# Numerical Analysis of Drag Force Acting on 2D Cylinder Immersed in Accelerated Flow

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}, and the drag for each acceleration is compared. Additionally, the effect of the initial velocity on the drag acting on the circular cylinder is investigated at two initial velocities. As a result, a supercritical region, typically found under steady state conditions, is observed. Furthermore, vortex shedding is observed at a high initial velocity. This flow characteristic is explained via comparison with respect to the recirculation length and separation angle.

## 1. Introduction

^{4}to 1.64 × 10

^{5}; thus, the overall drag change for other Reynolds number ranges is unknown. Mason and Yang [7] performed wind tunnel experiments to investigate forces on a two-dimensional square cylinder during a period of rapid acceleration. The results show, in a fragmentary way, that when flow accelerated from an initial quiescent state, both the amplitude and frequency of force coefficient fluctuations exceeded those recorded during steady flow tests. Previous studies compared accelerated and non-accelerated flows in small Reynolds number ranges. Therefore, the studies with wind tunnel experiments provide limited understanding of the aerodynamic characteristics in accelerated flow.

## 2. Computational Methods

#### 2.1. Governing Equations and Numerical Method

#### 2.2. Computational Domain and Boundary Conditions

#### 2.3. Validation of the Present Method

#### 2.3.1. Grid Convergence

^{2}and the drag coefficient is defined as

^{2}/d where s is the displacement of the fluid flow. In this study, for a more intuitive understanding, it was denoted as a nondimensional time $\widehat{t}$, defined as

#### 2.3.2. Choice of Turbulence Model

#### 2.3.3. Time Step Convergence

#### 2.4. Scope of Study

^{2}as listed in Table 2. The Reynolds number, $Re$ is defined as

^{2}are studied. Fackrell [17] extended the study on unidirectional constant acceleration of an initial stationary fluid to include a flow with a small initial velocity ($R{e}_{0}$ < 40), and the case of low Reynolds number in this study was set with reference to this.

## 3. Drag in Accelerated Flow at Low Initial Velocity

#### 3.1. Overshoot of Drag Force

^{2}from the initial constant velocity ($R{e}_{0}$ = 40). When the flow accelerated, an overshoot phenomenon of the fluid force is evident. The drag coefficient ${C}_{d}$ is defined as

#### 3.2. Difference between Non-Accelerated and Accelerated Flow

#### 3.3. Drag Changes over Dimensionless Time and Flow Time

#### 3.4. Vortex Formation and Development

## 4. Drag in Accelerated Flow at High Initial Velocity

#### 4.1. Difference between Non-Accelerated and Accelerated Flow

#### 4.2. Drag Changes over Dimensionless Time and Flow Time

#### 4.3. Vortex Shedding Formation Development

## 5. Comparison of Fluid Force by Initial Velocity

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Comparison of different grid configurations (experimental data from Sarpkaya and Garrison [16]).

**Figure 6.**Comparison of different turbulence models (experimental data from Sarpkaya and Garrison [16]).

**Figure 7.**Comparison of different time steps (experimental data from Sarpkaya and Garrison [16]).

**Figure 9.**Comparison of drag coefficient ${C}_{d}$ between non-accelerated flow (Bullivant [20]) and accelerated flow ($R{e}_{0}=40$).

**Figure 21.**Comparison of drag coefficient ${C}_{d}$ between non-accelerated flow (Bullivant [20]) and accelerated flow ($R{e}_{0}=1000$).

First Grid Height (m) | Total Number of Grids | Number of Grids around the Cylinder | |
---|---|---|---|

Mesh 1 | 1.9 $\times {10}^{-6}$ | 454,012 | 940 |

Mesh 2 | 2.9 $\times {10}^{-6}$ | 229,211 | 800 |

Mesh 3 | 5.9 $\times {10}^{-6}$ | 376,680 | 1600 |

a/g | $\mathit{a}\text{}(\mathbf{m}/{s}^{2})$ |
---|---|

1 | 9.81 |

0.5 | 4.905 |

0.1 | 0.981 |

0.05 | 0.4905 |

0.01 | 0.0981 |

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**MDPI and ACS Style**

Son, H.A.; Lee, S.; Lee, J.
Numerical Analysis of Drag Force Acting on 2D Cylinder Immersed in Accelerated Flow. *Water* **2020**, *12*, 1790.
https://doi.org/10.3390/w12061790

**AMA Style**

Son HA, Lee S, Lee J.
Numerical Analysis of Drag Force Acting on 2D Cylinder Immersed in Accelerated Flow. *Water*. 2020; 12(6):1790.
https://doi.org/10.3390/w12061790

**Chicago/Turabian Style**

Son, Hyun A., Sungsu Lee, and Jooyong Lee.
2020. "Numerical Analysis of Drag Force Acting on 2D Cylinder Immersed in Accelerated Flow" *Water* 12, no. 6: 1790.
https://doi.org/10.3390/w12061790