# Propeller Slipstream Effect on Aerodynamic Characteristics of Micro Air Vehicle at Low Reynolds Number

^{*}

## Abstract

**:**

^{5}. Significant aerodynamic performance benefits could be found for a propeller in the tractor configuration. The numerical results showed that the propeller slipstream effect on the wings was highly dependent on the size of the propeller, and the major slipstream effect was working at 60% inboard wingspan, whereas less effects were observed towards the wingtip. The propeller slipstream increased the local angle of attack on the up-going blade side. This effect simultaneously augmented the section lift. The unsteady Reynolds-averaged Navier–Stokes (URANS) simulations helped to improve understanding of the interaction of the propeller wake and the wing-fuselage, which is an important aspect to guide the design of future efficient and controllable micro air vehicles. The results indicated that, in MAV designs, the slipstream from the propeller had a significant effect on the wing aerodynamics, regarding both performance and stability of the vehicle.

## 1. Introduction

_{m}), as an important characteristic, is often overlooked when considering airfoil performance. The flying wing configuration is normally desired for MAV designs and such a flying wing configuration must make a negative slope of the pitching moment curve (C

_{m,α}), and Cm at α = 0° (C

_{m,0}) must be positive (+) (Nickel and Wohlfahrt, 1994) [18]. The requirements cannot be achieved by a traditional cambered airfoil, and hence a reflex camber must be designed which has a concave shape and locates near the trailing edge of the airfoil, shifting the pressure distribution aft and placing more upward force on the lower surface of the airfoil. However, the addition of reflex camber reduces the overall lift generation capabilities of the airfoil but is necessary for stable MAV flight. The limited amount of literature on cambered plate wings with a reflexed camber designed at trailing edge for low Reynolds numbers suggests that there is a need to expand the understanding of propeller-induced flow effects on reflex camber aerodynamic characteristics. To accomplish this goal, a computational study was performed to investigate the mutual aerodynamic influences between an MAV configuration and its tractored propeller. This is based on our previous studies on laminar separation bubbles [8] and planform effects [11] in a similar low Reynolds number range. The propeller–wing mutual interaction was studied and the comparison of wing aerodynamic characteristics of propeller on and off was conducted.

## 2. Computational Framework

#### 2.1. Governing Equations and Solution Details

**n**is the normal vector to the control volume surface, and S is the control volume surface area.

_{ia}), indicating 2.55D

_{ia}and 7.6D

_{ia}, respectively. The stationary domain, on the other hand, was set as a cubic block with a distance being roughly about 12.75D

_{ia}, 20.5D

_{ia}, and 12.75D

_{ia}for upstream, downstream, and height, respectively; see Figure 1e,f. Structured mesh for both rotational and stational domain was generated, shown in Figure 1a,b. Mesh with high quality was considered and generated due to the importance of interpolation relationship between the interface surfaces, and a mapped mesh topology was proceeded between the interface boundaries. For the rotating domain, two O-topologies were created to cover the propeller and the center spinner segments. The O-grid included 10 cells normal to the propeller wall surface with a first cell distance of 2 × 10

^{−5}m. There were 30 grid points in propeller radial direction and 56 grid points in the circumferential direction. A cylindrical wake block was used to ensure a good resolution of the blade wakes and the tip vortices, which have a significant influence on the MAV domain. For the outer domain, a similar mesh topology as we showed in the validation case section was used. The total size of the mesh was about 8 × 10

^{6}nodes.

#### 2.2. Specifications of Validation Cases

^{+}value of the first cell distance was ensured to be in the order of O(1). The stretching ratio for the mesh was less than or equal to 1.2. Validation results are summarized in Table 1. The aerodynamic results comparisons, in Figure 2e,f, showed that Model 2 (wind tunnel settings) gave a better lift coefficient as compared with the experimental data. The results from Model 1 were close to the experimental data at low incidences but under-predicted at high incidences. The drag values showed a similar conclusion, showing potentially the stronger wall interference at higher incidences (Mueller [9]). From the mesh sensitivity study, the larger mesh size showed a reasonably better comparison than the coarse mesh. Therefore, for the propeller-wing-fuselage model presented later in this paper, a similar mesh topology, as shown for the validation case, was chosen and applied on the wing-fuselage part. The mesh for the propeller was integrated with the wing-fuselage mesh. The general topology is that an O-grid mesh was used around the propeller, and an H-type mesh was on the outer zone inside the rest of the rotating domain (details are shown in Figure 1).

#### 2.3. Present Investigation Case

^{5}.

_{1}/$\overline{c}$), maximum concave and reflex camber (h

_{2}/$\overline{c}$), maximum concave camber location (d

_{1}/$\overline{c}$), and the maximum reflex camber location (d

_{1}/$\overline{c}$); further details are shown in Ref. [11].

_{f}, of 0.059 m, rear height, h

_{t}, of 0.021 m, and a total length h

_{L}= 0.216 m (Table 2). This design of the fuselage was dictated by the size and placement of the components. The fuselage layout affects the center of gravity margin and hence the static stability. For this purpose, the battery was designed to be movable to adjust the center of gravity. Another interesting point is how the fuselage affects the overall aerodynamics. Brion [29] simulated the fuselage and wing separately and the relevant aerodynamic forces are shown and discussed. However, the authors did not mention anything about the interaction between the wing and the fuselage. Ramamurti’s [30] numerical results showed MAV with fuselage reduced the lift-to-drag ratio dramatically and the drag for all configurations considered was nearly the same. The effects of the fuselage were also investigated in the present study.

_{t}= 0.068 m ahead of the wing planform. It had a diameter of 8 in, the pitch was 4 in, and the hub diameter was 0.014 m. Figure 3e shows the propeller geometry and the blade azimuth angle. The propeller rotated in an anti-clockwise direction viewing from the front, and Figure 3f shows the propeller geometric characteristics. The aerodynamic balance determined a horizontal component X and a vertical component Y of the total force acted on the MAV model (Figure 3d). To obtain the overall lift and drag force on the model, horizontal and vertical components (i.e., X and Y components) were transferred into L and D components (i.e., based on the incoming freestream coordinates), as shown in Equation (7).

^{−5}s with 30 sub-iterations was applied for this study (is equivalent to 0.5 degrees per time step). To have reasonable numerical results, the y

^{+}value of the first grid point in the order of O(1) was required. Figure 4 shows the numerical aerodynamic force coefficients versus the blade azimuth angle. It shows that periodic pulses were produced. This type of signature was found to be relatively independent of the advance ratio and appeared to be mainly associated with the local loading on the propeller itself.

## 3. Results and Discussion

#### 3.1. Propeller Slipstream Effects on Aerodynamic Performance

_{L,max}, was about 0.81 at the incidence of 12°. The propeller had negligible lift contribution at low angles of attack. The vertical stabilizer also showed a near zero contribution on the lift coefficient. At high angles of attack, the propeller had a significant contribution on the lift, which improved the maximum lift coefficient.

_{T}is roughly around −0.09). The main drag force was formed from the wing-fuselage. The vertical stabilizer, however, showed a negligible drag contribution for the entire range of incidences.

_{My}, indicated that the MAV with a propeller spun clockwise as viewed from the rear and the moments caused a left yaw. However, it was negligible at low incidences around α = 0° with a value of approximately 9e

^{−5}. A linear increase in the propeller yawing moment can be found from the plot.

_{Mα}, was about −0.0033 (for the linear section at incidence between 6° and 36°). The propeller showed a negative contribution on the statically longitudinal stability and a positive pitching moment slope can be identified in Figure 7f.

_{p}distribution on the Zimmerman wing at r/R = 1 (or z/b = ± 0.25). The C

_{p}distribution locations are indicated by the dash line for the up-going and down-going blade sides. Both C

_{p}with and without slipstream at 0° flight condition are presented in Figure 8b–e: the instantaneous C

_{p}distribution is plotted with various azimuth angles (in solid line). The C

_{p}plots show that the positive lift force was generated at the positive camber area around x/c = 0.25 and the negative lift force was obtained from the negative camber, which was located near the trailing edge. The negative lift was also generated at near leading-edge area on the down-going blade side. The averaged C

_{p}at 2z/b = 0.5, in Figure 8f, shows that a similar amount of lift was produced by the isolated MAV model and the MAV propeller model. However, the negative lift generated at the reflex camber region by the MAV propeller model was quite significant, and more negative lift was produced due to the propeller slipstream effect. In comparison, the amount of negative lift almost doubled as compared with the isolated MAVs (dashed line). Therefore, less reflex camber could be used for the MAV with the propeller installed. The turning point is the point where the negative lift force started to occur, which shifted toward the leading edge slightly due to the propeller slipstream effect.

#### 3.2. Propeller Slipstream Effect on the Flow Structure

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Non-conformal mesh interface for propeller MAV geometry, (

**a**) propeller-MAV configuration, (

**b**) detailed structured mesh for propeller-MAV, (

**c**) Mesh slice cut though domains, (

**d**) propeller structured mesh, (

**e**) computational domain in front view, and (

**f**) computational domain in side view.

**Figure 2.**Mesh topology and aerodynamic coefficients for wing planform, (

**a**) C-H mesh topology, (

**b**) mesh at leading-edge, (

**c**) O-grid mesh topology, (

**d**) spanwise mesh spacing, (

**e**) lift coefficient, (

**f**) drag coefficient.

**Figure 3.**MAV and propeller geometrical descriptions, (

**a**) Mav in top view, (

**b**) airfoil profile, (

**c**) MAV in 3D view, (

**d**) aerodynamic force decomposition, (

**e**) propeller azimuth angle, and (

**f**) propeller geometrical information(chord and pitch angle distribution).

**Figure 4.**Propeller time history aerodynamic forces coefficient development, (

**a**) drag coefficient, (

**b**) lift coefficient, (

**c**) side force coefficient, (

**d**) rolling moment coefficient, (

**e**) yawing moment coefficient, and (

**f**) pitching moment coefficient.

**Figure 6.**Propeller wing in tractor configuration, (

**a**,

**b**) wing local effective angle of attack due to propeller slipstream effect.

**Figure 7.**Averaged aerodynamic coefficients versus α at J = 0.468, (

**a**) lift coefficient, (

**b**) drag coefficient, (

**c**) side force coefficient, (

**d**) rolling moment coefficient, (

**e**) pitching moment coefficient, and (

**f**) yawing moment coefficient.

**Figure 8.**Instantaneous and averaged C

_{p}distributions at various spanwise location with α = 0° and ω = 555 rad/s, (

**a**) MAV wing spanwise locations, (

**b**,

**c**) wing spanwise location of 2z/b = 0.25 and propeller zimuth angle of 0° and 90°, (

**d**,

**e**) wing spanwise location of 2z/b = 0.5 and propeller zimuth angle of 0° and 90°, (

**f**) pressure coefficient comparison between isolated wing and wing-MAV at spanwise location of $2z/b=\pm 0.5$.

**Figure 9.**Instantaneous C

_{l}, C

_{d}distribution at various propeller azimuth angles at ω = 555 rad/s, (

**a**–

**d**) lift and drag coefficient distribution along the wing span with changing of propeller azimuth angle from ${0}^{\xb0}\mathrm{to}{135}^{\xb0}$.

**Figure 10.**Instantaneous flow structure around the MAV at $\mathsf{\alpha}={0}^{\xb0},\phi ={0}^{\xb0}$, (

**a**–

**d**) flow field around MAV, (

**e**,

**f**) airfoil sectional flow structure with up-going blade at spanwise location of 2z/b = 0.25 and 0.5, (

**g**,

**h**) airfoil sectional flow structure with down-going blade at spanwise location of 2z/b = 0.25 and 0.5, (

**i**) flow structure at propeller’s azimuth angle $\phi ={0}^{\xb0}$.

Case | Grid Size | C_{L} | C_{D} | |
---|---|---|---|---|

Model 1 | G1 | 190 × 135 × 60 | 0.1744 | 0.01913 |

G2 | 220 × 165 × 90 | 0.1775 | 0.02068 | |

G3 | 250 × 195 × 120 | 0.1781 | 0.02052 | |

Model 2 | G1 | 190 × 135 × 60 | 0.1899 | 0.01890 |

G2 | 220 × 165 × 90 | 0.1900 | 0.01877 | |

G3 | 250 × 195 × 120 | 0.1901 | 0.01879 | |

Experiment [1] | NA | 0.1906 ± 0.02 | 0.0220 ± 0.003 |

MAV model | ${\mathbf{d}}_{\mathbf{t}}\text{}\mathbf{(}{\mathbf{d}}_{\mathbf{t}}/\overline{\mathit{c}}$) | ${\mathbf{h}}_{\mathbf{f}}\text{}\mathbf{(}{\mathbf{h}}_{\mathbf{f}}/\overline{\mathit{c}}$) | ${\mathbf{h}}_{\mathbf{L}}\text{}\mathbf{(}{\mathbf{h}}_{\mathbf{L}}/\overline{\mathit{c}}$) | ${\mathbf{h}}_{\mathbf{t}}\text{}\mathbf{(}{\mathbf{h}}_{\mathbf{t}}/\overline{\mathit{c}}$) | $\mathbf{t}(\mathbf{t}/\overline{\mathit{c}}$) |

0.068(31.7%) | 0.059(26.6%) | 0.216(97.6%) | 0.021(9.49%) | 2e^{−3}(0.93%) |

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**MDPI and ACS Style**

Chen, Z.; Yang, F.
Propeller Slipstream Effect on Aerodynamic Characteristics of Micro Air Vehicle at Low Reynolds Number. *Appl. Sci.* **2022**, *12*, 4092.
https://doi.org/10.3390/app12084092

**AMA Style**

Chen Z, Yang F.
Propeller Slipstream Effect on Aerodynamic Characteristics of Micro Air Vehicle at Low Reynolds Number. *Applied Sciences*. 2022; 12(8):4092.
https://doi.org/10.3390/app12084092

**Chicago/Turabian Style**

Chen, Zhaolin, and Fan Yang.
2022. "Propeller Slipstream Effect on Aerodynamic Characteristics of Micro Air Vehicle at Low Reynolds Number" *Applied Sciences* 12, no. 8: 4092.
https://doi.org/10.3390/app12084092