Xiaodong Tian and Philip J. W. Roberts
School of Civil and Environmental Engineering,
Georgia Institute of Technology, Atlanta, GA, 30332, USA
E-mail:
proberts@ce.gatech.edu
Abstract:
A new three-dimensional Laser-Induced Fluorescence (LIF) system is described.
The system is capable of measuring three-dimensional concentration fields
continuously and almost instantaneously. It is particularly designed for studies
of jet or plume mixing in stratified and unstratified, stationary or flowing
environments. Applications of this system to various plume flows are presented.
In this paper we report measurements on vertical and horizontal round buoyant
jets in stratified and unstratified crossflows. The horizontal buoyant jets
discharge orthogonal to the crossflow so that the plume trajectory is
three-dimensional. Three-dimensional visualizations of jets were reconstructed
from a serious of slices, which show familiar shapes and trajectories.
Trajectories of jets and variation of dilution along the trajectory were
extracted. The results fit previous study well and show the effect of nozzle
orientation clearly.
Keywords:
laser-induced
fluorescence, stratified flows, buoyant Jets, flow visualization, dilution
The use of Laser-Induced Fluorescence (LIF) has enabled acquisition of high spatial and temporal resolution images of the instantaneous scalar concentration fields in flows, which have proven very useful to understanding the mechanics of turbulent mixing processes. Many studies have been reported since the earliest ones by Owen (1976) and Dimotakis et al. (1983). Most of them are planar LIF (PLIF). Even relatively simple jet and plume flows are inherently three-dimensional, however, and PLIF cannot reveal this three-dimensionality.
Three-dimensional LIF systems have recently begun to be used to overcome these deficiencies. In these applications, the laser sheet is swept through the flow at high speed; images are captured with a synchronized camera and saved. Through suitable post-processing and calibration, the three-dimensional concentration field can then be obtained. These are now practical because of recent advances in instrumentation, especially opto-electronics, low-light high-speed cameras, high-speed scanning mirrors, image capture and processing, and mass storage devices. Furthermore, new LIF systems can be used in stratified flows by using refractive index matching (Daviero et al. , 1999). In this paper, we report several studies of plume flows using a three-dimensional LIF system combined with refractive index matching.
A schematic
depiction of the experimental configuration is shown in Figure 1. The system and
experimental procedures are described in detail in Roberts and Tian (2000). The
tow tank is glass-walled 6.10 meters long by 0.91 meters wide by 0.61 meters
deep. A tow carriage powered by a variable speed DC electric motor carriage runs
on smooth bearings on precision stainless steel rods the length of the tank. The
effluent, a mixture of water, salt, and fluorescent dye, is supplied from a
reservoir by a rotary pump. The flowrate is measured by a precision rotameter.
The tank can be linearly stratified using a two-tank filling system (Daviero,
1998).
Fig. 1 Schematic depiction of experimental arrangement
The LIF system is controlled by two computers, one for overall timing control, and one for image capture. The beam from an Argon-Ion laser strikes two orthogonal fast galvanometer scanning mirrors that move the beam in the horizontal (y) and vertical (z) directions. The beam then strikes a large plano-convex lens so that it is always refracted parallel to the axis of the tow tank. The flow images are captured by a CCD camera, which is attached to the tow carriage and moves with it so that the discharge appears to be stationary relative to the camera. The CCD camera resolution (number of active pixels) is 530 by 515, and output is 8-bit resolution. The present experiments were done with a camera frame rate of 100 or 200 frames per second. The images are written to disc in real time, enabling long duration experiments to be recorded.
The laser and image
acquisition are controlled and synchronized by an I/O Board. A TTL signal is
sent to the frame grabber board to initiate frame capture, and the frame grabber
board in turn sends a signal to the camera to begin image acquisition
(exposure). Simultaneously, the I/O Board begins sending an analog voltage to
move the vertical (z) mirror. The beam
makes one sweep down and back while the camera is exposing. A signal is then
sent to the horizontal (y) mirror to
move the beam a small distance horizontally. The cycle then begins again with
another TTL signal that downloads the previous frame, clears the camera buffer,
and begins the next exposure. This is repeated so that multiple vertical
“slices” through the flow are obtained. After a predetermined number of
“slices” the beam returns to the starting point and the cycle starts again.
For example, 20 slices at 200 frames per second yields an effective sample rate,
at which the whole sequence of images through the flow is captured, of 10 Hz.
Quantitative scalar concentration data are obtained by calibration as outlined in Ferrier et al. (1993). The images are corrected pixel-by-pixel for lens luminance variation (vignetting), individual pixel response, attenuation due to clear water, dye, salt, and ethanol, using the methods of Daviero et al. (2001). The multiple “slices” through the flow field are then regenerated, using three-dimensional image processing software, into a three-dimensional image of the flow. The time of scanning through the flow is sufficiently short to “freeze” the larger turbulent scales.
To
illustrate the system, applications are given of a round jet into unstratified
and stratified crossflows. Four experiments were done in this paper. Two of them
were given of a vertical round jet into unstratified and stratified crossflows.
The other two were given of the same jet under same ambient flows, but rotating
the jet 90 degree to horizontal position (the discharging direction was
orthogonal to the crossflows). All experiments were performed as shown in Figure
1, in which a more dense effluent was discharged downwards. The results are
reported here as inverted, i.e. as a positively buoyant effluent discharging
upwards. This is allowable because the
relative density difference between the effluent and receiving water is small
and is therefore significant only for buoyancy forces and not inertia forces
(the Boussinesq assumption).
For all experiments, the nozzle
diameter d was 0.40 cm, the effluent
flowrate Q was 6.31 cm3/s,
and the current speed u was 4.0 cm/s.
The density difference between the effluent and ambient at the nozzle level was
26~28 kg/m3. For the stratified experiments, the density profile was
approximately linear with a buoyancy frequency,
=0.32
s-1 for vertical case and 0.52 s-1 for horizontal case,
where g is acceleration due to
gravity, r0
is a reference density, taken as 1,000 kg/m3, and dr/dz
is the vertical density gradient. Under such
conditions, the buoyant flows were close to buoyancy dominated flows (Wright,
1984).
Two three-dimensional visualizations of the outer surface of the unstratified jets are shown in Figure 2. Similar views of the time-averaged jets are shown in Figure 3. In these figures, the surface threshold level is set just above zero. The unstratified jet shows a familiar shape and trajectory; the stratified jet shows flattening near its terminal rise height. The horizontal buoyant jets have lower rising height than that in vertical buoyant jets.
(a) Vertical buoyant jet (b) Horizontal buoyant jet
Fig.
2 Rendering of instantaneous threshold concentration surface
of unstratified jet
Once
three-dimensional data like these are obtained, a great amount of information
can be extracted from it. For example, Figure 4 shows vertical profiles of
tracer concentration at various distances. Constant contours of tracer levels
are shown by gray shading. The familiar kidney shapes are apparent, with the
maximum concentrations appearing to the side of the plane through the jet
centerline. Trajectories and variation of dilution along the trajectory can also
be obtained, shown as Figure 5 to Figure 7. This information should be of great
value in improving mathematical plume models. In these two figures, BDNF means
buoyancy dominated near field and BDFF means buoyancy dominated far field.
is a length scale defined by Wright
(1984).
is the dilution at centerline. Comparing with the BDNF and BDFF results from
Wright(1984), both trajectory and dilution relations obtained in this paper fits
well with the BDFF results. Because the stratification compress vertical mixing
and the effect of stratification is more important with the distance increasing
from the nozzle, the vertical buoyant jet keeps almost same trajectory and
dilution in unstratified crossflows and stratified crossflows when
and both trajectory and dilution
diverge rapidly when
(shown in Figure 6). In stratified
crossflows, the jet collapses at some point and therefore it stop rising and the
dilution keeps constant. However, in unstratified crossflows, the jet keeps
rising and the dilution keeps increasing until it reaches the water surface.
Shown in Figure 7, the dilution of vertical jets is much lower than that of
horizontal jets at same rising height. This is because horizontal jets have a
much longer trajectory than that of vertical jets at same rising height.
However, the dilution of vertical jets and horizontal jets is almost same when
, if we look at the dilution along the horizontal distance from the nozzle.
Similar results can be obtained in stratified cross flows.
(a) Vertical jet in a unstratified crossflow (b) Vertical jet in a stratified crossflow
(c) Horizontal jet in a unstratified crossflow (d) Horizontal jet in a stratified crossflow
Fig. 3 Rendering of time-averaged threshold concentration surfaces of unstratified and stratified jets
(a) Horizontal jet in a unstratified crossflow (b) Horizontal jet in a stratified crossflow
Fig. 4 Vertical concentration profiles through unstratified and stratified jets
(a) Trajectory (b) Centerline dilution
Fig. 5 Relations of trajectory and dilution of vertical buoyant jets in unstratified crossflows
(a) Trajectory comparison of vertical jets in (b) Centerline dilution comparison of vertical jets
unstratified and stratified crossflows in unstratified and stratified crossflows
Fig. 6 Trajectories and dilutions of vertical buoyant jets in unstratified and stratified crossflows
(a) Variation of dilution with vertical distance (b) Variation of dilution with horizontal
in unstratified crossflows distance in unstratified crossflows
Fig. 7 Variation of dilution of buoyant jets in unstratified crossflows
A scanning laser system has been developed to enable three-dimensional Laser-Induced Fluorescence imaging in fairly large-scale turbulent unstratified and stratified flows. This can now be done at reasonable cost due to recent instrumentation advances, particularly in scanning mirrors, high-speed low-light CCD cameras, and image acquisition and storage.
Example applications to vertical and horizontal round buoyant jets discharging into unstratified and stratified crossflows are reported. Visualization results and some quantitative information can be obtained. All results proved that the new system is very useful to studies of turbulent mixing process. We plan to apply the system to a wide variety of jet and plume problems related to the discharge and mixing zones of wastewaters in the environment.
References
Daviero, G. (1998). “Hydrodynamics of Ocean Outfall Discharges in Unstratified and Stratified Flows.” PhD Thesis, School of Civil Engineering, Georgia Institute of Technology, Atlanta.
Daviero, G. J., Roberts, P. J. W., and Maile, K. (2001). “Refractive Index Matching in Large-Scale Stratified Experiments.” Experiments in Fluids, to be published.
Dimotakis, P. E., Miake-Lye, R. C., and Papantoniou, D. A. (1983). “Structure and dynamics of round turbulent jets.” Physics of Fluids, 26(11), 3185-3192.
Ferrier, A., Funk, D., and Roberts, P. J. W. (1993). “Application of Optical Techniques to the Study of Plumes in Stratified Fluids.” Dynamics of Atmospheres and Oceans, 20, 155-183.
Owen, F. K. (1976) “Simultaneous Laser Measurements of Instantaneous Velocity and Concentration in Turbulent Mixing Flows.” AGARD-CP193, Paper No. 27.
Roberts, P.J.W. and Tian, X. (2000), “Three-dimensional imaging of stratified plume flows.” Fifth International Symposium on Stratified Flows, Vancouver, Canada, July, 2000.
Wright, S. J. (1984). “Buoyant Jets in Density-Stratified Crossflow.” Journal of Hydraulic Engineering, ASCE, 110(5), 643-656.