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Data on the upwards annular flow of air-water mixtures
Chemical Engineering Science, 1965, Vol. 28, pp. 71-88. Pergamon Press Ltd., Oxford. Printed in Oreat Britain.
Data on the upwards annular flow of air-water mixtures L. E. GILL, G. F. HEWITTand P. M. C. LACEY* Chemical Engineering Division, U.K.A.E.A. Research Group, Atomic Energy Research Establishment, Harwell (Receiwd 26 September 1964) Ah&act-Data are presented for fihn thickness, film flowrate and pressure gradient for upwards co-current air-water ammlar two-phase flow in a 1%in. bore perspex tube using two types of injector, a multijet type and an annular slot. Film flowrates, flhn thicknesses and pressure gradients were all observed to be lower with the multijet injector than with the ammlar slot. The results for pressure drop were compared with the Lockhart and Martinelli correlations and with correlations based on homogeneous flow; the former was found to predict the values closest. The Lockhart and Martinelli hold-up correlation generally overpredicted the flhn thickness-this is due to the presence of entrainment, Very different patterns of entrainment were observed for the two injectors. For higher liquid rates the entrainment results were found to agree with the correlating line obtained previously for vertical flow using the correlation method of WICKS and DUKLER,provided the appropriate “critical Weber numbers” were used for the two types of injector. As in earlier work, at lower liquid rates the entrainment is less than that predicted by the correlating line extrapolated from high liquid rates, and is a function of the gas flowrates. It transpired that the point where the entrainment curve joins the line of the correlation occurs at values of yi+ of 16-18 and may be related to the formation of large roll waves on the film surface. The inter-relation of film thickness, pressure drop and film flow rate by velocity profile theories has been studied and is discussed; systematic deviations from theory are found.
1. INTRODUCTION
this present work are found to agree well with the data obtained later [4] for the porous sinter, though this conclusion would not necessarily hold for very high water flow rates nor for positions close to the injector. The flow rates chosen for the studies here are such that the flow is always in the annular regime. At the lowest air flow rate, 100 lb/hr, the boundary between annular and “chum” or “semi-anmilar” flow is approached [5].
STUDIESof air-water annular flow in 14 in. bore vertical tubes have been carried out at Harwell for a number of years. In the earlier work [I, 21 the water was injected through a number of jets at the entrance and in the more recent work [3,4, 51 the water was introduced into the walls through a porous section of wall. In the latter case, therefore, the water at the entrance is entirely on the tube wall whereas with the jet injector it is largely in the form of suspended droplets in the gas phase. The porous sinter injector has the advantage of providing a well defmed condition at the entrance. The annular slot injector-in which the liquid is introduced around a slanting periferal gap in the wall-was used in the intermediate stage of the Harwell work [6, 71 and was a first attempt at achieving this aim. The present paper augments the data previously published and provides a link between the earlier and later work. The experiments were carried out in 1960 and 1961 and both multijet and annular slot injectors were used. The annular slot data in
2. EXPERIMENTAL 2.1
Techniques of measurement
The technique of measurement of the dependent variables (film thickness, pressure drop and film flow rate) have been described in detail elsewhere [ 1,2,7] but the principal features will be briefly restated. 2.1.1 Film thickness. Film thickness was measured by the electrical conductivity techniques described elsewhere [2, 41. The probes used were 4 in. diameter stainless steel rods let into the tube wall with their ends flush with the wall surface, each pair being mounted with 3 in. between centres in
* Present address: Department of Chemical Engineering, University of Exe&, Exeter, Devon.
71
L. E. GILL, G. F. HEWITC and P. M. C. LACEY
SLIGHTLY DIAMETER
SMALLER THAN
INCHES
“1
0
1 DIRECTION
OF FLOW
FIG. 1. Film separator.
the line of flow. The generalised calibration [7] was used and the conductivity of the circulating water, to which NaCl had been added, was measured at frequent intervals. The conductivity was corrected for temperature [8]. 2.1.2 Filmflow rate. The fdm flow rate was measured by separating the Ghn from the droplet-laden gas core, as shown in Fig. 1, and allowing it to spill over into a compartment whence it was taken to a cyclone separator. The outlet to atmosphere from the cyclone was controlled by a valve and some air was bled slowly from the flow tube via the cyclone. This air leak was small compared to the flow in the tube and was controlled until the tube wall just above the separator became dry. The water from the cyclone was collected and its rate of flow estimated from the time taken to fill a calibrated tube; at high flow rates it was weighed. Though crude, the method worked quite well, 72
except at high liquid rates, when special care was needed. 2.1.3 Pressure drop. The water-purge technique [7] was applied. The manometer circuit and other details are given in reference [9]. 2.2 Air and water supplies Air from the site mains was filtered and passed through reducers to a surge tank and hence through further reducers and an orifice to the flow tube. The orifice was operated at constant inlet pressure by throttling downstream. A series of fully corrected orifice tables produced on the Harwell Mercury computer were used for obtaining the orifice differential appropriate to any required flow rate. (See reference [lo] for details of computer programrne). Water was supplied from a thermostatically controlled tank via a centrifugal pump. On leaving the flow tube the mixture was separated
Data on the upwards annular flow of air-water mixtures using a cyclone separator, the air from the cyclone being discharged into the atmosphere and the water returned to the sump tank. 2.3 The Jlow tube The layout of the flow tube is given in Fig. 2. Only two pressure tapping points, 6 ft apart, were used as it was assumed that the pressure gradient was constant [9]. Four sets of conductance probes were inserted in the tube. The Glm removal device was placed above the top pressure tapping and a telescopic joint was used at the outlet to assist changing the injector etc. The total length of the tube from air inlet to two-phase outlet was about 12 ft. 2.4 The water injectors Since the method of water injection was considered to have a very large effect on the parameters 8
--_=7\
TO ClCLONE
RAOIAL JETS
-
TELESCOPIC FLANGE JOINT
FILM REMOVAL DEVICE --
FILU TNICKNESS PROBES
”
TOTAL “EIGHT IT- 4’
-
FIG. 3. Multijet injector. 36”
PRESSURE TAPPING -t
I
WATER
INJECTOR -
FIG.2. Flow tube layout.
of flow two methods were chosen which would give results as different as possible. These are described below. 2.4.1 The multijet injector. The multijet injector (see Fig. 3) was used as in the original air-water at Harwell carried out by BENNETTet aZ.[l, 21. The water enters the tube through eight radially placed jets, which are placed at the entrance to the tube proper. The resultant mixing, however, is not well de&red and this injector has only been used in the present studies because it allowed a direct comparison with the earlier work. 73
L. E. GILL, G. F. HEWITTand P. M. C. LACEY
FIG. 4. Details of annular slot injector.
2.4.2 The annular slot injector. A much better defined inlet condition can be achieved by using the annular slot injector shown in Fig. 4, which is self-explanatory. Since the liquid is introduced more gradually into the flow tube the entrainment at the inlet will be lower than for the multijet injector. The injector has an annular calming length before the wafer enters the tube, which ensures that there is no extra dynamic head at any point around the circumference of the slot, and the slot itself is convergent. The convergent slot was found to give a uniform distribution at much lower flow rates than was a parallel slot. (Even with the annular slot injector, however, there is some uncertainty as to whether the liquid will bend over and form a iilm at the inlet or whether it wti. penetrate the gas stream and cause some adventitious entrainment at the inlet). 74
2.5 Experimental procedure The object was to provide data for both injectors at a fixed distance (7.5 ft) from the injection point. It is recognised that the dependent variables measured-namely, film flow rate, fYm thickness and pressure gradient-are changing continuously with length. The changes in film flow rate are considerable [3] but those in flm thickness and pressure gradient are less severe except near the injector [2, 3, 91. At the beginning of the experiment the air and water rates were set as near as possible to the required conditions and when flow had become steady the exact flow rates were recorded, and the pressure drop, film thickness and G.hn flow rate were then measured, in that order. The film thickness was measured at the top pair of conductance probes and the value obtained was assumed to apply [9] at the take-off point which was only about 1 ft further on.
3. b!XJLTS The basic data obtained are tabulated in reference [9]. 3.1 Pressure gradient Measured pressure gradient is plotted against liquid rate with air rate as a parameter in Fig. 5
Data on the upwards annular flow of air-water mixtures
I
1
500
I
moo
1500
2500
LIQUID RATE- IbJbr.
FIG. 5.
Pressure gradient measurements -
(multijet injector) and Fig. 6 (annular slot injector). As would be expected, the gradient increases with both air and liquid rate. It will be seen on comparing the figures that the annular slot liquid 70.
multijet injector.
entrance gives, in general, higher pressure gradients than the multijet type. A more direct comparison is presented in Fig. 7 where the ratio of pressure gradients for the annular slot and multijet injectors
I
I
60-
Air
I 500
I 1000
I
LIPUID
FIG. 6.
I
I500 RATE -
2000 lb. / hr.
Pressure gradient measurements -
75
ammlar slot injector.
Rate
100
l
200
0
SW
l
400
x
500
A
600
l
700
v
800
1[
I
2500
3000
L. E. GILL, G. F. HEWITT and P. M. C. 1.6,
I Air
LACEY
I
I
Rate
lb./hr.
I.5
1,s -
600
1.2:
.
700
.
600
0
.
+
M-;rx
: *: 00
0,9-
4
f
.#. I.0
E
.
T”
+ .
6
0
l
f
.
a .
04 -
0.7
I 500
0
1 1500
I 1000
2000
llOlJlO RATE - lb./ hr. FIG:
7.
Comparison
of pressure gradients for annular slot and multijet injector.
Air
Rate
Lb./hr 100 zoo 300 400
/
1000
so0
LlOUlO
FIG. 8.
Film
thickness
2L30
RATE-lb./hr
data -
76
multijet
injector.
0 + I
500 600 700
A . .
1100
*
I
I500
l
2500
Data on the upwards annular flow of air-water mixtures Air Ralr Lblhr: 100 200
l
0
300 400
+ x
100
.
000 700
. .
/
I
500
1000
zoo0
I500
2500
10
LIPUID RATE- Iblhr.
FIG. 9. Film thickness data -annular
is plotted against water rate with air rate as a parameter. It is seen that the pressure gradient is nearly always higher for the annular slot injector. The ratios pass through a minimum at 100-300 lb/hr of water. The maximum difference recorded between the two types of injectors is about 40 per cent. The effect of air rate at constant liquid rate on the ratio of pressure drops appear to be somewhat variable; in general the lowest air rate (100 lb/hr) gives lowest values of the ratio and as the air rate is increased the ratio rises rapidly (presumably on moving away from the transition to semi-annular flow) and then falls slowly again as air rate increased further. It should be emphasised, in making this comparison, that the experimental errors in both measurements are combined. 3.2 Film thickness The results for film thickness are presented in Figs. 8 and 9 respectively. As would be expected,
slot injector.
film thickness increases with increasing liquid rate and decreasing gas rate. The characteristic difference between the multijet and annular slot injectors are brought out clearly by comparing the two sets of curves. In the case of the multijet type, at high gas flow rates the film thickness tends to level out with increasing liquid rate whereas with the annular slot the thickness continues to increase markedly. There is considerably more scatter in the measurements of film thickness than in those of pressure drop. The ratios of film thickness for the annular slot to that for the multijet injector are plotted in Fig. 10. Here again, the ratio is nearest to unity when the liquid rate is in the region 100-300 lb/hr. The effects of liquid and gas rate are approximately in the same sense as those for pressure drop. 3.3 Liquid$lm
flow rate
In reference 2 it was found convenient to plot the results for film flow rate in the form film flow 77
L. E. GILL, G. F. HEWITTand P. M. C. LACEY
Ib./hr 100 l 200 0 JO0 + 400 I so0 A Woo l 700 . 000 Im
A -
Id-
I+-
. . I .
7 I.5 -
&
'I I.2 -
l
. I +
.
l
1. T I.1 -0 .+
x
. t
!m:
t
l
.
f
x
lo- o O
I
o
+
.
0.9-
t 500
0.7 0
I IO00 LlPUlO
FIG.
RATE-
I 1500
2000
lL/hr
10. Comparison of film thickness data for annular slot and multijet injector.
rate versus total liquid flow rate and the same has been adopted here. This method obscures some of the finer details in the low liquid flow rate region but the full results are available in reference [9]. The film flow rate/total liquid rate plots are given in Figs. 11 and 12. Apart from the data at 100 lb/hr air flow rate, method
500
loo0
1500 TOTAL
FIG. 11.
the lines of film flow rate versus total liquid rate drop progressively further away from the equality line as the air rate is increased. For the multijet injector very similar results are obtained to those reported. previously [2]-the film flow rate tends to level off and at high total liquid rate becomes relatively insensitive to further increases in hquid
Film flow
LIQUID
FLOW RATE -
2000
lb/hr.
rate results using mukijet injector.
78
2500
3000
Data on the upwards annular flow of air-water mixtures
TOTAL LIQUID FLOW RATE -Ib/hr.
FIG.12. Film flow rate results using annular slot injector.
discussed in reference [7]. The normal calculation of accelerational pressure drop does not take into account the continuous change which occurs in the liquid content of the gas stream. That this term can be large (up to one third of the total pressure gradient) has been demonstrated by DUKLER and MAGIROS1141. For the present results, however, since we have no information on the change of entrainment with length, it is impossible to make an accurate estimate of this pressure drop. Its effect would probably be largest at the highest 4. INTERRELATTON OF INDIVIDUAL DEPENDENT flow rates and would vary according to the type of VARIABLESWITH THE CORRESPONDING INDEPENDENT injector. This difficulty should be borne in mind VARIABLES when considering the following comparisons of 4.1 Correlations of pressure drop the pressure drop data with the empirical correlaThe two best known approaches to pressure drop tions: it should also be remembered, however, that correlation are to treat the flow as homogeneous this effect has been ignored in the original work on [l 1, 121, or to relate the ratio of the two-phase to which the correlations were based and indeed in a single phase pressure gradient to the ratio of almost all other work on two-phase pressure drop. the single phase gradients, this latter approach 4.1.1 Homogeneous correlations. As was discussed being that of LOCKHARTand MARTINESLLI [13]. in reference [7] there is some difference of opinion The main difficulty in comparing the pressure [l 1, 121 as to which viscosity should be used when drop data with the empirical correlations is in calculating the frictional pressure drop for the estimating the accelerational term. This feature is homogeneous flow correlations. Either the liquid With the annular slot injector the pattern is rather different and somewhat irregular trends are sometimes observed, presumably due to the separation effect mentioned above. For both types of injector, at a constant liquid rate, the film flow rate was lower at 100 Ib/hr of air than it was at 200 lb/hr, i.e. a reversal of the general trend of the data. This is presumably a result of the approach to the semi-annular flow regime [5]. rate.
79
L. E. GILL, G. F. HEWITTand P. M. C. LACEY
viscosity [l l] or a reciprocal mean viscosity [12] can be used and these two approaches give different results. Using the mean viscosity the predicted pressure gradient was always lower than the experimental one; if, on the other hand, the liquid viscosity was used, then the predictions were usually higher than the experimental figures. There was a slight shift in favour of the liquid viscosity model in going from the multijet to the annular slot injector. There was very considerable scatter at the lower values of pressure gradient (up to 250 per cent) and, on the whole, the homogeneous model cannot be regarded as very useful in correlating the present data. 41.2 The Lockhart-Martinelli model. The experimental total pressure gradients were compared with those calculated from the Lockhart-Martinelli model and the result for the multijet injector are shown in Fig. 13. A much closer prediction is obtained using this correlation, particularly at low pressure gradients. The correlation was somewhat closer for the multijet injector but for both this and the annular slot injector the results at high
Air Rate lb. /hr.
FIG. 13.
Comparison
4.2 Hold-up correlation LOCKHART and MARTINELLI [13] have suggested that hold-up is correlated by the same parameter X as is used in their correlation of pressure drop. X is defined by:
X =
. .
300 400
0 D
. .
100 boo 700
0 0 8
l + *
800
*
*
GRADIENT
n
(1)
Gas turbulent Liquad turbulent
0 LJ
I
W/d& J W/d&
where (dP/dL), and (dP/dL), are the pressure gradients for the liquid and gas phases respectively, when flowing alone. Providing that no entrainment is present then it can be shown that X should correlate the hold-up [16]. When entrainment does occur then the correlation should fail and the hold-up will be less than that predicted. That this is in fact the case for the present results is shown in Fig. 14 for the multijet injector; as before the results from the annular slot are similar [9]. (The hold-up was calculated from the measured film
100 200
,.ov I.0 PRESSURE
Gas turbulent Lrquid IIXOUI
pressure gradient showed under-prediction of the pressure gradient. This latter effect has also been observed by COLLIER [15] for steam-water flow.
I
PREDICTED
I11111 FROM
I
IO
Lockhart
I9!!111
100 IHartinelli
CORRELATION
of calculated and experimental pressure gradients: multijet injector.
80
-
lb./h?
ft.
Lockhart/Martinelli
correlation -
Data on the upwards annular flow of air-water mixtures 13 was assumed (the multijet had been used) and the line of equation (3) is quite close to that obtained by WICKS and DUKLER for horizontal flow. Two main points of interest arise from comparing the present data with this correlation: (i) Do the data for the multijet injector agree 4.3 The Wicks and Dukler correlation for entrainwith the data which were obtained previously ment with the same injector (reference [2]) and WICKS and DUKLER [17] have shown that for which were correlated by equation (3) ? horizontal air-water flow, the entrainment could (ii) Does the change of We, from 13 to 22 be correlated using the LOCKHARTand MARTINELLI successfully bring the results for the annular parameter X and the dimensional correlating group slot into line with the results for the multiR, where: jet injector ? The results are plotted in Figs. 15 and 16. It will (2) be seen that for both injectors (i.e. after introducing In equation (2), E is the entrained phase flow the appropriate value of We=) the results agree rate (lb/hr), qL and qo are the volumetric rates of remarkably well in the region X > 0.08 with the flow of the liquid and gas respectively and the line given by COLLIERand HE.SVITT[2]. For any “critical” Weber number, We,, was taken, on the given gas rate, the points corresponding to high basis of the work of HINZE [ 181to be 13 for “sudden liquid rates (high values of R) fall upon the Colliershock”, as in a tee type of water entry, and 22 for Hewitt correlating line; at lower water rates the gradual acceleration, as for an annular slot injector. points break away and lie on a line of smaller In presenting and analysing BENNET-PSentrainment slope. This point of changeover appears to correresults, COLLIERand HEWITT [2] showed that for spond to an approximately constant &n flow rate X > 0.08 the data were correlated by a single line: ( - 100 lb/hr) which is of the same order as that X = 0.069 R”‘3g (3) at which roll waves become well established [5]. The value of v: (the dimensionless iilm thickness) For these results a critical Weber number of
thickness, and the hold-up in the gas core calculated by assuming a homogeneous mixture of the entrainment with the gas. The gas core term of the entrainment was negligible compared with the Glm thickness term. The validity of this assumption was co&rned in later work).
‘OF------
FIG. 14.
Correlation
of holdup in terms of Lockhart multijet injector.
81
and Martinelli parameter
X -
L. E. GILL,G. F. H~AVITT and P. M. C. LACSY l.O_
I
I I,,,!,,
I
1 I11/11,
WICKS AND DUKLER METHOD
1 Il/,!W
,
FOR CORRELATION OF ENTRAINMENT-MULTIJET
I 1/,111, INJECTOR.
’
’ “““’
FIGURE 15
RG. 15..
WICKS
and
DUKLZR
method for correlation of entrainment - multijet injector. in its use in other systems; first of all, however, other liquids should be used to enable a dimensionless rather than a dimensional correlating group to be derived; the latter will probably only apply to air-water systems.
corresponding to the transition is 16-18 and this suggests that the changeover may be associated with the breakdown of the outer layers of the film into turbulent eddies. The complete entrainment curve can then be defined: y: > 16-18
X = 0.069 R”+’
y: < 16-18
X = kR0’16
(3)
5. INTERRELATION OF DEPENDENTVARIABLES
(3a)
In the work described here three dependent variables (viz. pressure drop, fihn thickness and liquid film flow rate) were measured for a number of values of three main independent variables (viz. air rate, water rate and liquid injector). Two types of dependent variable relationships can be used : (0 Relationships which allow the calculation of one of the dependent variables from the measured values of the other two. These relationships are theoretical and direct and involve no arbitrary correlation of the experimental results. They do not need to invoke the independent flow variables. (ii) Relationships which allow the calculation
Here, k is a function of the gas velocity and depends on the position at which the value of JJ~ of 16-18 occurs on the line of equation (3). Equation (3a) is derived from the data of reference [2] where much more information was obtained at the lower liquid flow rates. From the data of reference 2, k varies in the range 0.03408 for the air rates 150-700 lb/hr. Again, it will be noted that the results for 100 lb/hr of air give higher entrainment in the X > 0.08 region than would be suggested by the correlation, possibly resulting from the approach to churn flow. The success of the correlation in predicting both the annular slot and multijet entrainment may give some confidence 82
Data on the upwards annular flow of air-water mixtures I.0
. ,
, , , / , , ,,
I
I v11111,
I I1l111,
! I III!,
4 I I/18’1,
,I
no. 16. WICKSand DUKLER method for correlation of entrainment - annular slot injector.
of one of the dependent variables from a knowledge of only one of the others. These relationships usually also involve the independent variables. Relationships of the first kind for upward flow are typitied by those Of CALvERTand WILLIAMS[19], ANDERSONand MANTZOURANIS [20], and DUKLER [21] as modified by HEWITT [22]. In the second class of relationships come the C.I.S.E.* film thickness correlation [23], the hold-up pressure drop correlation of ARMAND [24], and the film thickness/roughness relationships proposed by GILL, HEWITT and LACEY[4]. Treatments which are somewhat hybrid between the two classes are those of ROBERTSand HARTLEY [25] and the pressure drop correlation of ANDERSON and MANTZOURANIS [20]. These relationships can involve all three dependent variables and are still empirical. Both classes of relationships were used [9] in * Centro Informtioni Studi Esperienze,Milan, Italy. 83
the analysis of the present data but we shall confine our discussion to relationships of the first type. 5.1 Interrelation of film thickness, film flow rate and pressure drop
The most complete theoretical treatment of annular flow is that of DUKLER 1211 and this has been modified for upwards flow by HEWITT [22] This theoretical treatment adopts the dimensionless velocity protie approach used frequently in the solution of single phase flow problems. Proper allowance is made for the variation of shear stress across the liquid film and it is in this respect that the analysis differs most from the similar treatment of ANDERSONand MANTZOURANIS [20]. (There are slight differences, too, in the exact form of the dimensionless velocity profile used.) The Dukler treatment involves the solution of a non-linear differential equation; this can only be done numerically and a computer programme has been written (see reference [6]) which allows the film flow rate to be calculated from the pressure drop and
L. E. GILL, G. F. HEWITT and P. M. C. LACEY
FIG. 17. Comparison of film flow rates with values calculated from modtied DUKLER analysis multijet injector.
film thickness-all dependent variables. Film flow rates calculated by the computer from the present data for the multijet injector are compared with the actual flow rates in Fig. 17; (again, the annular slot injector gives somewhat similar results). The pressure gradients used in these calculations were corrected for the accelerational pressure drop. The flow rates are compared in terms of the dimensionless film flow rate W+ where:
wLF is the liquid film flow rate (lb/hr), r. the radius of the tube (ft) and ,u~ the liquid viscosity (lb/ft hr). This method of plotting is equivalent to comparmg wLr values since r. and ,uL are tied for the present data, except for some slight variation in pL due to temperature fluctuation. The film flow rate is predicted reasonably well, the scatter being worst at the lowest flow rates. On plotting the ratio of actual to predicted film flow rate against the film thickness (as in Fig. 17
of reference [2]) the definite trends observed previously and reported in reference 2 were not obtained.7 The main difference between the present data and those of reference 2 is the greatly increased range of water flow rate; the results at low liquid rates do follow the trend originally observed. A more sign&ant general trend in the results emerges, however, when film thickness is calculated from pressure drop and film flow rate. In order to do this calculation it is necessary to use an iterative procedure and this procedure is much easier with the ANDERSON and MANTZOURANIS analysis than with DUKLER’S. A computer programme had been developed previously which, by means of a multistage iterative procedure for the ANDERSON.and MANTZOURANISanalysis, calculates each one of the dependent variables from the other two. The ANDERSON and ~~ANTZOURANIS analysis used here was the uncorrected version t In reference 2 a corrected version of the ANDERSON and MANTZOURANIS analysis was used-that this differsvery little from the DUKLER analysis which is used here is demonstrated by Fig. 11 of reference 6. 84
Data on the upwards annular flow of air-water mixtures
EXPERIMENTAL
FIG. 18.
Comparison
Comparison
thou
of experimental and calculated film thickness. Uncorrected and MANTZOIJRANBtheory - multijet injector.
EXPERIMENTAL
FIG. 19.
FILM THICKNESS-
FILM
THICKNESS-thou.
of experimental and calculated film thickness. Uncorrected and MANT~OURANIStheory - annular slot injector.
85
ANDERSON
ANDEISON
L. E. GILL,G. F. HE~rrr and P. M. C. LACEY and its efficacy was tested by comparing w+ calculated by this method with w+ calculated from the Dukler method. With exception of the results at the lowest air rate the w’ values from the Dukler theory were only slightly higher than those from the Anderson and Mantzouranis analysis. In Figs. 18 and 19 the film thickness calculated from the ANDERSONand MANTZOURAMS analysis is compared with the measured value. The agreement ( f 30 per cent) is quite close but the differences between experimental and calculated film thickness cannot be ascribed to experimental scatter as there is a definite trend. This trend gives over-prediction of film thickness at low film thickness and underprediction at high film thickness. The latter effect may be due to the failure of the conductance probes to allow for the large waves present on thick films (see reference [7] for discussion of limitations of probes). Figure 20 shows a comparison of experimental and calculated pressure gradients for the multijet injector data; (again, a similar plot was obtained for the annular slot data but has not been reproduced). Although most of the data lie in the band
EXPERIMENTAL
f 30 per cent there is more scatter in the pressure drop calculation since any difference between calculated and actual film thickness is roughly squared in comparing pressure gradients. 6. CONCLUSIONS The effect of liquid injector design is very significant. The jet type of injector gives higher entrainment, lower pressure gradient and lower film thickness than the annular slot type. These differences are obscured when the results are analysed in terms solely of the dependent variables. In correlating pressure drop it was found that the LOCKHART and MARTINELLIcorrelation predicted the pressure gradient better than did the homogeneous models. The LOCKHART and MARTINELLI hold-up correlation, on the other hand, did not fit the data too well, owing to the entrainment; this was expected from previous work. The method of WICKS and DUKLER [14] correlated the entrainment data very well in the high entrainment region and good agreement was obtained with earlier A.E.R.E. data [2] for vertical flow. The use
NON-ACCELERATIONAL
PRESSURE
GRADIENT-Ib./fl*tt
FIG. 20. Comparison of calculated and actual pressure gradients. Uncorrected ANDERSON and MANTZOURANIS theory - multijet injector.
86
Data on the upwards annular flow of air-water mixtures
of different critical Weber numbers (as suggested by WICKS and DUKLER)brought the results for the two types of injector into line. At low liquid rates the entrainment is lower than that predicted by extrapolation of the COLLIER and HEWITTline. On examination of the results and also those reported earlier [2] it transpired that the entrainment is predicted by the COLLIERand HESVI~Tline for y: values greater than 16-18 and this provides a useful criterion for the change-over point. A correlating method for low entrainment is suggested on the basis of previous data [2]. The use of Glm velocity profile theories interrelating Glm thickness, film flow rate and pressure gradient has provided some interesting results. The data fit these theories remarkably well in view of the known wavy nature of the liquid am; systematic trends however are apparent. In particular, as the film thickness is increased it is first under-predicted and later over-predicted. The work described provided a useful basis for much further experimentation at Harwell; it was felt that only by studying the system in finer detail could a real advance in understanding be made. In general, therefore, this further work has concentrated on measuring rather more detailed
parameters such as wave velocities, velocity and entrainment distributions.
gas core
Acknowledgements-The authors wish to acknowledge the contributions made to this work by Messrs. P. C. LQVJK+ROVE and R. J. KINO who assisted in development of many of the techniques and by Miss D. PHIXLPSand her group in preparing tapes for the computer.
NOTATION mass rate of flow of entrained liquid (lb/hr) pressure gradient for flow of gas alone in the (dP,dL): channel (lb force/ft%)
(dP/dL)r. pressure gradient for flow of liquid alone in the channel (lb force/ftaft)
qc volumetric gas flow rate (ft3/hr) qL
R ;: w+ WLP We,
X Y{ Yi+ W PL To
volumetric liquid flow rate (f@/hr) entrainment parameter defined by equation (2) radius of flow tube (ft) “friction velocity” (ft/hr) = &T~/PL) dimensionless film flow rate defined by_ equa_ tion (4) liquid flow rate in the film (lb/hr) critical Weber number (dimensionless) Martinelli parameter defined by equation (2) (dimensionless) film thickness (ft) dimensionless tllm thickness = (u*PLY~/~L) viscosity of liquid (lb/ft hr) density of liquid (lb/f@ wall shear stress (pdl/fts)
THORNTONJ. D. and BENNE~ J. A. R., Trans. Znstn. Chem. Engrs., 196139 101
COUIW J. G. and Hswrrr, G. F., Trans. Znstn. Chem. Engrs. 1961 39 127. GILL L. E., IIawrrr G. F., HITCHON J. W. and LACEYP. M. C., Chem. Engng. Sci. 1963 18 525. GILL L. E., Hmwrrr G. F. and LACEYP. M. C., Chem. Engng. Sci. 1964 19 665. HALL-TAYLOR N., H~wrrr G. F. and LACEYP. M. C., Chem. Engng. Sci. 1963 18 537. Hawrrr G. F., KING I. and LOVEGROVEP. C., Bit. Chem. Engng. 1963 8 311. HEWITT G. F., KING R. D. and LOVEGROVEP. C., Chem. Proc. Engng. 1964 45 191. Hswtrr G. F., Tables of the resistivity of aqueous sodium chloride solutions. 1961 AERE R-3497. (H.M. Stat. Off., London). GILL L. E. and Hxwrrr G. F., Further data on the upwards annular flow of air-water mixtures. AERE R-3935, 1962 (A.E.R.E., Harwell, Berks.) Hswn-r G. F., Some computer programmes. AERE M-922, 1962. (A.E.R.E., Harwell, Berks.) OWENSW. L., Two-phase pressure gradient. Paper 41. International Developments in Heat Transfer (Vol. II) 1961. (Inst. Mech. Engrs., -London). _ M&DAMS W. H.. WOOD W. K. and H_EROMON L. C. Jr.. Trans. Amer. Sot. Mech. Enars., _ . 1942 64 193. LOCKHARTR. W. and MARTINELLIR. C., Chem. Engng. Prog. 1949 45 39. DUKLER A. E. and MAGIROSP., Entrainment andpressure drop in concurrent gas-liquid flow. Part ZZ: Liquid property and momentum eficts. (Unpubl. rept., Univ. of Houston, Houston, Texas). COLLIERJ. G., Pressure drop data for the forced convective flow of steam-water mixtures in vertical heated and unheated annuli. AERE R-3808. 1962. (H.M. Stat. off., London). Hawrrr G. F. Some calculations on hold-up, heat transfer and nucleation for steam-water flow in a 0.5 cm bore tube. AERE R-3984,1962. (A.E.R.E., Harwell, Berks. To be publ). WICKS M. and DUCKLER A. E., Amer. Inst. Chem. Engrs. J., 1960 6 463. HINZE J. O., Amer. Inst. Chem. Engrs. J., 1955 1 289. CALVERTS. and WILLIAMSB., Amer. Inst. Chem. Engrs. J., 1955 178. ANDERSONG. H. and MANTZOIJRANI~G. B., Chem. Engng. Sci., 1960 12 109. DIJKL.ER A. E., Chem. Engng. Progr. Symposium Series No. 30,196O !I6 1.
87
L. E. GILL, G. F. HEWITTand P. M. C. LACEY [22] Hawrrr G. F., Analysis of annular two-phase flow: Application of the Dukler analysis to vertical upward flow in a tube. AERE R-3680, 1961, (H.M. Stat. Off., London). [23] CASAGRANDEI., Correlating liquidfilm thickness in cylindrical geometry. (Unpubl. rept. C.I.S.E., Milan, 1961). 1241 ARMANDA. A., The resistance during the movement of a two-phase system in horizontal pipes. Izcestiya Vsesoyuznogo Teplotechnicheskoga Instituta, 1946 1 16. [25] ROBERTSD. C. and HARTLEYD. E., A correIation of pressure drop data for two-phase annular fiw in vertical channels. Nuclear Res. Memo. No. Q 6, 1961. (Unpubl. memo., Dept. of Nuclear Engng, Queen Mary College, London).
88
Data on the upwards annular flow of air-water mixtures L. E. GILL, G. F. HEWITTand P. M. C. LACEY* Chemical Engineering Division, U.K.A.E.A. Research Group, Atomic Energy Research Establishment, Harwell (Receiwd 26 September 1964) Ah&act-Data are presented for fihn thickness, film flowrate and pressure gradient for upwards co-current air-water ammlar two-phase flow in a 1%in. bore perspex tube using two types of injector, a multijet type and an annular slot. Film flowrates, flhn thicknesses and pressure gradients were all observed to be lower with the multijet injector than with the ammlar slot. The results for pressure drop were compared with the Lockhart and Martinelli correlations and with correlations based on homogeneous flow; the former was found to predict the values closest. The Lockhart and Martinelli hold-up correlation generally overpredicted the flhn thickness-this is due to the presence of entrainment, Very different patterns of entrainment were observed for the two injectors. For higher liquid rates the entrainment results were found to agree with the correlating line obtained previously for vertical flow using the correlation method of WICKS and DUKLER,provided the appropriate “critical Weber numbers” were used for the two types of injector. As in earlier work, at lower liquid rates the entrainment is less than that predicted by the correlating line extrapolated from high liquid rates, and is a function of the gas flowrates. It transpired that the point where the entrainment curve joins the line of the correlation occurs at values of yi+ of 16-18 and may be related to the formation of large roll waves on the film surface. The inter-relation of film thickness, pressure drop and film flow rate by velocity profile theories has been studied and is discussed; systematic deviations from theory are found.
1. INTRODUCTION
this present work are found to agree well with the data obtained later [4] for the porous sinter, though this conclusion would not necessarily hold for very high water flow rates nor for positions close to the injector. The flow rates chosen for the studies here are such that the flow is always in the annular regime. At the lowest air flow rate, 100 lb/hr, the boundary between annular and “chum” or “semi-anmilar” flow is approached [5].
STUDIESof air-water annular flow in 14 in. bore vertical tubes have been carried out at Harwell for a number of years. In the earlier work [I, 21 the water was injected through a number of jets at the entrance and in the more recent work [3,4, 51 the water was introduced into the walls through a porous section of wall. In the latter case, therefore, the water at the entrance is entirely on the tube wall whereas with the jet injector it is largely in the form of suspended droplets in the gas phase. The porous sinter injector has the advantage of providing a well defmed condition at the entrance. The annular slot injector-in which the liquid is introduced around a slanting periferal gap in the wall-was used in the intermediate stage of the Harwell work [6, 71 and was a first attempt at achieving this aim. The present paper augments the data previously published and provides a link between the earlier and later work. The experiments were carried out in 1960 and 1961 and both multijet and annular slot injectors were used. The annular slot data in
2. EXPERIMENTAL 2.1
Techniques of measurement
The technique of measurement of the dependent variables (film thickness, pressure drop and film flow rate) have been described in detail elsewhere [ 1,2,7] but the principal features will be briefly restated. 2.1.1 Film thickness. Film thickness was measured by the electrical conductivity techniques described elsewhere [2, 41. The probes used were 4 in. diameter stainless steel rods let into the tube wall with their ends flush with the wall surface, each pair being mounted with 3 in. between centres in
* Present address: Department of Chemical Engineering, University of Exe&, Exeter, Devon.
71
L. E. GILL, G. F. HEWITC and P. M. C. LACEY
SLIGHTLY DIAMETER
SMALLER THAN
INCHES
“1
0
1 DIRECTION
OF FLOW
FIG. 1. Film separator.
the line of flow. The generalised calibration [7] was used and the conductivity of the circulating water, to which NaCl had been added, was measured at frequent intervals. The conductivity was corrected for temperature [8]. 2.1.2 Filmflow rate. The fdm flow rate was measured by separating the Ghn from the droplet-laden gas core, as shown in Fig. 1, and allowing it to spill over into a compartment whence it was taken to a cyclone separator. The outlet to atmosphere from the cyclone was controlled by a valve and some air was bled slowly from the flow tube via the cyclone. This air leak was small compared to the flow in the tube and was controlled until the tube wall just above the separator became dry. The water from the cyclone was collected and its rate of flow estimated from the time taken to fill a calibrated tube; at high flow rates it was weighed. Though crude, the method worked quite well, 72
except at high liquid rates, when special care was needed. 2.1.3 Pressure drop. The water-purge technique [7] was applied. The manometer circuit and other details are given in reference [9]. 2.2 Air and water supplies Air from the site mains was filtered and passed through reducers to a surge tank and hence through further reducers and an orifice to the flow tube. The orifice was operated at constant inlet pressure by throttling downstream. A series of fully corrected orifice tables produced on the Harwell Mercury computer were used for obtaining the orifice differential appropriate to any required flow rate. (See reference [lo] for details of computer programrne). Water was supplied from a thermostatically controlled tank via a centrifugal pump. On leaving the flow tube the mixture was separated
Data on the upwards annular flow of air-water mixtures using a cyclone separator, the air from the cyclone being discharged into the atmosphere and the water returned to the sump tank. 2.3 The Jlow tube The layout of the flow tube is given in Fig. 2. Only two pressure tapping points, 6 ft apart, were used as it was assumed that the pressure gradient was constant [9]. Four sets of conductance probes were inserted in the tube. The Glm removal device was placed above the top pressure tapping and a telescopic joint was used at the outlet to assist changing the injector etc. The total length of the tube from air inlet to two-phase outlet was about 12 ft. 2.4 The water injectors Since the method of water injection was considered to have a very large effect on the parameters 8
--_=7\
TO ClCLONE
RAOIAL JETS
-
TELESCOPIC FLANGE JOINT
FILM REMOVAL DEVICE --
FILU TNICKNESS PROBES
”
TOTAL “EIGHT IT- 4’
-
FIG. 3. Multijet injector. 36”
PRESSURE TAPPING -t
I
WATER
INJECTOR -
FIG.2. Flow tube layout.
of flow two methods were chosen which would give results as different as possible. These are described below. 2.4.1 The multijet injector. The multijet injector (see Fig. 3) was used as in the original air-water at Harwell carried out by BENNETTet aZ.[l, 21. The water enters the tube through eight radially placed jets, which are placed at the entrance to the tube proper. The resultant mixing, however, is not well de&red and this injector has only been used in the present studies because it allowed a direct comparison with the earlier work. 73
L. E. GILL, G. F. HEWITTand P. M. C. LACEY
FIG. 4. Details of annular slot injector.
2.4.2 The annular slot injector. A much better defined inlet condition can be achieved by using the annular slot injector shown in Fig. 4, which is self-explanatory. Since the liquid is introduced more gradually into the flow tube the entrainment at the inlet will be lower than for the multijet injector. The injector has an annular calming length before the wafer enters the tube, which ensures that there is no extra dynamic head at any point around the circumference of the slot, and the slot itself is convergent. The convergent slot was found to give a uniform distribution at much lower flow rates than was a parallel slot. (Even with the annular slot injector, however, there is some uncertainty as to whether the liquid will bend over and form a iilm at the inlet or whether it wti. penetrate the gas stream and cause some adventitious entrainment at the inlet). 74
2.5 Experimental procedure The object was to provide data for both injectors at a fixed distance (7.5 ft) from the injection point. It is recognised that the dependent variables measured-namely, film flow rate, fYm thickness and pressure gradient-are changing continuously with length. The changes in film flow rate are considerable [3] but those in flm thickness and pressure gradient are less severe except near the injector [2, 3, 91. At the beginning of the experiment the air and water rates were set as near as possible to the required conditions and when flow had become steady the exact flow rates were recorded, and the pressure drop, film thickness and G.hn flow rate were then measured, in that order. The film thickness was measured at the top pair of conductance probes and the value obtained was assumed to apply [9] at the take-off point which was only about 1 ft further on.
3. b!XJLTS The basic data obtained are tabulated in reference [9]. 3.1 Pressure gradient Measured pressure gradient is plotted against liquid rate with air rate as a parameter in Fig. 5
Data on the upwards annular flow of air-water mixtures
I
1
500
I
moo
1500
2500
LIQUID RATE- IbJbr.
FIG. 5.
Pressure gradient measurements -
(multijet injector) and Fig. 6 (annular slot injector). As would be expected, the gradient increases with both air and liquid rate. It will be seen on comparing the figures that the annular slot liquid 70.
multijet injector.
entrance gives, in general, higher pressure gradients than the multijet type. A more direct comparison is presented in Fig. 7 where the ratio of pressure gradients for the annular slot and multijet injectors
I
I
60-
Air
I 500
I 1000
I
LIPUID
FIG. 6.
I
I500 RATE -
2000 lb. / hr.
Pressure gradient measurements -
75
ammlar slot injector.
Rate
100
l
200
0
SW
l
400
x
500
A
600
l
700
v
800
1[
I
2500
3000
L. E. GILL, G. F. HEWITT and P. M. C. 1.6,
I Air
LACEY
I
I
Rate
lb./hr.
I.5
1,s -
600
1.2:
.
700
.
600
0
.
+
M-;rx
: *: 00
0,9-
4
f
.#. I.0
E
.
T”
+ .
6
0
l
f
.
a .
04 -
0.7
I 500
0
1 1500
I 1000
2000
llOlJlO RATE - lb./ hr. FIG:
7.
Comparison
of pressure gradients for annular slot and multijet injector.
Air
Rate
Lb./hr 100 zoo 300 400
/
1000
so0
LlOUlO
FIG. 8.
Film
thickness
2L30
RATE-lb./hr
data -
76
multijet
injector.
0 + I
500 600 700
A . .
1100
*
I
I500
l
2500
Data on the upwards annular flow of air-water mixtures Air Ralr Lblhr: 100 200
l
0
300 400
+ x
100
.
000 700
. .
/
I
500
1000
zoo0
I500
2500
10
LIPUID RATE- Iblhr.
FIG. 9. Film thickness data -annular
is plotted against water rate with air rate as a parameter. It is seen that the pressure gradient is nearly always higher for the annular slot injector. The ratios pass through a minimum at 100-300 lb/hr of water. The maximum difference recorded between the two types of injectors is about 40 per cent. The effect of air rate at constant liquid rate on the ratio of pressure drops appear to be somewhat variable; in general the lowest air rate (100 lb/hr) gives lowest values of the ratio and as the air rate is increased the ratio rises rapidly (presumably on moving away from the transition to semi-annular flow) and then falls slowly again as air rate increased further. It should be emphasised, in making this comparison, that the experimental errors in both measurements are combined. 3.2 Film thickness The results for film thickness are presented in Figs. 8 and 9 respectively. As would be expected,
slot injector.
film thickness increases with increasing liquid rate and decreasing gas rate. The characteristic difference between the multijet and annular slot injectors are brought out clearly by comparing the two sets of curves. In the case of the multijet type, at high gas flow rates the film thickness tends to level out with increasing liquid rate whereas with the annular slot the thickness continues to increase markedly. There is considerably more scatter in the measurements of film thickness than in those of pressure drop. The ratios of film thickness for the annular slot to that for the multijet injector are plotted in Fig. 10. Here again, the ratio is nearest to unity when the liquid rate is in the region 100-300 lb/hr. The effects of liquid and gas rate are approximately in the same sense as those for pressure drop. 3.3 Liquid$lm
flow rate
In reference 2 it was found convenient to plot the results for film flow rate in the form film flow 77
L. E. GILL, G. F. HEWITTand P. M. C. LACEY
Ib./hr 100 l 200 0 JO0 + 400 I so0 A Woo l 700 . 000 Im
A -
Id-
I+-
. . I .
7 I.5 -
&
'I I.2 -
l
. I +
.
l
1. T I.1 -0 .+
x
. t
!m:
t
l
.
f
x
lo- o O
I
o
+
.
0.9-
t 500
0.7 0
I IO00 LlPUlO
FIG.
RATE-
I 1500
2000
lL/hr
10. Comparison of film thickness data for annular slot and multijet injector.
rate versus total liquid flow rate and the same has been adopted here. This method obscures some of the finer details in the low liquid flow rate region but the full results are available in reference [9]. The film flow rate/total liquid rate plots are given in Figs. 11 and 12. Apart from the data at 100 lb/hr air flow rate, method
500
loo0
1500 TOTAL
FIG. 11.
the lines of film flow rate versus total liquid rate drop progressively further away from the equality line as the air rate is increased. For the multijet injector very similar results are obtained to those reported. previously [2]-the film flow rate tends to level off and at high total liquid rate becomes relatively insensitive to further increases in hquid
Film flow
LIQUID
FLOW RATE -
2000
lb/hr.
rate results using mukijet injector.
78
2500
3000
Data on the upwards annular flow of air-water mixtures
TOTAL LIQUID FLOW RATE -Ib/hr.
FIG.12. Film flow rate results using annular slot injector.
discussed in reference [7]. The normal calculation of accelerational pressure drop does not take into account the continuous change which occurs in the liquid content of the gas stream. That this term can be large (up to one third of the total pressure gradient) has been demonstrated by DUKLER and MAGIROS1141. For the present results, however, since we have no information on the change of entrainment with length, it is impossible to make an accurate estimate of this pressure drop. Its effect would probably be largest at the highest 4. INTERRELATTON OF INDIVIDUAL DEPENDENT flow rates and would vary according to the type of VARIABLESWITH THE CORRESPONDING INDEPENDENT injector. This difficulty should be borne in mind VARIABLES when considering the following comparisons of 4.1 Correlations of pressure drop the pressure drop data with the empirical correlaThe two best known approaches to pressure drop tions: it should also be remembered, however, that correlation are to treat the flow as homogeneous this effect has been ignored in the original work on [l 1, 121, or to relate the ratio of the two-phase to which the correlations were based and indeed in a single phase pressure gradient to the ratio of almost all other work on two-phase pressure drop. the single phase gradients, this latter approach 4.1.1 Homogeneous correlations. As was discussed being that of LOCKHARTand MARTINESLLI [13]. in reference [7] there is some difference of opinion The main difficulty in comparing the pressure [l 1, 121 as to which viscosity should be used when drop data with the empirical correlations is in calculating the frictional pressure drop for the estimating the accelerational term. This feature is homogeneous flow correlations. Either the liquid With the annular slot injector the pattern is rather different and somewhat irregular trends are sometimes observed, presumably due to the separation effect mentioned above. For both types of injector, at a constant liquid rate, the film flow rate was lower at 100 Ib/hr of air than it was at 200 lb/hr, i.e. a reversal of the general trend of the data. This is presumably a result of the approach to the semi-annular flow regime [5]. rate.
79
L. E. GILL, G. F. HEWITTand P. M. C. LACEY
viscosity [l l] or a reciprocal mean viscosity [12] can be used and these two approaches give different results. Using the mean viscosity the predicted pressure gradient was always lower than the experimental one; if, on the other hand, the liquid viscosity was used, then the predictions were usually higher than the experimental figures. There was a slight shift in favour of the liquid viscosity model in going from the multijet to the annular slot injector. There was very considerable scatter at the lower values of pressure gradient (up to 250 per cent) and, on the whole, the homogeneous model cannot be regarded as very useful in correlating the present data. 41.2 The Lockhart-Martinelli model. The experimental total pressure gradients were compared with those calculated from the Lockhart-Martinelli model and the result for the multijet injector are shown in Fig. 13. A much closer prediction is obtained using this correlation, particularly at low pressure gradients. The correlation was somewhat closer for the multijet injector but for both this and the annular slot injector the results at high
Air Rate lb. /hr.
FIG. 13.
Comparison
4.2 Hold-up correlation LOCKHART and MARTINELLI [13] have suggested that hold-up is correlated by the same parameter X as is used in their correlation of pressure drop. X is defined by:
X =
. .
300 400
0 D
. .
100 boo 700
0 0 8
l + *
800
*
*
GRADIENT
n
(1)
Gas turbulent Liquad turbulent
0 LJ
I
W/d& J W/d&
where (dP/dL), and (dP/dL), are the pressure gradients for the liquid and gas phases respectively, when flowing alone. Providing that no entrainment is present then it can be shown that X should correlate the hold-up [16]. When entrainment does occur then the correlation should fail and the hold-up will be less than that predicted. That this is in fact the case for the present results is shown in Fig. 14 for the multijet injector; as before the results from the annular slot are similar [9]. (The hold-up was calculated from the measured film
100 200
,.ov I.0 PRESSURE
Gas turbulent Lrquid IIXOUI
pressure gradient showed under-prediction of the pressure gradient. This latter effect has also been observed by COLLIER [15] for steam-water flow.
I
PREDICTED
I11111 FROM
I
IO
Lockhart
I9!!111
100 IHartinelli
CORRELATION
of calculated and experimental pressure gradients: multijet injector.
80
-
lb./h?
ft.
Lockhart/Martinelli
correlation -
Data on the upwards annular flow of air-water mixtures 13 was assumed (the multijet had been used) and the line of equation (3) is quite close to that obtained by WICKS and DUKLER for horizontal flow. Two main points of interest arise from comparing the present data with this correlation: (i) Do the data for the multijet injector agree 4.3 The Wicks and Dukler correlation for entrainwith the data which were obtained previously ment with the same injector (reference [2]) and WICKS and DUKLER [17] have shown that for which were correlated by equation (3) ? horizontal air-water flow, the entrainment could (ii) Does the change of We, from 13 to 22 be correlated using the LOCKHARTand MARTINELLI successfully bring the results for the annular parameter X and the dimensional correlating group slot into line with the results for the multiR, where: jet injector ? The results are plotted in Figs. 15 and 16. It will (2) be seen that for both injectors (i.e. after introducing In equation (2), E is the entrained phase flow the appropriate value of We=) the results agree rate (lb/hr), qL and qo are the volumetric rates of remarkably well in the region X > 0.08 with the flow of the liquid and gas respectively and the line given by COLLIERand HE.SVITT[2]. For any “critical” Weber number, We,, was taken, on the given gas rate, the points corresponding to high basis of the work of HINZE [ 181to be 13 for “sudden liquid rates (high values of R) fall upon the Colliershock”, as in a tee type of water entry, and 22 for Hewitt correlating line; at lower water rates the gradual acceleration, as for an annular slot injector. points break away and lie on a line of smaller In presenting and analysing BENNET-PSentrainment slope. This point of changeover appears to correresults, COLLIERand HEWITT [2] showed that for spond to an approximately constant &n flow rate X > 0.08 the data were correlated by a single line: ( - 100 lb/hr) which is of the same order as that X = 0.069 R”‘3g (3) at which roll waves become well established [5]. The value of v: (the dimensionless iilm thickness) For these results a critical Weber number of
thickness, and the hold-up in the gas core calculated by assuming a homogeneous mixture of the entrainment with the gas. The gas core term of the entrainment was negligible compared with the Glm thickness term. The validity of this assumption was co&rned in later work).
‘OF------
FIG. 14.
Correlation
of holdup in terms of Lockhart multijet injector.
81
and Martinelli parameter
X -
L. E. GILL,G. F. H~AVITT and P. M. C. LACSY l.O_
I
I I,,,!,,
I
1 I11/11,
WICKS AND DUKLER METHOD
1 Il/,!W
,
FOR CORRELATION OF ENTRAINMENT-MULTIJET
I 1/,111, INJECTOR.
’
’ “““’
FIGURE 15
RG. 15..
WICKS
and
DUKLZR
method for correlation of entrainment - multijet injector. in its use in other systems; first of all, however, other liquids should be used to enable a dimensionless rather than a dimensional correlating group to be derived; the latter will probably only apply to air-water systems.
corresponding to the transition is 16-18 and this suggests that the changeover may be associated with the breakdown of the outer layers of the film into turbulent eddies. The complete entrainment curve can then be defined: y: > 16-18
X = 0.069 R”+’
y: < 16-18
X = kR0’16
(3)
5. INTERRELATION OF DEPENDENTVARIABLES
(3a)
In the work described here three dependent variables (viz. pressure drop, fihn thickness and liquid film flow rate) were measured for a number of values of three main independent variables (viz. air rate, water rate and liquid injector). Two types of dependent variable relationships can be used : (0 Relationships which allow the calculation of one of the dependent variables from the measured values of the other two. These relationships are theoretical and direct and involve no arbitrary correlation of the experimental results. They do not need to invoke the independent flow variables. (ii) Relationships which allow the calculation
Here, k is a function of the gas velocity and depends on the position at which the value of JJ~ of 16-18 occurs on the line of equation (3). Equation (3a) is derived from the data of reference [2] where much more information was obtained at the lower liquid flow rates. From the data of reference 2, k varies in the range 0.03408 for the air rates 150-700 lb/hr. Again, it will be noted that the results for 100 lb/hr of air give higher entrainment in the X > 0.08 region than would be suggested by the correlation, possibly resulting from the approach to churn flow. The success of the correlation in predicting both the annular slot and multijet entrainment may give some confidence 82
Data on the upwards annular flow of air-water mixtures I.0
. ,
, , , / , , ,,
I
I v11111,
I I1l111,
! I III!,
4 I I/18’1,
,I
no. 16. WICKSand DUKLER method for correlation of entrainment - annular slot injector.
of one of the dependent variables from a knowledge of only one of the others. These relationships usually also involve the independent variables. Relationships of the first kind for upward flow are typitied by those Of CALvERTand WILLIAMS[19], ANDERSONand MANTZOURANIS [20], and DUKLER [21] as modified by HEWITT [22]. In the second class of relationships come the C.I.S.E.* film thickness correlation [23], the hold-up pressure drop correlation of ARMAND [24], and the film thickness/roughness relationships proposed by GILL, HEWITT and LACEY[4]. Treatments which are somewhat hybrid between the two classes are those of ROBERTSand HARTLEY [25] and the pressure drop correlation of ANDERSON and MANTZOURANIS [20]. These relationships can involve all three dependent variables and are still empirical. Both classes of relationships were used [9] in * Centro Informtioni Studi Esperienze,Milan, Italy. 83
the analysis of the present data but we shall confine our discussion to relationships of the first type. 5.1 Interrelation of film thickness, film flow rate and pressure drop
The most complete theoretical treatment of annular flow is that of DUKLER 1211 and this has been modified for upwards flow by HEWITT [22] This theoretical treatment adopts the dimensionless velocity protie approach used frequently in the solution of single phase flow problems. Proper allowance is made for the variation of shear stress across the liquid film and it is in this respect that the analysis differs most from the similar treatment of ANDERSONand MANTZOURANIS [20]. (There are slight differences, too, in the exact form of the dimensionless velocity profile used.) The Dukler treatment involves the solution of a non-linear differential equation; this can only be done numerically and a computer programme has been written (see reference [6]) which allows the film flow rate to be calculated from the pressure drop and
L. E. GILL, G. F. HEWITT and P. M. C. LACEY
FIG. 17. Comparison of film flow rates with values calculated from modtied DUKLER analysis multijet injector.
film thickness-all dependent variables. Film flow rates calculated by the computer from the present data for the multijet injector are compared with the actual flow rates in Fig. 17; (again, the annular slot injector gives somewhat similar results). The pressure gradients used in these calculations were corrected for the accelerational pressure drop. The flow rates are compared in terms of the dimensionless film flow rate W+ where:
wLF is the liquid film flow rate (lb/hr), r. the radius of the tube (ft) and ,u~ the liquid viscosity (lb/ft hr). This method of plotting is equivalent to comparmg wLr values since r. and ,uL are tied for the present data, except for some slight variation in pL due to temperature fluctuation. The film flow rate is predicted reasonably well, the scatter being worst at the lowest flow rates. On plotting the ratio of actual to predicted film flow rate against the film thickness (as in Fig. 17
of reference [2]) the definite trends observed previously and reported in reference 2 were not obtained.7 The main difference between the present data and those of reference 2 is the greatly increased range of water flow rate; the results at low liquid rates do follow the trend originally observed. A more sign&ant general trend in the results emerges, however, when film thickness is calculated from pressure drop and film flow rate. In order to do this calculation it is necessary to use an iterative procedure and this procedure is much easier with the ANDERSON and MANTZOURANIS analysis than with DUKLER’S. A computer programme had been developed previously which, by means of a multistage iterative procedure for the ANDERSON.and MANTZOURANISanalysis, calculates each one of the dependent variables from the other two. The ANDERSON and ~~ANTZOURANIS analysis used here was the uncorrected version t In reference 2 a corrected version of the ANDERSON and MANTZOURANIS analysis was used-that this differsvery little from the DUKLER analysis which is used here is demonstrated by Fig. 11 of reference 6. 84
Data on the upwards annular flow of air-water mixtures
EXPERIMENTAL
FIG. 18.
Comparison
Comparison
thou
of experimental and calculated film thickness. Uncorrected and MANTZOIJRANBtheory - multijet injector.
EXPERIMENTAL
FIG. 19.
FILM THICKNESS-
FILM
THICKNESS-thou.
of experimental and calculated film thickness. Uncorrected and MANT~OURANIStheory - annular slot injector.
85
ANDERSON
ANDEISON
L. E. GILL,G. F. HE~rrr and P. M. C. LACEY and its efficacy was tested by comparing w+ calculated by this method with w+ calculated from the Dukler method. With exception of the results at the lowest air rate the w’ values from the Dukler theory were only slightly higher than those from the Anderson and Mantzouranis analysis. In Figs. 18 and 19 the film thickness calculated from the ANDERSONand MANTZOURAMS analysis is compared with the measured value. The agreement ( f 30 per cent) is quite close but the differences between experimental and calculated film thickness cannot be ascribed to experimental scatter as there is a definite trend. This trend gives over-prediction of film thickness at low film thickness and underprediction at high film thickness. The latter effect may be due to the failure of the conductance probes to allow for the large waves present on thick films (see reference [7] for discussion of limitations of probes). Figure 20 shows a comparison of experimental and calculated pressure gradients for the multijet injector data; (again, a similar plot was obtained for the annular slot data but has not been reproduced). Although most of the data lie in the band
EXPERIMENTAL
f 30 per cent there is more scatter in the pressure drop calculation since any difference between calculated and actual film thickness is roughly squared in comparing pressure gradients. 6. CONCLUSIONS The effect of liquid injector design is very significant. The jet type of injector gives higher entrainment, lower pressure gradient and lower film thickness than the annular slot type. These differences are obscured when the results are analysed in terms solely of the dependent variables. In correlating pressure drop it was found that the LOCKHART and MARTINELLIcorrelation predicted the pressure gradient better than did the homogeneous models. The LOCKHART and MARTINELLI hold-up correlation, on the other hand, did not fit the data too well, owing to the entrainment; this was expected from previous work. The method of WICKS and DUKLER [14] correlated the entrainment data very well in the high entrainment region and good agreement was obtained with earlier A.E.R.E. data [2] for vertical flow. The use
NON-ACCELERATIONAL
PRESSURE
GRADIENT-Ib./fl*tt
FIG. 20. Comparison of calculated and actual pressure gradients. Uncorrected ANDERSON and MANTZOURANIS theory - multijet injector.
86
Data on the upwards annular flow of air-water mixtures
of different critical Weber numbers (as suggested by WICKS and DUKLER)brought the results for the two types of injector into line. At low liquid rates the entrainment is lower than that predicted by extrapolation of the COLLIER and HEWITTline. On examination of the results and also those reported earlier [2] it transpired that the entrainment is predicted by the COLLIERand HESVI~Tline for y: values greater than 16-18 and this provides a useful criterion for the change-over point. A correlating method for low entrainment is suggested on the basis of previous data [2]. The use of Glm velocity profile theories interrelating Glm thickness, film flow rate and pressure gradient has provided some interesting results. The data fit these theories remarkably well in view of the known wavy nature of the liquid am; systematic trends however are apparent. In particular, as the film thickness is increased it is first under-predicted and later over-predicted. The work described provided a useful basis for much further experimentation at Harwell; it was felt that only by studying the system in finer detail could a real advance in understanding be made. In general, therefore, this further work has concentrated on measuring rather more detailed
parameters such as wave velocities, velocity and entrainment distributions.
gas core
Acknowledgements-The authors wish to acknowledge the contributions made to this work by Messrs. P. C. LQVJK+ROVE and R. J. KINO who assisted in development of many of the techniques and by Miss D. PHIXLPSand her group in preparing tapes for the computer.
NOTATION mass rate of flow of entrained liquid (lb/hr) pressure gradient for flow of gas alone in the (dP,dL): channel (lb force/ft%)
(dP/dL)r. pressure gradient for flow of liquid alone in the channel (lb force/ftaft)
qc volumetric gas flow rate (ft3/hr) qL
R ;: w+ WLP We,
X Y{ Yi+ W PL To
volumetric liquid flow rate (f@/hr) entrainment parameter defined by equation (2) radius of flow tube (ft) “friction velocity” (ft/hr) = &T~/PL) dimensionless film flow rate defined by_ equa_ tion (4) liquid flow rate in the film (lb/hr) critical Weber number (dimensionless) Martinelli parameter defined by equation (2) (dimensionless) film thickness (ft) dimensionless tllm thickness = (u*PLY~/~L) viscosity of liquid (lb/ft hr) density of liquid (lb/f@ wall shear stress (pdl/fts)
THORNTONJ. D. and BENNE~ J. A. R., Trans. Znstn. Chem. Engrs., 196139 101
COUIW J. G. and Hswrrr, G. F., Trans. Znstn. Chem. Engrs. 1961 39 127. GILL L. E., IIawrrr G. F., HITCHON J. W. and LACEYP. M. C., Chem. Engng. Sci. 1963 18 525. GILL L. E., Hmwrrr G. F. and LACEYP. M. C., Chem. Engng. Sci. 1964 19 665. HALL-TAYLOR N., H~wrrr G. F. and LACEYP. M. C., Chem. Engng. Sci. 1963 18 537. Hawrrr G. F., KING I. and LOVEGROVEP. C., Bit. Chem. Engng. 1963 8 311. HEWITT G. F., KING R. D. and LOVEGROVEP. C., Chem. Proc. Engng. 1964 45 191. Hswtrr G. F., Tables of the resistivity of aqueous sodium chloride solutions. 1961 AERE R-3497. (H.M. Stat. Off., London). GILL L. E. and Hxwrrr G. F., Further data on the upwards annular flow of air-water mixtures. AERE R-3935, 1962 (A.E.R.E., Harwell, Berks.) Hswn-r G. F., Some computer programmes. AERE M-922, 1962. (A.E.R.E., Harwell, Berks.) OWENSW. L., Two-phase pressure gradient. Paper 41. International Developments in Heat Transfer (Vol. II) 1961. (Inst. Mech. Engrs., -London). _ M&DAMS W. H.. WOOD W. K. and H_EROMON L. C. Jr.. Trans. Amer. Sot. Mech. Enars., _ . 1942 64 193. LOCKHARTR. W. and MARTINELLIR. C., Chem. Engng. Prog. 1949 45 39. DUKLER A. E. and MAGIROSP., Entrainment andpressure drop in concurrent gas-liquid flow. Part ZZ: Liquid property and momentum eficts. (Unpubl. rept., Univ. of Houston, Houston, Texas). COLLIERJ. G., Pressure drop data for the forced convective flow of steam-water mixtures in vertical heated and unheated annuli. AERE R-3808. 1962. (H.M. Stat. off., London). Hawrrr G. F. Some calculations on hold-up, heat transfer and nucleation for steam-water flow in a 0.5 cm bore tube. AERE R-3984,1962. (A.E.R.E., Harwell, Berks. To be publ). WICKS M. and DUCKLER A. E., Amer. Inst. Chem. Engrs. J., 1960 6 463. HINZE J. O., Amer. Inst. Chem. Engrs. J., 1955 1 289. CALVERTS. and WILLIAMSB., Amer. Inst. Chem. Engrs. J., 1955 178. ANDERSONG. H. and MANTZOIJRANI~G. B., Chem. Engng. Sci., 1960 12 109. DIJKL.ER A. E., Chem. Engng. Progr. Symposium Series No. 30,196O !I6 1.
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L. E. GILL, G. F. HEWITTand P. M. C. LACEY [22] Hawrrr G. F., Analysis of annular two-phase flow: Application of the Dukler analysis to vertical upward flow in a tube. AERE R-3680, 1961, (H.M. Stat. Off., London). [23] CASAGRANDEI., Correlating liquidfilm thickness in cylindrical geometry. (Unpubl. rept. C.I.S.E., Milan, 1961). 1241 ARMANDA. A., The resistance during the movement of a two-phase system in horizontal pipes. Izcestiya Vsesoyuznogo Teplotechnicheskoga Instituta, 1946 1 16. [25] ROBERTSD. C. and HARTLEYD. E., A correIation of pressure drop data for two-phase annular fiw in vertical channels. Nuclear Res. Memo. No. Q 6, 1961. (Unpubl. memo., Dept. of Nuclear Engng, Queen Mary College, London).
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