# 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

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**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) |

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**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