# Research on Rotorcraft Blade Tip Vortex Identification and Motion Characteristics in Hovering State

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## Abstract

**:**

## 1. Introduction

_{2}for specific flow field data. The vortex structures can be well displayed by selecting appropriate vortex identification thresholds [13,16,17,23,24].

## 2. Experimental Equipment and Research Methods

#### 2.1. Experimental Model

#### 2.2. Experimental Equipment

_{1}− t

_{2}) through high-speed cameras. By image analysis technique, the particle displacement was obtained (namely, Δx and Δy). Through the particle displacement and exposure time interval (Δt), the velocity vector of each point in the flow field ΔV can be calculated by $U=\underset{{t}_{2}\to {t}_{1}}{\mathrm{lim}}\frac{{X}_{2}-{X}_{1}}{{t}_{2}-{t}_{1}}$ and $V=\underset{{t}_{2}\to {t}_{1}}{\mathrm{lim}}\frac{{Y}_{2}-{Y}_{1}}{{t}_{2}-{t}_{1}}$. Other flow parameters can be calculated based on the velocity of particles (including vorticity diagram of the flow field, velocity component diagram, flow diagram, swirl diagram, etc.).

#### 2.3. Ω Vortex Identification Method

_{max}[17,27]. Based on this, the vortex structures can accurately capture most of the conditions. This paper chooses the $\Omega $ method to analyze the blade tip vortex characteristics in hovering state. Because this paper is a two-dimensional flow field study, the calculation expression of the $\Omega $ vortex identification method becomes:

## 3. Results and Discussions

#### 3.1. Blade Tip Vortex Flow Structure

#### 3.2. Vortex Motion Characteristics Based on Vorticity

#### 3.3. Vortex Motion Characteristics Based on Q Criterion

#### 3.4. Vortex Motion Characteristics Based on Ω Criterion

#### 3.4.1. Ω Criterion Vortex Identification Results

#### 3.4.2. Vortex Boundary Identification

#### 3.5. Comparative Analysis of Blade Vortex Trajectory under Different Vortex Identification Criterion

## 4. Conclusions

- (1)
- When the rotor is at the hovering state, its aerodynamic characteristics can be considered as symmetrical and periodic changes;
- (2)
- At a certain rotate speed, as the collective pitch increases, the blade tension increases, the down washing speed of the blade tip vortex is increased, and the radial contraction is more serious. At the same time, the axial displacement is also faster;
- (3)
- With the increase of blade azimuth, blade tip vortex of the radial position moves to the hub and the axial location moves down gradually. At the same azimuth, with the collective pitch increases, blade tip vortex radial contraction is more obvious and axial displacement is larger;
- (4)
- In hovering state, as the blade tip vortex evolves, the vortex core radius gradually increases, and the vortex boundary gradually decreases. At a certain rotor rotate speed, as the collective pitch increases, the amplitude of the blade tip vorticity increases;
- (5)
- With different vortex identification methods, the obtained blade tip vortex center has a certain deviation. Compared with other methods, the Ω criterion can accurately distinguish vortices and shears, and can accurate quantitative the vortex core radius and vortex boundary.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Transient blade tip vortex flow structure (rotation speed of 2100 r/min, collective pitch of 6°).

**Figure 6.**Vorticity contours at different azimuth angles at the rotor rotation speed of 2100 r/min and the collective pitch of 6°.

**Figure 7.**Vorticity contours at different azimuth angles at the rotor rotation speed of 2100 r/min and the collective pitch of 9°.

**Figure 8.**Radial and axial trajectory of rotor blade tip vortex at different azimuth angles (based on vorticity criterion).

**Figure 9.**Vortex distribution identified by the Q criterion at different azimuth angles at the rotor rotation speed of 2100 r/min and the collective pitch of 6°.

**Figure 10.**Vortex distribution identified by the Q criterion at different azimuth angles at the rotor rotation speed of 2100 r/min and the collective pitch of 9°.

**Figure 11.**Radial and axial trajectory of rotor blade tip vortex at different azimuth angles (based on the Q criterion).

**Figure 12.**Vortex distribution identified by the Ω criterion at different azimuth angles at a rotor rotation speed of 2100 r/min and the collective pitch of 6°.

**Figure 13.**Vortex distribution identified by Ω criterion at different azimuth angles at a rotor rotation speed of 2100 r/min and the collective pitch of 9°.

**Figure 14.**Radial and axial trajectory of rotor blade tip vortex at different azimuth angles (based on the Ω criterion).

**Figure 15.**Vortex boundary with a rotor rotation speed of 2100 r/min and the collective pitch of 6° (Ω = 0.51).

**Figure 16.**Vortex boundary with a rotor rotation speed of 2100 r/min and the collective pitch of 9° (Ω = 0.51).

**Figure 17.**Schematic diagram of vortex boundary and vortex core boundary at 2100 r/min and 6° collective pitch.

**Figure 18.**Schematic diagram of vortex boundary and vortex core boundary at 2100 r/min and 9° collective pitch.

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**MDPI and ACS Style**

Du, H.; Kong, W.; Wang, Y.; Liu, W.; Huang, M.; Zhang, W.; Tang, M.
Research on Rotorcraft Blade Tip Vortex Identification and Motion Characteristics in Hovering State. *Symmetry* **2020**, *12*, 196.
https://doi.org/10.3390/sym12020196

**AMA Style**

Du H, Kong W, Wang Y, Liu W, Huang M, Zhang W, Tang M.
Research on Rotorcraft Blade Tip Vortex Identification and Motion Characteristics in Hovering State. *Symmetry*. 2020; 12(2):196.
https://doi.org/10.3390/sym12020196

**Chicago/Turabian Style**

Du, Hai, Wenjie Kong, Yan Wang, Wenjing Liu, Mingqi Huang, Weiguo Zhang, and Min Tang.
2020. "Research on Rotorcraft Blade Tip Vortex Identification and Motion Characteristics in Hovering State" *Symmetry* 12, no. 2: 196.
https://doi.org/10.3390/sym12020196