Experiments on the hydrodynamics of air-water countercurrent flow through vertical short multitube geometries

Experiments on the Hydrodynamics of Air-Water Countercurrent Flow Through Vertical Short Multitube Geometries Jinzhao Zhang Jean-Marie Seynhaeve Michel Giot Universit~ Catholique de Louvain, Unitd Thermodynamique et Turbomachines, Louvain-la-Neuve, Belgium

• A series of experiments were performed to improve understanding of the hydrodynamic mechanisms relevant to the flooding phenomenon in gas-liquid countercurrent flow through vertical short multitube geometries. In addition to the conventional measurements of global hydrodynamic parameters such as phasic flow rates and two-phase pressure drops, the local time-varying thicknesses of the liquid films trickling down the individual tubes were measured by means of conductance probes mounted flush at different locations of the inner wall surfaces. A PC-based data acquisition and analysis system was developed to collect these highly fluctuating data and to make detailed statistical analyses. The experimental results and visual observations revealed two dominant hydrodynamic instability mechanisms that have not been well taken into account by the existing semiempirical models.

Keywords: countercurrent two-phase flow, flooding, hydrodynamics, instability, interfacial wave, liquid film INTRODUCTION The flooding phenomenon is one kind of hydrodynamic limitation that can occur in gas-liquid countercurrent flows (CCF) through various types of geometries [1-3]. For a given superficial velocity of a liquid flowing down a vertical channel (JLi = constant), three critical points can be defined by continuously increasing the superficial velocity of an upward countercurrent gas flow (Ja), namely, the onset of flooding (OF) point at which the superficial liquid penetration velocity begins to decrease (Jz < JLi), the countercurrent flow limitation (CCFL) point at which the liquid penetration stops completely (JL = 0), and the dryout (DO) point at which the liquid film vanishes totally below the liquid entry (the film thickness hm = 0). Therefore, the flow regime in CCF through any geometry can be further divided into four subregimes of preflooding (before OF), flooding (between OF and CCFL), postflooding (between CCFL and DO), and postdryout (beyond DO). Although these definitions may not be strictly consistent with many others in the literature, which may cause some confusion, it would seem that they are more objective and suitable and can therefore avoid the large discrepancies in the flooding data bank. In addition to its importance to the safe and economical operations of various mass and heat transfer equipment, the flooding phenomenon is of special importance in nuclear reactor safety applications. It has been shown that the flooding phenomenon may occur as a limiting mecha-

nism that restricts the penetration of the emergency core cooling (ECC) liquid into the reactor core region of a pressurized water reactor (PWR) or a boiling water reactor (BWR) during a hypothetical loss-of-coolant accident (LOCA), and this may strongly affect the overall thermalhydraulic behavior of the reactor [4]. Recent large-scale tests of both integral transients and separate effects [5-12] demonstrated that the injected ECC liquid can be restricted by the upward vapor flow and can accumulate in the fuel element top nozzle area of PWRs or the upper plenum region of BWRs. Because of the geometrical discontinuities at the reactor upper tie plate (UTP) and the parallel channel effects in the reactor core, the injected ECC water flow in this region can be split into various flow regimes such as two-phase CCF, upward cocurrent flow, and single-phase liquid downward flow or gas upward flow. It has also been found that the above complicated and multidimensional (two- or threedimensional) CCF behavior is scale-dependent [9-12]. Therefore, it is very important to understand and to model the hydrodynamic behavior in countercurrent flow through the nuclear reactor upper tie plates. The nuclear reactor UTP is known to have a typical geometry of short multi-paths similar to the sieve tray or perforated plate in chemical engineering applications [13]. Previous basic model studies [14-21] focused mainly on the experimental determination of the liquid penetration rate as a function of the gas upward flow rate, namely, the flooding curve in thick orifice or perforated plates (path

Address correspondence to Professor Dr. Michel Giot, Universit6 Catholique de Louvain, Unite Thermodynamiqueet Turbomachines,B-1348 Louvain-la-Neuve, Belgium.

Experimental Thermaland Fluid Science 1992; 5:755-769 © 1992by Elsevier SciencePublishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010

0894-1777/92/$5.00

755

756

J. Zhang et al.

n u m b e r n > 1, path diameter d < 50 mm, path length l < 2d, and flow area occupied by the multi-paths y = 40%). The effects of the rod bundles and of the complex upper plenum structures as well as of the condensation heat transfer have also been studied [22-29]. Meanwhile CCF in parallel channels (n > 1, d > 4 mm, l > 10d) with or without UTPs and rod bundles as well as side-entry orifices have been investigated to simulate different flow regimes in a BWR core during the postulated LOCA transients [30-35]. These experiments showed that the CCF characteristics and flooding mechanisms in short multipath geometries are much more complicated than those in single-channel geometries, owing to the complex effects of hydrodynamics and geometry. However, neither the detailed local hydrodynamic behavior nor the scale effect of geometries has been well understood. This makes it difficult to determine the dominant physical mechanisms so as to apply these results to practical situations. A general predictive model for the flooding phenomenon is still lacking even for the single-channel CCF [1-3]. In the modern nuclear reactor safety analysis computer codes, the CCF hydrodynamic behavior is usually modeled by using constitutive equations for interfacial momentum transfer or specific flooding models [4]. As no accurate model for interfacial shear stress and entrainment is available for each geometry where flooding in CCF is expected, the existing computer codes with standard one-dimensional two-fluid models have been shown to be unable to predict well the multidimensional hydrodynamic behavior of CCF through UTPs [36-43]. Therefore, it would seem to be more appropriate to develop specific flooding models for this complex geometry. The most widely used models for the onset-of-flooding locus are the semiempirical correlations due to Wallis [1] and to Kutateladze [44]. Another type of correlation was introduced specially for perforated plates by Bankoff et al [14]. All of these correlations are obtained by linear regression of the experimental data in terms of the square roots of some kinds of dimensionless superficial velocities, namely, Jt

I ok-3l1': ' =Jkts-

rk=Jk(

k

OA~gL1)1/2,

I-i; =

!

'

O)

k=L,G

(2)

k = L,a

(a)

where d is the diameter of individual paths, L~ the Laplace capillary length defined by

(7" / 1/2 L 1 = (~-p--~pg]

(4)

and W an interpolative length scale defined as

W = dl-~L~,

0
(5)

with the empirical geometry exponent 13 determined by

/3 = tanh[ y(27r )d/l]

(6)

where y is the open area ratio occupied by the paths. It should be noted that these three scaling numbers

based on superficial velocities are of little dynamic significance in spite of the physical meanings that have been suggested in the development of these correlations [14-27, 45, 46]. Although good agreement between the correlations and experimental results is often claimed in the earlier studies, it appears very difficult to apply correlations to geometries different from those used in the experiments without changing the regression parameters. In fact, as the flooding phenomenon is closely dependent on various thermal-hydraulic and geometrical effects, the simple linear semiempirical correlations are not generally suitable for predicting the complicated hydrodynamic behavior. Moreover, these correlations appear to be inconsistent with the widely used two-fluid model computer codes, which use the conservation equations and the closure laws to analyze the hydrodynamics of various phenomena in nuclear reactor accidents [41, 42]. A more promising approach is to develop some mechanistic models based on the balance equations of two-fluid motion and on the dominant flooding mechanisms [47]. Several models have been developed on the basis of various proposed mechanisms such as the interracial instability within the tubes [17, 25, 48], the localized liquid penetration through perforated plates [12, 22, 24, 35], and the disintegration of the gas jets above the tubes [49-51], the lifting of the falling liquid jets below the tubes [15], and so on. Although some of these phenomenological models have been used to predict the available flooding data with at least partial success [41, 42], detailed information on the local hydrodynamic behavior is still required to improve them. Detailed measurements and analyses of the liquid film flow and the interracial wave behavior have been made in CCF through single channels [52-55]. It has been shown that the hydrodynamics of both liquid film and interracial waves play an important role in the flooding transition. As the interracial shear stress imposed by the gas flow increases, the film becomes rough and thick with large disturbance waves appearing on the surface. Close to the OF point, the film becomes highly agitated and chaotic, with growth and upward propagation of large solitary waves [56], breakup and entrainment of the liquid droplets from the wave crests [57], or formation and development of a rough thick film region [58]. Some recent studies suggest that the film dynamics close to the flooding transition follows a deterministic chaos [59]. In CCF through multipath geometries, the liquid film hydrodynamic behavior should be much more complicated because of the global flow oscillation caused by the hydrodynamic interaction between parallel paths. However, to our knowledge, no attempt has been made before to quantitatively study the multipath effects on the local hydrodynamic behavior of the liquid film in individual paths. The main objective of the present paper is to present more detailed information on the local hydrodynamic behavior in CCF through multitube geometries, to provide a basis for developing a general predictive model of the phenomena. The experimental study was performed with three vertical parallel tubes. Besides the conventional measurements of global hydrodynamic parameters (phasic flow rates and two-phase pressure drops), the local timevarying thicknesses of the liquid films in individual tubes were also measured. Detailed statistical analyses were made to obtain some useful information about the interracial wave structure and motion. Finally, two different

Hydrodynamics of Air-Water Countercurrent Flow 757 hydrodynamic instability mechanisms are suggested for further theoretical modeling work. It should be noted that owing to the low-number parallel tube geometries used in the experiments, the data presented are for the greater part shown only for the interracial instability mechanism within individual tubes. The global flow instability mechanism should be further studied with test sections of large perforations or multihole plates.

plexiglass circular tube ( D - - 1 0 0 mm, L = 7200 mm), with air supplied at the bottom ( H 1 = 2250 mm) by two parallel volumetric ROOTS compressors, and distilled water injected at the top ( H 2 = 1250 mm) through a chamfered slot into the channel by a centrifugal pump. The temperature of the recirculated water (TL) is controlled by a cooler. The open air circuit is operated at nearly atmospheric pressure and ambient temperature. As shown in Fig. 2, the test sections consist of three parallel tubes having an inner diameter of 36 mm (n = 3, d -- 36). The open area ratio of the three parallel tubes with respect to the test channel is similar to that of actual upper tie plates (3/= 38.8%). Three different length/ diameter ratios (l = 2d, 10d, and 20d) were chosen to study the possible length effects. These test sections will be referred to as T/S-n-d4 in this paper.

EXPERIMENTAL APPARATUS AND M E T H O D

Test Facility An air-water countercurrent flow test loop was built as shown in Fig. 1. The test channel consists of a vertical

Q

Air Outlet

Pressure Taps Differential Pressure Taps

O

Thermocouple

Flexible Pipe

Conductance Electrodes for Film Thickness Measurement

~_

Water Injection

Test Channel

Qli ] Test Section

Feed Water Flowmeter

v1

Downward Upward Water Water ~Flowmeter Flowmeter Level Detectors

Roots Compressors D.C. Motor

OrificeAir ' Flowraeters

Air

A.C. Motor

1

Air Injection

Water Cooler

Figure 1. Schematic view of the test loop.

758 J. Zhang et al. A detailed description of the test facility can be found elsewhere [60]. It should be noted that the loop has been well designed to avoid any vibration transmitted from the compressors, and to run at constant airflow rates more or less independently of the gauge pressure at the lower end of the test channel (Pl < 50 kPa). Moreover, both the test channel and the test section were installed carefully to keep them strictly vertical and to match as smoothly as possible at the connections, in order to obtain a uniform and smooth liquid film distribution.

into one of the two cylindrical vessels (Fig. 1). The corresponding volumetric flow r a t e s (QLd and QL,) are determined from measuring the time elapsed to fill the calibrated volumes between two liquid-level switches installed in the corresponding vessels. The flow diversion and reestablishment are operated by means of electric valves that are controlled by a data acquisition and control system based on a personal computer, and the elapsed time is measured by the internal timer counters of the system. Care was taken to obtain accurate measurements within the range of 0.04-1 m a / h (accuracy < +4%).

Measuring Techniques In addition to the conventional measurements of the total inlet phasic volumetric flow rates (Toshiba-335/372-25A type electromagnetic flowmeter for QLi and standard oririce flowmeters for QGi), special techniques were developed to measure other hydrodynamic parameters relevant to the flooding mechanism.

Liquid Penetration and Carryover Rates The penetrated downward liquid flow collected at the lower end and the entrained upward liquid flow separated from the air by a cyclone at the upper end of the test channel are diverted

d=36 A

110

J

instantaneous Two-Phase Pressure Drop The two-phase pressure drop across the test sections is measured by a differential pressure transducer (Rosemount 1151 DP). A small constant flow rate of compressed air is continuously blown into the pressure taps through capillary tubes to prevent water from entering the pressure lines as recommended by Hew/tt [61]. Special care is taken to ensure only small uncertainties in the measurements (less than +2_5% within 0-1000 Pa). The same technique is used to measure the pressure at the lower end of the test section within the range on 0-5400 Pa (accuracy < + 2.5%).

Q~

A-A'

A' I I I I I

Q D=100

,,.a C.fi

D=IO0

:18

Az=l+36

ld=35

18 r

D = 100

5 B-B'

110

zg'"~'~~-N3

4.5 x 4.5

Figure 2. Test sections and conductance electrodes (all dimensions in mm).

Hydrodynamics of Air-Water Countercurrent Flow 759

Time-Varying Film Thickness in Individual Tubes Up to six pairs of stainless steel square electrodes (4.5 mm × 4.5 mm) are mounted flush at the cylindrically curved inner surface of individual tubes, with the electrodes running parallel to the axis of curvature at a spacing of S = 22 mm (see Fig. 2). In particular, two pairs of electrodes (hi, h 2) are located Ia = 35 mm apart at the middle of one test section tube to enable us to deduce the wave velocity (Vw) by cross correlation of the signals from these two probes. This conductance technique is used because of its simplicity of construction and suitability for complex geometries [61]. Moreover, the probes are well designed, machined, and installed to ensure reasonable sensitivity and linearity within the measurement range [61, 62]. A multichannei conductance micrometer was developed to apply 1 kHz ac currents (_+ 5 V) through the electrodes. It outputs the demodulated and amplified dc signals of the voltage drop (0-10 V) across standard electrical resistances (about 1 k l l ) as approximately linear functions of the instantaneous water conductance (G = 0 - 1 0 0 / t l 1 - 1 ) versus the film thickness (h = 0-3 mm). To reduce the influence of the variations in the water conductivity, a flow of water at a small flow rate is directed into a reference unit with a known film thickness (hr~f), which gives the instantaneous reference conductance (G,~f) at the loop temperature. If the tube geometries and electrode arrangements are identical for the test and reference units, the following relationship is established by the static calibration method: h =f hr~f

(7)

The uncertainty due to both calibration and conductivity change is estimated to be less than 1%. However, owing to both interracial wave and nonuniform film thickness distribution effects as well as to the electrode effects (electric double layer, capacitance, current leakage outside the probe zone, etc), the overall measurement seems to lead to a systematic underestimation of the average film thick-

Qli < l m 3 / h I Electr°malv~etic Water Flowmeter '

ness as high as 30% by comparison with the classic Nnsselt theory [60]. Data Acquisition System All the above measurement and control operations are performed by a multichannel data acquisition system (DAS) based on a personal computer (COPAM PC-401, 8086 processor, 8 MHz CPU speed). As shown in Fig. 3, the DAS consists of a data acquisition and control board (MetraByte DASH16) supported by a scientific system software (ASYST 2.0). The analog output signals from both transducers and micrometers are collected at given sampling frequencies (Fa) and periods (Tr), which can be selected according to both DAS characteristics and data processing techniques. Data Processing Techniques Because the instantaneous film thickness h(t) is in randora fluctuation by nature, the time series techniques can be used to make detailed statistical analysis by assuming that it is a stationary and ergodic stochastic process. Based on the AS¥ST 2.0 software, a combined data acquisition and analysis program is developed to collect the timevarying film thickness data of N = 4096 samples at a frequency of Fa = 512 Hz in a period of T r 8 S and to calculate the following statistical parameters: mean values h=, sample standard deviation values hsd, probability density function p(h), probability distribution function P(h), normalized auto-power-spectral density function G11(f), normalized autocorrelation function Rn(r), normalized cross-spectral density function G12(f) and phase angle 012(f), and normalized cross-correlation function R12(~'). The definitions of these quantities can be found in Ref. 63. The spectral density function estimates are computed by means of fast Fourier transform (FFT) procedures, and the correlation function estimates are computed by the inverse FFT of the spectra. Special measures are taken to reduce the possible leakage and aliasing errors. The fre-

•

Qo < 600 Nm3/h I Orifice Air Flowrneter AP < 1960Pa, P <7500Pa [ Pressure Transducers

=

1 2

5 Fa< 1 kHz

2 PC- 401

h < 3 ~nm [

Reference Unit

r,fmmmet~

I

I ' ' -

Qld < 1 mS/h [ Downward Water Flowmeter ~-~---~Elecuie Valves[ QIu _<1 m3/h [ Upward Water Flowrneter [ c - - ~ Detectors]

7 ~ N 1 kI-I2 (1) (2) Fa= 1 kHz

MetraByte DASH 16 ASYST 2.0

Fa < 30 kHz

Note : The numbers x stand fox A/D channels; (x) stand for Digital channels Figure 3. Instruments and data acquisition system (DAS).

760 J. Zhang et al. quency resolution of the spectra is estimated to be less than 0.5 Hz, with the normalized standard errors smaller than 14.4% [60].

Experimental Procedure and Presentation of Results A series of experiments were performed at carefully controlled conditions given in Table 1. Experiments are conducted in a water-first mode; that is, for a given constant Jzi, Ja is increased step by step from zero until the dryout (DO) point is reached. At each step, measurements are repeated at least three times after the stabilization of flow conditions, and the results are reported hereafter as the arithmetic mean values except for the time-varying film thickness. Because the most restrictive flow area is located in the test sections, both superficial velocities and dimensionless numbers refer to the inner diameter of the individual tubes (d). Furthermore, because of the limited space, only some of the results are reported in this paper. A complete presentation and detailed discussion of the experimental results can be found in a thesis [60]. RESULTS AND DISCUSSION

Liquid Penetration Rate An example of the measured superficial velocity of the liquid downward flow (JL) versus that of gas upward flow (JG) is shown in Fig. 4 for one test section T/S-3-36-20d. It can be observed that for a given JLi, the liquid downward flow will remain constant (JL = JLi) until Jc is increased to a critical value, at which JL begins to decrease and the film flow in individual tubes becomes chaotic. This is well defined as the OF point. As Jc is further increased, JL continues to decrease along the flooding curve until it reaches zero at the CCFL point. Consistent with many previous studies in both singlechannel and multipath CCF, it follows from Fig. 4 that the OF point appears at lower gas velocities if the injected liquid flow rates (or JLi) are increased. This can be understood by the fact that interfacial instability occurs more easily for thicker films. In the succeeding partial liquid penetration (or flooding) regime, however, the liquid downward flow rates almost follow the same curve--the flooding curve. This suggests that the liquid penetration rate is more or less independent of the liquid feed rate. Close to the CCFL point, a strong global flow instability occurs owing to the periodic oscillation of the froth layer above the parallel tubes, which makes it rather difficult to make accurate measurements. Nevertheless, it is evident from Fig. 4 that the CCFL point seems also to be more or

Table 1. Experimental Conditions Parameters

Loop pressure Pl (kPa) Loop temperature T1 (°C) Ambient temperature TG (°C) Water inlet flow QLi (m3/h) or JLi (m/s) Air inlet flow Qo (N- m3/h) or Jo (m/s)

Ranges

97-110 + 0.3 25-35 + 1.5 20-26 + 1 0.1-0.8 + 0.6% Qgi 0.01--0.08 ~ 0.6%

0-250 + 2.5% Qa 0-25 + 2.5% JG

JLi

0.06

,

,

"

6 .-'..~_

" ~ ,~ 0.04

, *JLi=0.009m/s OJLi=0.018m/s +JL~=0.036m/s xJ L i---O.054m/s-

,.J

0.02 X

0

0

"

5

CCFL

10

130

15

20

JG ( m / s ) Figure 4. Liquid penetration rate (T/S-3-36-20d). less independent of the injected liquid flow rates, which is again in agreement with most of the previous studies in single-channel CCF [1-3]. Similar liquid penetration behavior has been observed in experiments with other test sections [60]. The flooding data are presented in Fig. 5-7 in terms of three different scaling numbers (J*, K, and H*) defined by Eqs. (1)-(3). It can be observed that the partial liquid penetration (or flooding) data for the shortest test section (l = 2d) lie systematically above those for the longer test sections (l > 10d). This tendency is especially clearly shown by H* scaling in Fig. 7, suggesting that a shorter multitube geometry may enhance the liquid penetration. The above conclusion coincides with the observation made by Sudo and Ohnuki [17]. However, more systematic experiments are required to understand the effects of the diameters (d) and numbers (n) of the parallel tubes, as well as the entry shapes and so on. As shown earlier, the flooding data can be regressed to obtain the semiempirical correlations of the Wallis type [1],

j~l/2 + Mwj~I/2 = Cw

(8)

the Kutateladze type [44, 64], K~/2 + M r K ~ / 2 = CK

(9)

and the Bankoff typed [14], H i / 2 + MBH~. 1/2 = C B

(10)

where the so-called flooding parameters M and C are strongly dependent on the path geometries and entries, flow conditions, and fluid properties. Instead of proposing new correlations that have little general applicability, we compare several existing correlations with the present experimental data. The range of applicability of each correlation can be found in the corresponding reference. The selected Wallis-type correlations were proposed by Wallis [1, 30] with C W = 0.725

(11)

C W = 0.46d -1/4 = 1.056

(12)

M W = 1,

by Naitoh et al [22] with M W = 1,

Hydrodynamics of Air-Water Countercurrent Flow 761 by Murase and Suzuki [34] with

M w = 1,

C w = 0.85

0.8

and by Celata et al [20] with

M w = 1,

Cw = Y0.35 = 0.718

C r = 1.79

M K = I,

(15)

to Hawighorst et al [25],

(,,) ~

MK = O.8165 CK.(-~c ) 1/8

,

(16) to Bradford and Simpson [18[, (17)

Cr = 2.08

M r = 1.57,

and to Kokkonen and Tuomisto [21],

M r = 1.67,

¢q

-g-

0.5

,\

0.4

"~ \ \ ',~, \ \\ ','~ \ \

0.3 ~-

\

, \

~,

-

\, •

0

-

' 0.5

0.4

0

-

-

-

\\

\

-su~14s X~ _ _ _ Hawighorst [2 5

\..~**

"~.~.~.~"~,- .... Brodfo,'d [,a]-

0

, os

\-~' ~.s

'

1

\ ;",

2

Naitoh

2.s

Kv2 G Figure 6. Flooding curve in K scaling (T/S-3/36-1). where the dimensionless wettable perimeter L* is defined by L* = nqrd/L 1 (19) The flooding curves determined by the above correlations are shown in Fig. 6. Although the general trend of the liquid partial penetration behavior has been correctly predicted, a modification of the flooding parameters is still required to fit the data. It can also be concluded from Fig. 6 that the local interfacial instability within tubes predominates, at least for the present low-number parallel tube geometries. Finally, the present flooding data are compared with the correlation due to Bankoff et al [14], M B = 1,

C B = 1.07 + 4.33 × 10-3L *

(20)

which is shown in Fig. 7. It is obvious that the above correlation can be approximately applicable only to the shortest test section (l = 2d), when the scaling number H* approaches the Kutateladze number K. This is because the Bankoff correlation is an interpolation of both Wallis and Kutateladze correlations and takes into account the multipath geometries only for very short perforated plates with 0.7 _< l / d < 4,2 [14].

I

l=20d o l=10d + l=2d

0.8 0.6

-

-

Bankoff [14]

[22]

' , ---Mu rase[34] k\ ..... Celeto[20]-

',,"~Ii~

0

\

0.6

*

wo.u,s [1]

\

'X,lffl~~

0.1

\.

o l=lOd + l=2d

I

* l:20d o l=10d + l=2d

%!\

0.2

'~ %,

,

\

",,~

-¢

(18)

C K = 1.56

.1--2Od \

(14)

which are shown in Fig. 5 for comparison. It seems that no correlation predicts well the general trend of the partial liquid penetration behavior of the present study. In fact, the smaller negative slope of the experimental data suggests that the flooding phenomenon in the present geometries begins at a smaller gas flow rate but ends at a larger gas flow rate. The earlier OF point may be due to the premature local interracial instability caused by the disturbance wave growth in individual tubes, while the later CCFL point can be attributed to the global flow instability caused by hydrodynamic interactions between parallel tubes [60]. The deflection at Jr* 1/2= 0.18 also suggests two different mechanisms at lower and higher liquid flow rates. Although the experimental data can be best fit by changing the flooding parameters M w and Cw, it would seem that the above two kinds of instability mechanisms cannot be taken into account well by the simple linear equation, Eq. (8). An alternative correlation of the Kutateladze type can be derived analytically from interfacial instability theory [25, 44, 50, 64]. However, these two flooding parameters have to be determined from experiments, such as those due to Sun [45],

CK = 1 + t a n h

,

(13)

\

0.4

+ ~-~.g~

0.2

'~ °'---~+:'\` 1

0 1.5

jG, 1/2 Figure 5. Flooding curve in J* scaling (T/S-3-36-1).

0

0.s

1

1.s It

2

G*1/2

Figure 7. Flooding curve in H* scaling (T/S-3-36-1).

762 J. Zhang et al. Two-Phase Pressure Drop

1000

Examples of mean (or time-averaged) two-phase pressure drops across a test section (including 18 mm of the test channel below and above the test section) are shown in Fig. 8. For a given injected liquid flow (JLi), it appears that (Ap) m increases up to a maximum as J~ is increased close to (but not necessarily at) the OF point, and then fluctuates in the succeeding partial liquid penetration (or flooding) regime. The multiple peaks of ( A p ) m can be attributed to both change of the interfacial wave structure in the tubes and formation of a froth layer above the parallel tubes. Close to the CCFL point, (Ap) m tends to decrease with increasing Ja until the DO point is reached, when (AP) m again rises following the corresponding single-phase air upward flow curve (the dashed line in Fig. 8). The injected liquid flow rate (Jri) has a relatively weak influence on the pressure drop only in the preflooding CCF regime; that is, the pressure drop across the test section tends to increase with JLv Beyond the OF points, however, the fluctuations in the pressure drops appear more or less independent of the injected liquid flow rates. This behavior is quite similar to that observed in long parallel channels [30-36], although the pressure drop peaks are not clearly defined in the present study owing to the strong global flow instability [60]. The effect of tube length can be observed from Fig. 9. It seems that the two-phase pressure drop across the tubes becomes larger with longer test sections. This can be attributed to the increase in pressure drop due to interfacial friction with tube lengths. The sample standard deviation value of the pressure drop represents the dynamic or fluctuation component of the data. It follows from Fig. 10 that (Ap)sd also increases to maximum peaks near the OF points, indicating significant increases of the interfacial friction fluctuations caused by the radical changes of the wave structure. The same behavior has been observed in single-channel experiments [52]. It should be noted also that (Ap)sd in the flooding regime yields about 10% of the average value.

Liquid Film Flow

, J

800F

!

,

,

10

15

* l=20d ol=lOd + l=2d

E <1

400

I

200

F

0 0

5

20

JG (m/s) Figure 9. Two-phase pressure drop in different test sections (T/-3-36-1, JLi = 0.018 m/s). tube are shown in Fig. 11. Consistent with the observations in single-channel experiments [52-55], it can be noted that the liquid film surface is covered with nonperiodic and irregular waves even when there is no countercurrent gas flow (Fig. lla). As the gas flow is increased, large disturbance waves appear, which grow in amplitude as they propagate downwards (Fig. llb). At still higher gas flow rates close to the OF point (Fig. llc), very large liquid lumps (or roll waves) are generated and move over a substrate film covered with small ripples. Stationary waves are randomly observed growing near the gas entries of individual tubes, with small liquid droplets being torn off the wave crests. This just corresponds to the OF point. If the gas flow is further increased beyond the OF point (Fig. lld), the large waves appear to reverse direction and move upwards alternately in certain tubes, and the flow patterns become chaotic, with large lumps or jets of water being delivered rapidly through parallel tubes in a random manner. This kind of behavior is noted in the whole partial penetration regime [60]. As the gas flow is increased close to the CCFL point,

Typical time history records of the instantaneous liquid film thickness measured at the middle of an individual 1000

,

,

200

,

*JLi =0.009m/s OJLi=0.018m/s

800

XJLi = 0 . 0 5 4 m / s --JLi=Om]s+~+ ,

E

4oo I

.

200

x~

o

0

5

~,~

x~ +g ~k o

"O

...x-gll

"r" <~

-""

I ,

o-

10

i

XJLi = 0 . 0 5 4 m / s

100

o

20

Jo(m/s) Figure 8. Time-averaged pressure drop (T/S-3-36-20d).

re

x

xx++~ o~ o~° o ~ x+ x ÷ • ,+ xx+ xOo°~ x •

50

0

13

I io 15

!

OJLi =0.018m/s +JLi =0.036m]s

150

+JL; = 0 . 0 3 6 m / s 600

i

*Jc~=0.009m/S

of :i °' i 0

5

o +

•

ioo 10

15

20

JG(m/s)

Figure 10. Standard deviation of pressure drop (T/S-3-3620d).

Hydrodynamics of Air-Water Countercurrent Flow 763

1

1

i

!

a.JG=0.0 m/s 0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

0

I

0.5

0

1

I

0.5

0

t (s)

t (s)

i

i

d.JG=7.74m/s

bAG=3.95m/s

~=

0.8

0.8

0.6

0.6 0.4

=

0.4

0.2

0.2 0

0

I

0.5

0

1

0

0.5 t (s)

t (s) Figure 11° Time history records of film thickness (T/S-3-36-20d, JLi dry patches appear at certain parts of the tube walls, which are intermittently rewetted by the liquid jets entering occasionally into the tubes. As the liquid downward flow is too small to preserve a continuous film, the dry patches increase rapidly in size and number, and the transition to the DO point occurs very suddenly when the liquid is totally expelled from the top ends of the parallel tubes. The mean (time-averaged) film thickness h m is shown in Fig. 12. It remains nearly constant or increases slowly at smaller JLi before the OF point, and increases rapidly to a maximum as J~ is increased close to the OF point. The tendency to decrease thereafter is due to the decrease in the liquid downward flow along the flooding curve. However, a second maximum peak is observed for larger JLi beyond the OF point in spite of the same tendency for h m to decrease in the following partial penetration regime. The dashed lines in Fig. 12 correspond to the film thicknesses calculated from the classic Nusselt theory for a smooth laminar freely falling film flow down a vertical surface [65]; that is,

[ 3 /,2

,~1/3

hN = ~-~--g-ReL)

(21)

=

0.018 m/s).

where Re L = J L i d / P L

(22)

It appears that h s is larger than the measured value (h m) for smaller liquid flows in the preflooding regime but

0.8

i

i

"~

0 6/ • ~Jx~x ~, ]~--- - ~'x ~_~Xx

ol

0

ii,

5

i

*Jti =0.009m/s oJL~=0.018m/s +Jt~ =0.036rn/sXJt, :0.054m/s

I

i ,

10

15

20

J6 ( m / s ) Figure 12. Time-averaged film thickness (T/S-3-36-20d).

764 J. Zhang et al. smaller than h m for larger liquid flows. This can be attributed to the presence of interfacial waves and the possibly large uncertainties of the conductance probe technique. The chaotic film flow behavior can be further demonstrated by the standard deviation value of film thickness (h~d) in Fig. 13. It seems that the fluctuation of the film thickness for a given JLi increases rapidly to a maximum close to the OF point, indicating the formation of very large interfacial waves. The double peaks of hsd for the larger injected liquid flow rates suggest two different kinds of hydrodynamic behavior. The probability density function of the film thickness p(h) (Fig. 14) tends to decrease in amplitude and shift to broader distributions as Ja is increased for moderate JLi" The opposite tendency is observed at large JLr This again suggests that there exist different mechanisms of flooding for low and high liquid flow rates. Typical probability distribution functions P(h) are shown in Fig. 15. Defining the wave height (h w) as 95% of the film thickness fractile and the substrate film thickness (h s) as 5% of the fractile, it appears that h w increases very rapidly with Jc whereas h s remains nearly constant before the OF point. In fact, it can be observed from Figs. 16 and 17 that both h w and h s will reach their maxima close to the OF point and then decrease owing to the decrease in the liquid penetration flow rate in the flooding regime. For larger injected liquid flow rates, another peak appears beyond the OF point. This is consistent with the same tendencies of both h m and hsd in Figs. 12 and 13, respectively. Similar film flow behavior was observed for the other test sections and at other injected liquid flow rates [60]. It seems that the fluctuations in film thickness measurements become more significant for longer test sections (l = 10d or 20d) at larger JLi. However, as long as the effect of the global flow instability is not significant at small Jc before the OF point, the liquid film behavior is quite similar to that in single-channel flow [52-55]. A theoretical modeling of the wavy liquid film flow remains a great challenge even for the simplest case without countercurrent gas flow. Brauner [66] presents a

0.5

i

i

i

*Jti =0.009m/s ~~.x

0.4

oJu =0.018m/s+Je~ =0.036m/s xJu =0.054m/s__

0.3

6

l

i s'~" ' ix

a.Jki =0.018m/s

• ;(

E

JG = 0 . 0 m / s Jo =4.23m/s

':.1 . • . . . .

4

i: ; '~

-.-.Jo=5.67m/s(OF3 ..... JG=7.74m/s

!:~: :. . ~i i

r:

ij,

i

.,

2

.'-I

',..., , , . .,..

s. t

0

',

i i t I

0

0.5

1

h (mm)

6

i

,':~ .i,i ,,:,o i/ •

b.Ju =0.054m/s Jo=0.0 m/s .... Jo =2.82m/s -.-.Jo=3.17m/s(OFl .... Jo=4.68m/s

•: i I t

.l I

0

2/

0

O.5

1

h (mm) Figure 14. Probability density functions of film thickness (T/S-3-36-20d).

turbulent wavy film flow model that can predict substrate film thickness, wave amplitude, and frequency based on the known wave velocity. However, it seems rather difficult to apply directly to the present study owing to the developing effect with short tube lengths and the interfacial shear effect in the presence of countercurrent gas flows. More advanced models have to be developed to take these effects into account. Interfacial Wave Properties

X

v

0.2: 0.1 OF ~

0

0

5

,

CCFL *~,.~

10

DO

15

20

J0(m/s) Figure 13. Standard deviation of film thickness (T/S-3-3620d).

A typical normalized power-spectral density function G l l ( f ) is shown in Fig. 18. At low gas flow rates (Fig. 18a), the spectrum displays a clear maximum at a predominant frequency of about 11 Hz, which can be taken as the characteristic frequency of the large waves (Fw). The other peaks that appear at higher frequencies very likely correspond to the short small waves between successive large waves (see Fig. 11). The normalized cross-spectral density function G12(f) is also shown as a dashed line in Fig. 17. The similarity between Gl1(f) and G12(f) implies that the large waves preserve their shapes along the distance between these two conductance probes.

Hydrodynamics of Air-Water Countercurrent Flow 765

0.8 ,-,

2

0.6 0.4

1.5

I

l';, I

I

l::

l

....

l:

I

-.-.JG=5.67m/s(OF) -

h~

....JG=7.74m/s

0.2 V 0

, 'hs 0

-

JG=0.0 m/s

0.5

JG=4.23m/s

1

1

i

t~ [~x " ]\

~

i

*Jl.~=0.009m/s OJki=0.018m/s +Jki =0.036m/s-

,,

xJu =O.054m/s

0.5'

1.5

2 i~

0

h (mm)

0

Figure 15. Probability distributions of film thickness (T/S-336-20d, JLi = 0.018 m/s).

,i-

I

5

,

*~-,i°~

10

15

20

JG(m/s) Figure 17. Interfacial wave height (T/S-3-36-20d).

0.4

~ , I /h r~ " ~ ) / ~ x +/¢', u..J F x/ \~ / x ~ o .1~__.4.-~)k/ ¢oXX~

,

, * J o =O.O09m/s OJLi=0.018rn/s +JLi =0.036rn/sxJLi =0.054m]s

3 a.JG =2.7m/s

/

2

0o

0

5

10

15

20

JG(m/s)

0

/t

ld -

.... Gll

I

10

20

30

F (Hz)

The so-determined wave frequencies remain nearly constant ( F w = 8-12 Hz in the present experimental range) until Jc is increased close to the OF point, when the most pronounced peak of Gl1(f) approaches zero frequency (Fig. 18b). This suggests a significant change in the interfacial wave structure. During the flooding process, the delivery of large lumps of water through the tubes has been observed from time to time at relatively lower frequencies ( F < 1 Hz). It has been shown that this structural change occurs at smaller Jc for larger JLi and is sensitive to tube length [60]. The calculated normalized cross-correlation function R12(r) generally displays a clear maximum peak at a time delay (z) that corresponds to the time required for the film thickness signal to pass the distance between two conductance probes (ld). The interfacial wave velocity (Vw) can be thus determined by =

-"-G12

I

Figure 16. Substrate film thickness (T/S-3-36-20d).

vw

,~\!~

(23)

T

Figure 19 shows examples of the wave velocities determined in this manner at different values of JLi. It can be

3 b.J6 =5.67m/s(OF) .... G , .... Glz

2

0

10

20

30

F (Hz) Figure 18. Normalized spectral density function (T/S-3-3620d, JLi = 0.018 m/s).

766 J. Zhang et al. i

i

i

*JL~=0.009m/s +

OJLi=0.018m/s +JLi=0.036m/sx J Li =0.054m/s

o

2 1 0

0

5

, J . . . . . . . . . t. 10 15

20

JG(m/s) Figure 19. Interfacial downward wave velocity (T/S-3-3620d). observed that Vw tends to increase to a maximum as J~ is increased close to the OF point and then decreases in the partial penetration regime. The direction of the wave motion remains downwards until Jc is increased to some value beyond the OF point, when the large waves are found to move upwards intermittently. The chaotic wave patterns and the significant liquid entrainment prevent any reliable determination of Vw by the above method. The tendency of Vw to increase with Jc before the OF point can be attributed to the global flow instability in multitube geometries, where large liquid lumps or jets are delivered rapidly through the parallel tubes in a random manner. On the other hand, Vw is found to increase as JLi increases before the OF point and to then decrease more or less independently of JLi [60]° This is consistent with the previous studies in single-channel CCF [53, 54]. The effect of tube length appears insignificant in the present study [60].

Dominant Flooding Mechanisms Visual observations of the flow patterns give some complementary insight into the physical mechanisms. It has been shown that the flooding process is associated with such phenomena as the wave motion and liquid droplet entrainment in the test section, the falling liquid jet breakdown and reentrainment below the test section, and the two-phase froth layer formation and motion above the tubes. The strong instability of flow patterns can be attributed to the interactions between neighboring tubes, the significant inertial effects caused by abrupt flow area changes at both ends, and the additional momentum exchange due to the global oscillation of the froth layer [60]. Several mechanisms have been proposed for flooding in the complex multipath geometries based on the observed phenomena, but no single mechanism can explain well all aspects of the phenomenon [47]. For the present study, it appears that at least two kinds of hydrodynamic instabilities are responsible for the flooding phenomenon. At lower liquid flow rates (JLi < 0.018 m/s), annular film flows can be maintained in individual tubes at lower gas flow rates below the OF point. When the gas flow rate

is increased, disturbances first appear at the bottom ends of the tubes and then propagate upwards until the flow patterns in the whole tube length become disturbed together with significant entrainment of liquid droplets. The hydrodynamic behavior in this flow regime remains quite similar to that in a single-channel CCF [52-59]. Close to the OF point, a froth layer appears above the parallel tubes and tends to increase in height ( H I ) with the gas flow rates. The flow patterns within the parallel tubes now become rather chaotic owing to the effects of both local interfacial instability and global flow instability. The former is due to the interfacial shear stress imposed by the gas flow on the liquid films, which stimulates the generation and motion of large disturbance waves on the interface. The flooding inception seems independent of the froth layer height but closely related to both upward wave (or disturbance) propagation and liquid droplet entrainment. However, in the following partial liquid penetration (or flooding) regime, the global flow instability becomes dominant owing to both hydrodynamic interaction between parallel tubes and global oscillation of the increasing froth column above the tubes. This latter mechanism should be controlled by the interfacial instability above the tubes caused by the gas bubbling action [30, 50] or the transverse propagation of disturbance waves across the froth layer [15, 66]. At higher liquid flow r a t e s (JLi > 0.036 m/s), the froth layer appears much earlier at very small gas flow rates. Therefore, the effect of the global flow instability is significant even at lower superficial gas velocities. In this case, the liquid flow is limited first at the top ends of the tubes. The flow patterns in the lower parts of the tubes remain annular film flows in spite of the disturbances and droplet entrainment in the upper regions of thicker films. As the liquid penetration rates decrease in the flooding regime independently of the injected liquid flow rates, the film thickness will decrease also, and the interface of the film becomes less wavy. However, as the gas flow rate is increased further, the film will become rougher and thicker because of the effect of the increased interfacial shear stress. The hydrodynamic behavior in the succeeding process will follow that for lower liquid ftow rates as mentioned above. This explains why a second peak appears in the statistical parameters of the film thickness (h m, hsd, h s, and h w) beyond the OF point. For shorter parallel tubes (l < 2d), the inertial effects caused by the abrupt flow area changes at both ends tend to dominate over the interracial shear stress effects, because the annular film flow pattern cannot become fully developed in the tubes. Therefore, the global flow instability will be significant in this case, which leads to a higher liquid downward flow rate at the same gas flow rate. This explains why the liquid penetration and film flow behavior appears to be different from that in longer tubes (l _> 10d). More systematic studies are needed to clarify this geometrical scaling effect [60]. In summary, the hydrodynamics of CCF through multitube geometries seems to be dominated by at least two kinds of instability mechanisms. The local interfacial instability enhances the onset of flooding at smaller gas flow rates, and the global flow instability promotes the partial penetration of the liquid at larger superficial gas velocities. The latter is associated with the flow oscillations and pressure fluctuations as well as interfacial structural

Hydrodynamics of Air-Water Countercurrent Flow 767 changes. For the very short multihole plates typical of reactor upper tie plates, it may lead to redistributions of the phases over the whole flow cross section as well as radical changes in the velocity and pressure distributions with in both liquid and gas phases [12-15, 22-24, 67-69]. However, a detailed investigation of this global flow instability is beyond the scope of the present study. PRACTICAL SIGNIFICANCE / USEFULNESS The main objective of the present study was to make detailed measurements of various hydrodynamic parameters relevant to the mechanisms of flooding in multitube geometries. In addition to the global parameters that have been conventionally measured by other authors, the liquid film thickness measured in individual tubes provides some new insight into the phenomenon. In spite of the possibly large uncertainty of the conductance probe technique for the rather chaotic wavy film flow, this paper provides for the first time some quantitative detailed information about film flow and wave motion in CCF through multitube geometries that can be used as a guideline for developing more general predictive flooding models. Such models are required for nuclear reactor safety analyses and other engineering applications. CONCLUSIONS The hydrodynamic behavior of air-water countercurrent flows through vertical short multitube geometries has been investigated by a series of experiments with detailed measurements. Analyses of the experimental results and visual observations revealed two dominant mechanisms of flooding in such complex geometries. As long as the liquid holdup above the multiple tubes is small enough at lower JLi, the local interracial instability mechanism appears to be dominant for initiating the flooding phenomenon, and the hydrodynamic behavior in individual tubes is similar to that in single-path countercurrent fows. However, the effects of the global flow instability mechanism become stronger at higher JLi and tend to dominate in the partial penetration regime close to the CCFL point. On the other hand, in the present experimental range, the shortest test section (1 = 2d) presents a different hydrodynamic behavior, suggesting that a shorter tube length may enhance the liquid penetration. The existing semiempirical correlations fail to predict well the present flooding data unless the flooding parameters are modified. It seems that the scaling numbers J* and K are suitable for all test sections, but the interpolative number H* is applicable only for the shortest one (t = 2d). No theoretical model is available for the pressure drop across the test sections as well as for the film flow and wave motion behavior within the individual tubes. The results presented in this paper provide a preliminary basis for developing such models. RECOMMENDATIONS AND FUTURE RESEARCH NEEDS The present study deals with countercurrent flow in test sections of three parallel tubes. Due to the hydrodynamic interactions between these parallel tubes, the phase distributions in individual tubes are strongly nonuniform, and

the film thickness in individual tubes is highly disturbed and chaotic. A well-designed liquid injection system for individual tubes could better isolate the effects of local interracial wave and global flow instabilities. Moreover, systematic experimental studies are still required to determine the dominant effects of various parameters. For the modeling aspects, it is recommended that a phenomenological model based on the dominant mechanisms could be more applicable for predicting the general hydrodynamic behavior of countercurrent flow in such complex geometries. We wish to express our thanks to M. Boux, B. Francois, M. Joiret, and R. Wanten for their assistance in loop construction, instrument implementation, and experimental operation. Financial support supplied by the Commission of the European Communities (CEC) and by the Catholic University of Louvain (UCL) is gratefully acknowledged.

NOMENCLATURE A A1 C D d

F,f G

Gll(f) G12(f) g H h J L, 1

Id Z 1

M n

P Ap P(h) p(h) Q

Rll('r) R12(~') T Tr

cross-sectional area of the test section, m E cross-sectional area of the test channel, m 2 flooding parameter, dimensionless diameter of the channel, m (unless otherwise specified) diameter of the individual tube, m (unless otherwise specified) frequency, Hz conductance, / ~ - 1 normalized power-spectral density function, dimensionless normalized cross-spectral density function, dimensionless acceleration of gravity, m / s 2 height, m film thickness, mm superficial velocity (= Q/A), m / s length, m (unless otherwise specified) distance between two conductance probes, m (unless otherwise specified) Laplace capillary length ( = ~/A pg)l/2, m flooding parameter, dimensionless number of paths, dimensionless pressure, ea pressure drop, Pa probability distribution function of film thickness, dimensionless probability density function of film thickness, mm volumetric flow rate, ma/s (unless otherwise specified) normalized autocorrelation function, dimensionless normalized cross-correlation function, dimensionless temperature, °C time period, s

768 J. Zhang et al. t W

time scale, s interpolative length scale in Eq. (5), m

Greek Symbols empirical e x p o n e n t in Eq. (6), dimensionless Y o p e n a r e a ratio o f test section to test channel, dimensionless O12(f) phase angle of cross-spectral density function, rad k i n e m a t i c viscosity, m 2 / s V P density, k g / m 3 Ap density difference b e t w e e n liquid and gas ( = PL - Po), k g / m 3 o- surface tension, N / m ~- t i m e delay, s

Subscripts a acquisition B Bankoff d downward G gas i injected, inlet K Kutateladze L liquid m m e a n ( t i m e - a v e r a g e d ) value N Nusselt O F onset of flooding ref r e f e r e n c e S substrate film sd standard deviation value u upward W wave W Wallis REFERENCES 1. Wallis, G. B., One Dimension Two-Phase Flow, McGraw-Hill, New York, 1969. 2. Bankoff, S. G., and Lee, S. C., A Critical Review of the Flooding Literature, in Multiphase Science and Technology, G. F. Hewitt, J. M. Delhaye, and N. Zuber, Eds., Vol. 2, pp. 95-180, Hemisphere, Washington, D.C., 1986. 3. Hewitt, G. F., Countercurrent Two-Phase Flow, Fourth International Topic Meeting on Nuclear Reactor Thermal-Hydraulics, Karlsruhe, F.R.G. Vol. 2, pp. 1129-1144, 1989. 4. Rohatgi, U. S., Saha, P., and Chexal, V. K., Considerations for Realistic ECCS Evaluation Methodology for LWRs, Third International Topic Meeting on Nuclear Reactor Thermal-Hydraulics, Newport, R.I., Vol. 2, paper 8.1, 1985. 5. Soda, K., Tasaka, K., Abe, N., and Shiba, M., Boiling Water Reactor Loss of Coolant Tests--Single Failure Tests with ROSA-Ill, J. Nucl. Sci. Technol., 20(7), 537-558, 1983. 6. Dix, G. E., Nagasaka, H., Sutherland, W. A., Aoki, A., Eckert, T., and Katoh, M., Condensation and Countereurrent Flow Phenomena in BWR Upper Plenum Under Postulated Accident Conditions, ASME/JSME Thermal Engineering Joint Conf., Honolulu, pp. 221-231, 1983. 7. Fakory, M. R., and Lahey, R. T., Jr., An Investigation of BWR/4 Parallel Channel Effects During a Hypothetical Loss-of-Coolant Accident from Both Intact and Broken Jet Pumps, Nucl. Technol., 65, 250 265, 1984. 8. Murase, M., and Naitoh, M., BWR Loss of Coolant Integral Tests with Two Bundle Loop, 1. Thermal-Hydraulic Characteristics in Parallel Channels, J. Nucl. Sci. Technol., 22(3), 213-224, 1985.

9. Murao, Y., Iguchi, T., Okabe, K., Sugimoto, J., Akimoto, H., Okubo, T., Results of CCTF Upper Plenum Injection Tests, Twelfth Water Reactor Safety Research Information Meeting, NUREG/CP-0018, Vol. 2, pp. 306-341, 1984. 10. Iguchi, T., lwamura, T., Akimoto, H., Onuki, A., Abe, Y., et al., SCTF-III Test Plan and Recent SCTF-III Test Results, Nucl. Eng. Design, 108, 241-247, 1988. 11. Watzinger, H., Weiss, P., and Hertlein, R., Countercurrent Flow in Large Geometries--First Results from the Upper Plenum Test Facility, presented at the European Two-Phase Flow Group Meeting, Trondheim, Paper C1, 1987. 12. Hertlein, R., and Herr, W., Controlling Mechanisms for Countercurrent Flow in the Upper Part of a PWR Core, presented at the European Two-Phase Flow Group Meeting, Brussels, Paper E3, 1988. 13. Liu, C. P., and Tien, C. L., A Review of Gas-Liquid Countercurrent Flow Through Multiple Paths, in Heat Transfer in Nuclear Reactor Safety, S. G. Bankoff and N. H. Afgan, Eds., pp. 420-445, Hemisphere, Washington, D.C., 1982. 14. Bankoff, S. G., Tankin, R. S., Yuen, M. C., and Hsieh, C. L., Countercurrent Flow of Air-Water and Stream-Water Through a Horizontal Perforated Plate, Int. J. Heat Mass Transfer, 24, 1381-1395, 1981. 15. Liu, C. P., McCarthy, G. E., and Tien, C. L., Flooding in Vertical Gas-Liquid Countercurrent Flow Through Multiple Short Paths, Int. J. Heat Mass Transfer, 25(9), 1301 1312, 1982. 16. Lee, H. M., and McCarthy, G. E., Liquid Carry-over in Air-Water Countercurrent Flooding, in Heat Transfer 1982, Proc. Int. Conf. Heat Mass Transfer, Miinchen, pp. 237-242, 1982. 17. Sudo, Y., and Ohnuki, A., Mechanisms of Falling Water Limitation Under Countercurrent Flow Through a Vertical Flow Path, Bull. JSME, 27, 708-715, 1984. 18. Bradford, A. M., and Simpson, H. C., Penetration Effects Arising from Simulated Hot-Leg Injection in a 1/10 Scale PWR Test Facility, presented at the European Two-Phase Flow Group Meeting, Trondheim, Paper A4, 1987. 19. Tuomisto, R. H., Large-Scale Air/Water Flow Tests for Separate Effects During LOCAs in PWRs, Nucl. Eng. Design, 102, 171-176, 1987. 20. Celata, G. P., Cumo, M. Farello, G. E., and Setaro, T., The Influence of Flow Obstructions on Flooding Phenomenon in Vertical Channels, Int. J. Multiphase Flow, 15(2), 227-239, 1989. 21. Kokkonen, I., and Tuomisto, H., Air/Water Countercurrent Flow Limitation Experiments with Full-Scale Fuel Bundle Structures, Exp. Thermal Fluid Sci. 3, 581-587, 1990. 22. Naitoh, M., Chino, K., and Kawabe, R. Restrictive Effects of Ascending Steam and Falling Water During Top Spray Emergency Core Cooling, J. Nucl. Sci. Technol., 15(11), 806-815, 1978. 23. Thomas, D. G., and Combs, SK., Measurement of Two-Phase Flow at Core/Upper Plenum Interface for a PWR Geometry Under Simulated Reflood Conditions, NUREG/CR-3138, ORNL/TM-8204, 1983. 24. Sobajima, M., Experimental Modelling of Steam Water Countercurrent Flow Limit for Perforated Plates, J. Nucl. Sci. Technol., 22(9), 723-732, 1985. 25. Hawighorst, A., Kroning, M., Mewes, D., Spatz, R., and Mayinger, F., Fluiddynamic Effects in the the Fuel Element Top Nozzle Area During Refilling and Reflooding, CEC Report EUR-10165 EN, 1985. 26. Spatz, R., Laake, H. J., and Mewes, D., Counter-current Flow Behavior of Steam-Saturated Water and Steam-Subcooled Water in the Fuel Element Top Nozzle Area, Nucl. Eng. Design, 99, 131-139, 1987. 27. Spatz, R., and Mewes, D., The Influence of Wails and Upper Tie Plate Slots on the Flooding Mechanism in Fuel Elements With and Without Heat Transfer Between Steam and Water, Nucl. Eng. Design, 110, 413 422, 1989.

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Received November, 22, 1991; revised March 18, 1992