549

STEAM PLANT GROUP

METERING OF STEAM-WATER TWO-PHASE FLOW BY SHARP-EDGED ORIFICES

By Russell James*

This paper describes work conducted on the passage of steam-water mixtures through standard sharp-edged orifices for the prediction of flow conditions.

When the stagnation enthalpy or alternatively the dryness fraction at the orifice is known, it is shown that the mass flow rate can be approximately determined.

For the case where a steam-water mixture passes through a pipeline to the atmosphere or to a low-pressure receiver so that critical flow occurs at the outlet, both the mass flow rate and the stagnation enthalpy may be approximately evaluated using an orifice meter in series with a pressure tapping located at the point of critical flow. In this case, a trial-and-error method is necessary.

The experimental results were within a range of dryness fractions from 1 per cent to 56 per cent, orifice pressures from 75 to 275 lb/in2 abs., differentials from 15 to 780 mmHg under water and flow rates from 54 700 to 508 000 lb/h. Orifices of 5591 and 6.615 in diameter were installed in 7.9411 diameter pipes which were equipped with radius ( D and 0 /2 ) taps.

The method employs a correlation between the homogeneous dryness fraction Y, and a corrected dryness fraction x, necessary for evaluating the two-phase density used in the conventional single-phase meter equation.

INTRODUCTION SINCE THE ADVENT of the boiling water nuclear reactor, there has been accelerated interest in the concurrent flow of steam-water mixtures in pipes and channels, most of which work has been on density studies and in comparisons between the steam volume fraction and the steam weight fraction. These factors are important for reactor stability.

Experiments have been conducted to determine both the flow rate and enthalpy of steam-water mixtures passing to the atmosphere, by Banwell ( ~ ) t who used a pitot-type probe which collected a series of samples along the dia- meter of a vertical discharge and condensed them in a small calorimeter; and by Belin and Bainbridge (2) who used beta-ray absorption across the throat of a horizontal critical flow nozzle. The first is the more accurate of these two methods and has been widely used in the Wairakei geothermal area, New Zealand, for determining the output

The MS. of this paper mas$rst received at the Institution on 14th December 1964 and in its revised form, as accepted by rhe Council for publication, on 22nd June 1965.

* Department of Scienti'c and Industrial Research, Taupo, New Zealand. t References are given in Appendix I I I .

I'roc lnstn Mech Engrs 1965-66 +

characteristics of boreholes. Of late, howe---- 'he vertical flow of unsilenced mixtures has become less acceptable- because of noise and precipitation-and the second of the two methods might have been considered if its accuracy had been greater.

The first use of a sharp-edged orifice to measure flow was undertaken by the United States Naval Boiler and Turbine Laboratory, and reported by Murdock (3). Other than these results, there has been no work up to the present specifically to meter flow using such a device, although a theoretical correlation has been produced by Chisholm (4), who based his results on the work of Benjamin and Miller (5 ) and Monroe (6); these tests were not conducted for metering purposes but for the regulation of flow of saturated water flashing through orifices.

For single-phase flow through a sharp-edged orifice under industrial applications conventional formulae give accuracies better than k 2 per cent for the flow rate.

In the case of two-phase, steam-water mixtures where the pressure and enthalpy at the orifice is known, an ob- vious approach to the determination of flow rate is to assume that the mixture is evenly distributed with the

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550 RUSSELL JAMES

phases travelling at equal speeds and with pressure- temperature equilibrium, thus enabling the homogeneous density to be obtained. In practice, it is found that this approach gives flows which are less than the true ones with a greater error for a greater wetness proportion.

It can be said at present, therefore, that for steam-water flow through an orifice where the stagnation enthalpy is known, the flow rate cannot accurately be determined. In the case of geothermal boreholes under test in New Zealand which pass mixtures to the atmosphere, both the flow rate and the stagnation enthalpy are unknown. The problem in this case is therefore, on the face of it, a more difficult one. For determining two such unknowns, it is mathematically necessary to have two equations and there- fore, presumably, two metering devices. Where the mixture attains critical flow on passing to the atmosphere such a second device exists in the form of a critical pressure tapping at the pipe outlet. The relationship between the pressure at this tapping, the mixture stagnation enthalpy and the mass-velocity of the flow has already been pub- lished in a previous paper (7). I t became apparent that a trial-and-error solution for both unknowns was technically possible dependent on the feasibility of obtaining a good correlation for the orifice itself.

When a liquid and gas phase travel concurrently along a horizontal pipe, the type of flow depends on the propor- tion of liquid to gas. Qver a wide range of conditions varying from a high mass ratio of liquid to gas, to a low ratio, the conditions within the pipe vary through the following principal regimes :

(1) Bubble flow, where the gaseous phase exists as discrete bubbles ;

(2) Stratified flow, where gross separation between phases occurs with the water travelling along the bottom of the pipe in the form of a crescent in cross- section;

(3) Slug flow, caused by periodic waves of liquid completely filling the pipe cross-section and moving at greater speed than the average water velocity;

(4) AMdar flow, where the water phase forms an annulus around the rim of the pipe and the gas phase travels along the central core of the pipe with some degree of entrainment of liquid within the core;

(5) Dispersed flow, where the liquid is thoroughly entrained within the gaseous matrix.

It will be obvious that these flow regimes within a pipe may be the cause of considerable variation in pressure drops over a given length and that they may be sensitive to both diameter and geometry of the piping and the his- tory of the flow. For example, it is possible that a bend in a pipeline may change a condition of stratified flow to one of annular flow due to the effect of secondary flow caused by the bend; once established, it may take some consider- able distance along the pipe before the original condition is regained, if it ever is. It is also probable that considerable hunting between unstable regimes occurs causing Aucrua- tions in pressure-drop values, while where stability Proc Instn Mech Engrs 1965-66

exists, the equilibrium time necessary to change to another regime when the flow rate is altered, may be considerable. The condition may be considered as analogous to the case of single-phase flow in a pipe where the change from vis- cous to turbulent flow is dependent to some extent on whether the velocity has been increased from a low Reynolds number or decreased from a high one. These factors may explain the variation in pressure drop ob- tained by workers in this field.

For the case where a sharp-edged orifice is used in a pipe passing a steam-water mixture it is possible that a relatively high degree of mixing is engendered by the orifice and that the aforementioned effects of zonal conditions are much reduced. With this possibility in mind, the present series of tests was undertaken.

Notation C Coefficient of discharge. C,, C,

volume, respectively. D d Diameter, in. G Mass velocity, lbjft2 s. g h Specific enthalpy, Btu/lb. J L Specific latent heat, Btu/lb. P Pressure, lb/in2 abs. P Pressure, lb/ft2 abs. Re Reynolds number, r Ratio P2/Pl. U Velocity, ft/s. V Specific volume, ft3/lb. W Flow rate, lb/h. X Homogeneous dryness fraction. x, Y Expansion factor. P Y P Viscosity, cP.

:

Specific heats at constant pressure and constant

Main pipe inside diameter, in.

Acceleration due to gravity, ft/s2.

Mechanical equivalent of heat, ft lb/Btu.

Dryness fraction corrected for meter calculations.

Ratio d,,,/D. Ratio CJC,.

Density, lb/ft3. Meter differential, mmHg under water.

Subscripts C Where critical flow occurs.

Saturated liquid. Dry saturated vapour. g

m Metering orifice. TP Two-phase steam-water mixture. 0 1 At upstream manometer tapping. 2 At downstream manometer tapping.

f

Stagnation condition where velocity is zero.

REASON FOR THE PRESENT WORK The discharge to the atmosphere of up to a million pounds per hour of flashing steam-water from boreholes under

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METERING OF STEAM-WATER TWO-PHASE FLOW BY SHARP-EDGED ORIFICES 551

BY PASS

STEAM

B

ORIFICE METERS

LEVEL-CONTROL ' I ? - TANK

TES; ORlFlCE IN 7 9 in dio. PIPE

BYPASS

\ I COOLING \

TANK 'THERMOMETER

8

+ I I I I

6.06 in dia. DISCHARGE PIPE

I GEOTHERMAL EOREHOLE

I I

Fig. 1. Equipment usedfor tests

test has been a common occurrence at the geothermal steam fields of Wairakei, New Zealand. The determination of the enthalpy and flow rate of these mixtures with free discharge is often either costly, or unacceptable because of noise and precipitation.

The purpose of the present work is to describe the characteristics of a simple and inexpensive metering system, from which the mixture may be ejected into a horizontal silencer.

EQUIPMENT The source of steam-water used was a geothermal bore- hole producing flows of up to 600 000 lbjh at an enthalpy of 490 Btujlb.

Fig. 1 is a diagrammatic sketch of the equipment used. After separation in a cyclone, desired amounts of the steam and water phases were measured at orifice meters and then passed through throttle valves B and C to be remixed before entering the 7.9411 diameter pipe contain- ing the test orifice. The mixture finally passed through throttle valve D and the 6.06411 diameter discharge pipe to the atmosphere. Bypass pipes before the metering ori- fices allowed excess steam or water to be also discharged to the atmosphere to obtain the required conditions at the test orifice.

The critical-pressure tapping geometry at the outlet face of the 6.06411 diameter discharge pipe was as de- scribed in reference (7). A glycerine-damped gauge to- gether with a needle valve and a goose-necked syphon were used to obtain a pressure reading and to eliminate the pulsations associated with two-phase flow.

The lengths of straight pipe connecting the test orifice to the mixing point and to valve D were of 20 and 10 pipe diameters respectively. As the zonal condition of the mixture was not the subject of this study, no attempt was made to adjust the flow to a particular regime although Proc lnstn Mech Engrs 196546

it was considered that the flashing at valve C and the acceleration conditions at entry into the steam pipe would provide some degree of mixing. The test orifice plate assembly was in line with the requirements of reference (8) for D and Dj2 tappings (radius taps). Condensation pots were used together with a manometer containing mercury under water with a scale reading up to 810 mm (2.66 ft), equivalent to a differential of 14.5 lb/in2 abs.

As it is difficult to measure accurately the flow of saturated pressurized water because of local flashing at an orifice plate, it was necessary to introduce a cooling tank into the water line from the cyclone. The amount of undercooling was approximately 10 to 30 degF and was measured by a mercury-in-glass thermometer inserted in a temperature pocket placed in the line between the cooling tank and the orifice.

PROCEDURE Test 1 Throughout this test a 5.591-in diameter orifice was installed and the critical discharge pressure was held constant at 24.5 lb/in2 abs. as sketched in Fig. 2. Steam and hot water flows were measured at their respective meters while the various throttle valves were adjusted to give a desired mixture enthalpy at the test orifice. The level of the mercury at the steam and water manometers was now marked and the pressure and differential at the test orifice recorded. The pressure at the test orifice was then altered to a new value by further adjustments of valve D. It was necessary to adjust valves B and C so that the mercury levels remained at their marks thus keeping the enthalpy and flow constant. By these means the values of PI and (b at the test orifice were varied over a range at constant enthalpy and flow. As can be seen from Fig. 2 where the test results are plotted on multi-cycle logarith- mic paper, the above values are shown for stagnation

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552

1000

5 P *

L

TI C

3

cn I E E I

5 100

8

-J

c z w LL W LL 'c n LL W I- : z

f

RUSSELL JAMES

I

D AND h D _MANOMETER TAPS

C '%n2 obs + ._ * ._

E: VALVE 0

._ 0 0

ORIFICE 5.591 in dia

1 0 100 1000 10000

LINE PRESSURE AT UPSTREAM MANOMETER TAPPING,P, - Ib/in2 abs. Fig. 2. Results of experimental tests for p = 5.591/7.90 = 0.707 and PC = 24.5 lblin2 abs.

enthalpies of 300, 350,400, 450, 500, 600, 800 Btu/lb and for dry saturated steam.

The values of flow and stagnation enthalpy calculated from the steam and water orifice meters were checked for correctness during the test by their use in the empirical equation given in (7) for the critical pressure tapping,

where G, is the mass velocity through the discharge pipe. Values of P, calculated from this equation gave reasonable agreement with the test value of 24-5 Ib/in2 abs. and were a useful aid in the detection of gross errors in the flow conditions at the test orifice, caused by malfunctioning of equipment.

G,ho1'102 = 11 400P,0'96

Proc Insdn Me& Engrs 1965-66

To assist the checking of results and also to enable extrapolation into higher pressures, the saturated water curve and the dry saturated steam curve were calculated and plotted in Fig. '2 up to the critical pressure of about 3200 lb/inz abs. ; thus the steam-water results were extended pictorially over a wide pressure and enthalpy range.

Test 2 Similar to test 1 with a 6:615-in diameter orifice installed and with the critical discharge pressure controlled at

-24.5 lb/in2 abs. Stagnation enthalpies of 350,450,500 and 600 Btu/lb were plotted in Fig. 3. The 'kinks' in the 450

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LL n

1c

METERING OF STEAM-WATER TWO-PHASE FLOW BY SHARP-EDGED ORIFICES

HARP-EDGED ORIFICE DIAMETER =6.615 in IN 7.90 in dia. PIPE

D AND % D MANOMETER TAPS

1 0 100 1000 10 000

LINE PRESSURE AT UPSTREAM MANOMETER TAPPING, Pi - Ib/ in2 abs.

Fig. 3. Results of experimental tests for p = 6-615/7-90 = 0.837 and P, = 24.5 Ib/in2 abs.

553

and 500 Btu/lb enthalpy curves were checked by repeated tests and appear to be genuine, perhaps due to local zonal changes in the fluid flow characteristics occasioned by the use of a larger diameter orifice. The saturated water curve and the dry saturated steam curve are also calculated and plotted.

point for an enthalpy of 350 and the plotted curve, it was decided after checking the equipment and finding no obvious malfunctioning, to plot a run at the enthalpy of 365 Btu/lb. This, too, gave a similar disagreement as also does the 400 Btu/lb curve. There is also a ‘kink’ in the 450 Btu/lb curve similar to the ones of test 2.

Test 3 Similar to test 1 with the 6.615-in diameter orifice in- stalled and with the critical discharge pressure controlled at 34.6 lb/in2 abs. = ( 4 2 x 24.5). Curves of the following constant stagnation enthalpy were plotted and are shown in Fig. 4: 350,365,400,450,500 and 600 Btu/lb. Because of the disagreement seen between the calculated all-water Proc Iristn Mech Engrs 1965-66

Test 4 With the 5.591-in diameter orifice installed, all the hot water from the cyclone was permitted to flash through valve C into the test orifice line while the steam from the cyclone was discharged to the atmosphere, valve B being closed.

Valve B was now progressively opened, increasing Vol180 Pt I No 23 by guest on October 12, 2015pme.sagepub.comDownloaded from

554 RUSSELL JAMES

ER=6.6151n IN 7.90in dia. PIPE

1000

L N c

: L

0 U C 3

m I E E I

Q

0

TOO

+ z w Tr W LL 1L n LT W b- W z 0 7

2 10

1 10 100 1000 10 000

L I N E PRESSURE A T UPSTREAM MANOMETER TAPPING P, - Ib/ ln' abs

Fig. 4. Results of experimental tests for p = 6-615/7.90 = 0.837 and P, = 34.6 lblin2 abs.

gradually the steam content of the mixture under test, at the same time the hot water flow at C was held constant. This was continued until all the steam from the cyclone was passing through valve B, thus the whole bore output was being remixed in the test line. At this point, the situation was reversed and the steam flow was held constant while the flow of hot water was progressively reduced by throttling valve C and bypassing the excess hot water to the atmosphere. This was continued until valve C was closed and only steam passed through the test orifice.

Table 1 gives the 26 results with the enthalpy increasing from 362 to 1200 &tu/lb during the course of the test. Up to run 16, the hot water flow of enthalpy 362 Btu/lb was held constant with the steam flow increasing; from run Proc Instn Mech Engrs 1965-66

17 on, the steam flow was held constant with the hot water flow of enthalpy 362 Btu/lb decreasing.

Test 5 With the 6.615-in diameter orifice installed, this test was to determine the effect of large differences in flow rate within the relatively narrow stagnation enthalpy range 450-500 Btu/lb. The procedure was to fix the values of stagnation enthalpy and flow rate in the test line and then to vary the line pressures and manometer differentials over as wide a range as possible. This method is repeated at progressively increasing values of flow rate and is shown in Table 2 where it is seen that the range covered varies

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Run No.

0,062 0,065 0,085

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16

17 18 19 20 21 22 23 24 25 26

0.015 0.015 0.022

METERING OF STEAM-WATER TWO-PHASE FLOW RY SHARF-EDGED ORIFICES

421 416 512 497 500

Table 1. Test results

454 462 474 476 481

0.

0.148 0.154 0.156 0.166 0.168

0.173 0.198

PI, Ib/in2 abs

112 115 133 148 162 177 186 194 207 215 212 221 226 236 244 237

241

0.072 0.079 0.083 0,086 0.084

0.09 0.106

~ lbjh I

173

230 169 i ii! 245 262

24.3 258 27.8 275 29 i 276 31.8 ~ 286 32.6 I 283 35 ~ 292 35.2 , 293 39.6 38.8 37.8 39.3 40.9

596 I 502 41.4 617 512 42.7 631 512 42.8

617 ~ 516 ' 42.2 230 608 534 I 39.5 219 598 546 37 202 588 1 577 1 33.5 187 1 573 I 622 30.7 168 555 1 657 27.8

G, lb/ftz s

in 6.06411 diameter

P'Pe

363 359 381 382 397 393 406 407

--

308 427 31 1 432 300 , 416 305 424 313 434 308 428 314 1 436 316 440

308 1 427 276 383 257 ~ 357 219 304 189 262 154 1 214 .__

155 i 530 ~ 717 25.8 130 1 181 140 I 495 1 805 23.5 104.3 145 129 ~ 468 1 902 1 21.7 85 118 107 ' 471 1 1200 19.5 54.7 I 76

0.217 0,116 0.262 ~ 0.147 0.321 , 0.192 0.37 0.233 0.445 0.29 0.552 1 0.383 0.669 ' 0.51

i

555

- (bTP100 55'8PI

F-

2.76 2.62 3.1 3.26 3.76 3.98 4.07 3.84 4.48 4.14 4.22 4.38 4.72 4.54 4.54 4.76

4.57 4.71 4.88 5.2 5.46 5.92 6.1 6.34 6.47 7.86

from 169 300 at a stagnation enthalpy of 486 Btu/lb to 508 000 at a stagnation enthalpy of 492 Btu/lb.

DENSITY OF STEAM-WATER MIXTURES An elementary approach to the solving of flow rate would be to assume that the mixture was distributed in a homo- geneous manner, thus enabling the average specific volume of the fluid to be determined from the value of dryness fraction and the specific volumes of the phases. The dryness fraction, however, depends upon the local enthalpy (at pressure P,) which is derived from the stagna- tion enthalpy and the fluid velocity at the orifice upstream pressure tapping. Calculations, however, show there would be little difference between the stagnation enthalpy and the local enthalpy at P I ; a trial-and-error solution would not be necessary. Apparently, therefore, this method would be valid if the flow could be considered as approximately homogeneous. In practice, of course, it is by no means homogeneous and the above method is found to give errors in flow of about 100 per cent for very wet mixtures. The method of approach considered in this paper was to determine experimentally values of W and + for a given orifice and to calculate the value of p1 from usual orifice equations. The value of pI was then used as if the flow were homogeneous to determine x, in the equation

A comparison was then made between x, and the con- ventional dryness fraction, x, and was found to be pre- ferable to comparing either densities or specific volumes, both of which involve the parameter of enthalpy. As can be seen from Fig. 5 which co-ordinates x, and x from the experimental results of Fig. 2, an approximate straight line is obtained on multi-cycle logarithmic paper giving the simple relationship :

x m = x1.5 . . . . * (2)

Figs 6 and 7 are similar plots of the data taken from Figs 3 and 4 which were for the larger orifice tested (6.615 in). It can be seen that these results do not form as precise a curve as that given in Fig. 5; this may be due to using an orifice with a large beta ratio resulting in a less effective mixing of the fluid. A comparison between Figs 6 and 7 shows the possibility that the region between x = 0.1 and x = 0.2 has some dependence on the value of critical discharge pressure; to test this, the data of Table 2 are plotted in Fig. 8 where for a given value of x, it is seen that x, increases with Pc for low values of Pc but is relatively insensitive to variation in P, at higher values.

For the 5.591-in orifice, the results of Table 1 are plotted in Fig. 9 and also show some dependence on flow rate. All test results are plotted in Fig. 10 for both sizes of orifice tested; also plotted are the nine results of the U.S. Naval Boiler and Turbine Laboratory as given by Murdock (3).

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556 RUSSELL JAMES

Table 2. Test results

PI, b/inz abs.

-___ 61 69 94

126 154 180 220 264 67 84

105 133 167 203 250 86

106 121 145 181 213 254 108 124 146 171 204 238 275 124 144 165 192 217 252 294 147 160 189 21 1 242 263 166 179 196 227 238 190

pc > b/in2 abs.

Run No.

-- 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74

4 T P

___ 226 185 102 61 40 33 22 16

262 178 112 80 54 43 27

339 23 1 180 143 101 72 48

376 279 203 165 129 90 65

424 322 260 199 166 116 90

517 43 1 317 262 189 171 605 513 395

G, lb/ft2 s

in 6.06411 diameter

PiPC

D, in

ho, Btu/lb

454

486 I c 4r I

483

.1 482

4 487

4 490

1

W

lb/h 1oDD'

171.3

~

4,

7P-, I

I 2i7.6

I

~

2 6 . 5

4, 329

I I

I I &

398

4;7

X

0206 0.199 0.178 0.156 0.14 0-126 0.106 0.088 0.236 0-22 0.205 0,188 0.17 0,152 0.134 0,217 0.204 0.195 0.179 0.162 0.146 0.13 0.20 0-19 0.177 0.165 0.149 0.134 0.118 0.19 0.176 0.166 0.154 0.141 0.127 0.11 0.181 0.175 0.162 0.15 0,136 0.128 0-175 0.168 0.16

5 6. 7. 0.086 0.083 0.065 0.048 0.036 0.033 0.024 0.018 0.011 0.01 0.08 0.07 0.057 0,053 0.037 0.099 0.09 0.08 0.075 0.064 0.051 0.037 0.095 0.085 0.073 0.068 0.062 0.047 0,036 0.085 9.078 0.072 0.062 0,058 0,044 0,037 0,081 0.077 0.066 0.061 0.048 0.046 0.080 0.075 0.064 0.056 0.053 0-068

6.63 4.8 1.94 0.86 0.46 0.33 0.18 0.11 7.0 3.8 1.91 1.08 0.58 0.38 0.19 7.05 3.9 2.66 1-77 1 .o 0.605 0.33 6.23 4.02 2.49 1.73 1.13 0.67 0.42 6.12 4.0 2.82 1.85 1.37 0.82 0.55 6.3 4.82 3.0 2.22 1.4 1.16 6.54 5.14 3.61 2.41 2.08 5.15

238 I

1 I I .1

235 I

1

3 i6

I

I i

382

1 457

~

55y3 1 I ~

~

615

I

+ 706

I 4

492

306 277 546

0.146 0.14 1 0.167

508 ! ,

Table 3. Variation inflow rate, W approximately constant down to x = 0.05. For values of x < 0.05, variation in x, increases. The effect of these unequal variations on calculations of flow rate has to be taken into account together with orifice pressure. Per- centage variations in flow rate, W, at different orifice pressures and at different values of x are given in Table 3.

Orifice pressure, lb/in2 abs.

X ~ Percentage variation in W

100 0.5 f 4.5 0.22 & 12 0.05 z t 8.6

COMPARISON WITH T H E RESULTS OF CHISHOLM

Using the data of Benjamin and Miller, Chisholm (4) correlated the parameters

x WL, and -- W L N 1 WL CL 1 --x WVN

Vol180 Pt I No 23

rt 4.2 & 10.5 f: 4.4

0.5

0.05 400

~

It is seen that variation in x, increases to f20 per cent as values of x decrease from 1.0 to 0.2, and remains Proc Instn Mech E m s 1965-66 by guest on October 12, 2015pme.sagepub.comDownloaded from

METERING OF STEAM-WATER TWO-PHASE FLOW BY SHARP-EDGED ORIFICES 557

~ I 1 I l i t

0.0001 0.001 0.01 0.1 ORIFICE DRYNESS, X,

1.0

Fig. 5. Correlation of x and x, from Fig. 2

where W,, is the liquid weight flow rate during single- phase flow with unit contraction coefficient and two-phase pressure drop, WL the liquid weight flow rate during two- phase flow, C, the liquid contraction coefficient, and W,, the vapour weight flow during single-phase flow with unit contraction coefficient and two-phase pressure drop. These parameters gave a linear relationship when plotted on log-log paper, with a mean curve through the data represented by the equation

This equation agreed with the data of Benjamin and Proc Instn Mech Engrs 1965-66

*

Miller within f10 per cent. Test results from the present work are plotted using the above parameters in Fig. 11, where it is seen that marked divergence from Chisholm's curve occurs for the larger orifice and a lesser divergence for the smaller. This is pre- sumably due to the larger beta values used as it seems probable that agreement with Chisholm's curve would be attained for beta values less than 0.2; the largest beta value used in the tests of Benjamin and Miller was 0.147. The best agreement between the present results and Chisholm's curve is where the values of x exceed 0.15 and 0.20 for orifice beta sizes 0,707 and 0.837 respectively.

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558

I I I

0.0001 0.001 0.01 ORIFICE DRYNESS, x ,

Fig. 7. Correlation of x and x, f m m Fig. 4 Proc Instn Mech Engrs 1965-66

0.1 1.0

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METERING OF STEAM-WATER TWO-PHASE FLOW BY SHARP-EDGED ORIFICES 559

1o.c

_ . 0.0001 0.001 0 0 1 0.1

O R l F l C E DRYNESS, x ,

Fig. 8. Correlation of x and x, from Table 2

1 .o

COMPARISON WITH THE RESULTS OF MURDOCK

The data used by Murdock (3) were derived from two sources :

(1) The nine steam-water results at 580 lb/in2 abs. were obtained by the U.S. National Boiler and Turbine Laboratory.

(2) The Osborne field and laboratory results were conducted on air-water, gas-distillate, gas-water, and gas-salt water.

Murdock correlated the results by plotting the parameters d K P z P , and d A P J A P ,

where APT, is the pressure drop across the orifice for the two-phase mixture flowing; AP, is computed as if the gas phase alone was flowing through the meter; and APL is computed as if the liquid phase alone was flowing through the meter. The method of least squares was used to fit the data to a linear equation which was found to be:

~ /% = 1.26 /A+l A P, . . (4)

This equation is plotted as ‘Murdock’s curve’ in Figs 12 and 13. Proc Instn Mech Engrs 1965-66

As the present work is only concerned with the flow of steam-water mixtures, the only test results given by Mur- dock shown in Fig. 13 are the nine results of the N.B.T.L. which were all conducted at approximately 580 lb/in2 abs. and were at dryness fractions not less than 0-8 (stagnation enthalpies greater than 1050 Btu/lb). Although Murdock’s curve gave a good fit for all his experimental data, the few steam-water results showed a trend. This was noted by Murdock who wrote that ‘although there is some slight indication of an upward trend in the steam-water tests, all data lie well within limits and it is the considered opinion of the author that this is due to experimental difficulties inherent in steam testing’.

In his conclusions, Murdock recommended that additional work be performed in the following areas :

(1) For beta ratios greater than 0.5. (2) At higher values of $/PI to permit use of Y

below 0.98.

Although the present work was conducted before Murdock‘s paper was available, it fortuitously followed these recommendations utilizing beta ratios of 0,707 and 0.837 for values of Y down to 0.82.

I n order to plot some of the present results using Val I80 Pt I No 23 by guest on October 12, 2015pme.sagepub.comDownloaded from

560 RUSSELL JAMES

10.0

1 0

m a W z F n. n v) 3 0 Ld z 111 0 0 2 0 * 0.1

0.01 0*0001 0 001 0.0 1 0 .I 1.0

ORIFICE DRYNESS, x ,

Fig. 9. Correlation of x and x, from Table 1

Murdock’s parameters, it was decided to take values at constant stagnation enthalpy from Fig. 2, a few from the experimental range and some from the extrapolated region of high pressure; this should make apparent any trends. Values of stagnation enthalpy taken were 300, 450, 600 and 800 Btu/lb and were plotted in Fig. 12. It is seen that in all cases, the constant enthalpy curves cross Murdock’s curve providing agreement at these intersections. Fairly good agreement was obtained only for the low stagnation enthalpy value of 300 Btu/lb (at pressures greater than 70 lb/in2 abs.). At the low pressure ends of the enthalpy curves, the effect of compressibility becomes pronounced from the test results derived from Fig. 2.

to calculate and plot the extension of the enthalpy curves into the low pressure region for negligible compressibility; when this is done the curve of 300 Btu/lb gives fair agreement over its whole range. Aside from this, however, Murdock’s curve cannot be said to give accurate results for steam-water mixtures except where the constant enthalpy curves fortuitously cross his curve. A possibility, however, is that agreement would be attained for high enthalpies and high pressures as for the N.B.T.L. results. Although the present work does not cover these ranges (of high pressure andenthalpy),

It is possible (assuming x, =

Proc Instn Mech Engrs 1965-66

it is worth while predicting such conditions using the relationship x, = From Appendix I

. ( 5 )

and

These values are given where compressibility effects are negligible and where YTp 21 Y,.

Taking a pressure of 580 lb/in2 abs. at the upstream manometer tapping as for the nine results of the N.B.T.L., the above parameters are calculated for various stagnation enthalpies and the results plotted in Fig. 13. It is seen that the curve drawn through these values gives good agree- ment with the N.B.T.L. values and even verifies the slight upward trend already noted. Over the limits of Fig. 13 good agreement with LWurdock’s curve is obtained. Calculations show, however, that outside this range the line through the calculated points crosses Murdock’s curve and passes to the right. A similar curve calculated for a pressure of 800 lb/in2 abs. shows good agreement at high enthalpies and a falling off to the right at enthalpies less than 850 Btu/lb.

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METERING OF STEAM-WATER TWO-PHASE FLOW BY SHARP-EDGED ORIFICES 56 1

1.0

0.01

0.001 0~0001 0.001 0.01 0.1 1.0

ORIFICE DRYNESS, Y,

Fig. 10. Correlation of x and x,

Curves drawn through points calculated at pressures of 200 and 50 lbiin2 abs. are shown for comparison pur- poses and it is seen that the lower the pressure, the greater the divergence from Murdock’s curve. Apparently, there- fore, Murdock’s curve is valid for high pressures and high enthalpies at one extreme, and for low enthalpies and low pressures at the other, together with the fact that curves of constant enthalpy fortuitously cross his curve at some point. This is liable to complicate the efforts of workers trying to fit their test data to his correlation as they are likely to obtain results of greatly varying accuracy. Where compressibility effects operate, greater divergence from Murdock‘s curve can be expected.

DETERMINATION OF FLOW AND ENTHALPY The formula for the flow of a single-phase fluid through a metering orifice is given by reference (9) as :

Adapting this formula for flow through a 5.591-in dia- meter orifice in a 7.9411 internal diameter pipe where the differential pressure across the orifice is given as mmHg

under water, and taking the value of the discharge coeffi- cient C as 0.61 (Appendix I),

W = 5530Y d4Sp1 . . . (8) For the 6.615411 diameter orifice in a 7.9411 internal diameter pipe,

The expansion factor, Y, equals 1 for the flow of liquids; for the flow of compressible fluids, from reference (9),

W = 9580Y 46 . . . (9)

Chisholm used a simplified version of equation (10) in his paper, applying it to steam-water flow through sharp- edged orifices where /3 < 0-147; it is also recommended for the present work where ,kl values are 0.707 and 0.837. It is recognized that this value of Y applies strictly only to single-phase flow through nozzles and venturis; how- ever, it was found to give a slightly better correlation (for Fig. 10) than the usual equation for Y applied to sharp- edged orifices. I t is unnecessary to calculate Y in equation (10) as graphical solutions are available (8) (9) for different values of y. Fig. 14 gives such a graphical solution for

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562 RUSSELL JAMES

steam-water mixtures only, where y is taken equal to 1.3 Therefore, (Appendix I). 1 54*3dm2 YTp

across an orifice is measured in mmHg under water, equation (7) becomes :

J- ~

-- Gh01'102 pco.96 - 11 400 . .

+TP For the case where the manometer pressure differential W = v'1-/34 x1 "(V,- V,)+ v,

For the critical flow of a steam-water mixture of stagnation enthalpy, ho, discharging to an ambient pressure less than the critical discharge pressure, P,, the following relation- ship was given (7):

154.3~l,,,~ Y 1- - 359 x 0*61dm2 Y

W - 25.4 - .j//1_p4 'G - (12)

J(1-/34) (-1 Where steam-water mixtures pass through an orifice, from equations (1) and (2) If the internal diameter of the discharge pipe is d,, then

- 1 224 OOOPco'86dc2 . . (13) hD1.102

w = - 1 p1 = ~ 1 . 5 ~ ~ + ( 1 - - ~ 1 9 ~ ~ ~5(v , - v,)+ v,

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METERING OF STEAM-WATER TWO-PHASE FLOW BY SHARP-EDGED ORIFICES 563

5

4

3

2

1

I / I rIGURES BESIDE TEST POINTS REPRESENT PRESSURE (lb/in2 abs.)

EXTRAPOLATED RESULTS FROM FIG.2 I

-_ -

0 2 3

J q - G Fig. 12. Comparison of experimental resuZrs of Fig. 2 with Murdock's curve

Equating equations (11) and (13) for steam-water mix- tures passing through an orifice and then attaining critical flow at the discharge pipe exit:

. . * (14) The homogeneous dryness fraction, x, is obtained at the upstream manometer tapping and is associated with the pressure PI at that tapping and with the local enthalpy. There is, however, little difference between the stagnation enthalpy, ho, and the local enthalpy at the manometer tapping, Stagnation enthalpy, h,, and homogeneous dryness fraction, x, can therefore be approximately related at pressure P1 as f r o c Instn Mech Engrs 1965-66

ho = (h,+xL) and x = - (h"Lk:) Therefore,

This equation applies for apparatus where critical flow is attained at the discharge pipe outlet, as shown in Fig. 2. Under the conditions prevailing at the orifice and dis- charge pipe, all the factors in equation (15) are known except the stagnation enthalpy, ho. Solving ho entails a

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564

1.5

1.4

1.3

1.1

RUSSELL JAMES

108

1.0

3 4 /*PG

Fig, 13. Constant pressure curves for steam-wuter Jlow at negligible compressibility (calculated from x, =

simple trial-and-error procedure; h, is then used in equa- tion (13) to calculate W. Example problems given in Appendix I1 will make this clear.

region of large flows. The cause of this phenomenon is probably that it is due to the specific zonal conditions operating in this region-a promising area for future research.

c . n - T n r T T c T n x T e b W l Y LL u a I W l I J

Conventional formulae for the metering of single-phase flow through sharp-edged orifices may be used to calculate the flow rate for steam-water mixtures if the dryness fraction x used in calculating the homogeneous density is amended to a value x, where:

This is not a precise relationship, particularly over the range x = 0.1 to x = 0.2 where the value of x, appears to show some dependence on flow rate in the low flow region and to become relatively independent only in the Proc Instn Mech Engrs 1965-66

x, = x1.5

For the case of a steam-water mixture which attains critical flow at the end of a pipe, it is possible to determine both the flow rate and the stagnation enthalpy using an orifice in series with a critical pressure tapping. This method is already in use in the geothermal steam fields and has successfully been used in the testing of a number of boreholes.

ACKNOWLEDGEMENT The author wishes to thank Mr Frank Scarf and Mr Tom Somerville for their collaboration during the present work.

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METERING OF STEAM-WATER TWO-PHASE FLOW BY SHARP-EDGED ORIFICES 565

0.72 0

1 . o

0.9

yTP

0 - 8

I I I I I 1 5 10 15 20

Value of y = 1.3 IF the steam tables are used to plot pressure against specific volume for dry saturated steam, the relationship over a pressure range from 4 to 600 Ib/in2 abs. is found to be PY1'058 = 470. These are, of course, under conditions of pressure-temperature equilibrium.

For the case of the adiabatic expansion of dry saturated steam through nozzles, orifices, etc., the index is usually taken as equal to the isentropic value of 1.3 for purposes of calculation because the expansion is so rapid that such equilibrium conditions Cannot be sustained. This leads to the well-known phenomenon of supersaturation.

In the case of a steam-water mixture flowing through a sharp- edged orifice to a region of lower pressure, the time taken to pass the plate is too short to permit water to flash into steam and accordingly the mass of eachphase remains substantially constant- the steam alone increasing in volume in a manner comparable to the expansion of dry saturated steam. The lower the downstream

Proc Instn Mech Engi-s 1965-66

pressure with the greater tendency for the water to flash, the greater the mixture velocity with less time available for flashing. The flow may therefore be considered as metastable with isentropic expan- sion and y = 1.3.

Derivation of Murdock's parameters For the flow of a steam-water mixture through an orifice, let

-- WTF =KYTP ' ~ # T P P T P * - . (18)

where K is a constant for the meter used and includes a value of

For the flow of the steam fraction only through the same orifice, C = 0.61.

Wg =KY,l/&i . . . . (19) If compressibility is negligible, then YTP N Y, N 1. Dividing equation (18) by equation (19),

For steam-water flow through orifices] VTp = x,V,+(l -x,)Vf. From equation (2), x, N x ' ' ~ . Then

For the flow of the water fraction only through the orifice,

W, = K \'$;; . . . . . (21)

Dividing equation (21) by equation (19),

Substituting (1 - x ) / x = W,,W, and exchanging densities for specific volumes :

(22)

Equations (20) and (22) may be used under conditions of negligible compressibility (where dJT,100/55.8P1 < 2 per cent) for calculating Murdock's parameters

and

APPENDIX I1

Example 1 A 5-591-in sharp-edged orifice mounted in a 7.9-in diameter main and equipped with radius (D and &D) taps is used to meter a steam-water mixture which afterwards passes through a 6.06-h diameter pipe to the atmosphere; critical flow occurs at the dis- charge face where the pressure is 243 lb/in2 abs. Pressure dif- ferential across the orifice is 580 mmHg under water; pressure at the upstream manometer tapping is 100 lb/inZ abs. Determine both the flow rate and the total specific energy (i.e. stagnation enthalpy) of the mixture. P, = 24.5 Ib/in2 abs. d, = 6.06 in

PI = 100 Ib/in2 abs. V, = 4.45 ft:'/lb

d,,, = 5.591 in Vr = 0.0177 ft3/lb h, = 298.3 Btu/lb D = 7.9 in

c $ ~ ~ = 580 mmHg under water L = 889.8 Btujlb 5591 f12 = (m) = 0.5

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566 RUSSELL JAMES

Differential pressure as percentage of orifice pressure = &loo/ 55.8P1 where 1 lb/in2 abs. = 55.8 mmHg under water

From Fig. 14, YTp = 0.915. From equation (15),

h01.102 = 1450- 24.5°’96 ( - 6.06 ) z dr(T7 - 0,915 5591

Simplifying,

A trial-and-error solution gives ho = 456 Btu/lb. From equation (13),

224 000 24.5°’90 6.06’ = 209 5oo l ~ , h W = 4561.102

Actual values taken from Fig. 2; h, = 450 and W = 213 000.

Determination of flow only In example 1, both the flow rate and stagnation enthalpy were unknown. For the case where the stagnation enthalpy is known- or alternatively the value of dryness fraction at a given pressure- a direct solution of flow rate is possible.

Example 2 A steam-water mixture containing 31 per cent steam at the up- stream manometer tapping pressure of 150 lb/in2 abs., flows through a 6,615411 diameter sharp-edged orifice equipped with radius (D and 40) taps. The main pipe is 7.9 in diameter and the differential pressure on the manometer is 290 mmHg under water. Determine the total flow in Ib per hour. d,,, = 6.615 in diameter D = 7.9 in diameter

P I = 150 Ib/in2 abs. V, = 3.02 ft3/lb

4Tp = 290 mmHg under water V; = 0.0181 ft3/lb

Differential pressure as percentage of orifice pressure = &,-,lOO/ 55+3P1 where 1 lb/in2 abs. = 55.8 mmHg under water.

From Fig. 14,

From equation (2), YTP = 0.962

x, N x1.5

xm = 0.311’5 = 0.172 Therefore from equation (Il),

290 d0~172(3~02-0~0~81) +0.0181

W = 212 500 lb/h.

APPENDIX I11

REFERENCES

(I) BANWELL, C. J, ‘Flow sampling and discharge measurement in geothermal bores’, Trans. Am. SOC. mech. Engrs 1957 79, 269.

‘Estimation of dryness fraction and mass discharge of geothermal bores’, Proc. Instn mech. Engrs 1957 171, 967.

(3) MURDOCK, J. W. ‘Two-phase flow measurement with orifices’, Trans. Am. SOC. mech. Engrs (J . Basic Engng) 1962 84 (Scries D), 419.

(4) CHISHOLM, D. ‘Flow of steam-water mixtures through sharp-edged orifices’, Engng Boiler House Rev. 1958 73 (No. 8), 252.

‘Flow of saturated water through throttling orifices’, Trans. Am. SOC. mech. Engrs 1941 63, 419.

(6) MONROE, E. S. ‘Flow of saturated boiler water through knife-edged orifices in series’, Trans. Am. SOC. mech. Engrs 1956 78, 37’3.

(7) JAMES, R. ‘Steam-water critical flow through pipes’, Proc. Instn mech Engrs 1962 176 (No. 26), 741.

(8) British Standard Code B.S. 1042: 1964. (9) PERRY, J. H.

(2) BELIN, R. E. and BAINBRIDGE, A. E.

(5) BENJAMIN, M. W. and MILLER, J. G.

Chemical Engineers Handbook (Fourth edition) 1963 (McGraw Hill, New York).

(10) ISBIN, H. S., SHER, N. C. and EDDY, K. C. ‘Void fractions in two-phase steam-water flow’,J. Am. Inst. chem. Engrs 1957 3 (No. 1, March)2 136.

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567

Communications Dr D. Chisholm, B.Sc. (Associate Member)-This paper is on a subject which is becoming of increasing interest (11) and importance to the engineer. The author’s method of correlating his data using a ‘corrected’ dryness fraction has proved very effective, and is also convenient for com- putational work. However, in the absence of some better understanding of these relationships it would appear in- advisable to use equation (2) outside the range of conditions covered by the author’s tests. The extrapolation of the curves in Figs 2 and 3 requires some substantiation.

The author’s use of an orifice, in conjunction with the critical flow condition at exit from a pipe, to determine both the mixture mass flow and its dryness fraction is, as far as I am aware, the first demonstration of a form of technique which will have increasing industrial use in the future.

In Fig. 11 the author plotted his data using parameters developed previously by myself, and, following my original paper, the single-phase liquid flow ( WLN) has been evaluated neglecting the kinetic energy upstream of the orifice. The vaIues of in the tests previously analysed by the writer were such that the upstream kinetic energy

J 0.1 1 .o 10 100

1‘ ( W L N / wVN)

Fig. 15. Plot of experimental data using correlating groups from reference (4), allowing for upstream kinetic energy

Proc Instn Mech Engrs 196566

could be neglected but this is not the case in the author’s tests. The writer has replotted Fig. 11 taking account of this kinetic energy effect (W,, in Fig. 11 has been divided by (1 -p4)0’5)); this is shown in Fig. 15. It can be seen that the author’s data tend to lie about the line given by the equation

or

where W,, is the single-phase liquid flow rate correspond- ing to the two-phase pressure drop and C, is taken as 0.61. This compares with

which is the theoretical equation obtained (12) if one assumes metastable flow and no work done by one phase on the other. The coefficient of 1-1 above agrees closely with the value of 1.082 obtained by Bizon (13) with a /’3 value of 0.7 and steam-water mixtures at pressures in the region 1050-1350 Ib/in2 gauge.

It is perhaps of interest to draw attention to the rela- tionships between the parameters used in Figs 11 and 13. From equations (18), (21) and the equation

WLS = K(41.PPL)o’5

it can be shown, if negligible compressibility is assumed, that

and

Thus the horizontal ordinate in Fig. 13 is the reciprocal of that in Fig. 11; the vertical ordinates are similarly simply related. It might be expected, therefore, that plotting data as in Fig. 11 should also show the trend with pressure

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568 COMMUNICATIONS

obtained in Fig. 13; I have not observed (12) this, as yet. It can, however, be shown that the coefficient 1.1 above, becomes unity at the critical pressure.

REFERENCES

(11) ‘Metering of two-phase mixtures: Report of a meeting at NEL, 6th January 1965’, NEL Report No. 217, 1966 (National Engineering Laboratory, East Kilbride, Glasgow).

(12) CHISHOLM. D. and WATSON. G. G. ‘The flow of steam- , , water mixtures through sharp-edged orifices’, NEL Report No. 213, 1966 (National Engineering Laboratory, East Kilbride, Glasgow), also in Symposium on two-phase flow, University of Exeter, 21st-23rdJune 1965, Vol. 11, G201-222 (to be published) (University of Exeter).

‘Two-phase flow measurement with sharp-edged orifices and venturis’, Atomic Energy of Canada Ltd, Chalk River, Ontario, June 1965, AECL-2273.

Ing. G. Fernandez de la Garza (Mexicali, Mexico)- The empirical work of this paper leads to some results that have proved of great help in the measurement of steam wells.

They have been used successfully in the Cerro Prieto Steam Field, in the vicinity of the city of Mexicali, with wells somewhat larger than those in which the tests were conducted by Mr James, and with bigger diameters (15.00-in inner diameter for the pipes where the orifice was located and ll.00-in inner diameter for the pipe with the critical pressure tapping, instead of 7.9 in and 6.06 in, respectively).

The enthalpy measured by this method correlates very well with that obtained with downhole pressure and temperature measurements, and that is why it is assumed that Mr James’s method is still useful for bigger flows in bigger diameters.

Unfortunately it has not been possible to verify these results with separate measurements of steam and water flows yet; and it is intended to reproduce in the near future the actual conditions with measured quantities of steam and water and measure the resulting mixture by this method; and then it is expected to verify Mr James’s assumptions with still larger flows.

Professor J. W. Murdock (Philadelphia, Pennsylvania) -In his presentation of the experimental results of steam- water two-phase flow measurement the author has covered a wider range than has thus far appeared in the literature. The final result of Mr James’s empirical analysis will appeal to the working engineer because of the ease and simplicity of flow computation compared with present methods. I t is therefore important to subject this work to critical review and analysis so that both practising en- gineers and future researchers in this area will have a realistic appraisal as to the validity of Mr James’s analysis and resulting equations.

In prescribing orifices for accurate measurement of two-phase flow, serious consideration cannot be given to orifices that are not acceptable for single-phase flow measurement. Unfortunately, this eliminates all of the data on the f l = 0.837 orifice. Present American practice Proc Instn Mech Engrs 196.7-66

(13) BIZON, E.

(14) for orifices with 1D and l/2D taps limits the maximum ratio of orifice to pipe diameter to a value of 0.80 and prescribes that the optimum ratio be within 0.20 to 0.70. This places the p = 0-707 ratio orifice slightly above the optimum but still within acceptable limits.

Of the five tests described in this paper, only two, test 1 and test 4, are concerned with the = 0.707 orifice. The results of test 1, unfortunately, are only presented in graphical form as Fig. 2; those of test 4 are given in Table 1. Any analysis must be limited to the data given in Table 1, as it is impossible to obtain data from plots on log-log paper (Fig. 2) with any degree of precision.

Analysis of the tabulated data indicates that the single- phase steam run (No. 26) has a coefficient of discharge of 0.58 compared with the value of 0.61 given by the A.S.M.E. Fluid Meters Research Committee (I& a difference of about 5 per cent. The allowable tolerance for this orifice, however, is only 0.5 per cent when acting as a single- phase flow meter (run No. 26), resulting in one order of magnitude greater than that which could be considered acceptable. On the other hand, as the two-phase flow approaches the liquid phase (run No. 1) ( x = 0-062), the coefficient, when calculated using Mr James’s method, approaches 0.61. Since this is the region where Mr James’s correlation has the greatest scatter, serious questions can be raised as to the fundamental experimental accuracy.

In Fig. 14, values of the expansion factor YTp for two- phase flow are presented. The proposed YTp is the adia- batic expansion factor. Investigation (15) has verified that the orifice expansion factor is valid for single-phase steam flow. The validity of Fig. 14 can be questioned on two points, (1) only one acceptable orifice ratio could be used in its preparation, yet it covers all ranges of ratios, and (2) as the two-phase flow approaches single-phase steam, a discontinuity must take place since the orifice expansion factor has a different numerical value than the adiabatic one, a phenomenon that is neither indicated by Mr James’s experimental results, nor has been observed by myself.

This paper devotes a considerable amount of space to the comparison of the empirical x = x , , , ~ . ~ method versus the rational

(APT,/APG)1i2 to ( A P J L I P ~ ) ~ I ~

analysis. Since the rational analysis is currently used for all types of two-phase flow phenomena, Mr James’s comparisons were examined in considerable detail. Extrapolation of several orders of magnitude by calcula- tions based on an empirical relationship are more in the nature of speculation than proof. Until such time as actual data in the extrapolated regions are available, these comparisons could be misleading.

With the information presented in this paper, only an estimate of precision can be obtained. Information regard- ing size of the single-phase orifices of Fig. 1 is needed, together with the actual test data obtained, before the accuracy of the method can be evaluated,

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METERING OF STEAM-WATER 1WO-PHASE FLOW BY SHARP-EDGED ORIFICES 569

I n summary, it is not believed that Mr James has experimentally demonstrated that the (OPTp/APc)'~2 versus (APL/~PG)l ' z relationship cannot be used for correlation purposes, nor has he sufficient justification for the use of the adiabatic expansion factor (Fig. 14) to be applied to two-phase flow orifice computations. Engineers using the x = xm1.5 relationship should do so with the understanding that errors in total flow rate in the order of 12 per cent or higher may result, as these variations were observed during the tests (Table 3).

The opinions and assertions given in this contribu- tion are the private ones of the contributor and are not to be construed as official or reflecting the views of the (U.S.) Navy Department or the Naval Establishment at Large.

REFERENCES

(14) 'Fluid meters-their theory and application', Report of the A.S.M.E. Research Committee on Fluid Meters, 5th edition 1959 (American Society of Mechanical Engineers, New York).

(15) MURDOCK, J. W. and FOLTZ, C. J. 'Experimental evaluation of expansion factors for steam', Trans. Am. SOC. mech. Engrs 1953 75, 953.

Dr D. J. Ryley, M.Sc. (Eng.) (Member)-I propose to confine my remarks to discussing the 'kinks' which the author has observed in the parameters plotted in Figs 3 and 4 and I wish to take up the suggestion that these may be due to local zonal charges in the fluid flow occasioned by the use of a larger diameter orifice.

I think it more likely that the kinks result from a change- over in the flow regime between two of the types enumera- ted in the author's introduction. There is no existing flow regime diagram which is entirely satisfactory, but it is generally conceded that the best available is that due to Baker (16). Accordingly I have made a plot on the diagram in Fig. 16 of the curves for h, = 450 and 500 Btu/lb from Fig. 3 and h, = 450 Btu/lb from Fig. 4. In each case the placing on the diagram is evaluated for the highest and lowest pressure readings on the respective trend curves together with the reading a t which the kink has its origin on the main curve. Each locus displayed on the Baker diagram reads in alphabetical order from the lower to the higher pressure, the middle letter denoting the kink point.

It will be observed that in each case the flow pattern appears to change from a condition of principally annular flow at the upper pressure to mist flow at the lower pres- sure. Nevertheless, the points C , G and L are only mar- ginally within the annular flow regime as defined by Baker. If the experimental kink points B, F, K are as accurately known as appears to be the case from Figs 3 and 4 then it may well be that the dotted flow boundary (annular-mist) should be placed rather higher on the Baker diagram than the position suggested by the ori- ginator. An additional point of interest lies in the fact that, so far as I know, there are no other data for anything like so large a pipe as 8-in diameter.

It is not possible meaningfully to make a corresponding Proc Instn Mech Engrs 1965-66

where pc and p F are in lb/ft3; v = surface tension, dyn/cm; p = liquidviscosity, cP; G = vapour flow rate, lb/ftz h; L = liquid flow rate, lb/ft2 h.

Fig. 3, h, = 450 Btullb. A Fig. 3, h, = 500 Btu/lb. o Fig. 4, h, = 450 Btu/lb.

Fig. 16. Baker flow pattern diagram

plot of these loci on the Kozlov (17) diagram, In the first place this diagram does not distinguish between the annular flow and the mist flow regimes and in the second place the diagram requires the calculation of the volu- metric flow dryness fraction for ordinate. Since the slip is unknown this quantity cannot be found. The Baker diagram avoids this difficulty since it is based on the mass flow dryness fraction.

If the above explanation is correct, the question arises as to why kink points are not found on some of the other curves. I suggest that the author may find it of interest to work backwards from the Baker diagram to see whether any predicted deviations can be experimentally verified.

It also remains to be explained why the regime change is betrayed by a change in the manometer differential. I have spent a considerable time in an unsuccessful attempt to analyse this effect on the supposition that the momen- tum balance within a section enclosing the orifice under- goes a change with the flow type. Thus, in annular flow there would be an enhanced momentum loss upon the orifice annulus with a corresponding momentum adjust- ment in the opening revealing itself by a downstream pressure change. It was not, however, possible to envisage with confidence the adjustments occurring in the slip a t regime changeover, and hence to apply equivalent filament theory (IS). It was, however, possible to see, in a general way, that with a greater degree of liquid dispersion more liquid would pass entrained through the orifice and less liquid would be deposited on the orifice annulus subse- quently to creep through unentrained. To accelerate the greater weight of dispersed liquid an enhanced pressure drop across the orifice would be necessary, hence the sudden manometer change exhibited.

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570 COMMUNICATIONS

All the foregoing assumes that the flow is fully developed upstream of the orifice, which presupposes a long length of straight pipe. It is known, however, that disturbances in two-phase flow persist a long time and it may well be that effects from valves B and C and the T-junction are still operative at the orifice.

R E F E R E N C E S

(16) BAKER, 0.

(17) KOZLOV, B. K.

‘Simultaneous flow of oil and gas’, Oil Gas J . 1954 53 (No. 12, 26th July), 185.

‘Types of gas-liquid mixtures and stability boundaries in vertical tubes’, Zuhr. Tech. Fiz. 1952 24 (No. 4), 656.

‘Property definition in equilibrium wet steam’, Int. J. mech. Sci. 1964 6, 445.

(IS) RYLEY, D. J.

Mr B. Wood, M.A. (Member)-Mr Russell James has with single-minded persistence pursued the rather obdur- ate subject of metering of two-phase flows in steam. He mentions that the ‘theoretical’ approach gave rise to errors as high as 100 per cent. He refers possibly to the early days in New Zealand (1953) when, for want of any- thing better, elementary theory was employed to try to settle the order of discharges to be expected. Well dis- charges have been encountered elsewhere in excess of what could be accounted for by ‘sonic’ flow on homo- geneous theory. The validity of the simple sonic flow concept in two-phase media derived from density and compressiblity is now doubted, as sonic velocity in moderately wet steam has been found to be that in the vapour phase. In the 12 year interval the path has been trodden by many workers and theory has been improved by allowing for slip and supersaturation.

Mr James has taken consistently the other course of frank reliance on empiricism without theoretical guidance even as to the form of the results. It may be as well to point out that empiricism also has its weaknesses which

may render the results inaccurate, however carefully the tests are done. The obvious flaw in the present method is that cooling of the water is necessary to suppress flashing at the water orifice and this implies that the steam and water when re-united are not in equilibrium. Anyone con- cerned with wet steam problems learns to distrust synthe- tic mixtures. It is proper to doubt the measurements of the mixed flow through the orifice and also at the discharge from the pipe end, since these apply to mixtures in un- known state. The state will depend on the length of pipe before and after valve D and possibly on scale and other uncontrolled features of the test installation. They there- fore cannot be applied with any security to discharges of natural flashing mixtures nor to synthetic mixtures in another pipe arrangement or on another scale. It is pos- sible that the discrepancies with results from other workers and internal discrepancies within Mr James’s own results can be explained in this way.

It is surprising to read that the arrangement described is a ‘simple and inexpensive metering system’. In my opinion it suffers severely from the cumbrousness and cost of the cooling equipment for the water, since in places where it is applied there is usually no adequate cooling source and if there were then calorimetric methods could be applied with less difficulty. Accordingly there is still a pressing need for some more convenient method to give both enthalpy and mass flow. Admittedly the ray absorp- tion methods suggested by myself in 1953 and applied several years later in New Zealand used in conjunction with critical discharge can do this but the ray method as applied did not appear to be capable of sufficient accuracy because when the rays have to penetrate a steel pipe their absorption in the mass of fluid was not sufficiently great. A fairly simple way of avoiding this difficulty seems to be to use for the measuring section, which is not at high pressure, a thin wall pipe of some less dense material, e.g. fibre glass.

Author’s Reply Mr R. James-The re-plotting of Fig. 11 by Dr Chisholm was studied with interest and appeared to confirm the general consistency of the test results; a few reciprocal values from Fig. 13 were plotted on his new figure but the spread due to pressure effects was not great owing to transference from a linear scale.

Professor Murdock wishes to reject the results for beta ratios greater than 0.707 based upon the rules of single- phase flow-which would remove the figures with kinks- and then suggests that extrapolation of the remaining results is only speculation. As the remaining results are mainly shown in Fig. 2, interpolation between the pre- Proc Instn Mech E q r s 1965-66

cisely calculable single-phase points and the lines of the experimental points is surely more than speculation without in any way making claims of positive proof. Besides, predictions based on the results of both orifices give good agreement with the N.B.T.L. results, although well outside the pressure and quality range of the present work. Also, recent application of the overall correlation to the case of carry-over moisture in steam lines and its effect on manometer differentials as given in British Stan- dard 3812: 1964 gives good agreement for values of low moisture content.

It seems unreasonable to lay down criteria regarding Vd I80 Pt I NO 23 by guest on October 12, 2015pme.sagepub.comDownloaded from

METERING O F STEAM-WATER TWO-PHASE FLOW BY SHARP-EDGED ORIFICES 571

I~ 1 1 1 1 ' ' 1 I l l 0 AND h D MANOMETER TAPS

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the applicability of the orifice expansion coefficient for steam-water flow based upon its preferential use for single-phase flow, particularly in the present state of knowledge. The suggested discontinuity in the adiabatic expansion coefficient when steam-water flow changes to steam flow may be gradual at high dryness and is unlikely to have been observed considering the meagre test data existing.

Accuracy is always a problem in the study of two-phase flow with its pulsations, discontinuities and difficulties in obtaining clean-cut relationships.

Professor Murdock in his own paper, reference (3), referred to the 'experimental difficulties inherent in steam testing' which he uses to explain a trend away from his own correlation. This trend is, however, predictable by the present work and it would appear that Professor Murdock's experimental procedure is better than he thinks.

What is needed at the present time is not so much accuracy as statistics, in order that the overall picture can be outlined. The areas in which particularly accurate studies are needed will then become obvious. It is hoped

I I 1

that the present work will assist in providing such a skeleton outline.

With the limited evidence available, it seems likely that recommending beta ratios not greater than 0.7 may eliminate the kinks mentioned, the avoidance of which may be of positive benefit to Seiior Fernandez de la Garza whose intended testing of steam-water mixtures through orifices in pipes as large as 15 in diameter is anticipated with keen interest.

Dr Ryley's attitude may be different, however, with his concentration on such kinks and he may argue that their study must lead to a better understanding of zonal changes in two-phase flow. Although I have used the Baker chart in the study of steam-water flow through horizontal pipes, it has always ended with a circular argu- ment such as that arrived at by Dr Ryley, namely that the chart is initially used to delineate the zonal boundaries under study without usually getting a sharp distinction and one finally ends up by considering the use of the test data for correcting the boundaries of the chart! I should be both pleased and disappointed to find that the kinks were due to some aspect of the injection geometry; pleased that

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Fig. 17. Graph used to evaluate stagnation entha2py of steam-water mixtures Proc Instn Mech Engrs 1965-66 Vol180 Pt I No 23 by guest on October 12, 2015pme.sagepub.comDownloaded from

572 AUTHOR’S REPLY

the correlation would be improved if all the figures were similar to Fig. 2, and disappointed to know that the experi- mental set-up was unwittingly the cause of these anoma- lies. The tenuous evidence available does not support this view (of injection geometry dependence) and this may be inferred from a study of Figs 2 and 3. Almost identical mixture flows were supplied to both sizes of orifice at enthalpies 450 and 500 by the injection equipment but kinks in the plotted lines were only obtained for the larger orifice.

The persistence of a disturbance in the flow charac- teristics is also not likely to have been their source as the curves with kinks were first plotted from low pressure to high pressure and then the plotting was reversed back down to low pressure without modification in the spatial position of the kinks on the charts.

The evidence, therefore, favours zonal changes (i.e. flow regime changes) as the cause of the kinks and the test series was undertaken in the hope that local mixing a t the orifices tested would suppress such effects. It is not sur- prising that they have made their appearance when using the larger of the two orifices, as an attempt since then has been made to correlate x and x, using New Zealand pressure-drop test data for the horizontal flow of steam- water mixtures through 4- and 6-in diameter pipes, result- ing in a wider spread than that for orifices given in Fig. 14.

Mr Wood discusses ‘sonic’ flow concepts in two- phase media such as steam-water, but nobody has attempted to measure the speed of sound in such flowing mixtures. The term critical flow is generally used now, and the relationship between flow, enthalpy and critical pres- sure at discharge as determined previously, reference (7), is an integral part of the present paper. Recent work to be published has confirmed the validity of the above work and has extended the range of pipes tested down to 0.062 in inner diameter.

Although the water line was undercooled slightly by means of the cooling tank, flashing of this water always took place (at valve C) on injection into the lower pressure steam line; it is therefore considered that pressure- temperature equilibrium was attained at the test orifice and in the discharge pipe.

Fortunately, there was a by-pass at the cooling tank and a number of check tests were run at constant flow rate without cooling of the injection water; also a series of check tests at different wellhead pressures were run with

the whole, known, unseparated output of the borehole passing along the steam line and through the orifice-this was arranged by closing valves A and C. The results of these various checks were entirely consistent with those derived from separation of the phases with slight under- cooling of the injection water.

It is therefore considered that the causes of the ‘dis- trust of synthetic mixtures’ mentioned by Mr Wood (and due to metastability and flow regime variability) have largely been avoided.

Contrary to Mr Wood’s suggestion, there was no discrepancy between the 150 test results of the present work and the nine results of the National Boiler and Turbine Laboratory, U.S.A., which are the only other measurements of steam-water flow through sharp-edged orifices available; in fact there was good agreement.

The workers on the beta-ray method, reference (2),

did not pass their rays through the steel pipe, but fitted thin wall titanium or stainless steel ‘windows’ (0.003 in thick) diametrically opposed at the throat of a critical flow nozzle. As the pressures at the throat ranged up to 180 lb/in2 abs. the use of fibre glass would appear to be impracticable.

As Mr Wood mistakenly believes that cooling water would be required for the arrangement described in the paper, perhaps it should have been made clear that the only equipment necessary is as shown in Fig. 2 and that the separator and cooling tank were merely for purposes of calibration.

That the method is a ‘simple and inexpensive metering system’ is borne out by the actual use of a 4-in pipe com- plete with orifice assembly, valve and 3-in discharge pipe which were actually used to measure a small geothermal borehole situated some 90 miles away. Two technicians left Wairakei with the equipment to return the following day having determined the curves of mass flow and en- thalpy versus well-head pressure for an approximate total cost (including equipment) of about E30.

In order to simplify the calculation of enthalpy of such boreholes, an empirical chart has been derived from the test data of this paper and has proved of use in the rapid solution of steam-water mixtures as an alternative to the trial-and-error procedure adopted in Appendix 11. I t is here presented as Fig. 17; the value of the enthalpy so obtained is used in equation (13) to determine the flow rate.

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