Experiments in Fluids 35 (2003) 598–609 DOI 10.1007/s00348-003-0708-8
Simultaneous PIV and pulsed shadow technique in slug flow: a solution for optical problems S. Nogueira, R.G. Sousa, A.M.F.R. Pinto, M.L. Riethmuller, J.B.L.M. Campos
598 Abstract A recent technique of simultaneous particle image velocimetry (PIV) and pulsed shadow technique (PST) measurements, using only one black and white CCD camera, is successfully applied to the study of slug flow. The experimental facility and the operating principle are described. The technique is applied to study the liquid flow pattern around individual Taylor bubbles rising in an aqueous solution of glycerol with a dynamic viscosity of 113·10)3 Pa s. With this technique the optical perturbations found in PIV measurements at the bubble interface are completely solved in the nose and in annular liquid film regions as well as in the rear of the bubble for cases in which the bottom is flat. However, for Taylor bubbles with concave oblate bottoms, some optical distortions appear and are discussed. The measurements achieved a spatial resolution of 0.0022 tube diameters. The results reported show high precision and are in agreement with theoretical and experimental published data.
Symbols D internal column diameter (m) g acceleration due to gravity (m s)2) lw wake length (m) Qv liquid volumetric flow rate (m3 s)1) r radial position (m) r* radial position of the wake boundary (m) R internal column radius (m) Received: 28 May 2003 / Accepted: 12 August 2003 Published online: 25 October 2003 Springer-Verlag 2003 S. Nogueira, M.L. Riethmuller von Karman Institute for Fluid Dynamics, Chausse´e de Waterloo 72, B-1640 Rhode Saint Gene`se, Belgium R.G. Sousa, A.M.F.R. Pinto, J.B.L.M. Campos (&) Centro de Estudos de Feno´menos de Transporte, Departamento de Eng. Quı´mica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal E-mail:
[email protected] S. Nogueira Present address: Centro de Estudos de Feno´menos de Transporte, Departamento de Eng. Quı´mica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
The partial support of the Fundac¸a˜o para a Cieˆncia e Tecnologia—Portugal through project POCTI/EQU/33761/1999 and scholarship BD/20301/99 is gratefully acknowledged. POCTI (FEDER) also supported this work via CEFT.
Us uz ur z Z*
Taylor bubble velocity (m s)1) axial component of the velocity (m s)1) radial component of the velocity (m s)1) distance from the Taylor bubble nose (m) distance from the Taylor bubble nose for which the annular liquid film stabilizes (m)
Dimensionless groups Re Reynolds number (¼ qUls D) 1=2 3=2 Nf inverse viscosity number (¼ g Dl q) Greek letters d liquid film thickness (m) m liquid kinematic viscosity (m2 s)1) l liquid dynamic viscosity (Pa s) q liquid density (kg m)3)
1 Introduction Two-phase slug flow regime in a vertical pipe is characterized by large bullet-shaped bubbles, also called Taylor bubbles or gas slugs, which nearly occupy the entire cross section of the pipe. Between the gas slugs and the pipe wall flows a thin film of liquid. At the rear of the gas slugs there is a separated liquid region, the so-called bubbleÕs wake. In daily life, this type of flow is encountered, for example, in a drinking straw that is being emptied too rapidly. In many industrial applications slug flow is present, for example, in the production and transportation of hydrocarbons in pipelines, in nuclear reactors during emergency core cooling, in boilers and in condensers. In a slugging column, with flowing gas and liquid, the flow field is extremely complex. In order to understand the hydrodynamics of such a complicated flow, the first step is to study the entire field around a single gas slug rising in stagnant liquid through a vertical pipe. Campos and Guedes de Carvalho (1988) made a photographic study of the wake of isolated Taylor bubbles, and they identified three different types of wake regimes: laminar, transitional and turbulent, according to the value of Nf=( g1/2 D3/2 q)/l. They presented empirical correlations for the length of the wake lw as a function of Nf. The authors also suggested that, for long Taylor bubbles, the flow pattern in the wake is only determined by the velocity profile in the annular film. The flow in the annular region
can be described as a falling film without shear stresses at the gas–liquid interface. The present work shows how the simultaneous particle image velocimetry technique (PIV) and pulsed shadow technique (PST) can be applied to study the flow field around a single gas slug. The simultaneous use of these two techniques is of great importance and helps in validating computational fluid dynamics predictions and models. PIV is a nonintrusive technique that gives quantitative instantaneous whole-field velocity maps of the flow (Adrian 1991). This technique has recently been extended to the study of two-phase flows by seeding the liquid phase with fluorescent tracers. The use of fluorescent particles combined with optical filters placed in front of the camera helps to suppress the intense reflections near the wall and interface regions and allows the determination of velocity vectors close to the gas–liquid interface and to the wall (Philip et al. 1994; Sridhar and Katz 1995). However, this technique is not suitable to determine the exact position of gas–liquid interfaces and, therefore, the shape of the bubbles. The optical filters do not completely cut the laser reflections at the interfaces from the PIV image; moreover, they do not avoid that some fluorescent PIV particle images appear inside the bubble and near the interfaces. Shadowgraphy is a complementary technique that allows the determination of the shape of the bubble. It consists in using a uniform background illumination of the flow to acquire the image of the shadow of a bubble from a camera placed opposite to the illumination. For bubbly flow, there are some references in which the shadowgraphy technique was used together with PIV. Tokuhiro et al. (1998) determined the velocity fields around a single bubble and around a solid using PIV and simultaneously determined the shapes of the bubble and of the solid using a second CCD camera and an infrared shadow technique. The two cameras were facing each other, the shadow of the bubble (or solid) was produced from a square board of infrared-pulsed light emitting diodes (LEDs) located behind the bubble. The shadow was recorded by the front CCD camera, while the rear CCD camera recorded the PIV images. The laser, the LEDs and the two CCD cameras were synchronized. To study bubble growth in a squared tank, Dias and Riethmuller (2000) also performed simultaneous PIV and shadowgraphy measurements using two cameras. The PIV CCD camera was positioned at 90 with the laser sheet and parallel to the side of the tank, while the shadow CCD camera was positioned with an angle of 60 with the opposite wall of the tank. The background illumination was continuous white light located opposite to the shadow CCD camera. The PIV and shadowgraphy measurements were synchronized. The axisymmetry of a single bubble growing from a needle allowed valid results even with two cameras placed at different positions. The superposition of the bubble images acquired with the two different techniques showed that important optical effects occur at the gas-liquid interfaces. The shape of the bubble retrieved by the PIV image is always smaller than the real shape of the bubble. These authors advanced a first explanation, for this phenomenon.
There are few studies in which PIV has been applied to slug flow, for example, Polonsky et al. (1999b) studied the motion of an isolated gas slug rising in a vertical pipe filled with water, for different liquid flow rates. They used an interlaced image technique to perform PIV measurements around the nose of the gas slug, which could not be used for higher liquid velocities, such those encountered in the annular film around the gas slug, where they had to use a streak length method. The shape of the gas slugs was determined separately, with an image-processing procedure applied to a sequence of video interlaced images (Polonsky et al. 1999a) of the bubble rising in water coloured with a small amount of dye (0.001%) and illuminated by a 5-W laser. Van Hout et al. (2002) performed PIV measurements in slug flow for air–water systems, for stagnant water in the pipe. They determined the flow pattern around a single gas slug, and their results were in agreement with those of Polonsky et al. (1999b) for the liquid film. They determined also, separately, the shape of the Taylor bubble, using the same procedure as Polonsky et al. (1999a). In water, the permanent oscillations of the bubble bottom create nonstationary field near the rear of the bubble. With the technique used, the authors had problems determining accurately the velocity field in this region. Bugg and Saad (2002) studied the flow around a Taylor bubble rising in a viscous solution and described the flow in a laminar wake. Since they determined the shape of the Taylor bubble by sketching the profile by hand, directly from the PIV image, they could not accurately define either the velocity field close to the interface or the bubble shape. In the present work, the optical effects present at the interfaces are described and explained. In steady-state conditions, referential attached to the bubble, the use of nonsimultaneous shadowgraphy as a complementary technique to PIV is sufficient to overcome these optical effects. For unsteady-state conditions, however, it is necessary to record the shadow of the bubble at the precise instant of the PIV measurement using the same optical view as the one used for PIV. In this work a new technique for a simultaneous PIV and PST technique with one single black/white camera, applied to bubbly flow by Lindken and Merzkirch (2002), is implemented in slug flow. The results of the flow field and bubble shape all around a Taylor bubble rising in a viscous aqueous solution of glycerol are presented. The experimental data validation is also presented.
2 PIV in slug flow 2.1 Experimental facility The experimental investigation consists in the study of the flow field around a single Taylor bubble rising in a vertical column of stagnant liquid. The experimental facility used is sketched in Fig. 1. The experiments are performed in a transparent acrylic column of 6-m height and 0.032-m internal diameter. The box surrounding the test section (0.5 m·0.12 m·0.11 m)
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distance of 0.247 m. When a bubble successively crosses the two barriers, the two signals obtained from the two photocells are used to determine the velocity of the Taylor bubble.
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Fig. 1. Experimental facility
is filled with the studied liquid in order to minimize the optical distortion. The gas is released into the liquid column after closing pneumatic valve 2, by opening the pneumatic valve 1, generating a Taylor bubble. The volume of the bubble is controlled by a system that partially fills the volume between the two valves with the working fluid to reduce the volume of gas that is released. The volume of air used in these experiments varies between 40·10)6 m3 and 265·10)6 m3. The system is thermally isolated, and the difference in temperature measured between thermocouples 1 and 2 (Fig. 1) is less than 0.3C. The liquid viscosity at the temperature of each experiment is measured using a rotating Brookfield viscometer. The measurements are performed at the top of the column at a distance of around 4.5 m (140 D) from the injection section so that entrance effects are negligible (Moissis and Griffith 1962). The test liquids are water, glycerol and aqueous glycerol solutions, covering a wide range of viscosities (1·10)3 to 1640·10)3 Pa s). The results shown in the present work are obtained with a viscous solution of 113·10)3 Pa s.
2.2.2 PIV The PIV images are obtained by seeding the liquid with fluorescent particles and illuminating it with a doublecavity pulsed Nd:YAG laser with a wavelength of 532 nm (pulse duration of 2.4 ns) and an adjustable pulse separation (time between the pulsing of cavity 1 and cavity 2) at each laser firing. The fluorescent particles are a neutral, buoyant, orange vinyl pigment (water soluble) about 10 lm in diameter (Lefranc and Bourgeois). The PIV particle sizes are 0.2 pixels or 0.6 pixels, while the particle images size are around 2 pixels and 4 pixels in the PIV images, respectively, for measurements of the entire pipe and measurements of the annular film. The laser beam is formed into a laser sheet of about 1-mm thickness in the test section. A PCO (SensiCam) CCD camera, with a resolution of 1280 ( H)·1024 (V) pixels and 4096 grey levels, is positioned orthogonal to the laser sheet. A red filter (model OG-570, Image Optics Components), 95% opaque below 550 nm, is used to block the intense green laser reflections and to allow the passage of the light emitted by the fluorescent particles (around 590 nm). A 35-mmfocal length lens is used to determine the flow pattern inside the pipe, capturing a test section of 0.08 m·0.07 m. To obtain a close view of around 0.04 m·0.03 m and to examine the details of the liquid film, a 50-mm focal length lens and a 12-mm extension ring are used. The synchronization between the laser and the camera is made using the laser as the master, namely using the Standford signal generator box incorporated in the laser. The velocity measured in the flow field, for each fluid, varies around the bubble. Therefore, the time between the pulsing of the two laser cavities (pulse separation) is adjusted according to the measured velocities at each test section. The separation time varies from 1 ms, when analysing the flow field ahead and behind the Taylor bubble, to 250 ls in the annular liquid film, for the studied solution.
2.3 Mirage effect at the interfaces Perturbing optical effects, previously observed by Dias and Riethmuller (2000) in bubbly flow, are also present in slug flow. These optical effects forbid an accurate determination of the exact location of the interface between liquid and bubble on the basis of the PIV image only. Figure 2 shows a typical PIV image of the film surrounding a Taylor bubble. The theoretical liquid film thickness d is calculated using Eq. (3), and therefore the 2.2 position of the interface is determined and plotted in the Measurement techniques figure. One can observe particle images beyond the actual limit of the bubble. 2.2.1 To analyse this optical phenomenon at the interface, Laser diodes The pipe is equipped with two light barriers making use of silicon models have been cast with fluorescent PIV particles embedded in the material. These models consist of a laser diodes coupled with photocells, placed at a known
Fig. 2. Typical PIV image of the film around a Taylor bubble
cubic box with a cylindrical hole in the middle. The void region is occupied by air that simulates the Taylor bubble, while the silicon and the fluorescent PIV particles correspond to the liquid film. In Fig. 3, a shadow image of one of the models is shown. In this model the diameter of the cylindrical hole is known, and therefore there is no ambiguity concerning the position of the real interface. The tests performed consisted in illuminating the simulated flow with a laser sheet of variable width, hitting the model under a 90 angle, as it happens with the real bubble. As seen in Fig. 4, as the extent of the laser sheet increases from the top, images of particles begin to appear in the inner region of the simulated gas slug. Actually, two separate areas can be seen in the inner region close to the interface. The first band of particles can be well seen in Figs. 4a and 4b, while the second band starts appearing only in Fig. 4b. The two separated bands increase as the laser sheet width increases in Figs. 4c and 4d. This phenomenon has been analysed and according to the interpretation, light scattered by particles illuminated by the laser sheet can follow different paths before reaching the camera, forming regular images and also spurious particle images resulting from reflected and refracted light. From these considerations it is obvious that PIV images are not suitable for the determination of interface positions and there is a need to use shadowgraphy as a complementary technique.
3 Simultaneous PIV and PST
Fig. 3. Shadow image of a silicon model
3.1 Principle of the technique A new technique, developed for bubbly flow, recently presented by Lindken and Merzkirch (2002), is applied to slug flow in this work. It consists of a combination of simultaneous PIV and PST measurements performed with the same camera. A panel of light emitting diodes (LEDs) is located in the background of the test section, and it produces pulses synchronized with the PIV images. On the image recorded, three ranges of grey levels are observed: the levels corresponding to the images of tracers (highest range), a grey level corresponding to the light coming from the LEDs and crossing the test section (medium grey level)
Fig. 4. Typical PIV image of the silicon model when the laser sheet illuminates different regions far from the interface
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Fig. 5. Principle of the technique; the PIV particles create white points with high grey level value, while the bubble contour creates a dark image with lower grey levels
and the lowest grey level corresponding to the shadow of the bubble. It is, therefore, possible to extract, from a single image, the PIV particles image as well as the shadow from which the contour of the bubble can be determined. A red optical filter is placed in front of the camera for the PIV measurements, as mentioned in Sect. 2.2. This feature requires that the LEDs wavelength has to be selected such that the optical filter does not block it. Finally, the intensity of the two light sources must be adjusted until the grey levels in the images can be clearly differentiated. Figure 5 shows the different grey levels of the images along given lines, with and without bubble. It can be seen that the bubble shadow decreases the grey level in a distinct way. The different stages of processing for retrieving the contour of the bubble are the following: a median filter is applied to the image in order to suppress the PIV particles, a level-discrimination routine is applied to extract the contours, and the PIV algorithm is directly applied to the image.
3.2 Implementation of the technique for slug flow Figure 6 shows, in detail, the technical apparatus used in the measurements. The PST images are obtained by illuminating the flow from the back with a double-pulsed LEDs panel. The LEDs emit light at 650 nm, and the Taylor bubble produces a shadow, at that wavelength, that passes through the optical filter and is recorded on the camera. Tests were performed with a single LED before the implementation of the system in the test facility. The LEDs have to work in a pulsed mode and their response time has to be adjusted to a minimum value of few microseconds. The duration of the pulses must be small enough in order to acquire a perfectly defined shape of the bubble instead of a blurred image. According to this, a panel of 350 LEDs (3-mm diameter), with dimensions 0.25 m·0.30 m has been built. A diffuser paper is placed between the LEDs and the test section. Diffuse light is used in order to obtain a correct measurement of the bubble size because diffuse
Fig. 6. Upper view of the test section
light is not deflected at the object (Taylor bubble). The uniformity of the image is achieved by placing the LEDs panel out of focus. An electronic system has been designed that allows the triggering of the LEDs system with a time response of 5 ls and pulse duration of 12 ls, which corresponds to a maximum bubble displacement of 0.04 pixels. The synchronization between the camera, laser and LEDS (Fig. 7) is done in such a way that the pulses of the laser are recorded in the same frame of the CCD camera simultaneously with the pulses of the LEDS. The signals from the Standford signal generator create the laser pulses and also control both the camera and the LEDs. The signal AB of the generator controls the opening of the first image of the PCO camera (the duration of the opening is supposed to be the duration of the pulse), creates the pulsing of the LEDs array 125 ls after the rising edge of the signal (there is a characteristic time delay of 5 ls of the LEDs) and fires the first pulse of the laser (at the falling edge of the signal). The information of the laser light and the LEDs illumination is stored on the first frame of the CCD chip due to a small time delay on this frame, shown on Fig. 7. The camera opens again after a dead time of 1 ls and grabs the light of the pulse (controlled by signal CD) of the
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Fig. 7. Time diagram of the synchronization between the LEDs, laser and camera
Fig. 8. Sequence of steps used to determine the shadow of the Taylor bubble from the original simultaneous PIV and PST image
second cavity of the laser, as well as the illumination of the LEDs array pulsing (triggered 130 ls after the signal C of the Standford). To acquire an image of good quality, several important parameters must be adjusted: the intensity of the LEDs, the uniformity of the background illumination and the position of the LEDs panel in order to avoid shadows of the pipe in the liquid film surrounding the Taylor bubble.
3.3 Image processing The images recorded with this technique contain both the PIV (flow field) and the PST (bubble shape) information. The processing is performed separately. The processing of the image that is applied to obtain the shadow of the Taylor bubble is performed in several steps. Figure 8a shows an example of an image acquired with simultaneous PIV and PST. The PIV tracer particles in the flow create a highly noisy pattern of the grey levels (Fig. 5). Therefore a median filter is applied to the original image, and the re-
sult is shown in Fig. 8b. The characteristic size of the filter has to be larger than the tracer particles; therefore, a 5·5 pixel size median filter is used for the images capturing the entire pipe, while for the images capturing only the liquid film, a median filter of 7·7 pixels is applied. Different methods were tested based on the difference of grey levels of the background and the bubble shadow, which was optimised as mentioned before. Unlike the method used by Lindken and Merzkirch (2002), in which the bubble interfaces were determined from the derivative of the grey levels by applying a filter, the Taylor bubble shadow is extracted by subtracting this image (Fig. 8b) to a reference image with the background illumination (Fig. 8c), yielding the image of Fig. 8d. The complete shadow of the bubble is obtained after binarization of image in Fig. 8d with a selected threshold (Fig. 8e). Figure 8e shows the image of the bubble after filling the centre of the bubble. The filling of the bubble is not essential to determine the bubble shape but is of advantage when post processing the PIV results.
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The flow field in the liquid phase is determined by processing the acquired images with the cross-correlation window-displacement iterative multigrid algorithm (WIDIM), developed by Scarano and Riethmuller (1999). In this process, the interrogation windows are displaced (according to the first vectors estimative), and their size is reduced iteratively. The use of an interpolation function gives an estimate of the peak location with sub-pixel accuracy. The time interval between two successive images (pulse separation) is reduced to avoid loss of pairs from 3D motion and to respect the 1/4-window displacement rule (Keane and Adrian1990). A mask setting the velocity at the pipe wall to zero is used, so that no vectors are miscalculated in that area. The initial image has 1280 ( V)·1024 ( H) pixels, and the initial window size is 64·32 pixels, according to the privileged flow direction. Two refinements have been performed to reach final interrogation windows of 16·8 pixels. An overlap of 50% refines the grid spacing to 8·4 pixels and allows a resolution of 0.342 mm·0.171 mm (0.01 D ·0.005 D) in the measurements capturing the entire pipe and a resolution of 0.138 mm·0.069 mm (0.004 D ·0.002 D or 0.04 d ·0.02 d) in the measurements of the annular liquid film. The final PIV results are post-processed with the results of the PST technique. The velocity vectors at each position are multiplied by the grey levels of Fig. 8e at the same position, which are zero inside the bubble (black zone) and one outside (white zone). Thus the spurious velocity vectors coming from the ghost images of particles inside the Taylor bubble are deleted, while the velocity vectors in the liquid phase remain unchanged. The post-processing eliminates wrong vectors, still, it is possible to better resolve the flow close to the interface by implementing a digital mask into the PIV algorithm. Lindken et al. (1999) performed this for bubbly flow, using the digital masking technique developed by Gui and Merzkirch (1996), which allows a better resolution. The WIDIM algorithm is presently being developed in that sense. It is largely accepted that the main uncertainty associated with PIV measurements is less than a tenth of a pixel. The high resolution allowed by the PCO camera leads to an estimated overall uncertainty of 1.5%.
4 Results and discussion The technique presented has been applied to study the liquid flow pattern around individual slug bubbles rising in different aqueous glycerol solutions. The data reported in the present work are for a slug bubble, with volume of 40·10)6 m3, rising in a solution with dynamic viscosity of 113·10)3 Pa s and density of 1224 kg m)3, in a 32-mm internal diameter acrylic column. The measured bubble velocity is 0.196±0.005 m s)1, corresponding to a Reynolds number of 70 and an inverse viscosity number Nf of 200. The bubble wake for this value of Nf is closed and laminar according to Campos and Guedes de Carvalho (1988). For these conditions, the flow pattern in the wake of the gas slug is in steady-state relative to a reference frame moving with the bubble.
The images are recorded with 8 bits, which gives 256 levels of grey, although the PCO camera used allows the acquisition with 12 bits and, therefore, 4096 grey levels. Figure 5 shows that 8-bit recording gives sufficiently accurate gas–liquid interfaces, as can be seen by the clear drop of the grey level. Concerning the flow field, acquiring 8-bit images instead of 12-bit images does not affect the correlation robustness of the algorithm used (WIDIM), as was pointed out by Gouriet at al. (2001). The data presented are processed as described in the previous sections. A median filter of size 3·3 has been used to smooth the PIV results. The PIV vectors resolution depends on the part of the flow field studied as mentioned in Sect. 3.3.
4.1 Flow field around the nose of the Taylor bubble Figure 9a shows the liquid flow field ahead of the Taylor bubble using a fixed reference frame. Figure 9b shows the same flow field as seen by the bubble, i.e., using a moving reference frame. The axial coordinate z is taken relative to the nose of the bubble. The shape of the bubble, determined simultaneously as described, is also represented. These figures show that the rising Taylor bubble displaces the liquid ahead of it, and a strong radial displacement of liquid is observed. Along z, as the radius of the cross section of the bubble increases, the flow continuity leads to an increase of the liquid velocity. The liquid velocity just near the nose of the bubble (a stagnation point relative to the bubble) should be identical to the velocity of the bubble. The liquid velocity measured at the nose is 0.206 m/s, 5% higher than the bubble velocity. This slight discrepancy can be justified, in part, by the effect of the bubble expansion on the liquid velocity ahead. The presence of the bubble is felt until a distance of 0.36 D ahead of the nose of the bubble, where the liquid velocity at the axis of the tube drops to 1% of the velocity of the bubble. At 0.24 D, the liquid velocity at the axis is still 5% of the velocity of the bubble. Bugg and Saad (2002), for a less viscous solution, mention a liquid velocity of this order of magnitude, namely 5%, at 0.30 D. Polonsky et al. (1999b) and van Hout et al. (2002) refer to the onset of the reverse flow at about 0.66 D and 0.5 D, respectively, for bubbles rising in water. All these values are consistent with a simple principle that allows us to assume that the presence of the bubble should be felt further away when the inertial forces are larger compared to viscous ones. 4.2 Flow field around the Taylor bubble As the liquid starts moving, it acquires radial velocity and accelerates downwards around the slug bubble, creating a thin liquid film. The maximum liquid velocity in a given cross section of the film progressively approaches the bubble interface. This acceleration continues until the bubble radius and, by consequence the film thickness, becomes constant. At this point, the liquid flow is fully developed and the forces acting on a liquid element are in balance. More precisely, the liquid weight of the element is in balance with the viscous forces acting on the boundary surfaces of the element.
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Fig. 9a, b. Velocity profile around the nose of a Taylor bubble
rising in stagnant liquid: a Fixed frame of reference. b Frame of reference moving with the bubble. The vectors represented
correspond to one out of seven vectors, so that the main features of the flow can be observed
Fig. 10. Axial and radial com-
ponents of the velocity in the liquid film at r =0.41 D, between z =0 and z =4 D. Only one out of three points are represented
The data shown in Fig. 10 are obtained from three consecutive PIV images that are ÔstitchedÕ together, so that the entire bubble length can be studied without losing resolution and, therefore, accuracy. Figure 10 represents the axial and radial components, Uz and Ur, respectively, of the velocity along the liquid film at the radial position r / D =0.41. Again, the axial coordinate z is taken relative to the nose of the bubble. The axial component of the velocity increases along the film until the thickness of the film stabilizes and the flow gets fully developed. The data present some dispersion (7% around the mean value) because they are representative of instantaneous velocity. In spite of this, it is possible to conclude that the axial component of the velocity stabilizes at about Z *=1.6 D. The radial component of the velocity Ur increases around the nose and decreases in the liquid film, achieving the value of zero where the film gets fully
developed. This also happens for Z *=1.6 D, thus validating the result given by the axial component of the velocity. An estimate of the value Z * is given by the value of z for which the wall boundary layer, in development since the nose region, reaches the free streamline along the bubble interface. Supposing inviscid flow along the free streamline from the nose until Z *, Campos and Guedes de Carvalho (1988) presented the following equation to estimate Z *: 2 2 gd ð2mÞ þ Us Z : ð1Þ 2g The value of Z * determined from the present PIV experiments is approximately the double of the value of Z * predicted by Eq. (1), Z *=0.8 D. This is due to the several approaches assumed to deduce Eq. (1). Brown (1965)
film. The experimental profile represents the average of 30 instantaneous profiles along the stabilized film. The experimental profile is plotted over the liquid film as determined from the shadow of the bubble, i.e., the thickness of the liquid film, which is 0.00322 m. The calculation of the predicted velocity is based on the theoretical thickness of the film (0.00327 m), though it is only Brown (1965) deduced also the following equation to plotted until the experimental value, so that the results can predict the film thickness: be compared. The measurements are in good agreement 1=3 3 mUs d¼ ðR d Þ : ð3Þ with the theoretical profile and the error stays below 5%, except near the wall, where the velocity values are almost 2g zero, thus resulting in higher relative errors. The experiThe thickness of the stabilized film determined from mental and theoretical liquid film flow rates are also calthe shadow of the bubble is d =0.00322 m. According to culated by integration of the velocity profiles and the Eq. (3), the predicted value is d =0.00327 m, i.e., 2% results found match within 1%, thus validating the higher than the experimental value. experimental techniques. The gradient of velocity profile is Figure 11 shows the comparison between the theoreti- almost zero at the gas–liquid interface, therefore, proving cal and measured velocity in the stabilized annular liquid that the shear stresses at the bubble surface are negligible. deduced an equation for the velocity profile in a stabilized free falling film flowing around a slug bubble: ! g R2 r2 ðR dÞ2 R : ð2Þ u¼ ln m r 4 2
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4.3 Flow field at the rear of the Taylor bubble
Fig. 11. Comparison between the theoretical (Brown1965) and experimental velocity profiles at the stabilized film
4.3.1 Shape obtained from the pulsed shadow technique (PST) Figure 12 shows the shape of the bottom of a Taylor bubble obtained from pulsed shadow technique, as well as the instantaneous flow field in the wake: Fig. 12a shows a fixed reference frame and Fig. 12b shows a moving reference frame (at the bubble velocity). The shape of the bottom of the bubble is not a plane as the PST results show, but concave. A slight concave depression is seen in visualization studies and in PST images as well as in PIV images. As it is a depression, it is covered up by the 2D projection of the shadow of the bubble, and, as a consequence, part of the velocity profile in the wake region is hidden. Nevertheless, Fig. 12 allows for the derivation of useful information. The flow coming from the liquid film arrives at the bubble bottom and begins to decelerate in order to occupy all the tube cross section. The length needed to achieve the deceleration depends on the
Fig. 12a, b. Velocity profiles at the rear of the
Taylor bubble with the bubble interface obtained from PST: a Fixed reference frame. b Moving reference frame. The vectors represented correspond to one out of seven vectors
competition between the radial diffusion of momentum (inwards) and the axial convective transport of momentum (downwards). Even when the radial diffusion is very high, there is always the formation of a toroidal recirculation zone in the rear of the bubble, the so-called laminar bubble wake. Inside the wake, the fluid presents an intense recirculation with a mean velocity equal to the bubble velocity, i.e., the wake rises attached to the bubble. The wake zone can be clearly seen in Fig. 12b, which shows fluid travelling downwards, with increasing radial velocity, nearby that coming from the film, and fluid in the vicinity of the tube axis travelling upwards faster than the bubble. The recirculation path is incomplete, since the flow field inside the convex zone is not sketched, but it is there that the fluid changes direction closing the circular path (upwards near the axis to downwards in the vicinity of the fluid coming from the liquid film).
4.3.2 Shape designed from the figures The importance of the wake zone hidden by the shadow justifies the presentation of an approximate description of the bubble shape and flow field. In the PIV images (without the LEDs illumination, Fig. 13), the concave bubble shape is clearly seen, particularly near the axis of the tube, as well as the image of the fluorescent particles. With this information, the shape of the bottom was drawn over the shadow and the flow field post-processed with the resulting bottom shape. The result of this approximate treatment is shown in Fig. 14. Figure 14b shows some erroneous vectors inside the interior depression, close to the bubble bottom, resulting from a high 3D distortion of the velocity field as a consequence of the deviations of the light emitted by the fluorescent particles in the successive mediums (liquid/gas/liquid). This is a measurement problem and is difficult to solve since the distortion discourages any attempt to find a correction factor based on
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Fig. 13. PIV image of the bottom of a Taylor bubble without LEDs background illumination
the different refraction indexes to correct the velocity profile. To highlight the wake region, its boundary is drawn performing flow balances along the axial direction. Considering a frame of reference moving with the Taylor bubble, the liquid flow rate in each cross section is equal to Z R 2 Qv ¼ Us pR ¼ ðuz þ Us Þ2prdr; ð4Þ r 2
where UspR represents the downward liquid flow rate ahead of the bubble nose, u z+ Us the liquid velocity
Fig. 14a, b. Velocity profiles at
the rear of the Taylor bubble with the bubble interface at the rear drawn from the PIV images: a Fixed reference frame. b Moving reference frame (at the bubble velocity). The vectors represented correspond to one out of seven vectors
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Fig. 15a, b. Wake boundary determined from Eq. (4) along each
axial position superimposed on the velocity field and bubble shape at the rear of the Taylor bubble: a Fixed reference frame.
b Moving reference frame (at the bubble velocity). The marked line is r*/D calculated over z and r by Eq. (4). The vectors represented correspond to one out of seven vectors
Fig. 16a, b. Wake boundary determined from Eq. (4) along each
axial position superimposed on the velocity field and bubble shape at the rear of the Taylor bubble: a Fixed reference frame. b Moving reference frame (at the bubble velocity)
relative to a frame moving with the bubble and r * the radial position of the wake boundary. The integration of the experimental u z data makes possible the determination of r * along the wake region and the definition of the wake boundary, r*/D shown in Fig. 15. The end of the wake occurs at z =3.6 D, thus the wake length is 0.45 D, 17% smaller than the value predicted by Campos and Guedes de Carvalho (1988). Figure 16 shows the detail of the square in Figs. 15a and 15b. From the vectors presentation with a moving reference frame, the boundary of the wake is determined. The presentation with fixed reference frame gives the wrong impression that fluid is entering the wake.
5 Conclusions In the present work a new technique that allows the simultaneous determination of the Taylor bubbleÕs shape and the flow field around the bubble, solving optical distortion effects that appear in two-phase PIV measurements, has been successfully implemented. The technique consists of performing simultaneous PIV and pulsed shadow technique with a single black and white CCD camera. The measurements achieved a spatial resolution of 0.0022 tube diameters. The results obtained show high precision, solving completely the optical effects at the nose, in the annular film and in the rear of the bubble. The results in the annular liquid film are compared with the
free falling film theory, thus validating the experimental technique. The laminar close wake, rising up attached to the Taylor bubble, is clearly seen, the recirculation flow pattern is accurately determined and the wake boundary is defined. For the first time, the portion of the wake flow inside the concave bottom of the Taylor bubble is described. The optical distortion identified in this region, caused by the light crossing successive interfaces, is discussed.
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