# An Experimental Investigation of Passive Jet Control Method on Bridge Tower Wake

^{1}

^{2}

^{*}

## Abstract

**:**

^{5}to 2.27 × 10

^{5}by changing the yaw angle. A measurement plane with 9 × 19 measurement points was horizontally set at the middle height behind the model. The wake characteristics of the test model without control, i.e., the baseline case, was first tested in the yaw angle range from 0° to 90°; then, four kinds of passive jet control cases were tested to study their control effects on the bridge tower wake. To evaluate the wake characteristics, three main aspects, i.e., mean velocity, turbulence intensity, and velocity frequency, were investigated. The meas-urement results indicate that the passive jet control method can achieve an effect in suppressing the turbulence of the wake but can slightly modify the mean velocity distribution. The dominant frequency distribution region was eliminated when the yaw angle was small but slightly expanded at a large angle. The differences between cases show a trend that the larger the suction coefficient is, the better the control effects are.

## 1. Introduction

## 2. Experimental Setup

#### 2.1. Bridge Tower Model

#### 2.2. Passive Jet Rings

_{suc}is the summary area of the suction slits on one passive jet ring projection to the plane perpendicular to the direction of flow; l = asin α + bcos α is the total projection length of the ring perpendicular to the incoming flow; H is the height of the passive jet ring; h is the length of the suction slit; d is the width of the suction slit; a and b are the length of the long and short side of the ring, respectively; n

_{a}and n

_{b}are the number of the slits distributed on each long and short side, respectively, and α is the yaw angle of the ring.

#### 2.3. Experiment Details and Measurement Point Arrangement

_{0}is set to 10 m/s, corresponding to the range of Reynolds numbers (Re = ρU

_{0}L/μ, where ρ is the air density, μ is the dynamic viscosity coefficient of air, L is the projection length of the tower cross-section) from 1.38 × 10

^{5}to 2.27 × 10

^{5}, which varies by the projection length (L = Bsin α + Dcos α) when the yaw angle α changes. As the yaw angle changes, the corresponding positions of the suspenders vary, revolving the same degrees around the bridge tower. The locations of the first four imaginary suspenders behind the tower are labeled A1 to A4. When the yaw angle continues to increase, the imaginary suspenders behind the other side tower come into the wake zone of the tower model, the locations of which are labeled B1 to B4. There are five test conditions in this study, recorded as Case 0–Case 4. Case 0 is the baseline condition, in which only a tower model is tested, without passive jet control. Case 1–Case 4, corresponding to the category of the passive jet ring from 1 to 4, respectively, are controlled conditions, in which fourteen passive jet rings are installed on the tower model, distributed at the interval of 100 mm. The ring in the middle is installed 1.5 m from the ground, the same height as the probe. The yaw angle changes from 0 to 90 in Case 0 to Case 2, and from 0 to 30 in Case 3 to Case 4, because few suction slits work at a large angle in Case 3 and 4. The test conditions are shown in Table 1, and the value of suction coefficients at different yaw angles in each case are listed in Table 2.

## 3. Results and Discussions

#### 3.1. Mean Velocity Distribution

_{0}) distribution in each test condition, where the black arrows refer to the local wind velocity vector. The general distribution trend of wind velocity is almost the same, and it can be divided into three regions. A low-value zone is located near the position (0, 0), which can be regarded as the low-speed region. This region is created due to the bridge tower shielding effects and the recirculation zone. Due to the limitation of the cobra probe, the mean velocity is always downstream, which is not tally with the fact; thus, the low-speed region is defined as the location where the data acceptance ratio (the proportion of non-zero data) of the probe is less than 50%. A slow diffusion region is located downstream of the low-speed region, where the speed is approximately half of the incoming wind speed. The high-speed region is distributed on two sides of the Y-axis, where the mean speed is almost not affected by the bridge tower model.

_{1}/BD) of the low-speed region is shown in Figure 5, where S

_{1}is the area where the data acceptance ratio is less than 50% in the tower wake. In Case 0, there is a notable minimum area at 10 degrees equal to 0.386, and the second minimum area is equal to 0.503 at 80 degrees. This indicates that the low-speed area of the rectangular column with corner cuts minimizes not at the position perpendicular to the incoming flow, but at the position of little degree rotation. In Case 1 and Case 2, the low-speed region extends downstream compared with Case 0, every 0–90 degrees; in Case 3 and Case 4, an obvious expanding low-speed region can be observed at 10 and 20 degrees. These phenomena can be explicated by the previous study (Chen et al., 2015), where the PIV results show that the wake vortex is pushed by jet flow and stretched, which would induce the expansion of the low-speed region.

#### 3.2. Turbulence Intensity Distribution

#### 3.3. Dominant Frequency Distribution

_{s}L/U

_{0}, where f

_{s}is the shedding frequency, i.e., the dominant frequency in the wake). The distribution of dimensionless frequencies is obtained, as shown in Figure 9. To eliminate interference from dominant frequencies with small peak values, and for the comparison between cases, a threshold value of power spectral density (PSD) was set. Only the frequencies whose peak value was over the threshold value were counted, and the remaining zones were filled with zeros. If no PSD threshold was set, there is always a dominant frequency anywhere in the wake field, no matter how weak the energy level corresponding to that frequency. The threshold value of PSD in Figure 9 is set as 0.5. In this figure, most St numbers of wake in each case are uniform, but some divergences are mostly located in the middle of wake, especially in Case 0. Comparing the cases, we can find that divergences decline in Cases 1 and 2; especially in Case 1, the St numbers are almost uniform, and the distribution appears clean.

_{2}/BD) of the region in each case. The threshold value of PSD is also set as 0.5. Two trends in different sections of the yaw angle appear. When the yaw angle is small (0–10 degrees), Cases 1, 3, and 4 all reveal a great control effect. Cases 1–4 attain [36.0, −47.2, 59.1, 50.6] and [63.3, 26.9, 78.0, 61.9] percent reduction of area in 0 and 10 degrees, respectively. However, when the yaw angle increases, the area expands, where Case 1 shows the least expansion, except at 80 degrees, with no more than 4% of the area expanding. As in the turbulence intensity distribution, a drop of the area appears at 80 degrees in Case 0, which causes the amplification of the negative control effects of all cases at 80 degrees. Case 2 has the same trend of the area variation by degrees as Case 1, but the effect is worse—29% amplification of area is the maximum at 30 degrees, without considering 80 degrees. Cases 1 and 3 have larger suction coefficients, so these cases perform better than others. If only a small yaw angle is taken into consideration, Case 3 would be recommended, because the position of the suspenders would come out of the wake region at large yaw angles. For engineering applications, Case 1 would be better for various yaw angles.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Knisely, C.W. Strouhal Numbers of Rectangular Cylinders at Incidence: A Review and New Data. J. Fluids Struct.
**1990**, 4, 371–393. [Google Scholar] [CrossRef] - Norberg, C. Flow around Rectangular Cylinders: Pressure Forces and Wake Frequencies. J. Wind Eng. Ind. Aerodyn.
**1993**, 49, 187–196. [Google Scholar] [CrossRef] - Shimada, K.; Ishihara, T. Application of a Modified K-ε Model to the Prediction of Aerodynamic Characteristics of Rectangular Cross-Section Cylinders. J. Fluids Struct.
**2002**, 16, 465–485. [Google Scholar] [CrossRef] - Assi, G.R.S.; Bearman, P.W.; Meneghini, J.R. On the Wake-Induced Vibration of Tandem Circular Cylinders: The Vortex Interaction Excitation Mechanism. J. Fluid Mech.
**2010**, 661, 365–401. [Google Scholar] [CrossRef] - Zdravkovich, M.M. REVIEW—Review of Flow Interference Between Two Circular Cylinders in Various Arrangements. J. Fluids Eng.
**1977**, 99, 618. [Google Scholar] [CrossRef] - Carmo, B.S.; Sherwin, S.J.; Bearman, P.W.; Willden, R.H.J. Flow-Induced Vibration of a Circular Cylinder Subjected to Wake Interference at Low Reynolds Number. J. Fluids Struct.
**2011**, 27, 503–522. [Google Scholar] [CrossRef] - Bearman, P.W. Circular Cylinder Wakes and Vortex-Induced Vibrations. J. Fluids Struct.
**2011**, 27, 648–658. [Google Scholar] [CrossRef] - Wang, H.; Yang, W.; Nguyen, K.D.; Yu, G. Wake-Induced Vibrations of an Elastically Mounted Cylinder Located Downstream of a Stationary Larger Cylinder at Low Reynolds Numbers. J. Fluids Struct.
**2014**, 50, 479–496. [Google Scholar] [CrossRef] - Li, Y.; Tang, H.; Lin, Q.; Chen, X. Vortex-Induced Vibration of Suspenders in the Wake of Bridge Tower by Numerical Simulation and Wind Tunnel Test. J. Wind Eng. Ind. Aerodyn.
**2017**, 164, 164–173. [Google Scholar] [CrossRef] - Amitay, M.; Smith, B.; Glezer, A. Aerodynamic Flow Control Using Synthetic Jet Technology. In Proceedings of the 36th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 12–15 January 1998. [Google Scholar] [CrossRef]
- Amitay, M.; Honohan, A.; Trautman, M.; Glezer, A.; Amitay, M.; Honohan, A.; Trautman, M.; Glezer, A. Modification of the Aerodynamic Characteristics of Bluff Bodies Using Fluidic Actuators. In Proceedings of the 28th Fluid Dynamics Conference, Snowmass Village, CO, USA, 29 June–2 July 1997. [Google Scholar] [CrossRef]
- Crook, A.; Sadri, A.M.; Wood, N.J. The Development and Implementation of Synthetic Jets for the Control of Separated Flow. In Proceedings of the 17th Applied Aerodynamics Conference, Norfolk, VA, USA, 28 June–1 July 1999; Volume 99, p. 3176. [Google Scholar] [CrossRef]
- Fransson, J.H.M.; Konieczny, P.; Alfredsson, P.H. Flow around a Porous Cylinder Subject to Continuous Suction or Blowing. J. Fluids Struct.
**2004**, 19, 1031–1048. [Google Scholar] [CrossRef] - Wang, J.; Feng, L.; Xu, C. Experimental Investigations on Separation Control and Flow Structure around a Circular Cylinder with Synthetic Jet. Sci. China Ser. E Technol. Sci.
**2007**, 50, 550–559. [Google Scholar] [CrossRef] - Dong, S.; Triantafyllou, G.S.; Karniadakis, G.E. Elimination of Vortex Streets in Bluff-Body Flows. Phys. Rev. Lett.
**2008**, 100, 204501. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Feng, L.H.; Wang, J.J. Synthetic Jet Control of Separation in the Flow over a Circular Cylinder. Exp. Fluids
**2012**, 53, 467–480. [Google Scholar] [CrossRef] - Feng, L.-H.; Wang, J.-J.; Pan, C. Proper Orthogonal Decomposition Analysis of Vortex Dynamics of a Circular Cylinder under Synthetic Jet Control. Phys. Fluids
**2011**, 23, 014106. [Google Scholar] [CrossRef] - Chen, W.-L.; Xin, D.-B.; Xu, F.; Li, H.; Ou, J.-P.; Hu, H. Suppression of Vortex-Induced Vibration of a Circular Cylinder Using Suction-Based Flow Control. J. Fluids Struct.
**2013**, 42, 25–39. [Google Scholar] [CrossRef] - Chen, W.-L.; Li, H.; Hu, H. An Experimental Study on a Suction Flow Control Method to Reduce the Unsteadiness of the Wind Loads Acting on a Circular Cylinder. Exp. Fluids
**2014**, 55, 1707. [Google Scholar] [CrossRef] - Chen, W.-L.; Wang, X.; Xu, F.; Li, H.; Hu, H. Passive Jet Flow Control Method for Suppressing Unsteady Vortex Shedding from a Circular Cylinder. J. Aerosp. Eng.
**2017**, 30, 04016063. [Google Scholar] [CrossRef] [Green Version] - Chen, W.-L.; Gao, D.-L.; Yuan, W.-Y.; Li, H.; Hu, H. Passive Jet Control of Flow around a Circular Cylinder. Exp. Fluids
**2015**, 56, 201. [Google Scholar] [CrossRef] - Zhang, L.-Q.; Chen, G.-B.; Chen, W.-L.; Gao, D.-L. Separation Control on a Bridge Box Girder Using a Bypass Passive Jet Flow. Appl. Sci.
**2017**, 7, 501. [Google Scholar] [CrossRef] - Chen, W.L.; Huang, Y.W.; Gao, D.L.; Meng, H.; Chen, G.B.; Li, H. Passive Suction Jet Control of Flow Regime around a Rectangular Column with a Low Side Ratio. Exp. Therm. Fluid Sci.
**2019**, 109, 109815. [Google Scholar] [CrossRef] - Chen, W.L.; Huang, Y.W.; Meng, H. Wake-Induced Vibration of a Suspender Cable in the Rear of a Bridge Tower. J. Fluids Struct.
**2020**, 99, 103166. [Google Scholar] [CrossRef] - Mallipudi, S.; Selig, M.; Long, K. Use of a Four Hole Cobra Pressure Probe to Determine the Unsteady Wake Characteristics of Rotating Objects. In Proceedings of the 24th AIAA Aerodynamic Measurement Technology and Ground Testing Conference, Portland, OR, USA, 28 June–1 July 2004; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2004; pp. 1–9. [Google Scholar]

Designation | Type of Passive Jet Ring | Slits Number at Long Side | Slits Number at Short Side | Length of Slits |
---|---|---|---|---|

Case 0 | without control | - | - | - |

Case 1 | Category 1 | 9 | 7 | 80 mm |

Case 2 | Category 2 | 7 | 5 | 60 mm |

Case 3 | Category 3 | 0 | 7 | 80 mm |

Case 4 | Category 4 | 0 | 5 | 60 mm |

Yaw Angle | 0° | 10° | 20° | 30° | 40° | 50° | 60° | 70° | 80° | 90° |
---|---|---|---|---|---|---|---|---|---|---|

Case 1 | 0.654 | 0.656 | 0.658 | 0.660 | 0.661 | 0.663 | 0.664 | 0.665 | 0.667 | 0.669 |

Case 2 | 0.350 | 0.357 | 0.363 | 0.367 | 0.371 | 0.374 | 0.378 | 0.381 | 0.385 | 0.390 |

Case 3 | 0.654 | 0.535 | 0.449 | 0.379 | - | - | - | - | - | - |

Case 4 | 0.350 | 0.287 | 0.240 | 0.203 | - | - | - | - | - | - |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Huang, Y.; Chen, W.
An Experimental Investigation of Passive Jet Control Method on Bridge Tower Wake. *Appl. Sci.* **2022**, *12*, 4691.
https://doi.org/10.3390/app12094691

**AMA Style**

Huang Y, Chen W.
An Experimental Investigation of Passive Jet Control Method on Bridge Tower Wake. *Applied Sciences*. 2022; 12(9):4691.
https://doi.org/10.3390/app12094691

**Chicago/Turabian Style**

Huang, Yewei, and Wenli Chen.
2022. "An Experimental Investigation of Passive Jet Control Method on Bridge Tower Wake" *Applied Sciences* 12, no. 9: 4691.
https://doi.org/10.3390/app12094691