplied voltage (in volt) and current (in ampere), and and are the outside diameter and the length of the heated tube, respectively. and represent the measured temperatures of the tube surface and the saturated water, respectively. The tube surface temperature used in Eq. (1) is the arithmetic average value of the temperatures measured by five thermocouples brazed on the tube surface.

Figure 2 shows changes of the boiling heat transfer coefficients due to tube inclination changes. According to the experimental results, the effect of the tube inclination angle on pool boiling heat transfer is very large. As the inclination angles are 30 deg and 75 deg, the maximum and minimum heat transfer coefficients are found, respectively. For example, decreases about seven times when is changed from 30 deg to 75 deg at the wall superheat of =7 K. Kang’s previous study [11] suggested that enhanced heat transfer is closely related with both mechanisms of the decrease in bubble slugs and the increase in liquid agitation.

As Kang [11] explained, one of the factors decreasing heat transfer when =0 deg is bubble slug formation on the uppermost point of the tube circumference. As the inclination angle increases, the distance of bubble movement along the tube surface increases. This movement of bubbles increases the intensity of liquid agitation. And the formation of the bubble slug on the tube is also decreased. Increasing the inclination angle to =30 deg, the intensity of liquid agitation gets much stronger due to the lengthened distance of the movement of bubbles. Therefore, much increase in the heat transfer coefficient is observed at =30 deg.

As the inclination angle changes from 30 deg to 75 deg, the intensity of bubble slugs on the tube upper region gets stronger (see the curve
#2 in Fig. 4). The effect of liquid agitation on heat transfer enhancement is compensated much with the formation of bubble slugs. Therefore, the heat transfer coefficient is decreased as the inclination angle changes from 30 deg to 75deg. Since the intensity of liquid agitation for the angles less than 90 deg is not so strong, small changes in the bubble slug formation can result in much variation in heat transfer.

For the vertical tube, effects of bubble slugs are highly observed at the upper most regions (see the curve #2 in Fig. 4). If a tube is inclined slightly (=75 deg for the present) from the vertical position, the intensity of liquid agitation is decreased very much due to the slower flow of bubbles. To get stronger liquid agitation, enough distance is needed for the flow of bubbles to be fully developed (the fully developed flow is defined as the active swirling flow along the tube surface, which results in stronger liquid agitation). If the inclination is changed from 90 deg to 75 deg, the length of bubble movement along the tube surface was shortened. Therefore, the flow is not fully developed comparing with the vertical case and this results in the decrease in the intensity of liquid agitation. Moreover, the bubble coalescence at the upper region of the tube length (see the curve #2 in Fig.4) seems not decreasing so much. Another possible cause for the decrease in the heat transfer coefficient as the inclination angle changes from 90 deg to 75 deg is the increase of the bubble slug formation on the upper most regions of the tube circumference (see the curve #1 in Fig. 4).

Variations in heat transfer coefficients with location are shown in Fig. 5. In the figure three thermocouples at the top (T/C1), middle (T/C3), and bottom (T/C5) of the tube axial length were selected for the comparison. As Kang [11] explained, one of the factors decreasing heat transfer when =0 deg is bubble slug formation on the uppermost point of the tube circumference. The formation of bubble slugs on the tube surface decreases heat transfer. Kang [11] further suggested that the two competing mechanisms for heat transfer from inclined tubes are liquid agitation and bubble coalescence. If liquid agitation is active, an increase in the slope of versus curve with increasing should occur. On the other hand, if active bubble slugs exist, a decrease in the slope of versus curve with increasing should be observed. When the tube is inclined at=30 deg, bubbles were observed to move along the tube length for some distance and agitate relevant liquid. Moreover, the formation of the bubble slug on the tube is also decreased. This increases in liquid agitation and decrease in the formation of bubble slugs result in easy liquid access to the heating surface. The effects of liquid agitation on is clearly observed at T/C3 location at =30 deg. One possible explanation of the observation is resulted from the decrease in the formation of bubble slugs at this location. For the vertical tube, bubble slugs are formed at the upper most regions at lower heat fluxes like the present study. However, the local heat transfer coefficient at T/C1 and =30 deg is not so much changed comparing with the value at =0 deg. As heat flux is increased beyond 70 kW/m², the slop of versus curve at T/C1 location and =30 deg decreases slightly. This suggests strong bubble slugs formation on this region. For the horizontal tube (=0 deg), since no active liquid agitation is expected, the slope of the versus curve is more or less constant regardless of thermocouple locations.

Since no changes are observed for the slopes of versus curves of the tube T/C1 location and at =90 deg, one might speculate that effects of bubble slugs on heat transfer coefficients are compensated for by the active liquid agitation. If a tube is inclined slightly (=75 deg for the present) from the vertical the intensity of liquid agitation is decreased very much (Why is this the case?). Since effects of liquid agitation on heat transfer coefficients are clearly observed at T/C3, the smaller value in the slope of versus curve comparing with the other curves suggests that the intensity of liquid agitation around these regions is weak. The schematic of the degree of the intensity of heat transfer mechanisms shown in Fig. 3 suggests that decreases in liquid agitation and bubble slugs formation at the top region of the tube length as the inclination angle changes from 90 deg to 75 deg. To get strong liquid agitation some distance from the point of bubble generation is necessary. If a tube is inclined from the vertical position, the distance of bubble moving along the tube is shortened. Therefore, the flow is not fully developed comparing with the vertical case and this results in somewhat abrupt decrease in liquid agitation. As the inclination angle changes from 90 deg to 75 deg, the degree of the bubble slug formation on the upper most regions of the tube circumference increases. Since the effects of the bubble slugs around the top region of the tube length is not very strong as shown in Fig. 5(a) variation in the intensity of liquid agitation could result in much change in heat transfer coefficient. Moreover, the degree of the bubble slug formation on the tube upper most side of the tube circumference has increased at 75 deg. As explained for the inclination angle of 30 deg, this is also very effective heat transfer mechanism for the case to decrease heat transfer rate. (The discussion for =75 deg appears to be highly speculative. I am not sure I see the effects of liquid agitation at T/C1 and T/C3 (slope changes?) Please explain!)

The major conclusion drawn from this experimental investigation is that the inclination angle has a significant effect on the boiling heat transfer coefficients from the outside of a tube. When the angles are 30 deg and 75 deg, maximum and minimum heat transfer coefficients are observed, respectively. The maximum value of the ratio between two heat transfer coefficients for =30 deg and 75 deg is about seven at =7 K. The major reason for the enhanced heat transfer is thought as the increase in the intensity of liquid agitation. The results found here can be applied to the designs of any passive heat exchangers to reduce heat transfer area for the given heat load or to enhance heat transfer for the fixed heat transfer area by considering the tube angle of inclination.

This work was supported by grant No. 2000-1-304-012-3 from the Basic Research Program of the Korea Science & Engineering Foundation.

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(a) water storage tank	(b) heated tube