# The Effect of Single Dielectric Barrier Discharge Actuators in Reducing Drag on an Ahmed Body

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Simulations

#### SDBD Actuator Model

## 3. Experimental Setup

## 4. Validation Study

#### SDBD Actuator Model Validation

## 5. Results

#### 5.1. Numerical Simulations

#### 5.2. Experiments

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Comparing the mean velocity profiles at $x/L=0.25$ and $y/L=0$ for the the grid quality study at $Re=7.68\times {10}^{5}$.

**Figure 3.**Distribution of mean ${n}^{+}$ on the Ahmed body surfaces at Reynolds number of $Re=7.68\times {10}^{5}$.

**Figure 6.**Different locations of single dielectric barrier discharge (SDBD) on the surface of the Ahmed body.

**Figure 9.**Profiles of the streetwise velocity component in the wake region of ${35}^{\circ}$ slant angle of the Ahmed body.

**Figure 11.**Velocity vector plot over actuator region for ${35}^{\circ}$ slant angle case 2. (

**a**) actuator off, (

**b**) actuator on.

**Figure 12.**Streamlines on the symmetry plane for slant angle ${35}^{\circ}$ and $Re=2.25\times {10}^{5}$. (

**a**) Actuator off, (

**b**) case 1, (

**c**) case 2, (

**d**) case 5.

**Figure 13.**Streamlines on the symmetry plane for slant angle ${35}^{\circ}$ and $Re=7.68\times {10}^{5}$: (

**a**) actuator off; (

**b**) case 2.

**Figure 14.**Pressure coefficient profile in the rear and slanted surface at $Re=2.25\times {10}^{5}$, before (clean) and after (case 2) actuators.

**Figure 15.**Isosurface plot of ${\lambda}_{2}^{*}=-0.004$ and contours of surface pressure for case 2 with the slant angle of ${35}^{\circ}$. For (

**a**,

**b**) the SDBD actuator is off, and for (

**c**,

**d**) the SDBD actuator is on.

**Figure 16.**Isosurface plot of ${\lambda}_{2}^{*}=-0.004$ and contours of surface pressure for case 5 with the slant angle of slant angle of ${35}^{\circ}$. For (

**a**,

**b**), the SDBD actuator is off, and for (

**c**,

**d**) the SDBD actuator is on.

**Figure 17.**(

**a**) Turbulent kinetic energy, (

**b**) streamwise velocity and (

**c**) coefficient of pressure for case 5 at $x/L=0.001$, $z/L=0.15$ (near wake) and $Re=2.25\times {10}^{5}$.

**Table 1.**Comparison of drag coefficients based on different spatial grid distributions at $Re=7.68\times {10}^{5}$.

Name | Slant Angle | ${\mathbf{N}}_{\mathbf{total}}$ | $\overline{{\mathbf{C}}_{\mathbf{d}}}$ | $\mathbf{\Delta}\overline{{\mathbf{C}}_{\mathbf{d}}}$ |
---|---|---|---|---|

Grid 1 | ${25}^{\circ}$ | $2.4\times {10}^{6}$ | 0.292 | − |

Grid 2 | ${25}^{\circ}$ | $5.7\times {10}^{6}$ | 0.280 | $4.02\%$ |

Grid 3 | ${25}^{\circ}$ | $7.5\times {10}^{6}$ | 0.277 | $1.07\%$ |

Grid 1 | ${35}^{\circ}$ | $2.4\times {10}^{6}$ | 0.280 | − |

Grid 2 | ${35}^{\circ}$ | $5.7\times {10}^{6}$ | 0.267 | $4.85\%$ |

Grid 3 | ${35}^{\circ}$ | $7.5\times {10}^{6}$ | 0.266 | $0.68\%$ |

Study | Slant Angle | Method | $\overline{{\mathbf{C}}_{\mathbf{d}}}{}_{(\times {10}^{-1})}$ |
---|---|---|---|

Present Study | ${25}^{\circ}$ | Numerical SST $k-\omega $ | 2.80 |

Guilmineau et al. [13] | ${25}^{\circ}$ | Numerical SST $k-\omega $ | 3.21 |

Meile et al. [22] | ${25}^{\circ}$ | Experimental | 2.99 |

Angelis et al. [23] | ${25}^{\circ}$ | Experimental | 2.85 |

Present Study | ${35}^{\circ}$ | Numerical SST $k-\omega $ | 2.67 |

Guilmineau et al. [13] | ${35}^{\circ}$ | Numerical SST $k-\omega $ | 2.99 |

Meile et al. [22] | ${35}^{\circ}$ | Experimental | 2.79 |

Angelis et al. [23] | ${35}^{\circ}$ | Experimental | 2.58 |

Study | Experimental ${}_{(\times {10}^{-1})}$ | Numerical ${}_{(\times {10}^{-1})}$ | $\mathbf{\Delta}\overline{{\mathbf{C}}_{\mathbf{d}}}$ |
---|---|---|---|

Without Actuator | 3.30 | 3.03 | $8.2\%$ |

Actuator Off | 3.20 | 3.06 | $4.4\%$ |

Actuator On | 3.00 | 2.86 | $4.7\%$ |

**Table 4.**The maximum velocity and body force magnitude generated by an SDBD actuator at zero freestream velocity.

Present Study | Bouchmal [19] | Suzen et al. [18] | |
---|---|---|---|

Maximum velocity [m/s] | 0.93 | 0.93 | 1 |

Body Force Magnitude [N/m${}^{3}$] | 1456 | 1444 | 1250 |

**Table 5.**Numerical results at a frequency of 4.5 kHz and at $Re=2.25\times {10}^{5}$ for an Ahmed body with a slant angle of 25${}^{\circ}$. Here, $\Delta {C}_{d}$ denotes the drag reduction, and $\Delta {C}_{d-Act}$ denotes the actuator drag reduction (+ sign indicate reduced drag).

${25}^{\circ}$ | ${35}^{\circ}$ | |||||||
---|---|---|---|---|---|---|---|---|

Study | Status | V (kV) | ${\mathbf{C}}_{\mathbf{d}}\phantom{\rule{0.166667em}{0ex}}{}_{(\times {10}^{-1})}$ | $\Delta {\mathbf{C}}_{\mathbf{d}}$ | $\Delta {\mathbf{C}}_{\mathbf{d}-\mathbf{Act}}$ | ${\mathbf{C}}_{\mathbf{d}}\phantom{\rule{0.166667em}{0ex}}{}_{(\times {10}^{-1})}$ | $\Delta {\mathbf{C}}_{\mathbf{d}}$ | $\Delta {\mathbf{C}}_{\mathbf{d}-\mathbf{Act}}$ |

No Actuator | - | - | 3.03 | - | - | 2.87 | - | - |

Case 1 | OFF | - | 3.04 | −0.33% | - | 2.85 | +0.60% | - |

Case 1 | ON | 8 | 3.02 | +0.33% | +0.66% | 2.83 | +1.40% | +1.20% |

Case 1 | ON | 10 | 3.06 | −0.99% | −0.66% | 2.91 | −1.40% | −2.00% |

Case 1 | ON | 12 | 3.10 | −2.31% | −1.98% | 2.93 | −2.20% | −2.80% |

Case 2 | OFF | - | 3.06 | −0.99% | - | 2.87 | 0.00% | - |

Case 2 | ON | 8 | 3.03 | 0.00% | +0.99% | 2.86 | +0.30% | +0.30% |

Case 2 | ON | 10 | 3.00 | +0.99% | +1.98% | 2.85 | +0.70% | +0.70% |

Case 2 | ON | 12 | 2.85 | +5.61% | +6.60% | 2.78 | +3.10% | +3.10% |

Case 3 | OFF | - | 3.02 | +0.33% | - | 2.91 | −1.50% | - |

Case 3 | ON | 8 | 3.02 | +0.33% | 0.00 % | 2.92 | −1.70% | −0.20 % |

Case 3 | ON | 10 | 3.02 | +0.33% | 0.00% | 2.92 | −1.70% | −0.20% |

Case 3 | ON | 12 | 3.01 | +0.66% | +0.33% | 2.93 | −2.10% | −0.60% |

Case 4 | OFF | - | 3.00 | +0.99% | - | 2.93 | −2.10% | - |

Case 4 | ON | 8 | 3.01 | +0.66% | −0.33% | 2.94 | −2.40% | −0.30% |

Case 4 | ON | 10 | 3.00 | +0.99% | 0.00% | 2.95 | −2.80% | −0.70% |

Case 4 | ON | 12 | 3.00 | +0.99% | 0.00% | 2.95 | −2.90% | −0.80% |

Case 5 | OFF | - | 3.01 | +0.66% | - | 2.87 | 0.00% | - |

Case 5 | ON | 8 | 3.00 | +0.99% | +0.33% | 2.87 | 0.00% | 0.00% |

Case 5 | ON | 10 | 2.98 | +1.65% | +0.99% | 2.86 | +0.30% | +0.30% |

Case 5 | ON | 12 | 2.95 | +2.64% | +1.98% | 2.84 | +1.00% | +1.00% |

Study | Slant Angle | ${\overline{\mathbf{C}}}_{\mathbf{d}-\mathbf{on}(\times {10}^{-1})}$ | ${\overline{\mathbf{C}}}_{\mathbf{d}-\mathbf{off}(\times {10}^{-1})}$ | $\mathbf{\Delta}{\mathbf{C}}_{\mathbf{d}}$ |
---|---|---|---|---|

Case 2 | ${25}^{\circ}$ | 2.86 | 3.06 | +6.50% |

Case 2 | ${35}^{\circ}$ | 2.78 | 2.87 | +3.14% |

Multi-Configuration | ${25}^{\circ}$ | 2.89 | 3.03 | +4.62% |

Multi-Configuration | ${35}^{\circ}$ | 2.84 | 2.90 | +2.12% |

Study | Status | V (kV) | ${\mathbf{C}}_{\mathbf{d}}$ | $\mathbf{\Delta}{\mathbf{C}}_{\mathbf{d}}$ | $\mathbf{\Delta}{\mathbf{C}}_{\mathbf{d}-\mathbf{Act}}$ |
---|---|---|---|---|---|

No Actuator | - | - | 0.33 | - | - |

Case 2 | OFF | - | 0.32 | +3.00% | - |

Case 2 | ON | 12 | 0.30 | +9.10% | +6.10% |

Multi-Config. | OFF | - | 0.32 | +3.00% | - |

Multi-Config. | ON | 8 | 0.31 | +6.10% | +3.10% |

Multi-Config. | ON | 10 | 0.31 | +6.10% | +3.10% |

Multi-Config. | ON | 12 | 0.30 | +9.10% | +6.10% |

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**MDPI and ACS Style**

Karimi, S.; Zargar, A.; Mani, M.; Hemmati, A. The Effect of Single Dielectric Barrier Discharge Actuators in Reducing Drag on an Ahmed Body. *Fluids* **2020**, *5*, 244.
https://doi.org/10.3390/fluids5040244

**AMA Style**

Karimi S, Zargar A, Mani M, Hemmati A. The Effect of Single Dielectric Barrier Discharge Actuators in Reducing Drag on an Ahmed Body. *Fluids*. 2020; 5(4):244.
https://doi.org/10.3390/fluids5040244

**Chicago/Turabian Style**

Karimi, Saber, Arash Zargar, Mahmoud Mani, and Arman Hemmati. 2020. "The Effect of Single Dielectric Barrier Discharge Actuators in Reducing Drag on an Ahmed Body" *Fluids* 5, no. 4: 244.
https://doi.org/10.3390/fluids5040244