# Combined Passive/Active Flow Control of Drag and Lift Forces on a Cylinder in Crossflow Using a Synthetic Jet Actuator and Porous Coatings

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Synthetic Jet Actuators

#### 1.2. Porous Coatings

#### 1.3. Summary

## 2. Materials and Methods

#### 2.1. Experimental Setup

#### 2.2. Test Samples

#### 2.3. Numerical Setup

#### 2.4. Porous Medium Model

#### 2.5. SJA Model

#### 2.6. Domain and Boundary Conditions

- ‘Combined SJA and Porous Coating’ (SJPC) model by making both [E] and [F] internal boundaries.
- ‘Porous Coating Only’ (PCO) model by making [E] a wall and [F] an internal boundary.
- ‘SJA Only’ (SJO) model by making [F] a wall and [E] an internal boundary.

#### 2.7. Mesh Development

#### 2.8. Verification and Validation

## 3. Results

#### 3.1. Experimental Results

#### 3.1.1. Uncertainty and Baseline Values

#### 3.1.2. Combined Cases

#### 3.2. Numerical Results

#### 3.2.1. Effect of ${f}^{+}$

#### 3.2.2. Flow Field and Wake Behaviour

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

SJA | Synthetic jet actuator |

SJ | Synthetic jet |

RMS | Root-mean-square |

VR | Velocity ratio |

PPI | Pores per inch |

FDM | Fused deposition modelling |

SLA | Stereolithography |

URANS | Unsteady Reynolds-averaged Navier-Stokes |

SST | Shear stress transport |

UDF | User-defined function |

SJPC | Combined SJA and porous coating configuration |

PCO | Porous coating only configuration |

SJO | SJA only configuration |

## Appendix A. Actuator Surface UDF

- # inc lude “udf . h”
- DEFINE_PROFILE(unsteady_velocity, thread, position)
- {
- face_t f;
- realt = CURRENT_TIME;
- real V_max, L, freq, pi, time, h, d;
- d = 0.08695;
- pi = 3.14159;
- freq = 4;
- L = 0.0571 * 2;
- V_max = L * freq * pi * d;
- begin_f_loop (f, thread)
- {
- F_PROFILE(f, thread, position) = V_max * sin(2 * pi * freq * t);
- }
- end_f_loop(f, thread)
- }

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**Figure 1.**Experimental apparatus used in current study (

**a**) Combined SJA and porous coating test sample (

**b**) Water tunnel test section and SJA setup (full details in Section 2.1).

**Figure 3.**Test samples used in experimental phase of current study (

**a**) Smooth baseline and SJO configuration (top), SJPC and PCO configuration (bottom), (

**b**) schematic showing assembly of cap and main body.

**Figure 4.**Mesh and boundary conditions for the CFD model of the cylinder in cross-flow with combined SJA and porous coating. (

**a**) Outer domain and (

**b**) detailed view of the cylinder.

**Figure 5.**Averaged experimental results of drag and RMS lift coefficient as a function of momentum coefficient ${C}_{\mu}$ for each configuration, with error bars indicating experimental uncertainty. (

**a**) ${C}_{d}$ vs. ${C}_{\mu}$ and (

**b**) ${C}_{l\left(rms\right)}$ vs. ${C}_{\mu}$.

**Figure 7.**Distribution of pressure coefficient ${C}_{p}$ around the cylinder for different SJA actuation frequencies (

**a**) ${f}^{+}=0.15$, (

**b**) ${f}^{+}=1$, and (

**c**) ${f}^{+}=4$.

**Figure 8.**Numerical results for the dependence of drag and lift coefficient as a function of SJA frequency for each configuration: (

**a**) ${C}_{d}$ vs. ${f}^{+}$ and (

**b**) ${C}_{l\left(rms\right)}$ vs. ${f}^{+}$.

**Figure 9.**Comparison of instantaneous flow velocity fields at a phase angle corresponding to (

**a**,

**c**,

**e**) maximum expulsion and (

**b**,

**d**,

**f**) maximum ingestion of the synthetic jet: (

**a**,

**b**) SJPC at ${f}^{+}=4$, (

**c**,

**d**) SJPC at ${f}^{+}=1$, (

**e**,

**f**) SJO at ${f}^{+}=1$.

**Figure 10.**Comparison of flow-fields of velocity magnitude: (

**a**) Instantaneous flow-field for SJPC at ${f}^{+}$ = 4 and PCO at comparable instants in the wake vortex roll-up period. (

**b**) Time-averaged flow-field for SJPC and SJO at ${f}^{+}$ = 1.

**Figure 11.**Summary of wake analysis: (

**a**) Turbulence intensity comparison in wake of SJPC at ${f}^{+}=4$ (top) and ${f}^{+}=1$ (bottom) at downstream locations $x/D=1.5,2.5,3.5$. (

**b**) Relationship between ${C}_{d}$ and wake width w for ${f}^{+}>1$.

Author | Study | $\mathit{\theta}$ (°) | ${\mathit{C}}_{\mathit{\mu}}$ (×10${}^{-3}$) | ${\mathit{f}}^{+}$ | $\mathit{Re}$ | $\Delta \phantom{\rule{3.33333pt}{0ex}}{\mathit{C}}_{\mathit{d}}$ |
---|---|---|---|---|---|---|

Amitay et al. [4] | Exp. | 0–180 | 0.03–0.6 | 11.5–20 | 4000, 7.5 $\times {10}^{4}$ | −30% |

Catalano et al. [6] | Num. | 60–120 | 6.5 | 2–14 | 500, 3900 | −13% |

Tensi et al. [23] | Exp. | (−)60–180 | 0.81–6.48 | 0.33–1 | 1.0 × 10${}^{5}$ | +36% |

Fujisawa & Takeda [5] | Exp. | 60–120 | 0.41–6.5 | 1–5 | 9.0 $\times {10}^{3}$ | −30% |

Glezer et al. [25] | Exp. | 60 | 0.6 | 1.15–23 | 7.6 $\times {10}^{4}$ | −17% |

Current study | Num. | 90 | 3.6 | 0.15–4 | 4.2 $\times {10}^{4}$ | $-46\%$ |

Author | Study | Coating | Turb. Model | $\mathit{R}\mathit{e}$ | $\Delta \phantom{\rule{3.33333pt}{0ex}}{\mathit{C}}_{\mathit{d}}$ | $\Delta \phantom{\rule{3.33333pt}{0ex}}{\mathit{C}}_{\mathit{l}\left(\mathbf{rms}\right)}$ |
---|---|---|---|---|---|---|

Bruneau et al. [11] | Num. | Full | DNS | 2400–3×10${}^{4}$ | - | −75% |

Naito et al. [31] | Num. | Full | DNS/LES | 100–1 × 10${}^{5}$ | +70% | −73% |

Zhang et al. [8] | Num. | Full | k-$\omega $/LES | 4.7 $\times {10}^{4}$ | −30% | - |

Klausmann & Ruck [10] | Exp. | Partial | - | 3 $\times {10}^{4}$–1.4 × 10${}^{5}$ | −13% | - |

Guinness & Persoons [9] | Num. | Partial | k-$\omega $ | 4.2 $\times {10}^{4}$ | −15% | −54% |

**Table 3.**Comparison of key flow characteristics for smooth cylinder at $Re$ = 4.2 $\times {10}^{4}$ in the current study and the literature.

Author | $\mathit{Re}$ | ${\mathit{C}}_{\mathit{d}}$ | ${\mathit{C}}_{\mathit{l}\left(\mathit{rms}\right)}$ | $\mathit{Sr}$ |
---|---|---|---|---|

Current | 4.2 $\times {10}^{4}$ | 1.18 | 0.969 | 0.255 |

Klausmann & Ruck [10] | 4.2 $\times {10}^{4}$ | 1.24 | - | - |

Roshko [43] | 4.2 $\times {10}^{4}$ | 1.2 | - | - |

Liu et al. [42] | 9.3 $\times {10}^{4}$ | 1.31 | 0.88 | 0.196 |

Case | ${\overline{\mathit{C}}}_{\mathit{d}}$ | ${\overline{\mathit{C}}}_{\mathit{l}\left(\mathit{rms}\right)}$ | ${\mathit{U}}_{{\overline{\mathit{C}}}_{\mathit{d}}}$ | ${\mathit{U}}_{{\overline{\mathit{C}}}_{\mathit{l}\left(\mathit{rms}\right)}}$ |
---|---|---|---|---|

Smooth | 1.17 | 0.117 | 0.03 | 0.01 |

SJO | 1.22 | 0.182 | 0.06 | 0.01 |

PCO | 0.99 | 0.029 | 0.03 | 0.003 |

SJPC | 1.02 | 0.158 | 0.03 | 0.01 |

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## Share and Cite

**MDPI and ACS Style**

Farrell, G.; Gibbons, M.; Persoons, T.
Combined Passive/Active Flow Control of Drag and Lift Forces on a Cylinder in Crossflow Using a Synthetic Jet Actuator and Porous Coatings. *Actuators* **2022**, *11*, 201.
https://doi.org/10.3390/act11070201

**AMA Style**

Farrell G, Gibbons M, Persoons T.
Combined Passive/Active Flow Control of Drag and Lift Forces on a Cylinder in Crossflow Using a Synthetic Jet Actuator and Porous Coatings. *Actuators*. 2022; 11(7):201.
https://doi.org/10.3390/act11070201

**Chicago/Turabian Style**

Farrell, Gearóid, Michael Gibbons, and Tim Persoons.
2022. "Combined Passive/Active Flow Control of Drag and Lift Forces on a Cylinder in Crossflow Using a Synthetic Jet Actuator and Porous Coatings" *Actuators* 11, no. 7: 201.
https://doi.org/10.3390/act11070201