An experimental investigation of multiphase flow involving a liquid (water) and a gas (air) is performed. The results for three different scenarios are presented: fixed bubble, ascending bubble, and dispersed-bubble turbulent pipe flow. This study involves a comparison of statistical data collected using two sensing systems, a wavefront sensor and a high-speed video camera. A signal analysis technique based on signal attenuation is developed for data collected using the wavefront sensor. The three experiments performed provide experimental evidence that the Shack-Hartmann wavefront sensor, operating on signal attenuation, is a viable method for the study of multiphase bubble flows.
Multiphase flow is defined as the simultaneous flow of several phases, with the simplest case being two-phase flow. The flow of two phases is found in many industrial processes including chemical and nuclear reactors, distillation towers, pipeline transport, injection of fluids for secondary recovery of oil and geothermal power plants.
One form of two-phase flow is gas-liquid dispersed-bubble turbulent pipe flow. This flow is of significant importance in chemical and petroleum process industries where the interfacial area between phases needs to be large for improved process efficiency. Bubble size, velocity of bubbles, and their distribution along the pipe are all important parameters for optimizing the efficiency of processes that rely on dispersed-bubble turbulent pipe flow.
Noninvasiveness is a desired attribute in any multiphase flow measurement technique given that the interference between the flow and the measurement device can affect the measured values. Many of the existing multiphase flow measurement techniques rely on the ability of the sensing apparatus to discriminate between certain physical properties that vary between phases, such as electromagnetic radiation attenuation or electrical impedance.
A large number of investigations reported over the last fifteen years describe the application of nonintrusive flow sensing techniques applied to the measurement and the study of multiphase fluid flows [
The long-term goal of a larger research program is to apply optical tomography to the investigation of multiphase pipe flow. The multiple projection line-integrated data collected in the optical tomography system is obtained using Shack-Hartmann wavefront sensors (SH-WFS) [
A weak index-of-refraction system is not considered in the current investigation. What is performed here, rather, is an examination of the response of a single SH-WFS to a flow for which the SH-WFS has not been designed: a gas-liquid multiphase flow involving strong index-of-refraction variations (
This paper begins by describing the experimental apparatus and optical equipment used during this investigation. The response of the SH-WFS is investigated for the detection of both a single stationary air bubble and multiple ascending bubbles. This investigation is followed by a comparison of the performance of the SH-WFS to a high-speed video camera (HSVC) for detection of multiple ascending bubbles and for dispersed-bubble turbulent pipe flow. To conclude, the overall performance of the SH-WFS for application to index-mismatched multiphase flows is discussed.
Two different experimental systems are used during the investigation to examine the performance of the Shack-Hartmann wavefront sensor. In the first setup, a small vertical half-pipe section is used to examine the aberrating effects of both a single stationary bubble and of multiple ascending bubbles. The second system, a multiphase flow facility, is used to study the horizontal bubble flow under turbulent flow conditions. In both experimental systems, an acrylic optical contour is used to correct for the optical aberrations induced by the curvature of the water-filled pipe section [
The optical diagnostics used in the investigation consist of a Shack-Hartmann wavefront sensor (SH-WFS), and a high-speed video camera (HSVC). The HSVC provides the advantage of two-dimensional images. Consequently, it also provides a good method by which the performance of the SH-WFS system can be examined when applied to a gas-liquid multiphase flow involving strong index-of-refraction variations.
The general arrangement of the SH-WFS with respect to both the half-pipe and the full-pipe is illustrated in Figure
Schematic of the Shack-Hartmann wavefront sensor around the pipe and half-pipe: (a) laser-diode collimated light source, (b) optical contour, (c) pipe/half-pipe, and (d) 1D Shack Hartmann wavefront sensor.
Traditional Shack-Hartmann wavefront sensing applications involve the comparison of focal-spot centroidal locations produced by both a reference wavefront and an aberrated wavefront. The reference wavefront is often an unaberrated wavefront, produced by transmission through a medium without index-of-refraction variations. The change in the focal-spot centroidal location between the aberrated and unaberrated wavefronts is then computed for each subaperture, quantifying the distortion of the aberrated wavefront [
Given that the current investigation involves optical transmission through water continuous media (
The HSVC used during the experiments is a Photron Ultima 1024, capable of acquiring images at frame rates ranging from 60 to 16,000 fps. This camera is able to operate at a full 1024
The HSVC enables images of the flow to be collected at high rates and then postprocessed for statistical quantities that can be compared to statistical data derived using the SH-WFS.
When using optical diagnostics to investigate pipe flow, special care needs to be taken to ensure that the strong optical aberrations induced by the fluid-filled pipe wall do not negatively impact the optical measurement being performed.
Prior to commencing this investigation, a custom-made corrective optic (referred to as an optical contour) was designed and manufactured using a computer numerically controlled (CNC) 5-axis machining station and used to correct for the aberrations induced by the water-filled acrylic pipe. The original design and manufacture of the optical contour is described in de Witt et al. [
The camera and the beam source are positioned perpendicular to the pipe axis as shown in Figure
The half-pipe test section shown in Figure
Air bubbles are introduced into the half-pipe apparatus using two different methods. A single stationary bubble is introduced by injecting a known volume of air through a syringe into a small-diameter hose. A small-diameter hose is placed in the water-filled acrylic half pipe in a manner that ensures that the end of the hose is aligned with the sensing area of the SH-WFS.
For the generation of multiple ascending bubbles, a piece of porous material (sand packing of 2.54 cm length and 1.27 cm diameter) is connected to a regenerative blower (EG&G Rotron Blower, with a maximum flow of 0.008684
The multiphase flow facility was designed and built specifically to study dispersed multiphase flow using optical methods. The facility can operate using air, water, and oil; however, only air and water are considered in the current investigation.
A schematic of the multiphase flow facility is shown in Figure
Description of the components of the flow facility.
Visualization Section. A 3.05 m long section of 5.72 cm inner diameter cast acrylic pipe with corrective optical contour forms the main diagnostic section.
Pumping System. A centrifugal pump capable of delivering 7.25
Piping. ABS black plastic pipe with 50.8 mm inner diameter is used for the fluid stream. Flow metering is performed on two straight section runs at the top of the flow facility. Flow rate for both water and oil is measured using a Panametrics UFP-1000 portable ultrasonic liquid flowmeter.
Separation and Storage. A 196 L vertical cylindrical tank with a diameter of 45.72 cm is designed for the separation of water and air.
Air Injection. A pipe of 38.1 mm diameter is connected to a 25 mm compressed air supply, and air injection is performed through a series of four 12.7 mm holes, each separated by
The performance of the SH-WFS is first examined by conducting experiments with a single bubble and with multiple ascending bubbles in the water-filled half-pipe.
A single stationary bubble is introduced into the half-pipe apparatus by injecting a known volume of air (average volume = 0.0344 ± 0.0035
The left part of Figure
Scheme of the wavefront passing through the bubble in the half-pipe and plot with the intensity response from the wavefront sensor, (a) incoming wavefront, (b) single bubble, (c) lenslet array, and (d) pixel array.
Due to low-signal levels, an evaluation that computes intensity attenuation is performed. To compare the intensities, the attenuation for each lens is calculated as the summed absolute difference between the reference intensity profile and the intensity profile collected with the air bubble in place. The attenuation is then passed through a thresholding algorithm that only accepts attenuations larger than 50 counts. A threshold of 50 counts is determined by quantifying noise as the summed absolute difference for multiple reference intensity profiles.
This thresholding algorithm is found to reject variations caused by electronic noise and results in clearer plots. The maximum value of attenuation is well above the threshold level and is greater than 1000 counts. The resulting plot in Figure
Contour of intensity difference with time for one bubble (a); profile of intensity difference at one time sample (b).
In order to ascertain the benefits of using the SH-WFS for bubble measurements, Figure
Schematic of the wavefront passing through the bubble in the half pipe and plot with the intensity response from the wavefront sensor, (a) incoming wavefront (b) single bubble (c) pixel array.
Contours of intensity difference with time for one bubble without lenslet array (a) and profile of intensity difference at one time sample without lenslet array (b).
The bubble diameter can be calculated from Figure
A more severe threshold is applied to the case without lenslet array in order to filter the data. The contour plot of the differences between intensity profiles (Figure
Data for multiple ascending bubbles in the half-pipe apparatus is collected at a line rate of 2.5
For the case of multiple ascending bubbles, the subaperture spot centroidal location does not shift significantly when compared to the unaberrated reference signal. Furthermore, the signal for multiple bubbles is not fully attenuated as it is for a single bubble. It is suspected that scattered light from one bubble may be detected by other subapertures not directly aligned with that bubble. Even though the amount of light extinction is less than that for the case of a single bubble, the extinction is still more quantifiable than a shift in spot centroidal location. Consequently, the same signal analysis routine as performed for the single bubble experiment is used, with results shown in Figure
Variation in intensity measured for the bubble flow in the half-pipe.
When the lenslet array is removed from the SH-WFS, the data collected is more difficult to interpret. Figure
Variation in intensity measured for the bubble flow in the half-pipe without the lenslet array.
Two main experiments are performed involving the application of both the SH-WFS and the HSVC to the study of air bubbles in water. The first experiment involves ascending bubbles in the water-filled half-pipe, and the second involves dispersed-bubble turbulent pipe flow.
The flow is analyzed using both the SH-WFS and the HSVC. The high-speed video data is collected at a frame rate of 2
Data taken with the HSVC for the case of ascending bubbles in the half-pipe. The circles show clusters of bubbles observed.
Analysis of the SH-WFS data reveals the average diameter of the bubbles as
Statistical analysis for the diameter of spherical particles in the flow and velocity of the ascending bubbles.
Processing data collected during the multiple ascending bubble experiment reveals the difficulties associated with either sensing system when multiple bubbles are present. For instance, in the case of results from the SH-WFS it is difficult to say what is happening when two contour peaks are very close together. This behavior may be attributed to two bubbles, with one behind the other, or to interactions between bubbles, such as coalescence. Data collected using the HSVC presents similar challenges, as denoted by the circles in Figure
As in the case for the water-filled half-pipe, the bubble flow investigated using the multiphase flow facility is performed by collecting data using both the HSVC and the SH-WFS. The multiphase flow facility enables the horizontal turbulent pipe flow to be investigated. This type of flow behaves in a fundamentally different manner from the previously discussed ascending bubble flow. Due to the presence of strong shear forces, bubbles in the horizontal dispersed-bubble turbulent pipe flow are more likely to be ellipsoid in shape rather than spherical. Also, the flow of bubbles is affected by the velocity field of the continuous phase (carrying fluid), with bubbles moving slower along the walls and faster towards the centerline of the pipe. While comparing the two measurement methods, an analysis of bubble size, velocity, and position within the pipe is performed.
The water velocities that resulted in dispersed-bubble flow using the multiphase flow facility ranged from 1.31 m/s to 1.82 m/s. Seven separate water velocities are investigated. Figure
Typical results from the HSVC for each water velocity sample.
It is not possible to quantify the amount of air injected during these tests due to the air flow rates being below the sensing range of the gas turbine flow meter. The flow rate of injected air is, however, assumed to be constant for all water velocities investigated given that a fixed flow restriction is imposed to the air inlet hose for all cases.
Figure
Typical results from the SH-WFS for each water velocity sample. Letter “C” in each plot represents the center of the pipe.
The SH-WFS is only able to detect across 24.5 mm of the 57.15 mm inner diameter cast acrylic pipe, and consequently it is necessary for the frame of reference of the SH-WFS detector to be aligned with the physical space of the pipe. This is performed by placing a dark object along the center of the pipe and by noting the subaperture (subaperture 18) where a loss of signal occurred. This subaperture is then referenced as the pipe centerline and labeled by a dark solid line in all plots. Even though the sensing length of the SH-WFS is 28.67 mm, only 24.5 mm of the sensing length results in meaningful intensity measurements. The optical contour causes a reduction of the collimated light at the entry of the pipe and magnification at the exit; this effect reduces the width of the collimated beam within the pipe by 5%. For more details about the behavior of light through the optical contour, the interested reader is referred to de Witt et al. [
In order to compare HSVC data to SH-WFS data, HSVC data is extracted only when a bubble crosses a reference line. Each bubble-crossing event yields data with regards to the following characteristics: the vertical position of the bubble in the pipe, the bubble size (both horizontal and vertical major axes), and the number of frames for the bubble to move through the reference line (bubble horizontal velocity). The use of a reference line to analyze data from HSVC enables a direct comparison to velocity data measured using SH-WFS.
Bubble size is measured with the help of a grid that is superimposed on each image. The grid that is used has a minimum size of 1 mm per cell. Approximately 350 bubble-crossing events are detected at the highest water velocities, while only 50 to 80 bubble-crossing events are detected at the lowest velocities.
Image analysis is not required for the SH-WFS data; however, as with the HSVC data, the SH-WFS data is also analyzed manually. The sizes and velocities are obtained from the summed absolute difference of intensity data. A similar grid to the one used with the HSVC is used to detect the size of the objects (bubbles) in the contour plots. The size of the bubbles is calculated by multiplying the size of the pixel in the sensor (
Given that the line-scan camera is a one-dimensional sensor, it is only possible to quantify bubble size in the cross-flow direction. Consequently, the data collected with the SH-WFS includes the vertical position of the bubble in the pipe, the size of the bubble (vertical axis dimension), and the number of frames (time) that it would take for each bubble to move through the sensing plane.
The image distortion effects due to the presence of the optical contour are also taken into account, and the data presented here is the corrected physical dimension. The magnification used for the optical contour is as reported in de Witt et al. [
Of the more than 1000 bubbles analyzed using the HSVC data, only 26% of the bubbles reveal spherical shape. The remaining bubbles are ellipsoidal in shape. An analysis of the shape of the bubbles is made using the data acquired with the HSVC and a ratio of bubble size in the flow direction (
Analysis of the sphericity of bubbles with the high-speed video.
Investigations by Crowe et al. [
This variation in bubble aspect ratio will affect velocity calculations made using the SH-WFS measurements given the assumption that bubbles are spherical. Bubbles are more likely to be elongated in the flow direction, resulting in a reduction in measured bubble velocity using the SH-WFS. The data presented in this paper is taken very close to the injection point which results in increased bubble shape variations. The assumption of sphericity has been made by other researchers investigating the horizontal bubble flow [
Figure
Comparison of position of bubbles in the pipe versus size of the bubbles.
A pattern is observed in the size information computed using the SH-WFS data where bubble size falls into discrete bands. These discrete bands result as the size calculation is performed based on the width of each lenslet, resulting in a resolution of 0.448 mm with an uncertainty of
With the exception of the largest water velocity, the maximum bubble size for all data collected with the SH-WFS is smaller than the maximum size calculated using the HSVC. The SH-WFS is also able to detect smaller bubbles than the HSVC. While small bubbles can be seen in the high-speed video, it is very difficult to obtain an accurate size calculation due to a limit in sensor resolution. The minimum size acquired for the SH-WFS was 0.224 mm while for the HSVC the minimum size is 0.54 mm, more than double that of the SH-WFS. The cause for this difference is believed to be attributed to the depth of field of the HSVC. Bubbles outside the depth of field of the HSVC would be blurred, making it more difficult to resolve them. The SH-WFS, on the other hand, involves collimated laser light. Consequently, it does not have a depth of field but rather is able to detect bubbles independent of where they are located within the pipe. If the HSVC had a smaller field of view like the SH-WFS, the resolving capability of the HSVC would have improved. The number of pixels in the SH-WFS is also larger than that for the HSVC, which also results in the noted difference. Had a higher resolution HSVC been used, the results would have been more comparable.
A comparison of bubble velocity data with pipe position is shown in Figure
Comparison of position of the bubbles in the pipe versus velocity of the bubbles.
This paper has investigated the performance of a SH-WFS for the analysis of dispersed-bubble turbulent flow. The presence of dispersed bubbles in the continuous water media is found to cause extinction of the collimated light source for the SH-WFS.
A statistical comparison between the SH-WFS and HSVC reveals good agreement for two different experiments: ascending bubble flow and horizontal pipe flow. The depth of field of the HSVC makes it more difficult to detect small bubbles (less than 0.55 mm) when compared to the SH-WFS, and consequently the SH-WFS has a better resolution than the HSVC for the optical configuration investigated. Had the HSVC had a smaller field of view or larger number of pixels, its resolution would have improved.
The three individual experiments that were performed-single fixed bubble, multiple ascending bubbles, and horizontal dispersed-bubble turbulent pipe flow, all provide strong experimental evidence that the SH-WFS is a reliable method for the study of multiphase bubble flows. The SH-WFS has certain advantages/disadvantages when compared to other measurement systems.
In comparison to the HSVC, the SH-WFS has the advantage of being able to detect bubbles at any plane inside the pipe whereas bubble measurement using the HSVC was more dependent on the depth of field of the camera lens system. The bubble detection procedures for the SH-WFS are simpler than those for the HSVC, providing a computational advantage during postprocessing operations. Given that the SH-WFS is a one-dimensional sensor, it has the advantage of being able to store more frames and to collect them at higher frame rates. The one-dimensional nature of the SH-WFS does pose a disadvantage when compared to the HSVC, given that it is difficult to measure convection velocity without first having to make assumptions about bubble dimension in the flow direction (i.e., the spherical bubble assumption).
The SH-WFS has been shown to perform as an extinction-based sensing technique when applied to a flow containing components with strong index-of-refraction variations, such as the liquid-gas flow investigated here. Additional sensing capability exists when the system is applied to flows with weak index-of-refraction variations, such as two immiscible fluids with minor index of refraction differences. This would enable the SH-WFS to detect both dispersed bubbles and oil droplets in a water-glycerin continuous flow, for instance. Exploration of this research topic has been left as a future investigation.
The authors would like to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) through its Discovery Grant Program and to acknowledge the National Council of Science and Technology of Mexico (CONACyT) for its financial support.