Ind. Eng. Chem. Res. 2007, 46, 5043-5050
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Experimental Investigation of Pressure Drop during Two-Phase Flow in a Coiled Flow Inverter Subhashini Vashisth and K. D. P. Nigam* Department of Chemical Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi-110016, India
Experimental investigation of the pressure drop for a gas-liquid two-phase flow system was conducted in an innovative device known as a coiled flow inverter (CFI). This configuration consists of helical coils with equispaced 90° bends introduced at specific intervals in the coils. The idea is to create random mixing in a cross-sectional plane because of helical coils and complete flow inversion via the insertion of bends. The coils were prepared using a tube for which the following parameters were varied: internal diameter (0.0050.015 m); curvature ratio, which is defined as coil diameter/tube diameter (6.7-20); pitch (1-2.5); and number of bends (1-15). The liquid flow rate was varied from 3.33 × 10-6 m3/s to 1 × 10-3 m3/s, and the gas flow rate was changed from 8.33 × 10-5 m3/s to 1 × 10-3 m3/s. Sixteen CFIs of different geometric configurations were tested. Comparison of the two-phase friction factor with that of different geometries, such as straight tube and straight helix for single-phase and two-phase systems, was made to account for the increment in pressure drop. It was observed that, because of the effect of secondary flow and flow inversion, the twophase frictional pressure drop in these types of flow inverters is greater than that of a straight helix and straight tube, by a factor of ∼2.5-3, respectively. The experimental data obtained for different CFI geometries were compared with the published works on helical coils. An empirical correlation for the two-phase friction factor in CFI was developed. The proposed correlation separately accounts for the effect of curvature ratio, number of bends, and gas and liquid flow rates, and it also retains the identity of each phase. The correlation was observed to fit the experimental data within (15% and can also effectively predict the friction factor for the straight helix. Introduction The knowledge of two-phase flow in coiled tubes is important for the design of heat exchangers, oil pipeline systems, steam generators, thermosyphons, nuclear reactors, and other process equipment. Coiled tubes are of special interest, because of their many practical advantages, such as compactness, ease of manufacture, and higher efficiency in heat and mass transfer. Many theoretical and experimental studies have been reported in the literature on coiled tubes that concern steady and transient flows.1-9 Extensive reviews on flow fields in curved ducts are also available.10-13 Despite these advantages, a careful analysis of the data shows that very high Dean number (De) is required to induce significant mixing in a cross-sectional plane. To overcome this limitation, a novel concept was introduced to develop an economical and effective alternative to helical coils: the coiled flow inverter (CFI).14 This device gives much better performance, in terms of narrower residence time distribution and higher heat- and mass-transfer coefficient. The CFI exploits the innovative technique of bending of helical coils for the effective utilization of the centrifugal force to our advantage. The geometrical configuration of the CFI consists of 90° bends inserted in coils, equally spaced, before and after the bend. One such unit has several consecutive 90° bends and coils, depending on the number of bends that are involved. The flow generated in this device due to the curvature of a stationary surface bounding the flow continuously changes direction. This results in complex secondary flows in a plane normal to the principal flow direction. It is induced in a crosssectional plane, because of the difference in centrifugal force * To whom correspondence should be addressed. E-mail:
[email protected].
experienced by different elements of fluid being at different axial velocities. The direction of centrifugal force is always perpendicular to the axis of the coil. Hence, because of the change in direction of centrifugal force by any angle, the plane of vortex formation also rotates by the same angle. Figure 1 displays the development of velocity contours in a straight helix and after the introduction of one and two bends. When flow enters the curved region, because of centrifugal action, the heavier phase (i.e., liquid), which is subjected to a larger centrifugal force, moves away from the center of curvature, whereas the gas flows toward the center of curvature. A separation of phases in this way causes significant slip between the phases. This process is a continuous function of the coil geometry. Complete flow inversion occurs at the bends, which further improves its performance, in comparison to helical coils. It is evident from Figure 1 that the velocity contour inverts by 90° after the first bend and similarly after the second bend. The occurrence of this phenomenon increases mixing between the fluid elements of different age groups and temperatures. The details of the optimal configuration of the aforementioned device can be found in refs 14-16. Single-phase hydrodynamic and heat-transfer studies that have been conducted on a laboratory and pilot scale in CFI show significant narrowing of residence time distribution14 and 25-30% increment in the Nusselt number,17 in comparison to helical coils. The present work attempts to provide two-phase frictional pressure drop data in CFI, which may further be used in scaleup and scaledown of the device. These experimental data will also provide support for modeling and simulation of such complex flows using modern tools of computation for scale-up strategies. The important studies of flow in helical coils18-22 primarily use the Lockhart-Martinelli18 (L-M) approach to predict the two-phase pressure drop. Other studies23-27 have modified the
10.1021/ie061490s CCC: $37.00 © 2007 American Chemical Society Published on Web 06/12/2007
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Ind. Eng. Chem. Res., Vol. 46, No. 14, 2007
Figure 1. Working concept of the coiled flow inverter.
L-M parameters to correlate their pressure drop data. The L-M correlations were originally developed for straight horizontal two-phase flow, and it relies on the knowledge of single-phase friction loss in tubes, which is not affected by the tube inclination. In view of the severe influence of tube inclination on pressure drop in two-phase flow, even for a 2.75° upward flow,27 the use of the L-M approach for inclined tubes is not justified. The L-M approach for coiled tubes results in restricted correlations, because in a coil of reasonable curvature, the tube cannot remain horizontal. In the present study, we have also developed an empirical correlation to predict the two-phase friction factor for both laminar and turbulent regimes, covering a wide range of operating and geometrical parameter using 16 CFI configurations. The correlations also successfully predict the straight helical coil data that have been reported in the literature. The CFI has many potential areas of application, such as use in inline mixers, reactors, heat exchangers, biosensors, and membranes.28 Experimental Section Preparation of the Coiled Flow Inverter (CFI). Thickwalled, transparent poly(vinyl chloride) (PVC) tubing was used to prepare the coils. The PVC tubes were wound around a square-shaped frame that comprised of cylindrical rods (Figure 2). The coil diameter was varied over a range of D ) 0.0670.2 m and the internal diameter of the tube was varied over a range of d ) 0.005-0.015 m. The range of curvature ratio, which is defined as λ ) D/d, was determined to be 6.7-20 and dimensionless pitch (defined as H ) p/d) was determined to be 1-2.5. The straight, unfolded length of the tubing was kept at
a length of 27 m. The angle at the bend was 90°, equally spaced before and after the bend. The complete unit consisted of squareshaped subunits that have been joined together, keeping the bend angle as a constraint.The coils were fixed and carefully tightened with clamps to avoid deformation of tubes. Fabrication of the equipment was done at Instrument Design Development Centre, IIT Delhi, India. Experimental Setup and Methodology. The schematic diagram of the experimental setup for the present study is shown in Figure 2. The experimental apparatus consisted of an air supply system; a liquid storage tank; a centrifugal pump; a test section (CFI); and control and measuring systems for the flow rate, pressure drop, and other accessories. The transparent wall of the PVC tubes facilitated visual observation of flow patterns. Air was drawn from a compressor and its flow rate was measured and controlled using an air rotameter (Scientific Devices, Pune, India). The flow rate of the water from a reservoir was measured using a rotameter (Scientific Devices, Pune, India) and controlled with valve. The pressure drop across the test section was measured with a differential pressure gauge (ARR Solution, Hirlekar; DPG 1); after the flow became steady, the flow rate of the liquid and the differential pressure gauge readings were recorded. Next, air was introduced into the test section through a small static mixer used to mix two phases. Before the test section, a straight length of ∼1 m was provided, to avoid the fluctuations in the line. The fluid mixture moved through the CFI test section and was separated at the gas-liquid separator. The water was recycled back to the water reservoir. A quick shut-off and displacement method was used to measure the gas holdup. Valves C and D at both ends of the test section were simultaneously closed, along with valves A and B, to close
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Figure 2. Schematic diagram of the experimental setup.
air and water lines. Valves E and D were then opened to permit the accumulation of the trapped air in the water-filled graduated measuring cylinder. The volume of the air collected was read at atmospheric pressure by adjusting the height of the overflow device. Similar experimental methodology was also adopted in our laboratory for two-phase flow in helical coils (see Saxena et al.9). Results and Discussion The experiments were performed for an air-water system in a CFI. The liquid flow rate was varied from 3.33 × 10-6 m3/s to 1 × 10-3 m3/s, and the gas flow rate was changed from 8.33 × 10-5 m3/s to 1 × 10-3 m3/s. The physical properties of the fluids were taken under ambient temperature and pressure conditions. Sixteen CFIs of varying design parameters were tested. Table 1 shows the design configuration of the aforementioned CFIs. A total of 5250 data points were collected. Effect of Gas and Liquid Velocity on Two-Phase Friction Factor. Figure 3 illustrates the effect of the ratio of liquid to gas velocity (VSL/VSG) on the two-phase friction factor in a CFI with parameters of NBend ) 5, H ) 1, and λ ) 10. As the ratio VSL/VSG increases, the friction factor decreases. It was also observed that, at a constant value of VSL/VSG, when the gas velocity was increased, the friction factor had a tendency to
Table 1. Geometrical Considerations of the Coiled Flow Inverter (CFI)a coil
d (m)
D (m)
H
λ
NBend
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.005 0.01 0.015 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.1 0.1 0.1 0.08 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
1 1 1 1 1 1.5 2 2.5 1 1 1 1 1 1 1 1
20 10 6.7 8 20 10 10 10 10 10 10 10 10 10 10 10
5 5 5 5 5 5 5 5 1 3 7 15 1 3 7 15
a
Length of the tubing ) 27 m; angle at the bend ) 90°.
decrease. This is due to the introduction of a slip effect. The relative velocity difference between the two phases results in a slip effect. Also, the centrifugal force acting on the liquid phase is greater than that acting on the gas phase, because of its greater density. Therefore, the pressure drop increases as the total velocity (VT ) VSG + VSL) increases. Hence, the gas holdup is less in the CFI, in comparison to that in a straight helix.
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Figure 3. Effect of the ratio of liquid-phase to gas-phase velocities (VSL/ VSG) on the two-phase friction factor in the coiled flow inverter (CFI) with λ )10, H ) 1, and NBend ) 5.
Figure 4. Effect of the curvature ratio (λ) on the two-phase friction factor in CFI with H ) 1, NBend ) 5 with varying liquid velocity at VSG ) 1.06 m/s. Table 2. Range of Liquid Velocity (VSL) and Gas Velocity (VSG) for Different Flow Regimes two-phase flow regime
VSG (m/s)
VSL (m/s)
smooth-stratified, SS stratified-wavy, SW plug flow, PL slug flow, SL wavy flow, WL churn flow, CH
0.85-2.12 2.55-6.37 0.85-5.31 5.73-12.74 6.37-12.74 0.85-12.74
0.04-0.05 0.07-0.13 0.17-0.72 0.20-1.19 0.06-0.28 0.30-1.28
However, for the same total velocity, a higher liquid flow rate results in much greater frictional losses. Similar trends were obtained for a CFI with differing numbers of bends and, hence, are not presented here for the sake of redundancy. Effect of Curvature Ratio. The curvature ratio (λ) is the ratio of coil diameter to the tube diameter; hence, the λ values were varied to study the effect of the curvature ratio on the two-phase friction factor. Figure 4 shows the variation of the friction factor with liquid-phase Reynolds number for different values of λ. It may be observed that the friction factor decreases as the liquid-phase Reynolds number (NRe,SL) increases. It may also be noted from the figure that the transition of flow patterns occurs at different values of the critical Reynolds number (NRe,critical). The value of NRe,critical decreases as λ increases. This is due to the fact that, for smaller-λ coils, the intensity of the
Figure 5. Effect of number of bends on the length of thetwo-phase frictional pressure drop in CFI with λ )10, H ) 1 with varying liquid velocity at VSG ) 1.06 m/s.
secondary flow is very high, in comparison to that of higher-λ coils. The secondary flow has a stabilizing effect on laminar fluid flow, which leads to a higher NRe,critical. This phenomenon is visible from the experimental data shown in Figure 4. For single-phase flow in coiled tubes, similar observations were made by different authors29-32 and they gave different correlations to calculate NRe,critical. Table 2 shows the various flow regimes encountered for the range of VSG and VSL values used in the present study. Effect of Number of Bends on Two-Phase Frictional Pressure Drop. To study the effect of number of bends in the CFI, geometries with 1, 3, 5, 7, and 15 bends, with H ) 1 and λ )10 were fabricated. Figure 5 shows the effect of the number of bends on the pressure drop. The solid line represents the pressure drop in a straight helix or coiled tube (i.e., NBend ) 0). As the number of equally spaced 90° bends is introduced within a straight helix, the pressure drop per unit length increases, which is due to the flow resistance offered by complete flow inversion at the bends. The increase in the pressure drop is initially less, because the number of bends is 1 and 3, ∼1.21.7 times greater than that of a straight helix. It was also noted that there was not much difference in the gas holdup. As the number of bends was increased up to 15, the pressure drop becomes ∼2.4 times greater than that of a straight helix. A considerable decrease in gas holdup was observed. The probable reason for such an observation is due to the fact that the pressure drop in CFI is affected by the dissipation of energy, when mixing of fluid elements of different ages occur. This increases the pressure drop as the number of bends increases. The second reason is due to viscous forces, which, in turn, are dependent on the axial velocity gradient in the cross section of the tube. This has a tendency to reduce it, because of weaker velocity gradients caused by the interchange of velocities at the bends. When the number of bends is less, the first factor is less effective but the second one shows its substantial effect, causing less of an increase in the pressure drop. As the number of bends is increased, the influence of the first factor becomes dominant, which enhances the pressure drop. Similar observations were also made for single-phase flow studies in the aforementioned device.14 Effect of Pitch on Two-Phase Frictional Pressure Drop. To study the effect of pitch on the two-phase pressure drop, the dimensionless pitch was varied over a range of H ) 1-2.5. It was determined that pitch has a negligible effect on pressure
Ind. Eng. Chem. Res., Vol. 46, No. 14, 2007 5047
Figure 7. Comparison of two-phase friction factor of CFI with a straight tube and a straight helix for single-phase and two-phase flow.
Figure 6. Comparison of experimental two-phase frictional pressure drop multiplier with data from Banerjee et al.,20 Boyce et al.,21 Mandal and Das,35 and Xin et al.36
drop for the range of VSG and VSL values studied. Hence, it was not considered in the proposed friction factor correlations. Comparison of the Present Data with the LockhartMartinelli Correlation and the Modified Lockhart-Martinelli Correlation. The Lockhart-Martinelli (L-M) approach18 is widely used for correlation of a two-phase frictional pressure drop in straight tubes, and a modified L-M method has been used for helical coils.24,33,34 In the L-M method for straight tubes, the parameter ΦL,St, which is defined as
(
)
-∆PTP,St -∆PL,St
ΦL,St )
1/2
is correlated by the empirical function X, which is given as
X)
(
-∆PL,St -∆PG,St
)
1/2
whereas in the modified L-M method, the parameter ΦL,Coil, which is defined as
ΦL,Coil )
(
)
-∆PL,Coil -∆PL,Coil
1/2
is correlated to X, which, in this case, is given as
X)
(
-∆PL,Coil -∆PG,Coil
)
1/2
The experimental data obtained was correlated using the L-M method. The values of ΦL for different liquid and gas flow rates,
Figure 8. Parity plot for the two-phase friction factor. T
different numbers of bends, and different curvature ratios are plotted against X in Figure 6. It can be observed that ΦL is strongly dependent on the flow rate. When the flow rate of either liquid or gas is higher, a large deviation from the L-M curve can be observed. Similar observations were reported in the literature for helicoidal pipes.21,34 The experimental data are dispersed in a range of +70% to -30% around the L-M curve in the turbulent-laminar and turbulent-turbulent cases. The deviation of the experimental data from the L-M prediction can be attributed to the water column accumulation in the CFI. It
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Table 3. Single-Phase and Two-Phase Friction Factor Correlations Used for Straight and Helical Coiled Tubes geometry
friction factor correlation used Single-Phase System 1. laminar regime (Hagen-Poiseuille law):
fL,st ) straight tube
16 NRe
2. turbulent regime (Blasius resistance law):
fL,st )
0.079 (NRe)0.25
1. laminar regime:a
16 [1 + 0.33(log(De))4] NRe
fL,coil ) coiled tube
2. turbulent regime:b
d 0.08 + 0.012 D (NRe)0.25
()
fL,coil )
Two-Phase System straight tubec
fTP,st ) fL,st(VSL/Vm)2
[
1 + 9.63
coiled tubed
( ) NRe,SG NRe,SL
0.747
]
(NRe,SL)-0.019
fTP )
fTP,coil ) fL,coil(VSL/Vm)2
{
1 + 1.17
a From Mishra and Gupta.30 Akagawa et al.23
b
( )[( ) fL,st fL,coil
fTP,st (Vm/VSL)0.747 - 1 fL,st
From White.38
c
From Inoue.39
single-phase pressure drop data of ref 14 for CFI with NBend ) 7, it was determined that the two-phase pressure drop increased 5-fold. A two-phase gas-liquid pressure drop was also predicted considering flow through two straight helix joined by a 90° elbow bend. The calculation of a two-phase pressure drop over the elbow bend is more complex than that of single-phase flow, where the phase density is essentially constant. The straight helix frictional pressure loss can be used to calculate the loss in elbow bend pressure, regardless of the orientation of the plane of the bend. The predicted and experimental pressure drop for singlephase14,17 and two-phase flow through CFI were compared. It was observed that the predicted value was ∼15%-20% less than the experimental pressure drop observed in CFI for singlephase flow, whereas the difference was as high as 30%-60% in the case of two-phase flow. Hence, we attempted to develop a new correlation for the two-phase friction factor in CFI. The data were divided into two regions: data for NRe,SL < 9000 (the laminar case) and NRe,SL g 10 200 (the turbulent regime).
d
]}
From
may be concluded that the L-M method and the modified L-M method is applicable for a very small range of flow rates in helical coils and CFI. In the absence of any two-phase flow data on CFI, a comparison of pressure drop data was made against several other existing correlations and models for gas-liquid flow for a straight helix. Figure 6 also shows a comparison of ΦL with the experimental data of Bannerjee et al.,20 Boyce et al.,21 Mandal and Das,35 and Xin et al.36 for helical coils. It was observed that the present experimental data on two-phase frictional pressure drop deviate (by >50%) from the reported literature data.20,21,35,36 Comparison of the Single-Phase and Two-Phase Friction Factors in CFI with a Straight Tube and a Helical Coil. A comparison of the friction factor in single-phase and two-phase flow in a straight tube, a coil tube, and CFI (NBend ) 5, 15) are shown in Figure 7. The transition point from laminar to turbulent flow at the respective critical Reynolds number (NRe,critical) is shown as a step change in the figure. In the case of CFI, two such step changes were observed, which shows the change of flow regimes. At NRe < 5000, the decrease in the friction factor was more pronounced as NRe,SL is increased. At NRe,SL > 5000 and again at NRe,SL > 9000, the friction factors are observed to be higher, which marks the transition of flow regimes. The various correlations used to calculate the friction factor for straight tube and coiled tubes for single-phase and two-phase flow systems are mentioned in Table 3. It is observed that the two-phase frictional pressure drop in CFI is ∼2.5-fold greater than that in the helical coiled tubes. When compared to straight tubes, this pressure drop increases 3-fold. The pressure drop in CFI increases ∼8-fold and ∼12fold, in comparison to the single-phase pressure drop in coiled tubes and straight tubes, respectively. When compared with the
29.4(NBend)0.15λ0.19(NRe,SG)0.06 (NRe,SL)0.94 (for 400 < NRe,SL e 9000) (1)
fTP )
0.065(NBend)0.003(NRe,SG)0.001 λ0.003(NRe,SL)0.13 (for NRe,SL g 10 200) (2)
The nonlinear data regression method was used to obtain eqs 1 and 2. The maximum deviation between the predicted friction factor and the experimental data was
