# Study on Traveling Wave Wall Control Method for Suppressing Wake of Flow around a Circular Cylinder at Moderate Reynolds Number

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Model and Validation

#### 2.1. Governing Equations and TWW

#### 2.2. Computational Domain and Boundary Conditions

^{−6}, and the convergence residual standard of momentum equation and turbulence parameters is 3.0 × 10

^{−7}.

#### 2.3. Validity Investigation

## 3. Results and Discussion

#### 3.1. Influence of Different Propagation Directions

#### 3.2. Influence of Different Wave Amplitudes

#### 3.3. Influence of Different Wave Numbers

#### 3.4. Influence of Different Wave Velocities

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Comparisons of aerodynamic coefficient and the Strouhal number with previous results. (

**a**) ${\overline{C}}_{d}$ versus Re. (

**b**) ${S}_{t}$ versus Re.

**Figure 4.**Four types of propagation direction of TWW. (

**a**) Downstream. (

**b**) Upstream. (

**c**) Corotating-Clockwise. (

**d**) Corotating-Counterclockwise.

**Figure 5.**Lift and drag coefficient time history curves under various propagation directions. (

**a**) Downstream. (

**b**) Upstream. (

**c**) Corotating-Clockwise. (

**d**) Corotating-Counterclockwise.

**Figure 6.**Characteristic values of lift and drag coefficient for different propagation directions. (

**a**) ${C}_{l}^{\prime}\&{\overline{C}}_{l}$. (

**b**) ${C}_{d}^{\prime}\&{\overline{C}}_{d}$.

**Figure 7.**The contour of vorticity when wave starts at $t=1.8\mathrm{s}$. (

**a**) t = 1.80 s. (

**b**) t = 1.96 s. (

**c**) t = 2.16 s. (

**d**) t = 2.31 s. (

**e**) t = 2.46 s. (

**f**) t = 2.61 s. (

**g**) t = 2.97 s.

**Figure 8.**The vorticity contours of TWW cylinder with “Upstream” propagation. (

**a**) t = 2.16 s. (

**b**) t = 2.31 s. (

**c**) t = 2.46 s. (

**d**) t = 2.61 s. (

**e**) t = 2.97 s.

**Figure 9.**The vorticity contours of TWW cylinder with “Corotating-Clockwise” propagation. (

**a**) t = 2.16 s. (

**b**) t = 2.31 s. (

**c**) t = 2.46 s. (

**d**) t = 2.61 s. (

**e**) t = 2.97 s.

**Figure 10.**Lift and drag coefficients of TWW cylinder under various wave amplitudes. (

**a**) $\widehat{A}/D$ = 0.01. (

**b**) $\widehat{A}/D$ = 0.02. (

**c**) $\widehat{A}/D$ = 0.03. (

**d**) $\widehat{A}/D$ = 0.04. (

**e**) $\widehat{A}/D$= 0.05.

**Figure 11.**Characteristic values of lift and drag coefficient under different wave amplitudes. (

**a**) ${C}_{l}^{\prime}\&{\overline{C}}_{l}$. (

**b**) ${C}_{d}^{\prime}\&{\overline{C}}_{d}$.

**Figure 12.**Lift and drag coefficients under different wave numbers. (

**a**) N = 3. (

**b**) N = 4. (

**c**) N = 5. (

**d**) N = 6.

**Figure 13.**Characteristic values of lift and drag coefficient under different wave numbers. (

**a**) ${C}_{l}^{\prime}\&{\overline{C}}_{l}$. (

**b**) ${C}_{d}^{\prime}\&{\overline{C}}_{d}$.

**Figure 14.**Lift and drag coefficient under different wave velocities. (

**a**) $c/{U}_{\infty}=0.5$. (

**b**) $c/{U}_{\infty}=1.0$. (

**c**) $c/{U}_{\infty}=1.5$. (

**d**) $c/{U}_{\infty}=2.0$. (

**e**) $c/{U}_{\infty}=2.5$. (

**f**) $c/{U}_{\infty}=3.0$. (

**g**) $c/{U}_{\infty}=3.5$. (

**h**) $c/{U}_{\infty}=4.0$. (

**i**) $c/{U}_{\infty}=4.5$. (

**j**) $c/{U}_{\infty}=5.0$.

**Figure 15.**Characteristic values of lift and drag coefficient under different wave velocities. (

**a**) ${C}_{l}^{\prime}{\overline{C}}_{l}$. (

**b**) ${C}_{d}^{\prime}{\overline{C}}_{d}$.

${\mathit{N}}_{\mathit{c}}$ | ${\mathit{N}}_{\mathit{m}\mathit{e}\mathit{s}\mathit{h}}$ | $\mathbf{\Delta}\mathit{t}\left(\mathit{s}\right)$ | ${\overline{\mathit{C}}}_{\mathit{d}}$ | ${C}_{d}^{\prime}$ | ${C}_{l}^{\prime}$ | ${\mathit{S}}_{\mathit{t}}$ | ${\mathit{y}}_{\mathit{m}\mathit{i}\mathit{n}}^{+}$ | ${\overline{\mathit{y}}}^{+}$ | ${\mathit{y}}_{\mathit{m}\mathit{a}\mathit{x}}^{+}$ |
---|---|---|---|---|---|---|---|---|---|

100 | 82,456 | $2.5\times {10}^{-4}$ | 1.0999 | 0.0873 | 0.8329 | 0.267 | 0.745 | 8.331 | 16.232 |

150 | 92,304 | $2.5\times {10}^{-4}$ | 1.3675 | 0.0949 | 0.9927 | 0.249 | 0.442 | 5.589 | 11.405 |

200 | 101,504 | $2.5\times {10}^{-4}$ | 1.3420 | 0.0884 | 0.9702 | 0.243 | 0.334 | 4.116 | 8.389 |

250 | 111,600 | $2.5\times {10}^{-4}$ | 1.2674 | 0.0812 | 0.9211 | 0.243 | 0.247 | 3.187 | 6.902 |

300 | 120,594 | $2.5\times {10}^{-4}$ | 1.2224 | 0.0822 | 0.8956 | 0.243 | 0.184 | 2.580 | 5.750 |

$\mathbf{\Delta}\mathit{t}\left(\mathbf{s}\right)$ | ${\mathit{N}}_{\mathit{c}}$ | ${\mathit{N}}_{\mathit{m}\mathit{e}\mathit{s}\mathit{h}}$ | ${\overline{\mathit{C}}}_{\mathit{d}}$ | ${C}_{d}^{\prime}$ | ${C}_{l}^{\prime}$ | ${\mathit{S}}_{\mathit{t}}$ |
---|---|---|---|---|---|---|

$1.0\times {10}^{-3}$ | 250 | 111,600 | 1.1433 | 0.0591 | 0.7928 | 0.226 |

$5.0\times {10}^{-4}$ | 250 | 111,600 | 1.2378 | 0.0745 | 0.9003 | 0.237 |

$2.5\times {10}^{-4}$ | 250 | 111,600 | 1.2674 | 0.0812 | 0.9211 | 0.243 |

$1.0\times {10}^{-4}$ | 250 | 111,600 | 1.2819 | 0.0853 | 0.9351 | 0.243 |

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**MDPI and ACS Style**

Liu, X.; Bai, W.; Xu, F.
Study on Traveling Wave Wall Control Method for Suppressing Wake of Flow around a Circular Cylinder at Moderate Reynolds Number. *Appl. Sci.* **2022**, *12*, 3433.
https://doi.org/10.3390/app12073433

**AMA Style**

Liu X, Bai W, Xu F.
Study on Traveling Wave Wall Control Method for Suppressing Wake of Flow around a Circular Cylinder at Moderate Reynolds Number. *Applied Sciences*. 2022; 12(7):3433.
https://doi.org/10.3390/app12073433

**Chicago/Turabian Style**

Liu, Xin, Weifeng Bai, and Feng Xu.
2022. "Study on Traveling Wave Wall Control Method for Suppressing Wake of Flow around a Circular Cylinder at Moderate Reynolds Number" *Applied Sciences* 12, no. 7: 3433.
https://doi.org/10.3390/app12073433