Automation and Robots for Disaster Response

Ground Effect on the Thrust Performance of Staggered Rotor System

By inergency On Mar 23, 2024

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1. Introduction

In recent years, the swift advancement of distributed electric propulsion technology and advancements in flight control have propelled the growth of eVTOLs equipped with multi-rotor systems, thereby opening new avenues for Urban Air Mobility (UAM) [1,2,3,4,5]. Moreover, UAM aircraft face the challenge of navigating complex urban traffic environments and undergoing frequent takeoff and landing processes [6,7]. The presence of ground effect amplifies the risk of accidents during low-altitude flight and the rotorcraft’s takeoff and landing procedures [8]. Many new drone configurations cannot be evaluated for ground effect intensity using traditional theories [9]. Thus, it is imperative to study the effect of ground on the operation of new types of rotorcraft.

The primary parameter through which ground effect impacts rotorcraft is rotor thrust, typically measured by the ratio of IGE to OGE rotor thrust. While extensive research has been conducted on the single-rotor ground effect, including model establishment [10,11], computational fluid dynamics simulations [12,13,14,15], and experimental flow visualization [16,17], which have validated the reliability of thrust ratio models [10], it is important to note that existing studies have shown limitations in directly applying single-rotor IGE models to multi-rotor aircraft [18,19]. This limitation presents challenges for the control of multi-rotor aircraft during takeoff, landing, and low-altitude flight.

Multi-rotor aircraft are subject to intensified ground effects due to rotor interactions. Sanchez-Cuevas [19] enhanced the Cheeseman-Bennett model for the planar quadrotor ground effect by integrating rotor interactions into the flight controller. Similarly, He [20] proposed a singularity-free planar multi-rotor quasi-steady ground effect model, which, based on experiments, considers blade geometry and rotor interactions. Both studies observed heightened ground effects at equivalent distances from the ground.

Comprehending the principles of multi-rotor ground effects necessitates visualization studies of the flow field. Yonezawa [21] conducted numerical studies on quadrotors of varying configurations, revealing that reducing rotor distance fosters a more pronounced outwash region between rotors, thus intensifying the ground effect. However, instances of thrust loss in the multi-rotor ground effect have also been documented. Dekker [22] conducted flow visualization studies on parallel rotor systems in ground effect, uncovering that augmenting rotor distance engenders asymmetric backflow, causing fluctuation and loss of rotor thrust. This phenomenon was further elucidated by Healy [23], who observed that recirculation effects induce significant turbulence. Tanabe [24] employed numerical simulations to illustrate the principle of power increase followed by a decrease in quadrotor aircraft approaching the ground, attributed to recirculation effects. Otsuka [25] observed thrust loss with increasing rotor distance in measurements of quadrotor systems, attributing it to circulation flow effects.

Besides planar configurations, coaxial rotors [26,27] and staggered rotors [28,29] have showcased remarkable performance. However, owing to the intricate rotor interactions arising from rotor overlap, performance in the ground effect may vary. Experimental studies by Silwal [30] on coaxial rotors suggest that rotor interactions and ground effect are in competition, with individual rotor performance exhibiting non-monotonic variation with altitude. Numerical simulations of the tandem rotor ground effect [31] observed recirculating flow in the middle of the rotors. In visualization studies of scaled tandem rotor systems in ground effect conducted by Ramasamy [32], it was observed that rotor height above ground affects outflow velocities differently along the longitudinal and lateral axes. Tan [33] conducted numerical simulations of tandem rotors, revealing radial outward expansion in the overlap region of the rotors, with radial outward flow exhibiting greater velocity peaks. Mehrabi [34] conducted experiments on non-overlapping tandem rotors in the ground effect, showing the occurrence of fountain flow near the non-overlapping tandem rotors. The interaction between the wake of tandem rotors and fountain flow influences rotor performance.

Research on the ground effect of multi-rotors mainly focuses on planar rotors, coaxial rotors, and tandem rotors. For the new configuration of staggered-rotor aircraft, the lateral distance between the top rotor and the bottom rotor will have an important impact on the effectiveness of ground effects. Previous research has mainly focused on the tandem rotor CH-47 and its scaled model under fixed parameters, while careful consideration of multiple factors such as ground height and lateral distance is of great significance for studying the ground effects of staggered rotors.

The paper presents experiments on the thrust of staggered rotor systems IGE, aiming to investigate the thrust of the staggered rotor and the impact of the ground on thrust enhancement IGE. It particularly focuses on examining how height above ground and lateral distance influence rotor systems, contributing to the assessment of the feasibility of utilizing staggered rotor configurations for eVTOL operations in UAM, especially during near-ground flight and the takeoff and landing processes. Firstly, the paper provides a brief overview of the flow model of staggered rotor IGE, outlines the experimental setup, and discusses the choice and configuration of experimental variables. Secondly, in order to maintain experimental rigor, we validate the accuracy of the experimental equipment and conduct an error analysis. Thirdly, the paper delves into a detailed discussion of the effects of three parameters, rotor speed, altitude above ground, and lateral distance, on rotor thrust performance in ground effect and the enhancement of thrust performance. Furthermore, the paper conducts a comparative analysis between isolated rotor systems and staggered rotor systems to elucidate the evolution of ground effect in staggered rotor systems.

3. Error Analysis and Validation

To demonstrate the credibility and measurement accuracy of the experimental results, new experimental verifications were conducted. Tests were performed using 1 kg and 4 kg mass standard blocks, and after multiple measurements, the results were recorded as 1.003 kg and 4.004 kg, respectively. The maximum measurement deviation was found to be 0.3%, indicating that the measurement accuracy of the sensor aligns with the requirements of the experiment. The measurement error of angular velocity is attributed to the motor’s structure. Depending on the chosen motor, the systematic error is 4.26 RPM.

The thrust coefficient (y) is calculated based on the rotational speed (x₁) and thrust (x₂). According to the calculation method of uncertainty [38], the determination of uncertainty is as follows:

$u_{y}^{2} = {(\frac{\partial y}{\partial x_{1}} u_{x_{1}})}^{2} + {(\frac{\partial y}{\partial x_{2}} u_{x_{2}})}^{2} + \dots + {(\frac{\partial y}{\partial x_{n}} u_{x_{n}})}^{2}$

(3)

Substitute the thrust coefficient:

$Δ C_{T}^{2} = {(\frac{1}{ρ A {(Ω R)}^{2}} Δ T)}^{2} + {(\frac{- 2}{ρ A Ω^{3} R^{2}} Δ Ω)}^{2} = {(\frac{C_{T}}{T} Δ T)}^{2} + {(\frac{- 2 C_{T}}{Ω} Δ Ω)}^{2}$

(4)

$\frac{Δ C_{T}}{C_{T}} = \sqrt{{(\frac{Δ T}{T})}^{2} + 4 {(\frac{Δ Ω}{Ω})}^{2}}$

(5)

According to calculations, the maximum measurement error of C_T is 1.4%

5. Discussion

The fountain effect generally refers to the phenomenon where multiple airflows from the rotor ground effect collide with the ground, forming a stagnation region where the airflow has nowhere to go but ultimately rises. A large amount of turbulence is generated by the downwash airflow hitting the ground and changing direction. Simulations and experiments conducted by several scholars [20,22,23,32,33] using different propeller blades, airfoil shapes, and pitches have consistently demonstrated the existence of fountain flow. The fountain flow brings a significant amount of turbulence, further promoting turbulence development and causing it to rise to the rotor plane, resulting in reduced thrust for the rotor. According to the research by He [20] and our experiments, changes in rotor speed have almost no effect on the thrust loss caused by the fountain flow. The staggered rotor system exhibits both inhibitory and enhancing effects, consistent with the conclusion of Silwal [30] et al. The loss caused by the fountain flow represents an inhibitory effect, and similarly, the top rotor has an inhibitory effect on the bottom rotor, while the ground effect manifests as an enhancing effect, as shown in Figure 14. The specific competitive mechanism depends on the relative strengths of the enhancing and inhibitory effects and warrants further discussion.

5.1. Combination of Rotor to Rotor Interactions and Ground Effect

As the staggered rotor system approaches the ground, it encounters complex flow dynamics characterized by rotor-vortex-ground coupling interference. In this scenario, the mutual interference between rotors induces certain thrust losses while the rotor experiences an increase in thrust IGE. The combined influence of these two effects results in intricate variations in the thrust of the staggered rotor system. This interplay between aerodynamic interference and ground effect underscores the complexity of rotorcraft dynamics, particularly in low-altitude flight scenarios. Further analysis and experimentation are crucial to fully understand and optimize the performance of staggered rotor systems in such conditions.

5.1.1. Impact on Thrust IGE

From Figure 10, it is evident that the sum of thrusts from two isolated rotor systems is significantly greater than that of most staggered configurations, indicating that the complex interference between rotors affects the performance of staggered rotor systems. However, this does not necessarily imply that this influence on rotor thrust performance is unfavorable. Under the condition where l = 2.0, the staggered rotor thrust is even slightly greater than that of the two isolated rotors. This could be ascribed to the reduction in the overlap area, causing the top rotor’s downwash to contract almost completely, avoiding the inflow region of the bottom rotor. Thus, the interference experienced by the bottom rotor is minimal, while the shedding of the bottom rotor tip vortices induces upwash on the tip region of the top rotor, causing a marginal increase in system thrust. In Figure 12, within the two regions where (h = 0.5) and (l ≤ 1.0), and (h = 1.0) and (l ≤ 0.5), the thrust performance of the rotors remains nearly unchanged with increasing lateral distance. This is because, in these scenarios, where the rotor is at a low altitude, the improvement in thrust performance due to ground effect predominates. The ground effects on the aerodynamics of the staggered rotor system far outweigh the effect of aerodynamic interference within the system. This is attributed to the low altitude, where the ground effect predominantly enhances the thrust. The aerodynamic influence of the ground on the staggered rotor system surpasses the impact of aerodynamic interference within the system. However, as the altitude increases, the ground effect weakens, and a balance point is reached where the influence of the ground and aerodynamic interference within the system are of similar magnitude. With further increases in distance above the ground, where the intensity of the ground effect is lower than the balance point, the effects of aerodynamic interference between rotors become more significant. Increasing the lateral distance results in a noticeable improvement in rotor thrust performance under these conditions.

In Figure 15, in different experimental ranges, these two types of interference exhibit significant differences in their effects on thrust, ultimately manifesting as optimal thrust performance at (l = 2.0) and (h = 0.5) and poorest performance at (l = 0) and (h = 2.0). With the increase in lateral distance and the decrease in distance above the ground, thrust performance improves significantly. However, the difference lies in that the increase in lateral distance brings about a nearly uniform enhancement in performance, whereas the influence of distance from the ground shows a more pronounced increase within the range of 0.5 ≤ h ≤ 1.0.

5.1.2. Impact on Thrust Ratio IGE

Figure 16 illustrates how the thrust ratio varies with lateral distance and distance above the ground, corresponding to variations in thrust. Unlike thrust performance, however, the ratio value reflects the gain of the rotor ground effect in different configurations. With an increase in lateral distance, the ratio tends to decrease, with this trend being more pronounced under conditions closer to the ground. Among all rotor configurations tested, the ground effect is most significant for (l = 0), with a thrust increment of up to 32.8%. The region where the ground effect significantly improves rotor performance remains predominantly under conditions of closer proximity to the ground and smaller lateral distance, consistent with the previous analysis.

5.2. Effect on the Top and Bottom Rotors at h = 2.0

In the previous analysis, it was observed that some rotor configurations still exhibit significant ground effects at (h = 2.0). Subsequent analysis will investigate the impact on the top and bottom rotors separately.

Figure 17 illustrates the variation of the ratio for the top rotor, bottom rotor, and staggered rotor system at h = 2.0 and h = 0.5. The thrust is compared to that of the staggered rotor system separately in OGE conditions. It is noteworthy that almost all bottom rotors exhibit thrust performance without ground effect and even experience slight thrust losses at h = 2.0. For isolated rotors, the closer they are to the ground, the more significant the ground effect becomes, while in the staggered rotor system, the opposite phenomenon occurs. At h = 2.0, the top rotor contributes nearly all of the thrust enhancement, which is entirely contrary to the scenario at h = 0.5, where the bottom rotor predominantly contributes to the enhancement. The top rotor continues to demonstrate significant thrust augmentation within the range of 0 ≤ l ≤ 1.5, with the maximum thrust increment reaching 109.5%. This implies that at h = 2.0, the performance of the staggered rotor system IGE, the top rotor primarily contributes to thrust enhancement, while the bottom one, due to being affected by the fountain flow effects, downwash of the top rotor, and ground influence, exhibits a pseudo-OGE state.

The disparity in thrust performance between the rotors in the staggered rotor system at h = 2.0 can likely be attributed to the combined effects of fountain flow and turbulent development. The non-coplanar arrangement of the two rotors in the staggered rotor system induces asymmetrical fountain flow, which may contribute to the differences in thrust performance. Previous studies [22,23,25] have indicated that fountain flow rises to the rotor plane, generating substantial turbulence that can lead to rotor thrust loss. In staggered rotor configurations with partially overlapping regions, the fountain flow may rise even higher, and the presence of a multi-stream downwash could lead to multiple fountain flows. The mixing of these multiple fountain flows may further enhance turbulence development, as observed in studies such as Tan’s research [33] on the ground effect of tandem rotor systems. Due to the vertical separation between the top and bottom rotors, the turbulence induced by fountain flow likely predominantly affects the bottom rotor, while the top largely avoids the turbulent interference zone. As the lateral distance expands, the upward extent of the fountain flow decreases. However, the bottom rotor also avoids interference from the top rotor, and their effects are of comparable magnitude. Consequently, the bottom rotor exhibits a pseudo-OGE state with a thrust ratio of 1. The increased lateral distance reduces the strength of the downwash in the staggered rotor system, weakening the impact of downwash IGE while enhancing the inflow to the top rotor, resulting in reduced thrust.

6. Conclusions and Future Work

The study primarily concentrates on evaluating the performance of staggered rotors under the influence of ground effects. Under these conditions, the following conclusions have been drawn:

(1): In the ground effect, increasing rotor speed improves the thrust performance of both isolated rotor and staggered rotors, but the rotor speed barely affects the ratio of thrust IGE or OGE.
(2): As the distance above the ground increases, both isolated rotors and staggered rotors experience a decrease in thrust performance and thrust ratio. The position where the ground effect disappears for staggered rotor systems is farther away (h_oge > 2.0) compared to the position where the ground effect disappears for isolated rotor systems.
(3): As the lateral distance expands, the staggered rotor thrust improves, but the ratio of thrust decreases.
(4): The weakening effect of mutual interaction between staggered rotors and the strengthening effect of ground effect both coexist. The impacts of these two effects distribute differently: while the increase in lateral spacing leads to a uniform reduction in the interaction between rotors, affecting both thrust performance and thrust ratio almost evenly, the enhancement of ground effect due to decreasing distance from the ground experiences a sharp increase within the 0.5 ≤ h(H/R) ≤ 1.0 interval.
(5): At h(H/R) = 2.0, certain configurations of staggered rotor systems are still influenced by ground effect. In this scenario, the thrust variation of bottom rotor behaves similarly with OGE state while the top rotor thrust experience an increase.

The thrust of the staggered rotors was measured using a validated experimental setup and contrasted with that of the isolated rotor under the same conditions. The investigation examined the underlying mechanisms driving variations in thrust, which result from interactions among rotors and between rotors and the ground. Understanding these interactions can offer valuable insights for optimizing the design of multi-rotor drones.

Our work will consider the ground effects of staggered rotors and introduce variables such as rotor radius, angle of attack, power, etc. By considering key parameters like rotor radius, lateral spacing, and height above ground as variables, through training a regression analysis model, we will develop a surrogate model capable of accurately predicting the ground effect aerodynamic forces of staggered rotors. Subsequently, we plan a rational flight path for the autonomous landing of the aircraft. Perform flow field visualization studies on ground effect experiments of staggered rotors with specific parameters, aiming to fully elucidate the flow phenomena observed and reveal flow patterns.

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