Parameter Analysis of Active Flap Control for Rotor Aerodynamic Control and Design

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Introduction
Improving the rotor's performance and reducing aerodynamic noise and vibration are critical aspects of helicopter design. Active flap control (AFC) [1][2][3] has become a hot spot in helicopter rotor design in recent years due to its ability to reduce vibration and noise. The key feature of the AFC rotor is that the blade is equipped with a trailing edge flap (TEF), which deflects up and down relative to the main blade, as shown in Figure 1 [4][5][6]. The geometry of the blade can be dynamically changed by rotating the TEF.
AFC can control rotor vibration; for example, a BK117 helicopter equipped with AFC achieved substantial vibration reduction [7]. AFC can also be used for noise control. Chia et al. observed noise reduction of up to 6 dB [8]. In addition, it can also be used to improve the rotor performance. For example, Ravichandran et al. improved the hovering efficiency of a helicopter under a heavy load by deflecting the TEF downward [9]. AFC has also been applied to improve wind turbines' energy generation capacity and the power generation ability of wind tunnels [10,11]. In the helicopter industry, the FRIENDCOPTER project [12] of Eurocopter and Airbus and the smart material-actuated rotor technology (SMART) [3,13] by DARPA, NASA, and Boeing have fully verified the vibration reduction, noise reduction, power control, and performance of the AFC rotor and demonstrated the application prospect of this new active control technology.
Research on AFC rotors has primarily focused on the design and driving mechanism and the analysis of vibration reduction, noise reduction, or performance improvement. Many structural designs have been developed to manufacture rotors and achieve controllable deflection. AFC is powered by a piezoelectric actuator, electrohydraulic system [12], or other methods. Improved designs include the induced-shear piezoelectric actuator [14] and pneumatic artificial muscles based on bionic structures [15]. New controllers have been proposed, such as the adaptive and discrete-time model predictive controller. Most simulation studies have used computational fluid dynamics (CFD) calculations using a deformation mesh [16], overset grid [17,18], or the newly developed viscous vortex particle method [19]. However, these simulation strategies must be meticulously designed and handled carefully.
Regarding AFC aerodynamics and performance research, the focus of this paper, Hassan et al. [20] tested and analyzed the HH-06 airfoil equipped with a TEF, considered the influence of the overhanging length on hinge moment, and provided guidance for the design of AFC airfoils. Xing et al. [21] studied the effect of a TEF on the dynamic stall vortex and unsteady aerodynamic force of a pitching airfoil. They observed a decrease in the maximum drag and pitching moment coefficient in the simulation and found that increasing the chord length was an effective control method. By optimizing the nonharmonic control law, Kody et al. achieved a power reduction of 9.5% at a large advance ratio [22] and improved the performance and vibration simultaneously by optimizing the control of a dual-segment TEF [23]. In addition, Jose and Baeder [18], the author's team [24], and Jain et al. [25] also discussed the aerodynamic performance loss caused by leakage flow in the gaps of the airfoil and rotor.
Many studies focused on the blade design of the AFC rotor and the characteristics of airfoils (including dynamic airfoils) with TEFs, but few conducted detailed analyses and comparisons of this rotor with different designs and control parameters. Multiple experiments have been conducted on existing AFC designs, such as SMART, including vibration control, noise control, and power control. However, these experiments used scaled rotors with specific shapes and did not consider different TEF sizes and installation positions. Thus, they cannot be used to improve the size, control performance, and design of AFC rotors. The  (2) Numerical simulations must consider the unique aerodynamic shape of the TEF and model highorder deflection. It is also challenging to simulate the motion between the main blade and the TEF and the flow field near the TEF (such as slot flow [26]) in sufficient detail. Therefore, the authors combined the advantages of the reverse overset assembly technique (ROAT) [27], arbitrary Lagrangian-Eulerian (ALE) numerical simulation, and experience in AFC airfoil simulation in previous research to establish an AFC rotor numerical model and verify the grid independence. The effect of AFC on the blade surface load is verified. We investigate the effects of the parameters on the flow conditions, TEF size and position, and control performance. Suggestions for AFC rotor design are provided based on the observed phenomena, such as the environmental consistency of the AFC control and resonance amplification.

Simulation Method
2.1. The Motion Overset Mesh Method. The grid assembly of the AFC rotor uses the ROAT proposed by the author in a previous study [27]. The AFC rotor grid used in the CFD simulation is obtained by overlapping the main blade grid    International Journal of Aerospace Engineering and the TEF grid to ensure that the grid near the body follows the TEF's rigid transformation without causing grid deformation, and high grid quality in complex movements is obtained. The main steps of the ROAT method are shown in Figure 2(a). In step 1, the grids are searched to find the donor cells. The cell volume and the wall distance of each cell are compared with that of the donor cell to obtain the initial classification results based on the competition criterion. In step 2, several cells are selected as interpolation cells from the initial classification results according to the user's boundary setting. Finally, in step 3, the final overset assem-bly result is obtained by combining the donor cell and interpolation cell information. Compared with the deformation mesh technology [16], this strategy can model the gaps in the actual structure, thus giving a more realistic flow field simulation result, and has been verified and applied in our previous research. In addition, a straightforward motion description method of the TEF based on coordinate system transformation is proposed. The concept of this method is that the movement of one coordinate system relative to another can be described by translation and rotation. Complex motion can be converted into ground motion after 5 International Journal of Aerospace Engineering several simple conversions by repeating this step many times, as shown in Figure 2(b) [28]. The coordinate transformation function is shown in equation (1).

CFD Method.
This paper uses the CFD method based on the unsteady Reynolds-averaged Navier-Stokes equations (URANS) to obtain high accuracy and efficiency. This method, shown in equation (2), is commonly used in rotor flow field simulation.
where W = ½ρ, ρu, ρv, ρw, ρE T is the conserved variable, ρ is the density, u = ½u, v, w T is the velocity of the flow in a grid cell, E is the total energy per unit mass, and FðWÞ and GðWÞ are the inviscid and viscous fluxes, respectively. The calculations were performed using the rotorcraft aerodynamics and aeroacoustics solver (RADAS) [29]. The ROE-MUSCL (Roe's upwind scheme and monotone upstream-centered schemes for conservation laws) spatial discretization scheme is chosen for the blade grid with the implicit lower-upper symmetric Gauss-Seidel (LU-SGS) temporal discretization and the Spalart-Allmaras (S-A) turbulence model. In contrast, a central differencing scheme is used for the background grid of the AFC rotor and calculated using the inviscid Euler equation. Furthermore, the dual time-stepping scheme is adopted to calculate the load fluctuation in unsteady flow. These settings are consistent with the author's previous research on an AFC airfoil [24], similar to Strawn's research [30], and have been fully verified in rotor simulations.   [20] is used as the verification case. The original airfoil shape and the deflected airfoil are shown in Figure 3(a); the TEF is deflected downward by 4°. The overset grids are shown in Figure 3(b). The cell number of main airfoil is 18 thousand, and the cell number of the TEF is 13.5 thousand, with 10.01 thousand cells in the background. The flow field obtained by the RADAS for the inflow condition of AOA = −4:03°and Ma = 0:758 is shown in Figure 3(c). Figure 3(d) shows the comparison of the surface pressure coefficients obtained from the experiment [20], RADAS, FLUENT software, and Jose and Baeder [18]. The results show that the simulation of the AFC airfoil by the RADAS is of reasonable accuracy.

Verification of AH-1G
Rotor's Forward Flight. Figure 4 shows the flow field vorticity results of the AH-1G rotor in forward flight with a tip Mach number of 0.65 and an advance ratio of 0.19. This rotor has two rectangular blades with a chord length of 0.727 m, an aspect ratio of 9.8, and a linear negative twist of -10°/R. In the simulation, the Reynolds number is 9:73 × 10 6 , the rotor pull coefficient is 0.0464, and the trim result is θðψÞ = 6:10 − 5:03 sin ψ + 1:19 cos ψ.
The cell number of each main blade is 1.197 million, with 2.56 million cells in the inner background and 3.60 million cells in the outer background. Figure 5 depicts the normal force obtained from the RADAS and an experiment reported by [31] for different radii. The proposed method is suitable for the rotor simulation in forward flight.

Model Parameters.
A numerical simulation of the 3D AFC rotor is carried out. The change in the TEF deflection angle is calculated by a harmonic oscillation function as shown in equation (3), where θ t is the deflection angle of the TEF, θ T 0 is the offset angle, A t is the deflection amplitude (the downward deflection is positive), ω tef is the frequency, and φ tef is the phase of control. The AFC rotor's base parameters are listed in Tables 1-3.
The chordwise gap between the TEF and the main blade is 1.0%c, and the spanwise gap is 0.075%R.

Grid Layout and Overset
Assembly. The grid layout is shown in Figure 6, where the incoming flow is in the positive direction of the x-axis. Similar to Aoyama et al.'s research [2] on the rotor blade vortex interaction, there are two Cartesian background grids with different sizes to ensure high accuracy and reduce the overall number of grid points. The dimensions of the coarse outer background are 15R length (x-axis: -5R to 10R), 10R width (y-axis: -5R to 5R), and 6R height (z-axis: -3R to 3R) with 0.48 million cells. The grid resolution in the X and Y directions are 0.096c and 0.025c, respectively. The dimensions of the fine inner background are 3.9R length (x-axis: -1.4R to 2.5R), 2.8R width (y-axis: -1.4R to 1.4R), and 0.5R height (z-axis: -0.25R to 0.25R) with 2.8224 million cells. The blade mesh has a C-H topology, and the overset interpolation boundary of the main blade and TEF is 1c and 1c tef from the wall faces in the normal direction. The cell number of each main blade is 1.428 million, and the cell number of the TEF is 0.405 million. The presented overset grid set is considered as the baseline set, and the detailed grid independence verification is applied in the following section.
The assembled grid is shown in Figure 7. The inner background grid is embedded in the outer background grid, and two main blades are embedded in the inner background grid. The main blade grid cells surround the TEF's grid and overlap it. The grid system constitutes an overset grid with multiple overlapping levels.
3.3. Verification of Grid Independence. The grid independence of the uncontrolled AFC rotor is verified. While the topology of the main blade grid remains unchanged, grids with different cell numbers are tested to consider the influence of the blade. Two groups of fine inner background grids are tested to consider the influence of background grid. The size of the baseline inner background grid is 0.096c as group 1, and that of the refined inner background grid is 0.065c as group 2. Similarly, blade grids with different cell numbers are used; the details are listed in Table 4. Thus, as described   International Journal of Aerospace Engineering in Section 3.2, the baseline grid set is with the relative cell number of blade grid of 1 and with group 1 as the inner background grid. The first layer grid of each main blade grid and TEF's grids is y + ≤1. Figure 8 shows the calculation results for different grid sizes. As shown in Figure 8(a), the peak values of the normal force in the 0.7R section are lower (higher) than the reference baseline for a relative grid size of 0.25 (0.5). The results for a grid size of 2.0 are slightly different from the baseline. There is no apparent difference between group 1 and group 2 with different background grid cells, as shown in Figure 8(b). Therefore, the grid size of 1.0 in group 1, namely, the baseline grid set, selected in this study meets the simulation requirements.
3.4. AFC Control Performance. Figure 9 shows the vertical force distribution of the rotor disk without AFC control and with AFC control for the -120°phase and 40°phase. The parameters of baseline case without AFC control are the same as that listed in Tables 1 and 2, while other AFC parameters listed in Table 3 are set to 0. And the case with AFC control is the same as listed in Tables 1-3. Since there is no trim control, the blade load is the largest in the tip region when the azimuth angle is 90°and the smallest in the root region when the azimuth angle is 270°without AFC control, as shown in Figure 9(a). For the AFC control with the -120°phase, the TEF deflection frequency is 2ω (denoted as 2P); thus, the TEF is downward deflected near  Figure 7: Overset assembly of the AFC rotor grids. 9 International Journal of Aerospace Engineering the 90°azimuth, increasing the thrust of the blade. In contrast, the TEF is upward deflected in the 40°phase control case, reducing the blade's thrust. The vertical force is similar for the -120°phase control and no control but substantially different for the 40°phase control. Figure 10 shows the vertical force of the 0.8R section. Figure 10(a) shows the vertical force for different azimuth angles, and Figure 10(b) shows its change rate with respect to the azimuth angle. The change rate of the vertical force is significantly different for the cases with and without AFC control. According to Lighthill's acoustic analogy and Farassat's formulation 1A [32], the load and its time derivative, namely, the force and its change rate, determine the loading noise of the rotor. As can be seen in Figures 9 and  10, the AFC control can introduce significant change in the distribution of the force and its change rate. A properly selected AFC control parameter could have the potential to decrease the overall load or its change rate and lead to a noise reduction, such as the control phase of 40°shown in Figure 10.

Parameter Analysis and Discussion
As described in Section 3.1, the parameters of baseline case without AFC are the same as that listed in Tables 1 and 2, while other AFC parameters listed in Table 3 are set to 0. And the parameters of the two baseline cases with AFC control are the same as listed in Tables 1-3, with a control phase of -120°or 40°, respectively. In the following sections, all the parameter analysis cases are based on the baseline cases. Only the parameter to be studied is changed, while other parameters remain to be identical to the baseline cases. The two control phases of baseline cases with AFC are selected to show possible influence of AFC parameters for different control phases.

Operation and Flow Condition
4.1.1. Rotational Speed and Advance Ratio. Different advance ratios and rotational speeds (20π, 40π, and 60π rad/s) are tested to evaluate the performance of the AFC rotor under different operating conditions. The thrust coefficient and torque coefficient are shown in Figure 11. The rotor thrust coefficient and torque coefficient increase with the advance ratio and rotational speed because the maximum speed on the advancing side of the blade is only about Ma = 0:72 at a maximum advance ratio of 0.32 and a rotational speed of 60π rad/s. No wide range stall which could lead to obvious aerodynamic performance loss occurs. The thrust and torque coefficients are slightly smaller for -120°p hase control than without AFC control. Although the thrust is slightly higher at 40°phase control than without AFC control, the torque coefficient is significantly different, i.e., higher at 20π rad/s and lower at 60π rad/s. In general, the difference in thrust between with and without AFC control is about 1%. It is slightly higher at high advance ratios. The torque coefficient exhibits a similar phenomenon. The cases at a given rotation speed with a certain AFC control and without AFC control exhibit a constant torque coefficient offset at the advance ratio over 0.15. And the torque offset is different under various rotation speed and for different control phases. It can be concluded that at the advance ratio over 0.15, each set of AFC control will introduce a specific resistance offset which is affected by the rotation speed to the rotor and lead to a specific difference in the torque coefficient. Figure 12 shows the rotor thrust coefficient and torque coefficient at collective pitch angles of 4°to 8°. Similarly, the rotor's thrust coefficient and torque coefficient increase with the collective pitch angle, and the thrust coefficient increases almost linearly. No wide range

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International Journal of Aerospace Engineering stall occurs. The rate of rise of the torque coefficient increases with the pitch angle. The changes in the thrust and torque coefficients are generally similar to those of a conventional rotor [33]. Furthermore, the difference in the parameter values between AFC control and no control does not change significantly with an increase in the collective pitch angle. Figure 13 shows the thrust coefficient and torque coefficient for different TEF chord lengths (0.15c, 0.2c, 0.25c, 0.3c, and 0.35c). As the TEF's chord length increases, the thrust coefficient decreases slightly, as shown in Figure 13(a). The reason is that an increase in the chord length increases the peak value of the instantaneous thrust, whereas the thrust decreases in other conditions (such as the upward deflection time), as shown in Figure 14. As depicted in Figure 14(a), the TEF is not always in a downward deflection on the advancing side; thus, the vertical force does not show an increasing trend all the time and the thrust coefficient value changes by 1%. As the chord length increases, the torque coefficient increases slightly  13 International Journal of Aerospace Engineering (from 0.15c to 0.25c) and then decreases. The reason is that the deflection of the TEF increases the drag. However, the TEF's continuous up and down deflection provides a driving force, as shown in Figure 15. In the rotor frame, the horizontal force is "drag" that contributes to the torque when it is positive and in the opposite direction to that of rotation and is "driving force" that counteracts the torque when it is negative and in the same direction with that of rotation. As the TEF chord length increases, the driving force increases, and the torque coefficient decreases. Similar phe-nomena were also observed in the reference [21] and the author's previous research on AFC airfoils.

The Span
Length of TEF. The inner end face of the TEF remained the same, and the span length (0.09R, 0.12R, 0.15R, 0.18R, and 0.21R) was adjusted. Similar to the results for an increase in the chord length, the rotor thrust coefficient decreases slightly due to the disturbance of the flow field by the TEF, but the change is relatively small (within 1%), as shown in Figure 16(a). However, unlike the 15 International Journal of Aerospace Engineering results for increasing the chord length, the rotor torque coefficient slowly increases with the span length. The change in the driving force is smaller when the span length increases than when the chord length increases due to an increase in drag because of the TEF, as shown in Figure 17 and compared with Figure 15. Figure 18 shows the effect of the TEF installation position (0.65R, 0.7R, 0.75R, and 0.8R) on the rotor's aerodynamic characteristics. As the installation position moves toward the rotor tip, the difference in the thrust coefficient between AFC control and no AFC control decreases. The thrust coefficient increases with the TEF installation position for the -120°phase control and is lower than that in the uncontrolled case. It shows a gradual downward trend for the 40°phase control while the thrust coefficient is higher than that in the uncontrolled case. The reason is that the high-thrust area of the rotor decreases as the TEF installation position moves to the rotor tip ( Figure 19). In the -120°phase control case, the root side region of the TEF compensates for the thrust loss when the TEF is installed near the tip; however, this phenomenon is not   Figure 20. The thrust coefficient and torque coefficient are significantly larger at a TEF deflection frequency of kω (the product of the blade number and the rotation frequency, e.g., 2P and 4P in the test cases), than at other frequencies. When the frequency of the flow field disturbance due to deflection is a multiple of the rotation frequency, stable superposition occurs, resulting in a significant change in the aerodynamic force and a resonance phenomenon. The peak-to-peak value is larger at 2P than that at 4P. As the deflection frequency increases, the trend of the torque coefficient is similar to that of the thrust coefficient. However, it should be noted that the phases required to reach the peak of the thrust or torque coefficient differ for different frequencies. Further analysis is required to obtain the optimum phase.

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International Journal of Aerospace Engineering  Figure 21 shows the thrust coefficient and torque coefficient for different TEF amplitudes (2, 4, 6, 8, and 10°). In contrast to the response of the thrust coefficient to the installation position close to the tip, the thrust coefficient decreases as the TEF amplitude increases for the -120°p hase but increases for the 40°phase, as shown in Figure 21(a). The reason is that the force of the TEF deflection decreases for the -120°phase case and increases for the 40°phase case. An increase in the deflection amplitude strengthens this effect. Moreover, unlike the thrust coefficient, the torque coefficient increases with the TEF amplitude due to additional drag, regardless of the direction of TEF deflection (Figure 21(b)). The trend is similar to the -120°phase case and the uncontrolled case. Figure 22 shows the thrust coefficient and torque coefficient for different TEF offset angles (-2, -1, 0, 1, and 2°). Since the offset angle only changes the average deflection angle of the TEF, the response is similar to an increase in the camber of the airfoil. Thus, the phenomenon is similar to that of the AFC airfoil [34]. An increase in the TEF offset angle results in a linear increase in the thrust coefficient and torque coefficient of the rotor ( Figure 22).

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Conclusion
An AFC rotor with a TEF was simulated using the overset assembly method, multiple coordinate systems, and the URANS solver. The accuracy and suitability of the method were verified. The effect of different operating conditions, TEF size and position, and the control parameters of the rotor were analyzed. The following conclusions were obtained, serving as a reference for the design of AFC rotors.
(1) The deflection of the TEF was equivalent to changing the camber of the airfoil, causing a change in load distribution and significantly influencing the change rate of the vertical force. In general, the deflection of the TEF reduced the thrust coefficient by about 1%, but the appropriate offset angle can compensate for the thrust loss. Hence, multiple purposes, such as optimization of rotor load distribution and significant reduction of vibration and noise, can be achieved by the application of the TEF control with limited penalty in thrust loss with a considerable flexibility compared with passive control methods (2) With AFC control, the trend of the rotor thrust and torque coefficients for different operating conditions was highly similar with that of conventional rotors. The influence of a certain set of AFC control parameters showed a predictable pattern for a certain rotor under various flight conditions. Therefore, universal design solutions of AFC parameters for a certain rotor should exist for given purposes (3) The control phase and frequency were the key factors affecting the thrust and torque coefficients. Changes in the thrust and torque were more significant at rotor harmonics with multiple of blade number, approximate to a resonance effect, which can be exploited in AFC rotor design (4) The deflection of the TEF increased the driving force, reducing the rotor power at large chord and span lengths (but may increase the power of TEF's deflection). As the chord length, span length, and amplitude increased, the change rate of the thrust and torque coefficients increased

Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.