Fluid Dynamics of Interacting Rotor Wake with a Water Surface

Abstract

Rotor-type cross-media vehicles always induce considerably complex mixed air–water flows when approaching the water surface, resulting in relative thrust loss and structural damage on rotor. The interactions between a water surface and rotor wake bring potential risks to the cross-media process, which is known as the near-water effect of the rotor. In this paper, experimental investigations are used to explore the fluid dynamics of the near-water effect of the rotor. Qualitative droplet observation was carried out on the 0.25 m and 0.56 m diameter commercial rotor blades and the 0.07 m diameter ducted fan near the water surface first to gain a qualitative understanding of droplet characteristics. The results show that the rotor wake caused water surface deformation, droplet tearing off, splashing, and entrainment into the rotor disk. The depression formed by the rotor downwash flow impacting the water surface is named as three modes: dimpling, splashing, and penetrating, and the correlation between the depression modes and the aerodynamic characteristics of the rotor is primary analyzed. The flow mechanisms of dimpling mode were studied using the particle image velocimetry (PIV) technique. The results showed that the cavity and liquid crown obviously alter the flow direction of water surface jets, but not all rotors near water enter the vortex ring state. Two splashing mechanisms were revealed, including the direct ejection of droplets at the rim of depression and the tearing of liquid crown by the water surface jets. The blade tip vortex in the surface jet is a potential cause of entrainment into the rotor disk and secondary breakup of the droplet.

1. Introduction

A cross-media vehicle (CMV), also known as a hybrid aerial underwater vehicle, is a novel vehicle that can cross the medium interface several times and fly in the air or dive underwater for a long time, which has a great potential application value in the fields of ocean observation and communication relay [1,2,3]. Its special cross-domain capability is not possessed by conventional vehicles, and it is also a technical difficulty in the development of cross-media vehicles.

Experiments have shown that during the cross-media process of CMV, the rotor operates very close to the water surface and induces a large-scale multi-phase flow field with mixed air, droplets, and waves (called mixed air–water flows) [4], as shown in Figure 1 from the Supplementary File. Rotors operating in mixed air–water flows have a different aerodynamic performance from that of IGE (in-ground effect) [5,6,7,8,9] and OGE (out-ground effect) [10]; this phenomenon is called the NWE (near-water effect) of the rotor. Different from IGE caused by the rotor on the rigid ground and IGE caused by fixed-wing vehicles on the static water surface or dynamic wave surface, the rotor under the NWE is much closer to the interface and the interface is water. Under the impact of the downwash flow of the rotor, the water surface undergoes violent deformation and droplet tearing off, which generates a large number of droplets. The droplet impact with the rotor blades leads the rotor aerodynamic characteristics to be quite complex.

Due to the slow development of large-scale cross-media vehicles, the study of the near-water effect caused by mixed air–water flows has not yet gained widespread attention. As early as 2016, Qi et al. [11] first found the “ distortion” of the ground effect caused by the interaction between the rotor wake and the water surface, and measured the thrust required for a quadrotor cross-media vehicle to hover at different rotor heights off the water surface. The IGE formula of the water entry process was derived and an active disturbance rejection controller (ADRC) was designed for the control of water entry height. However, this study mainly focused on the changes in rotor aerodynamic characteristics at rotor heights off the water surface between z/R = 0.75 and z/R = 6, where the rotor is not close to the water surface. Mi et al. [12] examined the impact of ducted fans on ground and water surfaces by the VOF (volume of fluid) method; the results showed that the vortex ring effect and thrust loss caused by the ground are stronger than those of the water surface, and the “ground effect” on the water surface of ducted fans is stronger than that on the ground. However, Huo et al. [13] and Nie et al. [14] experimentally found, for the first time, that the high-speed rotation of the ducted fan near the water surface caused violent deformation of the water surface with water vapor, resulting in a maximum of 60% thrust loss of the propulsor thrust compared to OGE. Yan et al. [15] carried out numerical simulations to investigate the effects of water surface and wave surface on the aerodynamic performance of a 12 m diameter Caradonna–Tung rotor by the VOF method using STAR CCM, and found that the water effect of the rotor is a relatively weak ground effect. It was not until 2023 that Bai et al. [4] first experimentally investigated the aerodynamic characteristics of 0.56 m and 0.25 m commercial rotor blades from z/R = 0.1 to z/R = 4, and provided a preliminary definition of the near-water effect of the rotor. They found that NWE is not simply a thrust loss due to a depression on the water surface. As the rotor heights off the water surface decrease and the rotor speed increases, the droplets always cause torque and power increases, and a thrust decrease compared to IGE operation, which has a significant effect on the cross-media capability of CMV. After that, Xu et al. [16] experimentally investigated the near-water effect of 0.13 m commercial three-bladed rotor blades from z/R = 0.4 to z/R = 3, and unexpectedly found a maximum loss of 30% of the rotor’s thrust when close to the water’s surface compared to OGE operation. Wang et al. [17] carried out numerical simulations of the aerodynamic performance of a 1.16 m diameter three-bladed Quad Tilt-Rotor (QTR) aircraft in the near-water surface from z/R = 0.4 to z/R = 2.4 by the VOF method using fluent. The results showed that the soft water surface is impacted to form a “drainage area”, which increases the distance between the rotor and the water. The depression will deflect the water surface jet, causing the rotor to enter the vortex ring state. In addition, the water surface depression accelerates the tip vortex dissipation and reduces the non-constant fluctuation generated by the tip vortex. They therefore believed that NWE is not as strong as IGE.

It is now generally accepted that computational fluid dynamics (CFD) studies have shown that the relative thrust loss is due to the increase in the equivalent distance caused by water surface depressions. However, the phenomena of relative thrust loss and torque increase caused by droplets can only be observed experimentally. It is hard to capture the liquid surface tearing off and droplet splashing off in a large-scale rotor flow field through the VOF method. The CFD results may be significantly different from the real physical phenomena. This is due to the inherent difficulties in catching the fast-moving phase interface with a large curvature using mesh-based methods. The phase interface is typically smeared over a few grid cells, and is therefore highly sensitive to the grid resolution. Therefore, a reliable simulation of the splashing phenomena requires an extremely fine mesh, which can be very costly.

There have been various studies on the rotor wake characteristics for IGE operation using PIV; however, no study has reported such an experiment on water surface. Considering that these flows are present in similar phenomena, some concepts can be borrowed from the body of knowledge available for both helicopter brownouts and impinging gas jets on liquid surfaces in oxygen steelmaking, offering valuable insights applicable to our study. Molloy [18] classified the response of the liquid surface to an impinging jet into dimpling, splashing, and penetrating stages. There are also some studies [19,20,21,22,23,24] using CFD and experiments to analyze the generation mechanism of the tearing and splashing phenomenon of droplets. Lee et al. [25] carried out flow visualization and PIV to understand the fluid dynamics of the rotor wake as it interacted with a horizontal ground plane from z/R = 0.25 to z/R = 1, which revealed the flow mechanisms of stretching, diffusion, and shearing of blade tip vortex for IGE operation. Haehnel et al. [26] measured the rate of entrainment of particles being removed from a particle bed under the influence of an impinging jet and the associated surface shear stress, and found that there is a very good correlation between the surface shear stress computed from the Reynolds stress. Sydney et al. [27] carried out an air-sand dual-phase PIV experiment to segment the air and sand velocity field by gray threshold segmentation techniques to clearly identify both the mechanisms responsible for sediment entrainment as well as the mechanisms responsible for the vertical transport and suspension of sediment by the rotor flow. Wu et al. [28] conducted experimental and numerical simulations using rotor blades with a radius of 0.56 m under extreme ground effect (EGE) conditions (rotor height off the ground is less than half of the rotor radius) at z/R = 0.25. The aerodynamic performance, tip vortex trajectory, wall jet characteristics, surface pressure, and velocity fields were measured and analyzed. The proposed Prescribed Wake Model (PWM) shows quite a good agreement compared with CFD results for predicting tip vortex trajectory in EGE.

The foregoing results have shown that the detailed fluid dynamic mechanisms by which the rotor wake interacts with the water surface are very complicated [4]. However, it is these very mechanisms that influence the tearing off, splashing, and impacting of droplets. It is worth mentioning that it is difficult to measure the mixed air–water flows with the existing flow field measurement techniques, and only some of the conditions without droplet splashing can be measured at present. The goal of this study was not an attempt to completely solve the NWE problem, but a step forward to gain a better understanding of the interdependent factors that potentially contribute to its severity.

2. Experimental Setup and Measurements

2.1. Droplet Observation

The droplet observation experiments were conducted with a 0.25 m diameter, 0.56 m commercial rotor, and a 7 cm diameter commercial ducted fan in a pool of 0.4 m water depth. A continuous Nd: YAG laser with a maximum power of 30 Watts was used for illumination, and the droplet observation was made using a CCD camera with a resolution of 1280 pixels × 1024 pixels. The camera was positioned so that it was perpendicular to the plane of the light sheet, as shown in Figure 2. The camera frame rate was 1000 FPS. Several typical patterns of mixed air–water flows were selected for droplet observation. The droplets splashed more than 4 m away at high rotor speed, resulting in the laser and camera being placed away from the rotor. The 0.56 m diameter rotor has a rotor speed of 4100 r/min to 6400 r/min and a maximum blade tip velocity of 187.2 m/s, corresponding to a maximum tip Mach number of 0.55. For this experiment, values from z/R = 2 to z/R = 0.1 were used, which are referred to as the NWE conditions.

2.2. Particle Image Velocimetry

Two-component PIV measurements were carried out with a 0.25 m diameter rotor blade in a water tank, as shown in Figure 3 and Figure 4, of which the dimensions were about 4 m × 3 m × 2 m (height). Tap water was used for experiments, and the water was filtered using a water circulation purification device. The rotor was fixed on a rotor stack driven by a stepper motor for height adjustment above the water surface. For illumination of the downwash flow field, an Nd: YAG laser was adopted to generate a dual-pulse laser at 532 nm with frequency of 15 Hz in the experiments. An articulated optical arm (laser-guiding arm) was used to transmit the laser light to the region of interest in the experiments. The rotor speed was measured with a Hall effect sensor indexed to the rotor shaft, which provided a once-per-revolution synchronization signal. The data acquisition system included a digital synchronizer with phase delay capabilities that ensured phase locking to less than ±0.1 deg of blade rotation. Typically, 200 PIV image pairs were acquired at each water surface distance. The resolution of the CCD camera used in PIV was 2560 pixels × 2160 pixels and was properly waterproofed by being placed in a high-transmittance glass box. A smoke generator by heating the smoke oil was used to feed smoke into the water tank, and the average diameter of the tracer smoke particles was about 5 μm, and this type of particle has a nice following in the rotor flow. For the PIV experiments, the tracer particles were distributed as uniformly as possible before each sequence of flow measurements in the water tank.

Complex multiphase flows containing a large number of droplets are difficult to measure by conventional PIV; so, the purpose of this study is to obtain the rotor wake structure of a small rotor blade at a relatively low rotor speed and to gain some preliminary understanding of the interaction between the rotor wake and the water surface. Unexpectedly, many of the conditions where droplets are not visible to the eyes produce huge amounts of small droplet splashing that obscures the tracer particles in the same area. The spray at the edge of the depression produces strong laser reflections from outside the laser sheet into the camera, as shown in Figure 5a. The high intensity of laser reflections at the water–air interface causes overexposures that can damage the camera, and all of the abovementioned factors greatly affect the measurements, further limiting the ability of the PIV to measure the mixed air–water flows reduced by rotor. The main purpose of this paper is to observe the motion of the tip vortex, the surface jet, and the velocity profile near the liquid crown. Adverse reflections such as the high-intensity laser reflections on the fluctuating water surface cannot be limited by using rhodamine dye painted onto the ground plane. The only way to solve this challenge is to adjust the measurement window; the bottom of region of interest (ROI) is located at the edge of the liquid crown to avoid laser reflections from it, as shown in Figure 5b. z is defined as the axial direction and r as the radial direction. z/R represents the dimensionless axial distance from the bottom of the rotor blade to the water surface. r/R represents the dimensionless radial distance from the center of the rotor blade to the downstream.

3. Results and Discussions

3.1. Qualitative Description of Droplet Formation and Splash

3.1.1. Dimpling Mode

A CCD camera and a color camera are used to observe the rotor wake interaction with the water surface and the droplet generation of a 0.25 m diameter rotor blade, and the initial droplet generation can be well observed at a specific rotor speed for this size of blade. Observation of high-speed photographs shows greater insight into the droplet formation process, which is described below.

As the rotor wake hits the water surface, it creates a depression. Waves are formed inside the depression. These waves are pushed towards the edge of the depression by high-speed rotor wake. At the edge of the depression, these waves form a sheet structure that grows to a certain critical amplitude. From the high-speed video, droplet formation is observed and three stages could be identified. 1. The amplitude of the waves (which will be called “liquid crowns” from now on) increases at the edge of the depression. 2. At the rim of the liquid crowns, water–air interface instability grows and fingers are formed. 3. Fingers break up into one or several droplets, as shown in Figure 6 and Figure 7 [29].

According to the Kelvin–Helmholtz theory (K-H instability), as the rotor wake impinges on the water surface, the water surface jet is deflected upward. The deflecting jet exerts a shearing force on the water surface in the impact region, which drives the flows on the surfaces of the water [30]. The velocity difference on the two sides of the interface between the air and water induces the instability of the air–water interface. It is known that there are no droplets produced at the edge of the depression when the water surface jet momentum is very low. The dense phase tends to self-adjust by changing the shape of the depression to keep the force balance on the droplet; that is, the centripetal force required for the surface liquid to tend to curvilinear motion is always equal to that exerted on the surface liquid by changing the radius of curvature of the depression surface in this region. Once the required centripetal force becomes larger, due to a further increase in the gas flow rate, than the exerting centripetal force, droplets will be generated at the edge of the depression [31]. As such, the developed instability results in the growth and motion of the surface waves and finally the onset of droplet tearing off.

It should be noted that the mixed air–water flows are highly unsteady, and the above crown formation and fingers created can be observed at the same rotor speed. This condition with liquid crown formation, droplet tearing off, and without significant droplet entrainment into the rotor disk is tentatively defined as the dimpling mode of the near-water effect of the rotor.

3.1.2. Splashing Mode

A CCD camera is used to observe the rotor wake interaction with the water surface and the droplet generation of a 0.56 m diameter rotor blade. The droplet entrainment into the rotor disk and generation of water mist can be well observed at a specific rotor speed for this size of blade.

Mixed air–water flows at low rotor height with high rotor speed make up a very complex physical process that contains several flow phenomena with different mechanics, including deformation and fragmentation of liquid crown, formation of droplets, droplet motion in the rotor wake, impact of droplets onto rotor blade, etc. As shown in Figure 8a, when rotor speed N = 4500 r/min, the droplets tear off at the top of the liquid crown, and produce some droplets, which splash all around due to the effects of gravity and aerodynamic forces. The small droplets start to splash off along the diagonal upward direction, but the rotor is still in the dimpling mode at this rotor speed.

However, as the rotor speed increases to 6400 r/min, the angle formed by the splash path of the droplet with the water surface increases. The primary breakup of the liquid crown occurs, which decomposes into discrete large tears. In the process of rapid movement, the secondary breakup occurs, and the large tears break into small droplets, as shown in Figure 8b. It also produces a large amount of water mist, which is poorly followed and seems to be unaffected by the rotor inflow, moving in the opposite direction of the inflow and upward for several meters. Such a condition with the secondary breakup of droplet, droplet splash, and generation of water mist with obvious droplet entrainment into the rotor disk phenomenon is tentatively defined as the splashing mode of the near-water effect of the rotor.

3.1.3. Penetrating Mode

A color camera is used to observe the rotor wake interaction with the water surface and droplet generation of a 0.07 m diameter ducted fan. Unlike the NWE of rotor, which obviously acts within z/R = 1 to 0.1, the tested ducted fan generates a large-scale mixed air–water flow field at z/R = 26 away from the water surface. The flow tube shrinks due to the duct, and the downwash flow velocity of the ducted fan is larger, which violently interacts with the water surface, as shown in Figure 9.

The ducted fan wake impacts the water surface, causing a small number of droplets to splash all around at relatively low heights, while a large number of large tears and droplets move upward. As the ducted fan height off the water surface decreases, the scale of mixed air–water flows is reduced by the ducted fan, and the droplet splashing distance decreases. This mode is characterized by an obvious momentum exchange between the rotor wake and the water. The result of the increased momentum exchange between the wake and the water surface is a gradual decrease in the number of splashing droplets, which is replaced by an increase in the number and scale of the large tears, even those surrounding the duct, as shown in Figure 10a. The mixed air–water flows reduced by the ducted fan are much more unsteady than those of the rotor. There is a large number of large tears surrounding and entering the duct, which collide with the high-speed fan, resulting in some moments in which the large tears can be observed to be broken up into small droplets and spray, as shown in Figure 10b. Such a condition with the generation of amounts of large tears surrounding and entering the duct is tentatively defined as the penetrating mode of NWE.

3.2. Relation between Depression Modes and Aerodynamic Characteristics of Rotor

As mentioned above, rotors exhibit three typical depression modes for NWE operation. Figure 11 shows the schematic of typical depression modes proposed in this paper. By further analyzing the experimental data on aerodynamic performance, it can be found that different depression modes tend to show distinct aerodynamic characteristics. Due to the lack of clear observations and quantitative descriptions of the droplet impingement process on the rotor blade, the depth of depressions, and the droplet generation rate, the different aerodynamic characteristics described here are only the main features of the aerodynamic performance curves, and the critical discriminant conditions and non-dimensional numbers need to be defined by further research.

3.2.1. Dimpling Mode

The image source model proposed by Cheeseman and Bennet [32] did not consider viscosity and boundary layer effects, and thus it was only valid for z/R > 0.5. Hayden [33] summarized the flight test data for various helicopters operating IGE, and proposed a similar form of thrust approximation, which is also invalid for rotor heights below half of the radius for the same reason. Therefore, this study analyzes the NWE aerodynamic characteristics of the rotor from z/R = 0.1 to z/R = 0.45 using previous IGE and NWE experimental data [4]. Figure 12 shows the thrust characteristics of 0.25 m diameter blades, which are always in dimpling mode for this size rotor. The NWE and IGE curves grow in the same trend in the dimpling mode, but the slope of the increasing thrust coefficients’ curve is lower, as shown in Figure 12a. It is obvious that the water surface is less effective in increasing the thrust coefficients than the ground due to the alteration in the downwash flow by the presence of the water surface. Figure 12b shows the trends in the thrust curves for the 0.25 m blade at different throttles, which are the same as those for the IGE condition. The thrust increment increases as the rotor height off the water surface decreases. In these cases, there are no droplets entering the rotor disk and it can be approximated that only the depression has an effect on the aerodynamic performance of the rotor (the vortex ring state of the rotor should also be considered; this will be discussed in Section 3.3.1).

As mentioned in Section 3.1.1, when the rotor wake hits the water surface, it creates a depression. The depression or “puddle” essentially changes the actual distance between the water surface and the rotor, thus weakening the impact of the high-pressure area on the vehicle [17]. Consequently, compared with the OGE, the thrust coefficients of the vehicle in the NWE increase, but this increment is smaller than that of the IGE.

3.2.2. Splashing Mode

Figure 13 shows the thrust characteristics of 0.56 m diameter blades, which are always in splashing mode for this size rotor at high rotor speed. As the rotor height off the water decreases, the increment in thrust coefficients increases at a relatively low rotor speed due to the stronger high-pressure area under the lower wing of the rotor. The thrust curve increases monotonically between z/R = 2 and z/R = 0.7, showing the same trend as the dimpling mode. However, since z/R = 0.7, when the throttle reaches 100%, some droplets start to enter the rotor disk, causing a turning point in the thrust curve. After the turning point, both the thrust increment from the high-pressure area below the rotor and the thrust loss from the droplets increase with decreasing rotor height off the water surface. This is also the condition where the torque of the rotor increases significantly. The net effect is that the thrust increment from NWE begins to decrease. As the rotor height becomes small, these trends become significant. And the higher the rotor speed, the further away from the water the turning point appears. But the thrust increment is almost always present and significantly lower than in IGE.

Compared to the dimpling mode, the deformation of the water surface in the splashing mode is more violent, the depression is larger, and the droplets begin to enter the rotor disk and impact the rotor blade. Factors contributing to the loss of relative thrust compared with IGE are the weakening of the high-pressure area caused by the depressions mentioned in the dimpling mode, and the complex interaction of the droplets with the rotor blade. Droplet impact with the rotor may form a water film on the upper wing [34,35,36], which affects the flow of the airfoil. However, there is no research to show how droplets in mixed air–water flows affect the aerodynamic characteristics of the rotor; further research on droplet dynamics is needed. One of the challenges is to obtain the parameters of the droplets reduced by the rotor, such as size distribution, liquid water content, and terminal velocity, since these droplets are different from the droplets in the rainfall environment, and the different Weber numbers affect the interaction of the droplets with the rotor blade. Splashing mode is the most common condition for most cross-media vehicles, and the unsteady effects of droplets on rotor thrust, torque, rotor speed, and blade structure cannot be ignored.

3.2.3. Penetrating Mode

The IGE of a ducted fan is different from that of the rotor. A high-pressure area was created between the system and the ground that interrupted the jet flow from the duct, which increased the lift of the propeller. However, as the rebounded flow was pulled into the system again, the lift of the duct decreased and the total lift was lost. The downwash flow bounced off the ground as the ducted fan approached the ground and entered the vortex ring state. Mi [12] argued that the soft water surface was impacted by the high-speed jet flow from the duct and formed a “drainage area”. The water surface had a blocking effect similar to that of the ground, and the degree of the effect was weaker than that of the ground. The total lift of the ducted fan was between OGE and IGE. However, the experimental results in Section 3.1.3 show that in the penetrating mode, the high-speed downwash flow hits the water surface and generates a large amount of momentum exchange, resulting in a large number of droplets and large tears being ejected upwards and entering the duct, where they surround the duct and impact with the fan.

As shown in Figure 14, in the range of z/D < 8 near the water surface, the thrust decreases with the height of the water surface, and the higher the throttle, the greater the thrust loss. The maximum thrust loss is about 52%, which is in good agreement with the measurement by Huo et al. [13]. The data given by the experiments are averaged over 3 s sampled at each measured point; the unsteady characteristics of aerodynamic performance can be found in study [4], which shows significant thrust fluctuation in NWE condition. Note that the penetrating mode is not a phenomenon unique to ducted fans, and it has also been seen with a three-bladed rotor blade of 0.12 m diameter for NWE operation [16]. Such thrust loss is a result of not only the decrease in rotor thrust coefficient due to droplet-rotor interaction but also the decrease in rotor speed due to the amounts of splash and droplet impacts on the rotor. Compared to OGE, NWE in penetrating mode causes a considerable thrust loss rather than thrust increment like the IGE of the rotor.

3.3. PIV Measurements in Dimpling Mode

3.3.1. Time-Averaged Velocity Field Results

Figure 15 shows the time-averaged velocity field superposed by the velocity magnitude field near the ground for three rotor heights off the water surface with a fixed rotor speed N = 4360 r/min. It is clear to see the water surface jet flow resulted from the outward expansion of the rotor wake after hitting the water surface. As mentioned in Section 3.1.1, the rotor wake forms a depression when it reaches the surface of the water and after deflection by the liquid crown. A shear layer (green region) and an almost stationary flow region (blue region) are sequentially distributed above the water surface jet region. For the three rotor heights of z/R = 0.5, 0.2, and 0.1, high localized flow velocities were produced at the rim of the depression and at the top of the liquid crown at about r/R = 1 and r/R = 1.4. Much of the local increase in flow velocity near the water surface is because of the persistence of the tip vortices to relatively older wake ages as a consequence of vortex-stretching effects. These high localized velocity areas increase the velocity gradient near the water surface. As is known to all, any factor that is able to increase the shear force being exerted on the crater surface and the velocity of surface liquid can increase the rate of droplet generation. Thus, vortex-stretching effects above the liquid crown may promote droplet tearing off due to K-H instability. The velocity decreases quickly after r/R = 1.6 as the water surface jet becomes fully developed and expands away from the rotor.

It can be seen that the effect of the depression and the liquid crown is to slightly deflect the flow upwards, but different from the results in the study [17], which showed that the rotor enters the vortex ring state near the water surface. The results of the PIV experiments in this study show that there is a flow around the liquid crown after the deflection by depression, without any vortex ring downstream.

In addition, the decrease in rotor height increases the intensity of the momentum exchange in the rotor wake at the initial liquid level, resulting in a smaller jet velocity near the water surface and a larger static pressure under the rotor. It is clear that the closer the rotor is to the water surface at the same rotor speed, the larger the splash and crown formed, and the more droplet tearing off is broken. Therefore, as mentioned in [21], there are two mechanisms of droplet generation: one is droplet tearing off due to the instability of the water surface caused by the shear of the water surface jet, and the other is direct ejection. The finger structure in Figure 7 demonstrates that droplet tearing off due to K-H instability is the first to occur at a low-momentum exchange between the rotor wake and the water surface.

An interesting phenomenon is that the helicopter approaching the water surface produces a droplet or water mist field similar to the dust cloud in the helicopter brownout, and the pattern of this droplet field is very different from the pattern of the mixed-water flows induced by CMV. This may be explained by the fact that the helicopter, although it has large downwash and water surface jet velocities, is far away from the water surface at the same normalized rotor height, which results in a relatively low momentum exchange. Therefore, the helicopter wake mainly produces droplets caused by the shear of the water surface jet instead of directly ejected droplets.

In IGE operations, the wake turns rapidly from a mostly axial direction to a radial direction as it approaches the wall and then expands outward over the ground plane. In NWE operations, the rotor wake also expands directly, but the difference in the degree of expansion before hitting the water slightly changes the position of the crown formation. The closer the rotor is to the water surface, the greater the depth and the smaller the radius of the depression that is formed.

3.3.2. Phase-Averaged Vorticity Field Results

Figure 16 shows the phase-averaged velocity vector field superposed by the vorticity field at different rotor heights off the water surface. Due to the extremely low rotor height off the water surface, the tip vortices reached the water surface flow rapidly before they diffused. At z/R = 0.2 and 0.1, only vortices produced at the tip of the blade are visible; older tip vortices appear to be rapidly dissipated by shearing in the developing water surface jet after flowing over the rim of the depression and there are no significant vortices above the liquid crown.

A total of 40 PIV image pairs were acquired to detach blade tip vortex positions at different wake ages at each water surface distance, as shown in Figure 17. Ψ represents the wake age angle. The center of the connecting line is the centroid (mean) of the data subset, and the line represents the error between the data and the mean data. It is believed that the average coordinates of the vortex of the overall data are within the elliptical range with a confidence level of 95%.

Figure 17 shows that the blade tip vortex continues to diffuse for 1 to 2 revolutions after flowing over the rim of the depression, and there are still vortices entrained by the water surface jet above the liquid crown. Obviously, the blade tip vortices that do not reach the water surface are relatively fixed, as shown in Figure 17a. However, the position of older blade tip vortex that passed over the rim of the depression was clearly dispersed. The reason for such discrepancy is not only aperiodic motion caused by inherent vortex instabilities and propagation of flow unsteadiness [37], but also the effect of highly unsteady depressions on the rotor wake, which further promotes the aperiodic motion of blade tip vortex. At different moments, depressions of different depths and liquid crowns of different heights change the trajectory of the tip vortex motion. Therefore, all the older tip vortices that have flowed over the depression are “averaged out” in the phase-averaged vorticity field.

3.3.3. Phase-Averaged Velocity Profile Results

Figure 18 shows a phase-averaged radial velocity profile, and the highest flow velocities of the water surface jet occur at about r/R = 1.5. The swirl velocity induced by a tip vortex inside the water surface jet is in the same direction as the water surface wash velocity, and this results in a significant augmentation of the local flow velocities near the water surface. Therefore, the local peak velocity of the jet is caused by the tip vortex. Between r/R = 1.6 and r/R = 1.8, the water surface jet fully develops, the width of the jet becomes wider, and the centerline velocities decrease. Note that in the z/R = 0.1 and 0.2 cases, the maximum velocity of the surface jet at r/R = 1.8 is still as high as 5 m/s. Therefore, for multi-rotor CMV, the water surface jet with large kinetic energy is able to carry splashed droplets generated by a single rotor to enter the adjacent rotor disk, causing potential thrust loss. In the z/R = 0.1, 0.2, and 0.3 cases, between r/R = 1.3 and r/R = 1.5, as the rotor height decreases, the distance between the axis of peak centerline velocities of the water surface jet and the water surface gradually increases, which indicates that the liquid crown and the depression have an obvious lifting effect on the water surface jet. However, in the z/R = 0.5 case, the axis of peak centerline velocities of the jet at different radial positions is almost at the same height, and the lifting effect almost disappears, which can be explained as a low-momentum exchange when the rotor is far away from the water surface, resulting in smaller depression depth and liquid crown height. As the rotor speed increases, the depression becomes deeper, and the liquid crown’s deflecting effect on the airflow increases, leading to a further increase in the lift angle. This might result in a vortex ring state. However, the current results show that the lifting effect of the crown at 4200 r/min is not strong enough to make the rotor enter the vortex ring state.

As described in Section 3.1, the mechanisms of the interaction between the rotor wake and the free surface and the motion of droplets in the water surface jet are very complex. The primary breakup and secondary breakup of droplets occur, which are affected by the rotor wake; some of these droplets move upward and enter the rotor disk, causing thrust loss. Figure 19 shows a phase-averaged axial velocity profile at different axial positions. In the development of the water surface jet, peaks of positive axial velocities due to blade tip vortex convection occur at various radial locations, e.g., r/R = 1.4 and 1.6. These positive axial velocity components are a potential cause of entrainment and transport of droplets into the inflow of the rotor under the relatively low-momentum exchange between the water surface and the rotor wake.

3.3.4. Fluctuating Characteristics of Rotor Wake for NWE Operation

Reynolds stress is an additional stress due to turbulence, reflecting the turbulence fluctuation characteristics of the flow field. Calculating the Reynolds stress in the near-surface flow field of the rotor wake quantifies the shear effect of the rotor wake near the liquid crown. Figure 20 and Figure 21 show the normalized Reynolds shear stress and turbulent kinetic energy field, where u’ and v’ are the radial and axial fluctuation velocities, respectively.

Unlike the IGE state where the Reynolds stress is concentrated in an area parallel to the ground, the NWE state has the Reynolds stress concentrated in a straight line at an angle to the water surface due to the lifting effect by the liquid crown and depression, as seen in Figure 20. The smaller the rotor height off the water surface, the larger the angle formed between the concentrated Reynolds stress distribution area and the water surface, which is consistent with the conclusion in Section 3.3.3.

As seen in Figure 21, the turbulent kinetic energy of the water surface jet gradually increases during its development along the radial direction, which is due to the fact that the rotor wake containing a large number of vortex sheets is highly turbulent. As seen in Figure 21b,c, as the rotor heights off the water surface decreases, the peak turbulent kinetic energy occurs at about r/R = 1.4, and the peak areas are more concentrated, leading to a region where the blade tip vortex begins to stretch after reaching the water surface and interacts with the jet during diffusion. The turbulence fluctuation caused by the blade tip vortex in this region may promote the secondary breakup of the droplet in the rotor wake since r/R = 1.4 is exactly where the liquid crown is located [38].

Note that the fluctuating characteristics described here are only applicable to specific depression modes and specific rotor speeds. With the increase in rotor speed, the depression becomes deeper, the liquid crown becomes higher, the lifting effect of the liquid crown on the water surface jet becomes stronger, and the distribution characteristics of Reynolds stress and turbulent kinetic energy are likely to change. In this paper, due to the lack of quantitative measurement of droplets in splashing mode, we can only preliminarily analyze the distribution characteristics of Reynolds shear stress peak area in dimpling mode, but the correlation of turbulence fluctuation in the water surface jet and secondary breakup of droplets deserves attention in the future.

4. Conclusions

Experiments were conducted to examine the fluid dynamic behavior of a rotor wake as it interacted with a water surface. The aerodynamic performance, kinematic characteristics of droplets, and velocity fields for NWE operation were measured, analyzed, and discussed in detail. The following conclusions can be drawn from the present investigation:

(1)

Generally, considering the different mixed air–water flows patterns generated by the rotor and droplets’ splashing, NWE can be categorized into three modes: dimpling, splashing, and penetrating. This conclusion helps in the study of the relationship between models and prototypes of rotors near the water surface in the future.

(2)

The relationships between those three depression modes and the aerodynamic characteristics of NWE were established. The evidence obtained from this study suggests that compared with the OGE, the trend in thrust increment in NWE is the same as IGE, while this increment is smaller than that of the IGE in dimpling mode. This type of NWE can be observed on the two-bladed rotor blade with a diameter of 0.25 m. In splashing mode, a clear turning point occurs in the thrust curve, after which the thrust increment begins to decrease due to droplets. However, there is almost always a net effect of thrust increment, which means that the thrust loss due to droplets is less than the thrust increment due to the high-pressure area. This type of NWE can be observed on the two-bladed rotor blade with a diameter of 0.56 m. While in penetrating mode, the thrust loss is always present even at relatively far rotor heights off the water, the thrust loss decreases with the rotor away from the water surface. This type of NWE can be observed on the 7 cm diameter ducted fan and the 0.13 m diameter three-bladed rotor blade.

(3)

Important aspects of the droplet generation process were identified from high-speed imaging. The formation of finger structure was identified. Two droplet tearing-off mechanisms were revealed: water–air interface instability due to K-H instability and direct ejection due to wake impingement on the water surface. Understanding the two droplet generation mechanisms helps to study the similarities and differences between the droplet fields reduced by CMV and helicopter.

(4)

The PIV results show that in the dimpling mode, the rotor does not necessarily enter the vortex ring state, although the depression and the liquid crown deflect and lift the wake. Since the rotor disk is very close to the water surface, the rotor hits the water surface and develops a water surface jet along the radial direction, which quickly shears the blade tip vortex and causes it to dissipate quickly. A localized high-velocity region occurs in the surface jet caused by the stretching of the blade tip vortex, and the increased velocity gradient near the water surface may promote air–water interface instability at the water surface, tearing off more droplets.

(5)

The depressions and liquid crowns formed by the rotor wake are highly unsteady, which further promotes the aperiodic motion of the blade tip vortex and changes its trajectory of diffusion. Meanwhile, the turbulence fluctuation caused by the blade tip vortex above the liquid crown may promote the secondary breakup of the droplet.

Due to the limitation of the measurement technique, this study can only measure and analyze the velocity field without droplets, while the multiphase flow field of air and droplets at relatively high rotor speed cannot be obtained at the same time. Note that obtaining the determination basis and critical conditions of different depression modes also depends on a large number of aerodynamic performance experiments. Meanwhile, the depths of the depressions in different depression modes are significantly different and have different lift and deflection effects on the rotor wake; so, the conclusions obtained in this study for the dimpling mode are not necessarily applicable to the splashing mode, but there is a better understanding of the near-water effect of the rotor.