# Experimental Analysis of a Bubble Wake Influenced by a Vortex Street

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Set-up and Data Processing

^{2}. Demineralized water with PIV seeding particles (details are listed in Table 1), which have a density very close to water, is supplied continuously through the duct with adjustable volumetric flow rates (250–875 L/h). The single bubble is produced by a hypodermic needle, which is pushed through a septum into the fluid flow. The bubble (CO

_{2}or air) is kept in place using a spherical cap. A cylinder is brought into the duct to produce vortices of different frequencies by means of a von Karman vortex street. The streamwise distance between the cylinder and the bubble is varied while the transverse distance is held constant. In Figure 1, the staggered configurations of bubble and cylinder within the duct are sketched in detail. The first configuration (Figure 1a) has the cylinder diameter as the distance between the bubble and cylinder; the second (Figure 1b) has several cylinder diameters as the distance. This is chosen in order to observe different wake interactions.

^{®}(The MathWorks, Natick, MA, USA), the PIV data are processed further. Fast Fourier Transformation (FFT) is used to obtain frequencies dominating the bubble wake or the cylinder wake, respectively. Strouhal numbers are calculated using the frequencies obtained by FFT. The frequency analysis is carried out 1 cm downstream of the bubble or the cylinder (see Figure 4).

_{b}and the mean velocity that approaches the bubble ${v}_{\infty}$. For ${v}_{\infty}$, which is calculated from the volumetric flow rate $\dot{V}$ and the cross-section of the duct A

_{duct}:

## 3. Results and Discussion

#### 3.1. Characterization of the Vortex Street

#### 3.2. Characterization of the Single Bubble

#### 3.3. Characterization of the Single Bubble Wake Influenced by the Vortex Street

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Brauer, H. Grundlagen der Einphasen-und Mehrphasenstroemungen, 1st ed.; Sauerlaender AG: Aarau, Switzerland, 1971. [Google Scholar]
- Clift, R.; Grace, J.R.; Weber, M.E. Bubbles, Drops, and Particles; Dover Publication, Inc.: Mineola, NY, USA, 1978. [Google Scholar]
- Fan, L.S.; Tsuchiya, K. Bubble Wake Dynamics in Liquids and Liquid-Solid Suspensions; Butterworth-Heinemann: Quebec City, QC, Canada, 1990. [Google Scholar]
- Tsuchiya, K.; Mikasa, H.; Saito, T. Absorption dynamics of CO
_{2}bubbles in a pressurized liquid flowing downward and its simulation in seawater. Chem. Eng. Sci.**1997**, 52, 4119–4126. [Google Scholar] [CrossRef] - Tsuchiya, K.; Ishida, T.; Saito, T.; Kajishima, T. Dynamics of interfacial mass transfer in a gas-dispersed system. Can. J. Chem. Eng.
**2003**, 81, 647–654. [Google Scholar] [CrossRef] - Dani, A.; Guiraud, P.; Cockx, A. Local measurement of oxygen transfer around a single bubble by planar laser-induced fluorescence. Chem. Eng. Sci.
**2007**, 62, 7245–7252. [Google Scholar] [CrossRef] - Hanyu, K.; Saito, T. Dynamical mass-transfer process of a CO
_{2}bubble measured by using LIF/HPTS visualisation and photoelectric probing. Can. J. Chem. Eng.**2010**, 139, 551–560. [Google Scholar] [CrossRef] - Saito, T.; Toriu, M. Effects of a bubble and the surrounding liquid motions on the instantaneous mass transfer across the gas-liquid interface. Chem. Eng. J.
**2015**, 265, 164–175. [Google Scholar] [CrossRef] - Bork, O.; Schlueter, M.; Raebiger, N. The impact of local phenomena on mass transfer in gas-liquid systems. Can. J. Chem. Eng.
**2005**, 83, 658–666. [Google Scholar] [CrossRef] - Joshi, J.B.; Nandakumar, K.; Evans, G.M.; Pareek, V.K.; Gumulya, M.M.; Sathe, M.J.; Khanwale, M.A. Bubble generated turbulence and direct numerical simulations. Chem. Eng. Sci.
**2017**, 157, 26–75. [Google Scholar] [CrossRef] - Alméras, E.; Cazin, S.; Roig, V.; Risso, F.; Augier, F.; Plais, C. Time-resolved measurement of concentration fluctuations in a confined bubbly flow by LIF. Int. J. Multiph. Flow
**2016**, 83, 153–161. [Google Scholar] [CrossRef] [Green Version] - Falcone, M.; Bothe, D.; Marschall, H. 3D direct numerical simulations of reactive mass transfer from deformable single bubbles: An analysis of mass transfer coefficients and reaction selectivities. Chem. Eng. Sci.
**2018**, 177, 523–536. [Google Scholar] [CrossRef] - Weber, P.S.; Marschall, H.; Bothe, D. Highly accurate two-phase species transfer based on ALE Interface Tracking. Int. J. Heat Mass Transf.
**2017**, 104, 759–773. [Google Scholar] [CrossRef] - Krauβ, M.; Rzehak, R. Reactive absorption of CO
_{2}in NaOH: Detailed study of enhancement factor models. Chem. Eng. Sci.**2017**, 166, 193–209. [Google Scholar] [CrossRef] - Zdravkovich, M.M. Review of flow interference between two circular cylinders in various arrangements. J. Fluids Struct.
**1977**, 1, 239–261. [Google Scholar] [CrossRef] - Zdravkovich, M.M. The effects of interference between circular cylinders in cross flow. J. Fluid. Struct.
**1987**, 1, 239–261. [Google Scholar] [CrossRef] - Sumner, D. Two circular cylinders in cross-flow: A review. J. Fluid. Struct.
**2010**, 26, 849–899. [Google Scholar] [CrossRef] - Zhou, Y.; Alam, M.M. Wake of two interacting circular cylinders: A review. Int. J. Heat Fluid Flow
**2016**, 62, 510–537. [Google Scholar] [CrossRef] - No, H.; Call, M.; Tokuhiro, A.T. Comparison of Near Wake-Flow Structure Behind a Solid Cap with an Attached Bubble and a Solid Counterpart. In Proceedings of the 4th Joint Fluids Summer Engineering Conference, Honolulu, HI, USA, 6–10 July 2003; pp. 1721–1725. [Google Scholar]
- Tokuhiro, A.T.; No, H.; Call, M.; Hishida, K. Comparison of near wake-flow structure behind a solid cap with an attached bubble and a solid counterpart. JSME Int. J. Ser. B
**2006**, 49, 737–747. [Google Scholar] [CrossRef] - Tokuhiro, A.; Fujiwara, A.; Hishida, K.; Maeda, M. Measurement in the wake region of two bubbles in close proximity by combined shadow-image and PIV techniques. J. Fluid. Eng.
**1999**, 121, 191–197. [Google Scholar] [CrossRef] - Tokuhiro, A.; Maekawa, M.; Iizuka, K.; Hishida, K.; Maeda, M. Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques. Int. J. Multiph. Flow
**1998**, 24, 1383–1406. [Google Scholar] [CrossRef] - Roshko, A. On the Development of Turbulent Wakes from Vortex Streets. Tech. Rep. Arch. Image Libr.
**1954**, 1–28. [Google Scholar] - Chen, Y.N. Jahre Forschung über die Kàrmànschen Wirbelstrassen-Ein Rückblick. Schweiz. Bauz.
**1973**, 44, 1079–1096. [Google Scholar] - Williamson, C.H.K. Three-Dimensional Wake Transition. In Advances in Turbulence VI; Moreau, R., Gavrilakis, S., Machiels, L., Monkewitz, P.A., Eds.; Springer: Dordrecht, The Netherlands, 1996; pp. 399–402. [Google Scholar]
- Barkley, D.; Henderson, R.D. Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech.
**1996**, 322, 215–241. [Google Scholar] [CrossRef] - Tomboulides, A.G.; Orszag, S.A. Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech.
**2000**, 416, 45–73. [Google Scholar] [CrossRef] - Le Clainche, S.; Vega, J.M. Higher order dynamic mode decomposition. SIAM J. Appl. Dyn. Syst.
**2017**, 16, 882–925. [Google Scholar] [CrossRef] - Oellrich, L.; Schmidt-Traub, H.; Brauer, H. Theoretische berechnung des stofftransports in der umgebung einer einzelblase. Chem. Eng. Sci.
**1973**, 28, 711–721. [Google Scholar] [CrossRef] - Komasawa, I.; Otake, T.; Kamojima, M. Wake behavior and its effect on interaction between spherical-cap bubbles. J. Chem. Eng. Jpn.
**1980**, 13, 103–109. [Google Scholar] [CrossRef] - Böswirth, L.; Bschorer, S. Technische Strömungslehre, 10th ed.; Springer: Berlin, Germany, 2014. [Google Scholar]
- Perry, A.E.; Fairlie, B.D. Critical points in flow patterns. Adv. Geophys.
**1975**, 18, 299–315. [Google Scholar] - Dallmann, U. Topological structures of three-dimensional vortex flow separation. In Proceedings of the AIAAA 16th Fluid and Plasma Dynamics Conference, Danvers, MA, USA, 12–14 July 1983. [Google Scholar]
- Chong, M.S.; Perry, A.E.; Cantwell, B.J. A general classification of three-dimensional flow fields. Phys. Fluids A Fluid Dyn.
**1990**, 2, 765–777. [Google Scholar] [CrossRef] - Le Clainche, S.; Li, J.I.; Theofilis, V.; Soria, J. Flow around a hemisphere-cylinder at high angle of attack and low Reynolds number. Part I: Experimental and numerical investigation. Aerosp. Sci. Technol.
**2015**, 44, 77–87. [Google Scholar] [CrossRef] - Le Clainche, S.; Rodríguez, D.; Theofilis, V.; Soria, J. Flow around a hemisphere-cylinder at high angle of attack and low Reynolds number. Part II: POD and DMD applied to reduced domains. Aerosp. Sci. Technol.
**2015**, 44, 88–100. [Google Scholar] [CrossRef] - Hunt, J.C.R.; Wray, A.A.; Moin, P. Eddies, Streams, and Convergence Zones in Turbulent Flows. Center for Turbulence Research. In Proceedings of the Summer Program, Stanford, CA, USA, 27 June–22 July 1988; pp. 193–208. [Google Scholar]
- Jeong, J.; Hussain, F. On the identification of a vortex. J. Fluid Mech.
**1995**, 285, 69–94. [Google Scholar] [CrossRef] - Kolář, V. Vortex identification: New requirements and limitations. Int. J. Heat Fluid Flow
**2007**, 28, 638–652. [Google Scholar] [CrossRef] - Hu, J.C.; Zhou, Y. Flow structure behind two staggered circular cylinders. Part 1. Downstream evolution and classification. J. Fluid Mech.
**2008**, 607, 51–80. [Google Scholar] [CrossRef] - Elsinga, G.E.; Scarano, F.; Wieneke, B.; van Oudheusden, B.W. Tomographic particle image velocimetry. Exp. Fluids
**2006**, 41, 933–947. [Google Scholar] [CrossRef]

**Figure 3.**PIV processing: raw image (

**a**) and instantaneous velocity field with physical coordinates (

**b**).

**Figure 4.**Nomenclature (

**a**); procedure of velocity analysis (

**b**) and frequency analysis (power spectrum) (

**c**).

**Figure 5.**Strouhal numbers of the bubble. Red diamond items belong to the red (right) axis, and blue star items belong to the blue (left) axis.

**Figure 6.**Non-dimensional streamwise velocity component $v/{v}_{\phi}$ of the single bubble for two different Reynolds numbers (

**a**,

**b**); and nomenclature (

**c**). $r/{d}_{B}$ denotes the surface of the single bubble.

**Figure 7.**Vertical root mean square velocities downstream the bubble at the rear stagnation point, $\phi =180\xb0$ ($y/{d}_{B}=$ 0: surface of the bubble). (

**a**) Comparison with and without the vortex street; (

**b**) comparison of different configurations and Reynolds numbers.

**Figure 8.**Horizontal velocity profiles (

**a**) and velocity fields with stream traces (

**b**) around a single bubble (no cylinder).

**Figure 9.**Horizontal velocity profiles (

**a**) and velocity fields with stream traces (

**b**) around a staggered configuration of a single bubble and a cylinder (L* = 2.75).

**Figure 10.**Horizontal velocity profiles (

**a**) and velocity fields with stream traces (

**b**) around a staggered configuration of a single bubble and a cylinder (L* = 1).

**Figure 11.**Instantaneous velocity fields and stream traces of a staggered configuration of a single bubble and a cylinder (L* = 1); Re

_{b}= 163, Re

_{cyl}= 484.

Parameters | Settings |
---|---|

Camera | PCO dimax HS2 (PCO AG, Kelheim, Germany), 1400 × 1000 Px ^{2}, 12 bit |

Objective | Zeiss macro planar 2/50 mm |

Laser | Quantronix Darwin-Duo-100M, Nd:YLF (Quantronix Inc., Hamden, CT, USA), total energy > 60 mL, average power at 3 kHz > 90 W |

Seeding Particles | PS-FluoRed-Fi203, monodisperse 3.16 µm, abs/em = 530/607 nm (MicroParticles GmbH, Berlin, Germany) |

Frame Rate | 500 fps |

Acquisition Time | 20 s |

Number of Images Processed | 10,000 |

Spatial Resolution (vector-to-vector spacing) | 0.36 … 0.69 mm (24 Px) |

Temperature | 20 ± 1.5 °C |

PIV Data Processing Software | PivView 3.60 (PivTec GmbH, ILA_5150 GmbH, Aachen, Germany) |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rüttinger, S.; Hoffmann, M.; Schlüter, M.
Experimental Analysis of a Bubble Wake Influenced by a Vortex Street. *Fluids* **2018**, *3*, 8.
https://doi.org/10.3390/fluids3010008

**AMA Style**

Rüttinger S, Hoffmann M, Schlüter M.
Experimental Analysis of a Bubble Wake Influenced by a Vortex Street. *Fluids*. 2018; 3(1):8.
https://doi.org/10.3390/fluids3010008

**Chicago/Turabian Style**

Rüttinger, Sophie, Marko Hoffmann, and Michael Schlüter.
2018. "Experimental Analysis of a Bubble Wake Influenced by a Vortex Street" *Fluids* 3, no. 1: 8.
https://doi.org/10.3390/fluids3010008