Key words: Bend; Two phase flow; Pressure loss; Flow pattern; Model ..... [13] Paliwoda, A., âGeneralized method of pressure drop calculation across pipe.
Experimental investigation and modelling of two phase flow in horizontal 90◦ and 180◦ bends Abstract In this research the influences of horizontal 90◦ and 180◦ bends on the two phase pressure loss and flow pattern for air–water mixtures inside a 2.4 cm smooth pipe are investigated. Based on experimental pressure loss data in bends a prediction model is proposed. Comparison of new model with previous models in the literature shows that this model provides a better estimate of pressure loss in bends. Several experiments are also accomplished to observe flow pattern in presence of bends. In region of flow, the flow pattern in the recovery region is temporarily turned into annular flow. Based on the present visualization, two flow pattern maps are proposed to describe the effect of bends on transition of flow pattern. Key words: Bend; Two phase flow; Pressure loss; Flow pattern; Model Introduction Bends have many industrial applications such as in heat exchangers, boilers, refrigerators, transport pipes etc. Either single-phase or two-phase can occur in the applications. For single-phase flow, extensive studies have been carried out by various investigators [1-4]. As the flow enters into the bend, the centrifugal force drives the more rapid fluid in the concave part of the bend while the fluid in the convex parts is slowing down so the maximum axial velocity move to the outer wall and results in the consequence of a secondary flow. This phenomenon causes more pressure loss when comparing to that of a straight tube [1]. In fact the bend pressure loss can be summarized under friction and form losses. The magnitude of such secondary flows obviously reduces with an increase of bend radius, and with a decrease of fluid velocity. So Dean defined a dimensionless number in curved pipes, which is now called the Dean number ( De = Re(2 R d )0.5 ), where d is the pipe inside diameter and R is the curvature radius and R d is the curvature ratio of the bend. The Dean number represents the ratio of the square root of the product of the inertial and centrifugal forces to the viscous force and is the criterion for magnitude of secondary flow. When the Dean number exceeds a critical value, a secondary vortex pair with counter-rotating circulation is found near the outer wall. In two-phase flow the bend pressure loss is additionally increased due to the dissipation caused by the momentum exchange between the phases, and the separation and remixing of the gas and the liquid phase, and changing in flow pattern in the bend [5, 6]. Limited investigations are carried out in two phase bend pressure loss subject. Sekoguchi et al. [7] have investigated the air-water
flow through a 90° bend with curvature ratio of 1.5 and inside diameter of 2.54 cm. They analyzed the two-phase pressure loss across the bend data using parameters φbl and Xb . Sekoda et al. [8] also considered in similar work pressure loss in 90◦ horizontal bend with inside pipe diameter of 1.8 cm and curvature ratios of 5.02 and 2.36. Fitzsimmons [9] performed his experimental work on water-steam system and 90◦ bend with inside diameter of 5.08 cm and two curvature ratios of 1.04 and 2.56 at pressures of 55, 83 and 110 bar. He demonstrated his results in φblo versus x diagram. Chisholm [10] with help of this experimental results developed equations for pressure loss predictions based on a two-phase multiplier for 90° and 180° bends. Mandal et al. [11] have investigated two phase air-Newtonian liquid flow through 45◦, 90◦, 135◦ and 180◦ bends. Their correlations have been developed to prediction the two phase friction factor. Azzi et al. [5, 6] have also investigated the pressure loss in vertical upward air-water flow through 90◦ bend. Based on experimental pressure loss data, they proposed a prediction model in style of a two phase flow multiplier. There are other two phase bend pressure loss models in the literature such as models by Sookprasong [12] for horizontal 90◦ bends, Paliwoda [13] for horizontal 45◦, 90◦ and 180◦ bends, Subbu [14] for horizontal 180◦ bends and Usui [15] for horizontal and vertical 180◦ bends. Azzi has considered these models theoretically with comparison of effective independent parameter and limitation of every model [16]. Pressure loss predictions by different models under the same condition and comparison of results show significant difference. Thus the experimental investigation of pressure loss in bends and development of a suitable prediction model is necessary. The information concerning two phase flow patterns inside a bends is very limited. Wang et. al. [17, 18] investigated the influences of return bends on the two phase flow patterns for air-water mixtures inside small diameter tubes (3, 4.95, 6.9 mm). They classified two phase flow across the test tube into five regions which include the (I) upstream region; (II) de-accelerating region; (III) return bend; (IV) recovery region; and (V) downstream region. They also developed a two phase flow regime map in presence of the 180◦ return bend. The lack of consistent experimental data in the presence of bends implies the necessity for additional experimental investigations. Experimental setup A schematic diagram of the experimental set up incorporating 90◦ bend for pressure loss measurements and flow visualizations in two phase pipe flow in horizontal position is shown in Fig 1. Water is circulated by a centrifugal pump from a storage tank acting also as separator to the ball valve and further via a needle valve. From this point, water travels through a water rotameter, and a one way check valve and then into the mixing section. Air supplied by an air compressor passing through a ball valve, air rotameter, needle valve and check
valve is blended with water in the mixing section. Downstream of the mixer, the air-water mixture flows through the bend test section to the storage tank, where the gas and liquid phases are separated. Water is recirculated and air returns to the atmosphere. In order to develop various two-phase flow patterns (by controlling the flow rates of gas and liquid), a two-phase gas and liquid flow mixer was used. The mixer consisted of a perforated stainless steel tube (6.3 mm I.D.) inserted into the liquid stream by means of a tee and a compression fitting. The end of the tube was silver-soldered. Four holes (3 rows of 1.5 mm, 4 rows of 3 mm, and 8 rows of 4 mm) were positioned at 90° intervals around the perimeter of the tube and this pattern was repeated at fifteen equally spaced axial locations along the length of the stainless steel tube (refer to Fig. 2). For better mixing of two phase in a part of pipe a helical plate (20 cm length) was placed. The two-phase flow leaving mixer enters the test section. The test section in total includes an inlet pipe to the bend and an outlet pipe, each with a length of 3 m, resp., about 125 diameters to ensure the full development of the flow. These pipes are made from glass, allowing, thus, additionally for optical inspection of the flow pattern. The inner diameter of the test section and the pipe wall thickness are 24 mm and 3 mm, respectively. At the bend section two bends of 90° and 180° with curvature ratios of 1.5 and 2.1 respectively are used. For measuring the evolution of the pressure profile along the straight pipes, 11 ring chambers acting as pressure equalisation taps, are fixed around the outer wall of the pipes constituting the test section, five in the inlet pipe and six in the outlet pipe. The taps were located at the bottom of the pipe in order to ensure that only water could get into the pressure measuring system. The pressure at the location of first pressure tap is taken as the system pressure reference. Details of the pressure tapping arrangement are shown in Fig. 3. The pressure loss was measured by a monometer. The height of mercury in it was 20 cm. Results and Discussion Two sets of experiments have been carried out, consisting the study of the effect of bends on pressure loss and its effect on flow pattern. Experiments were repeated a number of times to ensure reproducibility of the data. In all experiments the system pressure was less than 1 barg and the temperature of the liquid and gas used in the experiments was at 25 ± 1°C. Evaluation of the Two-Phase Pressure Loss across the Bend It is evident that far upstream and downstream of the bend, where the flow is not perturbed, the piezometric line exhibits a linear form manifesting a constant pressure gradient. Close to the bend, the gradient of these lines changes as a consequence of the additional effect of the self establishing secondary flow superimposed to the main flow. So the pressure drop due to the bend was
obtained from the difference between the static pressure of the upstream fully developed flow region and the static pressure of the downstream fully developed flow region across the bend. The evolution of the pressure difference along the upstream and downstream piping as a function of the liquid and gas flow rate for given curvature and bend diameter are plotted in Fig. 4 and 5 and then the pressure loss due to the bends for each experiment is measured with use of graphical method [5,10,16]. Pressure Loss Modelling Modelling is based on the two-phase flow multiplier concept, defined as the ratio made up of the bend pressure loss in two-phase flow and that in singlephase liquid flow with the same total mass flow rate as reference. In this model, it is tried to take into consideration the effect of all of the variables on two phase bend pressure loss. So it is written as a function of the mass flow rate, the mass flow quality, the density and viscosity ratios, the curvature ratio and the dimensionless Dean number expressing the important effect of centrifugal force. Basing on the experimental data and by using the least square method for multidimensional mathematical fitting, the following correlations was obtained; For 90◦ bend: ρ − ρG 2 0.4599 0.7 = A + 1.003De Lo x (1 − x) 0.1 L φ Lo ρL
o.14
µ L − µG µL
o .12
(1)
For 180◦ bend: ρ − ρG 2 0.3895 0.7 φ Lo = A + o.998 De Lo x (1 − x) 0.1 L ρL
o .14
µ L − µG µL
o .12
(2)
With ρ K x2 A = (1 − x) + L Go ρ G K Lo
(3)
The single-phase liquid flow bend pressure loss is determined according to the method of Beij [3]. Comparison between Proposed Model and Other Models The pressure loss for 90◦ bend under experimental conditions is evaluated by models of Chisholm B-type, Sookprasong, Paliwoda, Azzi and the new model. Then average relative error for each model for prediction of bend pressure loss is calculated and shown in Table 1 using equation 4. error = ∑
xMeasured − xCalculated xmeasured
(4)
The results indicate that the new model and Paliwoda model have less error than other models and Azzi model that is for vertical 90◦ bends has the largest error. In this manner, the bend pressure loss for 180◦ bend is calculated by models of Chisholm B-type, Paliwoda, Subbu, Usui and the new model. The average
relative errors are shown in Table 2. The results indicate that new model and Chisholm B-type model have less error than other models. So new models have the least error and consequently are the most suitable models for prediction of pressure loss due to the 90◦ and 180◦ bends. Flow Pattern in Bend In this part, the effect of 90◦ and 180◦ bends on two phase flow pattern in the upstream and downstream of the bends in different flow rates of liquid and gas are investigated by observation. The observed flow pattern became characterized on the flow map proposed by Ghajar [19] for horizontal and straight pipes then the change of flow pattern is considered. It is clear that the effect of bend is temporary and after recovery region, the flow pattern rechanges to that in the upstream. It is observed that in the 90◦ bend, the slug-bubbly and slug-bubbly-annular flow patterns change to the annular flow. The slug-wavy flow pattern except low flow rates of liquid was not seen and observed flow was annular. Also in the region of slug flow, pattern is changed to annular. Results show that 90◦ bend does not have influence on plug and stratified flow patterns. 180◦ bend has the same type but a lesser effect on flow pattern than 90◦ bend. Because the curvature ratio of 90◦ bend is less, it causes a greater centrifugal force and more disturbances in two phase flow and consequently more change of flow pattern. Two-Phase Flow Pattern Map with the Influence of Bend Based on the present flow visualization, two flow pattern maps are proposed to describe the effect of 90◦ and 180◦ bends on the transition of two-phase flow pattern (Fig 6, 7). Conclusion Two phase flow pattern and pressure loss for air-water mixtures inside 2.4 cm smooth pipe with 90◦ and 180◦ bends is investigated. Conclusions of present study include: 1. In comparison to the predictions of the selected models a more accurate model is proposed for calculating the two-phase flow pressure loss in horizontal 90◦ and 180◦ bends. It takes into account all the parameters influencing the pressure loss and includes the theoretical boundaries of single-phase flow of gas as well as liquid. 2. The observations show, in 90◦ and 180◦ bends, the slug-bubbly and slugbubbly-annular flow patterns change to the annular flow. The slug-wavy flow pattern except low flow rates of liquid was not seen and observed flow was annular. Also in the region of slug flow, it is changed to annular. Bends do not have influence on plug and stratified flow patterns. In fact the bends do not have effect on flow pattern when the liquid or gas flow rate is low.
3. The 90◦ bend have larger effect in the changing of flow pattern, because of the more curvature ratio. 4. Based on the flow visualization, two flow pattern maps are proposed to describe the effect of bends on the transition of two-phase flow pattern. References [1] Ito, H., “Flow in curved pipes”, JSME Int. J., 30 543–552, (1987). [2] W.R. Dean, “Note on the motion of fluid in curved pipe”, Phil. Mag. 4, 208– 223, (1927). [3] Beij, KH, “Pressures losses for fluid flow in 900 bends”, J. Research National Bureau of Standards, 21, 1–18, (1938). [4] Miller, DS, “Internal flow systems”, BHRA Fluid Engineering, (1978) [5] Azzi, A., Friedel, L., Kibboua, R., Shannak, B., “Reproductive accuracy of two-phase flow pressure loss correlations for vertical 90º bends”, Forschung im Ingenieurwesen, 67, 109–116, (2002). [6] Azzi, A., Alger, U.S.T.H.B., Friedel, L., “Two-phase upward flow 90º bend pressure loss model”, Forschung im Ingenieurwesen, 69, 120–130, (2005). [7] Sekoguchi, K, Sato, Y, Karayasaki, A, “The influence of mixers, bends and exit section on horizontal two-phase flow”, Int. Symp. on Res. in Cocurrent Gas Liquid flow., Univ. of Waterloo, Canada, Vol. 1, (1968). [8] Sekoda, G., Sato, K., Kayasaki, T., “Horizontal two- phase air- water flow characteristics in the disturbed region due to 90º bed”, Soc. Mech. Engrs., 35, (1969). [9] Fitzsimmons, DE, “Two-phase pressure drop in piping components”, Report Hanford Laboratories, HW-80970, Rev. 1, (1964). [10] Chisholm, D., “Two- phase flow in pipelines and heat exchangers”, G. Godwin, (1983). [11] Mandal, S.N., and Das, S.K., “Pressure losses in bends during two-phase gas-newtonian liquid flow”, Ind. Eng. Chem. Res., 40, 2340-2351, (2001). [12] Sookprasong, P., “Two-phase flow in piping components”, PhD Thesis University of Tulsa, (1980). [13] Paliwoda, A., “Generalized method of pressure drop calculation across pipe component containing two-phase flow of refrigerants”, Rev. Int. Froid 15(2), 120- 126, (1992) [14] Subbu, S.K., Das, S.K., Biswas, M.N., Mitra, A.K., “Pressure drop in Ubends for air- water flow”, Int. J. Eng. Fluid Mech., 3, 239- 248, (1990). [15] Usui, K., Aoki S, I.A., “Flow behaviour and pressure drop of two-phase flow through C-shaped bend in vertical plane, (I) Upward flow”, J. Nucl. Sci. Technol., 17, 875- 887, (1980). [16] Azzi, A., Friedel, L., Belaadi, S., “Two-phase gas/liquid flow pressure loss in bends”, Forschung im Ingenieurwesen, 65, 309-318, (2000)
[17] Wang, C.C., Chen, I.Y., Yang, Y.W., Hu, R., “Influence of horizontal return bend on the two-phase flow pattern in small diameter tubes”, Experimental Thermal and Fluid Science, 28, 145–152, (2004). [18] Wang, C.C., Chen, I.Y., Yang, Y.W., Chang, Y.J., “Two-phase flow pattern in small diameter tubes with the presence of horizontal return bend”, International Journal of Heat and Mass Transfer, 46, 2975–2981, (2003). [19] Ghajar, A.J., “Two- phase heat transfer in gas- liquid non- boiling pipe flows”, 3rd International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, 21 – 24 June 2004, Cape Town, South Africa
Nomenclature d
inside diameter of the pipe
ρ
density
R
Radius of curvature
µ
viscosity
Re Reynolds number
Subcripts
De Dean number
b
bend
L
liquid
K
single phase flow bend loss coefficient
x
vapor quality
X
Lockhart-Martinelli parameter G
Greek symbol φ
two-phase flow loss multiplier
Lo
Go
liquid only flowing with the total mass flux gas or vapour gas or vapour only flowing with the total mass flux
Lout=3 m
P3
Lin=3 m
Air
P1
Water Storage Tank
P2
Ball valve Air Compressor
Air Flow Meter
Needle valve Mixing Section
Check Valve
Ball Valve
Needle valve
Water Flow Meter
Check Valve
Figure 1. Schematic diagram of the experimental setup for the 90° bend.
Figure 2. Mixer
L=150 cm
88d
10
L=150 cm
58d
40d
9
8
20d 10d 2d
7
6
5 4 3
2.4cm
Manometer
10d 20d
1 40d
L=150 cm
2
2d
0 58d
2 mm
L=150 cm
Refrence System pressure
Figure 3. Pressure taps position along the bend test section with the corresponding normalised distances from the bend flanges
Experimental pressure difference [mm Hg]
0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -1500
Water flow rate Air flow rate [lit/hr] [lit/hr]
681 970 762 856 1120 1502 1265 1431 1630 1385
-1000
3759 1014 3050 2819 1323 1208 2152 2451 2560 3770
-500 0 500 1000 1500 Distance to/from the bend [mm]
2000
2500
Figure 4. Experimental two-phase flow pressure difference profile upstream and downstream of a 90◦ bend with horizontal plane as a function of the liquid and gas flow rate
Experimental pressure difference [mm Hg]
0 -5 -10 -15 -20 -25 -30 -35 -1500
Water flow rate Air flow rate [lit/hr] [lit/hr]
952 671 831 1002 1067 1228 1266 1385 1425 1565
-1000
1563 3373 2721 3268 3817 1370 1457 1397 2361 1746
-500 0 500 1000 1500 Distance to/from the bend [mm]
2000
2500
Figure 5. Experimental two-phase flow pressure difference profile upstream and downstream of an 180◦ bend with horizontal plane as a function of the liquid and gas flow rate
Table 1. Average relative errors for prediction of 90◦ bend pressure loss Model
Average relative error [%]
New model
8.93
Chisholm
12.68
Sookprasong
22.27
paliwoda
8.98
Azzi
57.53
Table 2. Average relative errors for prediction of 180◦ bend pressure loss Model
Average relative error [%]
New model
11.64
Chisholm
11.66
paliwoda
25
Subbu
58.59
Usui
48.21
Figure 6. Proposed two-phase flow pattern map with the influence of 90◦ bend for d=2.4 cm and R/d=1.5
Figure 7. Proposed two-phase flow pattern map with the influence of 180◦ bend for d=2.4 cm and R/d=2.1
