- Email: [email protected]
A comparison between flooding correlations and experimental flooding data for gas-liquid flow in vertical circular tubes
Chemrcal Engurecring Science. Vol. 40. No. 8. pp. 1425-1440. Printed in Great Britain.
1985. C
A COMPARISON BETWEEN FLOODING AND EXPERIMENTAL FLOODING DATA FLOW IN VERTICAL CIRCULAR
53.0010.00 000%2509;85 1985 Pergamon Press Ltd.
CORRELATIONS FOR GAS-LIQUID TUBES
K. W. McQUILLAN and P. B. WHALLEY Department of Engineering Science, University of Oxford, Parks Road, Oxford, U.K 2 Augusr 1984)
(Receiwd
Abstract-In gas-liquid two phase flow flooding limits the stability ofcountercurrent flow where the liquid flows as a falling film and the gas rises along the centre of the tube. This paper describes the compilation of a data bank containing 2762 experimental flooding data points and the use ofthis data bank to test a total of 22 flooding correlations. As a result of the comparisonsa modified form ofthe correlation presented by Alekseev et al., 1972, Heat Transfer Soviet Res. 4, 159-I 63 is recommended for the most accurate prediction of flooding conditions.
1. INTRODUCTION
2.
In gas-liquid two phase flow in tubes flooding limits the stability of the counter-current flow regime in which the liquid falls as a film along the walls of the tube and the gas forms a rising central core. If the gas velocity rises above the flooding gas velocity the falling liquid film becomes unstable and some liquid is carried upwards along the tube by the gas. Flooding is of importance in both the power and process industries and consequently has been widely studied with the aim of providing methods by which flooding conditions may be calculated. As a result of this research there are a large number of correlating equations at the disposal of the engineer who wishes to predict the flooding gas velocity in a given situation. These correlations are of two main types. The first group are based largely on experimental flooding data, often supplemented by dimensional analysis. This type of emipirical flooding correlation must be used carefully, particularly when predictions are required for conditions or fluids other than those for which the correlation was developed. The second group of equations are based on physical and mathematical modelling of the flooding event, and should therefore be more widely applicable. However, the complicated nature of flooding has resulted in several different mechanisms being postulated as its cause, and furthermore several of the theoretical flooding equations require the use of empirical equations to calculate, for example, the mean liquid film thickness and interfacial shear stress. The present work uses a data bank containing 2762 experimental flooding points to test the performance of the more widely used empirical and theoretical flooding correlations. The data bank contains flooding information for a wide range of flow conditions and fluid physical properties, and is therefore expected to give information about both the accuracy and versatility of various flooding correlations. 1425
THE FLOODING
DATA BANK
literature survey has revealed a considerable amount of flooding data, and this has been collected together to form a data bank containing 2762 flooding points, of which 885 are for systems other than air and water. Table 1 summarises the sources of flooding data for air--water systems, and also gives details of tube geometries used in each investigation. Table 2 summarises the sources of flooding data for other fluid systems, and also gives the relevant fluid physical properties and tube geometries. Figure 1 presents the flooding data in graphical form, the dimensionless gas and liquid velocities are defined later. The data bank is biased towards air-water flow (68 y0 of the data) and against flow in large diameter tubes (78 o/0of the data is for tubes of diameter less than 50 mm). The following considerations were necessary when compiling and using the data bank. A
2.1. Entrance and exit eficts Several investigations, e.g. those of Wallis (1961)and Tien et al. (1979), have shown that the conditions necessary to cause flooding are sensitive to the way in which the gas and the liquid enter and leave the tube. Some flooding correlations (see e.g. Wallis, 1961; Tien er al., 1979) allow for differences in entrance and exit conditions by including constants which assume different values for different end conditions. However, several different types of end conditions have been used to obtain the experimental flooding data points used in this paper, and it is not possible to devise criteria by which the various end conditions may be grouped and accounted for. It should also be noted that the end conditions used in flooding experiments are often chosen for experimental convenience and do not always have direct industrial relevance. Furthermore, there are some circumstances for which flooding predictions are required for end conditions
1426
K. W. MCQUILLAN
and P. B. WHALLEY
Table 1. Experimental flooding data for air-water systems Dataset identification number
Ref.
I 2 3 4 5 6 7 8 9
Tube diameter range (m)
Tube length range (m)
Number of data points
0.012 to 0.025 0.025 0.032 0.032 0.004 to 0.025 0.051 to 0.254 0.013 to 0.153 0.022 to 0.054 0.03 to 0.05 0.019 to 0.14 0.032
1.2 2.4 0.9 0.23 to 3.7 0.06 to 1.8 NK 1.3 NK 2.0 NK 0.5 to 2.0
150 18 20 105 85 56 210 433 24 89 90
Wallis (1961) Nicklin and Davidson (1962) Hewitt and Wallis (1963) Hewitt er al. (1965) Grolmes et al. (1974) Richter (1977) Bharathan et al. (1978) Machej and Sokol (1979) Marinelli er al. (1979) Richter (1981) Whalley and McQuillan (1983)
10
11
that the dimension is not known.
NK-indicates
.
L
I
I
I
I
I
I
I
I
0.4
O-6
0.8
"ee
I
10
I- 2
*1/2
Fig. 1. Experimental flooding data points.
which are not easily defined. For example it may be necessary to calculate if flooding will occur at the top of vertical thermosyphon reboiler tubes. Consequently it was decided to ignore end effects when comparing the correlations with the contents of the data bank. This is expected to cause significant disagreement between the correlations and the data but not to affect the comparison between the various correlations, the best of which will account most successfully for changes
in other
parameters.
2.2. The use of superficial quantities The available flooding correlations variety of physical groups, and when
use a large analysing the
various correlations and data care was necessary to distinguish between actual and superficial quantities, particularly for liquid velocities and Reynolds numbers. It should be noted that:
(1)
Water Diethylene-glycolsolution Water Ethylene-glycol Glycerol solution Water Glycerol solution Water Glycerol solution
Water Glycerol solution Siliconeoil Water Siliconeoil Surfynol A, B Chevron white oil No. 3, 59
Feind (1960)
Wallis (1962)
Clift er al. (1965)
Shiresand Pickering (1965)
Pushkina and Sorokin (1969)
Imura et al. (1977)
Suzuki and Ueda (1977)
Hewitt (1977)
Tien et al. (I 979)
13
14
15
16
17
18
19
20
21
Water/steam,pressure: 0.9 bar Water/steam,pressure: 30 to 70 bar
Augelloand Martini (1982)
23
24
_. - -
NK-indicates that the property or dimension is not known.
Siliconeoil
Kalb and Smith (1981)
Wallis et al. (1980)
22
Water Glycerol solution Set-octyl solution
Water Ethyl alcohol Ethylene glycol n-Heptane
Water Glycerine Ethyl alcohol
Water Millet jelly (NK) Soap solution (NK)
Kamei et al. (1954)
12
Liquids tested
Reference
Data set identification number
0.074O.095
0.052
0.008
0.016-0.070
0.0134.032
0.010-0.029
0.01l-0.021
0.013-0.300
0.027
0.032
0.019
0.02-0.05
0.0189-0.0491
2.3
1.5
0.61
0.91
1.22-2.44
[email protected]
NK
NK
0.3050.915
1.80
NK
[email protected]
2.50
0.0008~.0180
0.0009-0.0100
0.00~).030
0.001-0.002
0.001~.016
0.001-0.082
0.00~3.ooo
0.00-0.02
NK
Liquid viscosity range (Ns/m*) -
741.0-818.0
961.0
818.0
0.0001-0.00012
0.0003
O.ooO8
82O.t%lOOO.O 0.001-0.098
820&l 173.0
1ooo&1170.0
685.0-1097.0
IOOQO-1100.0
1OCtl&1160.0
locOO-1210.0
lOOO.o-1250.0
998&l 109.0
NK
Tube diameter Tube length Liquid density range (m) range (kg]m3) range (m)
Table 2. Experimentalflooding data for non air-water systems
0.01880.029
0.058
0.017
0.017-0.072
0.0174.072
0.0374.072
0.020-0.072
0.0560.072
,-.
111
16
68
499
78
52
118
44
0.0654.072 0.0354.072
103
85
0.05-0.074 0.058-0.072
19
NK
Liquid surface tension range Number of data points (N/m)
? t: P
? E
9 Eti
c i
1428 where:
K. W.
MCQU~LLAN
U, = V, = M, = p, = p, = 6 = D = Re, =
actual liquid velocity (m/s) liquid superficial velocity (m/s) liquid mass flow rate (kg/s) liquid density (kg/m3) liquid viscosity (Ns/m’) mean liquid film thickness (m) tube inside diameter (m) liquid Reynolds number Re,, = superficial liquid Reynolds number.
the type (v:)++(v*)* B
Pg)14 Kg = ~,P&?fJ(P,- Pg)l-4 Kl = V,AIc(p,
and therefore 4Re, = Re,,.
(6)
In the present work superficial quantities are used and the correlations have been adjusted where appropriate. 2.3. Calculation of the mean liquid film thickness The mean liquid film thickness is an important parameter in several flooding correlations, and consequently some authors, e.g. Grolmes et al. (1974) and Imura et al. (1977) have converted flooding liquid flow rates into mean liquid film thicknesses for graphical presentation of their results. For the purposes of compiling the flooding data bank it was convenient to convert the film thicknesses to liquid superficial velocities, and in order to do this it was necessary to use the same conversion equation as had been used in the original work. CORRELATIONS
The predictions of 22 flooding correlations were compared with experimental data. The correlations fall into two groups as suggested in the introduction. These two groups contain experimental correlations, 17 of which are considered in the present work and a smaller group of theoretical correlations. 3.1. Experimental flooding correlations A study of experimental flooding correlations demonstrates the importance of two dimensionless groups, the dimensionless superficial velocity and the Kutateladze number. Wallis (1961) pioneered the use of dimensionless superficial velocities for the prediction of flooding conditions. He defined the liquid and gas dimensionless superficial velocities according to the equations
where: VI* = V: = ps = g =
P? = Yr&@(p,
--&)I
-+
(7)
v:
-P,)>
-+
(8)
= PsPt,{S%,
= c.
(9)
Table 3 gives details of the correlations of this type which are tested in this report. The use of the Kutateladze number in flooding correlations dates back to the work of Tobilevich et al. (1968) and Pushkina and Sorokin (1969). The Kutateladze numbers are given by the equations
But using conservation of mass
3. FLOODING
and P. B. WHALLEY
liquid dimensionless superficial velocity gas dimensionless superficial velocity gas density (kg/m3) acceleration due to gravity (9.81 m/s’).
Wallis (1961) then suggested that flooding conditions could be predicted by the use of equations of
-
(10) (11)
where: K, = liquid Kutateladze number Kg = gas Kutateladze number 0 = surface tension (N/m). Table 4 gives details of experimental flooding correlations which use the Kutateladze number. The Kutateladze number may be related to the dimensionless superficial velocity by using the Bond number &
= D%(P, -Pg) d
(12)
&
= V-,*Boi
(13)
and then where: Bo = Bond number k = gas or liquid phase. The remaining experimental flooding correlations use neither dimensionless superficial velocities or Kutateladze numbers and are detailed in Table 5. 3.2. Theoretical flooding correlations Table 6 gives details of the theoretical flooding correlations tested in this paper. Two notable omissions from this table are the correlation of Shearer and Davidson (1965) and Cetinbudalkar and Jameson (1969). These two methods are not included because they both require the use of complicated solution techniques, which often makes their use impractical. Table 6 gives details of the basic equation used in each correlation, and also indicates those correlations which require the use of empirical equations. Figures 2-5 show the flooding curves predicted by the various correlations for air-water flow in a 0.032 m diameter tube. The discrepancies between the predictions of the correlations are considerable, even for correlations using a particular dimensionless group. 3.3. Film thickness calculations Several flooding correlations require the calculation of the mean thickness of the liquid film, and various equations have been used to do this. When converting data care was necessary to use the same conversion equation as had been used in the original work, but in testing correlations it was considered desirable to have a standard method of calculating film thickness so that differences in correlations would not be disguised. Bankoff and Lee (1984) discussed the claculation of the mean film thickness of a falling liquid film in both laminar and turbulent flow. They compared experimental film thickness data with the predictions of two
Wallis (1961)
Wallis (1962)
Hewittand Wallis (1963)
Clift et al. (1965) Hewitt (1977) Dukler and Smith (1979)
2
3
4
5
6
Ref.
1
Correlation identification number
0.016 v; < 0.09
0.01< VI’< 0.275
0.01$ Vf < 0.09
v; c 0.30
v: < 0.13
v: 6 0.49
Range of data =c
Vi “’ t Vg*1’2 = 0.88
Vttiz+AVt1/2 =C I g
0.34 VF”2•t v; ‘P = 0.79
where: C = 0.88 if VI’ < 0.3 C = 1.00otherwise
yl*‘0 + yg*l/Z= C
where: m =j(N) C =f(N)
where: C = 0.88 for smooth ends C = 0.725for sharp ends my;“z + y;l!Z = C
y/z + y
Equation
Notes
The constants A and C depend on fluid propertiesand tube geometry
N is the “inverseviscosityparameter”
C = 0.725 is used to test this correlation againstexperimentaldata. Seecorrelation6 for use of C = 0.88
Table 3. Empiricalfloodingcorrelations using dimensionlesssuperficialvelocities
Tobilevicher al. (1968)
Pushkina and Sorokin (1969) Alekseevet al. (1972)
Tien et al. (1979)
8
9
IO
Reference
1
Correlation identification number
0.012< K, G 3.43
v: < 1.0
10-6 <‘T,< 0.32
Res,< 8000
Range of data
Cl tanh {C2D*‘14}
C2 = 0.8 to 0.9
Cl = 1.79to 2.1
a = 0.65to 0.8
where: D* = D
aKf12t Ki” =
B. = D2(p,-/J,)9 u
cO.75
where, Fr = Q,s”%,-~g)0~75
K, = 0.2S76Fr-0~22 Boo.26
K, = 3.2
where: a = 0.129,b = - 14.14 if Fr > 0.012, o=O.o65,b= -10.12 otherwise
Equation
Table 4. Empirical floodingcorrelations using the Kutateladzenumber
v,
The constants a, Cl and C2 depend on liquid entrance and exit conditions. Averagevalues are used to test the correlation against data. D* is the dimensionless tube diameter,It is the square root of the Bond number
The equation presented by Alekseevet al. (1972)has a dimensional constant. In this report the exponenton the gravityterm has been adjusted to make both sides of the equation non-dimensional. The constant has beenadjustedaccordingly.Bois a Bond number
0.32(gD)“.5
T=-----
Fr is a Froude number
Notes
Range of data
Grolmes er al. (1974)
Diehl and Koppany (1969)
English et al. (1963) 1.0
,.
PI
0.4 !!E 0.15
+14x104= ’
Equation
~0.322pp.419a0.097
if FlF2 0 ps A = 0.7, B = 1.15otherwise
A =l,B=l
0
if E
p~.462p~.150~;.075
Fl = 1.0otherwise
Vg= 0.286
0.s
> IO,
1300 f! “25 02s
where: m = 92.0,n = 0.33if Resr < 1600, m = 315.4,n = 0.5 otherwise
.R’p 00pl WI P,
1.5
1.6C Re,, ,< 560
0.45 < Vs .yc F1 4 0 p,
Ml 0.1 ij-& s
Feind (1960) 200 C Res < 25000
Table continued over page
15
Ref.
Kamei er al. 200~ Re,,< 2800 (1954)
Correlation identification number
Table 5. Empiricalflooding correlations
The film thicknessmay bc converted to the liquid flow rate using the Nusselt equation
u dynes/cm
D inches
PI, P, lb/f+
v,,VPft/s
The correlationhas dimensional constants. The units used must be as follows:
The correlation has a dimensional constant. The form of equation presentedrequires the use of SI units
Notes
Correlation
Suzukiand 5x10~‘~X~3x10~z Ueda (1977)
Machejand 50 < Re, 6 2500 Sokol (1979)
17
Range of data
16
identification number Ref.
We=
d-%,-P,)
’
NI = F&P5
otherwise
A = 12.15 B = -0.333 c = I.426 1
K-4,
Nf <3x
A = 117.54 B = -0.124 c = 0.905
A = 7.66to 14.86 B = 18.37to 29.70
u’= ot 1.5/u-0.051
where: X=
Fr=AlogloXtB
Equation
Table 5. (Continued)
The constants A and B depend on the tube length, the liquid Reynoldsnumber and the liquid viscosity
Notes
lmura et al. (1977) Potential flow
Bharathanef al. (1978)
Richter (1981)
20
21
22
Roll wave
Separated flow
Hanging film
Wallisand Kuo (1976)
19
Separate cylinders
Model
Wallis (1969)
Reference
18
Correlation identification number
Mean film thickness, critical wavelength
Empirical equation
Momentum Interfacial shear, mean film thickness
Momentum Interfacial shear, mean film thickness
hPla=, Bernouilli
Bernouilli
Continuity, momentum
Basic equations =1
2/,v,tz 2&v;’ (1_a)z +F = (1-a)
+!t(~~5(!!$‘2
where:j, = 0.008
L4 Bd V;’ I’;”t j,l3o VB”
J =j, t 14.6(1-a)‘.s7
where:j, = 0.005
where:
2
u,+us={$+)~;’
K, = 1.87
(y;)%+L+(y;)ZiP+l
flooding equation
Table 6. Theoreticalflooding correlations
An interval halving technique was used to obtain an iterative solution for VB*
Bharathan et al. (1978)obtain the limitingcountercurrent flow curve by allowing a to vary. In this report the film thicknessis caiculatedusingeqs(l4)and(16) and Vi may then be related directly to Vf’
m=3 p=3
For comparison with data the constants were:
Notes
1434
K. W. MCQUILLAN~~~
P. B. WHALLEY
Llquld
Water
Gas Tube
Anr
Dnameter
Tub.?
O-032m l-0 m
Length Pressure
1.0
bar
s? *C%
>”
02-
0
02
04
06
08
I
I
12
10
1L
01
0
1
0, 2
I
I
I
0-L
0 6
0.8 “IP
Correlotlon Number Correlotlon Number Correlation
Number
2
WOlihS
11961 I I19621
3
Hewrtt
and
I
W~IIIS
Correlation
Number
L
C1Itt
Correlation
Number
5
Correlation
Number
6
Hewl:, Dukler
et
01
Wall,s
Correloi~on
Number
11
Kamel
et
Correlotron
Number
12
Felnd
I 1960
Correlotnon
Number
13
Engl,sh
119631
Correlotlon
Number
7
Tob,,ewch
et
COrrelDtlOll
Number
8
Pushk,no
and
corre,o+1on
Number
9
Correlot,on
Number
10
Alekseev T,en et
0,
aI
et 01 I1979
i 1972 I
I (7969) 1
Fig. 3. Empirical flooding correlations using Kutateladze IlUXXIberS.
equations and found good agreement. For laminar flow the equation used was that of Nusselt (1916) which may be written 6* = 0.908 ( Re,,)0~333 (14) where 8* is the dimensionless
film thickness
defined by
(15) For turbulent
flow Bankoff
and Lee (1984)
(1963,
Ko,,,,qny
I
IL 15
Grolmes
et
16
Suzuki
ond
Ueda
11977
Correlation
Number
17
Moche,
and
Sokol
11979
al
(1969
t 197‘
)
I 1
Fig. 4. Empirical flooding correlations in Table 5.
4
0
Liquid
Water
Gas Tube
Anr
Dgometer
Tube
0 032m 1 Om
Length Pressure
I
I
1
o-2
0-L
O-6
1 Obar
I
0-e
1 0
J
I
1.‘
1.2
v , p””
( 1968
Sorokan
I
Number
0
“c P COrrdatlOfl
and
1
I1954
01
Number
1.2
t ‘/I
Dlehl
01
et
Number
14
4
I
IL
Correlation 119791
Fig. 2. Empirical flooding correlations using dimensionless superficial velocities.
I
I
1.2
Correlat,on
119651
11977) and Smth
1
l-0
lh
recom-
Correlot~on
Number
18
WaIIns
Correlotson Correlat,on
Number Number
19 20
Wailns ,mura
Correlot,on
Number
21
Bhorothon
Correlotlon
Number
22
Richter
11969
I
and Kuo 119761 et 01 , ,977 I et I1981
qi
119761
/
Fig. 5. Theoretical flooding correlations.
mend the use of an equation
due to Belkin et al. (1959).
8* = 0.135(Re,,)0.583.
(16)
The above two equations are used in the present work to determine the mean liquid film thickness. The transition between the two equations is taken to occur at Re,, = 2064, (where the two equations predict the same liquid film thickness). Both of the above equations were developed for the calculation of the liquid film thickness in the absence of a counter-current gas
Gas-liquid flow in verticalcirculartubes flow, the presence of which would be expected to thicken the film. However, the results of Smith et al. (1984) indicated that the Nusselt (1916) equation gives good prediction of the film thickness even for gas velocities close to the flooding gas velocity. 4. COMPARISON
OF
FLOODING
WITH
CORRELATIONS
DATA
A computer program has been written to enable the predictions of a chosen correlation to be compared with the experimental flooding data bank. The results of the comparison are displayed graphically and in statistical form. Table 7 gives a statistical comparison between the correlations and the data bank. The following statistics are presented. (1)
Number
of points
Some of the correlations were unable to deal with all of the data points, either because the calculated flooding gas velocity was negative or, for correlations of the type f( I’:) +f( I’,*) = C, because the error in the calculation becomes unreasonably large. Table 7 therefore contains information detailing the number of points accepted by each correlation (a maximum of 2762 points). (2) Weighted percentage error The weighted percentage error is given for all the data, and also for the air-water and non air-water data separately. It is defined by the equation s,,
= [il{expiln(g>‘I
where:
- l.O}]
x 100%
(17)
n = number of flooding data points & = weighted mean percentage error (%) /tT = predicted flooding gas dimensionless superficial veiocity V& = experimental flooding gas dimensionless superficial velocity.
The weighting on the quoted error figure ensures that the errors occurring for V& < I’:= are equally important as those for P’& > Vf. (3) i2.m.s. weighted percentage error The r.m.s. weighted percentage error is given for all the data, and is defined by the equation
~wm =
[~,(expiln(~)i
-l-O}]*
X 10% (18)
where: E,,,, = weighted r.m.s. error (%). A tow r.m.s. error indicates a low scatter in the data. (4) Deviation The deviation is defined by the equation
c = [;pgg-
LO>] x 100%
where: < = deviation. Ideally the deviation should be zero.
1435
Figures 6 and 7 present two of the comparisons between correlations and data in a graphical form. A more complete series of comparisons is given by McQuillan and Whalley (1984). The empirical correlations are generally more successful than the theoretical correlations. The correlations which use dimensionless superficial velocities are noticeably less successful than the other empirical correlations, particularly for high liquid velocities and for non air-water systems. The best theoretical correlation is the modified form of the correlation presented by Bharathan et al. (1978). The correlation is successful over a range of liquid viscosities and surface tensions but it over-predicts the flooding gas velocity for large tube diameters. This over-prediction could be due to inaccuracies resulting from the use of the empirical interfacial friction factor equation for large tube diameters. The most successful empirical correlation is that of Alekseev et al. (1972), which works well over a range of tube diameters and liquid surface tensions, but over predicts flooding gas flow rates for high liquid viscosities as illustrated in Fig. 8. This overprediction may be corrected, and the deviation reduced to zero, by modifying Alekseev et al. (1972) correlation to give the new correlation: K,
= 0.286B0°~26Fr-0~22
-0.18 (20)
where: pw = water viscosity (taken as 0.001 Ns/m’). The performance of this modified correlation (identification number 23) is given in Table 7, from the statistics it may be seen that this modified correlation gives the most accurate prediction of the available data. Figure 9 illustrates the effect of introducing the viscosity parameter. 5. CONCLUSIONS
A flooding data bank has been compiled, containing a total of 2762 flooding data points from taken from 24 references. This data has been used to test the performance of 17 empirical flooding correlations and five theoretical flooding correlations. The comparison has been limited to flow in vertical circular tubes, and care should be taken where predictions are required for other geometries. The most successful correlation is a modified form of the empirical correlation presented by Alekseev et al. (1972). The most successful theoretical correlation is a modified form of the correlation presented by Bharathan et al. (1978). Correlations using dimensionless superficial velocities are not very successful, particularly at high liquid flow rates. NOTATION
(19)
1+ E Pw1 (
A a B b BO
c
constant constant constant constant Bond number constant
1 3
4
------
5
6
7
I._-
..-_,
_ _
2604 2734 2762 2634 2601 2653 130 58 62 93 62 90 60 69 39 45 57 40 59 33 39 50 35 61 89 59 72 50 50 56 -0.6 0.20 0.33 -0.12 0.08 -0.52 24 24 61 90 18 34 95 8 46 99 34 92 75 4 14 60 19 77 62 12 8 50 19 94 86 31 29 69 35 30 63 105 108 67 99 21 30 28 33 26 25 37 15 25 28 14 24 29 48 11 16 39 11 71 31 41 55 29 34 45 84 15 9 69 34 113 47 7 8 38 11 66 82 23 11 71 39 97 44 62 62 48 61 47 37 8 7 21 9 47 32 50 63 36 36 27 56 29 31 43 30 61 260 45 16 112 82 131 181 48 16 107 66 IO4 50 22 39 37 17 45 111 44 56 76 44 89 94 61 71 141 50 33 37 26 38 23 24 42 33 87 89 159 78 49
2
Note: figuresin bold indicate“best” performance.
Number of points 2615 GvTms l %I 94 E,, all data ( %) 53 EWm air-water (“i,) 55 E,, non air-water (%) 48 c -0.38 1 hll (%I 22 2 hln (%I 131 3 hvlIl(%I 72 4 e!vnl(%I 59 5 hl (%I 78 6 e,, (%I 62 7 hvlm(%) 29 8 e,m (%I 14 9 eWu(%I 43 10 hvm(%I 29 11 hII ( %I 80 l2 e, (%I 45 l3 &wm (%I 77 14 hn (%I 39 l5 &wm (“i,) 30 I6 E, (%I 29 l7 4vm (73 51 I8 Ewm (%I 139 l9 &wm (%I 150 2o hvm (%I 32 21 &wm (%I 71 22 &wm ( %I 23 23 &wm (%I 25 24 &wm ( %) 38
Data
9
10
Correlation 11 12 13
14
15
16
17
18
19
20
21
22
23
-._
.
-._
--_-..
.-
. .-
-._-
_..
__- ..^.
2762 2762 2762 2762 2619 2762 2762 2762 2758 2762 2734 2762 2759 2738 2762 2762 65 40 122 46 117 84 45 67 78 63 46 44 65 57 82 85 40 26 90 28 47 48 28 49 48 45 35 30 38 38 52 52 36 25 40 43 44 35 83 25 43 32 27 29 33 37 47 32 66 61 47 34 47 29 108 36 57 85 30 33 47 42 63 94 0.9 0.07 0.38 0.40 0.15 -0.07 0.24 -0.13 0.44 -0.15 0.34 0.4 0.4 0.22 0.34 0.00 218 69 114 122 90 63 103 69 143 122 74 123 67 57 129 85 94 54 28 62 34 151 34 43 51 33 44 36 34 9 80 32 61 16 18 9 8 9 25 23 9 14 17 21 10 37 32 12 45 27 13 15 10 12 12 42 9 10 28 31 11 48 15 30 78 19 29 61 15 20 36 22 39 21 20 40 25 16 21 40 18 42 79 43 51 26 42 86 82 33 38 50 97 30 131 41 83 18 47 42 42 50 32 41 18 34 26 18 27 32 47 24 62 8 41 8 17 24 48 37 33 7 12 36 21 35 7 44 54 20 19 20 11 10 15 74 61 94 18 18 22 17 9 16 96 15 48 27 33 18 56 51 56 47 32 14 20 25 69 16 10 9 9 7 35 37 35 8 29 16 39 12 59 6 52 9 34 25 10 6 6 13 9 15 9 5 26 35 11 53 11 15 34 27 35 21 20 30 14 21 21 18 40 42 25 61 23 55 131 58 101 151 22 76 58 12 92 22 30 107 65 49 157 87 37 18 18 16 11 7 10 6 11 38 52 12 31 11 110 18 133 28 74 70 51 67 18 68 47 18 42 17 82 42 63 78 6 39 9 36 22 22 34 34 24 20 40 57 52 75 27 38 70 30 64 3s 34 32 16 34 18 44 43 26 26 27 87 41 62 30 16 17 20 44 24 9 24 16 35 38 18 26 12 33 115 19 47 47 27 33 65 50 33 53 21 29 28 29 49 40 37 20 109 29 41 61 37 50 63 36 31 24 28 41 54 72 184 68 120 249 99 45 106 89 134 167 79 117 106 62 117 68 69 4 32 13 I5 8 29 42 28 16 4 9 45 55 47 42 78 32 51 I7 25 55 45 19 38 45 48 33 146 31 109 42
8
Table 7. Comparison betweencorrelations and data
Gas-liquid
flow in vertical circular tubes
Reference
I 0
1437
: Bharathon
et al
( 19 78 1
I
I
I
I
I
0.2
0.1
0.6
0.8
1.0
1.2
v *‘/2 Ce Fig. 6. Comparison
between correlation
I
Correlation Weighted Number
of Bharathan
I
Reference Number Mean of
Error Points
et al. (1978) and experimental
I : Alekseev
I
flooding
data.
I
et al
(1972
)
: 9
: 28 % : 2762
1clc
j-
jO-2 >0.’ I-
I
0
0.2
I
O-L
I
“Ce Fig. 7. Comparison
between correlation
of Alekseev
1
0.6
O-8
I
I.0
12
* ‘/2
et al. (1972) and experimental
flooding
data.
1438
K. W. MCQUILLAN~~~
P. B. WHALLEY
I
1
Reference Correlation Number Weighted Mean Error Number of Points
1
: Alekseev
et al
(19721
: 9 : 28% : 2762
11: 3-
5-
2 11 50 ,:2O- l-
o. 000
o- 01
0.001
Liquid Fig. 8. Comparison
I.0
0.1 ( Ns/
Viscosity
m2
1
.O
)
between correlation of Alekseev e? al. (1972) and experimental flooding data.
I
1
I
Reference Correlation Number Weighted Mean Error Number of Points
Liquid Fig. 9. Comparison
: : : :
I
Present 23 26% 2762
Viscosity
work
( Ns/m2
I
between modified Alekseev correlation and experimental flooding data.
flow in vertical circulartubes
Gas-liquid
Cl c2 D Fr Fl F2 f 9 K k M m : Nl P
Q
Re T u V We X a Y 6 E P r P c
constant constant tube diameter, m Froude number constant constant friction factor acceleration due to gravity, m/s2 Kutateladze number dimensionless wave number mass flow rate, kg/s constant number of flooding data points inverse viscosity parameter dimensionless group constant volume flow rate per unit wetted perimeter, m2/s Reynolds number dimensionless group velocity, m/s superficial velocity, m/s Weber number dimensionless group void fraction property parameter, m film thickness, m weighted error, o/O dynamic viscosity, Ns/m2 deviation density, kg/m3 surface tension, N/m
Subscripts g e
z 1 P s W
wm wrms
gas
experimental interfacial phase liquid predicted superficial wall, water weighted mean weighted root mean square
Superscripts * denotes non-dimensionalised indicated denotes a modified quantity Dimensionless groups Bond number
D2g(P, -P,) u
Bo
=
Dimensionless diameter
DC
= D[g(pl;p.)]I
Froude number
Fr
=
Q,[
g(pI-/d”]’
quantity
as
1 = J-jot
Kutateladze number
1439 K,
=
vk&b(PI
--&)I
-’
+
Inverse viscosity parameter
1
Reynolds numbers: liquid actual liquid superficial
Rerl
PI ViD =-=4Re, PI
gas actual
Re,
=
pg u, (D - 26) J%
gas superficial Dimensionless superficial velocity
W
= V,P;[gD(P, - Pg)] -*
Weber number
We
=
1
ff D2dp,
- pg) = z
Dimensionless liquid film thickness REFERENCES
AlekseevV. P., PoberezkinA. E. and Gerasimov P. V., 1972,
Determination of flooding rates in regular packings. Heat Transfer Soviet Rex 4 159-l 63. Augello L. and Martini R., 1982, Flooding experiments in tubular geometry with steam-water up to 70 bar. European Two-phase Flow Group Meeting, Paris, France, June 1982, paper A23. Bankoff S. G. and Lee S. C., 1984, A critical review of the flooding literature, in Multiphase Science and Technology, Vol. 2. Hemisphere, New York. Belkin H. H., MacLeod A. A., Monrad C. C. and Rothfus R. R., 1959, Turbulent liquid flow down vertical walls. A.I.Ch.E. J. 5 245-248. Bharathan D., Wallis G. B. and Richter H. J., 1978, Air-water countercurrent annular flow in vertical tubes. EPRI Report No. EPRI NP-786. Cetinbudalkar A. G. and Jameson G. J., 1969, The mechanism of flooding in vertical countercurrent two-phase flow. Chrm. Engng Sci. 24 1669-1680. Clift R., Pritchard C. L. and Nedderman R. M., 1965, The effect of viscosity on the flooding conditions in wetted wall columns. Chem. Engng Sri. 21 87-95. Diehl J. E. and Koppany C. R., 1969, Flooding velocity correlation for gas-liquid counterflow in vertical tubes. Chem. Engng Prog. Symp. Series 65 77-83. Dukler A. E. and Smith L., 1979, Two phase interactions in counter-current flow: studies of the flooding mechansim. Nureg Report No. NUREG/CRa17. English K. G., Jones W. T., Spillers, R. C. and Orr, V., 1963, Flooding in a vertical updraft partial condenser. Chem. Engng Pray. 59 51-54. Feind R., 1960, Falling liquid films with countercurrent air flow in vertical tubes. VDI Forschungsheft, Vol. 481. Grolmes M. A., Lambert G. A. and Fauske H. K., 1974, Flooding in vertical tubes. Inst. Chem. Engrs Symp. Multiphase Flow Sysfems, University of Strathclyde, Glasgow. Also published as Inst. Chem. Engrs. Symposium Series No. 38.
1440
K. W. MCQUILLAN and P. B. WHALLEY
Hewitt G. F., 1977, Influence of end conditions, tube inclination and physical properties on flooding in gas liquid flows, quoted by Bankoff and Lee (1984). Hewitt G. F. and Wallis G. B., 1963, Flooding and associated phenomena in falling film flow in a vertical tube. A.S.M.E. Paper presented at Multiphase Flow Symp., Philadelphia, pp. 62-74. Hewitt G. F.. Lacev P. M. C. and Nicholls B.. 1965. Transitions in film~flow in a vertical tube. AERE-R 4614: Imura H., Kusuda H. and Funatsu S., 1977, Flooding velocity in a counter-current annular two-phase flow. Chek En& Sci. 32 7987. Kalb C. E. and Smith J. K., 1981. An interuolative flooding model based on limiting flow regimes for countercurrent gas/liquid flow. Chem. Engng J. 22 113-l 23. Kamei Sy. Oishi J. and Okask T.. 1954. Floodine in a wetted y wall tower. Chem. Engng 18 k-388. Machei K. and Sokol W.. 1979, Determination of the parameters which affect the flooding of a tube. Int. Chem. Engng 19 696700. Marinelli V., Oliveti G. and Sabato A., 1979, Calculations of countercurrent flows of liquid and gas in the flooding regime. European Two-phase FIow Group Meeting, ISPRA, June 1979. McQuillan K. W. and Whalley P. B., 1984, A comparison between flooding correlations and experimental flooding data. AERE-R 11267. Nicklin D. J. and Davidson J. F., 1962, The onset of instability in two-phase slug flow. Proc. I. Mech. Symp. Two-phase Flow, London, Feb. 1962, paper 7. Nusselt W., 1916, Surface condensation of water vapour. VDI(Z), Vol. 60, 541-546, Vol. 60, 569-575. Pushkina 0. L. and Sorokin Y. L., 1969, Breakdown of liquid film motion in vertical tubes. Heat Transfer Soviet Res. 1 564.4. Richter H. J., 1977, Flooding experiments, large tubes. Paper presented at NRC 5th Water Reactor Safety Res. Information Meeting, Maryland, U.S.A.
Richter H. J., 1981, Flooding in tubes and annuli. Inr. J. Multiphase Flow 7 647458. Shearer C. 3. and Davidson J. F., 1965, The investigation of a standing wave due to gas blowinp. unwards over a liauid film; its Relation to flooding in wetted wall columns. J. Fkd Mech. 22 321-336. Shires G. L. and Pickering A. R., 1965, The flooding phenomenon in counter-current two-phase flow. Symp. TLvo-phase Flow, Exeter. U.K.. naner B5. Smith L., Chopra A. and Dukler-A.- E., 1984, Flooding and upwards film flow in tubes-I. Experimental studies. Int. J. Multiphase Flow 10 585-597. Suzuki S. and Ueda T., 1977, Behaviour of liquid films and flooding in countercurrent two-phase flow-l. Flow in circular tubes. Inr. J. Multiphase Flow 3 517-532. Tien C. L., Chung K. S. and Liu C. P., 1979, Flooding in twophase countercurrent flows. EPRI Report No. EPRI NP1283. Tobilevich N. Y., Sagan I. I. and Porzhezihskii Y. G., 1968, The downward motion of a liquid film in vertical tubes in an air-vapour countertlow. J. Engng Phys. 15 855861. Wallis G. B., 1961, Flooding velocities for air and water in vertical tubes. AEEW-R 123. Wallis G. B., 1962, The influence of liquid viscosity on flooding in vertical tubes. General Electric Company Report No. 62GLl32. Wallis G. B., 1969, One-dimensional Two-phase Flow. McGraw-Hill, New York. Wallis G. B. and Kuo J. T., 1976, The bchaviour of gas-liquid interfaces in vertical tubes. Int. J. Multiphase Flow 2 521-536. Wallis G. B., De Sieyes D. C., Rosselli R. J. and Lacombe J., 1980, Counter-current annular flow regimes for steam and subcooled water in a vertical tube. EPRI Report No. EPRI NP-1336. Whalley P. B. and McQuillan K. W., 1983, Flooding in twophase flow: the effect of tube length and artificial wave injection. AERE-R 10883. Physiochem. Hydrodyn. (1985).
1985. C
A COMPARISON BETWEEN FLOODING AND EXPERIMENTAL FLOODING DATA FLOW IN VERTICAL CIRCULAR
53.0010.00 000%2509;85 1985 Pergamon Press Ltd.
CORRELATIONS FOR GAS-LIQUID TUBES
K. W. McQUILLAN and P. B. WHALLEY Department of Engineering Science, University of Oxford, Parks Road, Oxford, U.K 2 Augusr 1984)
(Receiwd
Abstract-In gas-liquid two phase flow flooding limits the stability ofcountercurrent flow where the liquid flows as a falling film and the gas rises along the centre of the tube. This paper describes the compilation of a data bank containing 2762 experimental flooding data points and the use ofthis data bank to test a total of 22 flooding correlations. As a result of the comparisonsa modified form ofthe correlation presented by Alekseev et al., 1972, Heat Transfer Soviet Res. 4, 159-I 63 is recommended for the most accurate prediction of flooding conditions.
1. INTRODUCTION
2.
In gas-liquid two phase flow in tubes flooding limits the stability of the counter-current flow regime in which the liquid falls as a film along the walls of the tube and the gas forms a rising central core. If the gas velocity rises above the flooding gas velocity the falling liquid film becomes unstable and some liquid is carried upwards along the tube by the gas. Flooding is of importance in both the power and process industries and consequently has been widely studied with the aim of providing methods by which flooding conditions may be calculated. As a result of this research there are a large number of correlating equations at the disposal of the engineer who wishes to predict the flooding gas velocity in a given situation. These correlations are of two main types. The first group are based largely on experimental flooding data, often supplemented by dimensional analysis. This type of emipirical flooding correlation must be used carefully, particularly when predictions are required for conditions or fluids other than those for which the correlation was developed. The second group of equations are based on physical and mathematical modelling of the flooding event, and should therefore be more widely applicable. However, the complicated nature of flooding has resulted in several different mechanisms being postulated as its cause, and furthermore several of the theoretical flooding equations require the use of empirical equations to calculate, for example, the mean liquid film thickness and interfacial shear stress. The present work uses a data bank containing 2762 experimental flooding points to test the performance of the more widely used empirical and theoretical flooding correlations. The data bank contains flooding information for a wide range of flow conditions and fluid physical properties, and is therefore expected to give information about both the accuracy and versatility of various flooding correlations. 1425
THE FLOODING
DATA BANK
literature survey has revealed a considerable amount of flooding data, and this has been collected together to form a data bank containing 2762 flooding points, of which 885 are for systems other than air and water. Table 1 summarises the sources of flooding data for air--water systems, and also gives details of tube geometries used in each investigation. Table 2 summarises the sources of flooding data for other fluid systems, and also gives the relevant fluid physical properties and tube geometries. Figure 1 presents the flooding data in graphical form, the dimensionless gas and liquid velocities are defined later. The data bank is biased towards air-water flow (68 y0 of the data) and against flow in large diameter tubes (78 o/0of the data is for tubes of diameter less than 50 mm). The following considerations were necessary when compiling and using the data bank. A
2.1. Entrance and exit eficts Several investigations, e.g. those of Wallis (1961)and Tien et al. (1979), have shown that the conditions necessary to cause flooding are sensitive to the way in which the gas and the liquid enter and leave the tube. Some flooding correlations (see e.g. Wallis, 1961; Tien er al., 1979) allow for differences in entrance and exit conditions by including constants which assume different values for different end conditions. However, several different types of end conditions have been used to obtain the experimental flooding data points used in this paper, and it is not possible to devise criteria by which the various end conditions may be grouped and accounted for. It should also be noted that the end conditions used in flooding experiments are often chosen for experimental convenience and do not always have direct industrial relevance. Furthermore, there are some circumstances for which flooding predictions are required for end conditions
1426
K. W. MCQUILLAN
and P. B. WHALLEY
Table 1. Experimental flooding data for air-water systems Dataset identification number
Ref.
I 2 3 4 5 6 7 8 9
Tube diameter range (m)
Tube length range (m)
Number of data points
0.012 to 0.025 0.025 0.032 0.032 0.004 to 0.025 0.051 to 0.254 0.013 to 0.153 0.022 to 0.054 0.03 to 0.05 0.019 to 0.14 0.032
1.2 2.4 0.9 0.23 to 3.7 0.06 to 1.8 NK 1.3 NK 2.0 NK 0.5 to 2.0
150 18 20 105 85 56 210 433 24 89 90
Wallis (1961) Nicklin and Davidson (1962) Hewitt and Wallis (1963) Hewitt er al. (1965) Grolmes et al. (1974) Richter (1977) Bharathan et al. (1978) Machej and Sokol (1979) Marinelli er al. (1979) Richter (1981) Whalley and McQuillan (1983)
10
11
that the dimension is not known.
NK-indicates
.
L
I
I
I
I
I
I
I
I
0.4
O-6
0.8
"ee
I
10
I- 2
*1/2
Fig. 1. Experimental flooding data points.
which are not easily defined. For example it may be necessary to calculate if flooding will occur at the top of vertical thermosyphon reboiler tubes. Consequently it was decided to ignore end effects when comparing the correlations with the contents of the data bank. This is expected to cause significant disagreement between the correlations and the data but not to affect the comparison between the various correlations, the best of which will account most successfully for changes
in other
parameters.
2.2. The use of superficial quantities The available flooding correlations variety of physical groups, and when
use a large analysing the
various correlations and data care was necessary to distinguish between actual and superficial quantities, particularly for liquid velocities and Reynolds numbers. It should be noted that:
(1)
Water Diethylene-glycolsolution Water Ethylene-glycol Glycerol solution Water Glycerol solution Water Glycerol solution
Water Glycerol solution Siliconeoil Water Siliconeoil Surfynol A, B Chevron white oil No. 3, 59
Feind (1960)
Wallis (1962)
Clift er al. (1965)
Shiresand Pickering (1965)
Pushkina and Sorokin (1969)
Imura et al. (1977)
Suzuki and Ueda (1977)
Hewitt (1977)
Tien et al. (I 979)
13
14
15
16
17
18
19
20
21
Water/steam,pressure: 0.9 bar Water/steam,pressure: 30 to 70 bar
Augelloand Martini (1982)
23
24
_. - -
NK-indicates that the property or dimension is not known.
Siliconeoil
Kalb and Smith (1981)
Wallis et al. (1980)
22
Water Glycerol solution Set-octyl solution
Water Ethyl alcohol Ethylene glycol n-Heptane
Water Glycerine Ethyl alcohol
Water Millet jelly (NK) Soap solution (NK)
Kamei et al. (1954)
12
Liquids tested
Reference
Data set identification number
0.074O.095
0.052
0.008
0.016-0.070
0.0134.032
0.010-0.029
0.01l-0.021
0.013-0.300
0.027
0.032
0.019
0.02-0.05
0.0189-0.0491
2.3
1.5
0.61
0.91
1.22-2.44
[email protected]
NK
NK
0.3050.915
1.80
NK
[email protected]
2.50
0.0008~.0180
0.0009-0.0100
0.00~).030
0.001-0.002
0.001~.016
0.001-0.082
0.00~3.ooo
0.00-0.02
NK
Liquid viscosity range (Ns/m*) -
741.0-818.0
961.0
818.0
0.0001-0.00012
0.0003
O.ooO8
82O.t%lOOO.O 0.001-0.098
820&l 173.0
1ooo&1170.0
685.0-1097.0
IOOQO-1100.0
1OCtl&1160.0
locOO-1210.0
lOOO.o-1250.0
998&l 109.0
NK
Tube diameter Tube length Liquid density range (m) range (kg]m3) range (m)
Table 2. Experimentalflooding data for non air-water systems
0.01880.029
0.058
0.017
0.017-0.072
0.0174.072
0.0374.072
0.020-0.072
0.0560.072
,-.
111
16
68
499
78
52
118
44
0.0654.072 0.0354.072
103
85
0.05-0.074 0.058-0.072
19
NK
Liquid surface tension range Number of data points (N/m)
? t: P
? E
9 Eti
c i
1428 where:
K. W.
MCQU~LLAN
U, = V, = M, = p, = p, = 6 = D = Re, =
actual liquid velocity (m/s) liquid superficial velocity (m/s) liquid mass flow rate (kg/s) liquid density (kg/m3) liquid viscosity (Ns/m’) mean liquid film thickness (m) tube inside diameter (m) liquid Reynolds number Re,, = superficial liquid Reynolds number.
the type (v:)++(v*)* B
Pg)14 Kg = ~,P&?fJ(P,- Pg)l-4 Kl = V,AIc(p,
and therefore 4Re, = Re,,.
(6)
In the present work superficial quantities are used and the correlations have been adjusted where appropriate. 2.3. Calculation of the mean liquid film thickness The mean liquid film thickness is an important parameter in several flooding correlations, and consequently some authors, e.g. Grolmes et al. (1974) and Imura et al. (1977) have converted flooding liquid flow rates into mean liquid film thicknesses for graphical presentation of their results. For the purposes of compiling the flooding data bank it was convenient to convert the film thicknesses to liquid superficial velocities, and in order to do this it was necessary to use the same conversion equation as had been used in the original work. CORRELATIONS
The predictions of 22 flooding correlations were compared with experimental data. The correlations fall into two groups as suggested in the introduction. These two groups contain experimental correlations, 17 of which are considered in the present work and a smaller group of theoretical correlations. 3.1. Experimental flooding correlations A study of experimental flooding correlations demonstrates the importance of two dimensionless groups, the dimensionless superficial velocity and the Kutateladze number. Wallis (1961) pioneered the use of dimensionless superficial velocities for the prediction of flooding conditions. He defined the liquid and gas dimensionless superficial velocities according to the equations
where: VI* = V: = ps = g =
P? = Yr&@(p,
--&)I
-+
(7)
v:
-P,)>
-+
(8)
= PsPt,{S%,
= c.
(9)
Table 3 gives details of the correlations of this type which are tested in this report. The use of the Kutateladze number in flooding correlations dates back to the work of Tobilevich et al. (1968) and Pushkina and Sorokin (1969). The Kutateladze numbers are given by the equations
But using conservation of mass
3. FLOODING
and P. B. WHALLEY
liquid dimensionless superficial velocity gas dimensionless superficial velocity gas density (kg/m3) acceleration due to gravity (9.81 m/s’).
Wallis (1961) then suggested that flooding conditions could be predicted by the use of equations of
-
(10) (11)
where: K, = liquid Kutateladze number Kg = gas Kutateladze number 0 = surface tension (N/m). Table 4 gives details of experimental flooding correlations which use the Kutateladze number. The Kutateladze number may be related to the dimensionless superficial velocity by using the Bond number &
= D%(P, -Pg) d
(12)
&
= V-,*Boi
(13)
and then where: Bo = Bond number k = gas or liquid phase. The remaining experimental flooding correlations use neither dimensionless superficial velocities or Kutateladze numbers and are detailed in Table 5. 3.2. Theoretical flooding correlations Table 6 gives details of the theoretical flooding correlations tested in this paper. Two notable omissions from this table are the correlation of Shearer and Davidson (1965) and Cetinbudalkar and Jameson (1969). These two methods are not included because they both require the use of complicated solution techniques, which often makes their use impractical. Table 6 gives details of the basic equation used in each correlation, and also indicates those correlations which require the use of empirical equations. Figures 2-5 show the flooding curves predicted by the various correlations for air-water flow in a 0.032 m diameter tube. The discrepancies between the predictions of the correlations are considerable, even for correlations using a particular dimensionless group. 3.3. Film thickness calculations Several flooding correlations require the calculation of the mean thickness of the liquid film, and various equations have been used to do this. When converting data care was necessary to use the same conversion equation as had been used in the original work, but in testing correlations it was considered desirable to have a standard method of calculating film thickness so that differences in correlations would not be disguised. Bankoff and Lee (1984) discussed the claculation of the mean film thickness of a falling liquid film in both laminar and turbulent flow. They compared experimental film thickness data with the predictions of two
Wallis (1961)
Wallis (1962)
Hewittand Wallis (1963)
Clift et al. (1965) Hewitt (1977) Dukler and Smith (1979)
2
3
4
5
6
Ref.
1
Correlation identification number
0.016 v; < 0.09
0.01< VI’< 0.275
0.01$ Vf < 0.09
v; c 0.30
v: < 0.13
v: 6 0.49
Range of data =c
Vi “’ t Vg*1’2 = 0.88
Vttiz+AVt1/2 =C I g
0.34 VF”2•t v; ‘P = 0.79
where: C = 0.88 if VI’ < 0.3 C = 1.00otherwise
yl*‘0 + yg*l/Z= C
where: m =j(N) C =f(N)
where: C = 0.88 for smooth ends C = 0.725for sharp ends my;“z + y;l!Z = C
y/z + y
Equation
Notes
The constants A and C depend on fluid propertiesand tube geometry
N is the “inverseviscosityparameter”
C = 0.725 is used to test this correlation againstexperimentaldata. Seecorrelation6 for use of C = 0.88
Table 3. Empiricalfloodingcorrelations using dimensionlesssuperficialvelocities
Tobilevicher al. (1968)
Pushkina and Sorokin (1969) Alekseevet al. (1972)
Tien et al. (1979)
8
9
IO
Reference
1
Correlation identification number
0.012< K, G 3.43
v: < 1.0
10-6 <‘T,< 0.32
Res,< 8000
Range of data
Cl tanh {C2D*‘14}
C2 = 0.8 to 0.9
Cl = 1.79to 2.1
a = 0.65to 0.8
where: D* = D
aKf12t Ki” =
B. = D2(p,-/J,)9 u
cO.75
where, Fr = Q,s”%,-~g)0~75
K, = 0.2S76Fr-0~22 Boo.26
K, = 3.2
where: a = 0.129,b = - 14.14 if Fr > 0.012, o=O.o65,b= -10.12 otherwise
Equation
Table 4. Empirical floodingcorrelations using the Kutateladzenumber
v,
The constants a, Cl and C2 depend on liquid entrance and exit conditions. Averagevalues are used to test the correlation against data. D* is the dimensionless tube diameter,It is the square root of the Bond number
The equation presented by Alekseevet al. (1972)has a dimensional constant. In this report the exponenton the gravityterm has been adjusted to make both sides of the equation non-dimensional. The constant has beenadjustedaccordingly.Bois a Bond number
0.32(gD)“.5
T=-----
Fr is a Froude number
Notes
Range of data
Grolmes er al. (1974)
Diehl and Koppany (1969)
English et al. (1963) 1.0
,.
PI
0.4 !!E 0.15
+14x104= ’
Equation
~0.322pp.419a0.097
if FlF2 0 ps A = 0.7, B = 1.15otherwise
A =l,B=l
0
if E
p~.462p~.150~;.075
Fl = 1.0otherwise
Vg= 0.286
0.s
> IO,
1300 f! “25 02s
where: m = 92.0,n = 0.33if Resr < 1600, m = 315.4,n = 0.5 otherwise
.R’p 00pl WI P,
1.5
1.6C Re,, ,< 560
0.45 < Vs .yc F1 4 0 p,
Ml 0.1 ij-& s
Feind (1960) 200 C Res < 25000
Table continued over page
15
Ref.
Kamei er al. 200~ Re,,< 2800 (1954)
Correlation identification number
Table 5. Empiricalflooding correlations
The film thicknessmay bc converted to the liquid flow rate using the Nusselt equation
u dynes/cm
D inches
PI, P, lb/f+
v,,VPft/s
The correlationhas dimensional constants. The units used must be as follows:
The correlation has a dimensional constant. The form of equation presentedrequires the use of SI units
Notes
Correlation
Suzukiand 5x10~‘~X~3x10~z Ueda (1977)
Machejand 50 < Re, 6 2500 Sokol (1979)
17
Range of data
16
identification number Ref.
We=
d-%,-P,)
’
NI = F&P5
otherwise
A = 12.15 B = -0.333 c = I.426 1
K-4,
Nf <3x
A = 117.54 B = -0.124 c = 0.905
A = 7.66to 14.86 B = 18.37to 29.70
u’= ot 1.5/u-0.051
where: X=
Fr=AlogloXtB
Equation
Table 5. (Continued)
The constants A and B depend on the tube length, the liquid Reynoldsnumber and the liquid viscosity
Notes
lmura et al. (1977) Potential flow
Bharathanef al. (1978)
Richter (1981)
20
21
22
Roll wave
Separated flow
Hanging film
Wallisand Kuo (1976)
19
Separate cylinders
Model
Wallis (1969)
Reference
18
Correlation identification number
Mean film thickness, critical wavelength
Empirical equation
Momentum Interfacial shear, mean film thickness
Momentum Interfacial shear, mean film thickness
hPla=, Bernouilli
Bernouilli
Continuity, momentum
Basic equations =1
2/,v,tz 2&v;’ (1_a)z +F = (1-a)
+!t(~~5(!!$‘2
where:j, = 0.008
L4 Bd V;’ I’;”t j,l3o VB”
J =j, t 14.6(1-a)‘.s7
where:j, = 0.005
where:
2
u,+us={$+)~;’
K, = 1.87
(y;)%+L+(y;)ZiP+l
flooding equation
Table 6. Theoreticalflooding correlations
An interval halving technique was used to obtain an iterative solution for VB*
Bharathan et al. (1978)obtain the limitingcountercurrent flow curve by allowing a to vary. In this report the film thicknessis caiculatedusingeqs(l4)and(16) and Vi may then be related directly to Vf’
m=3 p=3
For comparison with data the constants were:
Notes
1434
K. W. MCQUILLAN~~~
P. B. WHALLEY
Llquld
Water
Gas Tube
Anr
Dnameter
Tub.?
O-032m l-0 m
Length Pressure
1.0
bar
s? *C%
>”
02-
0
02
04
06
08
I
I
12
10
1L
01
0
1
0, 2
I
I
I
0-L
0 6
0.8 “IP
Correlotlon Number Correlotlon Number Correlation
Number
2
WOlihS
11961 I I19621
3
Hewrtt
and
I
W~IIIS
Correlation
Number
L
C1Itt
Correlation
Number
5
Correlation
Number
6
Hewl:, Dukler
et
01
Wall,s
Correloi~on
Number
11
Kamel
et
Correlotron
Number
12
Felnd
I 1960
Correlotnon
Number
13
Engl,sh
119631
Correlotlon
Number
7
Tob,,ewch
et
COrrelDtlOll
Number
8
Pushk,no
and
corre,o+1on
Number
9
Correlot,on
Number
10
Alekseev T,en et
0,
aI
et 01 I1979
i 1972 I
I (7969) 1
Fig. 3. Empirical flooding correlations using Kutateladze IlUXXIberS.
equations and found good agreement. For laminar flow the equation used was that of Nusselt (1916) which may be written 6* = 0.908 ( Re,,)0~333 (14) where 8* is the dimensionless
film thickness
defined by
(15) For turbulent
flow Bankoff
and Lee (1984)
(1963,
Ko,,,,qny
I
IL 15
Grolmes
et
16
Suzuki
ond
Ueda
11977
Correlation
Number
17
Moche,
and
Sokol
11979
al
(1969
t 197‘
)
I 1
Fig. 4. Empirical flooding correlations in Table 5.
4
0
Liquid
Water
Gas Tube
Anr
Dgometer
Tube
0 032m 1 Om
Length Pressure
I
I
1
o-2
0-L
O-6
1 Obar
I
0-e
1 0
J
I
1.‘
1.2
v , p””
( 1968
Sorokan
I
Number
0
“c P COrrdatlOfl
and
1
I1954
01
Number
1.2
t ‘/I
Dlehl
01
et
Number
14
4
I
IL
Correlation 119791
Fig. 2. Empirical flooding correlations using dimensionless superficial velocities.
I
I
1.2
Correlat,on
119651
11977) and Smth
1
l-0
lh
recom-
Correlot~on
Number
18
WaIIns
Correlotson Correlat,on
Number Number
19 20
Wailns ,mura
Correlot,on
Number
21
Bhorothon
Correlotlon
Number
22
Richter
11969
I
and Kuo 119761 et 01 , ,977 I et I1981
qi
119761
/
Fig. 5. Theoretical flooding correlations.
mend the use of an equation
due to Belkin et al. (1959).
8* = 0.135(Re,,)0.583.
(16)
The above two equations are used in the present work to determine the mean liquid film thickness. The transition between the two equations is taken to occur at Re,, = 2064, (where the two equations predict the same liquid film thickness). Both of the above equations were developed for the calculation of the liquid film thickness in the absence of a counter-current gas
Gas-liquid flow in verticalcirculartubes flow, the presence of which would be expected to thicken the film. However, the results of Smith et al. (1984) indicated that the Nusselt (1916) equation gives good prediction of the film thickness even for gas velocities close to the flooding gas velocity. 4. COMPARISON
OF
FLOODING
WITH
CORRELATIONS
DATA
A computer program has been written to enable the predictions of a chosen correlation to be compared with the experimental flooding data bank. The results of the comparison are displayed graphically and in statistical form. Table 7 gives a statistical comparison between the correlations and the data bank. The following statistics are presented. (1)
Number
of points
Some of the correlations were unable to deal with all of the data points, either because the calculated flooding gas velocity was negative or, for correlations of the type f( I’:) +f( I’,*) = C, because the error in the calculation becomes unreasonably large. Table 7 therefore contains information detailing the number of points accepted by each correlation (a maximum of 2762 points). (2) Weighted percentage error The weighted percentage error is given for all the data, and also for the air-water and non air-water data separately. It is defined by the equation s,,
= [il{expiln(g>‘I
where:
- l.O}]
x 100%
(17)
n = number of flooding data points & = weighted mean percentage error (%) /tT = predicted flooding gas dimensionless superficial veiocity V& = experimental flooding gas dimensionless superficial velocity.
The weighting on the quoted error figure ensures that the errors occurring for V& < I’:= are equally important as those for P’& > Vf. (3) i2.m.s. weighted percentage error The r.m.s. weighted percentage error is given for all the data, and is defined by the equation
~wm =
[~,(expiln(~)i
-l-O}]*
X 10% (18)
where: E,,,, = weighted r.m.s. error (%). A tow r.m.s. error indicates a low scatter in the data. (4) Deviation The deviation is defined by the equation
c = [;pgg-
LO>] x 100%
where: < = deviation. Ideally the deviation should be zero.
1435
Figures 6 and 7 present two of the comparisons between correlations and data in a graphical form. A more complete series of comparisons is given by McQuillan and Whalley (1984). The empirical correlations are generally more successful than the theoretical correlations. The correlations which use dimensionless superficial velocities are noticeably less successful than the other empirical correlations, particularly for high liquid velocities and for non air-water systems. The best theoretical correlation is the modified form of the correlation presented by Bharathan et al. (1978). The correlation is successful over a range of liquid viscosities and surface tensions but it over-predicts the flooding gas velocity for large tube diameters. This over-prediction could be due to inaccuracies resulting from the use of the empirical interfacial friction factor equation for large tube diameters. The most successful empirical correlation is that of Alekseev et al. (1972), which works well over a range of tube diameters and liquid surface tensions, but over predicts flooding gas flow rates for high liquid viscosities as illustrated in Fig. 8. This overprediction may be corrected, and the deviation reduced to zero, by modifying Alekseev et al. (1972) correlation to give the new correlation: K,
= 0.286B0°~26Fr-0~22
-0.18 (20)
where: pw = water viscosity (taken as 0.001 Ns/m’). The performance of this modified correlation (identification number 23) is given in Table 7, from the statistics it may be seen that this modified correlation gives the most accurate prediction of the available data. Figure 9 illustrates the effect of introducing the viscosity parameter. 5. CONCLUSIONS
A flooding data bank has been compiled, containing a total of 2762 flooding data points from taken from 24 references. This data has been used to test the performance of 17 empirical flooding correlations and five theoretical flooding correlations. The comparison has been limited to flow in vertical circular tubes, and care should be taken where predictions are required for other geometries. The most successful correlation is a modified form of the empirical correlation presented by Alekseev et al. (1972). The most successful theoretical correlation is a modified form of the correlation presented by Bharathan et al. (1978). Correlations using dimensionless superficial velocities are not very successful, particularly at high liquid flow rates. NOTATION
(19)
1+ E Pw1 (
A a B b BO
c
constant constant constant constant Bond number constant
1 3
4
------
5
6
7
I._-
..-_,
_ _
2604 2734 2762 2634 2601 2653 130 58 62 93 62 90 60 69 39 45 57 40 59 33 39 50 35 61 89 59 72 50 50 56 -0.6 0.20 0.33 -0.12 0.08 -0.52 24 24 61 90 18 34 95 8 46 99 34 92 75 4 14 60 19 77 62 12 8 50 19 94 86 31 29 69 35 30 63 105 108 67 99 21 30 28 33 26 25 37 15 25 28 14 24 29 48 11 16 39 11 71 31 41 55 29 34 45 84 15 9 69 34 113 47 7 8 38 11 66 82 23 11 71 39 97 44 62 62 48 61 47 37 8 7 21 9 47 32 50 63 36 36 27 56 29 31 43 30 61 260 45 16 112 82 131 181 48 16 107 66 IO4 50 22 39 37 17 45 111 44 56 76 44 89 94 61 71 141 50 33 37 26 38 23 24 42 33 87 89 159 78 49
2
Note: figuresin bold indicate“best” performance.
Number of points 2615 GvTms l %I 94 E,, all data ( %) 53 EWm air-water (“i,) 55 E,, non air-water (%) 48 c -0.38 1 hll (%I 22 2 hln (%I 131 3 hvlIl(%I 72 4 e!vnl(%I 59 5 hl (%I 78 6 e,, (%I 62 7 hvlm(%) 29 8 e,m (%I 14 9 eWu(%I 43 10 hvm(%I 29 11 hII ( %I 80 l2 e, (%I 45 l3 &wm (%I 77 14 hn (%I 39 l5 &wm (“i,) 30 I6 E, (%I 29 l7 4vm (73 51 I8 Ewm (%I 139 l9 &wm (%I 150 2o hvm (%I 32 21 &wm (%I 71 22 &wm ( %I 23 23 &wm (%I 25 24 &wm ( %) 38
Data
9
10
Correlation 11 12 13
14
15
16
17
18
19
20
21
22
23
-._
.
-._
--_-..
.-
. .-
-._-
_..
__- ..^.
2762 2762 2762 2762 2619 2762 2762 2762 2758 2762 2734 2762 2759 2738 2762 2762 65 40 122 46 117 84 45 67 78 63 46 44 65 57 82 85 40 26 90 28 47 48 28 49 48 45 35 30 38 38 52 52 36 25 40 43 44 35 83 25 43 32 27 29 33 37 47 32 66 61 47 34 47 29 108 36 57 85 30 33 47 42 63 94 0.9 0.07 0.38 0.40 0.15 -0.07 0.24 -0.13 0.44 -0.15 0.34 0.4 0.4 0.22 0.34 0.00 218 69 114 122 90 63 103 69 143 122 74 123 67 57 129 85 94 54 28 62 34 151 34 43 51 33 44 36 34 9 80 32 61 16 18 9 8 9 25 23 9 14 17 21 10 37 32 12 45 27 13 15 10 12 12 42 9 10 28 31 11 48 15 30 78 19 29 61 15 20 36 22 39 21 20 40 25 16 21 40 18 42 79 43 51 26 42 86 82 33 38 50 97 30 131 41 83 18 47 42 42 50 32 41 18 34 26 18 27 32 47 24 62 8 41 8 17 24 48 37 33 7 12 36 21 35 7 44 54 20 19 20 11 10 15 74 61 94 18 18 22 17 9 16 96 15 48 27 33 18 56 51 56 47 32 14 20 25 69 16 10 9 9 7 35 37 35 8 29 16 39 12 59 6 52 9 34 25 10 6 6 13 9 15 9 5 26 35 11 53 11 15 34 27 35 21 20 30 14 21 21 18 40 42 25 61 23 55 131 58 101 151 22 76 58 12 92 22 30 107 65 49 157 87 37 18 18 16 11 7 10 6 11 38 52 12 31 11 110 18 133 28 74 70 51 67 18 68 47 18 42 17 82 42 63 78 6 39 9 36 22 22 34 34 24 20 40 57 52 75 27 38 70 30 64 3s 34 32 16 34 18 44 43 26 26 27 87 41 62 30 16 17 20 44 24 9 24 16 35 38 18 26 12 33 115 19 47 47 27 33 65 50 33 53 21 29 28 29 49 40 37 20 109 29 41 61 37 50 63 36 31 24 28 41 54 72 184 68 120 249 99 45 106 89 134 167 79 117 106 62 117 68 69 4 32 13 I5 8 29 42 28 16 4 9 45 55 47 42 78 32 51 I7 25 55 45 19 38 45 48 33 146 31 109 42
8
Table 7. Comparison betweencorrelations and data
Gas-liquid
flow in vertical circular tubes
Reference
I 0
1437
: Bharathon
et al
( 19 78 1
I
I
I
I
I
0.2
0.1
0.6
0.8
1.0
1.2
v *‘/2 Ce Fig. 6. Comparison
between correlation
I
Correlation Weighted Number
of Bharathan
I
Reference Number Mean of
Error Points
et al. (1978) and experimental
I : Alekseev
I
flooding
data.
I
et al
(1972
)
: 9
: 28 % : 2762
1clc
j-
jO-2 >0.’ I-
I
0
0.2
I
O-L
I
“Ce Fig. 7. Comparison
between correlation
of Alekseev
1
0.6
O-8
I
I.0
12
* ‘/2
et al. (1972) and experimental
flooding
data.
1438
K. W. MCQUILLAN~~~
P. B. WHALLEY
I
1
Reference Correlation Number Weighted Mean Error Number of Points
1
: Alekseev
et al
(19721
: 9 : 28% : 2762
11: 3-
5-
2 11 50 ,:2O- l-
o. 000
o- 01
0.001
Liquid Fig. 8. Comparison
I.0
0.1 ( Ns/
Viscosity
m2
1
.O
)
between correlation of Alekseev e? al. (1972) and experimental flooding data.
I
1
I
Reference Correlation Number Weighted Mean Error Number of Points
Liquid Fig. 9. Comparison
: : : :
I
Present 23 26% 2762
Viscosity
work
( Ns/m2
I
between modified Alekseev correlation and experimental flooding data.
flow in vertical circulartubes
Gas-liquid
Cl c2 D Fr Fl F2 f 9 K k M m : Nl P
Q
Re T u V We X a Y 6 E P r P c
constant constant tube diameter, m Froude number constant constant friction factor acceleration due to gravity, m/s2 Kutateladze number dimensionless wave number mass flow rate, kg/s constant number of flooding data points inverse viscosity parameter dimensionless group constant volume flow rate per unit wetted perimeter, m2/s Reynolds number dimensionless group velocity, m/s superficial velocity, m/s Weber number dimensionless group void fraction property parameter, m film thickness, m weighted error, o/O dynamic viscosity, Ns/m2 deviation density, kg/m3 surface tension, N/m
Subscripts g e
z 1 P s W
wm wrms
gas
experimental interfacial phase liquid predicted superficial wall, water weighted mean weighted root mean square
Superscripts * denotes non-dimensionalised indicated denotes a modified quantity Dimensionless groups Bond number
D2g(P, -P,) u
Bo
=
Dimensionless diameter
DC
= D[g(pl;p.)]I
Froude number
Fr
=
Q,[
g(pI-/d”]’
quantity
as
1 = J-jot
Kutateladze number
1439 K,
=
vk&b(PI
--&)I
-’
+
Inverse viscosity parameter
1
Reynolds numbers: liquid actual liquid superficial
Rerl
PI ViD =-=4Re, PI
gas actual
Re,
=
pg u, (D - 26) J%
gas superficial Dimensionless superficial velocity
W
= V,P;[gD(P, - Pg)] -*
Weber number
We
=
1
ff D2dp,
- pg) = z
Dimensionless liquid film thickness REFERENCES
AlekseevV. P., PoberezkinA. E. and Gerasimov P. V., 1972,
Determination of flooding rates in regular packings. Heat Transfer Soviet Rex 4 159-l 63. Augello L. and Martini R., 1982, Flooding experiments in tubular geometry with steam-water up to 70 bar. European Two-phase Flow Group Meeting, Paris, France, June 1982, paper A23. Bankoff S. G. and Lee S. C., 1984, A critical review of the flooding literature, in Multiphase Science and Technology, Vol. 2. Hemisphere, New York. Belkin H. H., MacLeod A. A., Monrad C. C. and Rothfus R. R., 1959, Turbulent liquid flow down vertical walls. A.I.Ch.E. J. 5 245-248. Bharathan D., Wallis G. B. and Richter H. J., 1978, Air-water countercurrent annular flow in vertical tubes. EPRI Report No. EPRI NP-786. Cetinbudalkar A. G. and Jameson G. J., 1969, The mechanism of flooding in vertical countercurrent two-phase flow. Chrm. Engng Sci. 24 1669-1680. Clift R., Pritchard C. L. and Nedderman R. M., 1965, The effect of viscosity on the flooding conditions in wetted wall columns. Chem. Engng Sri. 21 87-95. Diehl J. E. and Koppany C. R., 1969, Flooding velocity correlation for gas-liquid counterflow in vertical tubes. Chem. Engng Prog. Symp. Series 65 77-83. Dukler A. E. and Smith L., 1979, Two phase interactions in counter-current flow: studies of the flooding mechansim. Nureg Report No. NUREG/CRa17. English K. G., Jones W. T., Spillers, R. C. and Orr, V., 1963, Flooding in a vertical updraft partial condenser. Chem. Engng Pray. 59 51-54. Feind R., 1960, Falling liquid films with countercurrent air flow in vertical tubes. VDI Forschungsheft, Vol. 481. Grolmes M. A., Lambert G. A. and Fauske H. K., 1974, Flooding in vertical tubes. Inst. Chem. Engrs Symp. Multiphase Flow Sysfems, University of Strathclyde, Glasgow. Also published as Inst. Chem. Engrs. Symposium Series No. 38.
1440
K. W. MCQUILLAN and P. B. WHALLEY
Hewitt G. F., 1977, Influence of end conditions, tube inclination and physical properties on flooding in gas liquid flows, quoted by Bankoff and Lee (1984). Hewitt G. F. and Wallis G. B., 1963, Flooding and associated phenomena in falling film flow in a vertical tube. A.S.M.E. Paper presented at Multiphase Flow Symp., Philadelphia, pp. 62-74. Hewitt G. F.. Lacev P. M. C. and Nicholls B.. 1965. Transitions in film~flow in a vertical tube. AERE-R 4614: Imura H., Kusuda H. and Funatsu S., 1977, Flooding velocity in a counter-current annular two-phase flow. Chek En& Sci. 32 7987. Kalb C. E. and Smith J. K., 1981. An interuolative flooding model based on limiting flow regimes for countercurrent gas/liquid flow. Chem. Engng J. 22 113-l 23. Kamei Sy. Oishi J. and Okask T.. 1954. Floodine in a wetted y wall tower. Chem. Engng 18 k-388. Machei K. and Sokol W.. 1979, Determination of the parameters which affect the flooding of a tube. Int. Chem. Engng 19 696700. Marinelli V., Oliveti G. and Sabato A., 1979, Calculations of countercurrent flows of liquid and gas in the flooding regime. European Two-phase FIow Group Meeting, ISPRA, June 1979. McQuillan K. W. and Whalley P. B., 1984, A comparison between flooding correlations and experimental flooding data. AERE-R 11267. Nicklin D. J. and Davidson J. F., 1962, The onset of instability in two-phase slug flow. Proc. I. Mech. Symp. Two-phase Flow, London, Feb. 1962, paper 7. Nusselt W., 1916, Surface condensation of water vapour. VDI(Z), Vol. 60, 541-546, Vol. 60, 569-575. Pushkina 0. L. and Sorokin Y. L., 1969, Breakdown of liquid film motion in vertical tubes. Heat Transfer Soviet Res. 1 564.4. Richter H. J., 1977, Flooding experiments, large tubes. Paper presented at NRC 5th Water Reactor Safety Res. Information Meeting, Maryland, U.S.A.
Richter H. J., 1981, Flooding in tubes and annuli. Inr. J. Multiphase Flow 7 647458. Shearer C. 3. and Davidson J. F., 1965, The investigation of a standing wave due to gas blowinp. unwards over a liauid film; its Relation to flooding in wetted wall columns. J. Fkd Mech. 22 321-336. Shires G. L. and Pickering A. R., 1965, The flooding phenomenon in counter-current two-phase flow. Symp. TLvo-phase Flow, Exeter. U.K.. naner B5. Smith L., Chopra A. and Dukler-A.- E., 1984, Flooding and upwards film flow in tubes-I. Experimental studies. Int. J. Multiphase Flow 10 585-597. Suzuki S. and Ueda T., 1977, Behaviour of liquid films and flooding in countercurrent two-phase flow-l. Flow in circular tubes. Inr. J. Multiphase Flow 3 517-532. Tien C. L., Chung K. S. and Liu C. P., 1979, Flooding in twophase countercurrent flows. EPRI Report No. EPRI NP1283. Tobilevich N. Y., Sagan I. I. and Porzhezihskii Y. G., 1968, The downward motion of a liquid film in vertical tubes in an air-vapour countertlow. J. Engng Phys. 15 855861. Wallis G. B., 1961, Flooding velocities for air and water in vertical tubes. AEEW-R 123. Wallis G. B., 1962, The influence of liquid viscosity on flooding in vertical tubes. General Electric Company Report No. 62GLl32. Wallis G. B., 1969, One-dimensional Two-phase Flow. McGraw-Hill, New York. Wallis G. B. and Kuo J. T., 1976, The bchaviour of gas-liquid interfaces in vertical tubes. Int. J. Multiphase Flow 2 521-536. Wallis G. B., De Sieyes D. C., Rosselli R. J. and Lacombe J., 1980, Counter-current annular flow regimes for steam and subcooled water in a vertical tube. EPRI Report No. EPRI NP-1336. Whalley P. B. and McQuillan K. W., 1983, Flooding in twophase flow: the effect of tube length and artificial wave injection. AERE-R 10883. Physiochem. Hydrodyn. (1985).