Influence of Surface Tension on Air-Water Flows

Influence of Surface Tension on Air-Water Flows

Downloaded from ascelibrary.org by TECHNISCHE UNIVERSITEIT DELFT on 11/12/13. Copyright ASCE. For personal use only; all rights reserved.

I. W. M. Pothof1; A. D. Schuit2; and F. H. L. R. Clemens3 Abstract: Stricter environmental regulations have led to new wastewater treatment plants and a centralization of existing wastewater treatment plants. Therefore, pressurized wastewater mains have become an indispensable link between the collection systems and the treatment plants. In urban areas in particular, these pipelines include many inverted siphons to cross other infrastructure, like railways, motorways, other pipelines, and buildings. Accumulation of air in downward sloping sections of these wastewater mains reduces the transport capacity significantly. A dominant air transport mechanism is the air-entraining hydraulic jump at the tail of an accumulated air pocket. The novelty of this paper is a systematic investigation of the influence of surface tension on the air discharge in downward sloping pipe sections. Experiments have been performed with clean water, surfactant-added water, and wastewater. The experiments with surfactant-added water confirm that the air discharge increases significantly at lower surface tension. However, the lower surface tension of wastewater does not enhance the air transport in comparison with the air transport in clean water. DOI: 10.1061/(ASCE)HY.1943-7900.0000637. © 2013 American Society of Civil Engineers. CE Database subject headings: Pipe flow; Wastewater management; Hydraulic jump; Tension. Author keywords: Air-water pipe flow; Negative inclination; Surface tension; Wastewater; Hydraulic jump.

Introduction In a pipeline for liquid transport with downward sloping sections, air may have several negative consequences: 1. The transport capacity of wastewater mains decreases significantly when air accumulates in downward sloping reaches (Lubbers 2007; Pothof and Clemens 2008); 2. Inadmissible pressure shocks may occur due to the sudden release of air from hydropower tunnels (Wickenhäuser 2008) or water pipelines (Malekpour and Karney 2008); 3. Vibrations may occur in pumps or turbines; and 4. Allowable pressures may be exceeded during the filling of storm water storage tunnels (Vasconcelos and Wright 2009) or during pump start or valve stroking operations (Falk et al. 2004). This paper will focus on the first consequence: capacityreducing air pockets and air discharge as a function of pipe geometry, gas pocket length, and surface tension. Bliss (1942) and Kalinske and Robertson (1943) first identified three different flow regimes in air-water flow in downward-sloping pipes: 1. Blowback: the hydraulic jump at the end of a gas pocket entrains large numbers of air bubbles into the flowing water. The air bubbles coalesce into larger bubbles that rise to the pipe soffit and blow back through the jump. The hydraulic jump 1

Specialist, Industrial Hydrodynamics, Deltares, Dept. of Industrial Hydrodynamics, P.O. Box 177, 2600 MH Delft, The Netherlands (corresponding author). E-mail: [email protected] 2 Manager, Laboratory of Sanitary Engineering, Delft Univ. of Technology, Civil Engineering and Geosciences, P.O. Box 5, 2600 AA Delft, The Netherlands. 3 Professor, Delft Univ. of Technology, Civil Engineering and Geosciences, P.O. Box 5, 2600 AA Delft, The Netherlands. Note. This manuscript was submitted on August 4, 2011; approved on May 24, 2012; published online on May 29, 2012. Discussion period open until June 1, 2013; separate discussions must be submitted for individual papers. This paper is part of the Journal of Hydraulic Engineering, Vol. 139, No. 1, January 1, 2013. © ASCE, ISSN 0733-9429/2013/144-50/$25.00.

pumps more air into the water than the flowing water below the jump was able to carry on down. 2. Transitional flow: at certain air-water discharge ratios the downward sloping pipe contains multiple air pockets and hydraulic jumps. The air pockets are nearly stable. Blowback is no longer observed. The air entrainment in the hydraulic jumps is approximately equal to the air transport capacity of the flowing water. 3. Full air transport: all air entrained by the first hydraulic jump is carried down as a stream of small and medium-sized bubbles. The single hydraulic jump moves steadily up the pipe. The Froude number of the hydraulic jump determines the amount of air removed from the pipe. One or more air pockets and an associated head loss are present in Flow Regimes 1 and 2. Therefore, the air-water flow experiments focus on these flow regimes. Kalinske and Bliss (1943) determined the dimensionless water discharge Q2 =ðgD5 Þ ¼ sin θ=0.71 at which gas bubbles are ripped off an air accumulation by the hydraulic jump and start to move downward to the bottom of the slope. This equation cannot be considered an equation for the clearing velocity, as explained by Kalinske and Bliss: “...to maintain proper air removal, the actual value of the water discharge should be appreciably larger than Q” (Kalinske and Bliss 1943). Kent (1952), Gandenberger (1957), Mosvell (1976), and Escarameia (2007) investigated the water velocity required to keep air pockets of a certain size stable in a downward inclined pipe (Fig. 1). Wisner et al. (1975) developed an envelope curve from the available experimental data on clearing velocity until 1975. Glauser and Wickenhäuser (2009) investigated the motion of relatively thin bubbles (hc =D < 0.1) in downward sloping pipes at angles between 0 and 5°. Their clearing velocity is valid for thin bubbles and therefore not comparable to the results of the other authors. Pozos et al. (2010) pursued an analysis similar to that of Kalinske, Kent, and Escarameia for the clearing velocity. A key limitation of this approach is the assumption that the buoyancy force is linear in the air pocket volume, which is only correct for small air bubbles. The pressure distribution around a large air pocket is no longer hydrostatic due to the water acceleration toward normal depths.

44 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JANUARY 2013

J. Hydraul. Eng. 2013.139:44-50.

Water flow number for air pocket clearing, F w [-]


2

Escarameia (2007), 150 mm Kent, Mosvell (1976), 102 mm Pozos (2010), 76.2 mm Gandenberger (1957), 45 mm Bendiksen (1984), 24.2 mm Wisner (1975) Falvey (1980) Pothof (2010)

1.5

1

0.5

0 0

30 60 Downward pipe angle, [°]

90

Fig. 1. Experimental data and correlations by Falvey (1980) and Pozos et al. (2010) for the air pocket clearing flow number; legend includes pipe diameters (in millimeters) in which experiments were performed

If air may accumulate, due to intermittent operation for example, the behavior of elongated air pockets must be evaluated. Pothof has derived and validated the momentum balance for elongated air pockets in downward sloping pipes (Pothof and Clemens 2010). Falvey (1980) has combined several literature sources to obtain an expression for the clearing velocity. Fig. 1 shows the large spread in available correlations for the clearing velocity, which is partially caused by scale effects. The effect of air pocket length and pipe angle on the net air discharge is considerable, yet this was investigated only recently (Lubbers and Clemens 2007). The experimental investigations by Lubbers and Pothof on downward cocurrent air-water flow relate to small air-water discharge ratios (0.001 to 0.01) and moderate water velocities (0.1 to 1.5 m=s), so that the air pocket length varies from zero to the maximum length at these conditions. A numerical air transport model has been developed and validated against available experimental data (Pothof and Clemens 2011). Zukoski experimentally investigated the influence of surface tension and Reynolds number on the rise velocity of elongated bubbles (Zukoski 1966), which is closely related to clearing velocity. Literature on the surface tension of wastewater is scarce, to the authors’ knowledge. Given the fact that proteins and surfactant additives are present in wastewater, it is to be expected that the surface tension of domestic wastewater would be variable. A reduced surface tension of wastewater may enhance the air transport in downward sloping pressurized pipes. These hypotheses have been investigated experimentally by performing three series of air-water flow experiments in a large-scale facility at a wastewater treatment plant: 1. Clean water, 2. Clean water with surfactants, and 3. Raw wastewater. The experimental setup is described in detail, and the measurements are presented, analyzed, and discussed. This paper also presents measurements of the surface tension of domestic wastewater.

Materials and Methods The surface tension was measured using two different techniques. To get an impression of the possible range of surface tension values, samples from different sources were taken to the DelftChemTech

laboratory at Delft University of Technology (DUT) and the surface tension was measured by a pendant drop method using an instrument made by Krüss. The surface tension was measured 30 times at a frequency of 1 Hz, so that the average and standard deviation could be determined. The pseudodynamic surface tension was measured using a Wilhelmy plate tensiometer in a research laboratory. The influence of turbulence on the surface tension was explored qualitatively using this method. The third method is based on the force needed to pull a needle out of a liquid sample; a Kibron AquaPi tensiometer was used during the experimental work at the wastewater treatment plant (WWTP). The tensiometer was calibrated every day with tap water. A large-scale experimental facility was erected at the WWTP Nieuwe Waterweg in Hoek van Holland to perform cocurrent air-water flow experiments with raw wastewater and with surfactant-added water in addition to the experiments with clean water. A schematic layout is shown in Fig. 2. The facility includes a rising pipe, an upstream horizontal section with a length-diameter ratio of Lu =D > 10, a miter bend into the downward sloping section, a second miter bend to a downstream horizontal section, followed by horizontal or rising pipe work back to the reservoir or the WWTP. This lay-out guarantees that none of the injected air can escape in the upstream direction. The pipe material of the two horizontal sections and the downward sloping section was transparent PVC. The internal diameter of the transparent sections is D ¼ 0.192 m. The length of the downward sloping section is L ¼ 40.1 m (L=D ¼ 209). The pipe angle is θ ¼ 10°, which is typical for inverted siphons constructed with the horizontal directional drilling technique. Experimental Series 1 (clean water) and 2 (clean water + surfactants) were carried out by recirculating the water through a separation tank. Experimental Series 3 (wastewater) was carried out by extracting water from the inlet culvert into the presedimentation tank. The wastewater is returned into the outflow of the sand trap, which is approximately 10 m upstream of the extraction point. Recirculation of the wastewater back into the flow facility was very unlikely because the minimum inflow into the WWTP during the experiments (200 l=s) was roughly 4 times the maximum flow into the authors’ facility (45 l=s). The average dry-weather inflow into the WWTP is 185 l=s. The surface tension was adjusted by adding nonfoaming surfactants to the clean water tank, so that surface tension values between 40 · 10−3 and 70 · 10−3 N=m were obtained. During the air-water flow Series 2 and 3, samples for the surface tension measurements were extracted at 15 min intervals and analyzed immediately. Air was injected in the upstream horizontal section at the pipe soffit at a distance of 1.78 m (9.3D) from the downward sloping section. Since the air was injected via a relatively large connection, the air injection had no influence on the surface turbulence or the air transport in the downward sloping section. The air mass flow rate ˙ma was measured by a thermal air mass flow meter (Bronkhorst High-Tech); the measuring principle is based on a temperature drift measurement in an accurately split bypass flow. The mass flow rate was controlled to a preset volumetric flow rate Qa using water temperature T and pressure at the location of the upstream absolute pressure transducer. The upstream absolute pressure p1 was measured in the riser pipe upstream of the horizontal section. The downstream pressure tapping was located in the downstream horizontal section at least 6D downstream of the miter bend. This tapping was connected to a second absolute pressure transducer p2 and a differential pressure transducer Δp for optimum accuracy in the measured gas pocket head loss. The high pressure side of the differential pressure transducer was connected to the upstream pressure tapping. The absolute pressures were measured JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JANUARY 2013 / 45

J. Hydraul. Eng. 2013.139:44-50.

hydraulic grade line (HGL) Hfric

HGL without gas gas accumulation vsw

Hg HGL with gas

vw1

y1 p1


hydraulic jump

z1 vw2

y2 p2 z2 reference plane

Fig. 2. Definition sketch with upstream pressure transducer in horizontal section

with Druck PDCR4010 instruments, and the differential pressure was measured with a Rosemount 3051. The water flow rate Qw was measured with an electromagnetic flow meter (EMF), positioned in an upstream pipe segment without air. A flow control valve controlled the water flow rate to a preset value. These signals _ g , T, Qw , p1 , p2 , and Δp) were sampled at 100 Hz for at least (m 30 s to capture turbulent fluctuations and determine the 30 s average values. The gas pocket head loss was monitored over time until an equilibrium state was reached at which the aggregated gas pocket length had become constant. This stabilization process could take hours. The total energy conversion between the pressure tappings in the experimental facility, indicated by subscripts 1 and 2 in Fig. 2, includes losses ΔHfric due to wall friction and the miter bends, energy losses due to the air pocket ΔH g , hydrostatic pressure p=ρw g, and elevation z. The frictional head loss ΔH fric refers to situations without air. The air pocket head loss ΔHg represents all extra losses due to the presence of air in the downward sloping reach: p1 p þ z1 ¼ 2 þ z2 þ ΔH fric þ ΔHg ρw g ρw g

ð1Þ

Since the pressure transducers were installed at sufficient distance from the up- and downstream miter bends, the differences in kinetic energy could be neglected. The gas pocket head loss was approximately equal to the aggregated height of the air pockets in the downward sloping section: ΔHg ≈ Lg sin θ

ð2Þ

where θ and Lg are the pipe angle and the aggregated length of air pockets. Further details can be found in Pothof and Clemens (2011). At a given water discharge, the total air discharge increases at increasing length of the air pockets (i.e., at increasing gas pocket head loss). To compare the cocurrent air-water flow results with results at other pipe angles and other pipe diameters, the air and water discharge and the gas pocket head loss were nondimensionalized. The nondimensional gas pocket head loss is conveniently expressed as the ratio of the gas pocket head loss and the elevation difference of the downward sloping reach (L sin θ): R¼

ΔH g L sin θ

ð3Þ

A dimensional analysis of the momentum balance on elongated bubbles in downward sloping or inclined pipes, including buoyancy and drag, revealed a Froude-scaling (Bendiksen 1984; Benjamin 1968; Kent 1952). This dimensionless number FX is also known as the flow number or pipe Froude number: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi QX ρw QX ð4Þ FX ¼ pffiffiffiffiffiffi ≈ pffiffiffiffiffiffi A gD ρw − ρg A gD where subscript X = gas (g) or liquid/water (w) phase; QX = phase discharge; A = pipe cross-sectional area; D = pipe diameter; g = gravitational acceleration; ρw = water density; and ρg = gas density. The approximation in Eq. (4) holds for low-pressure air-water systems where ρg ≪ ρw . The dimensionless number Fw is called the water flow number, to distinguish it from the Froude number of the stratified water film. A more elaborate discussion on dimensional analysis is available in Pothof and Clemens (2011). Table 1 shows the combinations of air and water flow number at which the equilibrium gas pocket head losses were measured. All tabulated combinations were measured with clean water (Series 1). Series 2 was measured at 20 different air-water discharge combinations with variable surface tension. Series 3 was measured at 25 discharge combinations with variable surface tension.

Experimental Results Surface Tension Measurements The influent to the WWTP stems from four different sources. Approximately 95% of the influent is domestic wastewater from the towns of Hoek van Holland (HvH) and ‘s Gravenzande (sG). The remaining 5% of the wastewater is industrial wastewater from two industrial plants (DSM and SVTM). The composition of the industrial wastewater differs significantly from the domestic wastewater, but the surface tension is consistently greater than 70 · 10−3 N=m. The surface tension was measured using the pendant drop method in February and April 2008 with relatively low water temperatures at the WWTP (10°C and 13°C). The surface tension of the domestic wastewater inflows varied between 58 · 10−3 and 68 · 10−3 N=m (Fig. 3). For the gas transport processes in the facility the dynamic behavior of the surface tension is also important. At first, the pendant drop method was extended for longer drop lifetimes and every second the surface tension of the drop was determined.


J. Hydraul. Eng. 2013.139:44-50.

Table 1. Measured Combinations of Air and Water Discharge Fw Fg 1000 0.4 0.8 2 4 6

0.09

0.18

0.27

2, 3

2 2

2, 3 3

0.36

0.45 2, 3 3

2, 3

2

2, 3

2, 3

0.54

3

0.63

0.72

0.81

0.9

2, 3 2, 3 3 2, 3

2, 3

2, 3 2, 3 3 3

2, 3 2 3 2, 3

3

0.98

1.07

1.16

2, 3

2

3

3

The measurement of the domestic HvH sample was stopped after 200 s because the drop was released from the capillary. The surface tension of the two domestic wastewater samples (HvH and sG) is decreasing in time toward 42 · 10−3 N=m and 47 · 10−3 N=m. This can be caused by surface active molecules with a small molecular diffusivity or by sedimentation of particles in the pendant drop (increase in density of the liquid in the drop). It is obvious that a larger standard deviation of the surface tension indicates a nonstationary surface tension of the sample. The pseudodynamic measurement indicates a large difference between the static surface tension and dynamic surface tension of wastewater. The air entrainment in the hydraulic jump depends (among other variables) on the surface tension of the wastewater at the hydraulic jump, which in turn is a function of the lifetime of the water surface at the hydraulic jump. With a typical air pocket length of 20 m (half the test section) and a water film velocity of 3 m=s, the typical surface lifetime is on the order of 6 s. The WWTP is fed by different sources including two combined sewer systems. During storm water events a mixture of domestic wastewater and storm water arrives at the WWTP. During all air-water flow measurements, performed during dry-weatherflow conditions, the wastewater surface tension was measured using the static needle method and varied between 40 · 10−3 and 50 · 10−3 N=m. These measurements were carried out in September and October 2008 with influent temperatures predominantly between 16 and 20°C. Fig. 4 shows a weak correlation with negative slope between the influent temperature and the wastewater surface tension (R2 ¼ 0.4). It was concluded that the static surface tension of domestic wastewater varied between 40 · 10−3 and 50 · 10−3 N=m when it arrived at the WWTP.

water temperature was 21.7 0.2°C for both series. The wastewater experiments were carried out in autumn with water temperatures predominantly between 15 and 20°C (average 16.7°C). These ranges of water temperatures affect the air-entrainment rates by less than 7% (Mortensen et al. 2011). The temperature influence on the surface tension is less than 4%. Therefore, the temperature influence on the air entrainment was not addressed separately. The measurements with clean water show stratified flow, so that the maximum gas pocket head loss occurs (Flow Regime 1). The second flow regime is the blowback flow regime with a single air pocket (2a) or with multiple air pockets (2b). The single air pocket was observed at Fw < 0.53. Up to 7 consecutive air-entraining hydraulic jumps were observed in the range 0.53 < Fw < 1.0. Fig. 5 shows the dimensionless gas pocket head loss and observed flow regimes. The nonfoaming detergents in Series 2 clearly affect the gas pocket head loss in the blow back flow regime with air-entraining hydraulic jumps (Fig. 6). A lower surface tension changes the shape of the large gas pockets—with typical dimensions on the order of the pipe diameter D—and decreases the average bubble diameter in the turbulent hydraulic jumps (Hinze 1955). Therefore, more air bubbles will reach the bottom of the inverted siphon and the net air discharge will increase accordingly. The average bubble diameter can be assessed from the average turbulence in the hydraulic jump and Hinze’s results. Fig. 7 plots the available gas pocket head loss data at two air discharge rates and variable surface tension as a function of the pipe Weber number WD.

Air-Water Flow Results

These data are compared with the experimental points for clean water (σw ¼ 72 · 10−3 N=m). The experimental data in Fig. 7 collapse to a single line in the blowback flow regime, showing that the pipe Weber number is a suitable scaling parameter for the gas

WD ¼ ρv2sw D=σ

80

ð5Þ

60

70

Feb. 21, 2008 Apr. 14, 2008

60

ST V M

SM D

w at er ra ve nz an H oe de k v. H ol la nd s'G

iw em

Te rra in

at

er

50

Fig. 3. Exploratory measurements of surface tension of different influent sources at wastewater treatment plant (WWTP); “demi water” = demineralized water, “terrain water” = extra treated effluent water used for clean water experiments; remaining four labels refer to four influent sources to WWTP

Surface tension [10-3 N/m]

-3

Surface tension (10 N/m)

The water temperature varied between 15 and 26°C during the experiments with clean water and nonfoaming detergents; the average

D


Note: The complete matrix was measured with clean water (Series 1). Experiments with surfactant-added water are labeled 2, experiments with wastewater are labeled 3. Experimental Series 2 was carried out in June and July 2008; Series 3 was carried out in September and October 2008 and March 2009.

50

40

30 10

12

14

16

18

20

22

Influent temperature [°C]

Fig. 4. Measured wastewater surface tension and influent temperatures JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JANUARY 2013 / 47

J. Hydraul. Eng. 2013.139:44-50.

[-] Gas pocket head loss, Hg L s in

1

(2a)

(3)

0

0.3

0.6 Water flow number, F w [-]

0.9

1.2

Fig. 5. Nondimensional gas pocket head loss including flow regime labels (1), (2a), (2b), and (3) and flow regime transitions (straight lines) at WWTP facility

Gas pocket head loss, Hg /(L sin ) [-]

1

Fw=0.63; Fg·1000=4 Fw=0.45; Fg·1000=0.4 Fw=0.63; Fg·1000=0.4

0.75

(σw ). Furthermore, it is concluded from Fig. 7 that the flow regime transitions also depend on the surface tension. It is recommended to extend the flow number with a surface tension correction factor: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi QX ρw σ w FX;σ ¼ pffiffiffiffiffiffi ð6Þ A gD ρw − ρg σ

(2b)

0.5

0

The flow number concept presented in Eq. (6) is provisionally recommended for other fluid-gas mixtures until direct evidence of its applicability has become available. It is anticipated that the different constituents in wastewater will influence the gas transport processes. For 6 days of initial tests with wastewater at constant air and water flow rates, the surface tension was measured every 15 min. These initial tests showed that the surface tension of dry-weather-flow wastewater varied within a bandwidth of 5 · 10−3 N=m (standard deviation of 3 · 10−3 to 4 · 10−3 N=m) during a 4-to 6-h measurement period. A trend in the surface tension data during these days could not be detected. Furthermore, the gas pocket head loss remained constant during the initial tests. Therefore, stabilized measurements could be performed at constant liquid and gas flow rates. Figs. 8 and 9 clearly show that the gas pocket head loss in wastewater is comparable with the head loss in clean water in all flow regimes, despite the smaller surface tension of wastewater.

Fw=0.72; Fg·1000=0.4

Discussion

0.5

0.25

0 40

50

60 Surface tension,

70

80

[10-3 N/m]

Fig. 6. Influence of surface tension on gas pocket head loss

1

tap water, Fg*1000=0.4

0.5 surfactant, Fg*1000=0.4 tap water, Fg*1000=4 surfactant, Fg*1000=4

0 10

The experiments with reduced surface tension showed that the air pocket head loss scales with the pipe Weber number. The validity of this Weber scaling suggests that a gas discharge model can be generalized to other fluid mixtures. The insensitivity of the air transport for the surface tension of wastewater may be caused by the lower molecular diffusion of the σ-reducing constituents in wastewater compared to the detergents used to reduce the surface tension of the clean water. In fact, the surface tension is a dynamic variable because the detergents need time to reach equilibrium between the interface concentration and the bulk concentration. In a lab analysis the dynamic evolution of the surface tension is dominated by molecular diffusion. Measurements of the dynamic surface tension of a couple of samples of wastewater and surfactant-added water were performed to investigate this dynamic behavior (Fig. 10). A solution with surfactants had a static surface tension of 44 · 10−3 N=m, which is comparable with the surface tension of the wastewater samples (Fig. 10). The average composition of the wastewater in the authors’ facility was a

Gas pocket head loss, Hg / (Lsin ) [-]

pocket head loss in this flow regime. If the proper length scale in the Weber number were based on a typical bubble diameter in the turbulent hydraulic jump (Hinze 1955), the data would not collapse to a single line. It is concluded from the Weber scaling in Fig. 7 that the pipe velocity and pipe flow number should be multiplied by the ratio ðσ=σw Þ1=2 to obtain identical results for the gas pocket head loss, for fluid systems with a surface tension other than air-water

Gas pocket head loss, Hgas / (L sin ) [-]


Fg·1000=0.4 Fg·1000=0.8 Fg·1000=2 Fg·1000=4 Fg·1000=6

(1)

Fg·1000=0.4 Fg·1000=0.4 WW Fg·1000=2 Fg·1000=2 WW Fg·1000=4 Fg·1000=4 WW

1

0.5

0 0

100 1000 Pipe Weber number, We D [-]

10000

Fig. 7. Gas pocket head loss as a function of pipe Weber number

0.3

0.6 0.9 Water flow number, F w [-]

1.2

Fig. 8. Gas pocket head loss in clean water (solid lines and markers) and wastewater (dashed lines, open markers)


J. Hydraul. Eng. 2013.139:44-50.

(10-3 N/m)

80

0.8

Surface tension,

0.6

Fg·1000=0.4

0.4

Fg·1000=0.8 0.2

Fg·1000=2

70 Manual stirring

60

Surfactant, 10-5 Wastewater

50

Fg·1000=4 0 0

0.2 0.4 0.6 0.8 Gas pocket head loss tap water, H g / (Lsin ) [-]

1

4∶1 mixture of Wastewater 1 (sG) and Wastewater 2 (HvH). The straight lines in Fig. 10 confirm that the dynamic surface tension is diffusion-controlled. The gradients in Fig. 10 do not differ by an order of magnitude. Therefore, the molecular diffusion in wastewater cannot explain the observed differences in the gas pocket head loss between wastewater and surfactant-added water. Another explanation for the observed differences takes the turbulent mixing in the water film into account. On one hand, if a new interface is created in the top of the inverted siphon, then turbulent mixing promotes the motion of surfactant particles toward the interface. On the other hand, turbulence may shed particles from the interface. Therefore, turbulence may affect the time scale at which the equilibrium surface tension is reached and the equilibrium surface tension itself. The influence of turbulence on the dynamic surface tension was assessed qualitatively by stirring a lab sample during a dynamic measurement. Fig. 11 shows that manual stirring of the sample accelerated the exponential decay of the surface tension, which means that the stirring accelerated the transport of surfactants toward the interface. The effect of stirring on the wastewater sample was much less pronounced; the decay of the surface tension was not accelerated by stirring. The influence of turbulence on the surface has not been investigated in sufficient detail to draw firm conclusions, but the exploratory experiments indicate that turbulence has a more positive influence on the surfactant-added water than on the wastewater. It is likely the case that the surfactants in wastewater (mainly proteins and fat molecules)

(10-3 N/m)

60 Wastewater 2

Surfactant, 10-5

50

Wastewater 1 40

30

0

0.04 Transformed time, t -0.5 (

0.08 -0.5

0.12

)

Fig. 10. Plot of dynamic surface tension versus t−0.5

40

0

100

200

300

400

500

Time, t (s)

Fig. 9. Comparison of gas pocket head loss in tap water and wastewater at different air flow numbers

Surface tension,


Gas pocket head loss wastewater, Hg / (Lsin ) [-]

1

Fig. 11. Dynamic surface tension in lab measurements with manual stirring to make a qualitative assessment of influence of turbulence on dynamic surface tension

are detached more easily from the interface than the surfactants in the surfactant-added water. Since convergence to a steady state is very slow, real systems are likely to operate frequently in transitional states that might depart significantly from the equilibrium conditions explored in this paper. If a system has been properly vented initially, air will accumulate until the equilibrium condition has been reached. In this case, the gas pocket head loss values in this paper represent the maximum persistent gas pocket head loss. If, on the other hand, the system is started from an empty pipe, the gas pocket head loss will reduce asymptotically toward the equilibrium condition. For systems with large discharge variations, the equilibrium conditions can be used in a dynamic modeling approach to assess the accumulation and breakdown of air pockets during normal operations. A practical modeling approach was presented in another paper (Pothof and Clemens 2011).

Conclusions and Recommendations The cocurrent air-water flow experiments show that the air transport by flowing water in downward sloping pipes is a function of the water flow number, pipe angle, and air accumulation. The experiments with surfactant-added water (45 · 10−3 < σw < 65 · 10−3 N=m) show that the gas pocket head loss decreases in proportion to the surface tension. It was shown that the gas pocket head loss scales with the pipe Weber number in the blowback flow regime. A consequence of the Weber number scaling is that the flow regime transitions also depend on the surface tension. It is recommended the flow number be extended with a surface tension correction factor: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi QX ρw σ w FX;σ ¼ pffiffiffiffiffiffi ð7Þ A gD ρw − ρg σ The flow number concept presented in Eq. (7) is provisionally recommended for other fluid-gas mixtures until direct evidence of its applicability has become available. It has been shown that the net air discharge by flowing water in a downward sloping reach increases as the surface tension is reduced. The net air discharge is affected by two physical processes: air entrainment in the hydraulic jump and bubble motion downstream of the hydraulic jump. Since the performed experiments do not discriminate both physical processes, it is not possible to draw a JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JANUARY 2013 / 49

J. Hydraul. Eng. 2013.139:44-50.


firm conclusion on how the surface tension influences the air entrainment into a hydraulic jump. It is recommended that Kalinske’s experiments (1943) be repeated over a range of surface tension values to establish the relation between surface tension and airentrainment rate in a hydraulic jump. The static surface tension of domestic wastewater varies between 40 · 10−3 and 50 · 10−3 N=m. Nevertheless, the composition of wastewater, i.e., lower surface tension and solids content, does not enhance the air transport in comparison with the air transport in clean water. The remarkable difference between surfactant-added water and wastewater is probably caused by the influence of turbulence on the dynamic surface tension. Indicative lab measurements suggest that turbulence accelerates the evolution of surface tension toward a static value for the surfactant-added water, while turbulence has the opposite effect in wastewater. In all likelihood, the surfactants in wastewater (mainly proteins and fat molecules) are detached more easily from the interface than the surfactants added to the clean water. It is recommended that the influence of turbulence on the dynamic surface tension be investigated in more detail.

Acknowledgments This study was undertaken as part of the CAPWAT project on capacity losses in pressurized wastewater mains. The authors wish to thank the participants of the CAPWAT project: water boards Delfland, Hollands Noorderkwartier, Brabantse Delta, Reest en Wieden, Rivierenland, Zuiderzeeland, Fryslân and Hollandse Delta, water companies Aquafin and Waternet, consultants Royal Haskoning, Grontmij Engineering Consultancy, Gemeentewerken Rotterdam, pump manufacturer ITT Water & Wastewater BV, Foundation Stowa, and the Dutch Ministry of Economic Affairs. The authors also wish to acknowledge the employees at the treatment plant for their flexible cooperation and interest in the project.

Notation The following symbols are used in this paper: A = pipe cross-sectional area [m2 ]; D = pipe diameter [m]; Fg = pipe flow number related to gas discharge [−]; Fw = pipe flow number related to water discharge [−]; g = gravitational acceleration [9.81 m=s2 ]; L = pipe length [m]; Lg = aggregated length of gas pockets [m]; Lu = upstream horizontal length of experimental facility [m]; ˙mg = gas mass flow rate [kg=s]; p1 = absolute pressure at the upstream end [N=m2 ]; p2 = absolute pressure at the downstream end [N=m2 ]; Qg = gas discharge [m3 =s]; Qw = water discharge [m3 =s]; R = dimensionless gas pocket head loss [−]; T = temperature [°C]; t = time [s]; vsw = superficial water velocity [m=s]; WD = pipe Weber number [−]; z1 = elevation upstream [m]; z2 = elevation downstream end [m]; ΔH fric = head loss due to wall friction [m]; ΔH g = head loss due to gas pockets [m]; Δp = differential pressure across test section [N=m2 ]; θ = pipe angle [°]; ρg = gas density [kg=m3 ];

ρw = water density [kg=m3 ]; σ = gas-fluid surface tension [N=m]; and σw = air-water surface tension [N=m].

References Bendiksen, K. H. (1984). “Experimental investigation of the motion of long bubbles in inclined tubes.” Int. J. Multiphase Flow, 10(4), 467–483. Benjamin, T. B. (1968). “Gravity currents and related phenomena.” J. Fluid Mech., 31(2), 209–248. Bliss, P. H. (1942). The removal of air from pipelines by flowing water, Iowa Institute of Hydraulic Research, Iowa City, IA. Escarameia, M. (2007). “Investigating hydraulic removal of air from water pipelines.” Proc. Inst. Civ. Eng. Water Manage., 160(1), 25–34. Falk, K., et al. (2004). “Multi-phase effects on pressure surges.” Proc., 9th Int. Conf. on Pressure Surges, BHR Group, Chester, UK. Falvey, H. T. (1980). Air-water flow in hydraulic structures, Water and Power Resources Service, Denver. Gandenberger, W. (1957). Über die wirtschaftliche und betriebssichere Gestaltung von Fernwasserleitungen, R. Oldenbourg, Munich. Glauser, S., and Wickenhauser, M. (2009). “Bubble movement in downward-inclined pipes.” J. Hydraul. Eng., 135(11), 1012–1015. Hinze, J. O. (1955). “Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes.” AIChE J., 1(3), 289–295. Kalinske, A. A., and Bliss, P. H. (1943). “Removal of air from pipe lines by flowing water.” Proc. Am. Soc. Civ. Eng., 13(10), 480–482. Kalinske, A. A., and Robertson, J. M. (1943). “Closed conduit flow.” Trans. Am. Soc. Civ. Eng., 108, 1435–1447. Kent, J. C. (1952). The entrainment of air by water flowing in circular conduits with downgrade slopes, Univ. of California, Berkeley, CA. Lubbers, C. L. (2007). On gas pockets in wastewater pressure mains and their effect on hydraulic performance, Delft Univ. of Technology, Delft, The Netherlands. Lubbers, C. L., and Clemens, F. H. L. R. (2007). “Scale effects on gas transport by hydraulic jumps in inclined pipes; comparison based on head loss and breakdown rate.” Proc., 6th Int. Conf. on Multiphase Flow (ICMF), Martin Luther Univ. of Halle-Wittenberg, Leipzig, Germany. Malekpour, A., and Karney, B. (2008). “Rapid filling analysis of pipelines using an elastic model.” Proc., 10th Int. Conf. on Pressure Surges, BHR Group, Edinburgh. Mortensen, J. D., Barfuss, S. L., and Johnson, M. C. (2011). “Scale effects of air entrained by hydraulic jumps within closed conduits.” J. Hydraul. Res., 49(1), 90–95. Mosvell, G. (1976). Luft I utslippsledninger (Air in outfalls), Norwegian Water Institute (NIVA), Oslo, Norway. Pothof, I. W. M., and Clemens, F. H. L. R. (2008). “On gas transport in downward slopes of sewerage mains.” Proc., 11th Int. Conf. on Urban Drainage, Edinburgh, Joint Committee IAHR/IWA Urban Drainage. Pothof, I. W. M., and Clemens, F. H. L. R. (2010). “On elongated air pockets in downward sloping pipes.” J. Hydraul. Res., 48(4), 499–503. Pothof, I. W. M., and Clemens, F. H. L. R. (2011). “Experimental study of air-water flow in downward sloping pipes.” Int. J. Multiphase Flow, 37(3), 278–292. Pozos, O., Gonzalez, C. A., Giesecke, J., Marx, W., and Rodal, E. A. (2010). “Air entrapped in gravity pipeline systems.” J. Hydraul. Res., 48(3), 338–347. Vasconcelos, J. G., and Wright, S. J. (2009). “Investigation of rapid filling of poorly ventilated stormwater storage tunnels.” J. Hydraul. Res., 47(5), 547–558. Wickenhäuser, M. (2008). Zweiphasenströmung in Entlüftungssystemen von Druckstollen [Two-phase flow in de-aeration systems for pressure tunnels], ETH, Zurich, Switzerland (in German). Wisner, P., Mohsen, F. N., and Kouwen, N. (1975). “Removal of air from water lines by hydraulic means.” J. Hydraul. Div., 101(HY2), 243–257. Zukoski, E. E. (1966). “Influence of viscosity, surface tension, and inclination angle on motion of long bubbles.” J. Fluid Mech., 25(4), 821–837.


J. Hydraul. Eng. 2013.139:44-50.