Ind. Eng. Chem. Fundam., Vol. 17, No. 4, 1978 277
The Application of a Laser-Schlieren Technique to the Study of Single Bubble Dynamics David1 S. Hacker” Department of Energy Engineering, University of Illinois, Chicago, Illinois 60680
Fathi D. Hussein’ Deparfment of Chemical Engineering, University of Houston, Houston, Texas
A laser-schlieren light screen method of sufficient sensitivity is used to measure the shape characteristics of single gas biubbles rising in fluids of different properties. The results of measurements made of axial dimensions of nitrogen bubbles rising in silicone oil and ethylene glycol, two representative Newtonian fluids of widely differing fluid properties, confirm the fact that surface tension is not an important parameter in influencing drag and rise speed. The work is in agreement with the observations of Calderbank and of Wegner and Parlange. These data have been correlated with a relationship for the Froude number derived on the assumption that viscous and inertial drag forces are additive. The relation has sufficient generality to predict the behavior of a wide distribution of bubble shapes and is given 2.52NR,e]1’2. by the following expression based on the equivalent radius of the gas volume NFr,= 1.63NR,./[8
+
Introduction The dynamics of gas bubbles dispersed in an extended liquid phase is an important factor in the design of gasliquid contacting equipment and the subject has provided a source of continuing research. Both theoretical analyses and experimental verification have provided physical interpretation and understanding of the phenomena associated with single-bubble processes and bubble swarms in Newtonian and non-Newtonian liquids. In particular, single-bubble studies have given information on drag, heat, and mass transfer coefficients, as well as bubble coalescence and growth processes (Leonard and Houghton, 1963; Calderbank et al., 19170; Raymond and Zieminski, 1971). Important in these developments have been the in situ measurements of bubble characteristics which have been used to confirm the shape and details of the wake structure (Hnat and Buckmaster, 1976). Schlieren shadowgraph and other photographic methods have been useful in the description of surface phenomena interfacial and wake turbulence (Maxworthy, 1967). All techniques, unfortunately, have been subject to several optical distortion effects. With the advent of the coherent gas laser, the experimentalist has an optical tool which now permits a more accurate measurement of refractive index effects and can provide him with a quantitative improvement in the quality of resolution of these events. Its use especially in measurements of the fast events such as the density variation across a moving shock wave is well known (Kiefer and Lutz, 1966). Its recent application to the holographic imaging of convective currents in heat transfer has also been sucessfully demonstrated (Vest, 1975). In this paper we will demonstrate a further application of laser-schlieren to the study of single bubbles moving in a fluid and to the measurement of the longitudinal axial dimension of the bubble in mot ion. The technique does not require accurate focussing of the image to obtain maximum contrast as is normally required in white light photography and the ‘Presently a doctoral candidate. This work was part of a Master’s Thesis problem. 0019-7874/78/ 1017-0277$01.OO/O
distortions due to the surrounding fluid can be eliminated with prior compensation and calibration of the instrument. This study was undertaken primarily to demonstrate the feasibility of this technique and compare results of measurements of bubble rise time and height with reported data obtained by other workers using a variety of techniques. In a series of experiments described it was sought to measure the vertical axial dimensions and rise speed of a single bubble of dry nitrogen gas passing upward through a column of either pure silicone oil or ethylene glycol and to correlate these data with selected nondimensional fluid dynamic groups such as Froude and Reynolds numbers. Design and Principle of Operation The principle of operation of the laser-schlieren system represented schematically in Figures 1 and 2 is based on the fact that the beam of laser light intercepting a moving bubble of different refractive index than the fluid is slightly shifted in direction. The index of refraction, 7,is related to the medium (i.e., gas or liquid density, p , ) by the “Gladstone-Dale’’ relation q=l+kp
(1)
where p is the density of the media and k is a constant for a given system, which depends only on the medium and on the wavelength of the incident beam. Two collimated beams are directed through flat windows of the column and serve as velocity stations to monitor the bubbles as they traverse the column. The optics of each light station consist of a double-concave lens, two cylindrical lenses, knife edge, and a NPN silicon photocell detector. The distance between the two light stations is fixed a t 46.5 cm as is shown in Figure 2. Light from the laser beam source (Spectra Physics 2-MW He-Ne gas laser) is passed through a narrow band-pass filter which transmits only the 6328-A beam. The beam is split into two equal beams by a 45’ inclined, half-silvered splitter plate. One portion of the beam is directed to the first station while the other is directed into the second light station. Each beam is passed through a double-concave lens of -8.6 mm focal length and then through a cylindrical 0 1978 American Chemical Society
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Ind. Eng. Chem. Fundam., Vol. 17, No. 4, 1978
Table I. Calibration of Schlieren System for Nominal 0.4-cm Glass Spheres
I I
mass of particle, g
caliper measured averaged diameter, cm
laser measured exptl diameter, cm
% error
0.184 0.174 0.173 0.178 0.190
0.558 0.490 0.490 0.490 0.503
0.505 0.475 0.469 0.533 0.490
9.49 3.06 3.06 -8.77 2.58
I
av
5.39%
Table 11. Typical Measured Heights and Rise Velocity of Nitrogen Bubbles in Silicone and Ethylene Glycol a t Room Temperature (Refer to Oscilloscope Traces of Figure 3)
t
--- Syringe
trace
A
ern
B
Figure 1. Schematic of optical system and apparatus. 876
5
4
3
2
C
D E F
1
A ) Upper optical Station 8'7'6'
5'
4'
3'
2'
9
10
11
B ) Bottom optical Station
Figure 2. Schematic of optical bench: 1, mirror mount; 2,2', double-concave lenses, -8.6 mm in focal length; 3,3',5,5', cylindrical lenses, 86 mm in focal length; 4,4', cross section of the column at the light stations; 6,6', knife edges; 7,7', photocells; 8,8', to the oscilloscope input; 9, splitter plate, half-silvered; 10, filter, 6328A; 11,He-Ne laser.
lens which is placed at a distance from the double-concave lens to give maximum definition. The beams are expanded into narrow two-dimensional pencil beams of about 0.8 x 30 mm. Each beam is then passed through the test section of the column and is converged by a second cylindrical lens, and half the ray split on a knife edge, which provides for the schlieren effect. The beam deflection is detected by the photocell placed behind the knife edge. A sensitive dual-beam Tektronix oscilloscope, Type 555, is used with a plug-in amplifier, Type 1A1, to monitor the output signal. Experimental Procedure Experiments were conducted in a 5.5 cm i.d. glass column, 122 ern in height. The liquids used were silicone oil (dimethyl polysiloxane: viscosity, 338.1 cP, density, 0.966 gm/cm3; and surface tension, 21.1 dyn/cm) and ethylene glycol (viscosity, 24.2 cP; density, 1.113 gm/cm3; and surface tension, 46.8 dyn/cm). Each fluid is carefully filtered to minimize possible internal light scattering. A preliminary calibration of the system was carried out using commercial nominal 4 cm diameter glass spheres. The light measured diameter of the single sphere was obtained from the width of the expanded time trace measured at one of the light stations. It is assumed that the sphere attains its terminal velocity before reaching the first light station and the diameter of the sphere is obtained by a simple relationship of the laboratory time, t h b , obtained from the width of the sweep at a particular station, and the velocity of descent. The descent velocity,
initial gas volume, cm3
measured height, cm
rise velocity, cm/s
1 2 3 1 1.5 4
0.9348 1.1543 1.3363 0.6100 0.7332 1.0341
14.6059 18.03 58 19.6509 22.2298 22.9125 24.6246
U,,, is determined from measurements between timing marks of the light interrupted at the velocity stations. dapp = u a v tlab (2) The incident collimated beam is almost totally reflected by the glass sphere and only at the equatorial plane of the sphere is light transmitted without deviation. Table I indicated a comparison of these measurements with actual sphere dimensions with an estimated error of f3.57 f 0.10%. The column was completely filled with liquid before each run. The vent valve at the top of the column was closed after filling with fluid ensuring that no gas space remains in the column. Nitrogen was then introduced from a graduated syringe inserted at the bottom of the column through a rubber stopper where it is captured by an inverted cup. The gas bubble formed in the cup is then released by manually rotating the cup. The gas bubble so formed rises uniformly through the liquid which completely fills the closed column. No change in gas volume will occur as the bubble rises through the column, provided the liquid completely fills the container and is incompressible, as demonstrated by Calderbank (1970). Bubbles of constant volume, ranging in size from 0.5 f 0.1 cm3 to 4.0 f 0.1 cm3, could be produced in this fashion. The light stations were checked periodically to assure alignment of the laser beam with the test section and to maximize signal intensity. The oscilloscope was triggered on the positive slope of the signal from the lower light station during passage of the bubble. A time-delay multiplier was set approximately for the time a bubble takes to rise from the lower station to the upper station. This was done to record the two signals on the oscilloscope simultaneously. To improve signal-to-noise ratio, the amplification and the time scale were expanded by introducing a third trace with a proper scale factors, as shown in Figure 3. In all cases photographs of the traces were taken using a Hewlett-Packard Polaroid oscilloscope camera operated with an open shutter. Table I1 was prepared to show the measurements of bubble height and rise velocities obtained from the traces of Figure 3. The fluctuations observed in the signal following the spike are believed to be due to the wake process behind
Ind. Eng. Chem. Fundam.. VoI. 17, No. 4, 1978 279
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32
30
28
-
26
-
. A
6
. 5 YI
f
0
0
0
D
Figure 4. Bubble rise velocity as a function of fluid viscosity.
Figure 3. Typical time traces obtained from photomultiplier diode for spherical cap bubbles moving in fluid.
their rise speeds were in all cases corrected using the Uno and Kintner (1956) correlation to correct for wall interference (3)
upper center beam heam traces obtained in silicone oil, A, B, C horizontal: magnification 0.1 0.1 sweep factor, slcm 0.5 0.5 vertical: V/cm 0.05 0.05 traces obtained in ethylene glycol, D, E, horizontal: magnification 0.1 0.1 sweep factor, slcm 0.2 0.2 vertical: V/cm 0.05 0.05
lower beam
0.1 0.1 0.005
F 0.1 0.2
0.005
the buhhle since the laser is extremely sensitive to small fluid density fluctuations. In typical oscilloscope traces shown in Figure 3, obtained for spherical cap nitrogen bubbles moving in silicone oil and ethylene glycol, the small fluctuations traiIing the major signal can be seen clearly. Experimental Results A. Rise-Speed Results f o r Constant Volume Gas Bubbles. It was visually observed that the bubbles in silicone oils were all of spherical cap shape for volumes greater than 0.75 cm3, while for volumes less than 0.75 cm3 the huhhles all had spherical tops with convex rear surfaces. The column was designed to permit the bubble to achieve its terminal velocity long before reaching the first light station. We were able to show that all gas bubbles achieved terminal velocity at a distance equivalent to 10 bubble diameters. Before starting each new experiment, the column was vacuum flushed of any residual gas which may have remained, and fresh fluid added where necessary to completely fill the column. On the other hand, huhhles of the order of 0.5 cm3 in volume were all observed to be of the spherical type in ethylene glycol, and oscillated slightly on their axis on ascent. For larger huhhle volumes (>3 cm3), all were observed to form stable spherical caps and move with a rectilinear motion. The measured rise velocities for bubbles in silicone and in ethylene glycol are shown in Figure 4. The values of
where UexDt is the observed velocity, U , is the corrected velocity in the ahsence of walls, and de and DT, are the diameter of the bubble and the column diameter, respectively. Important in these calculations is the implied assumption that the hubhle rises uniformly and linearly. This assumption is not necessarily accurate since some oscillatory motion does occur during ascent. One may naturally inquire into the effect of these oscillations on the rise-speed measurement. One finds that for motion of very small bubbles, i.e., NRe
