# Aerodynamic Effects of Knitted Wire Meshes—CFD Simulations of the Flow Field and Influence on the Flow Separation of a Backward-Facing Ramp

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## Abstract

**:**

## 1. Introduction

## 2. Setup

## 3. Numerical Method

## 4. Numerical Setup

## 5. Verification and Validation

#### 5.1. Grid Sensitivity Analysis

- Monotonic convergence: 0 < R < 1;
- Oscillatory convergence: −1 < R < 0;
- Monotonic divergence: R > 1;
- Oscillatory divergence: R < −1.

#### 5.2. Turbulence Model Sensitivity Analysis

#### 5.3. Validation with DNS Data

## 6. Results

#### 6.1. Effect on Flow Separation

#### 6.2. Induced Vortices

#### 6.3. Effect of the Number of Rows

#### 6.4. Effect of the Type B Knitted Wire Mesh Geometry

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Wire meshes under investigation.

**Left**: type A,

**right**: type B. A total of four stitches distributed in two rows are shown for each type.

**Figure 3.**Line probes S1 to S5 and R1 to R5 on the planes S and R used to evaluate the results. The lines indicate the planes that are oriented normal to the channel bottom.

**Figure 6.**Boundary layer profile in comparison with LES data [34] for an upstream turbulence intensity of 5%.

**Left**: normalized axial velocity,

**right**: normalized root-mean-square velocity fluctuations.

**Figure 9.**Simulated axial velocity magnitude at R4 for different turbulence models. The ordinate is clipped at Z = 20.

**Figure 10.**Simulated axial velocity magnitude at S4 for different turbulence models. The ordinate is clipped at Z = 20.

**Figure 11.**Simulated velocity magnitude profiles around the backward-facing ramp for the type A knitted wire mesh with two rows using different turbulence models.

**Figure 12.**Vertical distributions of axial velocity for the k-$\omega $ SST model in comparison with DNS data by Le and Moin [38] at several positions downstream of the step normalized by step height H. (1): X/H = 4, (2): X/H = 6, (3): X/H = 10, (4): X/H = 15.

**Figure 13.**Simulated flow separation affected by the knitted wire mesh with two rows. The velocity is shown on the plane R in between two stitches. On the bottom channel walls, the y+ value is presented. SB denotes a separation bubble, SP a stagnation point, RCA a recirculation area and RAF a reattached flow.

**Figure 14.**Simulated flow separation affected by the knitted wire mesh with two rows. The velocity in the horizontal direction is shown on the plane R in between two stitches. The arrows indicate recirculation areas.

**Figure 15.**Simulated flow separation affected by the knitted wire mesh with two rows. The velocity is shown on the symmetry plane S of a stitch. On the bottom channel walls, the y${}^{+}$ value is presented. SB denotes a separation bubble.

**Figure 16.**Simulated pressure distribution on the channel wall. The ramp edge is located at X/H${}_{2}$ = 14.

**Figure 17.**Isosurface of the Q-criterion around the knitted wire mesh. The red arrows mark the elongated streamwise vortex structures. The dashed lines indicate the knitted wires. The isovalue is set to 100,000 1/s${}^{2}$.

**Figure 18.**Streamlines around the knitted wire mesh with two rows. (1) Streamlines follow the curvature of the wire and extend from under the stitch towards the centerline. (2) Streamlines separate from 1, running inside of the stitch and over the wire towards the lateral outside of the stitch. (3) Streamlines running over the inside of the stitches. (4) Streamwise vortices emerging from 1, 2 and 3.

**Figure 19.**Comparison of simulated Q-criterion, turbulent kinetic energy, vorticity and axial velocity on a cross-section in the wake of the knitted wire mesh at X/H${}_{2}$ = 13.17.

**Figure 20.**Q-criterion and velocity for between one and five knitted wire rows at X/H${}_{2}$ = 11.5, 13.17, 14.83, 16.5 and 18.17, respectively. The X values represent the same distance downstream in the wake of the different wire meshes.

**Figure 21.**Simulated velocity field at the backward-facing ramp for type A and type B knitted wire meshes.

**Figure 22.**Simulated Q-criterion at the same downstream distance in the wake of the knitted wire meshes.

**Left**: type A at X/H${}_{2}$ = 13.17,

**right**: type B at X/H${}_{2}$ = 10.9. The X values represent the same distance downstream in the wake of the different wire meshes.

Parameter | Type A | Type B |
---|---|---|

Wire diameter | 0.28 mm | 0.7 mm |

Stitch width | 5.35 mm | 10 mm |

Stitch length | 4.7 mm | 4 mm |

Knitted wire mesh thickness h | 0.95 mm | 3.62 mm |

Parameter | Measure |
---|---|

H${}_{1}$ | 2 H${}_{2}$ |

H${}_{2}$ | 10 mm |

L${}_{1}$ | 6.66 H${}_{2}$ |

L${}_{2}$ | 3.2 H${}_{2}$ |

L${}_{3}$ | 20 H${}_{2}$ |

$\alpha $ | 20${}^{\circ}$ |

R1 | R2 | R3 | R4 | R5 | S1 | S2 | S3 | S4 | S5 | |
---|---|---|---|---|---|---|---|---|---|---|

X/H${}_{2}$ | 11.5 | 12.5 | 15.49 | 17.0 | 19.0 | 11.5 | 12.5 | 15.49 | 17.0 | 19.0 |

Y/H${}_{2}$ | 0 | 0 | 0 | 0 | 0 | 2.86 | 2.86 | 2.86 | 2.86 | 2.86 |

Line Probe | Metrics: Coarse vs. Medium | Metrics: Medium vs. Fine | ||||
---|---|---|---|---|---|---|

MRAE | NMSE | V | MRAE | NMSE | V | |

R1 | 0.0065 | 1.4$\times {10}^{-4}$ | 0.99 | 0.0032 | 2.3$\times {10}^{-5}$ | 1.00 |

R2 | 0.0052 | 7.7$\times {10}^{-5}$ | 0.99 | 0.0019 | 7.2$\times {10}^{-6}$ | 1.00 |

R3 | 0.0104 | 4.6$\times {10}^{-5}$ | 0.99 | 0.0107 | 5.8$\times {10}^{-5}$ | 0.99 |

R4 | 0.1022 | 2.6$\times {10}^{-4}$ | 0.93 | 0.0476 | 4.4$\times {10}^{-5}$ | 0.97 |

R5 | 0.0109 | 2.2$\times {10}^{-5}$ | 0.99 | 0.0139 | 5.8$\times {10}^{-5}$ | 0.99 |

S1 | 0.0405 | 1.8$\times {10}^{-3}$ | 0.96 | 0.0286 | 1.3$\times {10}^{-4}$ | 0.97 |

S2 | 0.1702 | 5.3$\times {10}^{-3}$ | 0.91 | 0.0260 | 7.4$\times {10}^{-5}$ | 0.97 |

S3 | 0.0268 | 2.0$\times {10}^{-4}$ | 0.97 | 0.0057 | 5.4$\times {10}^{-6}$ | 0.99 |

S4 | 0.0091 | 9.2$\times {10}^{-5}$ | 0.99 | 0.0059 | 1.3$\times {10}^{-5}$ | 0.99 |

S5 | 0.0243 | 3.7$\times {10}^{-5}$ | 0.98 | 0.0112 | 1.3$\times {10}^{-5}$ | 0.99 |

Mean | 0.0406 | 8.0$\times {10}^{-4}$ | 0.97 | 0.0155 | 4.2$\times {10}^{-5}$ | 0.99 |

Line Probe | Metrics: Medium vs. Grid-Independent | |||
---|---|---|---|---|

MRAE | NMSE | V | U | |

R1 | 0.0082 | 1.7$\times {10}^{-4}$ | 0.99 | −0.0847 |

R2 | 0.0066 | 6.1$\times {10}^{-5}$ | 0.99 | −0.0552 |

R3 | 0.0173 | 1.0$\times {10}^{-4}$ | 0.98 | −0.0136 |

R4 | 0.0607 | 2.7$\times {10}^{-4}$ | 0.97 | 0.0346 |

R5 | 0.0064 | 6.9$\times {10}^{-5}$ | 0.99 | −0.0141 |

S1 | 0.0273 | 4.9$\times {10}^{-4}$ | 0.97 | 0.0462 |

S2 | 0.0448 | 1.3$\times {10}^{-3}$ | 0.96 | 0.2211 |

S3 | 0.0075 | 3.8$\times {10}^{-5}$ | 0.99 | 0.0210 |

S4 | 0.0050 | 1.6$\times {10}^{-5}$ | 1.00 | 0.0111 |

S5 | 0.0225 | 4.1$\times {10}^{-5}$ | 0.98 | −0.0094 |

Mean | 0.0206 | 2.5$\times {10}^{-4}$ | 0.98 | 0.0157 |

Turbulence Model | Reattachment Length Clean in mm | Mean Reattachment Length Knitted Wire Mesh in mm | Mean Reduction |
---|---|---|---|

k-$\omega $ SST | 72.3 | 58.5 | 19.0% |

Standard k-$\omega $ | 77.5 | 67.9 | 12.3% |

$\gamma $-$R{e}_{\theta}$-k-$\omega $ SST | 62.0 | 48.9 | 21.2% |

Low Re k-$\epsilon $ | 74.1 | 59.0 | 20.4% |

Realizable k-$\epsilon $ | 34.5 | 31.3 | 9.2% |

Low Re SA | 62.4 | 53.6 | 14.2% |

Number of Rows | Mean Reattachment Length in mm | Mean Reattachment Length Clean in mm | Mean Reattachment Length Reduction |
---|---|---|---|

1 | 70.5 | 72.3 | 2.4% |

2 | 58.5 | 72.3 | 19.0% |

3 | 54.6 | 72.3 | 24.5% |

4 | 53.7 | 72.3 | 25.7% |

5 | 63.7 | 72.3 | 12.3% |

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**MDPI and ACS Style**

Harmening, J.H.; Devananthan, H.; Peitzmann, F.-J.; el Moctar, B.O.
Aerodynamic Effects of Knitted Wire Meshes—CFD Simulations of the Flow Field and Influence on the Flow Separation of a Backward-Facing Ramp. *Fluids* **2022**, *7*, 370.
https://doi.org/10.3390/fluids7120370

**AMA Style**

Harmening JH, Devananthan H, Peitzmann F-J, el Moctar BO.
Aerodynamic Effects of Knitted Wire Meshes—CFD Simulations of the Flow Field and Influence on the Flow Separation of a Backward-Facing Ramp. *Fluids*. 2022; 7(12):370.
https://doi.org/10.3390/fluids7120370

**Chicago/Turabian Style**

Harmening, Jan Hauke, Harish Devananthan, Franz-Josef Peitzmann, and Bettar Ould el Moctar.
2022. "Aerodynamic Effects of Knitted Wire Meshes—CFD Simulations of the Flow Field and Influence on the Flow Separation of a Backward-Facing Ramp" *Fluids* 7, no. 12: 370.
https://doi.org/10.3390/fluids7120370