Aerodynamic Performance Assessment of Distributed Electric Propulsion after the Wing Trailing Edge

Abstract

Distributed electric propulsion (DEP) with four propellers distributed along the rear edge of the wing (pusher DEP configuration) promote aerodynamic interactions to a higher level. To study the aerodynamic performance of DEP with the rear wing through simulations and experiments, the multi-reference frame (MRF) with sliding grid is combined with wind tunnel tests. The obtained results demonstrate that the lift and drag of DEP increase with the angle of attack (AoA) and are related to the relative position of the propellers and wing. The propeller has no significant effect on the lift of the wing, and the lift and the AoA remain linear when the AoA is less than 16°. By contrast, the lift coefficient is much higher than the baseline (isolated wing), and the lift is greatly improved with the increasing drag when the AoA is greater than 16°. This is because the flow around the wing of the pusher configuration remains attached due to the suction of the inflow of the propeller on the trailing edge vortex. In addition, the acceleration effect on the free flow improves the kinetic energy of the airflow, which effectively delays the separation of the airflow in the slipstream region.

1. Introduction

With the advantage of reducing noise and improving energy conversion efficiency, electric propulsion aircraft have captured the public fancy [1]. Research on the notion of electric propulsion for future aircraft is characterized by Leading Edge Asynchronous Propellers Technology (LEAP Tech) [2]. For distributed electric propulsion (DEP), propellers are distributed spanwise along the rear wing, increasing the lift at the stage of taking off or landing [3,4]. By changing the size and spacing of the propeller, the balance of the system increases the dynamic pressure over the wing [5]. Specially, it reduces the effect of gusts due to the increase in relative speed on the wing and increases safety through redundancy [6]. Additionally, the propulsion oriented in the wing wake leads to the drag decreasing with an increasing propulsive efficiency [3].

The United States and Europe have already invested in ground testing and flight tests related to electric propulsion [2,6,7,8,9], including LEAP Tech [1,10], X-57 [11], GL-10 [10], DEP propeller [12], and so on. Veldhuis, L.L.M. [13] and Rakshith, B. et al. [14] performed numerical simulations on the structure design with various parameters concerning the propeller/wing configuration. Patterson, M.D. et al. [15] designed the X-57 Maxwell with high-lift propellers and discussed the advantages and challenges of the high-lift propeller (HLP) at low speeds. Ananda Krishnan, G.K. et al. [16] compared the aerodynamic characteristics of the SR22 civil aircraft with a LEAP concept aircraft, demonstrating that the distributed propulsion system can reduce drag. An unmanned aerial vehicle (UAV) equipped with a DEP system is advantageous in a low-speed flight on a smaller scale. However, its unique flow characteristics pose the complexity of studying the aerodynamic performance of the DEP with numerical simulations and experiments [17].

Current studies involving DEP are mainly focused on simulating the effects of propellers on the wing or fuselage for large aircraft such as transport aircraft and solar aircraft. Patterson, M.D. et al. [15] at the Georgia Institute of Technology and Borer, N.K. et al. [18] at NASA conducted preliminary aerodynamic studies on the distributed propeller propulsion system. The vortex lattice calculation method only considered the influence of the slipstream on the wing. Simulations for mutual aerodynamic interference are limited to the analysis the flow field on the wing surface. Patterson, M.D. et al. [19] studied LEAP tech to analyze the aerodynamic interference between the propeller and the wing. Wang, J. et al. [20] showed the influence of wind field disturbance on the stability of a multirotor UAV with a dynamic model. Currently, playing a revolutionary role in the future of aviation, distributed propulsion technology involves the induced velocity of the propeller at each position of the wing set as the far field condition; the aerodynamic force of the wing is calculated separately [21,22,23,24]. Thus, it is not enough to use only one coupling method to study the aerodynamic interference of wings and propellers due to flow interactions.

Above all, considering that the complex low Reynolds aerodynamic environment imposes difficulties for the pusher configuration of the DEP system, the stronger rotor interferences and vortex movement in the outflow need verification through both simulations and experiments. Also, the strict design requirement for the location of the propeller requires knowing the effect of the horizontal spacing and vertical spacing, which is important for further flight tests. Eventually, it has a much wider reach than results from references that include only numerical simulations or experiments.

In Section 2, the pusher DEP configuration is presented with variables. In Section 3, lift and drag are obtained through wind tunnel testing. In Section 4, numerical simulations on the propulsion system are performed with FLUENT. Finally, Section 5 provides the conclusions.

2. Theoretical Analysis

As shown in Figure 1, DEP can be designed as a pusher configuration according to the relative positions of the propeller and the wing.

There are four small propellers equally distributed along the rear wing. The direction of rotation of the propeller is shown in Figure 1. Therefore, the propeller and the wing in the DEP interact with each other. This section analyzes the aerodynamics of the propeller and wing. In Figure 1, $D_{rp}$ is the dimensionless horizontal distance from the center of rotation of the propeller to the rear edge of the wing (where $c$ is the chord length of the propeller). $Xr (∆x/R)$ is the dimensionless vertical distance from the center of the propeller to the chord plane of the wing. The positive value indicates that the propeller is above the chord plane.

For the isolated rotor without interference, the lift and the drag coefficients are as follows [25]:

$$C_l=\frac{2L}{\rho V^{2}S}$$

(1)

$$C_d=\frac{2D}{\rho V^{2}S}$$

(2)

where L is lift, D is drag, $\rho$ is the density of air, V is the rotational velocity, and S is the reference area.

To characterize the aerodynamic interference between the propeller and the wing in the DEP system, the lift coefficient and the drag coefficient are applied to obtain the variation in the rotor interference [26].

3. Wind Tunnel Testing

3.1. Experimental Setup

A test bench was constructed as shown in Figure 2.

Four propellers were individually controlled by four motors and measured with a tachometer to determine the rotor speed. An ATI Gamma F&T sensor was connected on the wing to perform the force measurement. The DEP configuration is shown in

Table 1. Experimental parameters.

Part	Parameter	Numerical Value
Wind tunnel cross-section	-	600 mm × 600 mm
NACA4415 airfoil used for the wing	Span	300 mm
	Chord	150 mm
	Aspect Ratio	2
Four propellers	Diameter	76.2 mm
	Pitch	76.2 mm
	No. of blades	4
Operating conditions	Free-stream speed	18 m/s (typical)
	Prop RPM	18,000 rpm
	Wing Reynolds number	180,000

.

3.2. Error Analysis

The main sources of error in these experiments are the standard deviations of the rotational speed and the mean voltages from the force sensors. Typical values of the standard deviations of force are about 1% of the mean values. Rotational speed error is about 2.5 RPM per second. The statistical (random) error in the coefficient values for each run was estimated using the standard deviation of the repeated samples. This is a valid operation because, even though the dimensional values of the test variables are expected to vary from one run to another, the coefficient values are expected to be the same. To determine accuracy of the test measurements, all the key parameters were derived using the Kline–McClintok method [27]. Based on collected data, the partial derivatives computed can then calculate an estimate of systematic error. This was performed for Cl and Cd. Low uncertainty in all measured variables in all tests increases the confidence in the data and demonstrates a good measurement system. The values of uncertainty that are presented in this study were all calculated with 95% confidence levels.

3.3. Experimental Results

Figure 3 shows the distribution of Cl and Cd with different rotor locations, where $D_{rp}$ is the horizontal position, $Xr$ is the vertical offset, and ‘Baseline’ is the isolated wing without interference from any rotor.

It can be seen that the lift coefficient and drag coefficient increase linearly with the AoA in horizontal positions. The propeller has no significant effect on the lift of the wing when the AoA is less than 16°. It also can be seen that the drag coefficient of DEP with the pusher structure almost coincides with the baseline. However, the lift coefficient curve begins to show a decreasing trend when the AoA is higher than 16°. Specially, the lift coefficient of the DEP configuration is significantly higher than the baseline, which indicates that the lift is greatly improved. Also, the drag coefficient is also significantly increased in this case. Considering the effect of the horizontal position, as shown in Figure 3a,c, it can be seen that the lift and drag coefficients increased with the decreased horizontal distance. Additionally, the vertical offset seems have a greater impact on the aerodynamic performance of the wing. As a result, both the lift coefficient and drag coefficient of the wing gradually increase with the effect of the propeller. For the configuration with $Xr=1, { D}_{rp}=0.1c$, it is interesting to note that the lift coefficient obtained a maximum at 30° with an increasing tendency.

To determine the final performance of the DEP, Figure 4 presents the distribution of the L/D with different DEP configurations.

The lift is much improved at a higher AoA for the pusher configuration of the DEP, with a consistent tendency for a lower AoA. The effect of the horizontal position is more obvious for the performance of the wing, where the outflow is deformed by the propellers. Although L/D variation is within the experimental uncertainty limits with no significant difference inferred, delay in stall and increase in lift at a higher AoA are observed when the pusher props are placed above the wing chord line. Thus, it is important to study the flow field with a higher AoA.

4. Numerical Simulations

4.1. Simulation Setup

This step was taken to figure out the aerodynamic interference between the wing and propellers located at the rear of the wing as a pusher DEP. The geometry parameters are shown in

Table 2. Simulation parameters.

Part	Parameter	Numerical Value
Simulation calculation domain	-	600 mm × 600 mm
NACA4415 airfoil used for the wing	Span	300 mm
	Chord	150 mm
	Aspect Ratio	2
Four propellers	Diameter	76.2 mm
	Pitch	76.2 mm
	No. of blades	4
Boundary conditions	Speed inlet	18 m/s (typical)
	Rotation domain RPM	18,000 rpm

. For the simulation setup, the RANS model was applied to analyze the characteristics of the external flow field. Also, mesh refinement was performed on the propeller tip to capture the gradient of the physical field flow. In addition, the finite volume method was used to discrete the differential equations. Considering the low Reynolds number, the turbulence model k-w was selected to obtain the flow field of the DEP. Pressure correction and interpolation were performed using the semi-implicit method (SIMPLE) algorithm with the standard format. Momentum, energy equation, and turbulent viscosity are all in the second-order upwind discrete schemes. Finally, the sliding grid was used to deal with the interaction between the rotating and the stationary regions, and the multiple reference frame (MRF) method was applied as the initial condition for the slip mesh transient calculation. The mesh distribution is shown in Figure 5.

Four different mesh grids were used to verify the grid independence, as shown in

Table 3. Grid independence for $Xr=0,{ D}_{rp}=0.15c$, and AoA = 20°.

$\mathbf{Rotated} \mathbf{Region} \mathbf{Grid} \mathbf{(}\times {10}^5\mathbf{)}$	$\mathbf{Total} \mathbf{Grid} \mathbf{(}\times {10}^5\mathbf{)}$	Cl	Cl Error (%)	Cd	Cd Error (%)
1.89	85.47	0.95	−10.2	0.44822	+5.8
2.14	107.51	0.987	−7.9	0.43678	+3.1
2.55	133.64	1.013	−5.5	0.43466	+2.6
2.83	167.29	1.014	−5.4	0.43424	+2.5

.

It can be found that the error decreased with the increasing grids, and it is stable for the grid around 25 $\times {10}^5$, which was applied for the following simulations.

4.2. Simulation Result

To figure out the increased lift for a higher AoA, as presented in the experiments, as shown in Figure 6, we selected the velocity distribution at the 43% span section of pusher structures for an AoA ranging from 20° to 30°.

For the horizontal position at $D_{rp}=0.1c$, by changing the vertical offset of the propeller, it can be found that there is a significant difference in the inflow of the propeller where the upper inflow is mixed with the outflow of the wing. For the flow field near the trailing edge of the propeller, a deflection was found in the inflow direction of the propeller at $Xr=0.5$ with the increasing velocity. It was more obvious for the propeller mounted above the paddle. On the contrary, the interaction with the lower wing was weak. For the two pusher structures at a 30° AoA with a distance of $0.1c$ from the trailing edge and a vertical offset of $Xr=0.5$ and $Xr=1$, the airflow through the wing interacted with the rotor flow field, creating a stabilized leading edge vortex [28]. The vortex at $Xr=0.5$ interacted with the inflow of the propeller, and the vortex at $Xr=1$ began to affect the propeller’s tip vortex and down wash flow, forming another smaller vortex behind the paddle. Therefore, when the trailing edge of the wing approached the tip of the blade, the eddy current action was more intense, and the $Xr=1$ with a large vertical offset weakened the eddy current intensity above the wing, thereby increasing the lift.

Figure 7 shows a pressure contour for DEP structures ranging from 20° to 30°.

The pressure difference in the leading edge of the wing increased slightly with the positions for a lower AoA. Thus, the lift of the DEP system did not increase significantly. For AoA = 30°, the negative pressure area increased significantly, which directly increased wing lift and drag. In Figure 7c, it can be seen that the increment for the negative pressure on the wing reached the maximum when the distance from the propeller center to the rear edge was $0.1c$ to $0.15c$. Within a certain range, the small change in the flow direction of the propeller in the DEP has no significant effect on the aerodynamic performance. Similarly, the vertical installation position of the propeller significantly changes the DEP flow field distribution. When the central axis of the propeller is above the wind chord, the negative pressure region of the wing decreases. In short, the aerodynamic performance of the pusher DEP structure is affected by the vertical installation position of the propeller. Specifically, the vertical offset from the bottom improves the increment in the lift of the wing.

Figure 8 shows the vorticity distribution of the pusher configuration at 20° and 30°.

It can be seen that when the propeller is installed above the chord, the tip vortex of the wing acts on the propeller and merges with the propeller downwash flow. Also, the vortex of the wing interacts with the propeller vortex, where the trailing edge vortex is more obvious with the propeller vortex system at $Xr=1$. This indicates that the interference between the propeller and the wing may be advantageous to improve the performance of the DEP.

Figure 9 shows the pressure distribution at 43% spanwise.

In Figure 9a, it can be seen that the streamline changed with the pusher structure, which also affected the pressure distribution. The negative pressure of the trailing edge of the wing at $0.1c$ was slightly higher than that at $0.15c$, indicating that the change along the flow direction is advantageous to improve the aerodynamic interference and flight duration for a hover state. Figure 9b shows the pressure of the DEP with different vertical offsets at 30°. The pressure for $Xr=0.5$ is affected by the upper airfoil vortex with a sudden change. The pressure at the middle section is convexly distributed, with a slightly higher positive pressure than $Xr=1$. For a larger vertical offset $Xr=1$, the pressure distribution is relatively stable, with a higher maximum than the $Xr=0.5$, which indicated that this structure has better lift performance.

Figure 10 shows the lift distribution of propellers for the pusher DEP configuration.

It can be seen that propellers 1 and 3 obtained less lift, and propeller 2 was less affected by the wing tip vortex or the adjacent propellers with a larger lift. Propeller 4 was totally emerged in the wing tip vortex, with an increasing force variation. In addition, lift variation in $Xr=0{, D}_{rp}=0.1c$, and $Xr=0{, D}_{rp}=0.15c$ was completely consistent, and $Xr=0.5{, D}_{rp}=0.1c$, and $Xr=1{, D}_{rp}=0.1c$ also showed a similar tendency. However, $Xr=0{, D}_{rp}=0.1c$ and $Xr=0.5{, D}_{rp}=0.1c$ showed better performance. This further verifies that the closer the propeller is, the more interference there is. From the vertical offset, the propeller is mounted above the trailing edge string for better lift performance.

5. Conclusions

This paper proposed a pusher DEP configuration to study the aerodynamic performance of the mutual interference between the propeller and wing with wind tunnel tests and numerical simulations. Conclusions are as follows:

(1)

The propeller has no significant effect on the lift of the wing when the AoA is less than 16°. However, the lift coefficient is much higher than the baseline (isolated wing), and the lift of the pusher DEP system is significantly increased up to 73–87% without any decrease in L/D. In contrast, the drag coefficient is also higher than that of the isolated wing. With a higher AoA, it is interesting to note that the lift for the pusher configuration was also improved.

(2)

The wing of the pusher structure stalled at 16° AoA. This may be caused by the acceleration of the axial airflow affected by the propeller and the interference from the inflow and downwash caused by the slipstream. Accordingly, it increased the drag coefficient, especially for the DEP with a smaller horizontal distance between the propeller and the trailing edge of the wing. Also, a delay in stall and an increase in lift at a high AoA were observed when the pusher props were placed above the wing chord line.

(3)

The trailing edge vortex of the wing for the pusher DEP structure interacted with the flow field of the propeller, and it showed an increase in lift and drag increase. L/D variation was within the experimental uncertainty limits of the baseline case (isolated wing), and no significant difference was found. The propeller in the pusher DEP was subjected to the blocking effect of the wing or the eddy current of the trailing edge of the wing, and the lift was significantly increased.