Mechanisms of pool boiling heat transfer in subcooled and saturated liquid have been studied for a long time. Recently, it has been widely investigated in nuclear power plants for the purpose of acquiring inherent safety functions in case of power supply loss[1,2]. Pool boiling heat transfer is very attractive from the viewpoint of enhancing heat transfer rate in a limited space. Moreover, it can run without the support of any electric pumps. To design more efficient passive heat exchangers, the effects of several parameters on heat transfer must be identified. One of the major issues is the variation of local heat transfer coefficients (
A study on local heat transfer coefficients on a horizontal tube by Lance and Myers  reports that the type of boiling liquid can change the trend of local heat transfer coefficients along the tube periphery. Lance and Myers said that when the liquid was methanol the maximum local heat transfer coefficient was observed at the tube bottom, while the maximum was at the tube sides when the boiling liquid was n-hexane. Moreover, they reported that the difference among the local heat transfer coefficients decreased as the heat flux (
According to Gupta et al.’s results , when the liquid is water, the maximum and the minimum local heat transfer coefficients are observed at the bottom and top regions of the tube circumference, respectively. Kang  reported similar results using the same combination of heated tube diameter and liquid. Gupta et al. studied azimuthal angles (
To avoid circumferential temperature distribution on a horizontal tube the application of a porous layer on a part of the heating surface was studied by Dominiczak and Cieslinski . According to the results, the porous layer changes the location of the maximum wall temperature. The lowest temperature on the circumference was recorded within the upper gereratix due to the porous layer. Luke and Golenflo  observedthe diameter and frequency of a departure bubble is influenced by the azimuthal position of the active nucleation sites on the tube. Das  carried out an experimental investigation and suggested an equation to predict the local pool boiling heat transfer coefficient along the horizontal tube periphery at different pressures. Results by El-Genk and Gao  for a hemisphere also said that local heat transfer coefficients were changing along the circumference. Much difference between two local values at the bottom and sides was observed.
Previous studies on local heat transfer coefficients of a circular shape are summarized in Table 1. Both pool and flow boiling are of concern in the various saturated liquids. Most results are for horizontal tubes of diameter ranging from 7.6~51 mm. One exception is by Sateesh et al. . Sateesh et al. studied variations in local heat transfer coefficients along the tube periphery while controlling the inclination angle (
An analytic approach for pool boiling on a surface where the mechanism of sliding bubbles plays an important role has been studied by Sateesh et al. . Through the modeling process they suggested several equations to quantify the effects of natural convection, transient conduction and microlayer evaporation due to stationary bubbles, and transient conduction and microlayer evaporation due to sliding bubbles on pool boiling heat transfer.
Investigation of local heat transfer on a heated tube in subcooled liquid is important when the thermo-hydraulic
Summary of Experimental Conditions in Previous Studies
phenomena are closely related with the integrity of a nuclear reactor . Figure 1 shows a schematic diagram of the passive condensing heat exchanger (PCHX) adopted in the Advanced Power Reactor Plus (APR+). The PCHX cools down the secondary side of a steam generator to eventually remove decay heat from the reactor core. The heat exchanging tubes of the PCHX are inclined 3° from the horizontal position to prevent the occurrence of water hammer. The condition of the water in a passive condensate cooling tank (PCCT), which the PCHX is submerged in,
is first subcooled and becomes saturated as the PCHX operates.
Summarizing the published results, it is necessary (1) to evaluate local heat transfer coefficients on a nearly horizontal tube, and (2) to identify effects of liquid subcooling on local heat transfer coefficients. Therefore, the present study aims to investigate the effects of the inclination angle and liquid subcooling on pool boiling heat transfer. To the author’s knowledge, no previous results concerning these effects have been published. The results of this study could provide a clue to the thermal design of the PCHX.
A schematic view of the present experimental apparatus and the assembled test section is shown in Fig. 2. The water storage tank is made of stainless steel, with a rectangular cross section (950×1300 mm) and a height of 1400 mm.
This tank has a glass view port (1000×1000 mm) which permits viewing and photography of the tubes inside. The tank has a double container system. The sides of the inner tank are 800×1000×1100 mm (depth×width×height). The bottom side of the inner tank is situated 200 mm above the bottom of the outer tank. Drainage of the inside tank is done by the two passages situated on the bottom side. Outlets of the drain passages are 50 mm above the bottom side of the outer tank to reduce any possible effects of outside fluid on the flow of the inside tank. The inside tank has several flow holes (28 mm in diameter) to allow fluid inflow from the outer tank. To diminish the effects of inflow from outside tank, the holes are situated at 300 and 800 mm above the bottom of the inside tank. Although some areas around the hole can be affected by the inlet flow, it is not expected that the inflow would change the flow characteristics near the heated tube. Four auxiliary heaters (5 kW/heater) are installed in the space between the inside and the outside tank bottoms to boil the water and to maintain the saturated condition. To reduce heat loss to the environment, the left, right, and rear sides of the tank are insulated by fiberglass wool of 50 mm thickness.
The heat exchanger tubes are simulated by a resistance heater (Fig. 3) made of a very smooth stainless steel tube (
The tube outside is instrumented with five T-type sheathed thermocouples (diameter 1.5 mm). The thermocouple tip (about 10 mm) is bent at a 90 degree angle and the bent tip 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 through the brazing metal is calibrated by the one dimensional conduction equation. Since the thermal conductivity of the brass is nearby 130 W/m-ºC at 110ºC , the maximum temperature decrease through the brazing metal is 0.08ºC at 100 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 locations of the thermocouples are50, 100, 150, 200, and 250 mm from the heated tube bottom as shown in Fig. 3. The water temperatures were measured by a rod with six sheathed T-type thermocouples placed vertically at a corner of the inside tank. The thermocouples are brazed on the surface with equal space (i.e., 180 mm) similar to the heated tube. At the bottom side of the rod a small rod of 10 mm diameter was attached to fix it to the tank bottom, which has a hole of the same size. The upper side of the device has a hole to fix it to the tank wall with a bolt and nut. All thermocouples of the heated tube and the device were calibrated at a saturation value (i.e., 100 ℃ since all the tests were run at atmospheric pressure condition).
To fix the heated tube onto the right position, a supporter was manufactured as shown in Fig. 2. The heated tube and the supporter are assembled by nuts and bolts. To measure and control the supplied voltage and current two power supply systems (each having three channels for reading of voltage and current in digital values) are used. The capacity of each channel is 10 kW.
For the tests, the heat exchanging tube and the tube supporter were assembled and placed at the bottom of the tank. From the start of filling the water storage tank until the initial water level was 1000 mm from the outer tank bottom, the water was heated using four pre-heaters. When the water temperature (
The heat flux from the electrically heated tube surface is calculated from the measured values of the input power as follows:
The uncertainties of the experimental data are calculated from the law of error propagation . The data acquisition error (
and has a value of ±0.11 ℃. 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 Eq. (1). Since values of the heat transfer coefficient result from the calculation of
Before obtaining local heat transfer coefficients, heat transfer along the tube periphery has been analyzed based on the measured local temperatures at the given azimuthal angles. This kind of approach is necessary to estimate the local coefficients accurately. Lance and Myers  used an isolating method to cut off any possible heat transfer to the thermocouple along the tube periphery. For the present study a one dimensional heat conduction analysis was used to estimate the amount of peripheral heat transfer. As the liquid is in saturation and
Changes in water temperatures through the vertical height of the tank are shown in Fig. 4. Temperatures measured at four different locations are plotted as a
function of time (
Figure 5 shows plots of ∆
Some photos of pool boiling on a 3° inclined tube surface are shown in Fig. 6 for different ∆
is very weak and/or the density of nucleation sites is increased. At Δ
Variations in local heat transfer coefficients on the tube surface against the degree of subcooling are shown in Fig. 7. As ∆
average heat transfer coefficient reduces 65.2% as ∆
Figure 8 shows plots of
between the superheats for the maxima and the minima is 2.4℃ for
The peripheral distribution of the local heat transfer coefficient is shown in Fig. 9. The local heat transfer coefficient decreases as the azimuthal angle increases from the bottom (
transfer coefficient are 45° and 0° for the horizontal tube and the 3° inclined tube, respectively. The azimuthal angle for the minimum heat transfer coefficient is constant regardless of the inclination angle and has a value of 180°. The azimuthal angle for the maximum heat transfer coefficient moves to 45° when Δ
To predict the local and average heat transfer coefficients, an empirical correlation has been suggested by using the least-squares method and experimental data gained from the present experiments. The empirical correlation can be correlated as a function of the heat flux and the subcooling as follows:
The developed correlation predicts the measured experimental data within a ±10% error bound as shown in Fig. 10.
Three heat transfer mechanisms were considered to explain the heat transfer characteristics along the tube periphery as shown in Fig. 11. They are the density of active nucleation sites, sliding bubbles, and bubble coalescence. One of the major causes of the increase in heat transfer coefficients is liquid agitation due to sliding bubbles.
The mechanisms of transient conduction, microlayer evaporation , and the convective bubbly flow due to the sliding bubbles are important for heat transfer enhancement. Moreover, as a bubble moves along the tube periphery, it agitates relevant liquid, disrupts the thermal layer on the surface, and contributes to additional cooling. At
At the lowermost region of the tube (
The azimuthal angle for the maximum heat transfer coefficient is regarded as the location where the effects of liquid agitation and bubble coalescence are high and low, respectively. Therefore, it can be moved to other locations since these two mechanisms are dependent on the inclination angle, the degree of subcooling, and the heat flux. As shown in Fig. 8 and 9 the increases in heat flux and inclination angle move the azimuthal angle for the maximum heat transfer coefficient to the bottom side of the tube. The nose of active bubble coalescence moves to the bottom side of the tube as the heat flux increases.
As the tube is inclined from the horizontal position, the sliding lengths of bubbles along the tube periphery are increased. The sliding length increases in proportion to 1/cos
Since the creation, growth, and departure of bubbles are not easily done in subcooled water, liquid agitation due to rising bubbles is very weak. The chance of bubble coalescence is hardly observed as the degree of subcooling gets increased. The experimental results shown in Fig. 7 explain the effects of liquid subcooling on heat transfer coefficients. There is almost no difference among local heat transfer coefficients as the degree of subcooling increases more than 10℃ regardless of the inclination angle and the heat flux. One of the clues for this tendency can be observed visually in Fig. 6. In a highly subcooled liquid no active liquid agitation and bubble coalescence are expected. Therefore, the only effective heat transfer mechanism for this case is the density of nucleation sites. The variation of the local heat transfer coefficient throughout the azimuthal angle is shown in Fig. 9. The results for ∆
Local heat transfer coefficients on a smooth stainless steel tube of 50.8 mm diameter with 3° inclination have been investigated experimentally both in subcooled and saturated water at atmospheric pressure. The major conclusions of the present study are as follows:
(1) Much variation in local coefficients was observed along the tube periphery. The maximum values are observed at
(2) The increase in Δ
(3) An experimental correlation was suggested to predict the local and average heat transfer coefficients on a 3° inclined tube surface. The correlation can predict the experimental data within a ±10% error bound.