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Effect of drops on turbulence of kerosene–water two-phase flow in vertical pipe
International Journal of Heat and Fluid Flow 56 (2015) 152–159
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Effect of drops on turbulence of kerosene–water two-phase flow in vertical pipe F.A. Hamad a,⇑, P. Ganesan b a b
School of Science & Engineering, Teesside University, Middlesbrough TS1 3BA, UK Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia
a r t i c l e
i n f o
Article history: Received 19 March 2015 Received in revised form 29 July 2015 Accepted 30 July 2015
Keywords: Kerosene–water two-phase flow Turbulence Integral length scale Energy spectra
a b s t r a c t The effect of introducing kerosene drops on turbulence of kerosene–water two-phase in a vertical pipe is investigated experimentally. A hot-film and dual optical probes are used to measure the water velocity, turbulence fluctuation, drop relative velocity, volume fraction and drop diameter. Experiments are performed in a 78.8 mm diameter vertical pipe for four average water velocities of 0.11, 0.29, 0.44 and 0.77 m/s. The measurements were carried out for two area average volume fraction hai of 4.6% and 9.2% as well as for water single phase flow to investigate the effect of introducing kerosene drops on two-phase flow turbulence. The kerosene–water mixture was generated by adding the kerosene to constant flow rates of water. The results indicate that drops induced turbulence is a function of the ratio of the drop Reynolds number ðU r dB =mÞ to the turbulence Reynolds number ðu0 Lt =mÞ which decreased with higher water velocities. The results show that the Kolmogorov–Richardson scaling in the range of 4.5/3 to 6/3 for single phase flow which is replaced by 6/3 to 7/3 for two-phase flow. These values are less than 8/3 for air–water flow. Ó 2015 Elsevier Inc. All rights reserved.
1. Introduction The interaction between the drops/bubbles and liquid plays an important role in mass, momentum and energy transfer between the phases. The Turbulence structure in this type of flows is very complex due to: (i) the interaction between the drop-induced turbulence (bubble/drop motion) and shear-induced turbulence (the external force due to main flow). (ii) The modification of water radial velocity distribution due to the radial distribution of drop relative velocity, drop diameter and volume fraction. The introduction of drops can either enhance or attenuation the liquid turbulence (Serizawa and Kataoka, 1990). The two-phase flow turbulence has been investigated by a number of researchers in literature to understand the contribution of introducing the bubbles/drops on the continuous phase (Serizawa and Kataoka, 1990; Gore and Crowe, 1989, 1991; Serizawa et al., 1975; Wang et al., 1987; Liu and Bankoff, 1993; Farrar and Bruun, 1996; Cherdron et al., 1998; Hu et al., 2007; Shawkat et al., 2007). These studies indicated that: (i) introducing bubbles/drops into single phase water flow cause a sharp increase in turbulent intensity, particularly at low water ⇑ Corresponding author. E-mail addresses: [email protected] (F.A. Hamad), [email protected] (P. Ganesan). http://dx.doi.org/10.1016/j.ijheatfluidflow.2015.07.020 0142-727X/Ó 2015 Elsevier Inc. All rights reserved.
velocity, (ii) the increase in volume fraction more than 5% has very little effect on turbulence, (iii) the difference between the single phase and two-phase flow turbulence intensities diminished at higher water velocity, (iv) the effect is more pronounced at the pipe centreline than the wall region. The bubbles effect on energy spectrum has been investigated experimentally by a number of researcher (Shawkat et al., 2007; Lance and Bataille, 1991; Mudde et al., 1997; Rensen et al., 2005) to understand the influence of drop on energy production and dissipation. Lance and Bataille (1991) suggested the ratio of the bubble-induced kinetic energy and the kinetic energy of the flow without bubbles as appropriate dimensionless number (b) to characterize the type of the bubbly flow, defined as
b¼
1 aU 2t 2 u02 o
ð1Þ
where a is the volume fraction, Ut is the velocity of bubble/drop in still water, and u0o is the single phase velocity fluctuations. This dimensionless number is called bubblance parameter. They measured the liquid power spectrum in bubbly turbulence and a gradual change of the slope with increasing void fraction was observed. At low bubble concentrations the slope of the spectrum was close to the Kolmogorov’s value of 5/3. By increasing the volume fraction, the principal driving mechanism changed from external driving
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force to bubble generated turbulence and the slope become close to 8/3. The values of b depend on the nature of the flow, b < 1 for wall-induced turbulence and b > 1 for bubble-induced turbulence. Recent experiments (Martinez et al., 2010) found that the energy spectrum exponent is close to 3 for the bubbly turbulent flow when b = 1. The experimental study by Riboux et al. (2010) in the wake of a swarm of rising bubbles (b = 1) also found a spectral exponent 3. Shawkat et al. (2007) studied the structure of air– water bubbly flow in a 200 mm vertical pipe experimentally using hot film and dual optical probes. The slope of the spectrum was close to the Kolmogorov’s turbulent value of 5/3 which increased to 8/3 for two-phase flow. In contrast, there are few researchers found that the classical 5/3 power law for bubbly flow even for a gas volume fraction of 25% (Gore and Crowe, 1991; Mudde et al., 1997; Rensen et al., 2005). Gore and Crowe (1989, 1991) investigated turbulence modification caused by the addition of particles in a gas flow, and pointed out that the modification is well correlated with the so-called critical parameter, dB/Lt, the ratio of bubble/drop diameter (dB) to an integral length scale (Lt). The critical parameter can be regarded as the ratio of a characteristic length scale of turbulence induced by the dispersed phase to that of shear-induced turbulence. Hosokawa and Tomiyama (2010, 2004) proposed an eddy viscosity ratio (/), defined as
/¼
U r dB u0 Lt
ð2Þ
The eddy viscosity ratio (/) is the product of the length scales ratio, dB/Lt (Gore & Crowe’s parameter) and the velocity scales ratio Ur/u0 . Where Ur is the bubble relative velocity and u0 is the turbulence fluctuation. Turbulence enhancement due to bubble-induced turbulence is remarkable when the eddy viscosity ratio / is large but the effect is weak when / < 1. The eddy viscosity (/) can be modified to present the ratio of the bubble/drop Reynolds number ðU r dB =mÞ to the turbulence Reynolds number ðu0 Lt =mÞ. The literature review presented above shows that in spite of the extensive studies on turbulence for gas–liquid flow structure in a vertical pipe, there is still a dearth of research work for liquid–liquid flow. Hence, the objective of this paper is to investigate experimentally the effect of introducing kerosene drops on two-phase flow turbulence. The experimental data are used to calculate the integral length scale and the energy spectrum which are considered as an important variables in turbulence study. The measured parameters include water velocity, drop velocity, turbulence fluctuation, drop diameter and volume fraction in a vertical pipe of 77.8 mm diameter and 4500 mm length (L/D = 54). The measurements were performed at the centreline and near the wall (r/R = 0.9) for constant water velocities, U ws = 0.11, 0.29, 0.44 0.77 m/s (Re = 8600, 22,600, 33,800, 60,000) and area average volume fraction hai, b = 0%, 4.6% and 9.2%. 2. Experimental facility and measuring techniques The experimental facility used in the present study which is explained in details in Hamad and He (2010). Briefly, the test section is made of a transparent acrylic pipe of 77.8 mm inner diameter and 4500 mm length at L/D = 54. The water and kerosene were pumped from the storage tank to the test section via two flow meters, Y-junction and a 90° bend. The mixing of the phases is achieved by bringing the two pipelines together into a 152.4 diameter 90° bend using Y-junction. To remove the swirl generated due to the change of fluid flow from horizontal to vertical direction, a tube bundle consisting of four tubes is constructed and installed upstream of the test-section inlet. The mixture from the test
153
section outlet was returned to the storage tank via the horizontal pipe. A bypass chillier has been used to maintain the water temperature at 16 °C within the flow loop during the experiment. Two filtration units with 8 and 2 lm mesh size were used to maintain the water and kerosene in a clean condition. The clean fluids minimize the error of drop velocity measurements caused by contamination (Duineveld, 1994). The clean water and temperature control also minimize the shift in hot-film calibration curve and minimize the error of water velocity measurements. Kerosene was used as a dispersed phase in water to generate the liquid–liquid two-phase flow required in this study. The kerosene properties were: density (q) = 807 kg/m3, surface tension (r) = 0.030 N/m and dynamic viscosity (l) = 0.024 N s/m2. Hot-film and dual optical probes are used in this study 2.1. Hot-film probe A single normal boundary layer hot-film probe of 37 lm (DANTEC 55R15) has been used in this study. It was mounted in a standard DANTEC 55H20 probe support which in turn was mounted in a DANTEC 55H540 water-tight mounting tube with a 90° bend, which was fastened to the probe traverse mechanism. The hot-film probe was operated by a DANTEC 56C anemometer at an overheat ratio of 1.05 to avoid formation of air bubbles on the hot-film element. In order to calculate the continuous phase velocity correctly, it is necessary to eliminate any part of the signal which does not correspond to a continuous phase velocity and this is described in details in Hamad and Bruun (2000). Briefly, any noise in the signals that are not reflective of the continuous velocity phase is removed. The instantaneous water velocity U (t) can be calculated as,
U w ðtÞ ¼
E2 ðtÞ A B
!1=n ð3Þ
where A, B and n are calibration constant. The hot-film was calibrated by obtaining a set of calibration points (E, U) for single phase flow where E is the hot-film output voltage and U is the single phase flow velocity measured by Pitot tube placed at the centreline of the test section at L/D = 54. Selecting 10–20 points covering the required range of velocity (0.1–1.00 m/s), the values of (E, U) recorded and curve fitted to give the values of A, B and n used in Eq. (3). Recomposing the instantaneous water velocity U w ðtÞ ¼ U w þ u0 , with U w being the local mean water velocity and u0 the local turbulent water fluctuation. In a digital data analysis using a digital time record with a total number of points N, we have
U w ¼ RU w ðtÞ=N
ð4Þ
n o1=2 2 u0 ¼ RðU w ðtÞ U w Þ =N
ð5Þ
Shawkat et al. (2007) investigated the different methods used in literature to replace the gaps due the elimination of drops from the signal such that liquid turbulence statistics and spectra were not affected. He found that replacing the gap with a linear interpolation was the best method. In this study the value at point A was used to replace all the eliminated points as the difference between the values at points A and D are much smaller than gas–water two-phase flow cases. This is due to the significant differences in density, viscosity and surface tension of the kerosene and air which affect the bubble interaction between the probe and the kerosene drop or air bubble. The uncertainty in hot-film measurements may be attributed to one or more of the following factors: (i) calibration curve error, (ii) change in temperature of the fluid during the test, (iii) signal
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analysis and (iv) the type of drop-probe interaction. A detailed information about the accuracy of using hot-film probe can be found in Hamad and Bruun (2000) and Hamad and He (2010).
3. Results and discussion
2.2. Dual optical probe
Figs. 1a, 1b and 1c present the radial distributions of the turbulent fluctuation for water velocities of 0.29, 0.44 and 0.77 m/s and area average volume fraction hai of 0%, 4.6% and 9.2%. The results show that introducing kerosene drops in water cause a sharp increase in turbulent fluctuation but increasing the area average volume fraction hai has insignificant influence. The results also show that the difference in fluctuation between the single phase and two-phase flow decreased with higher water velocity and the influence of the drops is more pronounced at the pipe centreline. Based on these results and the eddy viscosity ratio in Eq. (2) from literature, two locations (r/R = 0 and 0.9) are selected for further analysis using integral length scale and energy spectra. Figs. 2–7 present the variation of turbulent fluctuations, local water velocities, drop relative velocities, volume fractions, drop diameters and drop frequency with average water velocity for different area average volume fraction hai at r/R = 0, 0.9. The results from these figures suggest that turbulence fluctuation can be related with various variables such as water velocity, drop relative velocity, volume fraction and drop diameter. For single phase flow;
The dual optical probe was made of two fibres to measure the volume fraction, drop cut chord and drop velocity. The axial distance between the two tips was 0.9 mm and they were separated laterally by approximately 0.45 mm centre to centre. The axial and lateral separation of the two fibres were optimized to detect the same droplet and to produce sufficient resolution to calculate the drop velocity accurately and at the same time minimize the meniscus effects from the first fibre tip affecting the reading from the second fibre. The optical probe cable used was 5 m long; it had a 100 lm core diameter and a 140 lm cladding diameter. The cladding provided a constant step in the refractive index at the core– cladding interface, which guided the light inside the fibre and also improved the mechanical properties of the fibre. The dual optical probe is used to measure the volume fraction, drop velocity and drop diameter. The local volume fraction at any radial position can be determined by the procedure as described in Hamad et al. (2000) as:
a ¼ lim
X
T!1
Dt d =T
ð6Þ
P
where Dt d the total dispersed phase residence time and T is the total sampling time. The drop velocity can also be calculated by applying the cross-correlation technique to the signals as
RðsÞ ¼
1 T
Z
T
E1 ðtÞE2 ðt þ sÞdt
ð7Þ
0
The RðsÞ for different values of ðsÞ to find the maximum time of flight ðsm Þ. The average drop velocity ðU B Þ can be evaluated from the time of flight ðsm Þ and the axial distance (Dx) between the two fibres tips as:
UB ¼
Dx
sm
ð8Þ
The signal from the first sensor can be used to calculate the drop diameter as:
dB ¼ 1:5U B DT 1
ð9Þ
The drop frequency (N) is calculated from the output of the leading sensor of the dual optical probe by counting the number of drops per second that pass the measurement point. The uncertainty in optical probe is a result of the probe geometry and the position where the probe hit the projected front area of the drop. The probe geometry includes the sensor diameter as well as axial and lateral distances between the sensors. This large distance between the two sensors may lead to a large number of drops hitting one sensor and missing the other one which affects the accuracy of time of flight calculated from cross-correlation method. The bubble-probe interaction can be classified into three types: (i) the blinding effect, when small bubbles are not detected due to imperfect probe dewetting; (ii) the drifting effect, when the bubble trajectory is altered leading to a smaller drop detection or no detection at all and (iii) the crawling effect due to bubble deformation and deceleration on the probe tip. The blinding and drifting effects lead to an underestimation of the volume fraction. In contrast, the crawling effect leads to an overestimation of the volume fraction. The error increases at low liquid velocity and volume fraction for the higher possibility of drifting and blinding effects under such conditions. A details information on accuracy of dual optical probe can be found Hamad et al. (2000) and Hamad and He (2010).
3.1. Local flow parameters
u0s aU w
ð10Þ
For two-phase flow;
u0TP a
ak U w dB U r
ð11Þ
where u0s is single phase turbulence fluctuation; U w is water velocity; u0TP is two-phase turbulence fluctuation; ak kerosene volume fraction. 3.2. Velocity time series and the integral length scale To understand the effect of drops on turbulence enhancement/attenuation, the time series of turbulence fluctuations recorded by hot-film probe in the axial direction are given in Fig. 8 for Average water velocities of 0.29 and 0.77 m/s and area average volume fraction hai of 0%, 4.6% and 9.2%. The axial velocity is clearly agitated by the present of kerosene drops in Fig. 8a for the low average water velocity; therefore the turbulence fluctuations amplitude in water phase becomes larger than that in the single-phase flow. This can be explained as a result of axial velocity acceleration around drops and the amplitude of the fluctuation enhanced to be in the order of the terminal rising velocity of a drop in stagnant water (about 0.15 m/s). It also can be observed that
Fig. 1a. Vaiation of turbulence fluctuation with radial distance for different area average volume fraction hai (average water velocity = 0.29 m/s).
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Turbulence fluctuation (m/s)
0.08 SP - CL
4.6%CL
9.2%CL
SP - Wall
4.6%Wall
9.2%Wall
0.06
0.04
0.02
0 0
0.2
0.4
0.6
0.8
1
Average water velocity (m/s) Fig. 1b. Vaiation of turbulence fluctuation with radial distance for different area average volume fraction hai (average water velocity = 0.44 m/s).
Fig. 2. Variation of turbulent fluctuation with average water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/ R = 0.9).
be observed that the contribution of drop in turbulence at low water velocity is very high at both centreline and near the wall. It decreases steeply near the wall where the boundary layer has a major contribution to the turbulence. On the other hand, the eddy viscosity decreases gradually at the centreline where the higher drop relative velocity and larger drops diameters are recorded as given in Figs. 6 and 8. In general, the effect of drop on turbulence is diminished at higher velocities. These results are supported by the finding for gas–liquid flow (Gore and Crowe, 1989, 1991).
Fig. 1c. Vaiation of turbulence fluctuation with radial distance for different area average volume fraction hai (average water velocity = 0.77 m/s).
agitation due to drops has less effect on turbulence fluctuation for the case of high water velocity (0.77 m/s) as fluctuation amplitude become similar to single phase flow. Referring to the Figs. 3 and 4, is clearly indicates that the velocity scale ratio Ur/u0 is an important parameter of the turbulence modification in bubbly flows (Hosokawa and Tomiyama, 2010, 2004). To study the effect of dB/Lt on turbulence, the autocorrelation function for different flow conditions for single and two-phase flows at the pipe centreline and near the wall are plotted in Fig. 9 to calculate Lt. The results show that the normalized time scale (Rs ) is a function of volume fraction but there is no clear trend as in the case of air–water flow data given by Shawkat et al. (2007) where the Rs decay faster than single phase flow. This behaviour may be attributed to a large difference between the properties of air and kerosene which both used as a second phase. The autocorrelation can be used to calculate the integral length scale using the following relation:
Lt ¼ U
Z
1
Rs ds
ð12Þ
0
Fig. 10a present the data of integral length scales for different water velocities and area average volume fraction at the pipe centre line and near the wall. The results show that the second phase has a small effect on integral length scale. It can be observed that there a case of transition in flow condition at water velocity = 0.44 m/s when the introduction of kerosene cause a clear peak of integral length scale. Fig. 10b present the variation of eddy viscosity ratio with average water velocity at the pipe centreline and near the wall. It can
3.3. Turbulence energy spectra The energy spectra analysis is expected to provide a valuable information on the flow structure as in the single phase flow. In case of two-phase flow, the signal corresponding to the liquid should be identified and separated by eliminating the drops and replace them with the same number of points with appropriate values. The signal becomes similar to single phase flow which can analysed to calculate and plot the energy spectra. Figs. 11–14 display the energy spectra for average water velocities (0.11, 0.29, 0.44 and 0.77) and different average volume fraction (a = 0. 4.6% and 9.2%) at the centreline and near the wall. The results show that: (i) the energy of large eddies (energy production zone) at low frequency is higher than the single phase flow at low water velocity (0.11 m/s, Re = 8600) indicating that there is a turbulence enhancement at both centreline and near the wall as shown in Fig. 11. It can also be observed from Fig. 11 that the dissipation for two-phase flow take place at wider range of frequencies compared to the single phase flow leading to lower values at high frequencies. The results in Fig. 11a display two different slopes (one for water and the other one for kerosene–water) of energy spectrum at low frequencies which is a unique behaviour. This unique behaviour may attributed to minor contribution of boundary induced turbulence in energy production compared to drop wake turbulence at this low water velocity. As the velocity increased, the enhancement of turbulence by drops decreases as it can be seen for the water velocities of 0.29 and 0.44 m/s (Re = 22,600 and 33,800). Increasing the water velocity further to 0.77 m/s shows that the introduction of second phase will decreases the energy production at low frequency and increase the dissipation at high frequencies at centreline and near the wall. (ii) For the intermediate frequency range (energy transfer zone), the turbulence energy for two phase flow cases is higher than
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Local water velocity (m/s)
1.2 1
Sp
4.6%CL
9.2%CL
sp
4.6%Wall
9.2%Wall
0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
1
Average water velocity (m/s)
Fig. 6. Variation of drop diameter with average water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/R = 0.9).
Fig. 3. Vaiation of local water velocity with average water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/R = 0.9).
Fig. 7. Variation of drop frequency with water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/R = 0.9).
Volume fraction (%)
20 15
4.6%CL
9.2%CL
4.6%Wall
9.2%Wall
10 5 0
0
0.2
0.4
0.6
0.8
1
Turbulence fluctuation (m/s)
Fig. 4. Variation of drop relative velocity with average water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/R = 0.9).
0.15 0.10 0.05 0.00 -0.05 -0.10 single phase
-0.15 0
Turbulence fluctuation (m/s)
the single phase flow for low water velocity (0.11 m/s), the discrepancy decreases with higher velocities and both become almost similar at high velocity (0.77 m/s). From the time series data for turbulent fluctuations in Fig. 10a, it can be observed that introducing of kerosene drops at low water velocity (0.11 m/s – Re = 8600) make a remarkable increase in fluctuation. The influence decreased for higher water velocities when the drop diameter and relative velocities decreased. The results from turbulent fluctuation also show that the effect of drops is more pronounced at the centre line for low water velocities (turbulence enhancement) but the fluctuation become comparable to single phase flow at higher values. On the other hand, introducing the second phase has no effect on turbulence fluctuations near the wall
9.2%
1
1.5
2
Time (s) (A) average water velocity = 0.29 m/s
Average water velocity (m/s) Fig. 5. Variation of volume fraction with average water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/R = 0.9).
4.6 %
0.5
0.15 single phase
4.6 %
9.2%
0.10 0.05 0.00 -0.05 -0.10 -0.15 0
0.5
1
1.5
2
Time (s) (B) average water velocity = 0.77m/s Fig. 8. Time series data of turbulence fluctuation in axial direction at the pipe centreline for: (A) average water velocity = 0.29 m/s and (B) average water velocity = 0.77 m/s.
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Centre line: U w =0.29 m/s
157
Near the wall: U w =0.29 m/s
Centre line: U w =0.44 m/s
Near the wall: U w =0.44 m/s
Centre line: U w =0.77 m/s
Near the wall: U w =0.77 m/s
Fig. 9. Atttocorrelation at centreline and near the wall for different area average volume fraction (hai = 0%, 4.6% and 9.2%).
Integral length scale (mm)
25
0.29m/s-CL 0.29m/s-W 0.11cm/s-CL
20
0.44m/s-CL 0.44m/s-W 0.11m/s-W
0.77m/s-CL 0.77m/s-W
15 10 5 0 0
2
4
6
8
10
Area average volume fraction (%) Fig. 10a. Variation of integral length scale with area average volume fraction for different average water velocities (0.29, 0.44 and 0.77 m/s). (CL: at the centre line (r/R = 0), W: near the wall (r/R = 0.9)).
Fig. 10b. Variation of eddy viscosity ratio (F) with area average volume fraction for different average water velocities (0.29, 0.44 and 0.77 m/s). (CL: at the centre line (r/R = 0), W: near the wall (r/R = 0.9)).
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(a) Centre line,
(a) Centre line
(b) Near the wall
(b) Near the wall
Normalized energy specta
Fig. 11. Axial turbulence energy spectra for different area average volume fraction (water velocity = 0.11 m/s). (a) At the centre line (r/R = 0) and (b) near the wall (r/R = 0.9).
1.E+00 single phase
1.E-01 1.E-02
4.6% N = 11 fd = 11 ft = 7
-5/3
1.E-03
9.2% 15 11 72
-6.6/3
1.E-04 1.E-05 1.E-06 1.E-07 1
10
100
1000
10000
Frequency, (s-1)
(a) Centre line
Normalized energy spectra
Fig. 13. Axial turbulent energy spectra for different area average volume fraction (average water velocity = 0.44 m/s). (a) At the centre line (r/R = 0) and (b) near the wall (r/R = 0.9).
1.E+00 single phase
1.E-01 1.E-02
-5/3
4.6%
9.2%
N=3 fd = 15 ft = 7
6 15 4
1.E-03 -6.6/3
1.E-04 1.E-05 1.E-06 1.E-07 1
(b) Near the wall
10
100
1000
10000
Frequency (s-1)
Fig. 12. Axial turbulent energy spectra for different area volume fraction (average water velocity = 0.29 m/s). (a) At the centre line (r/R = 0) and (b) near the wall (r/R = 0.9).
at low average water velocity (0.11) due to the very low number of drops (volume fraction) near the wall (Figs. 5 and 7). However, increasing the average water velocity (0.29 and 0.44 m/s) enhance
the turbulence but increasing the water velocity to 0.77 m/s attenuate the turbulence. From the energy spectra in Figs. 11–14, the Kolmogorov– Richardson scaling in the range of 4.5/3 to 6/3 for single phase flow which is replaced by energy spectra consisting of two separate straight lines for production zone and dissipation zone. The drop frequency (N), the integral length scale corresponding frequency (ft) and the drop diameter corresponding frequency (fd) are included in Figs. 11–14 to show how the energy spectrum affected by these variables. The slope of the line for production zone is very similar to single phase flow but the slope of the line for dissipation zone vary with average water velocity in the range of 6/3 to 7/3. The results indicate that changing volume fraction has no effect on energy spectra. The results clearly display that the spectra of kerosene–water flow has higher slope in dissipation zone than the single phase flow but less than 8/3 for air–water flow (Shawkat et al., 2007; Lance and Bataille, 1991). These values compared to air–water flow may be attributed to smaller drop diameters and drop relative velocity compared to the air bubbles. The results shows that the two-phase inertial region very similar to the single phase flow. The discrepancy between a single phase and two-phase flow is very clear in energy transfer and dissipation regions. The modification of the energy spectra may be attributed to: (i) the breakup of large scale eddies containing higher energy by the kerosene drops moving faster than water. (ii) The drop wake turbulence due the slip velocity between the drops and the continuous phase generate additional turbulence as described by Risso et al. (2008). If the drop wake turbulence immediately dissipated before decaying towards smaller eddies lead to energy spectra with same slope of 5/3 for single phase flow. The slope becomes higher than 5/3 if there is interaction between eddies induced by different drops.
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u0B ¼
159
dB U r : u0 Lt
3. The Kolmogorov–Richardson scaling in the range of 4.5/3 to 6/3 for single phase flow which is replaced by energy spectra consisting of two separate straight lines for production zone and dissipation zone. The slope of the line for production zone is very similar to single phase flow but the slope of the line for energy transfer and dissipation zone vary with average water velocity in the range of 7/3 to 5.6/3. 4. Increasing the volume fraction more from 4.6% to 9.2% has no effect on energy spectra.
(a) Centre line
(b) Near the wall Fig. 14. Axial turbulent energy spectra for different area average volume fraction (average water velocity = 0.77 m/s). (a) At the centre line (r/R = 0) and (b) near the wall (r/R = 0.9).
The data presented by Farrar and Bruun (1996) for average water velocity = 0.59 m/s showed that the energy spectrum composed of two power laws which are similar to the present finding but with different components of –5/3 for high frequency and 1 for higher frequency which are different from present work. The discrepancy between present work and Farrar and Bruun (1996) may be attributed to: (i) the modification of the experiment facility by increasing L/D from 17 to 54 to reach fully develop conditions; (ii) using the a bypass chillier unit connected to the storage tank to keep the temperature around 16 °C to avoid shift in hot-film calibration and velocity measurements. 4. Conclusions Experiments were performed in a 77.8 mm diameter vertical pipe to investigate the effet of drops on two-phase flow turbulence structure of kerosene–water bubbly flow. The water is in the range of 0.11 and 0.77 m/s, and area average volume fractions of 4.6% and 9.2%. A hot-film and dual optical probes are used to measure the liquid velocity, turbulence fluctuation, drop relative velocity, volume fraction and drop diameter. The main conclusions are: 1. The turbulence for two-phase flow can be correlated to the flow parameters as,
u0TP a
ak U w dB U r
:
2. The drops induced turbulence is a function of the ratio of the drop Reynolds number ðdB U r =mÞ to the turbulence Reynolds number ðu0 Lt =mÞ which decreased with higher water velocities as the ratio decreasing.
References Cherdron, W., Grotzbach, G., Samstag, M., Sengpiel, W., Simon, M., Tiseanu, I., 1998. Experimental investigation of air/water bubbly flow in vertical pipe. In: Third Int. Conf. on Multi-phase Flow, Lyon, France, June 8–12, 8 pages. Duineveld, P.C., 1994. Bouncing and Coalescence of Two Bubbles in Water, PhD Thesis, University of Twente, Netherlands. Farrar, B., Bruun, H.H., 1996. A computer based hot-film technique used for flow measurements in a vertical kerosene–water pipe flow. Int. J. Multiphase Flow 22, 733–752. Gore, R.A., Crowe, C.T., 1989. Effect of particle size on modulating turbulent intensity. Int. J. Multiphase Flow 15, 279–285. Gore, R.A., Crowe, C.T., 1991. Modulation of turbulence by a dispersed phase. Int. Trans. ASME 95, 235–267, J. Multiphase Flow, 15, 279–285. Hamad, F.A., Bruun, H.H., 2000. Evaluation of bubble/drop velocity by a single normal hot-film placed in a two-phase flow. Meas. Sci. Technol. 11, 11–19. Hamad, F.A., He, S., 2010. Evaluation of hot-film, dual optical and Pitot tube probes for liquid–liquid two-phase flow measurements. Flow Meas. Instrum. J. 21, 302–311. Hamad, F.A., Pierscionek, B.K., Bruun, H.H., 2000. A dual optical probe for volume fraction, drop velocity and drop size measurements in liquid–liquid two-phase flow. Meas. Sci. Technol. 11, 1307–1318. Hosokawa, S., Tomiyama, A., 2004. Turbulence modification in gas–liquid and solid– liquid dispersed two-phase pipe flows. Int. J. Heat Fluid Flow 25, 489–498. Hosokawa, S., Tomiyama, A., 2010. Effects of bubbles on turbulent flows in vertical channels. In: 7th International Conf. on Multiphase Flow, Tampa, USA, May 30– June 4. Hu, B., Matar, O.K., Hewitt, F.G., Angeli, P., 2007. Mean turbulent fluctuating velocities in oil–water vertical dispersed flows. Chem. Eng. Sci. 62, 1199–1214. Lance, M., Bataille, j., 1991. Turbulence in the liquid phase of a uniform bubble air– water flow. J. Fluid Mech. 222, 95–118. Liu, T.J., Bankoff, S.G., 1993. Structure of air–water bubbly flow in vertical pipe-1. Liquid mean velocity and turbulence measurements. Int. J. Heat Mass Transfer 36, 1049–1060. Martinez, M.J., Chehata, D., Van Gils, D.P.M., Sun, C., Lohse, D., 2010. On bubble clustering and energy spectra in pseudo-turbulence. J. Fluid Mech. 650, 287– 306. Mudde, R.F., Groen, J.S., Den, Van., akker, H.E.A., 1997. Liquid velocity field in a bubbly column: LDA experiments. Chem. Eng. Sci. 52, 4217. Rensen, J., Stefan, L., Vries, J.D., Lohse, D., 2005. The effect of bubbles on developed turbulence. J. Fluid Mech. 538, 153–187. Riboux, G., Risso, F., Legendre, D., 2010. Experimental characterization of the agitation generated by bubbles rising at high Reynolds number. J. Fluid Mech. 643, 509–539. Risso, F., Roig, V., Amoura, Z., Riboux, G., Billet, A.M., 2008. Wake attenuation in large Reynolds number dispersed two-phase flows. Philos. Trans. R. Soc. A 366, 2177–2190. Serizawa, A., Kataoka, I., 1990. Turbulence suppression in bubbly two-phase flow. Nucl. Eng. Des. 122, 1–16. Serizawa, A., Kataoka, I., Michiyoshi, I., 1975. Turbulence structure of water bubbly flow: II. Local properties. Int. J. Multiphase Flow 2, 235–246. Shawkat, M.E., Ching, C.Y., Shoukri, M., 2007. On the liquid turbulence energy spectra in two-phase bubbly flow in a large diameter vertical pipe. Int. J. Multiphase Flow 33, 300–316. Wang, S.K., Lee, S.J., Jones Jr., O.C., Lahey Jr., R.T., 1987. 3-D turbulence structure and phase distribution measurements in bubbly two-phase flow. Int. J. Multiphase Flow 13 (3), 327–343.
Contents lists available at ScienceDirect
International Journal of Heat and Fluid Flow journal homepage: www.elsevier.com/locate/ijhff
Effect of drops on turbulence of kerosene–water two-phase flow in vertical pipe F.A. Hamad a,⇑, P. Ganesan b a b
School of Science & Engineering, Teesside University, Middlesbrough TS1 3BA, UK Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia
a r t i c l e
i n f o
Article history: Received 19 March 2015 Received in revised form 29 July 2015 Accepted 30 July 2015
Keywords: Kerosene–water two-phase flow Turbulence Integral length scale Energy spectra
a b s t r a c t The effect of introducing kerosene drops on turbulence of kerosene–water two-phase in a vertical pipe is investigated experimentally. A hot-film and dual optical probes are used to measure the water velocity, turbulence fluctuation, drop relative velocity, volume fraction and drop diameter. Experiments are performed in a 78.8 mm diameter vertical pipe for four average water velocities of 0.11, 0.29, 0.44 and 0.77 m/s. The measurements were carried out for two area average volume fraction hai of 4.6% and 9.2% as well as for water single phase flow to investigate the effect of introducing kerosene drops on two-phase flow turbulence. The kerosene–water mixture was generated by adding the kerosene to constant flow rates of water. The results indicate that drops induced turbulence is a function of the ratio of the drop Reynolds number ðU r dB =mÞ to the turbulence Reynolds number ðu0 Lt =mÞ which decreased with higher water velocities. The results show that the Kolmogorov–Richardson scaling in the range of 4.5/3 to 6/3 for single phase flow which is replaced by 6/3 to 7/3 for two-phase flow. These values are less than 8/3 for air–water flow. Ó 2015 Elsevier Inc. All rights reserved.
1. Introduction The interaction between the drops/bubbles and liquid plays an important role in mass, momentum and energy transfer between the phases. The Turbulence structure in this type of flows is very complex due to: (i) the interaction between the drop-induced turbulence (bubble/drop motion) and shear-induced turbulence (the external force due to main flow). (ii) The modification of water radial velocity distribution due to the radial distribution of drop relative velocity, drop diameter and volume fraction. The introduction of drops can either enhance or attenuation the liquid turbulence (Serizawa and Kataoka, 1990). The two-phase flow turbulence has been investigated by a number of researchers in literature to understand the contribution of introducing the bubbles/drops on the continuous phase (Serizawa and Kataoka, 1990; Gore and Crowe, 1989, 1991; Serizawa et al., 1975; Wang et al., 1987; Liu and Bankoff, 1993; Farrar and Bruun, 1996; Cherdron et al., 1998; Hu et al., 2007; Shawkat et al., 2007). These studies indicated that: (i) introducing bubbles/drops into single phase water flow cause a sharp increase in turbulent intensity, particularly at low water ⇑ Corresponding author. E-mail addresses: [email protected] (F.A. Hamad), [email protected] (P. Ganesan). http://dx.doi.org/10.1016/j.ijheatfluidflow.2015.07.020 0142-727X/Ó 2015 Elsevier Inc. All rights reserved.
velocity, (ii) the increase in volume fraction more than 5% has very little effect on turbulence, (iii) the difference between the single phase and two-phase flow turbulence intensities diminished at higher water velocity, (iv) the effect is more pronounced at the pipe centreline than the wall region. The bubbles effect on energy spectrum has been investigated experimentally by a number of researcher (Shawkat et al., 2007; Lance and Bataille, 1991; Mudde et al., 1997; Rensen et al., 2005) to understand the influence of drop on energy production and dissipation. Lance and Bataille (1991) suggested the ratio of the bubble-induced kinetic energy and the kinetic energy of the flow without bubbles as appropriate dimensionless number (b) to characterize the type of the bubbly flow, defined as
b¼
1 aU 2t 2 u02 o
ð1Þ
where a is the volume fraction, Ut is the velocity of bubble/drop in still water, and u0o is the single phase velocity fluctuations. This dimensionless number is called bubblance parameter. They measured the liquid power spectrum in bubbly turbulence and a gradual change of the slope with increasing void fraction was observed. At low bubble concentrations the slope of the spectrum was close to the Kolmogorov’s value of 5/3. By increasing the volume fraction, the principal driving mechanism changed from external driving
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force to bubble generated turbulence and the slope become close to 8/3. The values of b depend on the nature of the flow, b < 1 for wall-induced turbulence and b > 1 for bubble-induced turbulence. Recent experiments (Martinez et al., 2010) found that the energy spectrum exponent is close to 3 for the bubbly turbulent flow when b = 1. The experimental study by Riboux et al. (2010) in the wake of a swarm of rising bubbles (b = 1) also found a spectral exponent 3. Shawkat et al. (2007) studied the structure of air– water bubbly flow in a 200 mm vertical pipe experimentally using hot film and dual optical probes. The slope of the spectrum was close to the Kolmogorov’s turbulent value of 5/3 which increased to 8/3 for two-phase flow. In contrast, there are few researchers found that the classical 5/3 power law for bubbly flow even for a gas volume fraction of 25% (Gore and Crowe, 1991; Mudde et al., 1997; Rensen et al., 2005). Gore and Crowe (1989, 1991) investigated turbulence modification caused by the addition of particles in a gas flow, and pointed out that the modification is well correlated with the so-called critical parameter, dB/Lt, the ratio of bubble/drop diameter (dB) to an integral length scale (Lt). The critical parameter can be regarded as the ratio of a characteristic length scale of turbulence induced by the dispersed phase to that of shear-induced turbulence. Hosokawa and Tomiyama (2010, 2004) proposed an eddy viscosity ratio (/), defined as
/¼
U r dB u0 Lt
ð2Þ
The eddy viscosity ratio (/) is the product of the length scales ratio, dB/Lt (Gore & Crowe’s parameter) and the velocity scales ratio Ur/u0 . Where Ur is the bubble relative velocity and u0 is the turbulence fluctuation. Turbulence enhancement due to bubble-induced turbulence is remarkable when the eddy viscosity ratio / is large but the effect is weak when / < 1. The eddy viscosity (/) can be modified to present the ratio of the bubble/drop Reynolds number ðU r dB =mÞ to the turbulence Reynolds number ðu0 Lt =mÞ. The literature review presented above shows that in spite of the extensive studies on turbulence for gas–liquid flow structure in a vertical pipe, there is still a dearth of research work for liquid–liquid flow. Hence, the objective of this paper is to investigate experimentally the effect of introducing kerosene drops on two-phase flow turbulence. The experimental data are used to calculate the integral length scale and the energy spectrum which are considered as an important variables in turbulence study. The measured parameters include water velocity, drop velocity, turbulence fluctuation, drop diameter and volume fraction in a vertical pipe of 77.8 mm diameter and 4500 mm length (L/D = 54). The measurements were performed at the centreline and near the wall (r/R = 0.9) for constant water velocities, U ws = 0.11, 0.29, 0.44 0.77 m/s (Re = 8600, 22,600, 33,800, 60,000) and area average volume fraction hai, b = 0%, 4.6% and 9.2%. 2. Experimental facility and measuring techniques The experimental facility used in the present study which is explained in details in Hamad and He (2010). Briefly, the test section is made of a transparent acrylic pipe of 77.8 mm inner diameter and 4500 mm length at L/D = 54. The water and kerosene were pumped from the storage tank to the test section via two flow meters, Y-junction and a 90° bend. The mixing of the phases is achieved by bringing the two pipelines together into a 152.4 diameter 90° bend using Y-junction. To remove the swirl generated due to the change of fluid flow from horizontal to vertical direction, a tube bundle consisting of four tubes is constructed and installed upstream of the test-section inlet. The mixture from the test
153
section outlet was returned to the storage tank via the horizontal pipe. A bypass chillier has been used to maintain the water temperature at 16 °C within the flow loop during the experiment. Two filtration units with 8 and 2 lm mesh size were used to maintain the water and kerosene in a clean condition. The clean fluids minimize the error of drop velocity measurements caused by contamination (Duineveld, 1994). The clean water and temperature control also minimize the shift in hot-film calibration curve and minimize the error of water velocity measurements. Kerosene was used as a dispersed phase in water to generate the liquid–liquid two-phase flow required in this study. The kerosene properties were: density (q) = 807 kg/m3, surface tension (r) = 0.030 N/m and dynamic viscosity (l) = 0.024 N s/m2. Hot-film and dual optical probes are used in this study 2.1. Hot-film probe A single normal boundary layer hot-film probe of 37 lm (DANTEC 55R15) has been used in this study. It was mounted in a standard DANTEC 55H20 probe support which in turn was mounted in a DANTEC 55H540 water-tight mounting tube with a 90° bend, which was fastened to the probe traverse mechanism. The hot-film probe was operated by a DANTEC 56C anemometer at an overheat ratio of 1.05 to avoid formation of air bubbles on the hot-film element. In order to calculate the continuous phase velocity correctly, it is necessary to eliminate any part of the signal which does not correspond to a continuous phase velocity and this is described in details in Hamad and Bruun (2000). Briefly, any noise in the signals that are not reflective of the continuous velocity phase is removed. The instantaneous water velocity U (t) can be calculated as,
U w ðtÞ ¼
E2 ðtÞ A B
!1=n ð3Þ
where A, B and n are calibration constant. The hot-film was calibrated by obtaining a set of calibration points (E, U) for single phase flow where E is the hot-film output voltage and U is the single phase flow velocity measured by Pitot tube placed at the centreline of the test section at L/D = 54. Selecting 10–20 points covering the required range of velocity (0.1–1.00 m/s), the values of (E, U) recorded and curve fitted to give the values of A, B and n used in Eq. (3). Recomposing the instantaneous water velocity U w ðtÞ ¼ U w þ u0 , with U w being the local mean water velocity and u0 the local turbulent water fluctuation. In a digital data analysis using a digital time record with a total number of points N, we have
U w ¼ RU w ðtÞ=N
ð4Þ
n o1=2 2 u0 ¼ RðU w ðtÞ U w Þ =N
ð5Þ
Shawkat et al. (2007) investigated the different methods used in literature to replace the gaps due the elimination of drops from the signal such that liquid turbulence statistics and spectra were not affected. He found that replacing the gap with a linear interpolation was the best method. In this study the value at point A was used to replace all the eliminated points as the difference between the values at points A and D are much smaller than gas–water two-phase flow cases. This is due to the significant differences in density, viscosity and surface tension of the kerosene and air which affect the bubble interaction between the probe and the kerosene drop or air bubble. The uncertainty in hot-film measurements may be attributed to one or more of the following factors: (i) calibration curve error, (ii) change in temperature of the fluid during the test, (iii) signal
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analysis and (iv) the type of drop-probe interaction. A detailed information about the accuracy of using hot-film probe can be found in Hamad and Bruun (2000) and Hamad and He (2010).
3. Results and discussion
2.2. Dual optical probe
Figs. 1a, 1b and 1c present the radial distributions of the turbulent fluctuation for water velocities of 0.29, 0.44 and 0.77 m/s and area average volume fraction hai of 0%, 4.6% and 9.2%. The results show that introducing kerosene drops in water cause a sharp increase in turbulent fluctuation but increasing the area average volume fraction hai has insignificant influence. The results also show that the difference in fluctuation between the single phase and two-phase flow decreased with higher water velocity and the influence of the drops is more pronounced at the pipe centreline. Based on these results and the eddy viscosity ratio in Eq. (2) from literature, two locations (r/R = 0 and 0.9) are selected for further analysis using integral length scale and energy spectra. Figs. 2–7 present the variation of turbulent fluctuations, local water velocities, drop relative velocities, volume fractions, drop diameters and drop frequency with average water velocity for different area average volume fraction hai at r/R = 0, 0.9. The results from these figures suggest that turbulence fluctuation can be related with various variables such as water velocity, drop relative velocity, volume fraction and drop diameter. For single phase flow;
The dual optical probe was made of two fibres to measure the volume fraction, drop cut chord and drop velocity. The axial distance between the two tips was 0.9 mm and they were separated laterally by approximately 0.45 mm centre to centre. The axial and lateral separation of the two fibres were optimized to detect the same droplet and to produce sufficient resolution to calculate the drop velocity accurately and at the same time minimize the meniscus effects from the first fibre tip affecting the reading from the second fibre. The optical probe cable used was 5 m long; it had a 100 lm core diameter and a 140 lm cladding diameter. The cladding provided a constant step in the refractive index at the core– cladding interface, which guided the light inside the fibre and also improved the mechanical properties of the fibre. The dual optical probe is used to measure the volume fraction, drop velocity and drop diameter. The local volume fraction at any radial position can be determined by the procedure as described in Hamad et al. (2000) as:
a ¼ lim
X
T!1
Dt d =T
ð6Þ
P
where Dt d the total dispersed phase residence time and T is the total sampling time. The drop velocity can also be calculated by applying the cross-correlation technique to the signals as
RðsÞ ¼
1 T
Z
T
E1 ðtÞE2 ðt þ sÞdt
ð7Þ
0
The RðsÞ for different values of ðsÞ to find the maximum time of flight ðsm Þ. The average drop velocity ðU B Þ can be evaluated from the time of flight ðsm Þ and the axial distance (Dx) between the two fibres tips as:
UB ¼
Dx
sm
ð8Þ
The signal from the first sensor can be used to calculate the drop diameter as:
dB ¼ 1:5U B DT 1
ð9Þ
The drop frequency (N) is calculated from the output of the leading sensor of the dual optical probe by counting the number of drops per second that pass the measurement point. The uncertainty in optical probe is a result of the probe geometry and the position where the probe hit the projected front area of the drop. The probe geometry includes the sensor diameter as well as axial and lateral distances between the sensors. This large distance between the two sensors may lead to a large number of drops hitting one sensor and missing the other one which affects the accuracy of time of flight calculated from cross-correlation method. The bubble-probe interaction can be classified into three types: (i) the blinding effect, when small bubbles are not detected due to imperfect probe dewetting; (ii) the drifting effect, when the bubble trajectory is altered leading to a smaller drop detection or no detection at all and (iii) the crawling effect due to bubble deformation and deceleration on the probe tip. The blinding and drifting effects lead to an underestimation of the volume fraction. In contrast, the crawling effect leads to an overestimation of the volume fraction. The error increases at low liquid velocity and volume fraction for the higher possibility of drifting and blinding effects under such conditions. A details information on accuracy of dual optical probe can be found Hamad et al. (2000) and Hamad and He (2010).
3.1. Local flow parameters
u0s aU w
ð10Þ
For two-phase flow;
u0TP a
ak U w dB U r
ð11Þ
where u0s is single phase turbulence fluctuation; U w is water velocity; u0TP is two-phase turbulence fluctuation; ak kerosene volume fraction. 3.2. Velocity time series and the integral length scale To understand the effect of drops on turbulence enhancement/attenuation, the time series of turbulence fluctuations recorded by hot-film probe in the axial direction are given in Fig. 8 for Average water velocities of 0.29 and 0.77 m/s and area average volume fraction hai of 0%, 4.6% and 9.2%. The axial velocity is clearly agitated by the present of kerosene drops in Fig. 8a for the low average water velocity; therefore the turbulence fluctuations amplitude in water phase becomes larger than that in the single-phase flow. This can be explained as a result of axial velocity acceleration around drops and the amplitude of the fluctuation enhanced to be in the order of the terminal rising velocity of a drop in stagnant water (about 0.15 m/s). It also can be observed that
Fig. 1a. Vaiation of turbulence fluctuation with radial distance for different area average volume fraction hai (average water velocity = 0.29 m/s).
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Turbulence fluctuation (m/s)
0.08 SP - CL
4.6%CL
9.2%CL
SP - Wall
4.6%Wall
9.2%Wall
0.06
0.04
0.02
0 0
0.2
0.4
0.6
0.8
1
Average water velocity (m/s) Fig. 1b. Vaiation of turbulence fluctuation with radial distance for different area average volume fraction hai (average water velocity = 0.44 m/s).
Fig. 2. Variation of turbulent fluctuation with average water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/ R = 0.9).
be observed that the contribution of drop in turbulence at low water velocity is very high at both centreline and near the wall. It decreases steeply near the wall where the boundary layer has a major contribution to the turbulence. On the other hand, the eddy viscosity decreases gradually at the centreline where the higher drop relative velocity and larger drops diameters are recorded as given in Figs. 6 and 8. In general, the effect of drop on turbulence is diminished at higher velocities. These results are supported by the finding for gas–liquid flow (Gore and Crowe, 1989, 1991).
Fig. 1c. Vaiation of turbulence fluctuation with radial distance for different area average volume fraction hai (average water velocity = 0.77 m/s).
agitation due to drops has less effect on turbulence fluctuation for the case of high water velocity (0.77 m/s) as fluctuation amplitude become similar to single phase flow. Referring to the Figs. 3 and 4, is clearly indicates that the velocity scale ratio Ur/u0 is an important parameter of the turbulence modification in bubbly flows (Hosokawa and Tomiyama, 2010, 2004). To study the effect of dB/Lt on turbulence, the autocorrelation function for different flow conditions for single and two-phase flows at the pipe centreline and near the wall are plotted in Fig. 9 to calculate Lt. The results show that the normalized time scale (Rs ) is a function of volume fraction but there is no clear trend as in the case of air–water flow data given by Shawkat et al. (2007) where the Rs decay faster than single phase flow. This behaviour may be attributed to a large difference between the properties of air and kerosene which both used as a second phase. The autocorrelation can be used to calculate the integral length scale using the following relation:
Lt ¼ U
Z
1
Rs ds
ð12Þ
0
Fig. 10a present the data of integral length scales for different water velocities and area average volume fraction at the pipe centre line and near the wall. The results show that the second phase has a small effect on integral length scale. It can be observed that there a case of transition in flow condition at water velocity = 0.44 m/s when the introduction of kerosene cause a clear peak of integral length scale. Fig. 10b present the variation of eddy viscosity ratio with average water velocity at the pipe centreline and near the wall. It can
3.3. Turbulence energy spectra The energy spectra analysis is expected to provide a valuable information on the flow structure as in the single phase flow. In case of two-phase flow, the signal corresponding to the liquid should be identified and separated by eliminating the drops and replace them with the same number of points with appropriate values. The signal becomes similar to single phase flow which can analysed to calculate and plot the energy spectra. Figs. 11–14 display the energy spectra for average water velocities (0.11, 0.29, 0.44 and 0.77) and different average volume fraction (a = 0. 4.6% and 9.2%) at the centreline and near the wall. The results show that: (i) the energy of large eddies (energy production zone) at low frequency is higher than the single phase flow at low water velocity (0.11 m/s, Re = 8600) indicating that there is a turbulence enhancement at both centreline and near the wall as shown in Fig. 11. It can also be observed from Fig. 11 that the dissipation for two-phase flow take place at wider range of frequencies compared to the single phase flow leading to lower values at high frequencies. The results in Fig. 11a display two different slopes (one for water and the other one for kerosene–water) of energy spectrum at low frequencies which is a unique behaviour. This unique behaviour may attributed to minor contribution of boundary induced turbulence in energy production compared to drop wake turbulence at this low water velocity. As the velocity increased, the enhancement of turbulence by drops decreases as it can be seen for the water velocities of 0.29 and 0.44 m/s (Re = 22,600 and 33,800). Increasing the water velocity further to 0.77 m/s shows that the introduction of second phase will decreases the energy production at low frequency and increase the dissipation at high frequencies at centreline and near the wall. (ii) For the intermediate frequency range (energy transfer zone), the turbulence energy for two phase flow cases is higher than
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Local water velocity (m/s)
1.2 1
Sp
4.6%CL
9.2%CL
sp
4.6%Wall
9.2%Wall
0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
1
Average water velocity (m/s)
Fig. 6. Variation of drop diameter with average water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/R = 0.9).
Fig. 3. Vaiation of local water velocity with average water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/R = 0.9).
Fig. 7. Variation of drop frequency with water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/R = 0.9).
Volume fraction (%)
20 15
4.6%CL
9.2%CL
4.6%Wall
9.2%Wall
10 5 0
0
0.2
0.4
0.6
0.8
1
Turbulence fluctuation (m/s)
Fig. 4. Variation of drop relative velocity with average water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/R = 0.9).
0.15 0.10 0.05 0.00 -0.05 -0.10 single phase
-0.15 0
Turbulence fluctuation (m/s)
the single phase flow for low water velocity (0.11 m/s), the discrepancy decreases with higher velocities and both become almost similar at high velocity (0.77 m/s). From the time series data for turbulent fluctuations in Fig. 10a, it can be observed that introducing of kerosene drops at low water velocity (0.11 m/s – Re = 8600) make a remarkable increase in fluctuation. The influence decreased for higher water velocities when the drop diameter and relative velocities decreased. The results from turbulent fluctuation also show that the effect of drops is more pronounced at the centre line for low water velocities (turbulence enhancement) but the fluctuation become comparable to single phase flow at higher values. On the other hand, introducing the second phase has no effect on turbulence fluctuations near the wall
9.2%
1
1.5
2
Time (s) (A) average water velocity = 0.29 m/s
Average water velocity (m/s) Fig. 5. Variation of volume fraction with average water velocity for different area average volume fraction hai at the pipe centreline (r/R = 0) and near the wall (r/R = 0.9).
4.6 %
0.5
0.15 single phase
4.6 %
9.2%
0.10 0.05 0.00 -0.05 -0.10 -0.15 0
0.5
1
1.5
2
Time (s) (B) average water velocity = 0.77m/s Fig. 8. Time series data of turbulence fluctuation in axial direction at the pipe centreline for: (A) average water velocity = 0.29 m/s and (B) average water velocity = 0.77 m/s.
F.A. Hamad, P. Ganesan / International Journal of Heat and Fluid Flow 56 (2015) 152–159
Centre line: U w =0.29 m/s
157
Near the wall: U w =0.29 m/s
Centre line: U w =0.44 m/s
Near the wall: U w =0.44 m/s
Centre line: U w =0.77 m/s
Near the wall: U w =0.77 m/s
Fig. 9. Atttocorrelation at centreline and near the wall for different area average volume fraction (hai = 0%, 4.6% and 9.2%).
Integral length scale (mm)
25
0.29m/s-CL 0.29m/s-W 0.11cm/s-CL
20
0.44m/s-CL 0.44m/s-W 0.11m/s-W
0.77m/s-CL 0.77m/s-W
15 10 5 0 0
2
4
6
8
10
Area average volume fraction (%) Fig. 10a. Variation of integral length scale with area average volume fraction for different average water velocities (0.29, 0.44 and 0.77 m/s). (CL: at the centre line (r/R = 0), W: near the wall (r/R = 0.9)).
Fig. 10b. Variation of eddy viscosity ratio (F) with area average volume fraction for different average water velocities (0.29, 0.44 and 0.77 m/s). (CL: at the centre line (r/R = 0), W: near the wall (r/R = 0.9)).
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(a) Centre line,
(a) Centre line
(b) Near the wall
(b) Near the wall
Normalized energy specta
Fig. 11. Axial turbulence energy spectra for different area average volume fraction (water velocity = 0.11 m/s). (a) At the centre line (r/R = 0) and (b) near the wall (r/R = 0.9).
1.E+00 single phase
1.E-01 1.E-02
4.6% N = 11 fd = 11 ft = 7
-5/3
1.E-03
9.2% 15 11 72
-6.6/3
1.E-04 1.E-05 1.E-06 1.E-07 1
10
100
1000
10000
Frequency, (s-1)
(a) Centre line
Normalized energy spectra
Fig. 13. Axial turbulent energy spectra for different area average volume fraction (average water velocity = 0.44 m/s). (a) At the centre line (r/R = 0) and (b) near the wall (r/R = 0.9).
1.E+00 single phase
1.E-01 1.E-02
-5/3
4.6%
9.2%
N=3 fd = 15 ft = 7
6 15 4
1.E-03 -6.6/3
1.E-04 1.E-05 1.E-06 1.E-07 1
(b) Near the wall
10
100
1000
10000
Frequency (s-1)
Fig. 12. Axial turbulent energy spectra for different area volume fraction (average water velocity = 0.29 m/s). (a) At the centre line (r/R = 0) and (b) near the wall (r/R = 0.9).
at low average water velocity (0.11) due to the very low number of drops (volume fraction) near the wall (Figs. 5 and 7). However, increasing the average water velocity (0.29 and 0.44 m/s) enhance
the turbulence but increasing the water velocity to 0.77 m/s attenuate the turbulence. From the energy spectra in Figs. 11–14, the Kolmogorov– Richardson scaling in the range of 4.5/3 to 6/3 for single phase flow which is replaced by energy spectra consisting of two separate straight lines for production zone and dissipation zone. The drop frequency (N), the integral length scale corresponding frequency (ft) and the drop diameter corresponding frequency (fd) are included in Figs. 11–14 to show how the energy spectrum affected by these variables. The slope of the line for production zone is very similar to single phase flow but the slope of the line for dissipation zone vary with average water velocity in the range of 6/3 to 7/3. The results indicate that changing volume fraction has no effect on energy spectra. The results clearly display that the spectra of kerosene–water flow has higher slope in dissipation zone than the single phase flow but less than 8/3 for air–water flow (Shawkat et al., 2007; Lance and Bataille, 1991). These values compared to air–water flow may be attributed to smaller drop diameters and drop relative velocity compared to the air bubbles. The results shows that the two-phase inertial region very similar to the single phase flow. The discrepancy between a single phase and two-phase flow is very clear in energy transfer and dissipation regions. The modification of the energy spectra may be attributed to: (i) the breakup of large scale eddies containing higher energy by the kerosene drops moving faster than water. (ii) The drop wake turbulence due the slip velocity between the drops and the continuous phase generate additional turbulence as described by Risso et al. (2008). If the drop wake turbulence immediately dissipated before decaying towards smaller eddies lead to energy spectra with same slope of 5/3 for single phase flow. The slope becomes higher than 5/3 if there is interaction between eddies induced by different drops.
F.A. Hamad, P. Ganesan / International Journal of Heat and Fluid Flow 56 (2015) 152–159
u0B ¼
159
dB U r : u0 Lt
3. The Kolmogorov–Richardson scaling in the range of 4.5/3 to 6/3 for single phase flow which is replaced by energy spectra consisting of two separate straight lines for production zone and dissipation zone. The slope of the line for production zone is very similar to single phase flow but the slope of the line for energy transfer and dissipation zone vary with average water velocity in the range of 7/3 to 5.6/3. 4. Increasing the volume fraction more from 4.6% to 9.2% has no effect on energy spectra.
(a) Centre line
(b) Near the wall Fig. 14. Axial turbulent energy spectra for different area average volume fraction (average water velocity = 0.77 m/s). (a) At the centre line (r/R = 0) and (b) near the wall (r/R = 0.9).
The data presented by Farrar and Bruun (1996) for average water velocity = 0.59 m/s showed that the energy spectrum composed of two power laws which are similar to the present finding but with different components of –5/3 for high frequency and 1 for higher frequency which are different from present work. The discrepancy between present work and Farrar and Bruun (1996) may be attributed to: (i) the modification of the experiment facility by increasing L/D from 17 to 54 to reach fully develop conditions; (ii) using the a bypass chillier unit connected to the storage tank to keep the temperature around 16 °C to avoid shift in hot-film calibration and velocity measurements. 4. Conclusions Experiments were performed in a 77.8 mm diameter vertical pipe to investigate the effet of drops on two-phase flow turbulence structure of kerosene–water bubbly flow. The water is in the range of 0.11 and 0.77 m/s, and area average volume fractions of 4.6% and 9.2%. A hot-film and dual optical probes are used to measure the liquid velocity, turbulence fluctuation, drop relative velocity, volume fraction and drop diameter. The main conclusions are: 1. The turbulence for two-phase flow can be correlated to the flow parameters as,
u0TP a
ak U w dB U r
:
2. The drops induced turbulence is a function of the ratio of the drop Reynolds number ðdB U r =mÞ to the turbulence Reynolds number ðu0 Lt =mÞ which decreased with higher water velocities as the ratio decreasing.
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