Extraction of 3D vortex structures from a turbulent puff in a pipe using two-color illumination and flakes
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A novel visualization technique was proposed to extract the three-dimensional vortex structure of a turbulent puff, which is a local turbulence event that is observed in pipe flows at relatively low Reynolds numbers. The technique is based on multi-color illumination of microscopic flakes that are suspended in the flow, which makes structural visualization more informative than conventional monochrome approaches. A special optical arrangement of two laser sheets, colored green and blue, was established for the circular pipe. Based on an image analysis sequence, the internal structure of the puff is reconstructed as a cross-sectional temporal 3D image consisting of voxels with unicolor degrees between green and blue, where an individual single vortex is extracted as a pair of two-color stripes. This allows quantification of the azimuthal wavenumber of the vortical structure that characterizes the puff. The wavenumber results agreed well with the results of previous studies, thus supporting the applicability of the proposed visualization technique.
KeywordsPipe flow Turbulence transition Flow visualization Flake
The turbulent flow transition in a pipe is one of the most fundamentally important unsolved problems that remain in fluid mechanics after the epoch-making study of Osborn Reynolds (Reynolds 1883). Reynolds indicated that this transition is dominated by a non-dimensional number, the so-called Reynolds number Re (=UD/ν, where U is the mean velocity, D is the pipe diameter and ν is the kinematic viscosity of the fluid); the flow has a local turbulence that consists of vortical structures that occur around a critical Reynolds number, Rec ~ 2000. In addition, Rec can be increased dramatically to more than 104 in more sophisticated flow facilities by reducing the inlet noise (more careful treatments of facilities push the critical Reynolds number up to 105, Pfenniger 1961). This is because Hagen–Poiseuille flows are stable for infinitesimal perturbations for finite range of Re (e.g., Drazin 2002), and thus the transition occurs from finite amplitude perturbations or imperfection of facilities. Nowadays Rec ~ 2000 has been used in practical situations of engineering. Such subcritical instability problem is a common problem in wall-bounded shear flows, namely, boundary layers, Poiseuille and Couette flow families. More recent statistical studies on the creation and advection of a localized turbulence called turbulent puff (Wignanski and Champagne 1973) in controlled pipe flow facilities have provided a physical insight into this phenomenon: Peixinho and Mullin (2006) mentioned that the lifetimes of puffs, and the persistence times of the advections, increase exponentially with increasing Re. Meanwhile, Hof et al. (2006) indicated that the variation of lifetime is super exponential: It means that a turbulent puff is fundamentally transient and has a finite lifetime, even at high values of Re. An increasing Re also accompanies the splitting of a puff toward formation of a turbulent slug (Wignanski and Champagne 1973), where the localized turbulence then grows into persistent turbulence. Avila et al. (2011) redefined Rec as the crossing point between the curves of the lifetime and the splitting time with respect to the Re as Rec = 2040 ± 10. Their results summarizing series of experimental and numerical works also support finite lifetime of puffs. Nevertheless, Peixinho and Mullin (2006) indicated that the lifetime of a turbulent puff approaches infinity around Re = 1750. The work of Tasaka et al. (2010), which used the same facility used by Peixinho and Mullin (2006), also confirmed that puffs are persistent for Re values higher than 1750 ± 10. However, there is a difference between the systems used in these studies to induce the flow in a pipe: the system in Peixinho and Mullin (2006) had a constant mass flux and one in Avila et al. (2011) was operated with a constant pressure gradient. The former can keep the Re exactly constant, regardless of the flow transition, but its pressure gradient fluctuates. Further, Peixinho and Mullin (2006) adopted a special procedure to evaluate the lifetime: A turbulent puff was created at Re = 1900 and thus setting Re was decreased to a prescribed value in the range 1580–1740. There is thus the possibility that this difference in the system and the procedure could cause small differences in the vortical structures of the puffs, and thus the lifetime characteristics may change.
A turbulent puff has a coherent structure that consists of a pair of streamwise vortices and low speed streaks (Faisst and Eckhardt 2003), and this structure has been confirmed by numerical simulations and experiments (Hof et al. 2004). This structure is called a traveling wave (TW), and has specific types of wavenumber in the circumferential direction. TWs are known as structures that sustain turbulence, and thus we suspect that it is important to carefully solve the problem of the experimental diversity of puffs and its dependence on the flow system. To clarify this problem, we need to perform a statistical analysis of the vortical structure of puffs. However, advanced particle image velocimetry (PIV) systems such as stereo-PIV and tomographic PIV cannot address this problem effectively because of the narrow dynamic range of PIV, i.e., the magnitude of the velocity fluctuation component in a puff often falls within the error level relative to the main flow velocity.
Visualization using flakes is a classical but feasible alternative to velocimetry-based approaches, and has been used to observe various flow structures that are subject to distortion (e.g., Park et al. 1981; Dominguez-Lerma et al. 1985; Bandyopadhyay 1986; Samanta et al. 2011). Using this method, local shear flows can be grasped directly as brightness information. Recently, interpretations of flow patterns visualized by adding flakes to fluid motion have been investigated (Goto et al. 2011; Einarsson et al. 2015). In addition, a methodology to quantitatively visualize vortex structures using flakes and multi-color illumination was proposed (Thoroddsen and Bauer 1999). Park et al. (2014) obtained vortex structures in wall turbulence using aluminum flakes and two laser sheets with different colors. This methodology is suitable for statistical investigation of the diversity of puffs because of its efficiency for problem-solving in researches, its direct vortex structure extraction capability and its ease of handling in comparison with PIV systems. We apply this methodology using two-color illumination and flakes to the visualization of 3D vortical structures in a puff. In this paper, our ideas for the optical set-up and several of the sequences required in the image analysis process are explained step-by-step. Furthermore, the extracted vortical structures are evaluated with respect to their relationships with the TWs.
2 Experimental setup and visualization methodology
For the visualization flakes, Kalliroscope flakes (AQ-1000, Kalliroscope Co.) are mixed into the test water. These flakes are platelets of protein crystal structures and the typical dimensions of the platelets are 6 × 30 × 0.07 μm (Thoroddsen and Bauer 1999). Traditional aluminum flakes and recently developed TiO2-coated mica platelets are also applicable for this visualization process. The advantages of using the Kalliroscope flakes are that they are thinner than the other available flakes (some μm in both aluminum flakes and mica platelets), which enables them to visualize fine structures and provide better responses to fluctuations of the flows. And, their relatively low density (1620 kg/m3 for Kalliroscope, 2700 kg/m3 for aluminum flakes, and 2800 kg/m3 for mica platelets) prevents them from sinking in the pipe. Furthermore, the Kalliroscope flakes are soft, whereas the other platelets are hard and cause damage to the acrylic pipe wall.
3 Experimental results
3.1 Visualized image of a passing puff
Figure 3b, c show snapshots of a passing turbulent puff, and Fig. 3d represents the laminar flow after the puff has passed. The corresponding times of these snapshots are indicated in the timeline image of Fig. 3a as white lines. Because of the tilt of the incident laser sheets relative to the horizontal plane, as shown in Fig. 2b, the illuminated areas in the snapshots (Fig. 3b–d) contain brighter areas with different colors as quadrupole distributions; the incident laser sheets from the opposite direction are reflected at the inside and outside walls of the pipe in the direction of the camera, depending on the face of the wall curve. Images corresponding to shear flow structures, which are expressed as fluctuation patterns on the images, are superimposed on this quadrupole pattern. The laminar flow in this situation, which is represented by the parabolic-shaped velocity profile of the Hagen–Poiseuille flow, shows a large-scale organized pattern on the image with gradual contrasts of blue and green. However, the flow does not show the fine fluctuation patterns, and we can thus assume that Fig. 3d is an image of the undisturbed case; variations of the flow structure are extracted as differences relative to this base image. Figure 3b is a snapshot of the foreside of the puff, and only the central part of the section is disturbed. As the puff passes through, the disturbed part extends towards the pipe wall. At the rear region of the puff shown in Fig. 3c, the entire section of the pipe is disturbed.
3.2 Image processing
To extract the three-dimensional vortical structure of a turbulent puff, image processing is required, even though the original image obtained by the presented technique (as shown in Fig. 3) provides a quantitatively good representation of the structure. In this section, the details of the image processing steps are explained individually to illustrate the meaning of each process. The process consists of three steps: background removal, color adjustment, and inclination compensation. In an actual analysis, of course, all three steps can be performed as a single task in a very short time of approximately 300 s, unlike the heavy processing required for PIV-based analyses.
3.2.1 Background removal
3.2.2 Adjustment of color balance
General imaging devices have uneven sensitivities to the colors of incident light, even if each color component of the light has the same intensity. This is because these devices have been designed to represent the sensitivity of human eyes to colors. Furthermore, each CMOS element in the devices has broad sensitivity to the wavelengths of the light and the sensitive bands overlap each other (e.g., El Gamal and Eltoukhy 2005). For example, pure blue light is not recognized as a “perfect blue” by the sensing elements, because it will contain small green and red components. In the presented technique, the vortex structures can be recognized as color stripe patterns, and we must therefore adjust the color balance of the image evenly to prevent erroneous recognitions. The test fluid contains numerous flakes and each flake has the light reflection characteristics shown in Fig. 2a. Fine multi-reflections occur between these flakes, and thus the corresponding color information of the vortex structure obtained from the incident two-color laser beams is captured as a probability distribution of the color intensities of blue (B) and green (G) at each pixel on these images. Suitable adjustment of the color balance then makes the extraction of the vortex structures possible according to their probability.
3.2.3 Compensation of illumination inclination
3.3 Extraction of the vortex structure
This study proposed a novel visualization technique using flakes to extract the three-dimensional vortex structures from a turbulent puff, which is a local turbulence event that appears in pipe flows, without performing velocity field measurements. Two-color (blue and green) laser sheets, which were arranged to be facing each other and tilted relative to the normal cross-section of the pipe, represented the vortex structures as colored stripes. A sequence involving subtraction of the laminar flow background image, adjustment of the color information and rearrangement of the images to a normal cross-section was used to achieve extraction of the three-dimensional vortex structure as voxels with unicolor information. The number of vortices at the trailing edge of the puff that was estimated from the reconstructed 3D vortex structure agrees with the values obtained in previous works.
The sequence of image processing summarized above does not require large computer resource and is not time-consuming in comparison with velocity field measurement based approaches. This advantage allows us for doing various trials to explore hidden physics under the complex fluid motions other than the measurement of longitudinal vortices stated here. For example, tracking the color voxel patterns representing longitudinal vortices may elucidate advection characteristics of the vortices efficiently.
This study was supported by JSPS KAKENHI through Grant No. 25420103. The authors would like to express their thanks for this support.
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