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Experimental study on flow pattern and heat transfer of inverted annular flow
Nuclear Engineering and Design 120 (1990) 293-300 North-Holland
293
EXPERIMENTAL STUDY ON FLOW PATrERN AND HEAT TRANSFER OF INVERTED ANNULAR FLOW N o b u y u k i T A K E N A K A , Koji A K A G A W A , Terushige F U J I I a n d K o j i N I S H I D A
Department of Mechanical Engineering, Kobe University, Rokkodai, Nada, Kobe, 657, Japan
Experimental results are presented on flow pattern and heat transfer in the regions from inverted annular flow to dispersed flow in a vertical tube using freon R-113 as a working fluid at atmospheric pressure to discuss the correspondence between them. Axial distributions of heat transfer coefficient are measured and flow patterns are observed. The heat transfer characteristics are divided into three regions and a heat transfer characteristics map is proposed. The flow pattern changes from inverted annular flow (IAF) to dispersed flow (DF) through inverted slug flow (ISF) for lower inlet velocities and through agitated inverted annular flow (AIAF) for higher inlet velocities. A flow pattern map is obtained which corresponds well with the heat transfer characteristic map.
1. Introduction When subcooled liquid is poured into a conduit the temperature of which is higher than the rewetting temperature, a post-dryout two-phase flow is formulated. The flow pattern near the inlet is inverted annular flow (IAF) which has a liquid core surrounded by a vapor annulus. With an increase in quality the liquid core is broken and finally the flow pattern changes to dispersed flow (DF). The flow pattern changes from separated to homogeneous flow inversely in comparison to that in a pre-dryout two-phase flow from a bubbly flow to an annular flow. This flow pattern is supposed to exist in the rod bundles of a light water reactor in a loss of coolant accident, in the steam generator of a fast breeder reactor and in a cryogenic fluid flow. Many experimental and theoretical studies on heat transfer in steady and unsteady IAF have been conducted to analyze reflooding phenomena in a hypothetical loss of coolant accident. IAF in a vertical tube was studied for the safety considerations of BWR and PWR type reactors. Heat transfer in IAF has been analyzed by modified Bromley's correlations, turbulent boundary layer theories and two-fluid models. Reviews of relevant literature are made in refs. [1-3]. However not so many studies have dealt with the whole flow patterns ranging from IAF to DF. Dougall and Rohsenow [4] studied post-dryout heat transfer on the inside of vertical tubes with upward flow using freon R-113. They visualized the flow pattern and
observed IAF in a low quality region and DF in a high quality region. They proposed two heat transfer models, a separated flow model for IAF using a turbulent boundary layer theory and a homogeneous model for D F using a Dittus-Boelta type equation. Chi and Vetere [5] studied post-dryout flow during the transient boiling of hydrogen in a horizontal tube and observed three flow patterns, IAF, inverted slug flow (ISF) and DF. Laverty and Rohsenow [6] observed the flow patterns in a vertical tube using liquid nitrogen as a working fluid. They reported that the liquid core of the IAF was tom into liquid filaments and droplets owing to the drag force at the liquid-gas interface and the flow pattern changed finally to a dispersed flow. Otten [7] measured the void fraction for liquid nitrogen IAF in a vertical tube using "r-rays. They also observed the flow pattern and concluded that the flow pattern changed to a dispersed droplet flow at the void fraction of 80%. Aritomi et al. [8] observed R-113 IAF in a vertical tube and reported that IAF changed to DF through inverted slug flow (ISF). De Jarlais and Ishii [9] performed an adiabatic simulation study of IAF using coaxial down flow jets of water and various gases. They observed the behaviors of the liquid-gas interface, the break-up mode and the break-up length. De Jarlais and Ishii [10] carried out a visual observation of two-component up-flows using R-113 and inert gases. The wall was heated up to temperatures higher than the rewetting temperature by hot oil. The results obtained in this experiment were compared with those obtained in the previous adiabatic simulation. They clarified the existence of the agitated
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N. Takenaka et al. / Experimental study on flow pattern and heat transfer
region where violent disturbances were observed at the liquid-gas interface between I A F and D F and proposed a mirror image theory in which IAF, agitated flow and D F corresponded to bubbly, slug and churn, and annular flows, respectively. Recently Ishii and Denten [11] reported detailed experimental results on the classification of the flow patterns, which are divided into four regimes, smooth, rough wavy, agitated and dispersed regimes, respectively. The axial extent of each flow regime is correlated and simplified correlations are only determined by capillary number for the liquid jet core. Visualizations of the flow patterns have been made using a quartz tube for a sight glass in many studies. Recently, a new method was attempted to visualize IAF by using real-time neutron radiography. Costigan and Wade [12] and Harris and Seymour [13] used a cold neutron beam from a reactor and Takenaka et al. [14] used a thermal neutron beam generated by using a cyclotron to visualize IAF in a stai.'nless steel tube. As most metals are transparent to neutron beams, while water is opaque to them, neutron radiography will be a useful method to study the flow pattern of IAF in high temperature and high pressure conditions. Many flow pattern maps for pre-dryout two-phase flow have been proposed, however, flow pattern maps for post-dryout two-phase flow have not been studied well. The present authors have been studying the flow pattern, heat transfer and pressure drop in the region from IAF to D F in a vertical and a horizontal tube using freon R-113 and liquid nitrogen as a working fluid to clarify the correspondence of these characteristics and some results have already been presented at Japanese conferences [1-3]. In this paper, the primary experimental results are presented on flow pattern transition and heat transfer of IAF in a vertical tube using freon R-113 to discuss the correspondance between the flow pattern and the heat transfer characteristics. The analytical results and comparisons with the experimental results will be published soon.
Fig. 1. Schematic diagram of experimental apparatus; (1) condenser, (2) tank, (3) separator, (4) pump, (5) test section, (6) subcooler, (7) super joint, (8) flow meter, (9) solenoid valve, (10) heat exchanger, (11) adjustable transformer, (12) bypass line.
separating the liquid and the vapor in a separator, 3, the vapor was condensed in a condenser tank, 1. Two types of test section were used for measuring the heat transfer coefficient and observing the flow patterns. The details of each test section are shown in figs. 2(a) and (b). The test section for measuring the heat transfer coefficient as shown in fig. 2(a) was made
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2. Experimental apparatus and procedures
"
(a)
800 690
700 600
A schematic diagram of the experimental apparatus is shown in fig. 1. The experiments were carried out under atmospheric pressure; freon R-113 as a working fluid was supplied to vertical test section, 5, through a flow meter, 8. The flow rate was adjusted by controlling the revolution of a pump, 4, and a needle valve to avoid the flow instabilities. The inlet liquid subcooling was controlled by a subcooler, 6, and heaters, 10. After
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Hot Patch Fig. 2. Test sections.
500 -- 400 -
-
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(b)
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295
N. Takenaka et al. / Experimental study on flow pattern and heat transfer Type 304 Stainless / Steel Tube
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of type 304 stainless steel tubes of 900 and 1485 mm in heating length, 10 mm in I.D. and 1 mm in thickness. AC electric power was supplied to the test section through brazed electrodes. In order to fix the quench front, a sheathed heater was coiled around the inlet electrode to form the hot patch. The heat loss from the test section covered with thermal insulators was estimated to be less than about 1% of the total heat input. The temperature was measured at twenty points along the tube by CA thermocouples of 0.1 mm in wire diameter welded on the outer surface of the tube. The measured temperature was assumed to be equal to the inner wall temperature as the temperature difference between the outer and the inner wall was estimated to be less than 1% of the temperature difference between the inner wall temperature and the saturation temperature. An attempt was made to measure the vapor and the liquid temperatures near the inlet and the outlet of the heated test section by inserting sheathed thermocouples through the ends of the heated test section. The temperature of the subcooled liquid core of IAF could be measured; however, the measured values in other flow regions were just equal to the saturation temperature. It was seen from the observation using the sight glass as described below that the thermocouples were always rewetted and the vapor temperature could not be measured in the present experimental conditions. Therefore, the thermal non-equilibrium of the dispersed flow could not be discussed experimentally in the present study. The test section for observing the flow patterns, shown in fig. 2(b), was similar to the test section as shown in fig. 2(a) except that a sight glass shown in fig.
3 was placed between the heated stainless tubes. The sight glass was made of a quartz tube of 35 mm in length, 10.5 mm in I.D. and 1.5 mm in thickness. It was heated by a nichrome wire coiled around the quartz tube in order to avoid the rewetting. Sheathed heaters were also coiled around the brazed flanges. The transition of the flow pattern along the tube was observed by using a quartz tube of 500 mm in length and 10.5 mm in I.D. heated by a nichrome wire coiled around it, although the heat flux could not be determined quantitatively. A high speed camera, a 35 mm still camera and a high speed video camera were used for observing the flow patterns. Before experimental runs, R-113 was circulated through the bypass line, 12, while the test tube was heated. Then R-113 was introduced to the test tube by operating the solenoid valves, 9, and a steady postdryout flow was obtained. The experimental conditions are as follows; the heat flux from 40 to 90 k W / m 2, the inlet velocity from 0.09 to 0.85 m / s and the inlet subcooling from 10 to 40 K.
3. Experimental results and discussion 3.1. Axial distribution of heat transfer coefficient
The heat transfer coefficient h is defined as q/(Tw T~) in the present study, where Tw is the wall temperature and T~ is the saturation temperature. The axial distributions of the heat transfer coefficient for the inlet subcooling ATe,b of 10 K and the inlet velocity vin of 0.42 m / s are shown in fig. 4 with the heat flux q as a parameter. It can be seen from the figure that the heat transfer coefficient is almost con-
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Fig. 4. Axial distributions of heat transfer coefficient with heat .flux as a parameter.
N. Takenaka et al. / Experimental study on flow pattern and heat transfer
296
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,
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,
,
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Fig. 5. Axial distributions of heat transfer coefficient with inlet velocity as a parameter.
0.4 ' 0.6' 0'.8 1.0 Xeq Fig. 7. Heat transfer coefficient against thermodynamic equilibrium quality with heat flux as a parameter.
stant near the inlet and increases with a large gradient, and finally with a rather small gradient at each heat flux. These three characteristic regions of heat transfer are defined as regions I, II and III, respectively. The distances from the inlet to the boundary points are denoted as zi_ . and zn_ m respectively. It is seen that both zi_ n and Zli_m decrease with increasing heat flux. It is expected that these three heat transfer characteristics correspond to the flow patterns. The axial distributions of the heat transfer coefficient for ATsub = 10 K and q = 50 k W / m 2 are shown in fig. 5 with vi. as a parameter. The characteristics of the axial distributions for vi, higher than 0.21 m / s are similar to those shown in fig. 4, while no increase with a large gradient is observed for vi, lower than 0.14 m/s. It is expected that the flow pattern transition for inlet velocities lower than 0.14 m / s will be different from those higher than 0.21 m/s. It is seen that both zi_ n and Zn_ m increase with increasing the inlet velocity. The axial distributions of
the heat transfer coefficient for Vin = 0.42 m / s and q = 6 0 k W / m 2 are shown in fig. 6 with ATe,b as a parameter. It is shown that both zI_ n and Zil_iil increase with increasing ATe,b. Figs. 7, 8 and 9 show the heat transfer coefficient plotted as a function of the thermodynamic equilibrium quality Xeq. In the figures, the thermodynamic equilibrium qualities at zl_ii and Zil_iii are denoted as X~ql_n and Xeqil_i n and are shown by broken fines. It is seen from figs. 7 and 9 that the heat transfer coefficient and the boundary points are correlated well by using the thermodynamic equilibrium quality. It is also seen from fig. 8 that these values are strongly dependent on the inlet velocity. These results show the same tendencies as those in pre-dryout two-phase flow heat transfer characteristics which are determined by the inlet velocity and the quality. Most of the previous correlations on post-dryout heat transfer were based on Bromley's equation [15] and
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Fig. 8. Heat transfer coefficient against thermodynamic equilibrium quality with inlet velocity as a parameter.
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N. Takenaka et al. / Experimental study on flow pattern and heat transfer
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-0.2
/
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Fig. 9. Heat transfer coefficient against thermodynamic equilibrium quality with subcooling as a parameter.
Dougall and Rohsenow's equation [4]. Bromley's equation was formulated for saturated natural convective film boiling heat transfer from a vertical surface. It has been modified to predict the post-dryout heat transfer in a low quality region. The modifications have been carried out to consider the effects of the liquid velocity and the thermal non-equilibrium caused by the superheated vapor and the subcooled liquid. Dougall and Rohsenow's equation was formulated for a thermal equilibrium dispersed flow based on the Dittus-Boelter equation. It has been modified to predict the post-dryout heat transfer in the high quality region by considering the thermal non-equiIbrium due to the vapor superheat. The solid lines in fig. 8 are calculated by DougallRohsenow's equation [4] for post-dryout dispersed flow, Nu = 0.023
Xeq +
(1 - Xeq)
/]
Prg°'4,
(1)
hD/kg.
where Nu = The physical properties are evaluated at the saturation temperature. Eq. (1) predicts fairly well the heat transfer coefficients in the high quality region where the flow pattern is expected to be a dispersed flow. Axial distributions of the heat transfer coefficient for a low inlet velocity of 0.09 m / s are shown in fig. 10 for ATe,b = 10 K with q as a parameter and in fig. 11 for q = 73 k W / m 2 with ATsub as a parameter. The solid lines in figs. 10 and 11 are calculated by eq. (1). The broken lines are calculated by Bromley's equation [15] for saturated film boiling which can be rewritten as eq. (2) with h versus Xeq coordinate,
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Fig. 10. Heat transfer coefficient against thermodynamic equilibrium quality for low inlet velocity with heat flux as a parameter.
With increasing quality, the heat transfer coefficient decreases sightly in the low quality region and then it is almost constant until the quality is equal to 1. Bromley's equation can only be adopted for the low quality region and indicates a similar tendency to, but smaller than, the experimental results. It can be seen that the flow pattern has little effect on heat transfer characteristics for lower inlet velocities, while those for higher inlet velocities are affected strongly. Similar heat transfer characteristics to those as shown in figs. 10 and 11 have been studied to predict the reflooding phase in a LOCA as the inlet velocity in a LOCA is low. Therefore, either Bromley's equation or Dougall-Rohsenow's equation can be modified to agree with the experimental results. However, as it is difficult to correlate a whole region from I A F to D F for higher inlet velocities by two correlations, the flow pattern transition for post-dryout two-phase flow should be clarified. *0
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Fig. 11. Heat transfer coefficient against thermodynamic equilibrium quality for low inlet velocity with subcooling as a parameter.
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N. Takenaka et al. / Experimental study on flow pattern and heat transfer
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Xeq Fig. 12. Heat transfer characteristic map.
(a)
(b)
Fig. 13. Flow pattern along a tube: (a) at lower inlet velocity; (b) at higher inlet velocity. 3.2. Heat transfer characteristic map and flow pattern map
It was clarified in the previous paragraph that the heat transfer characteristics could be divided into three regions along the tube for inlet velocities higher than 0.21 m / s but was not divided for inlet velocities lower than 0.14 m/s. The heat transfer coefficient was dependent on the thermodynamic equilibrium quality and the inlet velocity. In order to discuss these heat transfer characteristics, a heat transfer characteristic map as shown in fig. 12 is proposed, where the thermodynamic equilibrium qualities of the boundaries X e q i _ l i and Xeq]i_[i] are plotted against the inlet velocity. A broken line in the map shows the inlet velocity of 0.14 m/s, which indicates the boundary between whether the heat transfer characteristics along the tube were divided into three regions or not. It is found that the heat transfer characteristic regions I, II and III, are not strongly dependent on the heat flux nor the inlet subcooling and that they are determined by the thermodynamic equilibrium quality and the inlet velocity. Before discussing the relationship between the heat transfer map and the flow pattern map, flow patterns observed in a long quartz tube of 500 mm in length and 10 mm in I.D. are discussed. The quartz tube was heated by a nichrome wire coiled around it to avoid the rewetting though the heat flux could not be determined quantitatively. Two typical transitions of the flow patterns depending on the inlet velocity were observed and are shown schematically in fig. 13 for lower and higher inlet velocities.
For the lower inlet velocity, the flow pattern changes from IAF to D F through a flow pattern where liquid slugs are observed, which is defined as inverted slug flow (ISF). For the higher inlet velocity, the flow pattern changes from IAF to DF through a flow pattern which is characterized by periodic changes of a thick vapor film region and the agitated region as already reported by De Jarlais and Ishii [11]. In the agitated region, violent disturbances of the liquid-gas interface and small droplets entrained from a downstream edge of the liquid core are observed and the vapor layer seems to be very
1.2 1.0
,,.,=,0:/
XeqI~ Xeql-m
o IAF
(*kl
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q
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//
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/
.l.
/ j
~.e
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~0.6 O.4 0.2 0 -0.1
cIiI
I
0
0.1
I
I
I
0.2 0.3 0.4
l
0.5
Fig. 14. Flow patterns on heat transfer characteristic map.
N. Takenaka et al. / Experimental study on flow pattern and heat transfer
thin. This periodic flow pattern with the agitated region is defined as agitated inverted annular flow (AIAF) in this paper. It is expected from the qualitative observations of the flow patterns that the heat transfer characteristics along the tube as mentioned in the previous paragraph correspond strongly to the flow pattern. To clarify these relationships quantitatively, the flow patterns for the inlet subcooling ATe,b = 10 K were
299
observed through the sight glass equipped between the heated stainless steel tubes with a high speed camera, a 35 mm still camera and a high speed video camera. Three visual points, 0.3, 0.65 and 1.1 m from the inlet of the 1485 mm long tube were chosen for the observations. It was confirmed that the heat transfer coefficient for the distance with the sight glass is almost the same as that without the sight glass by neglecting the heat input at the quartz tube. The thermodynamic equilibrium quality is calculated at the inlet of the sight
glass.
IAF
The flow patterns, i.e., IAF, AIAF, ISF and D F are determined from observations with a high speed, a 35 nun still and a high speed video camera, are plotted on the heat transfer characteristic map in fig. 14. As A I A F is characterized by the periodic agitations, the flow pattern differences between A I A F and I A F and between A I A F and D F are fairly well determined. Photographs of typical flow patterns of IAF, A I A F and D F at points (a)-(d) in fig. 14 are shown in figs. 15 (a)-(d), respectively. It is successfully shown that the heat transfer characteristic regions I, II and III correspond to the flow patterns IAF, A I A F and DF, respectively.
4. Conclusions
AIAF
(C
ISF
tel DF Fig. 15. Flow patterns.
Flow pattern and heat transfer characteristics in the region from inverted annular flow to dispersed flow in a steady state were studied experimentally. The experiments were carried out using a refrigerant R-113 in a vertical tube of 10 mm (I.D.) at atmospheric pressure. The axial distributions of the heat transfer coefficient were measured and the flow patterns were observed. The following conclusions were obtained. (1) Heat transfer coefficient along the tube is affected by the heat flux, the inlet velocity and the inlet subcooling. The relationship between the heat transfer coefficient and the thermodynamic equilibrium quality is not strongly affected by the heat flux and the inlet subcooling, but much affected by the inlet velocity. (2) Heat transfer characteristic along the tube are divided into three regions: I, II and III. A heat transfer characteristic map using the thermodynamic equilibrium quality and the inlet velocity as coordinates is proposed. (3) The flow pattern changes from inverted annular flow (IAF) to dispersed flow (DF) through inverted slug flow (ISF) and changes from I A F to D F through agitated inverted annular flow (AIAF) for higher inlet velocity.
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N. Takenaka et al. / Experimental study on flow pattern and heat transfer
(4) The flow patterns in the regions I, II and III correspond well to IAF, A I A F and DF, respectively.
Nomenclature D h Hlg k Nu Pr q T ATsub Oin Xeq 2, P
tube inner diameter, (m) heat transfer coefficient, ( W / m 2 K), latent heat of vaporization, (J/kg), thermal conductivity, (W//m 2 K), Nusselt number, Prandtl number, heat flux, ( W / m 2), temperature, (K), subcooling, (K), inlet velocity, (m/s), thermodynamic equilibrium quality, axial distance from the inlet, (m), viscosity, (kg/ms), density, (kg/m3).
Subscript
g 1 s w
gas, liquid, saturation, wall.
References [1] K. Akagawa, N. Takenaka, T. Fujii, K. Nishida, Y. Kikuchi and A. Shibata, Flow pattern and heat transfer of inverted annular flow, 1st. Rep. Visualization of flow pattern by high speed camera, 2nd. Rep. Transition condition of flow pattem, 3rd. Rep. Heat Transfer, 4th. Rep. Pressure drop, Proc. 1987 Fall Meet. Atomic Energy Soc. Japan 1 (1987) 316-319. [2] K. Akagawa, N. Takenaka, T. Fujii, K. Nishida and Kikuchi, Flow pattern and heat transfer of inverted annular flow in a horizontal tube, 1987 Annual Meet. Atomic Energy Soc. Japan 1 (1987) 25.
[3] K. Akagawa, T. Fujii, N. Takenaka, K. Nishida, Kikuchi and A. Shibata, A study of flow pattern and heat transfer of inverted annular flow, Proc. ASME/JSME Thermal Engng. Conf. 5, Hawaii (1987) 127-134. [4] R.S. Dougall and W.M. Rohsenow, Film boiling on the inside of vertical tubes with upward flow of the fluid at low quality, MIT-TR-9079-26 (1963). [5] J.W.H. Chi and A.M. Vetere, Two-phase flow during transient boiling of hydrogen and determination of nonequilibrium vapor fraction, in Advances in Cryogenic Engng. 9 (Academic Press, New York, 1964) pp. 243-253. [6] W.F. Laverty and W.M. Rohsenow, Film boiling of saturated nitrogen flowing in a vertical tube, Trans. ASME, J. Heat Transfer 89 (1967) 90-98. [7] P. Ottsen, Experimental and theoreical investigation of inverse annular film flow and dispersed droplet flow, important under LOCA conditions, Riso Nat'l Lab. Rep. No. R-424, Denmark (1980). [8] M. Aritomi, A. Inoue, S. Aoki and K. Hanada, Thermal and hydraulic behavior of inverted annular flow, Proc. 2nd. Int. Topical Meet. on Nuclear Power Plant Thermal Hydraulics (1986). [9] G. De Jarlais and M. Ishii, Hydrodynamics of adiabatic inverted annular flow -an experimental study, Proc. 3rd. Multi-phase Flow and Heat Transfer Syrup. Miami (1983). [10] G. De Jarlais and M. Ishii, Inverted annular flow experimental study, NUREG/CR-4277, ANL-85-31 (1985). [11] M. Ishii and J.P. Denten, Experimental study of two-phase flow behavior of post critical heat flux region, Proc. Japan-US Seminar on Two-Phase Flow Dynamics, Ohtsu. J1 (1988). [12] G. Costigan and C.O. Wade, Visualization of the reflooding of a vertical tube by dynamic neutron radiography, Int. Workshop on Post-dryout Heat Transfer, Salt Lake 1-4 (1984). [13] D.H.C. Harris and W.A.J. Seymour, Application of real time neutron radiography at Harwell, Proc. 2nd. Int. Conf. Neutron Radiography (1986) 595-600. [14] N. Takenaka, K. Akagawa, A. Ono and K. Sonoda, Visualization of gas-liquid two-phase flow in a metalic tube, J. Flow Visualization Society Japan 8 (30) (1988)151-154. [15] L.A. Bromely, Heat transfer in stable film boiling, Chem. Engng. Prog. 46 (1950) 221-227.
293
EXPERIMENTAL STUDY ON FLOW PATrERN AND HEAT TRANSFER OF INVERTED ANNULAR FLOW N o b u y u k i T A K E N A K A , Koji A K A G A W A , Terushige F U J I I a n d K o j i N I S H I D A
Department of Mechanical Engineering, Kobe University, Rokkodai, Nada, Kobe, 657, Japan
Experimental results are presented on flow pattern and heat transfer in the regions from inverted annular flow to dispersed flow in a vertical tube using freon R-113 as a working fluid at atmospheric pressure to discuss the correspondence between them. Axial distributions of heat transfer coefficient are measured and flow patterns are observed. The heat transfer characteristics are divided into three regions and a heat transfer characteristics map is proposed. The flow pattern changes from inverted annular flow (IAF) to dispersed flow (DF) through inverted slug flow (ISF) for lower inlet velocities and through agitated inverted annular flow (AIAF) for higher inlet velocities. A flow pattern map is obtained which corresponds well with the heat transfer characteristic map.
1. Introduction When subcooled liquid is poured into a conduit the temperature of which is higher than the rewetting temperature, a post-dryout two-phase flow is formulated. The flow pattern near the inlet is inverted annular flow (IAF) which has a liquid core surrounded by a vapor annulus. With an increase in quality the liquid core is broken and finally the flow pattern changes to dispersed flow (DF). The flow pattern changes from separated to homogeneous flow inversely in comparison to that in a pre-dryout two-phase flow from a bubbly flow to an annular flow. This flow pattern is supposed to exist in the rod bundles of a light water reactor in a loss of coolant accident, in the steam generator of a fast breeder reactor and in a cryogenic fluid flow. Many experimental and theoretical studies on heat transfer in steady and unsteady IAF have been conducted to analyze reflooding phenomena in a hypothetical loss of coolant accident. IAF in a vertical tube was studied for the safety considerations of BWR and PWR type reactors. Heat transfer in IAF has been analyzed by modified Bromley's correlations, turbulent boundary layer theories and two-fluid models. Reviews of relevant literature are made in refs. [1-3]. However not so many studies have dealt with the whole flow patterns ranging from IAF to DF. Dougall and Rohsenow [4] studied post-dryout heat transfer on the inside of vertical tubes with upward flow using freon R-113. They visualized the flow pattern and
observed IAF in a low quality region and DF in a high quality region. They proposed two heat transfer models, a separated flow model for IAF using a turbulent boundary layer theory and a homogeneous model for D F using a Dittus-Boelta type equation. Chi and Vetere [5] studied post-dryout flow during the transient boiling of hydrogen in a horizontal tube and observed three flow patterns, IAF, inverted slug flow (ISF) and DF. Laverty and Rohsenow [6] observed the flow patterns in a vertical tube using liquid nitrogen as a working fluid. They reported that the liquid core of the IAF was tom into liquid filaments and droplets owing to the drag force at the liquid-gas interface and the flow pattern changed finally to a dispersed flow. Otten [7] measured the void fraction for liquid nitrogen IAF in a vertical tube using "r-rays. They also observed the flow pattern and concluded that the flow pattern changed to a dispersed droplet flow at the void fraction of 80%. Aritomi et al. [8] observed R-113 IAF in a vertical tube and reported that IAF changed to DF through inverted slug flow (ISF). De Jarlais and Ishii [9] performed an adiabatic simulation study of IAF using coaxial down flow jets of water and various gases. They observed the behaviors of the liquid-gas interface, the break-up mode and the break-up length. De Jarlais and Ishii [10] carried out a visual observation of two-component up-flows using R-113 and inert gases. The wall was heated up to temperatures higher than the rewetting temperature by hot oil. The results obtained in this experiment were compared with those obtained in the previous adiabatic simulation. They clarified the existence of the agitated
0 0 2 9 - 5 4 9 3 / 9 0 / $ 0 3 . 5 0 © 1990 - Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d )
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N. Takenaka et al. / Experimental study on flow pattern and heat transfer
region where violent disturbances were observed at the liquid-gas interface between I A F and D F and proposed a mirror image theory in which IAF, agitated flow and D F corresponded to bubbly, slug and churn, and annular flows, respectively. Recently Ishii and Denten [11] reported detailed experimental results on the classification of the flow patterns, which are divided into four regimes, smooth, rough wavy, agitated and dispersed regimes, respectively. The axial extent of each flow regime is correlated and simplified correlations are only determined by capillary number for the liquid jet core. Visualizations of the flow patterns have been made using a quartz tube for a sight glass in many studies. Recently, a new method was attempted to visualize IAF by using real-time neutron radiography. Costigan and Wade [12] and Harris and Seymour [13] used a cold neutron beam from a reactor and Takenaka et al. [14] used a thermal neutron beam generated by using a cyclotron to visualize IAF in a stai.'nless steel tube. As most metals are transparent to neutron beams, while water is opaque to them, neutron radiography will be a useful method to study the flow pattern of IAF in high temperature and high pressure conditions. Many flow pattern maps for pre-dryout two-phase flow have been proposed, however, flow pattern maps for post-dryout two-phase flow have not been studied well. The present authors have been studying the flow pattern, heat transfer and pressure drop in the region from IAF to D F in a vertical and a horizontal tube using freon R-113 and liquid nitrogen as a working fluid to clarify the correspondence of these characteristics and some results have already been presented at Japanese conferences [1-3]. In this paper, the primary experimental results are presented on flow pattern transition and heat transfer of IAF in a vertical tube using freon R-113 to discuss the correspondance between the flow pattern and the heat transfer characteristics. The analytical results and comparisons with the experimental results will be published soon.
Fig. 1. Schematic diagram of experimental apparatus; (1) condenser, (2) tank, (3) separator, (4) pump, (5) test section, (6) subcooler, (7) super joint, (8) flow meter, (9) solenoid valve, (10) heat exchanger, (11) adjustable transformer, (12) bypass line.
separating the liquid and the vapor in a separator, 3, the vapor was condensed in a condenser tank, 1. Two types of test section were used for measuring the heat transfer coefficient and observing the flow patterns. The details of each test section are shown in figs. 2(a) and (b). The test section for measuring the heat transfer coefficient as shown in fig. 2(a) was made
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1400
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1200 1100
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-550 500 450 - - 400 --350 300 250 -200 -150 100 50
2. Experimental apparatus and procedures
"
(a)
800 690
700 600
A schematic diagram of the experimental apparatus is shown in fig. 1. The experiments were carried out under atmospheric pressure; freon R-113 as a working fluid was supplied to vertical test section, 5, through a flow meter, 8. The flow rate was adjusted by controlling the revolution of a pump, 4, and a needle valve to avoid the flow instabilities. The inlet liquid subcooling was controlled by a subcooler, 6, and heaters, 10. After
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Hot Patch Fig. 2. Test sections.
500 -- 400 -
-
300 2OO IO0
(b)
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295
N. Takenaka et al. / Experimental study on flow pattern and heat transfer Type 304 Stainless / Steel Tube
I
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L Fig. 3. Details of sight glass.
of type 304 stainless steel tubes of 900 and 1485 mm in heating length, 10 mm in I.D. and 1 mm in thickness. AC electric power was supplied to the test section through brazed electrodes. In order to fix the quench front, a sheathed heater was coiled around the inlet electrode to form the hot patch. The heat loss from the test section covered with thermal insulators was estimated to be less than about 1% of the total heat input. The temperature was measured at twenty points along the tube by CA thermocouples of 0.1 mm in wire diameter welded on the outer surface of the tube. The measured temperature was assumed to be equal to the inner wall temperature as the temperature difference between the outer and the inner wall was estimated to be less than 1% of the temperature difference between the inner wall temperature and the saturation temperature. An attempt was made to measure the vapor and the liquid temperatures near the inlet and the outlet of the heated test section by inserting sheathed thermocouples through the ends of the heated test section. The temperature of the subcooled liquid core of IAF could be measured; however, the measured values in other flow regions were just equal to the saturation temperature. It was seen from the observation using the sight glass as described below that the thermocouples were always rewetted and the vapor temperature could not be measured in the present experimental conditions. Therefore, the thermal non-equilibrium of the dispersed flow could not be discussed experimentally in the present study. The test section for observing the flow patterns, shown in fig. 2(b), was similar to the test section as shown in fig. 2(a) except that a sight glass shown in fig.
3 was placed between the heated stainless tubes. The sight glass was made of a quartz tube of 35 mm in length, 10.5 mm in I.D. and 1.5 mm in thickness. It was heated by a nichrome wire coiled around the quartz tube in order to avoid the rewetting. Sheathed heaters were also coiled around the brazed flanges. The transition of the flow pattern along the tube was observed by using a quartz tube of 500 mm in length and 10.5 mm in I.D. heated by a nichrome wire coiled around it, although the heat flux could not be determined quantitatively. A high speed camera, a 35 mm still camera and a high speed video camera were used for observing the flow patterns. Before experimental runs, R-113 was circulated through the bypass line, 12, while the test tube was heated. Then R-113 was introduced to the test tube by operating the solenoid valves, 9, and a steady postdryout flow was obtained. The experimental conditions are as follows; the heat flux from 40 to 90 k W / m 2, the inlet velocity from 0.09 to 0.85 m / s and the inlet subcooling from 10 to 40 K.
3. Experimental results and discussion 3.1. Axial distribution of heat transfer coefficient
The heat transfer coefficient h is defined as q/(Tw T~) in the present study, where Tw is the wall temperature and T~ is the saturation temperature. The axial distributions of the heat transfer coefficient for the inlet subcooling ATe,b of 10 K and the inlet velocity vin of 0.42 m / s are shown in fig. 4 with the heat flux q as a parameter. It can be seen from the figure that the heat transfer coefficient is almost con-
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0.6
0.9
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Fig. 4. Axial distributions of heat transfer coefficient with heat .flux as a parameter.
N. Takenaka et al. / Experimental study on flow pattern and heat transfer
296
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,
,
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,
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Fig. 5. Axial distributions of heat transfer coefficient with inlet velocity as a parameter.
0.4 ' 0.6' 0'.8 1.0 Xeq Fig. 7. Heat transfer coefficient against thermodynamic equilibrium quality with heat flux as a parameter.
stant near the inlet and increases with a large gradient, and finally with a rather small gradient at each heat flux. These three characteristic regions of heat transfer are defined as regions I, II and III, respectively. The distances from the inlet to the boundary points are denoted as zi_ . and zn_ m respectively. It is seen that both zi_ n and Zli_m decrease with increasing heat flux. It is expected that these three heat transfer characteristics correspond to the flow patterns. The axial distributions of the heat transfer coefficient for ATsub = 10 K and q = 50 k W / m 2 are shown in fig. 5 with vi. as a parameter. The characteristics of the axial distributions for vi, higher than 0.21 m / s are similar to those shown in fig. 4, while no increase with a large gradient is observed for vi, lower than 0.14 m/s. It is expected that the flow pattern transition for inlet velocities lower than 0.14 m / s will be different from those higher than 0.21 m/s. It is seen that both zi_ n and Zn_ m increase with increasing the inlet velocity. The axial distributions of
the heat transfer coefficient for Vin = 0.42 m / s and q = 6 0 k W / m 2 are shown in fig. 6 with ATe,b as a parameter. It is shown that both zI_ n and Zil_iil increase with increasing ATe,b. Figs. 7, 8 and 9 show the heat transfer coefficient plotted as a function of the thermodynamic equilibrium quality Xeq. In the figures, the thermodynamic equilibrium qualities at zl_ii and Zil_iii are denoted as X~ql_n and Xeqil_i n and are shown by broken fines. It is seen from figs. 7 and 9 that the heat transfer coefficient and the boundary points are correlated well by using the thermodynamic equilibrium quality. It is also seen from fig. 8 that these values are strongly dependent on the inlet velocity. These results show the same tendencies as those in pre-dryout two-phase flow heat transfer characteristics which are determined by the inlet velocity and the quality. Most of the previous correlations on post-dryout heat transfer were based on Bromley's equation [15] and
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Fig. 8. Heat transfer coefficient against thermodynamic equilibrium quality with inlet velocity as a parameter.
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N. Takenaka et al. / Experimental study on flow pattern and heat transfer
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Fig. 9. Heat transfer coefficient against thermodynamic equilibrium quality with subcooling as a parameter.
Dougall and Rohsenow's equation [4]. Bromley's equation was formulated for saturated natural convective film boiling heat transfer from a vertical surface. It has been modified to predict the post-dryout heat transfer in a low quality region. The modifications have been carried out to consider the effects of the liquid velocity and the thermal non-equilibrium caused by the superheated vapor and the subcooled liquid. Dougall and Rohsenow's equation was formulated for a thermal equilibrium dispersed flow based on the Dittus-Boelter equation. It has been modified to predict the post-dryout heat transfer in the high quality region by considering the thermal non-equiIbrium due to the vapor superheat. The solid lines in fig. 8 are calculated by DougallRohsenow's equation [4] for post-dryout dispersed flow, Nu = 0.023
Xeq +
(1 - Xeq)
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where Nu = The physical properties are evaluated at the saturation temperature. Eq. (1) predicts fairly well the heat transfer coefficients in the high quality region where the flow pattern is expected to be a dispersed flow. Axial distributions of the heat transfer coefficient for a low inlet velocity of 0.09 m / s are shown in fig. 10 for ATe,b = 10 K with q as a parameter and in fig. 11 for q = 73 k W / m 2 with ATsub as a parameter. The solid lines in figs. 10 and 11 are calculated by eq. (1). The broken lines are calculated by Bromley's equation [15] for saturated film boiling which can be rewritten as eq. (2) with h versus Xeq coordinate,
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Fig. 10. Heat transfer coefficient against thermodynamic equilibrium quality for low inlet velocity with heat flux as a parameter.
With increasing quality, the heat transfer coefficient decreases sightly in the low quality region and then it is almost constant until the quality is equal to 1. Bromley's equation can only be adopted for the low quality region and indicates a similar tendency to, but smaller than, the experimental results. It can be seen that the flow pattern has little effect on heat transfer characteristics for lower inlet velocities, while those for higher inlet velocities are affected strongly. Similar heat transfer characteristics to those as shown in figs. 10 and 11 have been studied to predict the reflooding phase in a LOCA as the inlet velocity in a LOCA is low. Therefore, either Bromley's equation or Dougall-Rohsenow's equation can be modified to agree with the experimental results. However, as it is difficult to correlate a whole region from I A F to D F for higher inlet velocities by two correlations, the flow pattern transition for post-dryout two-phase flow should be clarified. *0
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,~ 40
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Fig. 11. Heat transfer coefficient against thermodynamic equilibrium quality for low inlet velocity with subcooling as a parameter.
298
N. Takenaka et al. / Experimental study on flow pattern and heat transfer
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(a)
(b)
Fig. 13. Flow pattern along a tube: (a) at lower inlet velocity; (b) at higher inlet velocity. 3.2. Heat transfer characteristic map and flow pattern map
It was clarified in the previous paragraph that the heat transfer characteristics could be divided into three regions along the tube for inlet velocities higher than 0.21 m / s but was not divided for inlet velocities lower than 0.14 m/s. The heat transfer coefficient was dependent on the thermodynamic equilibrium quality and the inlet velocity. In order to discuss these heat transfer characteristics, a heat transfer characteristic map as shown in fig. 12 is proposed, where the thermodynamic equilibrium qualities of the boundaries X e q i _ l i and Xeq]i_[i] are plotted against the inlet velocity. A broken line in the map shows the inlet velocity of 0.14 m/s, which indicates the boundary between whether the heat transfer characteristics along the tube were divided into three regions or not. It is found that the heat transfer characteristic regions I, II and III, are not strongly dependent on the heat flux nor the inlet subcooling and that they are determined by the thermodynamic equilibrium quality and the inlet velocity. Before discussing the relationship between the heat transfer map and the flow pattern map, flow patterns observed in a long quartz tube of 500 mm in length and 10 mm in I.D. are discussed. The quartz tube was heated by a nichrome wire coiled around it to avoid the rewetting though the heat flux could not be determined quantitatively. Two typical transitions of the flow patterns depending on the inlet velocity were observed and are shown schematically in fig. 13 for lower and higher inlet velocities.
For the lower inlet velocity, the flow pattern changes from IAF to D F through a flow pattern where liquid slugs are observed, which is defined as inverted slug flow (ISF). For the higher inlet velocity, the flow pattern changes from IAF to DF through a flow pattern which is characterized by periodic changes of a thick vapor film region and the agitated region as already reported by De Jarlais and Ishii [11]. In the agitated region, violent disturbances of the liquid-gas interface and small droplets entrained from a downstream edge of the liquid core are observed and the vapor layer seems to be very
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0.1
I
I
I
0.2 0.3 0.4
l
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Fig. 14. Flow patterns on heat transfer characteristic map.
N. Takenaka et al. / Experimental study on flow pattern and heat transfer
thin. This periodic flow pattern with the agitated region is defined as agitated inverted annular flow (AIAF) in this paper. It is expected from the qualitative observations of the flow patterns that the heat transfer characteristics along the tube as mentioned in the previous paragraph correspond strongly to the flow pattern. To clarify these relationships quantitatively, the flow patterns for the inlet subcooling ATe,b = 10 K were
299
observed through the sight glass equipped between the heated stainless steel tubes with a high speed camera, a 35 mm still camera and a high speed video camera. Three visual points, 0.3, 0.65 and 1.1 m from the inlet of the 1485 mm long tube were chosen for the observations. It was confirmed that the heat transfer coefficient for the distance with the sight glass is almost the same as that without the sight glass by neglecting the heat input at the quartz tube. The thermodynamic equilibrium quality is calculated at the inlet of the sight
glass.
IAF
The flow patterns, i.e., IAF, AIAF, ISF and D F are determined from observations with a high speed, a 35 nun still and a high speed video camera, are plotted on the heat transfer characteristic map in fig. 14. As A I A F is characterized by the periodic agitations, the flow pattern differences between A I A F and I A F and between A I A F and D F are fairly well determined. Photographs of typical flow patterns of IAF, A I A F and D F at points (a)-(d) in fig. 14 are shown in figs. 15 (a)-(d), respectively. It is successfully shown that the heat transfer characteristic regions I, II and III correspond to the flow patterns IAF, A I A F and DF, respectively.
4. Conclusions
AIAF
(C
ISF
tel DF Fig. 15. Flow patterns.
Flow pattern and heat transfer characteristics in the region from inverted annular flow to dispersed flow in a steady state were studied experimentally. The experiments were carried out using a refrigerant R-113 in a vertical tube of 10 mm (I.D.) at atmospheric pressure. The axial distributions of the heat transfer coefficient were measured and the flow patterns were observed. The following conclusions were obtained. (1) Heat transfer coefficient along the tube is affected by the heat flux, the inlet velocity and the inlet subcooling. The relationship between the heat transfer coefficient and the thermodynamic equilibrium quality is not strongly affected by the heat flux and the inlet subcooling, but much affected by the inlet velocity. (2) Heat transfer characteristic along the tube are divided into three regions: I, II and III. A heat transfer characteristic map using the thermodynamic equilibrium quality and the inlet velocity as coordinates is proposed. (3) The flow pattern changes from inverted annular flow (IAF) to dispersed flow (DF) through inverted slug flow (ISF) and changes from I A F to D F through agitated inverted annular flow (AIAF) for higher inlet velocity.
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N. Takenaka et al. / Experimental study on flow pattern and heat transfer
(4) The flow patterns in the regions I, II and III correspond well to IAF, A I A F and DF, respectively.
Nomenclature D h Hlg k Nu Pr q T ATsub Oin Xeq 2, P
tube inner diameter, (m) heat transfer coefficient, ( W / m 2 K), latent heat of vaporization, (J/kg), thermal conductivity, (W//m 2 K), Nusselt number, Prandtl number, heat flux, ( W / m 2), temperature, (K), subcooling, (K), inlet velocity, (m/s), thermodynamic equilibrium quality, axial distance from the inlet, (m), viscosity, (kg/ms), density, (kg/m3).
Subscript
g 1 s w
gas, liquid, saturation, wall.
References [1] K. Akagawa, N. Takenaka, T. Fujii, K. Nishida, Y. Kikuchi and A. Shibata, Flow pattern and heat transfer of inverted annular flow, 1st. Rep. Visualization of flow pattern by high speed camera, 2nd. Rep. Transition condition of flow pattem, 3rd. Rep. Heat Transfer, 4th. Rep. Pressure drop, Proc. 1987 Fall Meet. Atomic Energy Soc. Japan 1 (1987) 316-319. [2] K. Akagawa, N. Takenaka, T. Fujii, K. Nishida and Kikuchi, Flow pattern and heat transfer of inverted annular flow in a horizontal tube, 1987 Annual Meet. Atomic Energy Soc. Japan 1 (1987) 25.
[3] K. Akagawa, T. Fujii, N. Takenaka, K. Nishida, Kikuchi and A. Shibata, A study of flow pattern and heat transfer of inverted annular flow, Proc. ASME/JSME Thermal Engng. Conf. 5, Hawaii (1987) 127-134. [4] R.S. Dougall and W.M. Rohsenow, Film boiling on the inside of vertical tubes with upward flow of the fluid at low quality, MIT-TR-9079-26 (1963). [5] J.W.H. Chi and A.M. Vetere, Two-phase flow during transient boiling of hydrogen and determination of nonequilibrium vapor fraction, in Advances in Cryogenic Engng. 9 (Academic Press, New York, 1964) pp. 243-253. [6] W.F. Laverty and W.M. Rohsenow, Film boiling of saturated nitrogen flowing in a vertical tube, Trans. ASME, J. Heat Transfer 89 (1967) 90-98. [7] P. Ottsen, Experimental and theoreical investigation of inverse annular film flow and dispersed droplet flow, important under LOCA conditions, Riso Nat'l Lab. Rep. No. R-424, Denmark (1980). [8] M. Aritomi, A. Inoue, S. Aoki and K. Hanada, Thermal and hydraulic behavior of inverted annular flow, Proc. 2nd. Int. Topical Meet. on Nuclear Power Plant Thermal Hydraulics (1986). [9] G. De Jarlais and M. Ishii, Hydrodynamics of adiabatic inverted annular flow -an experimental study, Proc. 3rd. Multi-phase Flow and Heat Transfer Syrup. Miami (1983). [10] G. De Jarlais and M. Ishii, Inverted annular flow experimental study, NUREG/CR-4277, ANL-85-31 (1985). [11] M. Ishii and J.P. Denten, Experimental study of two-phase flow behavior of post critical heat flux region, Proc. Japan-US Seminar on Two-Phase Flow Dynamics, Ohtsu. J1 (1988). [12] G. Costigan and C.O. Wade, Visualization of the reflooding of a vertical tube by dynamic neutron radiography, Int. Workshop on Post-dryout Heat Transfer, Salt Lake 1-4 (1984). [13] D.H.C. Harris and W.A.J. Seymour, Application of real time neutron radiography at Harwell, Proc. 2nd. Int. Conf. Neutron Radiography (1986) 595-600. [14] N. Takenaka, K. Akagawa, A. Ono and K. Sonoda, Visualization of gas-liquid two-phase flow in a metalic tube, J. Flow Visualization Society Japan 8 (30) (1988)151-154. [15] L.A. Bromely, Heat transfer in stable film boiling, Chem. Engng. Prog. 46 (1950) 221-227.