# Effective Distance for Vortex Generators in High Subsonic Flows

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{*}increases, so a decrease in h* results in a decrease in L. MVGs must be placed closer to the location of separation because VGs have limited effectiveness downstream. The value of L for MVGs is about 5–30 h (M = 0.2) [3] or the order of 10 δ (low-speed flow) [2].

## 2. Experimental Setup

#### 2.1. Transonic Wind Tunnel

^{3}with the maximum pressure of 50 bars). A rotary perforated sleeve valve controls the stagnation pressure, p

_{o}. High-pressure air is discharged into a stilling chamber through flow spreaders. Inside the stilling chamber, acoustic baffles, three screens, and a honeycomb absorb control valve noise and reduce the intensity of freestream turbulence. The constant-area test section, which is assembled using solid sidewalls and perforated top/bottom walls (6% porosity), has a cross-sectional area of 600 mm × 600 mm and a length of 1500 mm. The operational Mach number ranges from 0.2 to 1.4. The unit Reynolds number has a maximum value of 2 × 10

^{7}/m. The centerline Mach number uniformity for the test section is 0.005. The value of p

_{o}is 172 ± 0.5 kPa and the stagnation temperature is 28–32 °C for this study. The test conditions are monitored and recorded using a National Instruments system (PXIe-8840 RT, PXI-7846, PXI-6511, and PXI-6513; Austin, TX, USA).

#### 2.2. Test Model

_{δ}, are 1.63 and 1.69 × 10

^{5}.

_{v}, was 0.2 δ and, for the Ramp type, w

_{r}, it was 0.5 δ. Pearcey [15] determined that there is increased mixing at the inner edge of the boundary layer as spacing increases. The spacing, D, between VGs was 3 δ (or D/h = 3–15) in order to establish an effective vortex pattern (D/h ≥ 3). An array of seven VGs was created. For the CRV type, the front, d, and rear, s, spacing are 1 δ and 0.5 δ, respectively.

#### 2.3. Instrumentation and Data Acquisition System

_{p}(=$\frac{p-{p}_{\infty}}{q})$ is 0.43%, where p

_{∞}is the freestream static pressure and q is the dynamic pressure.

_{ref}/I, and the pressure ratio, p/p

_{ref}, where I

_{ref}and p

_{ref}are the reference intensity and pressure, respectively. The value for B(T), which is the pressure sensitivity, is 0.66%/kPa. Thermal quenching results in a temperature sensitivity of −0.4%/°C. For the wind tunnel test, the I

_{ref}was recorded by taking the wind-off images that were immediately captured after the wind tunnel was shut down. A median filter function (removing noise from an image) in the Matlab program was used to transform the luminescent intensity to surface pressure using the calibration curve [23].

## 3. Results and Discussion

#### 3.1. Surface Pressure Pattern

_{p}pattern for a flat plate in the presence of VGs are shown in Figure 7 and Figure 8. For M = 0.64 and h* = 1.0, CRV VGs produce a stronger vortex (lower pressure). The vortex for CRV VGs decays faster than that for CoV and Ramp VGs. This is because of the interaction between two opposite vortices. For an airfoil, VGs are typically positioned on the upper surface to mitigate BLS. An increase in the value of C

_{p}upstream of the VGs represents greater device-induced drag and a reduction in lift, which mitigates the benefits. The induced vortex is weakest for Ramp VGs. For M = 0.83, the effect of the VG configuration on the global surface pressure pattern is similar to that for M = 0.64. There is a stronger induced vortex near the VGs as M increases.

_{p}distributions (h* = 0.2, 0.5, and 1.0) for M = 0.83 and y* = 0 that were measured using Kulite sensors and the PSP technique are shown in Figure 9. The horizontal axis is the normalized streamwise location, x* (=x/δ), and the origin is 3 mm downstream of the trailing edge of the VGs. There is a good agreement between two measurement techniques upstream of the CoV VGs. An increase in the value of C

_{p}represents a decrease in lift (performance penalty). The discrepancy downstream of the VGs is associated with thermal quenching using the PSP technique. More details are given in the following section. The downstream favorable pressure gradient is created by device-induced streamwise co-rotating vortices.

_{p,max}. The data for M = 0.64 and 0.83 are shown in Figure 10. The Kulite measurements (solid symbols) show that for CRV and CoV VGs, there is an increase in the value of C

_{p,max}as h* increases, but not for Ramp VGs. This is due to the spatial resolution of the discrete pressure taps. The PSP data (hollow symbols) show the effect of h* on the value of C

_{p,max}. Conventional VGs (h* = 1.0) result in an increase in value of C

_{p,max}more significantly than MVGs (h* = 0.2 and 0.5). The effect is particularly noticeable for CRV and Ramp VGs. This is a factor in quantifying the overall performance of VGs for BLS control.

#### 3.2. Effective Distance

_{p}in the presence of CoV VGs at y* = 0 is shown in Figure 11. The pressure measurements using Kulite sensors show that the value of C

_{p}for M = 0.64 and 0.83 is approximately the same upstream of the VGs. There is a greater downstream favorable pressure gradient for M = 0.83 because the vortex is stronger. A mild variation in the value of C

_{p}at farther downstream locations is determined.

^{*}(=8.4) for Ramp VGs is a maximum for h* = 0.5. The value of h* has a slight effect on L* for CRV VGs. For M = 0.64, the effect of h* on L* is less significant for all three VG configurations. The device-induced vortices in the presence of CoV VGs extend for a longer distance.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A(T) | constant for PSP calibration curve |

B(T) | pressure sensitivity |

C_{p} | surface pressure coefficient |

C_{p,max} | peak surface pressure coefficient upstream of vortex generator |

d | front spacing of counter-rotating vortex generator |

D | spacing between adjacent vortex generators |

h | height of vortex generator |

I | intensity of the emission |

I_{ref} | reference intensity of emission |

h* | normalized height of vortex generator, h/δ |

l | length of vortex generator |

L | effective distance |

L* | normalized effective distance, L/δ |

M | freestream Mach number |

p_{o} | stagnation pressure |

p_{ref} | reference pressure (= ambient pressure) |

q | dynamic pressure |

s | rear spacing of counter-rotating vortex generator |

T | temperature |

u | velocity |

U_{∞} | freestream velocity |

w | width of vortex generator |

x | coordinate along the centerline of model surface |

x* | normalized streamwise distance, x/δ |

α | angle of incidence of vortex generator |

δ | incoming boundary-layer thickness |

y | coordinate in spanwise direction |

y* | normalized spanwise distance, y/δ |

z | vertical distance from the surface |

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Parameters | Value |
---|---|

h/δ | 0.2, 0.5, 1.0 |

l/δ | 1.0 |

D/δ | 3.0 |

w_{v}/δ | 0.2 |

w_{r}/δ | 0.5 |

s/δ | 0.5 |

d/δ | 1.0 |

α | 15° |

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**MDPI and ACS Style**

Chung, P.-H.; Huang, Y.-X.; Chung, K.-M.; Huang, C.-Y.; Isaev, S.
Effective Distance for Vortex Generators in High Subsonic Flows. *Aerospace* **2023**, *10*, 369.
https://doi.org/10.3390/aerospace10040369

**AMA Style**

Chung P-H, Huang Y-X, Chung K-M, Huang C-Y, Isaev S.
Effective Distance for Vortex Generators in High Subsonic Flows. *Aerospace*. 2023; 10(4):369.
https://doi.org/10.3390/aerospace10040369

**Chicago/Turabian Style**

Chung, Ping-Han, Yi-Xuan Huang, Kung-Ming Chung, Chih-Yung Huang, and Sergey Isaev.
2023. "Effective Distance for Vortex Generators in High Subsonic Flows" *Aerospace* 10, no. 4: 369.
https://doi.org/10.3390/aerospace10040369