Experimental Study on Airflow Upwash and Control of Thrust Increase Induced by Ceiling Effect on Microrotor

In recent years, Information and Communication Technology has actively been used to improve productivity at construction sites. One such application is the use of micromulti-copters (hereinafter referred to as micro-air vehicles (MAVs)) for progress management at construction sites. In addition, inspection and monitoring of bridges and other structures have also been conducted, and implementation of some practical applications has already begun [1–16]. However, when an MAV hovers near an upper wall such as a bridge girder or ceiling, its lifting force (thrust) increases rapidly due to the ceiling effect, causing it to get pushed toward the upper wall, and the out-of-balance vehicle may collide with the structure, resulting in damage or crash. This is a bottleneck for the practical application of maneuverable and autonomous MAVs to indoor environments such as indoor construction sites. Several studies have proposed control methods for MAV flight in indoor environments [17–21]; however, the authors have not confirmed how to control the flow field around the MAV and the stability of the flight using hardware such as the MAV's body and rotor blade, which are important to protect the aircraft and structures in terms of fail-safe in the event of a loss of system control functions during flight.

There have been many experimental and numerical studies on the flow field around the rotor blades of MAVs hovering in the atmosphere and those hovering near a rigid wall considering the ceiling or ground effect [22–26]. Robinson et al. [23] investigated details of the flow fields around a single microrotor subjected to the ceiling effect using computational fluid dynamics and reported that the induced velocity across the rotor disk decreased as the nondimensional distance between the ceiling wall and the rotor based on the rotor radius (g/R = G) decreased, and that the thrust increased as the effective angle of attack increased. They also found that an increase in the effective angle of attack decreased the induced drag but increased the power. Jardin et al. [24] obtained thrust measurements and investigated the flow fields around a rotor using stereoscopic particle image velocimetry (PIV) measurements under constant rotational speed, thereby revealing how the aerodynamic performance of a single rotor assuming a part of a micromulti-copter is affected by the horizontal and vertical walls. As a result, the influence of the vertical wall boundary on the thrust was found to be negligible regardless of the distance between the tip of the rotor blade and the vertical wall boundary. In contrast, the thrust of the single rotor set near the horizontal wall boundary increased with decreasing G owing to the Venturi effect acting on the gap between the horizontal wall and the upper surface of the rotor. In particular, it increased in the case of G of less than 2 and 1 due to the ceiling and ground effects, respectively. In addition, our research group also conducted a preliminary study using computational fluid dynamics on the flow field near rotor blades and the ceiling wall by orienting MAVs close to a ceiling wall and reported that when the rotor blades are significantly close to the ceiling wall (G$≲$ 0.2), a condition of rapid thrust increase, an upwash flow, wherein the airflow is sucked from the lower blade surface into the gap between the upper blade surface and the ceiling is formed instead of the conventional downwash flow by blowing down from the upper to lower blade surfaces. Furthermore, aiming to control the increase in thrust due to the ceiling effect using a control system, the thrust increase by the ceiling effect was modeled using blade element theory [20] and momentum theory [21,27]. Moreover, an investigation of an autonomous flight control method for MAVs using this model is also in progress.

It has been reported that the thrust increase by the ceiling effect is rapid when G is extremely small (20% or less than the rotor blade radius), but the details of the mechanism remain unclear. In particular, the phenomena of airflow upwash when a rectangular blade is mounted has not been experimentally confirmed; moreover, the mechanism and its relationship to thrust have not been revealed. Furthermore, MAVs with a passive rotating spherical shell guard equipped with a passive gimbal mechanism to avoid damage to the MAVs due to the thrust increase caused by the ceiling effect [28] and MAVs with wheels mounted on the bodies that contact under bridges have been developed [29]; however, there are no examples of the development of MAVs that can control the rapid thrust increase without any attachments. This is important for the practical application of MAVs in enclosed and indoor environments. In addition, to realize further productivity and safety improvements through labor-saving operations in inspection, security, and construction management, there is an urgent need to develop technology to control the rapid increase in thrust, which is strongly desired from various fields such as environment pollution and smart disaster prevention.

This experimental study investigates the control of airflow upwash and thrust increase caused by the ceiling effect on the microrotor for an MAV hovering near the upper wall. The relationship between the vehicle thrust and flow field near the microrotor was investigated as a parameter of the gap between the microrotor and upper wall. This relationship between the gap and the thrust reveals the distance between the rotor blades and the ceiling unaffected by the ceiling effect, and is useful in identifying the range of safe flight. In addition, as mentioned above, practical verification of MAVs moving with the rotor blades near the structure and contacting the surface by wheels has also begun [29]. Therefore, clarification of the sudden thrust increase when the MAV is close to the ceiling wall (G ≲ 0.2) would contribute to the development of MAVs utilizing this thrust increase. In addition, the effectiveness of a novel passive technique for controlling the thrust increase based on this upwash of airflow was also discussed using a blade invented by our research group [30]. Specifically, thrust measurements using a load cell, ceiling wall pressure measurements using pressure transducers, and velocity field measurements near the vehicle using a hot-wire anemometer and two-dimensional PIV were conducted for an MAV equipped with simple rectangular blades and the thrust-control blades.

To achieve stable flight technology in the vicinity of obstacles to enable practical use of MAVs in indoor environments, the contributions of this study are as follows:

1. The detailed mechanism of the rapid increase in thrust (airflow upwash) when MAVs are significantly close to the upper wall (G ≲ 0.2) is identified.

2. The effectiveness of the thrust-control rotor in preventing the thrust increase is examined based on the upwash of airflow mechanism.

3. The generation mechanism of the airflow upwash phenomenon when an MAV equipped with rectangular blades approaches G ≲ 0.2 is experimentally investigated.

The aforementioned (1)–(3) contributions are discussed in detail in Secs. 3.1 and 3.2, respectively; moreover, the experimental results for rectangular and thrust-control blades are compared.

Figures 1(a)–1(c) show a schematic of the experimental setup, a photograph of a typical test vehicle with mounted rectangular rotor blade, and positioning of the hot-wire anemometer, , respectively. In addition, Fig. 2 and Table 1 are examples of 3D models of the rotor blades used in this experiment (rectangular rotor blade and thrust-control rotor blade, with $O=o/D=0.5$⁠, where $o$ is the pressure recovery hole diameter and $D$ is the outer diameter), as well as details of the rotor blade specifications and the operating conditions. In this experiment, a self-made microquadcopter was used as the test vehicle. The vehicle is composed of gear shafts, arms, body, and four replaceable two-blade rotor blades produced using a 3D printer (made of poly-lactic acid filament, with a fabrication accuracy of 0.2 mm, $D$ of 127 mm, blade pitch angle of 15 deg, distance of rotor blade center to vehicle center of 1 $D$⁠, and center to center distance between rotors of approximately 1.4 $D$⁠). The hub ratios of the rectangular and thrust-control rotor blades are h/D = 0.1 and 0.06, respectively (h is the hub diameter). The thrust-control rotor blade has a smaller hub diameter to maintain a larger pressure recovery hole area. Note that the results regarding the relationship between the distance to the ceiling and thrust variation for a rectangular blade with a hub ratio h/D= 0.06, which is the same as that of the thrust-control blade, are generally in quantitative agreement to that of h/D = 0.1. In general, the increase/decrease in solidity corresponds to the magnitude of the thrust generated by the rotor blades. Thus, we assume that the magnitude of the thrust increase ratio in the vicinity of the ceiling also corresponds to the solidity. However, reducing the solidity by uniformly shortening the chord length in the blade span direction or by reducing the number of blades is not practical in terms of power consumption because the thrust without the ceiling, which dominates the flight time of the MAVs, is significantly reduced. Therefore, this paper compares a typical case with the pressure recovery hole ratio O = 0.5, where the thrust coefficient without the ceiling is approximately equal to more than 90% of that of the base rectangular blade, as described. The comparison of both rotor blades with equal solidity by adjusting the number of blades and the chord length shows that the rectangular blades are smaller than the O = 0.5 blades in the thrust coefficient ratio closest to the ceiling, but the O = 0.5 blades have an advantage because the G where the thrust rises rapidly is smaller, and those the thrust coefficient without the ceiling is higher than the rectangular blades. The power source is a brushless motor (Oriental Motor Co., Ltd., Tokyo, Japan, BLUD60-A2) whose rotation speed can be adjusted in 1 rpm increments within the range of 0–5000 rpm (fluctuation of rotation ≤ 0.2%). The power source and the rotor blades were connected through gears to prevent differences in the rotational speed and phase between the rotor blades. The upper part of the test vehicle was completely covered with an acrylic plate (dimensions of 900 mm × 900 mm, 7.1 R × 7.1 R, which is approximately the same area as that in the previous experimental work of Jardin et al. [24]) that simulates the ceiling wall (hereinafter referred to as the upper wall), as shown in Fig. 1(a). Dimensionless distance $G$ represents the ratio of g to $R$⁠, which has a significant influence on the ceiling effect, and distance g (between the upper wall and the upper surface of the rotor disk) can be adjusted arbitrarily in the range of 3–100 mm by a vertical translation stage (movement distance resolution: 0.1 mm) installed underneath the support. In addition, the height from the ground to the rotor blade (⁠$l$⁠) was maintained above 3.5 $D$ so that the ground effect could remain negligible under any g in the experiment [23,24].

A noncontact tachometer (AGPTEK, Shenzhen, China, Digital Photo-Laser Tachometer, measurement accuracy for rotating: 0.05% + 1 digit) was used to measure the rotational speed of the rotor blades. A 6-axis force sensor (Leptrino Co., Ltd., Nagano, Japan, SFS080YA500U6, measurement resolution: ±0.001 N) mounted underneath the motor was used to measure the thrust force, and the obtained data were sent to a PC and analyzed by a data logger software (Leptrino Co, Ltd., Nagano, Japan, LGR101 UA). The sampling frequency of the data used for the time-averaging calculation was 1.2 kHz over 50 s (for example, 3333 rotational cycles of the rotor blade at 4000 rpm). To investigate the development of the swirl flow generated between the upper wall and the rotor disk for small g values (⁠$G ≲ 0.2$⁠), velocity measurements of the flow between the two surfaces, and measurements of the pressure on the upper wall were conducted. An I-type hot-wire anemometer (Kanomax Corporation, Osaka, Japan, Model 7000Ser., measurement accuracy for velocity) was used for velocity measurements. Calibration of the hot-wire anemometer was performed in a calibration wind tunnel with a wind-speed range of 0.4–20 m/s. A third-order polynomial approximation was used for the voltage-velocity relationship. The difference between the polynomial approximation and the data points was less than ±5.5%. The absolute circumferential velocity, |$vθ$|, of the swirl flow between the rotor blade and the upper wall was calculated from the composite velocities measured by the I-type probe, that is, |$vrθ$|, |$vrz$|, and |$vθz$|. However, in the case where large vortices were generated, the absolute value of the velocity could not be measured as |$vθ$|, and some errors occurred in the calculation of the time-averaged value. A pressure transducer (All Sensors, CA, USA, 1INCH-D-4V, measurement accuracy: ±0.625 Pa) was used to measure the time-averaged pressure on the upper wall (pressure hole diameter: 1.0 mm). The sampling frequency and length of the data obtained from the hot-wire anemometer and pressure transducer were 10 kHz and 5.0 s (for example, 333 rotational cycles of the rotor blade at 4000 rpm), respectively. Each plot of the thrust and wall pressure is the average of three experiments, with upper and lower limits indicated by error bars, and that of the time-averaged velocity is the average of two experiments with error bars.

The uncertainty of the thrust measurement was evaluated using the method of Abernethy et al. [31]. The maximum deviation at the typical rotational speed of 4000 rpm was ±8 rpm, the maximum deviation due to nonlinearity of the force sensor was ±0.25 N, and the measurements were repeated 30 times in the range of G$≲$ 0.13 in the thrust test using the rectangular blade. As a result, the bias limit from repeated measurements was 0.12%, and the thrust uncertainty was estimated to be within about 13%. Thus, the suppression range of the thrust increase obtained by mounting the thrust-control blades is sufficiently larger than this uncertainty. The uncertainty of the ceiling wall pressure obtained by the pressure transducer (51 repeated measurements at G = 0.047 for the rectangular blade) and velocity obtained by the hot-wire anemometer (44 repeated measurements at G = 0.19 for the rectangular blade), obtained in the same way, were approximately 1% and 2%, respectively. Therefore, these experimental results are sufficiently reproducible and reliable.

The PIV technique was used to analyze the time-averaged flow field on the meridian surface of the rotor blade. The system consisted of a PIV laser (Kato Koken, Kanagawa, Japan, G4000, 532 nm, 4 W output, and sheet thickness of approximately 1 mm), a high-speed camera (Kato Koken, Kanagawa, Japan, k6, 1280 × 1028 pixels, frame rate of 2000 fps, and shutter speed of 250 μs), and a smoke generator (Antari lighting & Effects LTD., Taoyuan, Taiwan, Model Z-800II, smoke agent: FLG-5, water-soluble glycol). White smoke (particle size: 1–2 μm) was used as the tracer, and it was introduced from the upstream side of the airflow due to the difficulty of filling the space near the rotor blades with white smoke (smoke inflow velocity when the rotor blades stopped: 0–1 m/s). The captured images were processed using the direct cross-correlation method after sharpening and gamma correction (γ = 1.4) with a PIV analysis system (Kato Koken, Kanagawa, Japan, FlowExpert2D2C). The inter-rogation window size is 32 × 32 pixels for both first and second images, and the search window for the second image is the inter-rogation window enlarged by 10 pixels in the vertical and horizontal directions. Time averaging was carried out over 20 cycles of blade rotation, and vectors with an average brightness (minimum value: 0, maximum value: 255) of less than 50 were deleted to correct for error vectors as the brightness is not sufficient to track the distance between particles. The relaxation time of the particle, calculated assuming the Stokes flow with reference to the work of Shukla and Komerath [26], is in the order of 0.01–0.02 ms. To evaluate whether this relaxation time is sufficient, we compared it with the onset period of the blade tip vortex, which occurs on the smallest time scale phenomenon in the velocity field in the present experiment. Consequently, since the shedding period of the blade tip vortex is about 7.5 ms, the assumed relaxation time is sufficiently small, such the errors related to particle tracking in the PIV measurement are negligible. The main sources of uncertainty are expected the brightness change in the two images [32] and the eliminating spurious vectors, which were each 0.1 pixel. In addition, considering the variation in circumferential velocity V_θ crossing the visualized cross section, the uncertainty was estimated to be approximately 5% of the median velocity of the flow field. Although the uncertainty is considered to be even larger when other errors are taken into account, there is no effect on the observation of airflow upwash, which is the focus of this study.

where $α$ is a coefficient considering the effective rotating projected area, $CTC$ is the theoretical thrust coefficient considering the ceiling effect, and $CT∞$ is the thrust coefficient at $G$ = $∞$(no upper wall).

Figure 3 shows the effect of blade speed (⁠$N$⁠) on the relationship between $G$ and $CTA$ (hereafter referred to as thrust characteristics) when single rectangular blade rotor is installed. $N$ was varied from 1000 rpm to 5000 rpm in increments of 1000 rpm. The Reynolds number (⁠$Re=cUθT/ν$⁠), for which the blade tip circumferential velocity (⁠$UθT$⁠) and chord length (⁠$c$⁠) are the representative velocity and lengths, respectively, is also shown. For the case of $G≥$ 0.4, which Nishio et al. [21] studied by introducing the theoretical equation, the $CTA$ obtained under the conditions of $G$ = $∞$ and $N=$ 4000 rpm was used as the $CTA∞$ value in the above theoretical formula. The result calculated with $α$ = 1 and extended to the range G ≤ 0.4 is also shown using a blue solid line for reference. For G > 0.2, the results of Nishio et al.'s equation (Eq. (4)) derived from momentum theory, which assumes that the fluid flows from the top to the bottom surface of the rotor blade, are consistent with the experimental results. Meanwhile, for G ≤ 0.2, the theoretical results deviate from the present experimental results. This indicates that even if we assume conventional downwash and adjust α to account for the effective area through which the fluid sucked in from the upper surface of the rotor blade passes, it is not possible to represent the increase in thrust due to the airflow upwash, which is the focus of this study, as discussed later. Focusing on the influence of the difference in rotation speed $N$ on the relationship between $G$ and $CTA$⁠, it can be seen that for $2000 rpm≤N≤5000 rpm$⁠, $CTA$ increases slightly with decreasing $G$ when $G≥$ 0.25, same as in the previous works [23,24], irrespective of the difference in the rotation speed. For $G ≲$ 0.2, when the rotor blade is closer to the upper wall, it can be seen that the thrust increases rapidly as $G$ decreases. Thus, these results confirm that for $2000 rpm≤N≤5000 rpm$ (13.2 × 10³ ≤ $Re≤$ 32.3 × 10³), the thrust is proportional to the rotational speed when the rotor blade geometry is fixed. On the other hand, for $N=$ 1000 rpm, which is the lowest rotation speed in this condition, the measured values have considerable variation due to the small thrust values obtained at the low rotation speed, although the trend is qualitatively the same as that for $2000 rpm≤N≤5000 rpm$⁠, as discussed above. Therefore, in this study, the rotational speed was fixed at $N=$ 4000 rpm, where the similarity law of the flow field holds and the variation in measurements is relatively small.

Figure 4 shows the typical examples of the relationship between the rotor blade geometry and thrust/power characteristics from the thrust tests at $N=$ 4000 rpm. The different plot colors show the results for the rectangular blade (h/D = 0.1) and the thrust-control blades (⁠$O=$ 0.4, 0.5, and 0.6), respectively. Figures 4(a)–4(c) show G − $CTA$⁠, G − $CTA/CTA∞$⁠, and G − $CTA/CTQ$⁠, respectively. Figure 4(a) shows that $CTA$ increases with decreasing $G$ for the thrust-control blades with the pressure recovery hole as well as for the rectangular blades, regardless of the difference in $O$⁠. Comparing the results for the rectangular and thrust-control blades, $CTA$ values of the thrust-control blades were lower at all values of $G$⁠. In addition, it can be seen that the decrease in the thrust coefficient increases as $O$ increases. Subsequently, we discuss in detail the effect of the pressure recovery hole on the control of the increase in thrust. For example, comparing $CTA$ values of the rectangular (h/D = 0.1) and thrust-control (⁠$O=$ 0.5) blades, the rectangular blade had a $CTA$ value of 0.022 when $G$ = $∞$⁠, whereas the thrust-control blade had a $CTA$ value of 0.020, which is approximately 90% of that of the rectangular blade. At $G=$ 0.047, when the rotor blade was closest to the upper wall and the thrust coefficient was the largest under the experimental conditions, the $CTA$ value was 0.057 for the rectangular blade and 0.041 for the thrust-control blade (⁠$O=$ 0.5), indicating that $CTA$ for the thrust-control blade was controlled to approximately 73% of that for the rectangular model.

We focus on $CTA/CT∞$⁠, which is the ratio of the thrust at each G to the thrust without the ceiling shown in Fig. 4(b). G − $CTA/CTA∞$ has the similar profile as G − $CTA$ shown in Fig. 4(a). $CTA/CTA∞$ increases slightly as the distance to the ceiling becomes shorter for both the rectangular blade and the thrust-control blade in the range of G ≥ 0.4. There is no significant difference in the rate of increase in both blades. Meanwhile, for G < 0.3, the $CTA/CTA∞$ of the rectangular blade is larger than that of the thrust-control blades O = 0.4, 0.5, and 0.6, indicating that the distance at which its rapid increase begins is further away from the ceiling. These results indicate that the thrust-control blade for $O=$ 0.5 maintains roughly the same $CTA∞$ as the rectangular blade while reducing the thrust increase near the upper wall for $G<$ 0.3 and shortening the onset range of rapid thrust increase.

Comparing the results in Fig. 4(c) with C_TA/C_Q of the rectangular blade, when O = 0.5, the C_TA/C_Q is approximately 55% without the ceiling and approximately 62% when the blade is closest to the ceiling. In addition, comparing the results between the thrust-control blades shows that O = 0.4 and 0.5 are comparable and O = 0.6 is smaller. Thus, the power consumption of the thrust-control blade is higher than that of the rectangular blade at any G. Although the thrust-control blades consume more power than the rectangular blade, it is expected to contribute to expanding the range where the MAVs can safely hover near the ceiling because the distance from the ceiling at which the rapid thrust increase begins is shortened.

Figures 5 and 6 show examples of normalized time-averaged velocity vectors on the meridian cross section obtained by PIV analysis and an enlarged view of Fig. 4(b),G − $CTA/CT∞$ of the quad-microrotor for G ≤ 0.35, as well as the presence (△) or absence (○) of airflow upwash, respectively. Figures 5(a) and 5(b) show the results for the rectangular and thrust-control blades (⁠$O=$ 0.5), respectively, and Panels (i)–(iv) show the results for $G=$ 0.047, 0.19, 0.25, and 1.3, respectively. From the PIV results and the visualization videos, in the case of Panels (iii) and (iv) in both Figs. 5(a) and 5(b), where $G$ > $Gup$ (⁠$Gup≈$ 0.21 and 0.13 for the rectangular blade and thrust-control blade (O = 0.5), respectively, shown in Fig. 6), it was confirmed that the thrust-control blade with pressure recovery hole (⁠$O=$ 0.5) forms flow fields similar to those of the rectangular blades, as in previous studies [23–25]. Specifically, in the space between the upper wall and the rotor disk, fluid is drawn in from the outer radius to the inner radius along the upper wall while preswirling and then pushed out from the upper surface of the blade to the lower surface, resulting in the swirling flow blowing down in the downward direction shown in these panels. In contrast, focusing on (i) $G=$ 0.047, where $G$ < $Gup$⁠, and the rapid increase in thrust was observed regardless of the rotation speed and the presence and size of the pressure recovery hole, in the thrust characteristics in Figs. 3 and 4, the airflow is inverted compared to the case of Panels (iii) and (iv) in Figs. 5(a) and 5(b). In addition, both the rectangular blade (Panel (a)(i)) and thrust-control blade (⁠$O=$ 0.5, Panel (b)(i)) are sucked into the swirl flow formed between the upper wall and the rotor disk from under the rotor disk. The outward swirling flow in the gap between the rotor disk and the upper wall is confirmed by the video observation, and it can also be seen on the meridian surface shown in the images of the PIV results that the flow proceeds in the outward direction of the radius. In comparison, the outward radial velocity in the gap of the thrust-control blade is smaller (⁠$O=$ 0.5) than that of the rectangular blade. In the case of (ii) $G=$ 0.19, where $G$ < $Gup$ for the rectangular blade and $G$ > $Gup$ for the thrust-control blade (O = 0.5) as shown in Fig. 6, and the rapid thrust increase is observed for the rectangular blade but not for the thrust-control blade (⁠$O=$ 0.5), as shown in Figs. 3 and 4, the rectangular blade ((a)(ii)) generates the upwash flow toward the gap between the upper wall and rotor disk to form an outward radial flow, similar to that in the case of (a)(i) $G=$ 0.047. The thrust-control blade ((b)(ii)) does not generate the upwash flow, resulting in a flow that blows down from the rotor blade. From Figs. 5 and 6, it is confirmed that the trust control blade (O = 0.5) generates the downwash flow as shown in Fig. 5(b)(ii) in the range of 0.13 ≤ G ≤ 0.21, where an upwash flow is observed for the rectangular blade. This means that the thrust-control blade O = 0.5 can approach the ceiling without the upwash (sudden thrust increase) up to approximately 60% of the distance between the ceiling and the rotor blade of the rectangular blade. This tendency is not limited to the case of $O=$ 0.5 shown in this figure; we have confirmed that such upwash flow occurs at the $G$ value where the thrust increases rapidly for other $O$ values of the thrust-control blade. Therefore, the sudden increase in thrust is due to the outward swirl flow formed in the gap between the upper wall and the rotor disk, which causes the pressure on the negative pressure surface of the blades to further decrease.

Figure 7 shows the relationship between the thrust coefficient in the absence of the upper wall (⁠$CTA∞$⁠) and the dimensionless distance at which the airflow upwash starts from the upper wall (⁠$Gup$ = g_up$/R$⁠) for the single thrust-control rotor at $N=$ 4000 rpm. g_up is the distance from the upper surface where the airflow upwash was stably confirmed from the visualization experiment for the entire surface of the rotor disk from the lower surface of the rotor blade to the upper surface. This result was obtained from the experiment with a single rotor and the result for the single rectangular rotor (without a pressure recovery hole) is indicated as rhombus plots also for reference. Note that the G − $CTA/CT∞$ and O − G_up relationships obtained with a single rotor and quad rotor for both the rectangular rotor and the thrust-control rotor were generally consistent. From this result, because the diameter of the pressure recovery hole becomes relatively large in relation to the diameter of the rotor blade, the thrust is small when no upper wall exists, in which case the ceiling effect is nonexistent. Meanwhile, from Figs. 6 and 7, the distance between the point where the rapid thrust increase starts and the corresponding flow upwash occurs becomes shorter as $O$ increases, suggesting that stable flight is possible up to closer to the upper wall. Therefore, for the implementation of the thrust-control rotor, the optimal $O$ should be selected according to the flight plan (how close the MAV needs to be to the upper wall) of the air vehicle.

In Sec. 3.1, the results of the flow visualization and thrust test showed that for G ≤ 0.2, when the thrust increases rapidly, an outward swirl flow is generated between the ceiling and the rotor blade, resulting in the airflow upwash simultaneously. In this section, we focus on the negative-pressure region caused by the development of outward swirl flow which is the cause of the airflow upwash. Specifically, we discuss the mechanism of the airflow upwash phenomenon by investigating the difference in the effects of the rectangular and thrust-control blades on the development of the swirling flow.

Figure 8 shows the influence of the value of $G$ on the wall pressure distributions at the upper wall. The horizontal axis is the radial distance (r/R), which is nondimensionalized based on the blade radius (R) with the center of the hub as the origin, and the vertical axis is the dimensionless wall pressure (P*, refer to Eq. (3)). No significant pressure drop was observed for 0.25 ≤ $G≤$ 1.3, where both the (a) rectangular and (b) thrust-control blades (⁠$O=$ 0.5) had a moderate thrust increase, as shown in Figs. 3 and 4, and formed the flow that blows down from the rotor blades, as shown in Fig. 5. On the other hand, under the condition of flow upwash, with $G≤$ 0.22 for the (a) rectangular blade and $G≤$ 0.094 for (b) thrust-control blade, the negative pressure region was generated from the blade tip to the hub center, and the magnitude of the negative pressure increased as $G$ decreased. However, for the (b) thrust-control blade with pressure recovery hole, the pressure in the vicinity of the recovery hole recovered, which controlled the range of the pressure drop in the negative pressure region.

Figure 9 shows the distributions of the dimensionless absolute circumferential velocities based on the blade tip velocity, (⁠$|Vθ*|=|Vθ|/UθT$⁠), which are the absolute values of the composite velocities measured by the hot-wire anemometer at the center of the gap between the rotor disk and the upper wall for $G=$ 0.19 and 0.25. In the case of the rectangular blade (a), the velocity distribution from near the root of the rotor blade (r/R ≈ 0.2) to the blade tip (r/R = 1.0) is similar to that under the forced vortex, where the velocity increases in proportion to the radius, whereas outside of the tip (r/R > 1.0), the distribution of $|Vθ*|$ decreases with increasing distance from the blade tip. At any position, the value of $|Vθ*|$ for $G=$ 0.19, where the flow inverts upward and forms the outward swirl on the measurement plane, is larger than that for $G=$ 0.25, where the flow is blown downwards from the rotor blade. On the other hand, for the thrust-control blade (⁠$O=$ 0.5) (b), which blows the uninverted flow downward from the rotor blade for both G = 0.19 and 0.25, there is no significant difference in $|Vθ*|$ between the different $G$ values.

From the results of Figs. 5, 8, and 9, the larger swirl velocity formed in the gap between the upper wall and the rotor disk, the larger the negative pressure on the upper wall. Thus, the pressure gradient on the upper wall is generated by the centrifugal force caused by the swirling flow. It was also observed that when the magnitude of the negative pressure is large, the airflow becomes upwash. Contrary to the rectangular blade, the control of the rapid thrust increase even when the thrust-control blade is closer to the upper wall is considered to be because of the pressure recovery hole supply flow near the root of the rotor blade in the gap between the upper wall and rotor disk, which attenuates the swirl flow and decreases the magnitude of the negative pressure.

$CTP/CTA∞$ is less than 1.0 at $G≥$ 0.25 for the rectangular blade (h/D = 0.1) and $G≥$ 0.19 for the thrust-control blade (O = 0.5), when the flow field is not inverted to upward, but exceeds 1.0 at $G≤$ 0.19 in the case of the rectangular blade and $G≤$ 0.047 in the case of the thrust-control blade (O = 0.5) when the rotor is close to the upper wall and the flow field is inverted to upward.

From the results of Figs. 8, 9, and 10, we discuss the phenomenon in which the airflow changes from a downwash flow to a upwash flow. Figure 11 shows a schematic diagram of the airflow around the rotor blade. Panels (a)–(c) show the case with no ceiling (G = ∞), the case with a ceiling and a blowdown flow (G > G_up), and the case with blowup flow close to the ceiling (G ≤ G_up), respectively. For (a) G = ∞, the airflow is drawn into the upper surface of the blade parallel to the axis of rotation by rotating the rotor, resulting in a downwash flow from the upper surface to the lower surface of the blade. Consequently, thrust is generated. In the case (b) where a ceiling exists and G > G_up, as reported in previous studies [23,24], the existence of the ceiling above the rotor blade causes the inward swirling flow between the ceiling and the rotor blade, which is drawn into the upper surface of the blade while preswirling, resulting in a downwash flow toward the lower surface of the blade. In this process, the angle of incidence of the fluid on the top surface of the blades changes, and the effective angle of attack increases, resulting in thrust increase. At this time, it is considered that the C_TP does not exceed C_TA∞, and thus, no airflow upwash is generated.

Meanwhile, when (c) G ≤ G_up, where the airflow is upwind near the ceiling investigated in this study, the swirling flow generated by the blade rotation is developed between the ceiling and the moving blade more than in (b) because the gap between them is narrower. The force from the negative pressure generated by the swirling flow (forced vortex) exceeds the force blowing down from the top surface of the blade to the bottom surface. Consequently, the air flow is considered to be upwash. When the airflow upwash is generated, large-scale separation is expected to occur on the negative pressure surface of the blade, and it is considered that the blade itself cannot contribute to the generation of thrust, as shown in Panels (a) and (b). This can also be explained by the fact that, at the closest approach G = 0.047, the force caused by the negative pressure derived from the swirling flow (integrated value of the static pressure on the ceiling wall) and the thrust coefficient of the test vehicle measured by the load cell are approximately matched.

Figure 12 shows the relationship between P^* and the size of the pressure recovery hole at $G=$ 0.047, where the distance to the upper wall is the smallest. Figure 12(a) shows the results for all types of test blades, including the rectangular type, and Fig. 12(b) shows the comparison results for only the thrust-control blades, where the horizontal axis is the dimensionless radial distance (r/OR), and the radial position is nondimensionalized by the product of O and R. From Figs. 12(a) and 12(b), it can be observed that the dimensionless wall pressure distributions of the rectangular and thrust-control blades are almost identical at the corresponding radial positions, from the blade tip to the outer diameter of the pressure recovery hole. Furthermore, at the radial position where the pressure recovery hole exists, it can be confirmed that the pressure recovers toward the atmospheric pressure. In addition, the larger the value of O, the smaller the area of negative pressure due to the swirling flow, which corresponds to a smaller thrust increase, as shown in Figs. 3 and 4.

This study attempts to elucidate the mechanism of the rapid-thrust increase that occurs in MAVs flying near ceiling through experiments. Furthermore, we proposed the design of a novel rotor blade with a pressure recovery hole as a technique to control the thrust increase based on the aforementioned mechanism and investigated the effect of this rotor blade in controlling the thrust increase.

As a result, it was observed that there was a rapid thrust increase when the distance between the rotor disk and the upper wall was extremely small (20% or less of the rotor blade radius for rectangular blades); furthermore, it was deduced that this thrust increase was caused by the pressure difference between the upper and lower blade surfaces generated by the rotor blade as well as the negative pressure area due to the swirling flow generated in the gap between the rotor blade and the upper wall during blade rotation. In this case, the blowing down of airflow, which was observed when the distance between the rotor disk and the upper wall was larger than approximately 20% of the rotor radius and in the absence of the upper wall, was not observed. However, it was confirmed experimentally that the airflow was inverted by the pulling effect from below the rotor disk toward the swirling flow between the rotor disk and the upper wall, which formed the outward swirling flow between the two surfaces. In the case of the novel rotor blade with a pressure recovery hole, which recovers the pressure in the negative pressure region generated between the two faces, as described above, under the experimental conditions of O = 0.5, it was confirmed that the distance between the two surfaces at which there is a rapid increase in thrust and the airflow inversion described above begins is shorter than that for the rectangular blade; moreover in the absence of an upper wall, the novel rotor blade exhibits approximately 90% of the thrust of the rectangular blade. Lastly, it was found that the increase in thrust can be controlled. These results suggest that although the power consumption increases, the implementation of the thrust-control blade helps to expand the range of proximity distance to the upper wall wherein MAVs can fly safely. It is also clear that the larger the opening ratio (O) of the pressure recovery hole, the narrower the negative pressure region between the two surfaces and the greater the extent of the pressure recovery toward atmospheric pressure. Notably, for the same diameter, the larger the O, the smaller the distance between the two surfaces at which the airflow inverts and the rapid thrust increase begins; however, the actual thrust when this distance is infinity (in the absence of an upper wall) becomes smaller. For this reason, to maintain the same thrust without upper wall with the thrust-control blade as with the rectangular blade, the rotational speed must be increased to increase power consumption. However, when MAVs hover near the upper wall, safety is the most important factor in avoiding collisions, even if power consumption increases, and thus the thrust-control blade is expected to be useful in practical use. Therefore, it is necessary to select the optimal pressure recovery hole diameter considering the flight environment of the MAVs.

This study was conducted in a stationary fluid environment using a relatively simple rotor blade geometry, but future research will investigate the practical use of this technology under dynamic conditions and conditions similar to actual environments, such as crosswinds, by mounting the thrust-control blade on the flying MAV.

This study was conducted as a part of collaborative research with Tokyu Construction Co., Ltd. The authors wish to express their appreciation to Tokyu Construction Co., Ltd. as well as Professor Kenichiro Nonaka of Tokyo City University for his valuable advice. We also thank Mr. Naoto Wada, who is a student at Tokyo City University, as well as Mr. Rei Kawamura, Mr. Shun Osano, Mr. Ryota Takahashi, Mr. Shota Nakano, and Mr. Shuya Endo, who are former Tokyo City University students, for their help with the experiments and data processing.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

$A$ =

cross-sectional area of rotor disk (m²)

$c$ =

blade chord length (m)

$CTA$ =

thrust coefficient based on rotational area of rotor disk (Eq. (1))

$CTA∞$ =

thrust coefficient at G = ∞ (no upper wall)

$CTC$ =

thrust coefficient based on momentum theory (Eq. (4))

$CTP$ =

thrust coefficient calculated from upper wall pressure (Eq. (5))

$D$ =

rotor diameter (m)

$g$ =

gap between upper wall and rotor disk (m)

$gup$ =

distance at which upwash starts from the upper wall (m)

$G$ =

dimensionless gap between upper wall and rotor disk (= g/$R$⁠)

$Gup$ =

dimensionless distance at which upwash starts from the upper wall (= $gup$/$R$⁠)

$h$ =

hub diameter (m)

$l$ =

height of rotor inlet from ground (m)

$N$ =

rotational speed (rpm)

$o$ =

pressure recovery hole diameter (m)

$O$ =

pressure recovery hole ratio with pressure recovery hole (= o/$D$⁠)

$P$ =

wall pressure (Pa)

$P*$ =

dimensionless wall pressure (Eq. (2))

$r$ =

radius of measurement point (m)

$R$ =

rotor radius (m)

$Re$ =

blade tip Reynolds number

$T$ =

thrust (N)

$TP$ =

thrust calculated from upper wall pressure (N)

$UθT$ =

circumferential velocity of test rotor-blade tip (m/s)

$V$ =

velocity (m/s)

$Vθ$ =

circumferential velocity (m/s)

$|Vθ*|$ =

dimensionless absolute circumferential velocity based on the blade tip velocity

$r,θ,z$ =

coordinate axes

$α$ =

coefficient considering effective rotating projected area for Eq. (3)

$ρ$ =

density (kg/m³)

$ν$ =

kinetic viscosity (m²/s)