For the analysis of propeller slipstream flow fields, extensive computational methods have been developed through long-term research both domestically and internationally. These include the vortex lattice method, the panel method, the actuator disk method, the multiple reference frame method, and the sliding mesh method, among others. The vortex lattice method, the panel method and actuator disk method are characterized by their simplicity and low computational grid requirements. However, the actuator disk method does not account for the rotational effects of the airflow upstream of the propeller, and the specification of blade loading relies heavily on engineering experience and heuristics. Consequently, it is primarily used in the conceptual design and preliminary analysis stages [33–37].

The MRF method and the sliding mesh method are among the most commonly employed approaches for slipstream simulation. The MRF method is a steady-state approximation. In this approach, the grid remains stationary, and the motion of the rotating region is simulated by introducing a rotating reference frame. In contrast, the sliding mesh method is a transient simulation technique that employs an unsteady solver, with the mesh dynamically moving over time. Since MRF assumes a steady flow, it offers higher computational efficiency but cannot accurately capture unsteady flow features. The sliding mesh method provides higher accuracy but demands significantly greater computational resources and time. While results from the sliding mesh method generally agree more closely with experimental data, the MRF method is also capable of capturing the overall flow field variations, and the observed trends are consistent with those obtained using the sliding mesh method. Considering the focus of this study—analyzing the influence of propeller slipstream effects on parameters such as wing/aircraft lift and drag—the MRF method adequately fulfills the research requirements.

The Reynolds-averaged Navier-Stokes (RANS) equations are solved numerically. For the rotating domain, the equations are formulated in a rotating reference frame. The governing equations in integral form are given in Equation 1. ∂ ∂ t ∭ V W dV + ∯ ∂ V H · n dS − ∯ ∂ V H ν · n dS + ∭ V G dV = 0 (1) where the definitions of all variables follow those in Ref. [38].

To validate the accuracy of the MRF method for computing the flow field around rotating bodies, a verification was performed using the measured surface pressure data for the Caradonna-Tung (C-T) rotor published in Reference [39]. The C-T rotor comprises two straight, untwisted blades of constant chord. The airfoil section is the NACA 0012 profile, and the blade radius is 1.143 m. A schematic of the model is shown in Figure 1.

The computational setup matched the experimental conditions: a tip Mach number (Mtip) of 0.52, a collective pitch angle (θc) of 0°, and a rotational speed (Ω) of 1,500 rpm.

A comparison between the pressure distributions obtained from the MRF simulation and the experimental data is presented in Figure 2 for several radial stations: r/R = 0.50, 0.68, 0.80, where c denotes the chord length. As shown in the Figure 2, the results calculated using the MRF method exhibit the same trends as the experimental pressure distributions and demonstrate good overall agreement with the test data.

The boundary conditions adopted in the present study include velocity inlet, pressure outlet, no-slip adiabatic wall, and symmetry plane, together with the sliding interface at the junction between the stationary and rotating domains. The sliding interface is modeled using a general mesh interface approach, which ensures the conservation of mass, momentum, and energy fluxes across both sides of the interface.

The cylindrical interface illustrated in Figure 3 is employed to represent the sliding interface. This cylinder encloses the rotating components of the propeller, namely the blades and the hub. All regions outside the rotating domain are defined as stationary domains. The interface between the two flow domains is handled via a fluid-fluid coupling scheme.

Figure 4 shows the boundary condition setup. As the inflow velocity is prescribed, the inlet boundary is specified as a velocity inlet with the inflow velocity defined. Solid surfaces such as the propeller blades are set as no-slip walls. The outlet is specified as a pressure outlet with an ambient pressure of 101 kPa and zero pressure gradient, while the far-field open boundary is defined using velocity components.

Three propeller configurations were selected for analysis, as illustrated in Figure 5: a five-bladed propeller with a disk radius of 285 mm, another five-bladed propeller with a 330 mm radius, and a four-bladed propeller with a 300 mm radius. The nacelle connecting the propeller to the wing segment was individually optimized to account for the different hub radii. The rotational direction for all propellers is clockwise when viewed from the upstream direction, as shown in Figure 6.

Based on an analysis of the influence of a single propeller’s slipstream on the aerodynamic characteristics of a wing section, the optimal propeller configuration was determined. This configuration was subsequently applied to a distributed propeller arrangement to investigate the aerodynamic performance of an aircraft without high-lift devices under low-altitude and low-speed conditions, and to assess the impact of the slipstream on the wing.

To avoid inter-propeller slipstream interference while considering propeller radius and wing span, five propellers were arranged along each wing. All distributed propellers rotate in the same clockwise direction (viewed from upstream) as the single propeller, consistent with Figure 6.

The full aircraft model, depicted schematically in Figure 7, features a conventional low-wing design with a vertical tail. Key dimensions include a wingspan of 11.9 m, a length of 7.7 m, a height (without landing gear) of 1.38 m, a wing area of 3.46 m², and a maximum fuselage width of 1.3 m. To reduce computational cost, a symmetric half-span model was employed for the simulations. The propellers are numbered 1 to 5 from the fuselage side towards the wingtip.

Structured hexahedral meshes were generated for both the single propeller configuration and the distributed propeller aircraft configuration. For all cases, the rotating components (blades and a portion of the hub) were embedded within a cylindrical rotational domain, as illustrated in Figure 3. To ensure high mesh quality, the computational domain was partitioned into two distinct zones: one encompassing the cylindrical rotational domain around the propeller, and the other covering the remaining stationary fluid region. These zones were connected using an overset (chimera) grid technique.

A grid independence study was performed for both the single propeller and distributed propeller aircraft configurations to ensure the adequacy of the selected mesh resolutions, as shown in Figure 8. For the single propeller case, the total mesh size was approximately 2 million cells across both stationary and rotating domains, distributed over 175 blocks, as shown in Figure 9. For the half-model simulation of the full aircraft, the mesh consisted of roughly 9 million cells across 1200 blocks, as shown in Figure 10. The near-wall mesh was refined to achieve a first-layer cell height satisfying y⁺≤1. In this full-aircraft simulation, the nacelles were omitted, and each propeller was modeled within its own rotating domain grid. The aircraft geometry was segmented into three main components: wing, fuselage, and tail. Forces and moments on each propeller were monitored individually.

To enable a direct comparison with the baseline configuration without propellers, a separate mesh was generated. This was done by removing the propeller components and their rotational domains from the existing full-aircraft mesh topology while preserving the node distribution and topology in the stationary domain, followed by local re-gridding.

To satisfy the power requirements of the propeller motor and account for the aircraft takeoff and landing conditions, a single propeller configuration is investigated at inflow velocities ranging from 28 m/s to 38 m/s, angles of attack from 0° to 10°, and propeller rotational speeds from 2000 rpm to 5,000 rpm.

Based on the numerical results and analysis of the single propeller configuration, an appropriate propeller configuration is selected for the distributed -propeller aircraft. A freestream velocity of 33 m/s is then adopted for the takeoff and landing analysis.

The numerical conditions for both single and distributed propeller configurations are summarized in Table 1.

The effect of rotational speed on the aerodynamic characteristics was investigated for three propeller configurations to compare their slipstream impacts. Figure 11 presents the lift and drag characteristics of the wing section for the three propeller types at different rotational speeds, under an inflow velocity of 28 m/s and an angle of attack of 0°.

In Figure 11, the slipstream effects of propellers with different radii (denoted as r285, r300, and r330) are compared. The resulting aerodynamic force coefficients of the wing segments under the propeller slipstream are represented by the ratio Cr.

Figure 11a shows that the influence of propeller slipstream on the wing-section lift coefficient exhibits a consistent trend with rotational speed for different propeller radii. Specifically, the lift coefficient decreases as the propeller radius increases. At any given speed, the configuration with the 285 mm radius propeller (CLr285) yields the highest lift coefficient. Conversely, for a fixed radius, the lift coefficient increases with rotational speed.

As shown in Figure 11b, the drag coefficient, however, exhibits a more complex dependence on radius. The drag coefficient, however, exhibits a more complex dependence on radius. The maximum drag coefficient occurs for the 285 mm propeller at 2000 rpm. As rotational speed increases, the drag coefficient for the 285 mm propeller (CDr285) decreases steadily. In contrast, the drag coefficients for the 300 mm (CDr300) and 330 mm (CDr330) propellers increase, with CDr300 demonstrating a steeper rate of increase than CDr330.

To further analyze the variation in the drag coefficient for the r285 case shown in Figure 11, the present study takes the 285 mm-radius propeller flow field as an example and selects the location at y = −0.5R for analysis, as illustrated in Figure 12a. The effects of the propeller slipstream on the drag characteristics are investigated at rotational speeds of 2000 and 5,000 rpm, with an inflow velocity of 28 m/s and an angle of attack of 0°.

As shown in Figures 12b,c, the slipstream downstream of the propeller becomes more concentrated at the y = −0.5R location. Meanwhile, the flow deflection effect is enhanced, with an obvious downward deflection that alters the flow from a horizontal state before impinging on the airfoil segment. The component of the aerodynamic force perpendicular to the wind-axis streamline is opposite to the component parallel to the chord direction. Consequently, the contributions to drag from these aerodynamic components partially cancel each other out. Furthermore, due to the velocity jump at the interface between the rotating and stationary domains arising from their differing velocity components, the analysis here focuses solely on the influence of the slipstream on the stationary domain, with the internal flow variations within the rotating domain not being discussed.

At the y = +0.5R location, the airflow deflects upward. A comprehensive comparison of the deflection magnitudes indicates that the downward deflection is stronger than the upward deflection. This mechanism leads to a gradual reduction in the drag coefficient with increasing rotational speed, which explains the flow characteristics presented in Figure 11b.

The flow field on the wing symmetry plane (y = 0) was analyzed to examine the effects of inflow velocity and angle of attack on the propeller slipstream. Figure 13 presents the velocity contours of the slipstream field on the symmetry plane (y = 0) for propellers of different radii rotating at 4,500 rpm. The minimum drag coefficient (CDr330) occurs under the inflow conditions specified in Figure 13a. As shown in Figure 13a, this correlates with the strongest airflow deflection within the slipstream zone generated by the r330 propeller, whereas the deflection is weakest for the r285 propeller. Comparing Figure 13a with Figure 13c under identical inflow conditions reveals that a propeller with a smaller disc radius produces a stronger and more concentrated flow acceleration, yielding a more pronounced slipstream effect. Furthermore, a comparison between Figures 13a,b indicates that at a fixed inflow velocity, a smaller-radius propeller exerts a greater influence on redirecting the slipstream and enhancing its velocity as the angle of attack increases. A comparison of Figures 13b,c shows that the extent of the slipstream zone increases with inflow velocity. In contrast, the high-velocity region on the wing upper surface induced by the slipstream diminishes at 38 m/s compared to 28 m/s.

To further investigate the modifications in the slipstream-induced flow field, the surface pressure on the wing section was analyzed, with the results presented in Figure 14. Figure 14 shows the pressure distribution on the upper wing surface for propellers of different radii at a rotational speed of 4,500 rpm.

Due to differences in blade design, the four-bladed r300 propeller induces a left-rotating airflow downstream. This rotation creates a low-pressure region on the rightwing section (as viewed from upstream). In contrast, as seen in Figure 14a, the five-bladed r285 and r300 propellers generate a low-pressure zone on the leftwing section due to the opposite sense of swirl imparted by the blade geometry.

As the angle of attack increases, the negative pressure zone on the wing surface expands, attributed to the enhanced impact of the high-speed slipstream (Figures 14b,c). Concurrently, at a fixed angle of attack, an increase in freestream velocity causes this low-pressure region to extend further upstream. However, the magnitude of the negative pressure peak is lower under high-speed conditions compared to low-speed conditions. This reduction in suction peak strength leads to a gradual decrease in the lift coefficient with increasing velocity.

As shown in Figure 15, according to the analysis of the lift and drag coefficients for the r285 propeller at different inflow velocities, the slipstream effect induced at a fixed rotational speed of 4500 rpm gradually weakens as the inflow velocity increases. Meanwhile, the inflow velocity itself is insufficient to strengthen the slipstream induction, resulting in a decrease in the lift coefficient of the wing segment. In addition, the drag coefficient increases gradually with rising inflow velocity.

It is clear that the propeller slipstream accelerates the flow along the axial direction, deflects the airflow direction, and increases the local inflow velocity. The static pressure changes abruptly across the propeller disk, which has a significant influence on the overall flow field over the wing. Furthermore, the overall aerodynamic characteristics are strongly affected by different propeller configurations, and can be altered by adjusting specific geometric or operational parameters.

The aerodynamic characteristics of the complete aircraft, including lift, drag, and lift-to-drag ratio (L/D), with and without propeller slipstream, are presented in Figure 16 at the typical flow conditions of 8° angle of attack, 4,500 rpm, and 33 m/s freestream velocity.

Figure 16 shows that the lift coefficient increases linearly with angle of attack up to approximately 8°, both with and without slipstream. Beyond this point, the rate of increase diminishes due to progressive flow separation on the wing surface.

The application of propeller slipstream increases the lift-curve slope and extends the linear range of the lift coefficient compared to the clean configuration. Furthermore, it improves the stall characteristics and increases the stall angle of attack.

Near an 8° angle of attack—relevant for takeoff and landing—the slipstream augments the lift coefficient by more than 50%. This demonstrates that a propeller positioned to energize the flow over the wing can effectively enhance lift during low-speed flight phases.

However, the slipstream also increases the drag coefficient. At 8° angle of attack, the drag is nearly double that of the non-slipstream condition. Consequently, the lift-to-drag ratio is lower across most angles of attack when the slipstream is present, except at 0° angle of attack where a slight improvement is observed.

A comprehensive analysis of the aerodynamic characteristics reveals that, in the presence of slipstream, both lift and drag are increased compared to the clean (no-slipstream) configuration. However, the incremental gain in drag outweighs the gain in lift, leading to an overall reduction in the aircraft’s lift-to-drag ratio.

The differentials in lift and drag coefficients between the slipstream and clean configurations are plotted in Figure 17, elucidating the impact of slipstream on aerodynamic performance. Both differentials exhibit a growing trend with increasing angle of attack. Notably, within an angle of attack of 6°, the lift differential rises significantly, whereas the drag differential shows no marked increase. This behavior may be attributed to the slipstream’s influence on the local flow: the propeller partially alters the direction of the incoming airflow ahead of the wing, resulting in a slight reduction in the effective angle of attack for wing sections within the slipstream. Concurrently, the energy imparted by the slipstream to the wing’s boundary layer mitigates the drag rise typically associated with flow separation.

At a propeller rotational speed of 4,500 rpm, an angle of attack of 8°, and an inflow velocity of 33 m/s, the pressure contours on the upper and lower surfaces of the full aircraft with and without slipstream effects are presented in Figure 18.

The rotation of the propeller accelerates the incoming flow, leading to an increase in the static pressure ahead of the wing. In the slipstream case, the low-pressure region on the upper wing surface is mainly distributed downstream of the propeller. Viewed along the flow direction, the wing leading-edge propeller rotates clockwise, inducing upward flow deflection on the inner side and downward deflection on the outer side of the slipstream.

Combined, these effects make the low-pressure region on the wing more intense and extensive compared with the no-slipstream condition. Behind a single propeller, the low-pressure region on the wing tip side is larger than that on the fuselage side.

In the slipstream case, the high-pressure region on the upper wing surface is also mainly located downstream of the propeller. On the wing leading edge behind a single propeller, the high-pressure zone on the tip side is larger than that on the fuselage side. For the lower wing surface, the high-pressure region becomes more intense and extensive when the slipstream effect is present.

To examine the effects of a single propeller’s slipstream on the wing in detail, Propeller No. 3 was selected for analysis. The pressure distributions on the wing at spanwise positions of ±0.6R from the propeller axis were compared, and the locations of these wing sections are illustrated in Figure 19. Finally, the pressure coefficient distributions over the wing sections at ±0.6R, with and without propeller slipstream, are presented in Figure 20.

Analysis of the pressure distributions in Figure 20 indicates distinct differences between the slipstream and clean-configuration cases. At the +0.6R station, the wing section exhibits higher suction under slipstream conditions. While the suction peak locations are nearly coincident, the leading-edge lower-surface pressure peak is more pronounced with the slipstream.

Conversely, at the −0.6R station, the leading-edge suction with slipstream is greater, but the associated suction peak magnitude is smaller compared to the clean configuration. The leading-edge lower-surface pressure is also higher in the presence of slipstream.

Despite the significant asymmetry in pressure distribution across the propeller axis, both sides contribute positively to the total lift generation.

Consistent with the previous section, Propeller No. 3 is still selected as the analysis object. The focus is placed on the flow phenomena reflected in the wing pressure and velocity contours, with and without the propeller slipstream effect (4,500 rpm), over the angle of attack range of 0°–14°.

Streamlines and pressure contours of the wing at the spanwise location y = 3.373 m (on the axis of the No. 3 propeller) are presented in Figures 21, 22 for both slipstream and no-slipstream cases. When the slipstream is present, the flow velocity downstream of the propeller is higher than in the no-slipstream case, and the deflection of the high-speed region is less pronounced with variations in the angle of attack. At low angles of attack, the propeller blades induce an upwash that deflects the slipstream below the wing toward the upper surface as the angle of attack increases.

As shown in Figure 22, the low-pressure region between the propeller and the wing is disrupted by the upwash flow with increasing angle of attack, which delays the suction peak and leads to a lower flow velocity near the leading edge compared with the clean wing configuration.

The pressure distribution along the wing chord at the spanwise station y = 3.373 m is shown in Figure 23. These data were obtained at a freestream velocity of 33 m/s and a propeller speed of 4,500 rpm, with increasing angle of attack.

The pressure distribution over the wing section is altered by the propeller slipstream. The downwash component decreases the local angle of attack, while the upwash component increases it. At low angles of attack, the suction peak near the leading edge is higher with slipstream than without it. As the angle of attack increases, this peak diminishes in the presence of slipstream because the propeller-induced flow washes over the leading edge, disrupting the local airflow. In contrast, without slipstream, the suction peak generally increases with angle of attack due to the accelerating flow over the leading edge.

On the pressure surface (lower surface), the peak pressure exhibits a consistent trend in both configurations, gradually becoming less negative (or more positive) with increasing angle of attack. However, due to the higher induced velocity, the pressure magnitudes on the wing are generally greater with slipstream than without it.

Figure 24 presents a comparison of the spanwise pressure distribution at a wing section located at x = 2.2m, under an 8° angle of attack with clockwise blade rotation, for conditions with and without slipstream.

In the absence of slipstream, the pressure distribution on the wing’s lower surface follows a regular pattern. With slipstream, however, the suction (negative pressure) on the upper surface is enhanced at most spanwise locations compared to the clean configuration.

A distinct pressure modulation induced by the propeller blades is evident. On the left side of the propeller axis, the slipstream generates five localized suction peaks on the upper surface, each corresponding to a region of lower pressure compared to the non-slipstream case. Concurrently, five distinct high-pressure zones appear on the lower surface.

Figure 25 presents the rotational vortex structures at different spanwise sections along the wing. Section 1 is located downstream of the propeller and upstream of the wing leading edge, while Section 2 is positioned near the wing trailing edge. Figure 25b shows the rotational vortex field in the region downstream of the propeller and upstream of the wing. Prior to interaction with the wing, the extent of the vortex field approximates the propeller disk area, retaining a relatively complete structure. However, at the wing trailing edge (Figure 25c), the vortex structure is no longer intact. The presence of the wing significantly disrupts the vortex, which develops in the spanwise direction at this location, thus exerting a considerable influence on the pressure distribution over the wing.

The power required by the propeller increases with its rotational speed. The measured relationship between power and speed is presented in Figure 26. The power for each propeller was measured individually, and the average value was used to represent the power at each rotational speed in the plot.

As shown in Figure 26, power consumption is relatively low at low rotational speeds, measuring below 100 W at 2000 rpm. The power then increases approximately parabolically with speed, reaching its maximum at 5,000 rpm.

This rapid increase in power demand poses a challenge for the nacelle motor design. The operational speed range of the propeller is ultimately limited by the maximum power output of the motor. Furthermore, at very high rotational speeds, propeller tip effects may become significant and require additional consideration in the aerodynamic design.