3.1 Flow field characteristics induced by μSDBD under the static atmosphere
A sampling frequency of 50 kHz corresponding to a sampling interval of Δt = 20 μs is used in the experiment, and the schlieren images of μSDBD plasma discharge with the peak-peak voltage of Vp-p = 12 kV and pulse frequency of f = 1000 Hz were recorded with an exposure time of 0.98 μs. To make the image clearer and reduce background interference, the background normalization technique is used. That is, each schlieren image is subtracted by the pre-discharge image, and then divided by the average grayscale of the pre-discharge image to get a dimensionless relative intensity value of the pressure wave. In Fig. 6, the electrodes and dielectric layer of the plasma actuator are represented by rectangular color blocks, with an exposed electrode at the top, a dielectric layer in the middle, and a covered electrode at the bottom. A clear pressure wave can be observed during μSDBD discharge. The pressure wave is cylindrical around the junction of the exposed and covered electrodes, and a flat wave is observed on the top of the cylindrical pressure wave. This is consistent with the typical topology of pressure waves caused by nSDBD mentioned in (Zhang et al. 2019; Nicolas et al. 2012), which is a cylindrical wave surrounding the electrode and a flat wave leaving the surface. The cylindrical part of the pressure wave is caused by the energy released from the edge of the exposed electrode, and the generation of flat wave is originated from the energy deposition during streamer propagation stage (Starikovskii et al. 2009).
After the discharge begins (t = 20 μs), the cylindrical pressure wave with a radius of r = 7.04 mm is formed. Over time, the pressure wave expands continuously, as well as the planar wave. When t = 60 μs, the intensity of the cylindrical pressure waves on both sides gradually weakens, while the intensity of pressure waves in and around the planar area remains essentially unchanged. A second pressure wave with low brightness can be seen at t = 120 μs. At the beginning of the discharge, a pressure wave will be generated on both the rising and falling edges of the microsecond pulse voltage, but the latter has a weak pressure wave strength. Benard et al. (2012) also pointed out that a pressure wave is generated on the rising and falling edges of the voltage. The intensity of the pressure wave is closely related to the voltage amplitude and the pulse rise time, and the positive pulse discharge shows a higher intensity. Only one pressure wave will be observed when the amplitude is low and after the voltage increases to a certain value, two pressure waves will be found and the flat wave can also be observed. When t = 120 μs, the range of the cylindrical pressure wave is further expanded to r = 41.84 mm. Figure 7 records the radius and propagation speeds of the cylindrical pressure wave induced by μSDBD. In our experiment, the velocity resolution of the high-speed schlieren system is 20.6 m/s. The propagation speed of the pressure wave is maintained at around 350 m/s (see Fig. 7), the value approximately equals to the local sound velocity, the phenomenon is in reasonable agreement with the results in (Zhang et al. 2019; Xie et al. 2019). The results indicate that μSDBD, nSDBD, and microsecond surface arc discharge (μSAD) have similar pressure wave structures and propagation speeds. Moreover, a thermal mass of 4mm×4mm can be observed above the junction of the exposed and covered electrodes of the actuator, and Zhu et al. (2013) pointed out that the generation of cylindrical pressure waves is due to fast energy release.
From the point of fluid transport, the thermal mass develops from the edge of the electrode, so the cylindrical wave develops around the edge of the electrode. This phenomenon has also been verified by the numerical simulation of (Unfer and Boeuf 2010). In the current research, the pulse width of the voltage during the discharge is 10 μs, both the rising and falling edges are 800 ns. This shows the energy release in a microsecond time scale, which results in a dramatic rising in the temperature and realizes "fast heating". The heat release leads to a rapid increase in local pressure because the time scale of density variations is much longer than temperature rising. When the local pressure exceeds a certain threshold, a pressure wave is generated due to gas expansion from the surface, exerting a short-term impact on the fluid, which is similar to the flow control mechanism of nSDBD actuation (Roupassov et al. 2008). Some researchers have claimed the main factor of an nSDBD to be the pressure wave due to rapid gas heating in the pulsed discharges (Zheng et al. 2014). Other researchers have claimed that two lumps of heated air were produced by the nSDBD actuation: one propagated along the boundary between the main and separated flows. The other propagated along the surface more slowly than the main flow. This heated air might excite the shear-layer instability, and the induced vortex shedding could result in momentum transfer and entrainment enhancement to the separated flow through the separated shear layer (Komuro et al. 2017; Komuro et al 2018).
3.2 Characteristics of nacelle inlet under crosswind condition
When the nacelle inlet is too close to the ground, the ground effect will induce the strong ground suction vortex, causing flow field distortion (Brix et al. 2000). To avoid the influence of the ground effect on the experimental results, the vertical distance between the nacelle inlet and the wind tunnel wall is set to be larger than 2 DH. A high-performance inlet must ensure a small total pressure loss and an evenly distributed flow filed at the exit (Seddon et al. 1985). Total pressure recovery coefficient PR is used to characterize the loss of the intake flow (Harrison et al. 2013), which is defined as the ratio of the average total pressure Pf (spatial average value of 252 measurement points) at the nacelle exit to the total pressure P0 of the undisturbed cross-section flow, ie:
The flow field distortion is estimated by DC(60), a parameter to measure the quality of the inlet flow field, which is given as:
Where P60 is the worst average 60 degree sector total pressure, see Fig.8. At 27℃, the density of air ρ is 1.177kg/m3 and U∞ is the velocity of the incoming flow.
The flow coefficient φ is usually used to characterize the flow capacity of the inlet. Under a certain flight Mach number, the flow coefficient is the ratio of the mass flow of air actually entering the inlet to the mass flow of air sucked in without decelerating boost or accelerating decompression at the same Mach number, defined as:
Where A∞ is the free flow tube area for far-field incoming flow. Ac is the inlet flow capture area (i.e. the projected area of the leading edge of the nacelle lip in a plane perpendicular to the direction of incoming flow). U∞ is the far-field incoming flow velocity. ρ∞ is the far-field incoming air density.
From the conservation of fluid mass:
In the experiment, the incoming flow velocity is less than 0.3 Ma. The compressibility is not to be considered, so the incoming flow density remains unchanged, i.e.
To satisfy the requirements of safe operation, the inlet in the ground state should achieve a high quality of air-intake when the flow speed of the wind tunnel is larger than 10.29 m/s (20 knots) (Colin et al. 2007). To simulate the typical state in the take-off phase, this paper selects the flow speed of the wind tunnel of U∞ = 15.42 m/s (30 knots), and the effect of crosswind angle on the flow field distortion was studied when the engine suction speed Ui = 20 m/s.
As shown in Fig. 9, when the angle of crosswind is small (β = 10°), PR along the whole cross-section is commonly high. A low-pressure area is mainly located near the wall and the lower right corner. The total pressure loss here is caused by the viscosity loss of the near-wall flow and the slight flow separation resulted from the crosswind. When β = 14°, low-pressure area is much obvious on the windward side, the quality of the outlet flow field gets worse. When β increases to 18°, PR in the low-pressure area becomes less than 0.9975. As β increases, PR further decreases, and the degree of flow separation also exacerbates. At a large crosswind angle of β = 45°, the low-pressure area PR is reduced to below 0.993, and the flow separation range expands to 50% of the cross-section. This shows that the total pressure distortion at the inlet exit is severe and the quality of the outlet flow field deteriorates sharply. In general, as the crosswind angle increases, the separation flow area begins to expand, and its influence range also continues to expand, resulting in a reduction in the PR and a large low-pressure area, which ultimately leads to intake distortion increase.
Based on the analysis above, the flow separation is obviously intensified at β = 14°, and the range of low-pressure area is large, so β = 14° is a critical value for the deterioration of the flow field quality. To study the influence of the suction velocity Ui on the flow field characteristics of the nacelle inlet, β is fixed at 14°, and the DC(60) are tested at three different speeds: U∞ = 15.42 m/s (30 knots), 25.70 m/s (50 knots), 35.98 m/s (70 knots). The profiles of the DC(60) as Ui is shown in Fig. 10. When U∞ = 15.42 m/s, 25.70 m/s and 35.98 m/s, DC(60) quickly decreases to the value below 0.3 at Ui = 19.96 m/s, 19.06 m/s and 18.30 m/s respectively, and then decreases continuously, eventually reaching 0. The flow coefficients φ of these turning points are 1.29, 0.74, and 0.51, and the range of φ (0.5 ~ 1.5) can reflect the typical crosswind conditions of the nacelle inlet from climb to level flight.
The phenomenon above can also be verified at β = 18° and 22°. Flow separation appears when the crosswind angle is relatively small (β = 14° ~ 22°). PR decreases mean the total pressure distortion degree increasing and the quality of the flow field worsening. The flow separation inside the inlet under crosswind conditions is the main reason for nacelle inlet distortion, and inlet distortion will suddenly increase with increasing crosswind speed. Especially when the speed is high (i.e. U∞ = 35.98 m/s), the crosswind separation range is wider, and the total pressure loss is also greater. Next, we will use μSDBD to explore the plasma flow control technology on increasing PR under crosswind conditions, reducing the crosswind separation regions, and improving the quality of the flow field.
3.3 Flow control effects of streamwise plasma actuation
To verify the flow separation control effect of the nacelle inlet under crosswind conditions by μSDBD plasma actuation, the experiment was carried out in a small angle crosswind range (β = 14°, 18°) to avoid the influence of reduced circulation capacity of the nacelle on the separation flow field. The layout of μSDBD actuator is streamwise.
3.3.1 Influence of pulse frequency on the flow control effect
Previous studies have shown that the unsteady plasma actuation can effectively improve the flow control effect with lower energy consumption accounting for the coupling of the flow field instability with shedding vortex frequency (Greenblatt et al. 2008). The effect of high-voltage pulse frequency on the flow control was studied in this section. The flow speed of the wind tunnel and the suction speed is fixed at U∞ = 25.70 m/s and Ui = 25.74 m/s respectively to simulate the work states during the climbing stage of aircraft (flow coefficient φ is close to 1). The voltage waveform with the peak-peak value Vp-p = 8 kV, pulse width of 10 μs and 800 ns rising and falling edges was applied to the actuator. The experiment was conducted under three actuation frequencies f = 500 Hz, 1000 Hz, and 2000 Hz. Obtained PR and DC(60) at the air-intake exit are given in Tab. 1.
Tab. 1 The air-intake exit PR and DC(60)
β(°)
|
Up-p(kV)
|
f(Hz)
|
PR
|
∆PR
|
DC(60)
|
∆DC(60)
|
14
|
0
|
0
|
0.999024
|
-0.000925
|
0.146748
|
0.882576
|
18
|
0.998099
|
1.029324
|
14
|
8
|
500
|
0.999103
|
-0.000275
|
0.115946
|
0.372833
|
18
|
0.998828
|
0.488779
|
14
|
8
|
1000
|
0.999098
|
-0.000309
|
0.119526
|
0.402375
|
18
|
0.998789
|
0.521901
|
14
|
8
|
2000
|
0.999103
|
-0.00035
|
0.116946
|
0.454253
|
18
|
0.998753
|
0.571199
|
The PR decreases with the crosswind angle β, while the DC(60) increases with β. When the crosswind angle increases by 4° without actuation, the PR at nacelle exit decreases 0.000925. With μSDBD plasma actuation, the PR of the air-intake exit is reduced by 0.00275 at f = 500 Hz. As the actuation frequency increases to 1000 Hz and 2000 Hz, the PR of the air-intake exit decreases by 0.000309 and 0.00035 respectively, which are lower than that of without actuation. It shows that μSDBD plasma actuation can improve the effect of PR reduction when the crosswind angle becomes larger. For example, PR can be significantly improved by 70.27 % when f = 500 Hz. Without actuation, DC(60) changed from 0.146748 to 1.029324, increased by 0.882576 when the crosswind angle becomes 18°. After applying μSDBD plasma actuation with f = 500 Hz, 1000 Hz, and 2000 Hz, DC(60) only increases by 0.372833, 0.402375, and 0.454253, which were 57.76 %, 54.20 %, and 48.53 % lower than that of without actuation (0.882576). This indicates that plasma actuation can reduce the distortion of the flow field when the crosswind angle increases effectively.
To further characterize the effect of plasma actuation on the flow separation control and reducing the deterioration of the quality of the flow field at the air-intake exit, Figure 11 shows the distribution of the PR under different frequencies. Plasma actuation can reduce the range of the low-pressure area of the air-intake exit and suppress the flow separation at different crosswind angles. At β = 14°, the plasma actuation can not only reduce the size of the low-pressure area but also change the position of flow separation. The low-pressure area in Fig. 11(a) is located in the lower right corner, and its circumferential range is about 45°. With plasma actuation of f = 500Hz, the low-pressure area shifted to the upper right and the circumferential range is reduced to approximately 25°. However, as the actuation frequency continues to increase, the location and range of the low-pressure area can hardly change, indicating that the μSDBD plasma actuation saturated at Vp-p = 8kV and increasing the frequency can no longer improve the flow control effect. At β = 18°, the low-pressure area of the baseline flow field is more obvious, whose range is about 145° and the PR value is relatively low (0.996). Similarly, with plasma actuation of f = 500 Hz, the low-pressure area is significantly reduced and the range is reduced to 45°. When the frequency increase to f = 1000 Hz and 2000 Hz, although the range of the low-pressure area can also be reduced to 60° and 66°, the flow control effect is not as good as that at f = 500 Hz. Analysis reason: It may be related to the structure of the flow field. Under crosswind conditions, the flow may be accompanied by the generation, development and shedding of vortices. As in airfoil flow control, there is an optimal coupling frequency for ns-DBDPA , Synthetic Jet Actuator, and High-frequency micro-vortex-generator. Thus, μSDBD also has an optimal coupling frequency in nacelle separation control. Because the experiment was carried out at a low speed, the main frequency of the vortex is relatively low. Besides, the actuation characteristics have a certain relationship with the frequency. When the actuation frequency is greater than the optimal frequency, the flow control effect will be worse (Gursul et al. 2007 and Wei et al. 2020).
The μSDBD plasma actuation can improve the effect of PR reduction when the β becomes larger. Besides, it can suppress the flow separation of the inlet and the distortion of the airflow at the nacelle exit under crosswind conditions. The flow control effect is best under the frequency f = 500 Hz and increasing the frequency to 1000 Hz and 2000 Hz cannot improve the flow control effect. It has to be noted that, the discussion on the frequency is based on this experiment condition. When under the actual flight conditions, the optimal value of the actuation frequency would be influenced by the factors such as crosswind speed, angle, and nacelle size. After applying the μSDBD plasma actuation, the pulse energy is concentratedly released in a very short time, resulting in the instantaneous heating of the surrounding gas. The fast heat gas charges the surface of the dielectric layer and enhances the mixing of mass and momentum between the boundary layer and the main flow, injecting more energy into the bottom of the boundary layer. So that the separated boundary layer reattaches. Thus, the flow control effect is achieved and the power consumption is reduced at the same time. The μSDBD plasma actuation can reduce the separation area effectively, resulting in improvement of PR and reduction of distortion of the airflow at the air-intake exit.
3.3.2 Energy optimization of streamwise plasma flow control
Limited by the power rating, to improve the flow control efficiency of μSDBD, it is important to optimize the actuator coverage area to achieve good flow control effects under the lowest power consumption. The analysis above indicated that when the crosswind angle is small, the low-pressure area of the air-intake exit is about 60° ~ 120°. While the arrangement range of the streamwise layout is 180°, the difference may cause energy waste. To further explore the more energy-efficient configuration, the groups of single actuators are set to 3, 6 and 9 to control the actuator coverage area to 60°, 120°, and 180° under the condition of U∞ = 25.70 m/s, β = 14°, f = 500 Hz, Vp-p = 8 kV. The center point of the coverage area is the midpoint of the half-circle on the windward side.
Figure 12 shows PR of the air-intake exit with the streamwise layout of 60°, 120°, and 180° coverage. The PR of 120° coverage is higher than the other two, however, with the increase of Ui, the difference among each other decrease and finally was relatively close. The distribution of PR under different actuator coverage is shown in Fig. 13. After the actuation is applied, when Ui = 13.54 m/s and the coverage is 60° and 180°, the low-pressure areas are significantly larger than the coverage of 120°. When Ui reaches 16.69 m/s, the 120° coverage can suppress the flow separation inside the inlet and make the low-pressure area disappears. While with 60° and 180° coverage can only achieve the same effect when Ui reaches 19.84 m/s. According to the obtained data (see Fig. 14), the μSDBD actuation discharge energy of different coverage areas is calculated by integrating the product of current and voltage. The result of 60°, 120°, and 180° coverage are respectively 0.732 mJ, 1.527 mJ, and 2.024 mJ, indicating that the 120° coverage μSDBD has better control effect and low energy consumption.
In general, when the streamwise layout μSDBD coverage is small, increasing the group of single actuators can expand the action range of the plasma aerodynamic actuation and make it more effectively perform flow control under the same actuation conditions. While the coverage reaches a certain threshold, continuing to expand the coverage area has little effect on improving the flow control effect. And a voltage drop will occur due to the power-supply limitation. Also, the range of the separation area is about 120°, which is as large as the control area of 120° coverage μSDBD. Compared with 180° coverage μSDBD, 120° coverage μSDBD can better concentrate the power of the power-supply to control the separation area. Therefore, the 120° coverage μSDBD gained low energy consumption for all given conditions with the scalable structure and operation, which is ideal for controlling nacelle flow separation.
3.4 Comparative research on flow control effect of streamwise and circumferential layout
An experiment (Jolibois et al. 2008) revealed that the layout of SDBD actuators could achieve different flow control effects by changing the direction of actuation. To explore the layout’s influence on flow separation, the actuator was arranged streamwise and circumferentially in this work. Experiments under different crosswind speeds and different suction speeds were carried out. The voltage with Vp-p = 8 kV and the optimum frequency f = 500 Hz is used, and crosswind angle β = 14°. The coverage area of the actuator was set to 120°.
The air-intake exit PR and DC(60) under different actuator layouts are shown in Figs. 15 and 16. When U∞ = 25.70m/s, there is little difference for air-intake exit PR between two layouts. The control effect decreases with the suction speed. Either U∞ = 25.70 m/s or U∞ = 35.98 m/s, DC(60) of the streamwise layout is significantly smaller than that of the circumferential layout. When U∞ reaches 35.98 m/s, the streamwise layout reduces DC(60) to 1.4076, 0.4474, 0.1408, and 0.1159 at the Ui = 13.54 m/s, 16.69 m/s, 19.84 m/s, and 22.98 m/s. Compared with the circumferential layout actuation, DC(60) is reduced by 19.45 %, 30.28 %, 30.01 %, and 41.68 %, indicating that the former has a better control effect.
To better reflect two layouts’ difference in flow control, Figure 17 and Figure 18 respectively show the total pressure distribution at air-intake exit under different actuator layouts when U∞ = 25.70 m/s and U∞ = 35.98 m/s.When U∞ = 25.70 m/s and Ui reaches 19.84 m/s and 22.98 m/s, the low-pressure area is obviously reduced after applying streamwise layout. The flow separation generally disappears and the total pressure distortion is also significantly reduced. When using the circumferential layout, the low-pressure area is larger than that of the streamwise layout and the PR of the high-pressure area is lower. After the U∞ increased to 35.98 m/s, the low-pressure area of the streamwise layout is smaller than the circumferential layout. The results indicate that the control effect of the streamwise layout is better than that of the circumferential layout, especially in low crosswind speed.
In general, there are two ways for plasma aerodynamic actuation to control the boundary layer: one is to increase the flow velocity in the boundary layer The other is to enhance the energy exchange of the boundary layer and the mainstream (Porter et al. 2007). The actuation position is crucial to suppress the flow separation Circumferential layout can induce gas flow to accelerated. Both are injecting energy into the boundary layer through discharges, which causes disturbance to the near-wall flows, promotes the mixing between the low-energy flow and the mainstream high-energy flow in the boundary layer and enhances the ability of the boundary layer to resist the backpressure gradient. The streamwise layout wraps the entire nacelle front edge to the vicinity of the separation point. Its actuation area is larger, while the circumferential layout is arranged in front of the separation point and it is not clear whether this is its optimum actuation position. In order to more effectively suppress the flow separation, it is necessary to conduct a deeper study on the position of the μSDBD.