A multiphase, micro-scale PIV measurement technique for liquid film velocity measurements in annular two-phase flow

International Journal of Multiphase Flow 68 (2015) 27–39

Contents lists available at ScienceDirect

International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w

A multiphase, micro-scale PIV measurement technique for liquid film velocity measurements in annular two-phase flow A.C. Ashwood a, S.J. Vanden Hogen a, M.A. Rodarte a, C.R. Kopplin a, D.J. Rodríguez a, E.T. Hurlburt b, T.A. Shedd a,⇑ a b

Multiphase Flow Visualization and Analysis Laboratory, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, WI 53706-1609, USA Bechtel Marine Propulsion Corporation, Bettis Laboratory, West Mifflin, PA 15122, USA

a r t i c l e

i n f o

Article history: Received 5 April 2014 Received in revised form 2 September 2014 Accepted 5 September 2014 Available online 16 September 2014 Keywords: PIV Micro-PIV Two-phase flow Annular flow Liquid film flow Wall shear Optical diagnostics

a b s t r a c t Prediction methods for two-phase annular flow require accurate knowledge of the velocity profile within the liquid film flowing at its perimeter as the gradients within this film influence to a large extent the overall transport processes within the entire channel. This film, however, is quite thin and variable and traditional velocimetry methods have met with only very limited success in providing velocity data. The present work describes the application of Particle Image Velocimetry (PIV) to the measurement of velocity fields in the annular liquid flow. Because the liquid is constrained to distances on the order of a millimeter or less, the technique employed here borrows strategies from micro-PIV, but micro-PIV studies do not typically encounter the challenges presented by annular flow, including very large velocity gradients, a free surface that varies in position from moment to moment, the presence of droplet impacts and the passage of waves that can be 10 times the average thickness of the base film. This technique combines the seeding and imaging typical to micro-PIV with a unique lighting and image processing approach to deal with the challenges of a continuously varying liquid film thickness and interface. Mean velocity data are presented for air–water in two-phase co-current upward flow in a rectangular duct, which are the first detailed velocity profiles obtained within the liquid film of upward vertical annular flow to the authors’ knowledge. The velocity data presented here do not distinguish between data from waves and data from the base film. The resulting velocity profiles are compared with the classical Law of the Wall turbulent boundary layer model and found to require a decreased turbulent diffusivity for the model to predict well. These results agree with hypotheses previously presented in the literature. Ó 2014 Elsevier Ltd. All rights reserved.

Introduction Two-phase annular flow occurs in a wide variety of industrial heat transfer equipment, including air conditioning and refrigeration systems, nuclear and coal power plants, and chemical processing systems. These flow conditions are difficult to analyze from an engineering perspective due to the complex interaction between the two phases. Prediction of the flow behaviors are also complicated by the distinct flow regimes, which can generally be described as the manner in which the two phases can be spatially distributed in the tube. A significant regime in many commercial and industrial processes is annular flow. Annular flow is characterized by a relatively fast moving gas core flowing through the center of a tube with a thin film along the circumference; liquid droplets are generally mixed into the fast ⇑ Corresponding author. E-mail address: [email protected] (T.A. Shedd). http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.09.003 0301-9322/Ó 2014 Elsevier Ltd. All rights reserved.

moving gas core and bubbles are generally entrained in the liquid film. Detailed measurements of liquid film velocities in annular flow are largely unavailable, hence simulation of the liquid film typically uses empirical correlations of a thickness averaged flow. Local velocity measurements are needed to guide the development of more detailed thin film fluid flow models that will enable physically based pressure loss, heat and mass transfer models. Several efforts have been made to study the nature of the velocity field within the thin liquid film of annular flow. Photochromic dye tracing was used to obtain axial flow profiles by Hewitt et al. (1990), employing the dye traces and backlit imaging to obtain velocity profiles. An initial study by Kawaji et al. (1993) using the Photochromatic dye activation (PDA) technique focused on stratified and wavy countercurrent flows and provided a beginning to using spot dye traces to study horizontal annular flow. Sutharshan et al. (1995) applied this methodology to horizontal annular flow and, together with qualitative analysis of the dye movement, provided evidence for the upwards transport of liquid

28

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39

flow in the presence of a disturbance wave. Lorencez utilized this technique in a turbulence structure near a wavy gas–liquid interface (Lorencez et al., 1997a,b). Their work found that a k   turbulence model could be used to predict the overall turbulence statistics. Other techniques include seeding with oxide powders to obtain the velocity of the liquid film surface (Fukano et al., 1985). A particle tracking technique was implemented by Hagiwara et al. (1995) in annular flow to gives some indication of circumferential velocity components within the liquid film. Falling films are sometimes used as an analogy for thin films in wavy and annular flow. Laser Doppler anemometry was used by Mudawar and Houpt (1993a,b) to study falling films. Their work indicated that the fluctuations due to waves dominate the flow and cannot exclude the possibility that the film is laminar in nature. PDA techniques have also been used to study falling film behavior (Moran et al., 2002; Karimi and Kawaji, 1998). The present work describes the application of Particle Image Velocimetry (PIV) to the measurement of velocity fields in the annular liquid flow. The technique described herein borrows strategies from micro-PIV because the liquid is constrained to distances on the order of a millimeter or less. Micro-PIV (l-PIV) was first introduced by Santiago et al. (1998) in the study of a Hele-Shaw flow over a microscopic elliptical cylinder. Prior to this group’s experiment, researchers had been utilizing macroscopic camera lenses to analyze macroscopic flows. Since then, l-PIV has been expanded to other microfluidic systems, such as flow through micro-channels and micro-electromechanical systems (MEMS) (Adrian et al., 1998; Meinhart and Zhang, 2000). Hassan (2002), Choi et al. (2002), Lindken and Merzkirch (2002) have employed l-PIV in vertical bubbly pipe flows. On the other hand, micro-PIV studies do not typically encounter the challenges presented by annular flow, including very large velocity gradients, a free surface that varies in position from moment to moment, the presence of droplet impacts and the passage of waves that can be 10 times the average thickness of the base film. A descriptive name, Thin Film Particle Image Velocimetry (TF-PIV), was suggested by Shedd (2001), for the technique described in this research to deal with these unique behaviors. This technique combines the seeding and imaging typical to micro-PIV with a unique lighting and image processing approach to deal with the challenges of a continuously varying liquid film thickness and interface. Schubring et al. (2009) were among the first to apply PIV to a shear driven film, focusing on horizontal wavy flow. In wavy flow, with its thick film providing an optical path for light originating from tracer particles to leave the test section, a light sheet illumination was possible. Thus, the entire near-wall velocity profile could be captured instantaneously. Recently, Zadrazil et al. (2012, 2013) applied similar techniques to wavy films of downward cocurrent annular flow. Despite significant effort, the current authors have found that it is quite difficult to image particles in this way in annular flow with film thicknesses below 0.5 mm because the liquid film is so thin and uneven. In addition, if the desired plane of measurement is located far from a side wall, the optical path through particle-laden liquid can diminish the image contrast to the point that individual particle images are nearly impossible to identify. Finally, in the case of a curved wall, even with refractive index correcting boxes, a small difference in the index of refraction can make it impossible to image the first 5, 10 or 100 lm from the wall (Rodríguez and Shedd, 2004). TF-PIV does not attempt to capture the entire cross-section of the liquid film. The axis of the lens system is directed perpendicular to the flow channel wall at the desired location of measurement. Large sets of particle images are obtained at a number of focal planes within the liquid, each of these planes is parallel to

the channel wall and translated progressively further from the wall. PIV vector interrogation is applied to the image sets obtained at each focal plane position and the mean velocity profile can be reconstructed from the mean velocity at each focal plane. It is a somewhat time consuming process, but provides benefits, such as flexibility of measurement location, very reliable mean velocity measurements, the ability to use very small particles (0.5 lm and smaller), which is important in the very thin films with large velocity gradients, and a large number of vectors measured at each focal plane that provide local statistics describing the velocity behavior. In honor of Prof. G.F. Hewitt’s 80th birthday and his leadership in the development of multiphase measurement techniques, this work presents an overview of the development of this technique; fuller detail of the development may be found in Kopplin (2004), Ashwood (2009), Vanden Hogen (2013). In addition, data are presented for air–water in two-phase co-current upward flow in a rectangular duct. These data are the first detailed velocity profiles obtained within the liquid film of upward vertical annular flow to the authors’ knowledge.

Experimental Flow loop The flow loop layout is shown in Fig. 1. Compressed air passes through an oil/particulate filter and then through two parallel Cole-Parmer model number 32907-81 air mass flow controllers so that a wide range of flows can be obtained. The air controllers have an uncertainty of ±1% of the 1024 SLPM (0.020 kg s1) full scale range. The compressed air flows downward through a 23.7 mm ID copper tube, then expands into an approximately 75 mm ID 180° bend at the bottom of the flow loop. The bend is filled with forty 5 mm ID plastic tubes parallel to the flow that act as flow straighteners, minimizing rotational motion in the air flow before mixing with the water. A reducer after the bend directs the flow into a 23.4 mm ID copper tube where, after 10 diameters, water is introduced perpendicular to the air flow through several 2 mm holes via a mixing tee. The two-phase mixture then transitions from a circular geometry to a rectangular duct geometry via a transition duct. The water was pressurized using a high-head, high capacity Ebara 2CDXU centrifugal pump whose outlet was regulated to 4 bar gage using a Cash Valve back-pressure regulating valve. This system allows a wide range of flows to pass through the flow loop without impacting the input pressure, significantly simplifying the liquid control apparatus and minimizing the possibility of flow-induced vibrations in the test section. Any flow not used in the test section was redirected to the reservoir. This created a constant circulation that helped to maintain the seeding particles well-mixed. Cold facility water passing through a coil of finned copper tube was used to remove the pump heat from the reservoir. The flow was controlled by two needle valves that were mounted following two Orange Research Versa-mount dial-indicating flow meters, models 2221FG and 2321FG, with ranges of 0–1 GPM ± 0.02 GPM (0–3.79 ± 0.076 LPM) and 0-5 GPM ± 0.1 GPM (0–18.93 ± 0.38 LPM), respectively. The rectangular duct was fabricated using 5.1 mm thick acrylic sheets. The inside dimensions of the duct measured 33.0 mm  20.3 mm for a hydraulic diameter of 0.0251 ± 2.5  104 m. A smooth, three-dimensional expansion section transitions the flow from the round mixing tube to the duct test section over a distance of 200 mm. TF-PIV measurements were obtained at 69 L/D upstream of the transition to the duct test section. The required entry length to achieve a fully developed annular flow in a vertical tube has been investigated by authors such as Ishii and Mishima

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39

29

Fig. 1. Vertical upward air/water flow test facility diagram.

(1989), Kataoka et al. (2000), Wolf et al. (2001); and Zhao et al. (2013). The work detailed in Ishii and Mishima (1989) and further developed in Kataoka et al. (2000) approximated that entrainment and deposition reach equilibrium based on the criterion:

developed case based on information detailed in Zhao et al. (2013) (for 620 < Refilm < 780 and 33; 400 < Reg < 41; 200 based on the range of experiments studied in this test series following definitions shown below).

L 440 We0:25 D ¼ Dcrit Re0:5 l

Refilm ¼

ð1Þ

The parameters WeD and Rel are the entrainment Weber number and liquid Reynolds number respectively and defined according to

2

WeD ¼

31=3

qg U 2sg D 4 ql  qg 5 r qg

Rel ¼

ql U sl D ll

ð2Þ

Here, D is the diameter of the channel, q and l refer to the fluid density and viscosity, respectively. The subscripts g and l represent gas and liquid quantities, respectively, while U sg and U sl refer to superficial gas and liquid velocities. The development length based on Kataoka et al. (2000) required to reach equilibrium based on this criterion ranged from L/D  55–72 for the current sample set (with only the maximum superficial vapor velocity flow rate exceeding the L/D = 69 condition). Wolf et al. (2001) experimentally observed entrainment and mean film thickness to take the longest distance to develop from the inlet condition for vertical annular flow with a porous wall liquid inlet condition. Wolf et al. (2001) suggested a flow development length of 150 L/D is necessary to be within 10% of the fully developed flow and 300 L/D for fully developed flow. More recently, Zhao et al. (2013) conducted experiments in vertical annular flow and found circumferential coherence of disturbance waves at L/D as short as 20. As such, the flow may not be completely developed in the present case, but less than 20% from the fully

qg U sg D ql U film d ql Q_ l ¼ Reg ¼ lL ll Per lg

ð3Þ

where d denotes the thickness of the liquid film, Per is the perimeter of the channel, and Q_ l is the liquid volumetric flow rate. TF-PIV optics A 12 bit LaVision Imager Intense camera with a 1376  1040 pixel CCD (charged couple device) sensor was used to obtain the TF-PIV data. The camera was mounted to two translational stages (see Fig. 2), one with transverse directionality and the other with axial directionality. The camera was equipped with a 10 Mitutoyo plan apo infinity-corrected long working distance microscope objective lens (numerical aperture = 0.28), and an Edmund Optics OG-570 longpass filter (part number NT46-062) with a cut-off position of 570 nm, where the filter was used to block the green light from the laser. The entire camera setup was then rigidly mounted to an aluminum frame to which the test section was mounted as well in order to minimize relative vibrations. A Starrett model number F2730-0 indicator was fixed to the aluminum frame in contact with the wall-perpendicular translation stage to accurately indicate the radial position of the focal plane of the camera into and out of the test section. The Starrett indicator had a range of 25 mm and a resolution of 0.0005 mm.

30

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39

Fig. 2. Instrumentation used to capture particle images in the liquid film of vertical annular flow.

The laser used in this experiment was a New Wave Research Solo PIV Nd:YAG laser. Unlike traditional PIV in which the measurement plane is defined by a sheet of light, TF-PIV relies on the depth of focus of the optical system to define the measurement plane, as in microPIV techniques. Thus, the region of interest is flood-exposed with the laser light. Instead of focusing the laser into a sheet, the light is intentionally diffused to a spot approximately 20 mm in diameter. Previous work has shown that the best contrast is obtained when the laser light is introduced at a glancing angle relative to the test section (Kopplin, 2004). Thus, for the vertical case, a mirror was used to deflect the laser light upward onto the test section as illustrated in Fig. 2. The particles used were 0.52 lm diameter Thermo Scientific polystyrene micro-spheres, which absorb the green 532 nm laser light and emit red–orange light at 612 nm. The seeding particles have a density of 1.05 g cm3. The filter between the objective lens and the camera allows the fluorescent light to pass while preventing the green laser light from exposing the CCD. The timing of the entire setup was controlled using LaVision DaVis software equipped with a LaVision PTU-9 system. The images obtained using this system represented a 1.10 mm  0.832 mm region of the flow with a 0.8 lm/pixel resolution. The density ratio, qp =ql , between the particle tracers and the liquid was no more than 5% different in this test series. Based on the information presented in Mei (1996) and Melling (1997), the tracers will follow the background turbulent scales in the liquid with negligible buoyancy effect. The time delay between the two single exposure PIV images in an image-pair was set by the user in such a manner that the pixel displacement between the two images was between 20 and 40 pixels (or 10–30% of the final interrogation window size), as previous work indicates that the uncertainty is minimized with pixel displacements in this range (Foster, 2005; Kopplin, 2004); within this

range, it was found by artificially displacing actual particle images that after interrogation, error was 0.1% or lower. PIV image pairs were acquired at 1 Hz and a total of 150 image pairs were captured at each radial location resulting in a total acquisition time of 150 s. Since waves on the film interface occur in the range of 10–30 Hz (Schubring and Shedd, 2008), data from many disturbance waves were acquired in each data set. On the other hand, the number of valid vectors do decrease far from the wall (outside of the base film) as is evidenced somewhat by the increased scatter in these data seen in Fig. 10, presented in the Results section. The number of valid vectors by approximately a factor of 10 between measurement locations within the base film and those outside of the base film. Determining the wall location One of the most difficult challenges in acquiring the images for TF-PIV is to accurately find the wall. This is difficult due, in part, to the depth of focus of the camera lens. An Edmunds Optics mylar sheet with a 25 mm  25 mm square grid of 0.0625 mm diameter dots with 0.125 mm spacing was placed in a small section of rectangular duct separate from the test section. Natural rubber tubing was then placed in the tube and inflated with air to ensure that the calibration grid was pressed against the wall surface. The micrometer stage was then axially adjusted toward the array until the dots were visually ill-defined (approximately twice their original diameter). The dots were then brought back into focus and the camera was adjusted axially away from the array until the dots were again ill-defined. The average of these differences into and out of the focal plane is the depth of focus. The measured depth of focus for the camera and lens system was estimated to be 6 lm based on this technique.

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39

Once the depth of focus was obtained, it was necessary to determine the location of the wall of the duct. Air and particle-filled water were allowed to run through the flow loop until particles were stuck on the wall of the test section. The camera was translated until the particles that were stuck to the wall were in sharp focus. The location where this occurred was the nominal wall location. Before beginning test images, the camera was translated away from the wall about 6 lm to ensure that the image series’ would include the wall location. Once the wall was found, 150 image-pairs were acquired at each position as a function of distance from the wall. Note that, for each location, an image was selected at random to verify that the pixel displacement was in the range of 10–30% of the final interrogation window size; if this condition was met, the camera was translated further into the film. If, however, the pixel displacement was too small or too large, the time delay between exposures was modified and the data set was taken again. This check was to ensure that the velocity vectors produced by the subsequent vector interrogation procedure were accurate (Foster, 2005). Although the nominal wall location was obtained as described above, the velocity data themselves were used to determine the exact location of the wall with respect to the entire set of locations measured. Occasionally, this location would differ from the nominal location by more than 6 lm. Data obtained starting at greater than 6 lm from the wall can be attributed to data obtained directly after the duct was cleaned (when fewer particles would be stuck to the wall) and user error (i.e., the particles stuck on the wall appeared to be in sharp focus, but were not, possibly due to reflections from other objects). The exact location of the wall was determined by applying a linear curve-fit to the velocity vs. displacement data in the viscosity dominated regime to determine the location where the film velocity would reach a value of 0 m s1, as shown in Fig. 3. The uncertainty in the wall location determined in this manner was determined numerically since a linear regression method was used to fit the velocity data and analytical propagation of uncertainty through the linear regression can be quite cumbersome (Coleman and Steele, 2009; Taylor, 1997). Individual data points were transferred to the Engineering Equation Solver (EES) (Klein, 2014) software package and the uncertainty propagation feature of the package was employed. The worst case uncertainty in wall location was found to be ±5 lm. Particle concentration Vectors are obtained in PIV by essentially dividing the particle images into small grids called interrogation regions and

31

using statistical methods to determine the displacement in each region from one frame to another. This yields one velocity vector per interrogation region. The particle seeding is important in obtaining velocity data using this method. Ideally, the particle density should be high enough to guarantee that every interrogation region in the image field contains many particles (say, 7), but not so high that the particles overlap or produce speckle. A unique problem to TF-PIV is that too large a particle concentration can create a background lighting effect that reduces the particle contrast to zero. As an example, consider imaging particles in a plane 100 lm from the wall in a thin annular film with a mean thickness of 200 lm. Because of the flood illumination of the liquid, particles throughout the entire film are exposed to the excitation light and will fluoresce, causing a background illumination that decreases the contrast of the desired image in the focal plane. This is exacerbated by the fact that a film with an average thickness of 200 lm will vary significantly in thickness, with waves perhaps approaching 2 mm or more in extent and troughs thinning to 50 lm. Thus, not only is the background illumination a contrast problem, it is also continuously variable. According to Thermo Scientific, the particle concentration in the packaged particles is 1:3  1011 particles per mL in solution. Typically about 5 mL of particle solution was added to 19 L of filtered water at startup. Based on the imaged volume (1.10 mm  0.832 mm  0.006 mm) for the current setup, this would result in an average of about 375 particles per image. This results in an average of about 4 in-focus particles per 128  128 interrogation region, but in reality, due to the mal-distribution of particles, each image was typically composed of more than 2/3 of the interrogation regions containing 6 or more particles, with the remaining containing fewer than 3. TF-PIV uncertainty The major sources of uncertainty in the TF-PIV measurement include statistical, resolution, calibration, and data filtering sources. The statistical and resolution uncertainties are random errors and their influence on PIV measurements can be reduced with a large number of samples. The subgrid pixel accuracy of the DaVis software used for the PIV vector processing is given at ±0.05 pixels for images with at least 7 particles per interrogation region. As noted above, most of the interrogation regions with valid vectors and 6 or more particles. Meinhart et al. (1999) reported that the spatial resolution was limited not by the actual diameter of the particles but by the effective diameter that was projected back to the camera sensor. The point spread diameter is given in Eq. (4) where M is the magnification, NA is the numerical aperture of the lens, and k is the emission wavelength of the particles used in the water.

ds ¼ 2:44 M

k 2 NA

ð4Þ

Meinhart goes on to define the effective diameter, de , projected on the camera sensor as:

h i1 2 2 2 de ¼ M 2 dp þ ds

ð5Þ

where dp is the actual particle diameter. Adrian (1997) also includes the error caused by the resolution of the recording medium dr (the pixel spacing on a digital sensor) to arrive at an approximate value for the recorded image diameter ds . Adrian assumes that the noise from the recording and the image intensity are Gaussian to arrive at Fig. 3. Example of velocity profile near the wall with linear regression-based line used to find location of the wall and wall shear.

h i1 2 2 2 ds ¼ de þ dr

ð6Þ

32

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39

These calculations lead to a PIV cross correlation uncertainty, dx, calculated using the following equation attributed to Adrian

ds 10

dx 

ð7Þ

The uncertainty in the velocity measurement can then be found using

dU ¼

dx M Dt

ð8Þ

The Mitutoyo M Plan Apo 10x microscopic objective used in conjunction with the 50.8 mm long lens tube resulted in an optical system with a numerical aperture of 0.28 and a magnification of 8 as dictated by the camera pixel size to imaging resolution

M measured ¼

Scamerapixel 6:45 lm ¼ ¼8 0:8 lm Simageresolution

ð9Þ

The uncertainty in displacement was found to be 2.2 lm, which leads to an uncertainty of 0.0054 m s1 for an image-pair separated by 50 ls (which occurs close to the wall). For an image-pair separated by 10 ls (which occurs far from the wall), the displacement uncertainty propagates to a velocity uncertainty of 0.027 m s1. Finally, the depth of focus was confirmed based on the arguments of Adrian (1997) who showed that the effective diameter is proportional to the depth of focus, dz ,

 1 2 2 de ¼ M 1:5 dz k þ dp

ð10Þ

The depth of focus, dz , evaluated according from Eq. (10), was determined to be 7.75 lm, which is nearly equal to the visually estimated value of 6 lm. The PIV algorithm used by the DaVis software also has inherent uncertainty. Work by Foster (2005) has indicated that the accuracy of the PIV algorithm in DaVis was very good when an appropriate time delay is used between images to keep the particle image separations between 10% and 30% of the final interrogation window size; in this study, a 20–40 pixel displacement range in a 128  128 interrogation window was used. The uncertainty associated with the post processing methods will be presented in Section ‘TF-PIV processing’. TF-PIV processing TF-PIV image processing Once acquired in sets of 150 image-pairs per location, per flow condition, the digital images first undergo image processing with a particle-isolating algorithm developed with commercial software (MATLAB). The steps for processing the images are as follows:  The contrast of the image is enhanced such that the full intensity range is used.  The images are treated with a 9  9 Gaussian low-pass filter with a standard deviation of 2.  An amplitude shifted Gaussian filter, or ‘‘particle filter,’’ is then applied to the images that is designed to specifically correlate to typical particle images.  An intensity threshold is applied to the image such that all of the pixels in the input image with an intensity greater than the mean of the image are assigned a value of 1 (white) and all other pixels are assigned a value of 0 (black). Fig. 4 is an example of a processed image-pair that has been overlaid onto the original image. The image processing code isolates between 90% and 100% of the particles with generally fewer than 5% generation of noise ‘‘particles’’. The lower right of Fig. 4

shows an example of a processed image-pair that has been overlaid onto the original image. As can been seen in Fig. 4, this image processing algorithm is able to isolate particles from larger structures, such as the reflection from the ripple in the right of the images and the bubble appearing near the center-left of the image and it is able to do this even with very low contrast between the particle images and the background and the varying background intensity. The dynamic contrast enhancement algorithm is an important first step, as images captured from the flow are prone to have non-uniform background illumination due to continually varying liquid thickness and the interaction of the illuminating light with the air/water interface. In addition, it was determined early on in the development of PIV for annular flow Shedd (2001), Kopplin (2004), Foster (2005) that particle images needed to be isolated from other structures in the captured images such as bubbles and reflections from waves. The particle filter discriminates between intensity patterns consistent with a particle image and larger, more gradually modulating intensities. Bubbles on the order of 1 lm may pass through the particle filter depending on the intensity pattern recorded by the camera, but bubbles or other features of the order of 10 lm or larger are nearly always eliminated. The algorithm for dynamic contrast enhancement is described in detail in Kopplin (2004) and Foster (2005), but will be summarized here. First, a copy of the acquired image is made. This copy is intensity inverted and aggressively smoothed with a Gaussian smoothing filter (radius 10). A fixed value of 50 is then subtracted from each pixel intensity, and the inverted, smoothed and shifted copy is added, pixel by pixel, to the original image. The resulting summed image is of low contrast, but quite uniform background intensity; it also will have the same mean brightness value regardless of the original intensity distribution, which simplifies subsequent operations. Finally, a linear contrast stretch is applied to the image before the particle filter is applied to it. The image processing was designed to perform a correlation of an ideal particle intensity profile, based on a Gaussian intensity distribution, with the captured images. As the ideal profile is convolved with the image, large correlation peaks will appear at particle locations, resulting in enhanced particle images. However, a non-negative Gaussian distribution acts as a low-pass filter and thus would tend to increase the background intensity across the image, lowering the contrast. If, however, the Gaussian distribution were shifted to have a mean value less than 0, large features of relatively uniform intensity will be eliminated (i.e., the correlation of the negative-biased Gaussian distribution and an array of uniform pixel intensities will be less than 0), while features whose dimensions fit within the positive peak of the distribution will be amplified. Fig. 5 shows an example of one of the typical particle filter distributions used in this work: a 9  9 Gaussian distribution, multiplied by 100, then shifted negatively until the sum of all the values in the matrix is equal to 10. These filters are generated dynamically and can be adjusted if needed to accommodate varying properties of captured images. It should be noted that no adjustments were needed for the images used in this study, except that a less negative filter (matrix sum of 8) was used for all of the images captured from the second laser due to a slight difference in the intensity between the two laser pulses. The resulting particle images are then analyzed with DaVis PIV interrogation software in order to estimate instantaneous velocity in each interrogation region of each image. All of the axial velocity vectors at a given displacement from the wall were then averaged together to obtain one velocity value representing the velocity at that location in the film.

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39

33

Fig. 4. An example of image processing for an image pair located 90 lm into the film in the vertical duct. (a) Original image, (b) contrast enhanced image, (c) application of gaussian smoothing filter, and (d) application of intensity threshold.

Post-processing in DaVis Once the images have been processed, they are analyzed using LaVision’s DaVis PIV interrogation software, which divides the image into interrogation regions, calculates the intensity cross-correlation of image-pairs, and extracts from this calculation an instantaneous velocity for each region. A variety of computational options are available within the software interface, many of which introduce considerable effects on vector uncertainty. The particular settings of this experiment will be discussed in this section. Analysis for this study was conducted with an initial interrogation window of 512  512 pixels, followed by a pass using a 256  256 pixel window and ending with 2 passes using a 128  128 pixel window. Each successive iteration applies a pixel offset to the cross-correlation region, which is equal to the displacement calculated on the previous pass, with a maximum

allowable deviation of 50 pixels on successively calculated displacement vectors. Most PIV software allows successive interrogation windows to overlap by a chosen percentage of their area; this value was set at 75%, a choice that balances the increase in calculation time with the increased accuracy of a high overlap in windows (data were processed using an overlap of 25% and 50% with negligible difference in the data). The 2D-FFT of each of the two n-by-n interrogation windows is calculated, the results are multiplied, complex conjugated, and the inverse FFT taken. This yields a cyclic cross-correlation, which although computationally faster for all but the smallest interrogation windows, does introduce potential for error. The first disadvantage of the cyclic cross-correlation is that it introduces a preferential weighting of zero displacement. Although this weighting can be detrimental to final accuracy for single-pass applications, the use of multiple passes with the accompanying changes

34

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39

were removed. Each vector that was greater than 1.8 times the root mean square (RMS) value of its neighbors was also removed. On the subsequent pass, each vector with fewer than 3 remaining neighbors was also removed. In the final pass, the RMS of the remaining vectors was calculated and vectors with greater than 2.5 RMS value of its neighbors were removed. Fig. 6 presents the vectors produced with these parameters from the image pair shown in Fig. 4. It can be seen in this image that the bubble and small, crescent-shaped ripple in the original image were not tracked by the interrogation software, but the vectors do show a flow upwards and to the left on the right-hand side of the image, consistent with the flow of a ripple at the angle shown in Fig. 4. Additional vector maps shown in Fig. 7 demonstrate a variety of instantaneous behaviors in the film.

Sensitivity to post processing parameters Fig. 5. Graphical representation of particle filter kernel used to isolate particle images within the captured images.

in initial window displacement can make the effect advantageous. After the initial pass, the program seeks to position the interrogation windows such that there is no relative displacement, and so is aided by the tendency of the FFT method to gravitate in that direction. Secondly, the cyclic cross-correlation process also tends to bias towards slightly lower than actual displacements. However, once again, adaptive multi-pass usually eliminates this error (Foster, 2005). As a final check on vector accuracy, both a median and peak filter are applied to the preliminary vector results. The peak ratio, Q, is defined as

Q¼

P1  min >1 P2  min

ð11Þ

where P 1 and P 2 are the peak heights of the first and second correlation peaks. The ratio is normalized by subtracting the minimum correlation value from each peak before finding the quotient. In order to eliminate vectors from the interrogation windows with conflicting velocity information, all regions with Q less than 1.3

The uncertainty in the post processing methods was tested in the vertical duct with U sg = 25.0 m s1 ; U sl = 9.95 cm s1. The baseline case (BL) was defined in the previous section; a 75% overlay of the interrogation regions was used with a median filter, vectors with <1.8 times the RMS value of its neighbor were removed, and regions with Q < 1:3 were removed. Data were processed with all of the parameters used in the baseline, except one value was changed to test the sensitivity of each step. The mean absolute difference (MAD) a given variable w between the cases is defined as:

MAD ¼

  1 XwBL  wcheck   100%  N N wcheck 

ð12Þ

First, the percent overlay was tested at both 25% and 50%. Next, the vector removal operation was disengaged so that the uncertainty of possibly erroneous vectors could be determined. The median filter and Q filter were also disengaged in turn to determine their impact. In the end, the vector removal, median filter and Q filter all had the greatest sensitivity to the vectors produced, but the MAD was no greater than 12%. All of the uncertainties are shown in Table 1.

Fig. 6. The vectors resulting from the vector interrogation of the image pair in Fig. 4. The scales are in pixels with a scale factor of 0.8 lm/pixel.

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39

35

Fig. 7. Four additional instantaneous vector maps randomly selected from data at 90 lm from the wall. The scales are in pixels with a scale factor of 0.8 lm/pixel.

Refractive index correction A correction to both the velocity and displacement data was required in order to compensate for the variations in the index of refraction through the acrylic test section and water. A simple test setup was constructed to measure the objective to image distance, as shown in Fig. 8 (see Vanden Hogen (2013)). A small acrylic test section was filled with water and a slide with dry particles on one side was mounted to a translational stage so it could freely translate inside the water. The translational stage holding the test slide used a digital micrometer with accuracy of ±1 lm to measure the displacement of the test slide. The LaVision Imager Intense CCD camera was mounted on a separate translational stage in order

Table 1 Post processing sensitivities (compared to the baseline) in the vertical duct for U sl = 9.95 cm s1 and U sg = 25.0 m s1. MAD = mean absolute difference. Group

MAD (%)

Post processing uncertainty 25% Overlay 50% Overlay No last vector removal No median filter No Q

7.5 3.9 11.9 11.4 11.4

translate it independently from the slide. The Starrett digital displacement indicator described above was used to measure the displacement of the camera on the translational stage. The test slide was moved away from the camera in increments of 5–20 lm. The camera was then moved towards the slide until the test slide was brought into focus. The displacement of both the camera and test slide were recorded and plotted as shown in Fig. 9. The displacement errors due to the different refractive indices can be formally derived and are plotted as the theoretical curve in this figure (Pautsch, 2007). The image distance was found to be 1.35 the objective distance for the present system (i.e., for every 1 lm the camera would translate, the image location would translate 1.35 lm into the flow). Note that this multiplier was also used to correct the velocities to compensate for magnification of the images.

Uncertainty in the derived wall shear Aside from the mean velocity profile, the wall shear is a key quantity that can be derived from the velocity data. This is performed using the same technique described earlier for finding the wall location: five to ten data points are located within the viscous region of the velocity profile and the slope is determined from a linear regression of these points. Note that this is an iterative

36

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39

Fig. 8. Test setup used to identify and validate index of refraction correction for both velocity and imaging plane location.

Recall that each velocity data point represents the mean of all axial velocity vectors obtained at the given transverse distance from the wall. No attempt was made in this study to separate vectors by fluid structure (i.e., base film versus wave). Additionally, film thickness and pressure measurements were also taken to provide comparison of the shear calculated via the PIV measurements and those obtained using a pressure transducer

Fig. 9. Experimental results validating model for index of refraction correction for the imaging plane location.

process; the viscous region is defined by locations within 5 wall units from the wall (i.e., yþ 6 5). Since yþ depends on the wall shear, some points may be added or removed from the estimation after the first calculation. Fig. 3 is again a useful visualization of this process. The uncertainty in the wall shear was determined numerically since a linear regression method was used to fit the velocity data. Individual data points for velocity and radial location were transferred to the Engineering Equation Solver (EES) (Klein, 2014) software package and the uncertainty propagation feature of the package was employed. The uncertainty was found to range from ±5% to ±15% of the derived wall shear. Experimental results Velocity profiles Velocity data in a vertical duct were obtained at a constant superficial liquid velocity, U sl , of 9.95 cm s1 and superficial gas velocities, U sg , of 20.1 m s1, 24.8 m s1, 29.5 m s1, 34.2 m s1. The velocity profiles obtained from these data (from a radial position, y, starting at the wall and ending out into the waves) are shown in Fig. 10. Data were also obtained at a constant superficial gas velocity, U sg of 24.8 m s1 and superficial liquid velocities, U sl , of 8.71 cm s1, 9.95 cm s1, 11.2 cm s1, 12.4 cm s1. The velocity profiles obtained from these data are shown in Fig. 10.

Fig. 10. Dimensional velocity profiles within the liquid film of vertical annular flow. (a) Velocity profiles with U sl = 9.95 cm s1 and varying U sg and (b) velocity profiles with U sg = 24.8 m s1 and varying U sl .

37

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39

in combination with an optical method designed by Shedd (1998) derived from Hurlburt and Newell (1996) and presented in Ashwood (2009). These pressure gradient measurements were converted to wall shear using the relations described in Eqs. (13) and (14), as shown in Schubring (2009), with the base film thickness measurements used at each location.

! qg U 2sg dP D  2 d D  2d 1 si ¼   qg g 4 4 Pabs dx #  " 2 D  2 d 1 dP D  ðD  2 dÞ2 sw ¼ si  þ qg g D 4 dx D

ð13Þ

Table 2 Shear results from pressure loss and TF-PIV in the vertical duct. U sg (m s1)

U sl (cm s1)

sw;PIV (Pa)

sw;DP (Pa)

Shear results 24.8 24.8 24.8 24.8 20.1 29.5 34.2

8.71 9.95 11.2 12.4 9.95 9.95 9.95

8.2 ± 0.7 9.1 ± 0.4 8.2 ± 0.6 10.2 ± 1.0 6.6 ± 1.1 10.3 ± 0.5 15.9 ± 0.8

10.2 ± 0.9 10.7 ± 0.9 11.3 ± 0.9 12.0 ± 0.9 7.2 ± 0.9 14.7 ± 0.9 18.9 ± 0.9

ð14Þ

In these equations, sI is the interfacial shear, sw is the wall shear, d is the mean liquid film thickness, dP=dx is the mean axial pressure gradient and g is the acceleration of gravity. The wall shear was obtained from the PIV data using the slope of the linear portion of the velocity profile near the wall as was illustrated in Fig. 3 assuming sw ¼ ll @u j . @y y¼0 The shear values obtained from both the PIV measurements as well as the pressure transducer data are presented in Table 2 where it can be see that the mean values determined from the pressure transducer are generally 20% higher than those obtained from the PIV data. The explanation for this is not entirely clear, but Shedd and Newell (2004) found that the liquid film of annular flow through square channels was consistently thicker in the center of the wall versus the corners. Fukano et al. (1984) noted similar behavior with respect to local mass flow measurements in a 8:1 aspect ratio rectangular channel. These data may indicate that the shear is higher near the corners, subsequently forcing liquid toward the center of the wall, but further data are needed to test this hypothesis. Finally, it is interesting to note that this technique reliably obtains data even at one plus-unit from the wall. This is a region where data are sparse in the single-phase literature. Discussion It has been a frequent assumption in annular flow modeling that the liquid film could be treated as a turbulent boundary layer taking on a so-called Law of the Wall, or Universal, velocity profile (UVP) (see, for example, Dobran (1983), Whalley (1987), Hurlburt et al. (2006)). One form applied to annular flow by Whalley (1987), for example, is that derived from von Kármán (1939),

8 þ for 0 < yþ < 5 > : þ 2:5 ln y þ 5:5 for 30 < yþ

ð15Þ

where

us ¼

rffiffiffiffiffiffi

sw u y us ; uþ ¼ ; yþ ¼ us ql ml

ð16Þ

Here, ml is the kinematic viscosity of the liquid. Fig. 11 presents a comparison of the data acquired, non-dimensionalized according to Eq. (16), the UVP given in Eq. (15) modified UVP based on Eq. (17).

8 þ for 0 < yþ < 5 > : þ 7:38 ln y  7:1 for 30 < yþ

Fig. 11. Comparison of dimensionless velocity profiles with the UVP (solid) and the UVP using an approximately 70% reduction in turbulent diffusivity. (a) Velocity profiles with U sl = 9.95 cm s1 and varying U sg and (b) velocity profiles with U sg = 24.8 m s1 and varying U sl .

From there, the equation for the buffer region between the linearand log-layers was obtained by matching boundary conditions at yþ ¼ 5 and yþ ¼ 30 as is commonly done. The cumulative effect of this change can be estimated by considering the following argument in the log region

ð17Þ

The datasets begin to collapse with the UVP defined according to Eq. (15), especially in the viscosity dominated regime near the wall, but agreement is not particularly good in the log region of the profile. As such, a modified version of the UVP was discerned based on the data. A best fit to all of the data was obtained in the log-region.

uþ ¼

1

j

ln yþ þ C

ð18Þ

where j is the Kolmogorov constant, typically about 2.5. Taking the derivative of Eq. (18) leads to the following: þ

du 1 1 þ ¼ j yþ dy

ð19Þ

38

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39

The inner variable form of the shear stress equation is now invoked.

  v K duþ 1¼ 1þ m dyþ

ð20Þ

The derivative of this equation yields:

v K ¼ mðjyþ  1Þ

ð21Þ

A ratio of the modified eddy diffusivity, modv K , and the original eddy diffusivity, v K , can be now be obtained.

modv K 0:14yþ  1 ¼ 0:4yþ  1 v K

ð22Þ

Based on this equation, the ratio of the two eddy diffusivities in the log-region is computed to be 0.29 for a yþ ¼ 30 and 0.34 for a yþ ¼ 300. This is somewhat consistent with Dobran (1983, 1985), who has shown that a model modifying the turbulent velocity profile by reducing the turbulent mixing somewhat as the gas–liquid interface is approached gives much better agreement to physical behavior. This was noted independently by Leuthner et al. (1999) as well. Further analysis of the turbulent nature of the film is difficult as this technique does not allow for the estimation of turbulence parameters such as Reynolds stresses in the wall-normal direction. In the transverse and axial directions, it is not clear that the technique as implemented enables the measurement of the smallest scales of turbulences. Estimates of the Kolmogorov length scale for the liquid film flow suggest that the smallest velocity scales are 10–20 times smaller than the mean velocity at a given distance from the wall. This would place the smallest fluctuations on the same order as the velocity uncertainty. Reynolds stresses in the transverse and axial directions indicated no correlation between transverse and axial fluctuations. Axial fluctuations exhibit relatively strong correlation, while transverse fluctuations correlate more weakly. The above analysis based on a turbulent boundary layer model assumes that the liquid film may be treated as a single, steady, well-mixed fluid flow. On the other hand, the liquid film of annular flow seems to be best described as a relatively steady base film with waves of various forms, sizes and velocities that flow over it with varying intermittencies. The data in this research were acquired randomly, and were not tagged with information about the structure of the liquid film. Wave velocities were not explicitly measured in this research, but from previous work (Schubring et al., 2010) it is directly inferred that interfacial waves travel at velocities between 2 and 3.5 m s1. This correlates extremely well with the velocities measured outside of the base film region in the current study. It is clear, then, that intermittent waves strongly impact the mean velocities reported here and, thus, the comparison with the universal velocity profile. As can be seen in Fig. 11, the Law of the Wall predicts lower velocities in the log and buffer regions for the measured shear. It is hypothesized that this is due to the intermittency of the relatively high velocity waves: the shear beneath the waves may be high, but they are present for only 20–25% of the time (Schubring et al., 2010), so do not significantly impact the mean shear measured in the viscous region. A statistical analysis by Shedd (2012) suggests, but does not yet prove, that the waves isolated from the base film may be well-predicted by von Kármán’s Law of the Wall. Summary In this work we have presented an implementation of particle image velocimetry that has successfully captured complete, mean

velocity profiles within the liquid film of vertical annular twophase flow. Annular flow presents many unique challenges to the implementation of PIV and we have described in detail how the technique was adapted to overcome them. TF-PIV may be used to measure the local wall shear, and the measurements for the 8 flows investigated here agree within 20% of the average values determined from pressure drop measurements. It is possible that this consistently low measurement may be explained by the intermittently turbulent nature of the film; more work is needed here. The results presented demonstrate that the UVP must be modified by decreasing the turbulent diffusivity in order to predict the measurements. This is in agreement with previously published hypotheses. Acknowledgements The authors appreciate the financial support of this project provided by Bechtel Marine Propulsion Corporation, ASHRAE, the Petroleum Research Fund, and the National Science Foundation under award No. CTS-0134510. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Support was also provided by the Graduate Engineering Research Scholars program at the University of Wisconsin-Madison. References Adrian, R.J., 1997. Dynamic ranges of velocity and spatial resolution of particle image velocimetry. Measurement 8, 1393–1398. Adrian, R., Durao, D.F., Durst, F., Heitor, M.V., Maeda, M., Whitelaw, J.H., 1998. Developments in Laser Techniques and Applications to Fluid Mechanics. Springer, Verlag Berlin Heidelberg. Ashwood, A.C., 2009. Characterization of the Macroscopic and Microscopic Mechanics in Vertical and Horizontal Annular Flow by. Ph.D. University of Wisconsin-Madison, Madison, Wisconsin. Choi, H.M., Terauchi, T., Monji, H., Matsui, G., 2002. Visualization of bubble-fluid interaction by a moving object flow image analyzer system. Ann. N. Y. Acad. Sci. 972, 235–241. Coleman, H.W., Steele, W.G., 2009. Experimentation, Validation, and Uncertainty Analysis for Engineers, third ed. John Wiley & Sons, Inc., Hoboken, NJ, USA. Dobran, F., 1983. Hydrodynamic and heat transfer analysis of two-phase annular flow with a new liquid film model of turbulence. Int. J. Heat Mass Transf. 26, 1159–1171. Dobran, F., 1985. Heat transfer in an annular two-phase flow. J. Heat Transfer 107, 472–476. Foster, R.E., 2005. Wave Behavior and Film Turbulence Measurements in Two-Phase Flow. M.S. University of Wisconsin-Madison, Madison, Wisconsin. Fukano, T., Akenaga, H., Ikeda, M., Itoh, A., Kuriwaki, T., Takamatsu, Y., 1984. Liquid film flowing concurrently with air in horizontal duct (4th report, effect of the geometry of duct cross-section on liquid film flow). Bull. JSME 27, 1644–1651. Fukano, T., Kawaji, B., Ousaka, A., 1985. Breakdown of a liquid film flowing concurrently with gas in a horizontal line. Phys. Chem. Hydrodyn. 6, 23–47. Hagiwara, Y., Yamaguchi, Suzuki, K., S., 1995. Interfacial wave structure and its effect on transport phenomena in horizontal wavy/annular two-phase flows. In: Morioka, S., van Wijngaarden, L. (Eds.), IUTAM Symposium on Waves in Liquid/ Gas and Liquid/Vapour Two-Phase Systems, The Netherlands, pp. 257–267. Hassan, Y.A., 2002. Multiphase bubbly flow visualization using particle image velocimetry. Ann. N. Y. Acad. Sci. 972, 223–228. Hewitt, G.F., Jayanti, S., Hope, C.B., 1990. Structure of thin liquid films in gas-liquid horizontal flow. Int. J. Multiph. Flow 16, 951–957. Hurlburt, E., Newell, T., 1996. Optical measurement of liquid film thickness and wave velocity in liquid film flows. Exp. Fluids 21, 357–362. Hurlburt, E.T., Fore, L.B., Bauer, R.C., 2006. A two zone interfacial shear stress and liquid film velocity model for vertical annular two-phase flow. In: Proceedings of the ASME Fluids Engineeering Division Summer Meeting 2006, vol. 2, Miami, FL, USA, pp. 677–684. Ishii, M., Mishima, K., 1989. Droplet entrainment correlation in annular two-phase flow. Int. J. Heat Mass Transf. 32, 1835–1846. Karimi, G., Kawaji, M., 1998. An experimental study of freely falling films in a vertical tube. Chem. Eng. Sci. 53, 3501–3512. Kataoka, I., Ishii, M., Nakayama, A., 2000. Entrainment and desposition rates of droplets in annular two-phase flow. Int. J. Heat Mass Transf. 43, 1573–1589. Kawaji, M., Ahmad, W., DeJesus, J.M., Sutharshan, B., Lorencez, C., Ojha, M., 1993. Flow visualization of two-phase flows using photochromic dye activation method. Nucl. Eng. Des. 141, 343–355. Klein, S.A., 2014. Engineering Equation Solver. F-Chart Software.

A.C. Ashwood et al. / International Journal of Multiphase Flow 68 (2015) 27–39 Kopplin, C.R., 2004. Local liquid velocity measurements in horizontal, annular twophase flow. M.S. University of Wisconsin-Madison, Madison, Wisconsin. Leuthner, S., Maun, A.H., Auracher, H., 1999. Influence of waves on heat transfer to falling films of a binary mixture. In: Celata, G.P., Marco, P.D., Shah, R.K., (Eds.), Two-phase flow modelling and experimentation 1999, vol. 2, Rome, Italy. Edizioni ETS, Pisa, pp. 1241–1247. Lindken, R., Merzkirch, W., 2002. A novel PIV technique for measurements in multiphase flows and its application to two-phase bubbly flows. Exp. Fluids 33, 235–241. Lorencez, C., Nasr-Esfahany, M., Kawaji, M., Ojha, M., 1997a. Liquid turbulence structure at a sheared and wavy gas-liquid interface. Int. J. Multiph. Flow 23, 205–226. Lorencez, C., Nasr-Esfahany, M., Kawaji, M., 1997b. Turbulence structure and prediction of interfacial heat and mass transfer in wavy-stratified flow. AIChE J. 43, 1426–1435. Mei, R., 1996. Velocity fidelity of flow tracer particles. Exp. Fluids 22, 1–13. Meinhart, C., Zhang, H., 2000. The flow structure inside a microfabricated inkjet printhead. J. Microelectromech. Syst. 9, 67–75. Meinhart, C.D., Wereley, S.T., Santiago, J.G., 1999. PIV measurements of a microchannel flow. Exp. Fluids 27, 414–419. Melling, A., 1997. Tracer particles and seeding for particle image velocimetry. Meas. Sci. Technol. 8, 1406–1416. Moran, K., Inumaru, J., Kawaji, M., 2002. Instantaneous hydrodynamics of a laminar wavy liquid film. Int. J. Multiph. Flow 28, 731–755. Mudawar, I., Houpt, R.A., 1993a. Mass and momentum transport in smooth falling liquid films laminarized at relatively high Reynolds numbers. Int. J. Heat Mass Transf. 36, 3437–3448. Mudawar, I., Houpt, R.A., 1993b. Measurement of mass and momentum transport in wavy-laminar falling liquid films. Int. J. Heat Mass Transf. 36, 4151–4162. Pautsch, A.G., 2007. Mass and Energy Transport Phenomena in the Thin Film of Spray Cooling Systems. Ph.d. thesis. University of Wisconsin - Madison, Madison, Wisconsin. Rodríguez, D.J., Shedd, T.A., 2004. Cross-sectional imaging of the liquid film in horizontal two-phase annular flow. In: 2004 ASME Heat Transfer/Fluids Engineering Summer Conference, Charlotte, NC. Santiago, J.G., Wereley, S.T., Meinhart, C.D., Beebe, D.J., Adrian, R.J., 1998. A particle image velocimetry system for microfluidics. Exp. Fluids 25, 316–319. Schubring, D. 2009. Behavior Interrelationships in Annular Flow. Ph.D. University of Wisconsin-Madison, Madison, Wisconsin. Schubring, D., Shedd, T., 2008. Wave behavior in horizontal annular air water flow. Int. J. Multiph. Flow 34, 636–646.

39

Schubring, D., Foster, R.E., Rodríguez, D.J., Shedd, T.A., 2009. Two-zone analysis of wavy two-phase flow using micro-particle image velocimetry (micro-PIV). Meas. Sci. Technol. 20, 065401. Schubring, D., Shedd, T., Hurlburt, E., 2010. Studying disturbance waves in vertical annular flow with high-speed video. Int. J. Multiph. Flow 36, 385–396. Shedd, T.A., 1998. An Automated Optical Liquid Film Thickness Measurement Method. M.S. University of Illinois at Urbana-Champaign, Urbana, IL. Shedd, T.A., 2001. Characteristics of the Liquid Film in Horizontal Two-Phase Annular Flow. Ph.D. University of Illinois at Urbana-Champaign, Urbana, IL. Shedd, T.A., 2012. Two-phase internal flow: toward a theory of everything. Heat Transfer Eng., 120904070957005. Shedd, T.A., Newell, T.A., 2004. Characteristics of the liquid film and pressure drop in horizontal, annular, two-phase flow through round, square and triangular tubes. J. Fluids Eng. 126, 807. Sutharshan, B., Kawaji, M., Ousaka, A., 1995. Measurement of circumferential and axial liquid film velocities in horizontal annular flow. Int. J. Multiph. Flow 21, 193–206. Taylor, J.R., 1997. An Introduction to Error Analysis, second ed. University Science Books, Herndon, Virginia, USA. Vanden Hogen, S.V., 2013. Micro-scale Visualization and Characterization of Vertical Annular Flow: A Study of Working Fluid and Tube Geometry. Master’s Thesis. von Kármán, T., 1939. The analogy between fluid friction and heat transfer. Trans. ASME 61, 705–710. Whalley, P.B., 1987. Boiling, Condensation and Gas-Liquid Flow. Clarendon Press, Oxford. Wolf, A., Jayanti, S., Hewitt, G.F., 2001. Flow development in vertical annular flow. Chem. Eng. Sci. 56, 3221–3235. Zadrazil, I., Markides, C.N., Matar, O.K., Naraigh, L.O., Hewitt, G.F., 2012. Characterisation of downwards co-current gas-liquid annular flows. In: Proceeding of THMT-12. Proceedings of the Seventh International Symposium On Turbulence, Heat and Mass Transfer Palermo, Italy, 24–27 September, 2012, p. 12, Connecticut. Begell House. Zadrazil, I., Markides, C.N., Matar, O.K., Hewitt, G.F., 2013. Wave structure and velocity profiles in downwards gas-liquid annular flows. In: 8th International Conference on Multiphase Flow (ICMF), pages ICMF2013–142, Jeju, Korea. Zhao, Y., Markides, C.N., Matar, O.K., Hewitt, G.F., 2013. Disturbance wave development in two-phase gas liquid upwards vertical annular flow. Int. J. Multiph. Flow 55, 111–129.