ACRONYMS AND NOMENCLATURE
- CFD
Computational fluid dynamics
- CAE
Computational structure mechanics
- SMA
Shape-memory alloy
- MFC
Macro fibre composite
- RANS
Reynolds-averaged Navier–Stokes
- AoA
Angle-of-attack
- A
Vibration amplitude
- T
Time
- C
Chord length
- U∞
Coming velocity
- Re
Reynolds number
- Cd
Drag coefficient
- Cl
Lift coefficient
- Cp
Pressure coefficient
- y+
Y plus wall distance
- Ma
Mach number
$\omega$Angular velocity
- f
Vibration frequency
- $\uptheta$
Rotated angle
1.0 INTRODUCTION
For new flight vehicles, higher mobility and adaptability are sought to satisfy the rapidly increasing demand for air transport. For civil aircraft, the aim is to enhance the economic performance and reduce the fuel consumption and exhaust emissions, resulting in strict aircraft design requirements. According to a report by the National Aeronautics and Space Administration (NASA), the payload of an aircraft can be increased by 20–40% by increasing the lift coefficient or reducing the drag coefficient by 5% during take-off(Reference Washburn, Gorton and Anders1). Correspondingly, the payload could be increased by 65% by increasing the lift coefficient by 5% during landing(Reference Scott, Joslin, Seifert and Theofilis2,Reference Khan, Grigorie, Botez, Mamou and Mébarki3) .
Active flow control technology effectively improves the aerodynamic performance of aircraft and provides a solution to requirements such as reduced noise and emissions and short departure and landing. Researchers have carried out various extensive investigations on active flow control technology, providing deep understanding on the unsteady flow characteristics around the aircraft and resulting in growing maturity of technologies such as smart materials, active control and mechatronics. Smart strategies can be implemented to control the separation phenomenon and thereby enhance the aerodynamic performance, thus improving the economy, mobility and adaptability of the aircraft.
Maldonado used synthetic jet actuators to enhance the performance of wind turbine blades and decrease the vibration by mitigating flow separation(Reference Maldonado, Farnsworth, Gressick and Amitay4). Botez conducted modelling, simulation and control for a miniature electrical actuator integrated into a new morphing wing application(Reference Botez, Kammegne and Grigorie5). The disadvantage of the conventional aileron lies in how it changes the camber of the wing. Indeed, the aileron rotates around its hinge point, thus creating a discontinuity in the slope of the aerofoil camber. Wu used linear ultrasonic motors with compliant runners, enabling full control over multiple degrees of freedom and resulting in an L/D ratio higher than that of a conventional, hinged control surface(Reference Wu, Costas, Zhong and Filippone6,Reference Baier and Datashvili7) . Researchers have reported the possibility of using SMA materials when developing shape-changing devices based on a morphing aerofoil model with a morphing flap to avoid the problem of the discontinuity caused by the operating principle of the traditional rigid aileron equipped with SMA actuators(Reference Botez, Koreanschi, Gabor, Tondji, Guezguez, Kammegne, Grigorie and Sandu8). For instance, in Iyyappan’s experiments, SMA was used to modify the upper surface of the aerofoil, obtaining notable results(Reference Iyyappan9). Kimaru proposed a concept based on an MFC actuator attached to the composite plate that extends along the main wing and connects the leading- and trailing-edge sections. Wind-tunnel tests proved that this conceptual design enhanced the aerodynamic performance(Reference Kimaru and Bouferrouk10). Johannes presented a hybrid morphing wing instrument, actuated using SMAs and MFCs embedded in both surfaces. Not only could the shape of the aerofoil be optimized as a function of the current mission profile, but also the shear layer was influenced(Reference Scheller, Jodin, Rizzo, Duhayon, Rouchon, Triantafyllou and Braza11).
In the above-cited research, the performance of the morphing aerofoil was usually investigated in wind-tunnel experiments, applying techniques such as particle image velocimetry (PIV), pressure measurements and laser Doppler velocimetry, especially for cases based on continuous deformation. PIV measurements were adopted to study the trailing edge of a NACA0012 morphing aileron, to investigate the physical effect on the flow of high-frequency low-amplitude actuation at high Reynolds numbers(Reference Jodin, Motta, Scheller, Duhayon, Döll, Rouchon and Braza12–Reference Chinaud, Rouchon, Duhayon, Scheller, Cazin, Marchal and Braza14). Abderahmane conducted a numerical investigation of the frequency–amplitude effects of dynamic morphing for a high-lift configuration at a high Reynolds number(Reference Abderahmane, Jean, Jean, Yannick and Braza15). Kancharla built a computational model based on finite elements and carried out potential flow computations to obtain the deflection of the upper and lower skins of an aerofoil subjected to aerodynamic pressure and hysteretic deformation of an SMA wire(Reference Kancharla and Roy16). Szubert reported a conceptual analysis and computational model for how the unsteady buffeting phenomenon develops in the transonic, low-incidence flow around a supercritical aerofoil(Reference Szubert, Grossi, Jimenez, Hoarau, Hunt and Braza17). Furthermore, he analysed the turbulent flow around a supercritical aerofoil at high Reynolds number and in the transonic regime, involving shock wave–boundary layer interaction and buffet, by employing numerical simulations and turbulence modelling(Reference Szubert, Asproulias, Grossi, Duvigneau, Hoarau and Braza18).
Against this background, a conceptual hybrid design for an active flow control aerofoil based on SMA and MFC is proposed. CFD simulations are carried out to evaluate the feasibility of the prototype design. In most previous research, the foil is in a static state, which is not appropriate for modelling continuous morphing effects, such as tail vibration. The arbitrary Lagrangian–Eulerian methodology has been utilized recently, but requires greater computational effort and may suffer from data transfer errors during the interaction between the Computer-Aided Engineering (CAE) and CFD computations. Consequently, this work proposes to use the unsteady flow characteristics during dynamic morphing to model vibration, instead of the classical static simulations.
The remainder of this article is organised as follows: The next section introduces the conceptual design, turbulence modelling and CFD model for tail vibration. Secondly, the aerofoil’s shape and corresponding aerodynamic performance in three morphing states obtained by the SMA action are obtained. Finally, results investigating the effects of morphing on the aerodynamic performance for different vibration frequencies and amplitudes are presented.
2.0 NUMERICAL SIMULATION METHODOLOGY
2.1 Conceptual design
The selected aerofoil is the supercritical RAE2822 foil, whose maximum thickness is 12.1%, located at 37.9% of the chord length, with a maximum curvature of 1.3%, situated at 75.7%c(Reference Cook, Mcdonald and Firmin19). A hybrid morphing aerofoil is designed based on the SMA driving mechanism for take-off and landing, with MFC actuators for cruise. The SMA-driven deformed wing body is shown in Fig. 1, with two SMA plates embedded in the main body and then encapsulated into an integral active deformation skin by using polydimethylsiloxane(Reference Hartl, Leal and Stroud20). When the pre-stretched SMA plate is energized and heated, its length will decrease, and the restoring force in the SMA plate moves the middle or tail structure of the wing toward the head, thereby achieving bending deformation of the skin. Three aerofoil bending states, including the original form, can be achieved by controlling the states of the middle and tail SMA plates individually. Besides, using the MFCs attached to both sides of the tail substrate, as shown in Fig. 1, a high-frequency and high-precision optimal periodic displacement of the tail can be realized. Reciprocating motion of the tail is achieved by alternately controlling the two groups of MFC to contract and elongate(Reference Jodin, Motta, Scheller, Duhayon, Döll, Rouchon and Braza12).
Figure 1. Conceptual design of a hybrid morphing aerofoil (state 1, original state for cruise; state 2, morphing by tail SMA for take-off; state 3, morphing by middle SMA for landing).
It is assumed the length of the SMA plates shrinks by 7–10% after temperature changes. Using the mechanical finite-element analysis toolbox Abaqus, the two forms shown in Fig. 1 are obtained under individual action of the rear or middle SMA plate. State 2, with a maximum curvature of 1.87% located at 66.95%, and state 3, with a maximum curvature of 2.1% situated at 72.44%, provide the aerodynamic geometric shape for the subsequent CFD analysis. State 3, with the maximum bending resulting from the middle SMA plate, could be used for landing, while state 2 is used for take-off in line with the requirement in terms of the running conditions of different aircraft.
2.2 Boundary conditions
The inflow boundary condition is the far-field pressure, with a static value of 38.08kPa (A), Mach number of 0.74, AoA of 3.2°, turbulence intensity of 1% and turbulent viscosity ratio of 1. On the solid wall, impermeability and no-slip conditions are applied.
2.3 Turbulence modelling
A density-based algorithm is used to consider the effect of compressibility at high Mach number. The density and viscosity of air are obtained from the ideal gas and Sutherland model, respectively. Considering that the subsequent analysis focuses on the effects of separation and vortex shedding on aerofoil performance, the turbulent model is of great significance(Reference Szubert, Grossi, Jimenez, Hoarau, Hunt and Braza17,Reference Han, Krajnović and Basara21) . Oliviu used the k–
$\omega$ Shear Stress Transport (SST) model in numerical simulations and validated it for a morphing wingtip at a Mach number of 0.2 and AoA between 0° and 5°(Reference Oliviu, Andreea, Ruxandra, Mahmoud and Youssef22). In transonic flow research, relevant studies have identified that the two-equation k–
$\omega$ SST model cannot produce any unsteadiness at the present incidence value, while the Spalart–Almaras model underestimates the amplitudes of the shock motion(Reference Abderahmane, Jean, Jean, Yannick and Braza15). Delayed Detached Eddy Simulation (DDES)(Reference Shinde, Marcel and Hoarau23) and Organised Eddy Simulation (OES) k–
$\varepsilon$(Reference Brazaa, Perrina and Hoarau24,Reference Bourguet, Braza, Harran and Akoury25) are frequently employed for separating flows at small angles of incidence to include the complex interaction between coherent structures and chaotic turbulence. It has been proven that OES k–
$\varepsilon$ can describe the interaction between transonic buffet and Von Kármán vortices, especially for supercritical aerofoils(Reference Simiriotis, Jodin, Marouf, Elyakime, Hoarau, Hunt, Rouchon and Braza26,Reference Jean, Simiriotis, Marouf, Szubert, Asproulias, Zilli, Hoarau, Hunt and Braza27) . After careful comparison with the OES k–
$\varepsilon$ model, DDES is also considered to be a proper model to capture the instability and flow detachment around a supercritical aerofoil(Reference Szubert, Asproulias, Grossi, Duvigneau, Hoarau and Braza18,Reference Marouf, Hoarau, Vos, Charbonnier and Tekap28,Reference Barbut, Braza, Hoarau, Barakos, Sévrain and Vos29) . Therefore, different kinds of turbulence models are adopted herein: k–
$\omega$ SST is applied when simulating the morphing caused by the SMA at a Mach number of 0.25 and AoA values of 0°, 3.2°, 7° and 10°, while DDES is used to simulate the tail vibration at a Mach number of 0.74 and AoA at 3.2°.
2.4 Numerical parameters
The corresponding numerical simulations are carried out after obtaining the wing’s geometric shape under the different bending deformations. The geometric arrangement of the computational model is shown in Fig. 2, with the avoidance of interference from the surrounding boundary. To reduce the mesh scale and computational time requirements, a two-dimensional RAE 2822 aerofoil with a chord length of 0.1m is chosen. The fully structured meshes used for the numerical simulations are generated using ICEM software. A grid convergence study is performed to evaluate the mesh density required to obtain grid-independent values for the aerodynamic coefficients, considering four meshes with 261k, 321k, 445k and 602k elements at Ma 0.74 and an AoA of 3.2°. The mean values of Cl and Cd are presented in Table 1. The numerical results converge, with a difference between M3 and M4 of less than 1% and 5% for Cl and Cd, respectively. Therefore, M3 and its detail is selected for subsequent simulations. Moreover, the grid applied in the present study yields a maximum value of Y plus wall distance of about 0.32, in accordance with the requirement for the turbulence models and ensuring optimal behaviour of the rear turbulent modelling.
Figure 2. Flowfield geometry configuration.
Table 1 The lift and drag coefficients for different mesh sizes
The suggested time step equation(Reference Szubert, Grossi, Jimenez, Hoarau, Hunt and Braza17) of 5 × 10−4c/U∞ indicates an appropriate time step (Δt) of about 0.25
$\upmu$s. The time step sensitivity is studied using values of 0.5
$\upmu$s, 1
$\upmu$s, 5
$\upmu$s and 10
$\upmu$s to decrease the computational time requirement. The frequency of fluctuation of Cl in Fig. 3 is similar, while Table 2 indicates that Δt = 10
$\upmu$s gives a larger average Cl than the other three settings. Therefore, the value of 1
$\upmu$s, which is on the same order as Jean’s setting(Reference Jean, Simiriotis, Marouf, Szubert, Asproulias, Zilli, Hoarau, Hunt and Braza27), is chosen to obtain accurate results with economic computational effort.
Table 2 Time-averaged coefficients for different time steps
Figure 3. Transient lift coefficient under different time steps.
2.5 CFD model for vibration
The above CFD model and settings are adequate to study the static deformation produced by the SMA. However, they cannot be used to model the dynamic morphing of the tail vibration. As a conceptual design to explore the initial instantaneous effect of vibration in terms of flow control, the wing under the action of the MFCs is simplified to the model shown in Fig. 4. The tail is assumed to be separate from the main body and to rotate slightly around the centre point R, located at 95% of the chord, within a specific angular range. For convenience of the CFD study, the fluid domain is divided into two regions. The primary fluid domain A outside of the rectangular frame contains the static mesh, while zone B inside the rectangular frame contains a dynamic mesh, moving with wall motion. The slit between the tail and the main body must be made as narrow as possible to decrease modelling errors. Based on practical physical instruments, the angular velocity of the vibration is largest at the horizontal position and zero at the upper and lower limit positions. It is reasonable to suppose that the angular velocity of the vibration changes according to the following cosine function:
\begin{equation}\omega=2\pi fA\times \cos(2\pi ft)\end{equation}
\begin{equation}\hspace*{-18pt}\theta=A \times \sin(2\pi ft)\end{equation}where f is the vibration frequency, t is time, and A is the vibration amplitude of the tip. In accordance with the gap and length of the tail, A is set to 0.05rad in the subsequent analysis, so that the rotation amplitude in the vertical direction of the wingtip is about 0.25mm. The aerodynamic performance is analysed under different operating conditions by changing the vibration frequency or amplitude.
Figure 4. Local fluid domain arrangement.
The aerodynamic performance analyses of the aerofoil model with a slit width of 0.1mm, 0.2mm and 0.35mm are shown in Fig. 5, indicating that the slit width has an apparent influence on the performance of the foil when using the current, simplified model, especially on Cl. With decreasing gap width, the relative error of Cl and Cd compared with the initial results decreases. The maximum error on Cl and Cd is less than 5% for a gap of 0.1mm but 12.2% for a gap of 0.35mm. In subsequent calculations, a slit width of 0.1mm is used. Note that this performance degradation is due to the computational modelling rather than the tail vibration itself. A comparison of Cp along the aerofoil versus experiment results (at Ma = 0.74 and AoA = 3.2°) is shown in Fig. 6, to evaluate the numerical results. Due to the influence of the gap, the numerical findings are slightly different from the experimental data on the pressure side of the foil. However, the overall results are in agreement with the experiments, confirming the reliability of the model.
Figure 5. Effect of gap width on Cl and Cd.
Figure 6. Comparison between numerical results and experimental data (Ma = 0.74, AoA = 3.2°).
3.0 RESULTS OF SMA MORPHING
The Cd and Cl of the aerofoil in the three different bending states for an AoA of 0°, 3.2°, 7° and 10° are analysed at a Mach number of 0.25. The results indicate that Cl increases drastically with beinding of the aerofoil, as shown in Fig. 7 and Table 3. As the middle SMA plate results in significant bending deformation, the lift coefficient in state 3 is the largest when the AoA is smaller than 10°. Also, note that, with increasing AoA, the increasing gradient of Cl is gradually reduced. In state 2 and 3, Cd is always larger than for the original form in Fig. 7, by 146.68% and 185.71% at 7°, respectively. The explanation for this can be seen in Fig. 8, which shows the Root-Mean-Square (RMS) tangential velocity at AoA = 7°.
Figure 7. Cl and Cd under different bending morphing and angles of attack (Ma = 0.25).
Figure 8. RMS tangential velocity at AoA = 7°.
Table 3 Comparison of Cl and Cd between morphing states and the original state
When the AoA is 7°, the RMS tangential velocity is nearly zero in the original state, suggesting that the flow is steady. However, the flow becomes unsteady in state 2 and 3, with Δv/U∞ reaching 20% and 24%, respectively, according to Fig. 8. Thus, the Cl and Cd in state 2 and 3 are quite different from in the original condition. For state 3, Cl is increased by 26.08%, and Cd by 185.71% compared with state 1. The results for state 2 in Table 3 show that Cl and Cd are both sharply increased. Because of the more drastic bending morphing, the general magnitude of Δv/U∞ in state 3 is larger, leading to the higher Cd.
When the AoA is 10°, the situation is different, with the Δv/U∞ values for the different shapes lying at the same level in Fig. 9, indicating that all the states are unsteady. These results are also supported by Fig. 10, where the flow is separated even in state 1. As a result, the difference between the two morphing states and the original form becomes smaller in Table 3, especially for Cd in state 3. The maximum Cd increase is 21.38% in state 3, being significantly smaller than the value of 185.71% obtained at AoA = 7°. Moreover, the percentage increase in Cl dramatically decreases to 8.34% and 5.13% for state 3 and 2, respectively.
Figure 9. RMS tangential velocity at AoA = 10°.
Figure 10. Pressure distribution and streamlines at AoA = 10° in state 1.
4.0 RESULTS OF TAIL VIBRATION BY MFCs
4.1 Effect of vibration frequency
The effects of the frequency and magnitude of the tail vibration are studied at an AoA of 3.2° and a Mach number of 0.74. According to Tian’s research(Reference Tian, Gao, Liu and Wang30), the natural transonic buffet frequency of RAE 2822 varies from 60 to 100Hz under different Mach numbers. Therefore, numerical investigations are carried out at various frequencies of 50Hz, 100Hz and 200Hz to explore the impact of the vibration frequency. It is found that Cl is significantly lower than for the original aerofoil in Figs 11 and 12 due to the influence of the slit above. The frequency has a complicated effect on Cl and Cd. Cl shows a peak at f = 50Hz, while the minimum Cd occurs at f = 100Hz, achieving a decrease of 1.66% compared with the foil at 0Hz in Table4. It can be inferred that high-frequency vibration of the trailing edge has a more significant influence on Cl than on Cd. Selecting an appropriate frequency could result in an increased ratio of Cl to Cd and meet the aim of decreasing the resistance during the cruise phase. With the tail rotating to the lower limit, the shock wave is strengthened and moves towards the tail direction, while both Cl and Cd start to increase to their maximum simultaneously. When the tail begins rotating upward, the shock wave is compressed, while Cl and Cd move in the opposite direction, as shown in Fig. 13. The vibration significantly locks in the buffet frequency, with Cl, Cd and the shock location being determined by the transient rotation of the tail. Cl reaches its maximum when the tail is at the lower limit. When Cl reaches the bottom limit, the rear is at the upper limit. By changing the frequency of the tail vibration, the buffet frequency of the foil could be changed.
Table 4 Cl and Cd under different vibration frequencies (AoA = 3.2°, Ma = 0.74, A = 0.05)
Figure 11. Effect of vibration frequency on Cl.
Figure 12. Effect of vibration frequency on Cd.
Figure 13. Pressure distribution and streamlines of aerofoil under different frequencies.
4.2 Performance under different angles of attack
With an incoming flow at a Mach number of 0.74, the influence of high-frequency vibration of the tail at AoA = 7° is further studied (Fig. 14). The results reveal that the fluctuation of Cl and Cd at 7° is consistent with the description above; That is, the trailing-edge vibration reduces the lift and drag coefficients synchronously. At this increased AoA, the amplitude of the fluctuation of Cl and Cd becomes larger. Besides, Cl and Cd undergo two cycles from the maximum to minimum during one period due to the excessive separation. The minimum length of the low-pressure area becomes smaller, as shown in Fig. 15(a), leading to a smaller minimum of Cl, as shown in Fig. 14. Compared with the performance data obtained at 0Hz, Cl decreases by 2.36% and 4.58% at AoA of 3.2° and 7°, respectively, while Cd is reduced by 1.66% and 5.53%, accordingly.
Figure 14. Cd and Cl at different AoA (f = 100Hz, A = 0.05).
Figure 15. Pressure distribution and streamlines of aerofoil under AoA = 7° (100Hz, A = 0.05).
4.3 Effect of vibration amplitude
A in the rotation function above, which is determined by the length and properties of the MFCs, represents different vibration amplitudes. Under the condition with a Mach number of 0.74, AoA of 3.2° and vibration frequency of 100Hz, the performance with a vibration amplitude of A0 = 0.05, 0.75A0 and 0.5A0 is analysed, and the numerical results are shown in Figs 16 and 17.
Figure 16. Cl at different vibration amplitudes.
Figure 17. Cd at different vibration amplitudes.
As the amplitude of the vibration is decreased, both the mean values of Cl and Cd and the magnitude of the fluctuation decrease due to the influence of the vibration amplitude on both sides of the camber. The lift coefficient increases accordingly due to the camber growth brought about by the tip’s moving down, but the effect is reversed when the tail moves in the opposite direction. As shown in Table 5, the MFC only slightly changes the time-averaged Cl and Cd values of the aerofoil. Taking the average value for comparison, Cl at A = 0.5A0, 0.75A0 and A0 decreases by 4.7% 3.43% and 2.36% compared with the results without vibration, respectively. The amplitude of the vibration has the same effect on the drag coefficient. The resistance coefficient is decreased by 2.32%, 1.99% and 1.66%, respectively, when A is equal to 0.5A0, 0.75A0 and A0. On the other hand, the vibration leads Cl and Cd to fluctuate considerably, as also reported by Abderahmane(Reference Abderahmane, Jean, Jean, Yannick and Braza15) and Jean(Reference Jean, Simiriotis, Marouf, Szubert, Asproulias, Zilli, Hoarau, Hunt and Braza27). Thus, the magnitude and frequency of the tail vibration should be carefully chosen based on the overall design as well as aerodynamic load analysis.
Table 5 Time-averaged Cl and Cd under different vibration amplitudes (AoA = 3.2°, Ma = 0.74, f = 100Hz)
5.0 CONCLUSIONS
The conceptual design for a wing with active flow control based on SMA and MFC is proposed herein. CFD simulations are carried out to evaluate its feasibility to improve the aerodynamic performance. The unsteady flow characteristics with dynamic morphing are investigated instead of classical static simulations with complicated coupling. Furthermore, numerical simulations are applied to analyse the performance under large bending deformation by the action of SMA plates or slight tail vibration applied by MFC at different frequencies, AoAs and vibration amplitudes. The following conclusions can be drawn from the results of the present study.
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1. The results of the numerical studies suggest that the proposed conceptual design for a wing with active flow control based on SMA and MFC is feasible to improve the aircraft’s aerodynamic performance.
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2. The large deformation produced by the SMA plates results in a significant increase in both Cl and Cd, suitable for take-off and landing. In state 3, Cl and Cd are increased by 41.06% and 24.94%, respectively, at an AoA of 3.2°, and by 8.34% and 21.38% at an AoA of 10°, compared with the initial form.
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3. The frequency and amplitude have a complicated effect on the performance of the wing under the action of MFCs. Cd decreases by 1.66% at 100Hz, with a simultaneous drop of 2.3% in the time-averaged Cl value. Cd is reduced more when the AoA becomes larger, with the decrease reaching 5.53% for an AoA at 7°. In conclusion, a decrease of Cd on the order of 1.66–2.32% is achieved when choosing an appopriate frequency and amplitude for cruise.
