The 10th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-10) Seoul, Korea, October 5-9, 2003
CALCULATION OF BOILING CURVES DURING REWETTING OF A HOT VERTICAL NARROW CHANNEL Jian Zhang, Futoshi Tanaka∗, Mulya Juarsa∗∗, Kaichiro Mishima Research Reactor Institute, Kyoto University Kumatori-cho, Sennan-gun, 590-0494, Osaka, Japan Phone: +81-724-51-2449, Fax: +81-724-51-2637 E-mail:
[email protected],
[email protected] KEY WORDS Vertical narrow channel, Gap cooling, Boiling curve, Rewetting, Critical heat flux, Transition boiling, Film boiling, In-vessel Retention
ABSTRACT In the present study, the heat-transfer mode in the gap cooling was studied by analyzing boiling curves obtained in the experiments on transient cooling and rewetting of hot vertical surfaces in narrow gap channels. First, the experiments were carried out using annular channels with a narrow gap between inner and outer walls. The inner rod of the channel was made of stainless steel and the outer wall of glass tube for visualization. The initial temperature of the wall ranged from 500oC to 800oC, and the size of the gap ranged from 0.5mm to 7.0mm. Two-dimensional time-dependent heat conduction model was introduced in the study to calculate a boiling curve using the measured temperature history of the outer surface of the inner wall. The calculated boiling curves for the present gap cooling were compared with existing correlations to understand the heat-transfer characteristics of the gap cooling. The effects of the gap size on the gap cooling and rewetting process were also discussed. The results indicated that the heat transfer during the gap cooling was significantly limited by the countercurrent flow limitation (CCFL) in a narrow gap. Under the same initial temperature condition, if the size of the gap was larger, the rewetting of the inner wall took place earlier at a higher heat flux and the critical heat flux was also higher, which approached to the heat transfer characteristics of pool boiling when the gap size was larger than 4.0mm. Finally, the contribution of axial heat conduction to the surface heat flux was discussed.
∗
Mitsubishi Heavy Industries Indonesia National Nuclear Energy Agency
∗∗
1
1. INTRODUCTION In the TMI-2 accident, although about half the core was melted and fell down into the lower head of the reactor pressure vessel (PRV), the molten core was cooled down successfully and retained in the PRV. One of the mechanisms of heat removal from the molten core was thought to be the formation of narrow gap between the PRV wall and the crust which was formed on the surface of the molten core. The gap allowed coolant to penetrate into the gap and to contribute heat removal from the molten core. To analyze the contribution of this gap cooling effect in the heat removal from the molten core, we need heat transfer coefficient during cooling down of a hot surface in the narrow gap. From this point of view, it is necessary to make clear the mechanism of the heat-transfer characteristics for the narrow gap. One of representative researches on the heat-transfer characteristics of narrow gaps was performed by Ishibashi and Nishikawa (Ishibashi, 1969). In their research, a remarkable effect of spatial restriction on the saturated boiling heat-transfer was reported. It was pointed out that in the saturated boiling heat-transfer in a narrow space, there was a coalesced bubble region having remarkably different characteristics beside the isolated bubble region, the heat transfer characteristics of which had already been confirmed. The gap size of the narrow space in which the effect of coalesced bubble is significant ranged from 0.5mm to 4.0mm at the atmospheric pressure condition. If the size of the narrow gap is larger than 4.0mm, the boiling region is isolated bubble region, while when the gap size is smaller than 0.5mm, the region is defined as liquid deficient region and the heat-transfer is much affected by the insufficient liquid supply. Recently, many experimental and theoretical researches on the heat-transfer during rewetting of hot vertical surfaces in narrow gap channels have been carried out (Monde, 1982, Chang, 1983, Ohtake, 1998 and Murase 2001). It was pointed that different from the heat-transfer modes of heating process, during the cooling process, three heat-transfer modes, i.e., film boiling (FB), transition boiling (TB) and nucleate boiling (NB) and two critical conditions, i.e., minimum film boiling heat flux (MFB) and critical heat flux (CHF) have some special characteristics. Monde et al. proposed a CHF correlation for natural circulation in a narrow space, and proved the coolability of the wall by penetrated water. Chang and Yao also investigated CHF in narrow vertical annuli with a closed bottom for various fluids at different pressures and proposed CHF correlations based on the condition for countercurrent flow limitation (CCFL). Ohtake et al. also performed quenching experiments. They pointed out that the heat-transfer characteristics during the rewetting were quite similar to those of conventional pool boiling. Murase et al. evaluated the effects of the superheat on the heat-transfer and CHF using existing experimental data and derived heat transfer correlations in a narrow gap. Besides those researches above cited, many experiments (Fujita, 1988, Jeong, 1997, Schmidt 1998 and Koizumi, 1999) on gap cooling have been performed and the heat-transfer models were proposed. However, it appears that the mechanism of the heat-transfer in
2
the gap cooling has not been fully understood yet. Therefore, the present study aimed to investigate heat-transfer modes in the gap cooling by analyzing boiling curves obtained in the experiments on transient cooling and rewetting of hot vertical surfaces in narrow gap channels. It was supposed that the gap cooling is a very complicated process depending on many factors such as cooling conditions, cooling method, initial temperature and gap sizes. To make clear the mechanism of the gap cooling, large amount of experiment data under various experimental conditions are required. For this purpose, in the present study, first, the experiments on transient cooling and rewetting of hot vertical surfaces in narrow gap channels were carried out using annular channels with a narrow gap under the atmospheric condition. The inner wall of the channel was made of stainless steel and the outer wall of quartz glass tube for visualization. The initial temperature varied from 500oC to 800oC and the size of the gap ranged from 0.5mm to 7.0mm. Then, the heat-transfer characteristic of the gap cooling was described by the boiling curve calculated by the measured temperature of the outer surface of the inner rod. The first report of the present experiment was presented by Tanaka (2003) recently. In the report, the characteristic of the transient heat-transfer was analyzed by comparing the boiling curves with existing correlations. The boiling curves were calculated by one-dimensional heat conduction equation. It was pointed that the minimum wall superheat for stable film boiling is high, which should be affected by the heat conduction within the wall in the axial. Therefore, in the present study, two-dimensional, time-dependent heat conduction model will be introduced to calculate more realistic boiling curves. Also, the heat-transfer characteristic of the present gap cooling will be analyzed by comparing the boiling curve with existing correlations. The effect of the heat conduction in the axial direction on the heat transfer mode will be discussed by comparing the boiling curves calculated by both two-dimensional and one-dimensional heat conduction equations. Finally, the effects of the gap size on the gap cooling process will be discussed by comparing the calculated boiling curves with various correlations.
2. EXPERIMENTAL APPARATUS AND PROCEDURE 2.1 Experimental Apparatus The overall test assembly is shown in Fig. 1. The test section was an annular channel with a narrow gap between inner and outer concentric tubes. The inner tube was made of stainless steel SUS304 tube with 7.0mm wall thickness, 24mm outer diameter (OD) and 300mm heated length. The outer tubes were made of quartz glass with 2mm wall thickness and 25mm, 26mm, 28mm, 32mm and 38mm OD. By combining these and the inner tube, five kinds of gap clearances were created; 0.5mm, 1.0mm, 2.0mm, 4.0mm and 7.0mm. The temperatures of the test section were measured at seven locations (marked by TC-1, TC-2, TC-3, TC-4, TC-5, TC-6 and TC-7) by sheathed K-type
3
Alumel-Chromel thermocouples. Those thermocouples were spot welded at their ends flush with the outer surface of the inner wall and were guided through the hole inside the inner tube. The thermocouple signals were amplified by a signal conditioner and recorded in a personal computer with frequency of 25Hz or 100Hz. A couple of semi-cylindrical ceramic heaters with 300mm heated length surrounding the test section was used to heat the inner tube by radiation heating up to 900oC. On the top end of the test section, a plenum made of SUS304 with capacity of 6 liters water was connected to the outer tube with silicon rubber tube and a valve for water supply. The water in the plenum was heated up by a band heater and to be kept at the saturation temperature. 2.2 Experimental Procedures Water Plenum size 6 Ltr
The quenching experiments except for the gap size 0.5mm at initial temperature 800oC were
Band Heater
carried out successfully for five kinds of gap sizes ID of Outer Tube
of 0.5mm, 1.0mm, 2.0mm, 4.0mm and 7.0mm at the initial temperatures of 500oC, 650oC and 800oC, respectively.
TC-1
Before the experiment started, the water in the plenum was heated up and maintained at the saturation temperature. At the same time, the inner tube was heated up with the ceramic heaters to the designed initial temperature. After the designed
TC-7
TC-2
Outer tube OD OD: 24 24
TC-3
Ceramic Heater
TC-4 TC-5 TC-6
10 Inner tube
Narrow Gap
initial temperature reached, the heater power was
(cladding) 20
switched off and the ceramic heaters were removed from the test section. Then, the valve connecting the test section and the water plenum
Fig. 1 Schematic diagram of the test section
was opened, and the saturated water was supplied from the plenum to the test section. The transient temperatures of the inner tube were measured by the thermocouples and recorded in the personal computer with the frequency 25Hz or 100Hz. Also, in all the experiments, the phenomena in the test section during the cooling process were observed using a digital video camera for better understanding.
3
EXPERIMENTAL RESULTS AND ANALYSES
3.1 Transient Temperature
4
A typical temperature history observed during the gap cooling for gap size 1.0mm at initial temperature 800oC is illustrated in Fig. 2. It was indicated that there existed three steps in the gap cooling. At the beginning of the cooling, the temperature decreased gradually, and the heat transfer mode was identified as film boiling process. After that, the temperature began to drop rapidly due to rewetting of the heated wall and a transition boiling process took place. Finally, the heat transfer mode turned into nucleate boiling in which the cooling process proceeded slowly again. In this study, it was observed that the rewetting process proceeded steadily but the fingers of liquid front were moving up and down. From this observation, the rewetting time was defined as the time at which the water front begins to touch the thermocouple location and the gradient of the temperature curve starts changing. Thus, the rewetting began at the rewetting time. It was observed from Fig. 2 that for the gap size 1.0mm, the rewetting of the hot surface was initiated at the bottom of the heated channel, i.e. at position TC-6, and following position TC-6, the top of the heated channel, i.e. position TC-7 was rewetted. After that, the rewetting front proceeded both from the top and bottom ends of the heated channel, and finally the rewetting process ended near the center of the heated channel. The effect of the gap size on the rewetting time is shown in Fig. 3. Looking at the case for the gap size 0.5mm, the rewetting front started only from the top end of the heated channel. It was indicated that the smaller the gap size is, the later the rewetting time is, which can be explained by the strong influence of CCFL in a narrow gap. It was also found that the smaller the gap size is, the longer time is required for rewetting. For the gap sizes 4.0mm and 7.0mm, the rewetting times are very close. Using the temperature history data, the boiling curves were calculated. Based on the boiling curves, the heat-transfer characteristics will be discussed in the following section. 700
600 TC-7
400
0
Rewetting time
TC-1 TC-2 TC-3 TC-4 TC-5 TC-6
200
0
100
o
600
Rewetting Time [Sec]
o
Temperature History [ C]
TC-7 TC-1 TC-2 TC-3 TC-4 TC-5 TC-6
o
Gap=1.0mm Tinitial=800 C
800
200
300
400
Gap=0.5mm Gap=1.0mm Gap=2.0mm Gap=4.0mm Gap=7.0mm
500 400 300 200 100 0 80
500
Tinitial=650 C
120
160
200
240
280 300
Distance from bottom [mm]
Time [Sec]
Fig.2 Time-dependent temperature history
Fig. 3 Effect of the gap size on rewetting time
3.2 Calculating of Boiling Curves In order to analyze the heat transfer modes during the transient gap cooling, a boiling curve was calculated by solving an inverse heat conduction problem using a measured temperature history. 5
Time-dependent two-dimensional heat conduction equation was introduced to study the effect of heat conduction in the axial direction to the rewetting process. The time-dependent two-dimensional heat conduction equation for the inner tube is
1 ∂T ∂ 2T 1 ∂T ∂ 2T = + + α ∂t ∂r 2 r ∂r ∂z 2
(1)
where, α is the thermal diffusivity of the inner tube. To solve this equation, the following assumptions were made. The initial condition for the system was assumed at the desired initial temperature Tinitial . It was assumed that the inner surface and the bottom of the inner tube are thermally insulated. The temperature of the top surface of the inner tube Tcal was calculated by the Berenson correlation (1961) on the assumption that the heat-transfer mode on the top surface is the same as that on a flat horizontal surface. The temperatures of the outer surface of the inner tube were assumed to be the measured temperatures. Therefore, the initial and boundary conditions are
t = 0 : T = Tinitial
z
J-1 J J+1
M
N-1 N
i+1
qout （I,J)
∆z
i
: ∂T ∂r = 0
(3)
r = Ro : T = T w
(4)
r = Ri
Thermally insulated
qr
qc
(2)
z=0
: ∂T
z=h
T = Tcal
∂z
=0
(5) (6)
Where, Ri , Ro and h are inner diameter, outer diameter
qin i-1
and heated length of the inner tube, respectively. Ri
Ro Thermally insulated Fig. 4 Diagram of calculating mesh ∆r
r
The finite different method was used to obtain a stable solution. The diagram of the mesh of the inner tube wall was shown in Fig. 4. The mesh size ∆r in the
r-direction was selected as 1.0mm, the mesh size ∆z in the z-direction was 10.0mm, and the time step ∆t was 0.01 second. The inner tube wall temperatures at those meshes at which no measurements were made were calculated on the assumption that the rewetting velocity was the same. The temperature at each mesh point was calculated by solving the above equations. Based on the calculated mesh temperatures, the heat flux qc at the outer surface of the inner tube was therefore calculated from the heat balance equation in the control volume as Tin, N − Ti n, N−1 1 1 ρc w ∆z∆r = ∆r (qin − q out ) + ∆zq r − ∆zq c , ∆t 2 2
(7)
where κ 1 − 1 3T n , qin = − w 3Tin, N + T n +T n i, N −1 4 i −1, N i −1, N −1 ∆z 4
6
(8)
κ 1 − 1 3T n + T n , q out = − w 3T n +T n i , N i + 1 , N i + 1 , N − 1 i , N 1 − 4 ∆z 4 qr = −
(9)
κw n , −T n T i, N −1 0.5∆r i, N
(10)
where, κ w , ρ and c w are thermal conductivity, density and heat capacity of the inner tube, respectively. The heat-transfer coefficient hcoe was therefore obtained by the equation
qc = hcoe ∆Tsat , ∆Tsat = Tw − Tsat .
(11)
Therefore, the boiling curve for each gap cooling process was drawn by the relationship between the heat flux qc and the wall superheat ∆Tsat .
3.3 Heat Transfer Characteristics The boiling curves for the gaps
TC-1 TC-2 TC-3 TC-4 TC-5 TC-6
1.0mm, 2.0mm, 4.0mm and 7.0mm at 800oC
temperature
were
3.3.1
2
calculated.
3
10
Heat Flux [kw/m ]
initial
Local Boiling Curves
The calculated boiling curves
Kutateladze(NB)
1
Vapor laminar flow 0
Figs.5,
6
and
1
10
2
10
10
o
3
10
Superheat [ C]
sizes 1.0mm, 2.0mm and 4.0mm were in
Bromley(FB) Murase(NB) at high superheat
positions TC1 through TC6 for gap shown
Murase(TB) Chunlin Xia Gap=1.0mm
Murase(NB) at low superheat
2
10
10
using the local heat flux of the
o
Tinitial=800 C
CHF by kutateladze
Fig.5 Local boiling curves for Gap 1.0mm
Fig.7,
respectively. It was indicated that the present boiling curves for the gap cooling were similar to those for pool
3
10 2
Heat Flux [kw/m ]
boiling. From the local boiling curves
TC-1 CHF by Kutateladze Tinitial=800oC TC-2 TC-3 Chunlin Xia Gap=2.0mm Murase(TB) TC-4 TC-5 TC-6 Bromley(FB) Murase(NB) at low superheat Murase(NB) at high superheat
for gap size 1.0mm as shown in Fig.5, it was
observed
that
there
is
little
difference among the local boiling curves except in the nucleate boiling region. From the average of the local
2
10
Kutateladze(NB) 1
Vapor laminar flow
10
boiling curves, for the gap size 1.0mm,
0
10
1
10
2
o
10
3
10
Superheat [ C]
the minimum superheat for stable film
Fig.6 Local boiling curves for Gap 2.0mm
boiling (MFB) ∆TMFB is about 220oC,
7
and the superheat ∆TCHF for CHF is about 80oC. The average value of CHF for From the local boiling curves of the gap some differences observed in the local boiling curves for the superheat ∆TMFB . The average superheat ∆TMFB is about 250oC, which is higher than that of gap
3
10 2
Heat Flux [kw/m ]
size 2.0mm shown in Fig.6, there were
o
TC-1 TC-2 TC-3 TC-4 TC-5 TC-6
the gap size 1.0mm is near 270 kw/m2.
2
CHF by Kutateladze
Chunlin Xia Gap=4.0mm Murase(TB)
Bromley(FB)
Murase(NB) at low superheat
10
Murase(NB) at high superheat Kutateladze(NB)
1
10
size 1.0mm, and the superheat ∆TCHF is close to 90oC, which is also higher than
Vapor laminar flow 0
10
that of gap size 1.0mm. The average value
Tinitial=800 C
1
10
2
o
10
Superheat [ C]
3
10
Fig.7 Local boiling curves for Gap 4.0mm
of CHF for the gap size 2.0mm is about 600 kw/m2. The local boiling curves for
the gap size 4.0mm were shown in Fig.7. It was observed that there are some scatters for the local boiling curves. The average superheat ∆TMFB is about 300oC and ∆TCHF is about 100oC, which are higher than that of gap size 2.0mm. The average value of CHF for the gap size 4.0mm is about 1000 kw/m2. 3.3.2
Influence of the Heat Conduction in the Axial Direction
The effect of the heat conduction in the axial direction was discussed by comparing the boiling curves calculated by both two-dimensional and one-dimensional heat conduction equations. The comparison results for the gap size 1.0mm at initial temperature 800oC are shown in the Fig.8. It is observed that the effects of heat conduction along the channel on the boiling curve are different at different positions. Since the rewetting process occurred from both top and bottom ends of the channel for the gap size 1.0mm, it is not difficult to understand that the effect of the heat conduction at the top and bottom positions of the channel is obvious, while the effect at the middle position of the heated channel is small. It is indicated that the minimum superheat for stable film boiling calculated by two-dimensional equation is lower than that calculated by one-dimensional equation. At the position TC-6 near the bottom of the heated channel, it is shown that the wall superheat ∆TMFB calculated by two-dimensional model reduced about 50oC compared with the result calculated by one-dimensional model. This means that at the rewetting time, the beginning of the abrupt drop of the temperature is caused firstly by the heat conduction in the axial direction where large temperature difference exists. This result indicates that there is a possibility that the heat conduction in the axial direction contributes to promote the rewetting process. For the gap size 2.0mm and 4.0mm, the same results as those for the gap size 1.0mm was observed. This result supports the conjecture proposed by Tanaka
8
(2003) that the heat flux is over-estimated in one-dimensional heat conduction equation when the heat conduction along the channel is large.
o
o
Gap=1.0mm, Tinitial=800 C, TC-2 position
Gap=1.0mm, Tinitial=800 C, TC-1 position Two-dimensional One-dimensional
3
Two-dimensional One-dimensional
3
Heat Flux [kw/m ]
10 2
2
Heat Flux [kw/m ]
10
2
10
1
2
10
1
10
10 0
1
10
2
10
10
o
3
0
10
10
1
2
10
Superheat [ C]
(2)
o
Gap=1.0mm, Tinitial=800 C, TC-3 position
Two-dimensional One-dimensional
3
Heat Flux [kw/m ]
10 2
2
Heat Flux [kw/m ]
o
Gap=1.0mm, Tinitial=800 C, TC-4 position
Two-dimensional One-dimensional
3
2
10
1
10
2
10
1
10 0
10
1
2
10
10
3
10
0
10
o
Superheat [ C]
1
2
10
o
o
Gap=1.0mm, Tinitial=800 C, TC-6 position
Two-dimensional One-dimensional
3
3
10
(4)
Gap=1.0mm, Tinitial=800 C, TC-5 position
Two-dimensional One-dimensional
3
10
2
2
Heat Flux [kw/m ]
10
10
o
Superheat [ C]
(3)
Heat Flux [kw/m ]
3
10
Superheat [ C]
(1)
10
10
o
2
10
1
2
10
1
10
10 0
10
1
2
10
10
3
10
o
1
2
10
o
10
Superheat [ C]
Superheat [ C]
(5)
Fig. 8
0
10
(6)
Comparisons of the boiling curves calculated by both
two-dimensional and one-dimensional heat conduction equations for gap size 1.0mm
9
3
10
3.3.3
Effect of the gap size
The effect of the gap size on the characteristic of the gap cooling was analyzed by comparing the boiling curves for various gap sizes at the same initial temperature. Figure 9 shows the comparison results for the gap sizes 1.0mm, 2.0mm 4.0mm and 7.0mm at initial temperature 800oC. Also, existing correlations were used to compare with the present boiling curves for better understanding of the heat-transfer characteristics of the gap cooling. In the film boiling region, the heat transfer coefficient due to laminar vapor flow was used. The effect of radiative heat transfer was also considered in the present study. The heat transfer coefficient due to laminar vapor flow in the gap is described by
κg , (12) hcoe = Nu. Dh where, Nu is the Nusselt number for the laminar vapor flow and is chosen as 4.0, and κ g and Dh are thermal conductivity of vapor and the hydrodynamic diameter (2 × gap size), respectively. The Bromley correlation (1950) developed for the film boiling in a pool boiling on vertical surface was also used in the present study. In the transition and nucleate boiling regions, the Murase (2001) correlation developed for gap cooling was used.
q ∆Ts
L κ f
κ f ∆Ts = C ρ g ∆h fg υ f
n1
PL n 2 , σ
(13)
where, ρ f and ρ g are density of liquid and vapor, g gravitational acceleration, σ surface tension, ∆h fg latent heat of vaporization, P
atmospheric pressure, κ f
and κ g
thermal
conductivity of the liquid and vapor, υ f liquid kinetic viscosity, respectively. L is calculated by
σ L= g ρ f − ρ g
(
)
0.5
,
(14)
where, coefficients C, n1 and n2 are C = 1.2 × 10 14
n1 = −5.5
n2 = 0.32 , for transition boiling region,
C = 1.1
n1 = 0.3
n2 = 0.32 , for nucleate boiling region at lower superheat,
C = 2.2
n1 = −0.1
n2 = 0.32 , for nucleate boiling region at high superheat.
CHF for the gap cooling was supposed to be lower than that of pool boiling due to the effect of CCFL. In the present study, the Chunlin Xia et al. (1996) correlation described in the following was used.
10
qCHF =
( (
) )0.25
∆h fg σg ρ f − ρ g ρ g2 4.59 + 0.11(
Lh
Dg
,
(15)
)
where D g is gap size and Lh is heated length. In the film boiling region, it is observed that the smaller the gap size is, the lower the heat transfer coefficient is. This is due to the effect of CCFL. The smaller the gap size is, the effect of CCFL is stronger. For the gap size 1.0mm, the boiling curve is close to the correlation calculated by the heat transfer correlation for vapor laminar flow, and for the gap size 4.0mm, the boiling curve is close to that calculated by the Bromley correlation of pool. It is observed that for the gap size 2.0mm, the boiling curve is between the results for the vapor laminar flow and the Bromley correlation. In the transition boiling
o
Tinitial=800 C, TC-1 position
region, it is shown that the Murase’s
TB
3
correlation
10
qualitatively; but over-predicts the
heat-transfer
coefficient
quantitatively. In the nucleate boiling region, it was indicated
2
10
1
10
that the Murase NB correlations
0
1
10
agree well with the present results both at the low superheat
Chunlin Xia Gap=4.0mm Chunlin Xia Gap=2.0mm Chunlin Xia Gap=1.0mm Bromley(FB) Gap=1.0mm Murase(NB) Gap=2.0mm at high superheat Gap=4.0mm Gap=7.0mm Murase(NB) at low superheat Kutateladze(NB) Vapor laminar flow
2
Heat Flux [kw/m ]
reproduces the present result
Murase(TB)
CHF by Kutateladze
10
2
o
10
Superheat [ C]
3
10
Fig. 9 Comparison of boiling curves for different gap size
and high superheat regions. For the case of gap size 7.0mm, the present result is mostly close to the Kutateladze NB correlation, which indicates that in this case, the heat-transfer characteristic is close to that of pool boiling. As regards to CHF for the gap sizes 1.0mm～4.0mm, it is indicated that Chunlin Xia’s CHF correlation reproduces the CHF observed in the present study, although the Chunlin Xia correlation slightly under-predicts the CHF. For the gap size 7.0mm, it turned out that the Kutateladze correlation reproduces the present CHF results well. From the results shown in Fig.9, the effect of gap size on the heat transfer characteristics was concluded as (1) For minimum film boiling heat flux (MFB), the smaller the gap size is, the lower the heat flux for MFB and the wall superheat at ∆TMFB are. This means that when the gap size is smaller, the
11
lower superheat is required for the beginning of transition from the film boiling. This is due to the strong CCFL effect occurred in the small gap clearance. (2) For critical heat flux (CHF), the smaller the gap size is, the lower the CHF and ∆TCHF are due to the effect of CCFL. This means that when the gap size is larger, the heat transfer coefficient is larger and the possibility of the occurrence of CHF is lower. (3) For film boiling process, it was found that when the gap size is smaller, the heat-transfer coefficient becomes smaller due to the restricted space, and with the increase of the gap size, the heat-transfer coefficient is increased and close to the heat-transfer characteristic of pool boiling. (4) For transition boiling process, it was found that the smaller the gap size is, the lower the heat-transfer coefficient is. (5) For nucleate boiling process, it was found that it is the most sensitive region affected by the gap size. It was indicated that over the range of gap size 1.0mm～4.0mm, the smaller the gap size is, the larger the heat transfer coefficient is, which is different from the heat-transfer characteristics of film boiling and transition boiling. It could be explained, as discussed by Ishibashi and Nishikawa, by the fact that the characteristics of boiling heat transfer in a narrow gap depend significantly on the gap clearance due to the constraint of bubble motion in the narrow gap. (6) From the present results, it was concluded that when the gap size is larger than 4.0mm, the heat-transfer characteristics approach to that of pool boiling. While when the gap size is in the range from 4.0mm to 1.0mm, the heat transfer characteristics are significantly affected by the constraint of fluid motion due to the proximity of the walls. Therefore, the heat-transfer coefficient needs to evaluate by special correlations for gap cooling. 4
CONCLUSIONS The quenching experiments for gap size from 0.5mm to 7.0mm at initial temperatures 500oC,
650oC and 800oC were carried out in the present study. Using the measured transient temperature history, the heat transfer characteristics of the gap cooling were analyzed by the time-dependent two-dimensional heat conduction equation. The calculated boiling curves were compared with the existing correlations developed by other researchers, and the heat transfer characteristics of the gap cooling depending on the gap clearance were discussed. In addition, by comparing the boiling curves obtained from two-dimensional and one-dimensional calculations, the effect of axial heat conduction on the rewetting process was discussed. Results obtained are: (1) The present boiling curves for the gap cooling were similar to those for pool boiling. (2) It was observed that there is a trend that the smaller the gap clearance is, the lower the wall superheat ∆TMFB and ∆TCHF are. The heat flux of the minimum film boiling and critical heat flux are also lower. (3) The heat conduction in the axial direction contributed to the beginning of the temperature drop
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and accelerated the rewetting process. For the study of rewetting process, the two-dimensional calculation should be performed for more realistic evaluation. (4) It is concluded that the heat transfer coefficient in the small gap depends significantly on the gap clearance. In the film boiling region, the heat transfer coefficient in the small gap becomes much smaller than that of pool boiling due to the strong effect of CCFL. In the nucleate boiling region, the heat transfer coefficient is significantly affected by the constraint of bubble motion in the narrow gap. (5) For the present study, the Chunlin Xia correlation reproduced the CHF well. In the transition and nucleate boiling regions, the Murase correlations reproduced the results well.
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