Two-phase flow structure close to orifice contractions during horizontal intermittent flows

International Communications in Heat and Mass Transfer 33 (2006) 698 – 708 www.elsevier.com/locate/ichmt

Two-phase flow structure close to orifice contractions during horizontal intermittent flows☆ Marco Fossa, Giovanni Guglielmini ⁎, Annalisa Marchitto Diptem, University of Genoa, Via all'Opera Pia 15a, 16145 Genoa, Italy Available online 27 March 2006

Abstract Two-phase horizontal intermittent flow through orifice contractions is experimentally investigated by means of a new impedance meter able to collect void fraction data simultaneously at different pipe locations. The investigation focuses on twophase structure in the region downstream of orifice. Experiments were carried out on horizontal air–water flows in 40 mm inner diameter pipes. Six different orifice plates were considered, as combinations of two restriction ratios and three plate thicknesses. The results demonstrate that the orifices generally induce a marked increase in the downstream void fraction values, and that this is associated to a reduction in film thickness in the stratified regions. © 2006 Elsevier Ltd. All rights reserved. Keywords: Two-phase; Intermittent flow; Orifice contractions; Void fraction; Slug frequency

1. Introduction Information on the two-phase behaviour of flows through valves, orifices and other pipe fittings is important for the control and operation of such industrial plants as chemical reactors, power generation units, refrigeration apparatuses, oil wells and pipelines. While orifice plates are mainly used for single-phase and two-phase flow measurements, single orifices or arrays of orifices are also often used to enhance flow uniformity and mass distribution downstream of manifolds and distributors. Other applications regard the enhancement of heat-mass transfer in thermal and chemical processes (e.g. distillation trays). The proper design and control of such systems, in which pipe fittings that change the flow area (valves, orifices, nozzles) are inserted, need reliable predictive procedures to evaluate local pressure losses as well as upstream and downstream effects on the flow structure and phase distribution. While single-phase flows across singularities have been extensively studied [1], major uncertainties exist with regard to two-phase flows; indeed, few studies on this subject are available, and these often refer to a limited set of operating conditions. With particular reference to orifice plates, most correlations and models for pressure drop ☆

Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (G. Guglielmini).

0735-1933/$ - see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2006.02.009

M. Fossa et al. / International Communications in Heat and Mass Transfer 33 (2006) 698–708

699

Nomenclature d D De f h hmin HL s t VM Vs VSG VSL x XL z

Orifice restriction diameter Pipe diameter Electrode spacing Slug frequency Average liquid film height Minimum liquid film height Liquid hold-up Electrode width Orifice thickness Mixture velocity (= VSG + VSL) Slug liquid velocity Superficial gas velocity Superficial liquid velocity Distance from the orifice downstream edge Liquid volume fraction Distance from the phase mixer

Greek letters αs Average void fraction in the slug body αmax Void fraction at which the PDF goes to zero αst Low void fraction peak σ Area ratio (σ = (D / d)2) Δτi Residence time associated with ith slug Δτ¯ Average residence time

evaluation [2–4] are discussed by Friedel [5]. Other references are the early study by Janssen [6], the work by Lin on two-phase flow-meters [7], the recent experimental investigation by Saadawi et al., which refers to two-phase flows across orifices in large-diameter pipes [8], and the study on multiple-orifice plates by Kojasoy et al. [9]. Some aspects of two-phase flow in such singularities appear to need further insight [10]. In most studies, researchers have primarily been interested in determining pressure drop. The effects of sudden changes in area upon two-phase flow structure appear to have only been investigated as an incidental occurrence. This is especially true of the change in void fraction, which has been determined primarily for use in pressure drop correlations. Measurements of the void fraction and its distribution have been performed by Patrick and Swanson [11] on air–water systems in vertical flow through expansions and contractions of flow area. The void fraction variation downstream of the singularities affected a transition zone of a few diameters. For sudden area expansions, a marked increase in the downstream void fraction values was observed, while the void fraction variations were less pronounced for area restrictions. The development of radial distribution of the void fraction through sudden contractions has been investigated by Guglielmini et al. [12] for bubbly and slug air–water vertical flows. Arosio and Guilizzoni [13] examined the behaviour of an air–water mixture flowing horizontally through sudden area enlargements. They found that the cross-sectional void fraction downstream of the enlargements increased by up to 80% of the asymptotic value. The structure of gas–liquid flow in horizontal pipes with abrupt area contractions has been investigated by Bertola [14], who found that void fraction variations display an opposite behaviour to that observed in cases of sudden enlargement. In the present study, local void fraction distributions have been evaluated for sharp-edged orifices with area contraction ratios σ equal to 0.73 and 0.54 during horizontal intermittent flow of air and water. The effect of orifice thickness has been also considered, thin and thick orifices being tested according to Chisholm's classification [3]. Measurements were taken in the region close to the singularity and at distances from the pipe orifice in the range of 0.7–2.3 pipe diameters. The main flow parameters (instantaneous area average void fraction, time average void fraction, film height) were inferred by means of the impedance technique applied to a system of ring electrodes. This

700

M. Fossa et al. / International Communications in Heat and Mass Transfer 33 (2006) 698–708

newly arranged instrumentation allows simultaneous reading of several probes, at a scan rate of 1 ms, thus enabling the time–space phase distribution very close to the singularity to be reconstructed. 2. Experimental apparatus and procedures The experimental apparatus consists of a horizontal test section in which air and water can be mixed to generate twophase flow under bubble, stratified and intermittent flow regimes. The mixer consists of a T-junction with a horizontal baffle, in which a stratified-phase configuration is imposed (see [15] for details of the influence of injection mode). The test section is about 12 m long and allows pressure and void fraction measurements to be taken. This study refers to horizontal air–water flows in a 40 mm inner-diameter pipe. The operating conditions cover the VSG = 0.3–4.0 m/s and VSL = 0.6–3.0 m/s gas and liquid superficial velocity ranges, respectively (reference pressure 1.1–1.4 bar, as measured 5 m downstream of the phase mixer). Intermittent flows (plug, slug) were observed. A singularity (orifice) was inserted 6 m downstream of the phase mixer. The effect of orifice geometry was examined by selecting 6 different singularities produced by combining 2 different area contraction ratios (σ = 0.73 and σ = 0.54) and 3 different thicknesses, nominally t / d = 0.025 (or 0.027 or 0.05), 0.20 and 0.59, with d being the restriction diameter. According to Chisholm's criteria [3] a restriction of t / d = 0.59 can be classified as a “thick” orifice. 2.1. Void fraction measurements Measuring the electrical impedance of the gas–liquid or solid–liquid mixture is quite a common technique for studying the form and extension of the phase interface close to a system of electrodes. Many studies have been carried out on impedance void meters; impedance probes able to yield information on the area average void fraction have been used by Asali et al. [16], Andreussi et al. [17], Tsochatzidis et al. [18], and Costigan and Whalley [19]. The void fraction sensors used in this investigation consist of pairs of ring electrodes positioned on the internal wall of the cylindrical test duct, flush to the pipe surface (Fig. 1). The metering device is based on that described by Devia and Fossa [20], which supplies a 21 kHz a.c. signal to the measuring electrodes. At this frequency, measurements of both signal amplitude and phase shift demonstrated that the liquid (tap water) behaves as a resistive medium. The uncertainty of the metering system (95% confidence level) is 1.5% in the 100–2000 Ω range of impedance values. The present version of the impedance meter allows multi-channel measurements to be performed. Currently, the analog meter outputs are sent simultaneously to the acquisition system, which samples voltage signals at 1 kHz frequency. A preliminary multi-channel acquisition on a known sinusoidal signal revealed that the duration of the complete scan of 8 probes is 0.48 ms, due to a time shift (multiplexing effect) of 0.06 ms per channel switch. The geometry of the probes was chosen in such a way as to make probe response fairly insensitive to the changes between the uniformly dispersed (bubble) regime and the stratified regime [20]. On the basis of preliminary tests, the probe aspect ratios De/D and s/D (D pipe diameter, De electrode spacing, s electrode width) were set at 0.34 and 0.071 respectively. Selection of the proper electrode aspect ratios also resulted in small measuring volumes as compared with hold-up spatial fluctuations. The calibration curve was obtained by means of the procedures described in detail in [20]. Electrode couple

FLOW

Liquid level

De/D=0.34

x/D=2.3

x/D=0.7

Fig. 1. Ring electrodes for void fraction measurement downstream an orifice plate. Distances refer to thin orifice edge.

M. Fossa et al. / International Communications in Heat and Mass Transfer 33 (2006) 698–708

701

1.0 D=60 mm, strat. D=70 mm, strat. D=70 mm, bubble Best fit

Areal average void fraction

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.2

0.4

0.6

0.8

1.0

Dimensionless conductance Fig. 2. Calibration of the impedance probe according to the stratified and bubble phase distributions.

Fig. 2 shows the calibration curve in terms of dimensionless conductance (i.e. referred to that of the pipe full of liquid). The data refer to the stratified and bubble flow configurations, different ring diameters, but the same aspect ratios. Uncertainty analysis on overall void fraction measurement has been performed elsewhere and found to be about 4%. The test section is equipped with several resistive probes at different locations along the pipe, 5 probes being located immediately downstream of the singularity (Fig. 3). Being x the distance from the downstream edge of the orifice, probe axes are located approximately at distances x / D between 0.7 and 2.3 diameters in the case of thin orifices (see Fig. 3) while for thicker orifices, probe axes are located between 0.3 and 1.9 diameters. 2.2. Data processing Void fraction measurements were performed both to detect the instantaneous phase distribution and to infer statistical, time-averaged, parameters. The statistical analysis was performed on 82 s of recording time and focused on evaluating the time-averaged cross-sectional void fraction α and the void probability density function (PDF, Fig. 4). As is well known, intermittent flow is associated with a twin-peaked PDF [21], in which the low void fraction peak corresponds to slug passage and the high void fraction peak corresponds to the stratified-phase regions. From PDF analysis, the following parameters can be determined: αS, which corresponds to the low void fraction peak; αst, at which the maximum of the right peak occurs; αmax, where the PDF tends to zero. The average liquid film height (h) and minimum liquid level (hmin) in the stratified regions have been calculated from αst and αmax values, respectively, by means of simple trigonometric considerations and the assumption of absence of gas inside the liquid layer. z2

Distance from the phase mixer

z1 s

Flow d

D

De

x

t

probe 2 probe 1

Fig. 3. Void fraction probe locations downstream an orifice plate.

702

M. Fossa et al. / International Communications in Heat and Mass Transfer 33 (2006) 698–708

Probability density function [%]

0.25

0.20

h

α st

0.15

α max 0.10

αs 0.05

0.00 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Void fraction Fig. 4. Void fraction PDF for flow parameter evaluation.

By analysing the liquid hold-up time traces, the number of slugs during the observation period was obtained and a residence time Δτi was associated with the ith individual slug. To this end, two threshold values were introduced. These values are the minimum liquid hold-up (slugs that do not reach this minimum value are regarded as travelling waves and discarded from counting) and the threshold value for the liquid hold-up according to which the residence times are calculated. This operation yielded the average residence time Δτ¯ and the slug frequency f. A detailed description of the procedure is given in [22]. 3. Results Extensive experimentation was performed with reference to a horizontal test section into which a restriction (orifice plate) was inserted. Fig. 5 shows the operating conditions investigated, located on the Taitel and Dukler [23] map. The void fraction measurements were processed according to the above-described procedure, from which the timeaveraged values, the minimum liquid heights in the stratified regions and the slug frequencies were obtained. Most results are represented as a function of the liquid volume fraction XL, defined as the ratio of the liquid superficial velocity VSL and the mixture velocity VM. 10

Superficial liquid velocity VSL

Bubbly

1

Intermittent Annular

0.1

stratified smooth 0.01 0.1

stratified wavy 1

10

Superficial gas velocity VSG Fig. 5. Operating conditions on Taitel and Dukler map.

M. Fossa et al. / International Communications in Heat and Mass Transfer 33 (2006) 698–708

b 0.45

0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20

VSL=2.0 m/s VSG=2.4 m/s

t/d=0.023 t/d=0.20 σ=0.54 t/d=0.59 t/d=0.023 t/d=0.20 σ=0.73 t/d=0.59

-4

-3

-2

t/d=0.023 t/d=0.20 σ=0.54 t/d=0.59 t/d=0.023 t/d=0.20 σ=0.73 t/d=0.59

Flow

Average void fraction α

Average void fraction α

a

703

-1

0

1

2

3

0.40

0.35

0.30

0.25

0.20 -4

4

Dimensionless distance from orifice edge x/D

VSL=0.6 m/s VSG=0.4 m/s

Flow

-3

-2

-1

0

1

2

3

4

Dimensionless distance from the orifice edge x/D

Fig. 6. a. Average void fraction as a function of the distance from orifice edge. b. Average void fraction as a function of the distance from orifice edge.

3.1. Void fraction spatial evolution Figs. 6a, b and 7 show plots of time-averaged area void fraction versus the distance from the downstream edge of the orifice for different flow conditions. Diagrams 6a and 6b focus on the situation very close to the orifice. The flow configuration described in Fig. 6a is the typical profile observed in most flow conditions investigated in the present study: the void fraction undergoes a step increase just downstream of the singularity and then decreases (up to 50% values) within a few diameters. This behaviour is representative of the majority of all operating conditions (see empty symbols in Fig. 5), especially at liquid superficial velocities higher than 0.6 ms. In such conditions, the restriction area ratio plays an important role since the void fraction increases as the area contraction ratio σ diminishes. Minor effects can be ascribed to the orifice thickness, with thicker orifices generally inducing slightly higher void fraction values. It should be noted that the experimental distances x from probe axes to the orifice edge are shorter for thick than for thin orifices; the void fraction comparison is therefore made at different abscissae. At low liquid superficial velocities (0.6 m/s) and in a limited range of liquid volume fraction XL values (0.5 b XL b 0.7), the void fraction goes through a minimum (Fig. 6b), which is sometimes preceded by a local maximum in the case of the thickest orifice (t / d = 0.59). In Fig. 5 the flow conditions corresponding to the second profile are represented by the filled symbols. Fig. 7 shows how the void fraction evolves along the test pipe, again in the typical case of void fraction increase just downstream of the orifice. It can be observed that the void fraction values along the pipe differ markedly as a result of the pipe restriction. Fig. 8a depicts the situation in terms of slip ratio values. The plot shows the slip ratio as inferred at

Average void fraction α

0.65 0.60

VSL=1.1m/s VSG=1.1m/s

t/d=0.023 t/d=0.20 σ=0.54 t/d=0.59 t/d=0.023 t/d=0.20 σ=0.73 t/d=0.59

Flow

0.55 0.50 0.45 0.40 0.35 0.30 -50

-40

-30

-20

-10

0

0

10

0

11

0

12

0

13

0

14

Dimensionless distance from the orifice edge x/D Fig. 7. Average void fraction variation along the test pipe.

704

M. Fossa et al. / International Communications in Heat and Mass Transfer 33 (2006) 698–708

a

b 3.0

3.0 t/d=0.023 t/d=0.20 σ=0.54 t/d=0.59

2.0 VSL=0.6m/s

1.5

2.5

Slip ratio S

Slip ratio S

2.5

1.0

t/d=0.023 t/d=0.20 σ=0.54 t/d=0.59

2.0 VSL=0.6m/s

1.5 1.0

VSL =1.1m/s

0.5

VSL=2.0m/s

VSL=1.1m/s

0.5

VSL=2.0m/s

0.0

0.0 0

1

2

3

4

5

6

0

Mixture velocity VM [m/s]

1

2

3

4

5

6

Mixture velocity VM [m/s]

Fig. 8. a. Slip ratio values (at x / D = 0.3 ÷ 0.7) as a function of the mixture velocity. Gas superficial velocity as a parameter. b. Slip ratio values (at x / D = 1.9 ÷ 2.3) as a function of the mixture velocity. Gas superficial velocity as a parameter.

x / D = 0.3 ÷ 0.7 as a function of the mixture velocity VM, with the liquid superficial velocity as a parameter. The figure refers to an orifice with an area ratio equal to 0.54, but similar trends apply to restrictions with an area ratio equal to 0.73. It is apparent that the local slip ratio is well below 1 for most flow conditions, thus demonstrating that the usual assumption in local pressure drop models concerning the perfect phase mixing is not physically well posed. Fig. 8b is the same as Fig. 8a, in which x / D = 0.3 ÷ 0.7, but in Fig. 8b measurements refer to the location x / D = 1.9 ÷ 2.3. The influence of the liquid superficial velocity is apparent: at low liquid superficial velocities, the slip ratio values are around 2 and above (thus approaching the values corresponding to the developed unrestricted flow), while at higher velocities, the slip ratio decreases and can again attain values below 1. The statistical analysis of void records for locations close to the orifice revealed that the decrease in the liquid level in the stratified regions corresponds to the increase in the void fraction. As a confirmation of the above considerations, the smaller the area ratio, the greater the decrease in the liquid level (in comparison with “fully developed” flow conditions). These conclusions are described in Fig. 9, in which the PDF functions for both positions – close to the

a

b x/D=103 α=0.48 x/D=0.35 α=0.72

10 σ=0.54

10

8

V SL =1.1 m/s X V=0.60 t/d=0.59

6

4

2

Probability density function [%]

Probability density function [%]

12

x/D=103 α=0.46 x/D=0.28 α=0.70

8

6

σ=0.73

V SL =1.1 m/s X V =0.60 t/d=0.59

4

2

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Void fraction

Void fraction

Fig. 9. PDF functions for both positions, close to the restriction and in the fully developed zone; (a) σ = 0.54; (b): σ = 0.73.

Dimensionless minimum liquid level, hmin/D

M. Fossa et al. / International Communications in Heat and Mass Transfer 33 (2006) 698–708 1.0

σ=0.54-t/d=0.023 σ=0.54-t/d=0.20 σ=0.54-t/d=0.59 σ=0.73-t/d=0.023 σ=0.73-t/d=0.20 σ=0.73-t/d=0.59

0.9 0.8

705

D=40mm z/D=1.9-2.3 Straight pipe data fit

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.2

0.4

0.6

0.8

1.0

Liquid volume fraction, VSL/VM Fig. 10. Dimensionless minimum liquid level in the stratified regions just downstream the restriction (x / D ≈ 2).

orifice and in the fully developed zone – are plotted for the two different contraction area ratios. It can be observed that the second peak, which is associated with the stratified-phase region, grows and moves to the higher void fraction values as it approaches the orifice. Fig. 10 shows the dimensionless minimum liquid thickness in the stratified region (as inferred at 2.3 or 1.9 diameters from the orifice) plotted against the liquid volume fraction for different orifice geometries, together with the fitting line of data concerning the unrestricted developed flow [22]. Finally, Fig. 11 shows the effect of the orifices on slug frequency, as inferred at the farthest of the probes located immediately downstream of the orifice (namely 2.3 diameters), for lower area ratio σ = 0.54 and higher area ratio σ = 0.73. The reference situation is the frequency obtained 255 diameters downstream of the phase mixer (or 103 diameters from the theoretical position of the orifice) in the pipe without orifice. Data are expressed in dimensionless form as a ratio between the difference (f2.3 − f255) and the frequency for the developed flow situation (f255). It can be observed that

2 σ=0.54-t/d=0.023 σ=0.54-t/d=0.20 σ=0.54-t/d=0.59 σ=0.73-t/d=0.023 σ=0.73-t/d=0.20 σ=0.73-t/d=0.59

(f2.3-f255) / f255

1

D=40 mm

0

-1

-2 0

1

2

3

4

5

6

Mixture velocity VM [m/s] Fig. 11. Slug frequency ratio. Reference frequency f255 is the measured one in the unrestricted pipe at 255 diameters downstream the phase mixer, (a) σ = 0.54; (b) σ = 0.73.

706

M. Fossa et al. / International Communications in Heat and Mass Transfer 33 (2006) 698–708 1.0 0.9

Orifice location σ=0.54 t/d=0.20

Flow

Liquid holdup HL

0.8 0.7 0.6

τ=23.050 [s]

0.5 0.4 0.3 0.2

τ=23.000 [s]

D=40 mm VSL=0.6 m/s XV=0.20

0.1 0.0 5940

5960

5980

6000

6020

6040

6060

Distance from phase mixer z [mm] Fig. 12. Instantaneous liquid hold-up along the test pipe just downstream the restriction. Parameter: time from 23.000 to 23.050 s.

for lower area ratio σ = 0.54 the slug frequency decreases as the mixture velocity increases; this behaviour is not observed at higher area ratios σ = 0.73. Figs. 12 to 13 show the spatial and instantaneous profiles of the liquid hold-up in the downstream region close to the orifice. These figures show the evolution of the spatial liquid hold-up at a time frame step of about 1 ms, while the time shift between channels is about 0.06 ms. Each figure contains the measurements of four probes during a sequence of 50 time intervals. Fig. 12 refers to the next interval in the sequence. In this case, the liquid hold-up undergoes a modification due to the movement of a slug tail. Finally, Fig. 13 clearly shows the arrival of a slug in the region downstream of the orifice. It can be observed that the liquid hold-up is initially at about 0.5 and suddenly rises to values very close to 1 as a result of the incoming slug. Furthermore, in the measuring location closest to the orifice, the liquid hold-up always remains below 0.9, probably to due to a situation of stable gas trapping at the corner of the restriction. Analysis of the instantaneous void fraction acquisitions yields an evaluation of the residence time of each slug and film crossing the test section. Through the average translational velocity information, it is possible to obtain the slug or film length. An example of this analysis is represented in Fig. 14a–b. With reference to the probe located at z = 6043 mm, starting from the time τ = 0.04 s, the same value of the liquid hold-up (here the reference value is HL = 0.8) 1.0 0.9

Flow

Liquid holdup HL

0.8 0.7

τ=11.500 [s]

0.6 0.5

τ=11.450 [s]

0.4 0.3 0.2 0.1 0.0 5940

Orifice location σ=0.73 t/d=0.20 5960

5980

6000

D=40 mm VSL=1.1 m/s XV=0.50 6020

6040

6060

Distance from phase mixer z [mm] Fig. 13. Instantaneous liquid hold-up along the test pipe just downstream the restriction. Parameter: time from 11.450 to 11.500 s.

M. Fossa et al. / International Communications in Heat and Mass Transfer 33 (2006) 698–708 1.0

D=40 mm VSL=1.1 m/s

FLOW Liquid fraction HL

0.8

X V =0.50

0.6

τ =0.001

0.2 0.0 50

60

70

80

0.8

0.4

0.2

0.2 0.0 40

50

60

70

80

90

40

τ=0.09 s

0.8 0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

50

60

80

90

80

90

τ=0.04 s

40

50

60

70

80

90

40

50

60

70

80

90

1.0

1.0 0.8

70

70

0.0

0.0 40

60

0.8

0.6

0.0

50

1.0

1.0

τ =0.33 s

τ=0.03 s

0.6

τ=0.02 s

0.4

90

1.0

Liquid fraction HL

0.8

0.0 40

Liquid fraction HL

1.0

0.6

0.4

0.8

1.0

707

τ=0.35 s

0.8

0.6

0.6

0.4

0.4

0.2

0.2

τ=0.50 s

0.0 40 50 60 70 80 90 40 50 60 70 80 90 Downstream distance from restriction [mm] Downstream distance from restriction [mm]

0.0

Fig. 14. Instantaneous liquid hold-up for slug residence time evaluation.

is reached at time τ = 0.33 s, after the liquid slug passes. For a slug residence time of 0.29 s, the corresponding dimensionless slug length can be calculated as 1s / D = Vs · Δτ / D ≌ 16. 4. Conclusions A new instrumentation based on the impedance method was applied to infer information on the behaviour of intermittent horizontal flows downstream of a sudden restriction. The investigation refers to measurements performed very close to orifice-type restrictions with different area ratios and thicknesses. The procedure is based on the statistical analysis of the instantaneous cross-sectional averaged void fraction and enables the main flow parameters (instantaneous and time-averaged void fraction values, slug frequency, film liquid level in the stratified region) to be evaluated. The results showed that the void fraction usually reaches a maximum at distances of around 1 diameter from the throat. The maximum can be up to twice the value recorded far from the orifice (“fully developed ” flow) and the corresponding slip ratio decreases to values less than 0.5. Similar results have been obtained by other authors, who measured the cross-sectional void fraction in sudden enlargements. The analysis of restriction flows showed that the liquid level in the stratified regions between two slugs is generally lower than the level observed in the reference

708

M. Fossa et al. / International Communications in Heat and Mass Transfer 33 (2006) 698–708

unrestricted situation, and that the smaller the area ratio is, the greater the liquid level decrease (and the void fraction increase) is. It was observed that, as an effect of the orifice, slug frequency slightly decreases for the lower area ratios σ = 0.54 as the mixture velocity increases. Finally, the simultaneous and instantaneous measurement of the void fraction, as picked up by series of probes, allowed the spatial profile of the phase distribution to be reconstructed with particular reference to the typical hold-up distributions in the different regions (gas pocket, slug tail, slug front) of the intermittent flow. Acknowledgement This study was funded through the MIUR grant COFIN 2004098758. References [1] I.E. Idelchik, G.R. Malyavskayafs, O.G. Martynenko, E. Fried, Handbook of Hydraulic Resistances, 3rd edition, CRC Press, 1994. [2] H.C. Simpson, D.H. Rooney, E. Grattan, Two-phase flow through gate valves and orifice plates, Int. Conf. Physical Modelling of Multi-Phase Flow, Coventry, 1983. [3] D. Chisholm, Two-Phase Flow in Pipelines and Heat Exchangers, Longman Group Ed., London, 1983. [4] S.D. Morris, Two phase pressure drop across valves and orifice plates, European Two Phase Flow Group Meeting, Marchwood Engineering Laboratories, Southampton, UK, June 1985. [5] L. Friedel, Two-phase pressure drop across pipe fitting, HTFS Report RS41, 1984. [6] E. Janssen, Two-phase pressure loss across abrupt area contractions and expansions: steam water at 600 to 1400 psia, 3rd Int. Heat Transfer Conf., vol. 5, 1966. [7] Z.H. Lin, Two phase flow measurement with sharp edge orifices, Int. J. Multiph. Flow 8 (1982) 683–693. [8] A.A. Saadawi, E. Grattan, W.M. Dempster, Two phase pressure loss in orifice plates and gate valves in large diameter pipes, in: G.P. Celata, P. Di Marco, R.K. Shah (Eds.), 2nd Symp. Two-Phase Flow Modelling and Experimentation, ETS, Pisa, Italy, 1999. [9] G. Kojasoy, P. Kwame-Mensah, C.T. Chang, Two-phase pressure drop in multiple thick and thin orifices plates, Exp. Therm. Fluid Sci. 15 (1997) 347–358. [10] M. Fossa, G. Guglielmini, Pressure drop and void fraction profiles during horizontal flow through thin and thick orifices, J. Exp. Therm. Fluid Sci. 26 (5) (2002) 513–523. [11] M. Patrick, B.S. Swanson, Expansion and contraction of an air–water mixture in vertical flow, AIchE J. 5 (1959) 440–445. [12] G. Guglielmini, A. Lorenzi, A. Muzzio, G. Sotgia, Two-phase pressure drops across sudden area contractions pressure and void fraction profiles, Heat Transfer 1986 (Proc. 8th Int. Heat Transfer Conf., San Francisco, 17–22 Aug. 1986), Hemisphere Pub. Corp. (5) 2261–2366. [13] S. Arosio, M. Guilizzoni, Local and averaged evolution of an intermittent two-phase flow in a duct with sudden expansion, 7th Int. Symposium on Fluid Control, Measurement and Visualization, Sorrento, 2003. [14] V. Bertola, The structure of gas–liquid flow in a horizontal pipe with abrupt area contraction, Exp. Therm. Fluid Sci. 28 (2004) 505–512. [15] M. Fossa, Gas–liquid distribution in the developing region of horizontal intermittent flows, Asme J. Fluids Eng. 123 (2001) 71–80. [16] J.C. Asali, T.J. Hanratty, P. Andreussi, Interfacial drag and film height for vertical annular flow, AIChE J. 31 (1985) 895–902. [17] P. Andreussi, A. Di Donfrancesco, M. Messia, An impedance method for the measurement of liquid hold-up in two phase flow, Int. J. Multiph. Flow 14 (1988) 777–785. [18] N.A. Tsochatzidis, T.D. Karapantios, M.V. Kostoglou, A.J. Karabelas, A conductance method for measuring liquid fraction in pipes and packed beds, Int. J. Multiph. Flow 5 (1992) 653–667. [19] G. Costigan, P.B. Whalley, Slug flow regime identification from dynamic void fraction measurement in vertical air–water flows, Int. J. Multiph. Flow 23 (1997) 263–282. [20] F. Devia, M. Fossa, Design and optimisation of impedance probes for void fraction measurements, J. Flow Meas. Instrum. 14 (4–5) (2003) 139–149. [21] O.C. Jones, N. Zuber, The interrelation between void fraction fluctuations and flow patterns in two-phase flow, Int. J. Multiph. Flow 2 (1975) 273–306. [22] M. Fossa, G. Guglielmini, A. Marchitto, Intermittent flow parameters from void fraction analysis, J. Flow Meas. and Instrum, 14, (4–5 82003) 161–168. [23] Y. Taitel, A.E. Dukler, A model for predicting flow regime transitions in horizontal and near-horizontal gas–liquid flow, AIChE J. 22 (1976) 47.