Active flow control for supersonic aircraft: A novel hybrid synthetic jet actuator

Sensors and Actuators A 302 (2020) 111770

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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna

Active flow control for supersonic aircraft: A novel hybrid synthetic jet actuator Jinfeng Li, Xiaobing Zhang ∗ College of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 29 June 2019 Received in revised form 25 October 2019 Accepted 27 November 2019 Available online 19 December 2019 Keywords: Active flow control Gas refilled rate Hybrid synthetic jet actuator Numerical simulation

a b s t r a c t In order to improve the performance of traditional synthetic jet actuators in active flow control for supersonic aircraft, a novel millimeter-scale hybrid synthetic jet actuator (HSJA) is proposed in this paper. It provides additional power for the jet spout stage and gas refresh stage by adding a piezo-driven diaphragm at the bottom of the plasma synthetic jet actuator (PSJA). On the one hand, the problem of the low jet velocity of the piezo-driven synthetic jet actuator (PDSJA) could be avoided due to the heating and pressurization of gas by arc discharge. On the other hand, more external gas would be refilled during the gas refresh stage due to the restoration of the piezo-driven diaphragm compared with the plasma synthetic jet actuator. In an attempt to optimize the structure of the novel hybrid synthetic jet actuator, the flow field of the actuator is numerically simulated. The results show that the peak velocity of synthetic jet and the gas refilled rate are both increased compared with the plasma synthetic jet actuator. The effectiveness of the proposed hybrid synthetic jet actuator is verified. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Recently, active flow control methods have become a research focus in aerospace applications [1]. The conventional device to active flow control is the piezo-driven synthetic jet actuator, which could form periodic low-momentum synthetic jet by a diaphragm vibration in a relatively small cavity. But the jet velocity of the general piezo-driven synthetic jet actuator is not over 45 m/s [2], which is difficult to play a role in flow control for supersonic aircraft. As a promising active flow control technique in supersonic aircraft, the plasma synthetic jet actuator has advantages of fast response [3], high-speed jet and simple structure [4]. However, due to insufficient power during the gas refresh stage, the gas pushed out of the cavity cannot be completely refilled, which will lead to a gradual decrease of the gas density in the cavity under the high-frequency excitation. Thereby it affects the performance of the plasma synthetic jet actuator in active flow control. In order to solve the problems of low gas refilled rate [5] of plasma synthetic jet actuators and low jet velocity of piezo-driven synthetic jet actuators, a novel hybrid synthetic jet actuator is proposed in this paper. As one kind of the active flow control devices, synthetic jet actuators [6] have been widely applied to improving aircrafts’

∗ Corresponding author. E-mail address: [email protected] (X. Zhang). https://doi.org/10.1016/j.sna.2019.111770 0924-4247/© 2019 Elsevier B.V. All rights reserved.

performance, such as drag reduction [7] and maneuverability improvement [8], etc. In recent years, both piezo-driven synthetic jet actuators and plasma synthetic jet actuators have been developed rapidly. Rimasauskiene et al. [9] have conducted a lot of experimental research on the structural design of piezo-driven synthetic jet actuators. And the highest value of the synthetic jet velocity 25 m/s was obtained with piezo-driven synthetic jet actuators. The numerical modeling to evaluate the efficiency of energy conversion of piezo-driven synthetic jet actuators is developed by Girfoglio et al. [2]. Mankbadi, Surti, and Golubev et al. [10–12] have carried out many valuable numerical simulations for piezo-driven synthetic jet actuators based on the viscous and inviscid numerical models and pave the way for optimizing piezo-driven synthetic jet actuators. Deng et al. [13] proposed a dual synthetic jet actuator (DSJA) which is transformed from piezo-driven synthetic jet actuators and applied it to high-power LED to solve the heat dissipation problem. Though the gas refilled rate could be guaranteed, the low jet velocity of piezo-driven synthetic jet actuators makes it unsuitable for the active flow control of supersonic aircraft. In order to improve the effectiveness of the synthetic jet on the mainstream, it is necessary to increase the momentum of the synthetic jet, especially in the field of flow control of supersonic aircraft. Therefore, more and more people turned their attention to plasma synthetic jet actuators. Grossman et al. [14] first proposed a model of plasma synthesis jet actuator in 2003 and established a one-dimensional theoretical analysis model of plasma synthetic jet actuator. And then they carried out a numerical simulation based on

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Fig. 1. Geometrical model of the novel hybrid synthetic jet actuator.

the phenomenological model. Their numerical simulation results show that the theoretical maximum velocity of the jet could reach 1.5 km/s, and the temperature in the cavity will exceed 2000k. An in-line digital holography technique which could be expected to observe the formation and evolution of plasma synthetic jet has been tested by Chareyron et al. [15]. Zong and Kotsonis have investigated the effects of energy deposition and actuation frequency on the formation and evolution characteristics of plasma synthetic jets by experiment and simulation [16]. An innovative lumped-element model (LEM), able to predict the temporal evolution of the main fluid-dynamic variables of the device, has been presented by Chiatto and de Luca [17]. Numerical simulation of plasma transient ignition process of energetic materials has been systematically studied [18]. Ibrahim et al. [19] have simulated the linear plasma synthetic jet actuator utilizing a modified Suzen-Huang model. Sary et al. [20] investigated the plasma synthetic jet for flow control by numerical modeling and parametric study. Zhang et al. [21] studied the influence of the discharge location on the performance of a three-electrode plasma synthetic jet actuator by experiments and numerical simulation. Narayanaswamy et al. [22] used a pulsedplasma synthetic jet actuator to control the unsteady motion of the separation of a shock wave/boundary layer interaction formed by a compression ramp in Mach 3 flows. At present, there are two major problems in the application of plasma synthetic jet actuators in active flow control: one of them is low electric energy conversion efficiency [23–25], and the other is low gas refilled rate [5,26]. The efficiency characteristics of the two-electrode plasma synthetic jet actuator driven by an energy-storage capacitor and high-voltage power supply were investigated [23]. Popkin and Cybyk [27] have investigated the flow field characteristics and energy conversion efficiency of spark jet actuators by means of experimental measurement and experimental microschlieren images and provided some methods to improve energy conversion efficiency. Tang [28] and Zong et al. [29] investigated the effects of capacitance energy on the performance of the plasma synthetic jet actuator. In order to improve the gas refill rate of the plasma synthetic jet actuator, many experts have carried out a lot of research. Zhou et al. [5] proposed a novel actuator called the ram-air plasma synthetic jet actuator (RPSJA) to improve the gas refill rate of the actuator. Emerick et al. [26] designed a non-zero net mass flux actuator which incorporates an active refill supply pressure hole. However, it is difficult to accurately control the gas backfilling process by adding holes. In order to improve the gas refilled rate of plasma synthetic jet actuators without reducing the velocity of the synthetic jet, a novel hybrid synthetic jet actuator is proposed in this paper. Coupling model of energy source term and the dynamic boundary is established to verify the feasibility of the novel hybrid synthetic jet actuator. In an attempt to achieve the best coupling effectiveness, the structural optimization design of the novel synthetic jet actu-

ator is carried out by numerical simulation. The results show that compared with plasma synthetic jet actuators, the novel hybrid synthetic jet actuator has better performance in the intensity of synthetic jet and the gas refilled rate.

2. Description of the novel hybrid synthetic jet actuator The novel hybrid synthetic jet actuator (HSJA) proposed in this paper is shown in Fig. 1. It consists of a boron nitride ceramic cavity with two electrodes, a top cap with holes, and a piezodriven diaphragm under the cavity. Due to the high-temperature resistance of Bi3TiNbO9 [30], which is one of the bismuth layer structured ferroelectrics, thus, it is chosen to be the material of the diaphragm. The synthetic jet is a kind of zero-net-mass-flux jet that transfers linear momentum to the flow system [31], which is formed under the combined action of high-voltage pulse and the piezodriven diaphragm. Similar to the plasma synthetic jet actuator [3], the entire working process of the novel hybrid synthetic jet actuator could be divided into three stages: energy deposition, jet spout, and gas refresh, as shown in Fig. 2. During the energy deposition stage, a strong pulsed arc is initiated by an energy-storage capacitor and high-voltage power, which heats and pressurizes the gas in the cavity rapidly. During the jet spout stage, the high-temperature gas is expelled through the hole at high velocity under the pressure difference between the inside and outside of the cavity and vibration of the piezoelectric diaphragm. During the gas refresh stage, as the vibration diaphragm recovery phase, the cavity volume is increased, the pressure inside the cavity is reduced. Consequently, the pressure difference between the internal and external of the cavity is increased. Ambient cold gas is refilled into the cavity to prepare for the next circle.

3. Physical model and numerical simulation methods 3.1. Assumptions and governing equations The formation mechanism of the plasma synthetic jet is very complicated, involving many subjects such as chemistry, thermodynamics, electromagnetism, fluid mechanics and so on, which leads to that the establishment of a precise plasma synthesis jet computational model for the plasma physiochemical process is difficult and computationally expensive. In addition, there is a multi-timescale coupling problem in the formation process of plasma. The detailed physicochemical process of the plasma is not considered in this paper. The gas discharge is equivalent to an external heating source. According to the Ref. [25], the complicated plasma discharge process could be simplified. And the physical model is based on the following assumptions.

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Fig. 2. Entire working process of the novel hybrid synthetic jet actuator.

1) The gas in the actuator cavity is in a local thermodynamic equilibrium state during the discharge process, the heat transfer and flow of the gas are described by the Navier-Stokes equation. 2) The thermodynamic and transport properties of the plasma gas are related to temperature. 3) Ignore the influence of the electromagnetic field generated during discharge and the influence of gravity; 4) Irrespective of ablation and blocking of the electrodes, the temperature of the cavity wall is kept at 293 K. 5) Thermal radiation is the main form of energy loss and is calculated by adopting the method of net emissivity. 6) The vibrating diaphragm at the bottom of the cavity is considered to be a moving wall with sinusoidal motion characteristics like a piston. The simplified control equations consisting of a continuity equation, a momentum equation, and an energy equation are given in the following: d + ∇ · u = 0 dt 

du = −∇ p + ∇ ·  dt

∂E + ∇ · (E + p) u = ∇ · ( · u) + ∇ · (∇ T) + q˙ el − 4εN ∂t

(1) (2) (3)

where  represents density of the gas, p represents pressure of the gas, u represent the velocity vector in the cylindrical coordinate system (x, r, ),  represents thermal conductivity of gas,  represents stress tensor, T represents static temperature, εN represents the net adiation coefficient, 4εN represents energy radiation loss, q˙ el represents the energy input source term and E represents the total energy of unit volume. The model is characterized by the consideration of energy deposition around the two electrodes and thermal radiation in the energy equation (3). E =  (e +

1 ||u||2 ) 2

e = p/( − 1)

(4) (5)

Where e represents specific internal energy and  = 1.16 [32] is the ratio of specific heats. Through the study of Naghizade-Kashani et al. [33], the net emissivity of plasma εN,atm at a standard atmospheric pressure could be know. εN = εN,atm ·

p patm

(6)

where εN represent the net emissivity of other pressures p, patm represents the standard atmosphere pressure. In order to solve these balance equations, the thermodynamic characteristic parameters and transport parameters of the plasma gas must be given first, such as thermal conductivity ␭ and viscosity coefficient under different temperature conditions. Considering the diversity of plasma composition and the complexity of the

kinetic equation solution, Capitelli et al. [32] provided an engineering fitting formula for the thermodynamic properties of the plasma in the temperature range of 50−100000 K, which is convenient for numerical simulation. As for the vibration diaphragm at the bottom of the novel hybrid synthetic jet actuator, it can be regarded as a dynamic boundary. The bottom boundary of the cavity is set to oscillate back and forth according to certain regulation. For the convenience of calculation, the vibration law of the ceramic diaphragm is simplified reasonably. When the amplitude of the diaphragm is small relative to the size of the cavity, it is considered that each point on the diaphragm has the same displacement at the same time. It is assumed that the sinusoidal voltage signal is used to drive the ceramic diaphragm. The driving frequency is f , the amplitude of the metal diaphragm is A and the initial phase angle is ϕ0 , then the displacement x of the ceramic diaphragm at any time t is: x = Asin(2ft + ϕ0 )

(7)

and the velocity expression of the movement is shown as follow: U (t) =

dx = U0 cos (2ft + ϕ0 ) dt

U0 = 2fA

(8) (9)

3.2. Calculating region and boundary conditions Due to the axial symmetry of the flow field, a two-dimensional axisymmetric model is established for the actuator to simplify the calculation. The grid generation software ICEM is used to perform initial meshing of the calculation area. To accurately investigat and analyz the complex flow field areas of the source term area and the outlet center area, it is necessary to refine the grid on these areas. The total size of the mesh is 233400. The specific meshing situation is shown in Fig. 3. In order to validate the reliability of adopting the numerical model of the plasma synthetic jet actuator, the following simulation was carried out based on the experiment conducted by Belinger et al. [34]. The diameter and height of the actuator cavity are both 4 mm. The diameter and height of throat are both 1 mm. In order to eliminate the influence of the boundary setting on the calculation result, the diameter of the external flow region is set to 50 mm, and the top boundary is 100 mm from the actuator outlet. The cavity and the throat of actuator are both set as a fluid-solid coupling surface, and the solid material is set as boron carbide ceramic (thermal conductivity is 33 W/(m·k), heat transfer coefficient is set as 8 W/(m2·k)), the environment temperature is set as 293 K and the wall thickness is set as 0.2 mm. The bottom wall of the external flow field is the same as the wall of the actuator cavity. The top and sides of the external flow field are set as the pressure outlet boundary conditions, the pressure and temperature are set to the

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Fig. 3. The meshing of calculating region: (a) the entire region (b) the internal flow region (c) the external flow region and actuator throat region.

ambient atmospheric pressure 101325 Pa and temperature 293 K [25], respectively. According to Belinger’s experimental results [34], the discharge duration is basically maintained 8 ␮s under these conditions that the capacitive power supply in high pressure (1 atm), small space (50 mm3 ) and a single gas discharge energy Ed > 50 mJ. It could be assumed that the energy in the discharge region (energy source term region) is uniformly distributed. As for a single discharge, the energy input expression in the discharge region is given in the following equation [35]:



q˙ el =

Q, t ≤ 8 s 0, t > 8 s

(10)

Where t represents time, Q represents the thermal energy deposition (W ⁄m3 ), and its expression is as follow [36]: Q =

qt qϕ1 = V1 td V1 t d

(11)

Where qt represents the thermal energy, td represents the electric discharge time,q represents the released electric energy during an electric discharge, ϕ1 represents conversion efficiency of electric energy into thermal energy [17,25,27], V1 represents the source term region volume (1/4 cavity volume). Pressure-based implicit method and unsteady solution are chosen to investigate the characterization of the novel synthetic jet actuator coupling of vibration and ionization. The axisymmetric swirl is selected in the calculation model geometry option, and the RNG k-␧ turbulence equation and energy equation is adopted. Energy source terms are imported in the quarter area of the actuator center. Dynamic mesh zones are set in the borders and areas associated with the bottom of the cavity. Through the way of preview mesh motion, the generation of the grid during the entire process is observed in advance, and it is determined that the general requirements for grid quality are met at all times. The two-dimensional unsteady balance equations are discretized by using the finite volume method. The commercial software fluent is used to solve the problem. The viscous terms are

Table 1 Mesh Sizes.

coarse medium Fine

Cells

Nodes

132650 233400 403650

133596 234761 406003

discretized by using a central difference scheme. The second-order upwind scheme is used for convection terms. The Roe-FDS scheme is used for space terms, and the second-order accuracy is used for time terms. The time step is 2 × 10−8 s. The maximum iterations of each time step are 20. 4. Verification In order to validate the numerical model, including the turbulence model, boundary conditions, and energy source term, the experiment of the plasma synthetic jet actuator carried out by Belinger [24,34] is considered. Grid independence verification and numerical model verification are carried out in this section. 4.1. Grid independence verification In order to carry out the grid independence verification, three cases with different mesh sizes are analyzed and compared as shown in Table 1. The released electric energy q = 50 mJ, the conversion efficiency of electric energy into thermal energy ϕ1 = 5 % [39], the vibration frequency f = 0 Hz and the amplitude A = 0 mm. The jet positive peak velocity Vp of three cases are shown in Fig. 4. The figure shows that the numerical results could be considered independent of the cell size when the number of cells is over 233400. 4.2. Verification of the numerical model The calculation region of the plasma synthetic jet actuator is the same as the hybrid synthetic jet actuator expects for no dynamic

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5. Results and discussion 5.1. Working progress of the novel hybrid synthetic jet actuator

Fig. 4. The jet positive peak velocity Vp for the three mesh sizes.

Fig. 5. The area-average velocity of synthetic jet at outlet time histories for PSJA.

boundary region, as shown in Fig. 3. The calculation regions include the internal flow region, the external flow region, and actuator throat region. The maximum working frequency of the actuator capable of maximizing gas refill rate is defined as saturation frequency fs , and the corresponding working period is the saturation period Ts . The saturation frequency of the plasma synthetic jet actuator is 4.429KHz, which could be got from Fig. 5. Comparing the simulation results in Fig. 5 with the results of Chiatto [17], it could be found that the two exit velocities have the same development trend. The flow field structure is shown in Fig. 6, which could be obtained by numerical simulation and experiment with a discharge energy of 50 mJ. The experiment and simulation results are very similar in the position of shock waves. Moreover, the maximum jet velocity difference between the numerical simulation and experiment [34] is only 2.18 %. Therefore, it can be proved that the numerical simulation result is credible.

The numerical simulation of the novel hybrid synthetic jet actuator has been conducted and analyzed under some conditions. As for single discharge, the discharge energy q = 50 mJ, the conversion efficiency ϕ1 = 5 %, the vibration frequency f = fs = 4.429 KHz and the amplitude A = 0.35 mm. Fig. 7 gives the velocity vector fields of the novel hybrid synthetic jet actuator at several key times. After discharge, the air in the cavity is heated and pressurized. At the end of the energy deposition stage(Fig. 7(a)), the synthetic jet has just been generated. Under the couple effects of the squeezing action of the piezo-driven diaphragm and high-temperature plasma in the cavity, the positive area-average velocity of synthetic jet at the outlet reaches the maximum value 151.77 m/s(Fig. 7(b)). And then the area-average velocity of the synthetic jet is gradually decreased. When t = 111.4 ␮s (Fig. 7(c)) it decreases to 0 m/s, which means that the jet spout stage is ended. During the early stage of gas refilled, the velocity of the synthetic jet is gradually increased under the pressure difference between the interior and exterior of the cavity, which is caused mainly by the vibration of the piezoelectric diaphragm. When t = 149 ␮s (Fig. 7(e)), the negative synthetic jet velocity reaches the maximum value 103.25 m/s. The speed of gas refresh equals to 0 when t = 222.2 ␮s (Fig. 7(f)), the first circle is over. Due to the piezo-driven frequency f is synchronized with the plasma actuator saturation frequency fs , the maximum velocity of the synthetic jet, the gas ejection rate Re and the gas refilled rate Rr are all improved.

Re =

Me Mc

(12)

Rr =

Mr Mc

(13)

Where Me represents the maximum ejected gas mass of the cavity in the first jet spout stage. Where Mr represents the maximum gas mass of the cavity in the first gas refresh stage, Mc represents the initial gas mass of the cavity. The performance comparison of the plasma synthetic jet actuator, piezo-driven synthetic jet actuators, and the novel hybrid synthetic jet actuator will be discussed detailedly in the next section.

Fig. 6. The experimental schlieren image (left) and the numerical contour of density (right) 20 ␮s after the end of the discharge.

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Fig. 7. Velocity vector fields of the novel hybrid synthetic jet actuator at several key times.

Table 2 Working conditions and results of PSJA, PDSJA, and HSJA. Case

q(mJ)

A (mm)

Vp (m/s)

Rr

Re

PSJA PDSJA HSJA

50 0 50

0 0.1 0.1

92.97 34.81 103.08

94.54 % 103.23 % 97.05 %

7.25 % 3.12 % 8.98 %

5.2. The performance comparison of the plasma synthetic jet actuator, the piezo-driven synthetic jet actuator, and the novel hybrid synthetic jet actuator In order to compare the flow field characteristics of the plasma synthetic jet actuator, piezo-driven synthetic jet actuator, and the novel hybrid synthetic jet actuator, the numerical models of the three actuators are built and analyzed. Their working conditions and results are shown in Table 2. The area-average velocity of synthetic jet at outlet and gas mass in cavity time histories for the plasma synthetic jet actuator, the piezo-driven synthetic jet actuator, and the novel hybrid synthetic jet actuator are shown in Figs. 8 and 9 respectively. It could be seen from Fig. 8 that the coupling effect between the piezo-driven and the capacitor discharge is well. The synthetic jets of the plasma synthetic jet actuator and the piezo-driven synthetic jet actuator have a good consistency, which achieves the desired result. At first, the synthetic jet at the outlet of the piezo-driven synthetic jet actuator does not appear obviously until at 20 ␮s, and the response times of the plasma synthetic jet actuator and the novel hybrid synthetic jet actuator are relatively short. Moreover, the velocity fields of the three actuators are shown in Fig. 10 when their area-average velocity at the outlet reaches the peak. The peak velocity Vp of the novel hybrid synthetic jet reaches 103.08 m/s, which is 2.96 times that of piezo-driven synthetic jet. This indi-

Fig. 8. The area-average velocity of synthetic jet at outlet time histories for PSJA, PDSJA, and HSJA.

Fig. 9. Gas mass in cavity time histories for PSJA, PDSJA, and HSJA.

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Fig. 10. The velocity fields of the three actuators when their area-average velocity at the outlet reach the peak: (a) PDSJA (b) PSJA(c) HSJA.

Fig. 11. The density fields of the novel hybrid synthetic jet actuator: the mass of the gas in the cavity is minimized when t = 117.6 ␮s; the refilled mass of gas reaches the peak when t = 220 ␮s.

cates that the new synthetic jet actuator is suitable for flow control of supersonic aircraft in terms of the jet velocity. Furthermore, the gas refilled rate Rr of the novel hybrid synthetic jet actuator is 2.51 % higher than that of the plasma synthetic jet actuator, and the gas ejection rate Re is 1.73 % higher than the plasma synthetic jet actuator. It seems that the novel hybrid synthetic jet actuator has only a small increase in the gas refilled rate Rr and the gas ejection rate Re in single pulse. On the one hand, under the action of multiple pulses, small differences in gas refilled rate

and gas ejection rate will be accumulated, which will finally have an important impact on the formation of the synthetic jet. On the other hand, the amplitude of the piezo-driven diaphragm is only 0.1 mm, which plays a relatively small role in the gas refilled stage. The amplitude can be appropriately increased within the material limit of the vibrating diaphragm, which will be discussed in the next section. The density fields of the novel hybrid synthetic jet actuator at two key moments are presented in Fig. 11. The figure shows

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Table 3 The Ek of the jets for PSJA, HSJA, and PDSJA. Case

A (mm)

qt (mJ)

Ek (mJ)

Ek /qt

HSJA PSJA PDSJA

0 0.1 0.1

2.5 2.5 0

0.0379 0.0209 0.00157

1.516 % 0.84 % –

that the novel hybrid synthetic jet actuator has some gas backfill effect. However, the gas ejection rate Re of all three actuators failed to exceed 10 %. The high-temperature and high-pressure gas is not fully converted into the kinetic energy of the jet, but it accumulates in the cavity as thermal energy. The temperature of the cavity is increased so that it is dissipated to the surrounding environment by heat convection and thermal radiation, which greatly reduces the utilization efficiency of the gas thermal energy. Therefore, increasing the gas ejection rate is advantageous for improving the conversion efficiency of the gas thermal energy converting into the kinetic energy of the jet. The detailed discussions are as follows.



Ek =

˙ m||u| |2 dt 2

(14)

˙ and velocity magnitude ||u| | at By monitoring the mass flow rate m the exit of the three actuators during the jet spout stage, the total kinetic energy Ek of the jets during the jet spout stage is obtained. The results are shown in Table 3. The Ek of the jets for the hybrid synthetic jet actuator is 0.0379 mJ, which is 1.69 times of the sum of the plasma synthetic jet actuator and the piezo-driven synthetic jet actuator. The results show that the hybrid synthetic jet actuator has higher kinetic energy conversion efficiency than the other two actuators. It can be seen from the above analysis and comparison that the novel hybrid synthetic jet actuator has a certain improvement in the velocity of synthetic jet, gas ejection rate and gas refilled rate compared to the traditional synthetic jet actuators. However, the refilled rate of the novel hybrid synthetic jet actuator (97.05 %) is still not fully refilled (100 %), and the gas ejection rate still not exceeds 10 %. Therefore, a possible optimized design of the novel hybrid synthetic jet actuator is discussed in the next section. 5.3. The optimized design of the novel hybrid synthetic jet actuator In an attempt to improve the performance of the novel synthetic jet actuator further, it is necessary to know the regulations of some possible influence factors on the synthetic jet. It is not difficult to speculate that the amplitude of the vibrating diaphragm may have an important influence on the performance of the actuator. Therefore, the optimum design of the exciter is mainly based on the amplitude of the vibrating diaphragm. The novel synthetic jet actuator models with different amplitudes are built and analyzed. The formation process and flow field characteristics of the synthetic jet actuators are compared and analyzed. It is easy to find that the area-average peak velocity of the synthetic jet increases linearly with the increase of the amplitude A in Fig. 12, which indicates that the amplitude plays a key role in the area-average peak velocity of synthetic jet. As shown in Table 4 and Fig. 13, the greater amplitude A, leads to the higher gas refilled rate Rr , the higher gas ejection rate Re and the faster peak velocity Vp . Moreover, the gas refilled rate of the novel synthetic jet actuator reaches 100.32 % when the amplitude is 0.35 mm, which is 5.78 % higher than the plasma synthetic jet actuator. It means that the ejected gas can be fully refilled when the amplitude exceeds

Fig. 12. The area-average velocity of synthetic jet at outlet time histories for four novel hybrid synthetic jet actuators (HSJA) with different vibration amplitude. Table 4 Results of several cases. Case

A (mm)

Vp (m/s)

Rr

Re

PSJA HSJA-0.1 HSJA-0.2 HSJA-0.35 HSJA-0.5

0 0.1 0.2 0.35 0.5

92.97 103.08 120.94 145.65 169.16

94.54 % 97.05 % 98.65 % 100.32 % 101.36 %

7.25 % 8.98 % 10.46 % 12.49 % 14.34 %

Fig. 13. The gas mass in the cavity time histories for four novel hybrid synthetic jet actuators (HSJA) with different vibration amplitude.

0.35 mm. The gas ejection rate of the novel synthetic jet actuator reaches 12.49 % when the amplitude is 0.35 mm, which is 5.24 % higher than the plasma synthetic jet actuator. In some sense, it achieves the goal of optimal design. The increase of the amplitude enhances the energy input. In the jet spout stage, the pressure in the cavity is increased, which causes the accelerated ejection of the gas in the cavity. In the gas refresh stage, the volume of the cavity continuously increases, leading to a continuous decrease of pressure in the cavity. And more external gas is drawn into the cavity. Thereby the novel synthetic jet actuator achieves the purpose of increasing the gas refill rate of the cavity.The novel hybrid synthetic jet actuator provides the device foundation for active flow control of supersonic aircraft. By controlling the discharge parameters of the novel hybrid synthetic jet actuator, the closed-loop turbulence control is realized during the flight of the supersonic aircraft, which can achieve the purpose of reducing the resistance and improving the maneuverability. 6. Conclusion A novel hybrid synthetic jet actuator is proposed with the hope of getting over some limitations of piezo-driven synthetic jet actu-

J. Li and X. Zhang / Sensors and Actuators A 302 (2020) 111770

ators and plasma synthetic jet actuators in active flow control of supersonic aircraft. The coupling model of energy source term and dynamic boundary of the novel hybrid synthetic jet actuator is established by the finite volume method. To ensure that the simulation results are credible, the grid independence verification and numerical model verification are carried out. The simulation results show that the novel hybrid synthetic jet actuator has a certain improvement in peak velocity of synthetic jet, gas refilled rate and gas ejection rate compared with plasma synthetic jet actuators. The novel hybrid synthetic jet actuator is optimized by simulation method, and the excitation condition that can make the gas fully refilled under the single pulse is obtained. According to the results and discussions, the conclusios are as follow: 1) The maximum velocity of the jet of the hybrid synthetic jet actuator could reach 169.16 m/s, which is 4.86 times that of the piezo-driven synthetic jet actuator and 1.82 times that of the plasma synthetic jet actuator. The gas refill rate of the novel hybrid synthetic jet actuator is 5.78% higher than that of the plasma synthetic jet actuator, and the gas ejection rate is 5.24% higher than the plasma synthetic jet actuator when the amplitude is 0.35 mm. 2) In the limited range of piezoelectric membrane materials, the intensity of synthetic jets and the gas refill rate would effectively increase as the amplitude increases. The gas refill rate of the novel hybrid synthetic jet actuator could exceed 100% when the amplitude is 0.35 mm. 3) The novel hybrid synthetic jet actuator solves the problem that the gas in the cavity of the plasma synthetic jet actuator cannot be fully refilled and causes the misfire, which increases the duration and reliability of the active flow control in supersonic aircraft. Declaration of Competing Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “Active flow control for supersonic aircraft: a novel hybrid synthetic jet actuator”. Acknowledgments

[8] [9]

[10]

[11]

[12]

[13]

[14] [15]

[16] [17]

[18]

[19]

[20] [21]

[22]

[23]

[24]

[25] [26] [27] [28]

This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors. References [1] G. Sary, G. Dufour, F. Rogier, K. Kourtzanidis, Modeling and parametric study of a plasma synthetic jet for flow control, AIAA Stud. J. 8 (2014) 1591–1603. [2] M. Girfoglio, C.S. Greco, M. Chiatto, L. de Luca, Modelling of efficiency of synthetic jet actuators, Sens. Actuators A Phys. 233 (2015) 512–521. [3] A. Belinger, N. Naudé, J.P. Cambronne, D. Caruana, Plasma synthetic jet actuator: electrical and optical analysis of the discharge, J. Phys. D Appl. Phys. 34 (2014) 345202. [4] E. Moreau, Airflow control by non-thermal plasma actuators, J. Phys. D Appl. Phys. 3 (2007) 605–636. [5] Y. Zhou, Z. Xia, Z. Luo, L. Wang, X. Deng, A novel ram-air plasma synthetic jet actuator for near space high-speed flow control, Acta Astronaut. (2017) 95–102. [6] L.N. Cattafesta, M. Sheplak, Actuators for active flow control, Annu. Rev. Fluid Mech. 43 (2011) 247–272. ˇ [7] K.D. Weltmann, J.F. Kolb, M. Holub, D. Uhrlandt, M. Simek, K.K. Ostrikov, S. ˇ B. Locke, A. Fridman, P. Favia, K. Becker, Hamaguchi, U. Cvelbar, M. Cernák,

[29]

[30] [31] [32]

[33] [34]

[35] [36]

9

The future for plasma science and technology, Plasma Process. Polym. (2018) 1800118. K.V. Anderson, D.D. Knight, Plasma jet for flight control, AIAA Stud. J. 9 (2012) 1855–1872. R. Rimasauskiene, M. Matejka, W. Ostachowicz, M. Kurowski, P. Malinowski, T. Wandowski, M. Rimasauskas, Experimental research of the synthetic jet generator designs based on actuation of diaphragm with piezoelectric actuator, Mech Syst Signal PR 50–51 (2015) 607–614. M. Mankbadi, V. Golubev, Modeling of acoustic streaming for micro-air vehicle propulsion and flow control, in: 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition, Orlando, 2009. M. Mankbadi, Large-scale simulations of acoustic synthetic jets, in: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, 2010. T. Surti, N. Fossum, V. Golubev, M. Mankbadi, H. Nakhla, Navier-stokes simulations of acoustic streaming for flow control and micro propulsion, in: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, 2010. X. Deng, Z. Luo, Z. Xia, W. Gong, L. Wang, Active-passive combined and closed-loop control for the thermal management of high-power LED based on a dual synthetic jet actuator, Energ Convers Manage 132 (2017) 207–212. K.R. Grossman, B.Z. Cybyk, D.M. VanWie, 41st Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2003. D. Chareyron, J.L. Marié, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, L. Méès, Testing an in-line digital holography ‘inverse method’ for the Lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence, New J. Phys. 4 (2012) 43039. H. Zong, M. Kotsonis, Formation, evolution and scaling of plasma synthetic jets, J. Fluid Mech. (2018) 147–181. M. Chiatto, L.D. Luca, Numerical and experimental frequency response of plasma synthetic jet actuators, in: 55th AIAA Aerospace Sciences Meeting, Grapevine, 2017. Y.X. Yuan, X.B. Zhang, Multiphase Hydrokinetic Foundation of High Temperature and High Pressure (in Chinese), Harbin Institute of Technology Press Harbin, Harbin, 2005, pp. 310–321. I.H. Ibrahim, M. Skote, Simulations of the linear plasma synthetic jet actuator utilizing a modified Suzen-Huang model, Phys. Fluids (1994) 11 (2012) 113602. G. Sary, G. Dufour, F. Rogier, K. Kourtzanidis, Modeling and parametric study of a plasma synthetic jet for flow control, AIAA Stud. J. 8 (2014) 1591–1603. Z. Zhang, Y. Wu, M. Jia, H. Zong, W. Cui, H. Liang, Y. Li, Influence of the discharge location on the performance of a three-electrode plasma synthetic jet actuator, Sens. Actuators A Phys. (2015) 71–79. V. Narayanaswamy, L.L. Raja, N.T. Clemens, Characterization of a high-frequency pulsed-plasma jet actuator for supersonic flow control, AIAA Stud. J. 2 (2010) 297–305. Y. Zhou, Z. Xia, L. Wang, Z. Luo, W. Peng, X. Deng, Discharge and electrothermal efficiency analysis of capacitive discharge plasma synthetic jet actuator in single-shot mode, Sens. Actuators A Phys. 287 (2019) 102–112. A. Belinger, P. Hardy, P. Barricau, J.P. Cambronne, D. Caruana, Influence of the energy dissipation rate in the discharge of a plasma synthetic jet actuator, J. Phys. D Appl. Phys. 36 (2011) 365201. L. Wang, Z.B. Luo, Z.X. Xia, B. Liu, Energy efficiency and working characteristics of plasma synthesis jets (in Chinese), Acta Phys Sin-Ch Ed 12 (2013) 400–409. T. Emerick, M.Y. Ali, C. Foster, F.S. Alvi, S. Popkin, SparkJet characterizations in quiescent and supersonic flowfields, Exp. Fluids 12 (2014). S.H. Popkin, B.Z. Cybyk, C.H. Foster, F.S. Alvi, Experimental estimation of SparkJet efficiency, AIAA Stud. J. 6 (2016) 1831–1845. M. Tang, Y. Wu, H. Wang, D. Jin, S. Guo, T. Gan, Effects of capacitance on a plasma synthetic jet actuator with a conical cavity, Sens. Actuators A Phys. (2018) 284–295. H. Zong, W. Cui, Y. Wu, Z. Zhang, H. Liang, M. Jia, Y. Li, Influence of capacitor energy on performance of a three-electrode plasma synthetic jet actuator, Sens. Actuators A Phys. (2015) 114–121. J. Wu, Advances in Lead-Free Piezoelectric Materials, Springer Singapore, Singapore, 2018, pp. 379–396. A.B. Liu, P.F. Zhang, B. Yan, C.F. Dai, J.J. Wang, Flow characteristics of synthetic jet induced by plasma actuator, AIAA Stud. J. 3 (2011) 544–553. A.D. Angola, G. Colonna, C. Gorse, M. Capitelli, Thermodynamic properties of high temperature air in local thermodynamic equilibrium: II accurate analytical expression for electron molar fractions, Eur. Phys. J. D 3 (2011) 453–457. Y. Naghizadeh-Kashani, Y. Cressault, A. Gleizes, Net emission coefficient of air thermal plasmas, J. Phys. D Appl. Phys. (2002) 2925–2934. A. Belinger, P. Hardy, N. Gherardi, N. Naude, J.P. Cambronne, D. Caruana, Influence of the spark discharge size on a plasma synthetic jet actuator, IEEE T Plasma Sci. 11 (2011) 2334–2335. S.B. Leonov, D. Yarantsev, Near-surface electrical discharge in supersonic airflow: properties and flow control, J Propul Power 6 (2008) 1168–1181. H. Wang, J. Li, D. Jin, M. Tang, Y. Wu, L. Xiao, High-frequency counter-flow plasma synthetic jet actuator and its application in suppression of supersonic flow separation, Acta Astronaut. (2018) 45–56.

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J. Li and X. Zhang / Sensors and Actuators A 302 (2020) 111770

Biographies

Jin-feng Li born in 1995, is a PhD candidate of Nanjing University of Science and Technology. Current fields of interest are active flow control and synthetic jet actuators.

Xiaobing Zhang born in 1968, is a professor of Nanjing University of Science and Technology at present. He got the PhD degree at Nanjing University of Science and Technology in 1995. Current fields of interest are multiphase flow, heat transfer and active flow control.