Abstract
The present study investigates the transport of dilute bubbles by transitional flow in a joining, cross-flow-type T-junction channel geometry with Reynolds numbers at the outlet branch from Re3 = 600 to 1800 and an inlet volume flow rate ratio of 1. Bubbles with diameters between db = 400 and 600 µm are considered. The schematic pattern of the single-phase flow is introduced based on streakline dye visualizations. Complex 3D flow due to the narrow channel design dominates the recirculation area and flow instabilities become important with increasing Reynolds number, which can be observed by the fading of dye intensity. A numerical method is presented with unsteady boundary conditions based on laser Doppler velocimetry measurements. Bubble trajectories are obtained by an Euler-Lagrange approach. Using high-speed shadowgraphy method combined with image processing, bubble sizes were measured, and bubble trajectories were evaluated. Experimental bubble trajectories and numerically predicted bubble positions show good agreement for Re3 = 600, which is also the case with the dye visualization image. For higher Reynolds numbers, measurements of the bubble trajectories are reported and compared to dye visualization images. The increasing flow instabilities influence the bubble transport, resulting in large variations of bubble locations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- µ 1 :
-
Liquid dynamic viscosity (kg/(m·s)))
- v 1 :
-
Liquid kinematic viscosity (m2/s)
- ρ 1 :
-
Liquid density (kg/m3)
- ρ g :
-
Gas density (kg/m3)
- σ :
-
Surface tension (N/m)
- ϕ:
-
Phase difference (°)
- A :
-
Channel cross-sectional area (m2)
- C D :
-
Drag force coefficient
- C L :
-
Lift force coefficient
- C wl :
-
Wall force coefficient
- d b :
-
Bubble diameter (m)
- d b,eq :
-
Equivalent bubble diameter (m)
- d c,eq :
-
Equivalent diameter of the channel (m)
- d p :
-
Tracer particle diameter (m)
- D :
-
Channel depth (m)
- Eo :
-
Eötvös number
- f :
-
Frequency (Hz)
- F D :
-
Drag force vector (N)
- F g :
-
Gravity force vector (N)
- F L :
-
Lift force vector (N)
- F P :
-
Pressure gradient force vector (N)
- F vm :
-
Virtual mass force vector (N)
- F wl :
-
Wall force vector (N)
- g :
-
Acceleration magnitude due to gravity (m/s2)
- g :
-
Acceleration vector due to gravity (m/s2)
- J′:
-
Force coefficient factor
- l c :
-
Cell edge length (m)
- Δl :
-
Traversing error (m)
- m b :
-
Bubble mass (kg)
- n wl :
-
Unit vector perpendicular to wall
- N b :
-
Number of pixels in a bubble
- p :
-
Liquid pressure (Pa)
- P :
-
Channel cross-sectional perimeter (m)
- Re 1, Re2, Re3 :
-
Reynolds number at branch 1, 2, or 3
- Re b :
-
Bubble Reynolds number
- s :
-
Spatial image resolution (m/px)
- s wl :
-
Bubble to wall distance (m)
- Sk 3 :
-
Stokes number
- Sr :
-
Shear number
- t :
-
Time (s)
- \({{\dot V}_{\rm{g}}}\) :
-
Syringe pump gas volume flow rate (m3/s)
- \({{\dot V}_{\rm{l}}}\) :
-
Syringe pump liquid volume flow rate (m3/s)
- w :
-
Liquid velocity vector (m/s)
- w b :
-
Bubble velocity vector (m/s)
- \({\overline w _1},\,\,{\overline w _2},\,\,{\overline w _3}\) :
-
Area-averaged velocity magnitude at branch 1, 2, or 3 (m/s)
- w n :
-
Liquid velocity component normal to measurement plane (m/s)
- \(\left\langle {{w_{\rm{n}}}} \right\rangle \) :
-
Time-averaged liquid velocity component normal to measurement plane (m/s)
- \({w^\prime }_{\rm{n}}\) :
-
Variation of the liquid velocity component normal to measurement plane (m/s)
- w r,h :
-
Relative bubble velocity component parallel to wall (m/s)
- w x, w y, w z :
-
Liquid velocity components (m/s)
- \(\left\langle {{w_x}} \right\rangle ,\,\,\left\langle {{w_y}} \right\rangle ,\,\left\langle {{w_z}} \right\rangle \) :
-
Time-averaged liquid velocity components (m/s)
- W :
-
Channel width (m)
- x b :
-
Bubble position vector (m)
- x, y, z :
-
Coordinates (m)
- Δx, Δy, Δz :
-
Spatial errors (m)
- z b,i :
-
Initial bubble position in z-direction (m)
- LDV:
-
Laser Doppler velocimetry
- CFL:
-
Courant-Friedrichs-Lewy
References
Brennen, C. E. 2005. Fundamentals of Multiphase Flow. Cambridge: Cambridge University Press.
Chesters, A. 1991. The modelling of coalescence processes in fluid-liquid dispersions: A review of current understanding. Chemical Engineering Research & Design, 69: 259–270.
Christopher, G. F., Anna, S. L. 2007. Microfluidic methods for generating continuous droplet streams. Journal of Physics D: Applied Physics, 40: R319–R336.
Costa, N. P., Maia, R., Proença, M. F., Pinho, F. T. 2006. Edge effects on the flow characteristics in a 90 deg tee junction. Journal of Fluids Engineering, 128: 1204–1217.
Crocker, J. C., Grier, D. G. 1996. Methods of digital video microscopy for colloidal studies. Journal of Colloid and Interface Science, 179: 298–310.
Czarske, J. R., Büttner, L., Razik, T., Müller, H. 2002. Boundary layer velocity measurements by a laser Doppler profile sensor with micrometre spatial resolution. Measurement Science and Technology, 13: 1979–1989.
Drenckhan, W., Langevin, D. 2010. Monodisperse foams in one to three dimensions. Current Opinion in Colloid & Interface Science, 15: 341–358.
Frense, E., Werner, T., Nöpel, J.-A., Rüdiger, F. 2022. Detection and evaluation of single bubble collisions using focused shadowgraphy. In: Proceedings of the 29th Symposium of Experimental Fluid Mechanics of GALA e.V., 17.4–17.8. Available at https://www.gala-ev.org/images/Beitraege/Beitraege2022/pdf/17.pdf.
Garstecki, P., Fuerstman, M. J., Stone, H. A., Whitesides, G. M. 2006. Formation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of break-up. Lab Chip, 6: 437–446.
Gholizadeh, H., Burton, R., Schoenau, G. 2012. Fluid bulk modulus: Comparison of low pressure models. International Journal of Fluid Power, 13: 7–16.
Heitkam, S., Sommer, A. E., Drenckhan, W., Fröhlich, J. 2017. A simple collision model for small bubbles. Journal of Physics: Condensed Matter, 29: 124005.
Hoppe, F., Breuer, M. 2018. A deterministic and viable coalescence model for Euler-Lagrange simulations of turbulent microbubble-laden flows. International Journal of Multiphase Flow, 99: 213–230.
Hoppe, F., Breuer, M. 2020. A deterministic breakup model for Euler-Lagrange simulations of turbulent microbubble-laden flows. International Journal of Multiphase Flow, 123: 103119.
Kamp, A. M., Chesters, A. K., Colin, C., Fabre, J. 2001. Bubble coalescence in turbulent flows: A mechanistic model for turbulence-induced coalescence applied to microgravity bubbly pipe flow. International Journal of Multiphase Flow, 27: 1363–1396.
Legendre, D., Magnaudet, J. 1998. The lift force on a spherical bubble in a viscous linear shear flow. Journal of Fluid Mechanics, 368: 81–126.
Liao, Y., Lucas, D. 2009. A literature review of theoretical models for drop and bubble breakup in turbulent dispersions. Chemical Engineering Science, 64: 3389–3406.
Liao, Y., Lucas, D. 2010. A literature review on mechanisms and models for the coalescence process of fluid particles. Chemical Engineering Science, 65: 2851–2864.
Müller-Fischer, N., Tobler, P., Dressler, M., Fischer, P., Windhab, E. J. 2008. Single bubble deformation and breakup in simple shear flow. Experiments in Fluids, 45: 917–926.
Nöpel, J. A., Frense, E., Korb, S., Dues, M., Rüdiger, F. 2019. Velocity measurement of a free jet in water with shear layer cavitation. In: Proceedings of the 27th Symposium of Experimental Fluid Mechanics of GALA e.V., 38.1–38.8. Available at https://www.gala-ev.org/images/Beitraege/Beitraege2019/pdf/38.pdf.
Patiño-Jaramillo, G. A., Iglesias, I., Vera, M. 2022. Laminar flow and pressure loss in planar Tee joints: Numerical simulations and flow analysis. European Journal of Mechanics - B/Fluids, 92: 75–89.
Pollack, G. L. 1991. Why gases dissolve in liquids. Science, 251: 1323–1330.
Ramamurthy, A. S., Zhu, W. 1997. Combining flows in 90° junctions of rectangular closed conduits. Journal of Hydraulic Engineering, 123: 1012–1019.
Ruan, J., Burton, R. 2007. Bulk modulus of air content oil in a hydraulic cylinder. In: Proceedings of the ASME 2006 International Mechanical Engineering Congress and Exposition, 259–269.
Takagi, S., Matsumoto, Y. 2010. Surfactant effects on bubble motion and bubbly flows. Annual Review of Fluid Mechanics, 43: 615–636.
Takemura, F., Magnaudet, J. 2003. The transverse force on clean and contaminated bubbles rising near a vertical wall at moderate Reynolds number. Journal of Fluid Mechanics, 495: 235–253.
Tomiyama, A., Kataoka, I., Zun, I., Sakaguchi, T. 1998. Drag coefficients of single bubbles under normal and micro gravity conditions. JSME International Journal Series B, Fluids and Thermal Engineering, 41: 472–479.
Van der Walt, S., Schönberger, J. L., Nunez-Iglesias, J., Boulogne, F., Warner, J. D., Yager, N., Gouillart, E., Yu, T. 2014. Scikit-image: Image processing in Python. PeerJ, 2: e453.
Yang, X., Mühlhausen, M. P., Fröhlich, J. 2021a. Interpolation methods for two-way coupled Euler-Lagrange simulation of finite-size bubbles. Chemical Engineering Science, 238: 116566.
Yang, X., Mühlhausen, M. P., Fröhlich, J. 2021b. Efficient simulation of bubble dispersion and resulting interaction. Experimental and Computational Multiphase Flow, 3: 152–170.
Funding
Open Access funding enabled and organized by Projekt DEAL.
Author information
Authors and Affiliations
Corresponding author
Additional information
Declaration of competing interest
The authors have no competing interests to declare that are relevant to the content of this article.
Rights and permissions
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Frense, E., Yang, X., Rüdiger, F. et al. Experimental and numerical study on the transport of dilute bubbles in a T-junction channel flow. Exp. Comput. Multiph. Flow 5, 396–410 (2023). https://doi.org/10.1007/s42757-022-0156-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42757-022-0156-4