# Freestream Turbulence Effects on the Aerodynamics of an Oscillating Square Cylinder at the Resonant Frequency

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Methods

#### 2.1. Governing Equations

#### 2.2. Turbulent Inflow Generation

#### 2.3. Boundary Conditions

## 3. Validation of the Implementation of Turbulent Inflow Generation Method

## 4. Numerical Setup

#### 4.1. Domain Configuration and Resolution Verification

#### 4.2. One-Degree-of-Freedom Oscillation of the Cylinder

#### 4.3. Freestream Turbulence Parameters

## 5. Flow Past an Oscillating Square Cylinder

#### 5.1. Fluctuating Lift and Its Power Spectrum Distribution

#### 5.2. Spatial Correlation in the Shear Layer and the Wake

#### 5.3. Turbulent Statistics and Recirculation in the Wake

## 6. Conclusions and Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Computational domain and the dimensions normalised by the side length of cylinder D; (

**b**) Definition of circumferential direction of a cylinder section. The coordinate origin is placed on the centre of the cylinder.

**Figure 2.**Contours of instantaneous spanwise vorticity over a stationary cylinder. $ILS=1.0D$, $TI=0.04$.

**Figure 3.**PSD of three velocity components collected at the centre of inflow plane. For the sake of clarity, the v and w spectra are shifted down by 2 and 4 decays, respectively. The grey line denotes a slope of −5/3.

**Figure 4.**Two-point correlations for two velocity components v and w on the central horizontal line, and auto-correlation for velocity component u. The black line denotes the analytical exponential correlation for the same integral length scale and the equivalent integral time scale.

**Figure 5.**PSD of lift coefficients against frequency ratio $f/{f}_{l}$. The spectra of “$ILS=1.0D$, $TI=0.04$” and “$ILS=0.2D$, $TI=0.10$” are shifted down in the vertical axis by 8 and 16 decades, respectively.

**Figure 6.**Two-point correlation of streamwise velocity. The reference point is at $x/D=1.0$, $y/D=0.6$. (

**a**) smooth inflow, and turbulent inflows with (

**b**) $ILS=1.0D$, $TI=0.04$, and (

**c**) $ILS=0.2D$, $TI=0.10$. Contours starts from 0 (in dark blue) to 1 (in dark red) with an increment 0.1.

**Figure 7.**Spanwise correlation of streamwise velocity. The locations of a group of spanwise probes from left to right are at (

**a**) wake, $x/D=1.0$, $y/D=0.0$, (

**b**) shear layer in the wake, $x/D=1.0$, $y/D=0.5$, and (

**c**) shear layer over the side surfaces, $x/D=0.0$, $y/D=0.65$.

**Figure 8.**Time and spanwise-averaged Reynolds normal stress $<\overline{{u}^{\prime}{u}^{\prime}}>/{U}_{C}^{2}$. (

**a**) smooth inflow; (

**b**) ILS = 0.2D, TI = 0.10.

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**MDPI and ACS Style**

Chen, Y.; Djidjeli, K.; Xie, Z.-T.
Freestream Turbulence Effects on the Aerodynamics of an Oscillating Square Cylinder at the Resonant Frequency. *Fluids* **2022**, *7*, 329.
https://doi.org/10.3390/fluids7100329

**AMA Style**

Chen Y, Djidjeli K, Xie Z-T.
Freestream Turbulence Effects on the Aerodynamics of an Oscillating Square Cylinder at the Resonant Frequency. *Fluids*. 2022; 7(10):329.
https://doi.org/10.3390/fluids7100329

**Chicago/Turabian Style**

Chen, Yongxin, Kamal Djidjeli, and Zheng-Tong Xie.
2022. "Freestream Turbulence Effects on the Aerodynamics of an Oscillating Square Cylinder at the Resonant Frequency" *Fluids* 7, no. 10: 329.
https://doi.org/10.3390/fluids7100329