FLOW PATTERN AND ITS TRANSITIONS
2.3. Experimental
Chapter-2
30
in hidden layer. The hidden layer consists of neurons that are equal to the total number of training variables. The hidden layer computes Euclidean distances between the each random variable and the training sample that represented by the hidden layer and then processed through a Gaussian activation function as
2
exp 2
i x xxi (2.4)
where x is the vector of random variables and xi is the ith training vector. The class layer computes the summation and gives out arithmetic mean of the output of hidden layer for each class, Hk. The output layer classifies any random variable by comparing the output of class layer for each class and then following the Bayes’ classification theorem as,
x argmax
g (x)
Hk k (2.5)
Flow Pattern and its Transitions
Figure 2.2: Schematic diagram of the experimental system.
Legends- C: Compressor, D: Diameter of the coil, H: Helical coil, M1, M2: U-tube Manometers, P: Pitch, Pm: Pump, PT1 – PT4: Pressure taps, RL1, RL2:Liquid Rotameter, RG: Gas Rotameter, Sc: Sample collector, SV1, SV2: Solenoid valves, S: Storage tank, Ti: Tracer input, V1 – V8: Valves.
Flow patterns were carefully observed at every set of flow rates (air and liquid). A snapshot of the same was taken by a digital camera (Model: SONY Cyber-short DSC-Hx10V, Sony Electronics Inc., Japan, pixel resolution: 18200000 pixels, shutter speed: 1/1600 sec, CMOS sensor with enhanced image processing, mega pixel: 18.2 (4896×3672) with 16X optical and 32X clear zoom, lens magnification: 4.28 – 68048 mm) to identify the flow patterns at steady state flow condition. The flow is illuminated by a sheet of light, then photographs were taken as a multiple image or as a video. Each experiment was repeated thrice to check its reproducibility and it was found above 98%. Pressure drop across vertical helical coil (PT1
and PT2) and horizontal straight tube (PT3 and PT4) were also measured by two U-tube
RG
V7
Pm V1 S
V2
V3 V4
V6
RL2
V5
M 1
M2
SV1 SV2
RL1
PT1
PT2
C H
P D
PT3 PT4
V8 Sc
Ti
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32
manometers (M1 and M2). The gas holdup at different flow conditions is measured by quick closing valve (Solenoid Valve). For this, two quick closing valves SV1and SV2are placed at the two ends of the test section (Figure 2.2). The experiments were carried out with three sets of helical coiled tubes of diameter 0.009, 0.015, 0.02 m. Each set of helical coil is arranged in three different pitches (pitch differences (p/Dc): 0.5, 1 and 1.5). The tubes are made up of transparent and flexible polyethylene pipe for better visualization and getting desired pitch arrangement. The present experiment was performed within the operating ranges of the liquid flow rates of 3.33 × 10-05 - 5.00 × 10-04 m3/s and the air flow rates of 1.67×10-05 - 1.00×10-04 m3/s. At steady state operation, the experimental data for flow patterns, for different operating conditions of two-phase (air-SCMC) flow in the vertical helical coil were noted.
2.3.1. Physical properties of the slurry system
The physical properties of the fluid (air, water and SCMC) used for the present study is are shown in Table 2.1. The density of liquid was measured by gravity bottle and the surface tension by tensiometer (Model: K9-MK1, Make: KRÜSS GmbH Co., Hamburg, Germany).
The rheological properties of SCMC solutions were measured by rheometer (Model: Haake Rheostress 1, Make: Thermo Electron Co., Karlsruhe, Germany). The apparent viscosity of SCMC solution was calculated by (Chhabra and Richardson 1999)
n n
t
eff n
d n U
K
4 1 ) 3
/ 8
( 1
(2.6)
where dt is internal diameter of tube, U is the average velocity of liquid, K is consistency coefficient, and n is flow behaviour index. For the slurry system, the average sizes of the particles were taken as 2.21 m (zinc oxide), 19.39 m (kieselguhr), and 96.0 m (aluminum oxide). The physical properties of the slurry are shown in Table 2.2. The sizes of the particles
TH-1484_10610718
Flow Pattern and its Transitions were measured by using laser particle size analyzer (Model: APA 2000, Make: Malvern Instruments Ltd., Malvern, U.K.).
Table 2.1: Physical properties of the system at 25 ± 1C.
System Concentration (kg/m3)
Flow behaviour index (n)
Consistency index K (Pa s)
Density l
(kg/m3)
Surface tension
l (N/m)
Water - -* - 999.70 0.0710
Air - -** - 1.1850 -
SCMC-1 0.5 0.9532 0.01801 1000.55 0.0747 SCMC-2 1.0 0.9099 0.02552 1000.83 0.0694
SCMC-3 1.5 0.8701 0.03617 1001.69 0.0683
SCMC-4 2.0 0.8338 0.05126 1001.96 0.0662 SCMC-5 2.5 0.8010 0.07266 1002.01 0.0657
SCMC-6 3.0 0.7717 0.10299 1002.03 0.0645
*viscosity of water: 0.79710-3 kg/m.s, ** viscosity of air: 1.86310-5 kg/m.s
The density of the slurry was calculated as per following equation (Abulnaga, 2002):
w s
w
l
m C C
/ 100 /
100
(2.7)
where m is a density of slurry mixture, Cw is solid concentration by weight (%), s is a density of solid particles in mixture and l is a density of liquid phase in mixture. The effective viscosity and density of slurry were calculated by using Thomas correlations (Abulnaga, 2002)which are given as:
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34
ls/ls
l/ls
12.5
Cc/p
10.05
Cc/p
22.73103exp
16.6
Cc/p
(2.8)
l p
c l
ls C
1 / (2.9)
where ls is a density of slurry, p is a density of particle and µls is a slurry viscosity.
Table 2.2: Physical properties of the liquid-solid slurry measured at 25 ± 1 0C
Particles Diameter (m)
Concentration (wt %)
Density (kg/m3)
Viscosity × 103 (kg/m-s)
Surface Tension (N/m)
Kieselguhr 19.00 5.000 990.418 1.041 0.072
Kieselguhr 19.00 10.00 981.137 1.084 0.072
Kieselguhr 19.00 15.00 971.855 1.131 0.073
Zinc oxide 2.210 10.00 981.562 1.126 0.072
Aluminum oxide
96.00 10.00 981.124 1.064 0.072
2.3.2. Particle size distribution
Aqueous slurry of hydrophilic neutral Zinc oxide, Kieselguhr and Aluminum oxide are used for the experiment. In a gas-liquid-solid slurry system, the particles are used usually smaller than 100 micron. In such cases, the spatial profile of the solid concentration is almost uniform. In the present study the average size of the particles are taken 2.2, 19 and 96 µm which are measured by laser particle size analyser. The particle size distribution of the Zinc oxide, Kieselguhr and Aluminium oxide are shown in Figure 2.3, 2.4 and 2.5 respectively.
TH-1484_10610718
Flow Pattern and its Transitions
Figure 2.3: Particle size distribution of zinc oxide particles
Figure 2.4: Particle size distribution of Kieselguhr particles
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36
Figure 2.5: Particle size distribution of aluminum oxide particle
2.3.3. Uncertainty analysis
In the present study, experiments were repeated five to six times, and the results obtained in these experiment were averaged. The advantage of the taking the average value is that the variations caused by various influences tend to be nullified. Using the average value, the standard deviation (STDEV) and standard uncertainty (U) of the repeated experiments were calculated. In the present study the mean (x̅) and standard deviation (STDEV) of the repeated experiments were calculated respectively as
N
i
xi
x N
1
_ 1
(2.10)
1 )
1(
2 _
Nx STDEV x
N
i i
(2.11)
The standard uncertainty (U) of the mean value was estimated by TH-1484_10610718
Flow Pattern and its Transitions
N STDEV
U (2.12)
The typical range of the means, standard deviations, and uncertainties of the flow patterns within a range of operating variables are reported in Table 2.3. Each value of superficial velocities in 1st column corresponds to the mean of 6 data points (i.e., N = 6). Relative uncertainty is calculated from standard uncertainty and mean value of the corresponding data set.
Table 2.3. Typical uncertainties of the flow patterns at constant tube diameter (dt = 0.015 m) and coil diameter (Dc = 0.0117 m)
Usl (m) Usg
(m)
SCMC
(kg/m3) N Flow patterns
Range of STDEV
(x10-3)
Range of uncertainty
(x10-3)
Range of relative uncertainty
% 0.566-1.132 0.094 1.0 6.0 Pug flow 4.176-2.137 0.875-1.705 0.302-0.077 0.189-1.132 0.189 1.0 6.0 Slug flow 3.142-3.445 1.284-1.412 0.124-0.683 0.189-0.566 0.283 1.0 6.0 Stratified flow 3.085-4.541 1.265-1.854 0.327-0.668