# Experimental Study on Plasma Flow Control of Symmetric Flying Wing Based on Two Kinds of Scaling Models

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

_{1}. Then, it charged the primary energy storage capacitor C

_{2}through the charging inductor L and the diode D

_{1}. The voltage of the primary storage capacitor C

_{2}was about 1.4 times of the input voltage by C

_{1}. When the semiconductor switching insulated gate bipolar transistor (IGBT) was working, C

_{2}performs pulse discharge. A positive high voltage pulse was generated by potential transformer (PT) boost and diode D

_{3}unidirectional conduction. The output actuation voltage (peak voltage) was adjustable from 0 to 10 kV, and the pulse frequency was adjustable from 0 to 2 kHz. The waveform of the no-load maximum output voltage is shown in Figure 6. Each single pulse duration time was microsecond magnitude. When the circuit exported a high-voltage pulse, the actuator performed a single pulse discharge. The number of high-voltage pulses produced in a second was the pulse repetition frequency.

## 3. Experimental Results

#### 3.1. Analysis of Discharge and Energy

#### 3.1.1. Effect of Actuation Length on Discharge Energy

#### 3.1.2. Effect of Actuation Voltage on Discharge Energy

#### 3.1.3. Effect of Actuation Frequency on Discharge Energy

#### 3.2. Force Characteristics

^{+}= f × l/U

_{∞}, in which f is the output actuation frequency of the power supply, l is the average aerodynamic chord length of the symmetric flying wing model, and U

_{∞}is the incoming flow velocity. In order to ensure that the dimensionless frequency was consistent, the incoming flow velocity of the large flying wing was 2.5 times that of the small flying wing. When the incoming flow velocity of the small flying wing was 30 m/s, the incoming flow velocity the large flying wing was 75 m/s. The dimensional frequencies F

^{+}were 0.36, 0.71, 1.07, 2.14, 3.57 and 7.13 with corresponding actuation frequencies f of 50 Hz, 100 Hz, 150 Hz, 300 Hz, 500 Hz, and 1000 Hz, respectively, to study the effect of the unsteady actuation on the lift and drag of the two-scale flying wing model.

^{+}= 0 was the same as that at 30 m/s, and the stall angle of attack was 15°. The microsecond pulse plasma actuation could also improve the aerodynamic performance of the large flying wing surface and delay the stall separation. It can be seen from Figure 13a that the actuation effect was more obvious when the dimensionless frequency was between 0.71 and 2.14, and the optimal dimensionless frequency was 1.07. The maximum lift coefficients corresponding to the dimensionless frequencies of 0.71, 1.07, and 2.14 were increased by 10.4%, 15.1%, and 10%, respectively, and the stall angles of attack were delayed by 3°, 4° and 3°, respectively. As can be seen in conjunction with Figure 12a and Figure 13a, the effect of high frequency actuation to improve the aerodynamic performance of the symmetric flying wing surface was lower than that of low frequency. It can be seen from Figure 13b that the air resistance of the large flying wing was affected by the actuation frequency. When the actuation was performed under low frequency condition, the drag coefficient was greater than that without plasma actuation, but the drag coefficient under the high frequency actuation condition was lower than that of no plasma actuation.

^{+}was equal to 1, the actuation effectwas most obvious and the similarity criterion was matched. The increase of the maximum lift coefficient of the large flying wing was less than that of the small flying wing. Because the incoming flow velocity increased, the separation vorticity in the flow field became stronger. It was necessary to inject more unit intensity energy into the flow field to suppress the separation of the surface boundary layer.

^{+}was equal to 1, the inflection point of the pitch moment coefficient curve was delayed by 2°, while in other dimensionless frequencies, the inflection point was the same as that of no plasma actuation. On the one hand, there was an optimal actuation frequency when the unsteady actuation dimensionless frequency was equal to 1, which was related to the incoming flow velocity, the feature size of the symmetric flying wing model. On the other hand, the effect of flow control was different from the same actuation intensity at different inflow speeds.

^{5}, and the Reynolds number of the large flying wing corresponding to the incoming flow velocity of 75 m/s was 2.9 × 10

^{6}. As shown in Figure 14, with the increase of the dimensionless frequency, the variation trend of the lift coefficient increment under different Reynolds numbers was consistent. The lift coefficient increment increased first and then decreased. The increment of the plasma actuation at low Reynolds number was more obvious. It can be seen that the optimal dimensionless frequency of flow control at low velocity was independent of the Reynolds number. However, the higher the Reynolds number, the greater the inertial force in the flow field, resulting in the flow field not being easy to control after stalling. Therefore, the effect of the same intensity disturbance on controlling the flow field stall separation at different incoming flow velocities was different. Increasing the intensity of unsteady actuation to improve the lift coefficient of the symmetric flying wing model at a higher Reynolds number and increasing the pitching moment coefficient are worthy of further study.

^{+}was 1.07. The effect of low frequency actuation was better than that of higher frequency. After actuation, the stall angle of attack of the small flying wing was delayed by 4°, the maximum lift coefficient was increased by 30.9%, and the drag coefficient could be reduced by 17.3%. After the large flying wing was actuated, the stall angle of attack was delayed by 4°, the maximum lift coefficient was increased by 15.1%, but the drag coefficient was increased.

#### 3.3. Flow Field Characteristics

## 4. Conclusions

^{5}and 2.9 × 10

^{6}are both 15°. When the actuation frequency of plasma flow control is 150 Hz, the unsteady actuation effect is the best, and the corresponding dimensionless frequency F

^{+}is 1.07, which is appropriate for the Strouhal similarity criterion. After actuation of the small flying wing, the stall angle of attack is delayed by 4°, the maximum lift coefficient is increased by 30.9% and the drag coefficient can be reduced by 17.3%. The effect of lift increase and drag reduction is good. For a large flying wing, the stall angle of attack is delayed by 4°, the maximum lift coefficient is increased by 15.1%, and the drag coefficient is increased. Similarly, the inflection point of the pitch moment is delayed at the optimal dimensionless frequency. In addition, the effect of low frequency actuation is better than that at a high frequency. The inertia force of the incoming flow at a low Reynolds number is small, and the plasma actuation effect is obvious, but at a high Reynolds number, the ability to promote the complete reattachment of the separation area is not enough due to the limitation of actuation intensity. The PIV test results of the flow field at different cross-sections show that the stall separation on the surface of the symmetric flying wing begins from the outer side, and then with the increase of the angle of attack the separation area begins to appear on the inside. The plasma flow control can not only delay the separation of the longitudinal boundary layer but also slow down the movement of the lateral vortex and inject momentum and energy into the flow field, thus effectively increasing the lift and reducing the drag.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Wang, F. The Comparison of Aerodynamic and Stability Characteristics between Conventional and Blended Wing Body Aircraft. Master’s Thesis, Cranfield University, Cranfield, UK, 2012. [Google Scholar]
- Patil, M.J.; Hodges, D.H. Flight Dynamics of Highly Flexible Flying Wings. J. Aircr.
**2006**, 43, 1790–1799. [Google Scholar] [CrossRef] [Green Version] - Zhang, L.; Zhou, Z.; Xu, X.P.; Wang, H.B. Comparison on aerodynamic and stealthy performance of flying wing unmanned aerial vehicle with three conformal intake inlets. J. Aerosp. Power
**2015**, 30, 1651–1660. [Google Scholar] - Chen, S.; Lyu, Z.; Kenway, G.K.; Martins, J.R. Aerodynamic Shape Optimization of the Common Research Model Wing-Body-Tail Configuration. In Proceedings of the AIAA Aerospace Sciences Meeting, Kissimmee, FL, USA, 5–9 January 2015. [Google Scholar]
- Nangia, R.; Palmer, M. Flying-Wings (Blended Wing Bodies) with Aft & Forward Sweep, Relating Design Camber & Twist to Longitudinal Control. In Proceedings of the AIAA Atmospheric Flight Mechanics Conference & Exhibit, Monterey, CA, USA, 5–8 August 2002. [Google Scholar]
- Mardanpour, P.; Richards, P.W.; Nabipour, O.; Hodges, D.H. Effect of multiple engine placement on aeroelastic trim and stability of flying wing aircraft. J. Fluids Struct.
**2014**, 44, 67–86. [Google Scholar] [CrossRef] - Huang, A.; Folk, C.; Silva, C.; Christensen, B.; Chen, Y.F.; Ho, C.M.; Jiang, F.; Grosjean, C.; Tai, Y.C. Applications of MEMS devices to delta wing aircraft: From concept development to transonic flight test. In Proceedings of the 39th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 8–11 January 2001. [Google Scholar]
- Roos, F.W. Microblowing for High-Angle-of-Attack Vortex Flow Control on a Fighter Aircraft. J. Aircr.
**2001**, 38, 454–457. [Google Scholar] [CrossRef] - Patel, M.P.; Ng, T.T.; Vasudevan, S.; Corke, T.C.; He, C. Plasma Actuators for Hingeless Aerodynamic Control of an Unmanned Air Vehicle. J. Aircr.
**2007**, 44, 1264–1274. [Google Scholar] [CrossRef] [Green Version] - Su, Z.; Li, J.; Liang, H.; Zheng, B.R.; Wei, B.; Chen, J.; Xie, L.K. UAV flight test of plasma slats and ailerons with microsecond dielectric barrier discharge. Chin. Phys. B
**2018**, 27, 459–468. [Google Scholar] [CrossRef] - Hsiao, F.B.; Liu, C.F.; Shyu, J.Y. Control of wall-separated flow by internal acoustic excitation. AIAA J.
**2012**, 28, 1440–1446. [Google Scholar] [CrossRef] - Krishnappa, S.; Jogi, N.; Nguyen, L.D.; Gudmundsson, S.; MacKunis, W.T.; Golubev, V.V. Towards Experimental Validation of Robust Control of Gust-induced Airfoil Limit Cycle Oscillations Using Synthetic Jet Actuators. In Proceedings of the AIAA Fluid Dynamics Conference, Washington, DC, USA, 13–17 June 2016. [Google Scholar]
- Zong, H.; Kotsonis, M. Effect of slotted exit orifice on performance of plasma synthetic jet actuator. Exp. Fluids
**2017**, 58, 17. [Google Scholar] [CrossRef] [Green Version] - Campbell, J.F. Augmentation of Vortex Lift by Spanwise Blowing. J. Aircr.
**1976**, 13, 727–732. [Google Scholar] [CrossRef] - Joseph, P.; Amandolese, X.; Edouard, C.; Aider, J.L. Flow control using MEMS pulsed micro-jets on the Ahmed body. Exp. Fluids
**2013**, 54, 1–12. [Google Scholar] [CrossRef] - Little, J. High-Lift Airfoil Separation Control with Dielectric Barrier Discharge Plasma Actuators. Ph.D. Thesis, The Ohio State University, Columbus, OH, USA, 2010. [Google Scholar]
- Yun, W.U.; Yinghong, L.I. Progress in Research of Plasma-assisted Flow Control, Ignition and Combustion. High Volt. Eng.
**2014**, 40, 2024–2038. [Google Scholar] - Little, J.; Takashima, K.; Nishihara, M.; Adamovich, I.; Samimy, M. Separation Control with Nanosecond-Pulse-Driven Dielectric Barrier Discharge Plasma Actuators. AIAA J.
**2012**, 50, 350–365. [Google Scholar] [CrossRef] - Tang, M.; Wu, Y.; Wang, H.; Guo, S.; Sun, Z.; Sheng, J. Characterization of transverse plasma jet and its effects on ramp induced separation. Exp. Therm. Fluid Sci.
**2018**, 99, 584–594. [Google Scholar] [Green Version] - Zheng, B.; Xue, M.; Ke, X.; Ge, C.; Wang, Y.; Liu, F.; Luo, S. Unsteady Vortex Structure Induced by a Trielectrode Sliding Discharge Plasma Actuator. AIAA J.
**2018**, 57, 467–471. [Google Scholar] [CrossRef] - Sidorenko, A.; Budovsky, A.; Pushkarev, A.; Maslov, A. Flight testing of DBD plasma separation control system. In Proceedings of the AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, USA, 7–10 January 2008. [Google Scholar]
- Wang, J.; Li, Y.; Xing, F. Investigation on oblique shock wave control by arc discharge plasma in supersonic airflow. J. Appl. Phys.
**2009**, 106, 073307. [Google Scholar] [CrossRef] - Benard, N.; Moreau, E. Electrical and mechanical characteristics of surface AC dielectric barrier discharge plasma actuators applied to airflow control. Exp. Fluids
**2014**, 55, 1846. [Google Scholar] [CrossRef] - Roupassov, D.V.; Nikipelov, A.A.; Nudnova, M.M.; Starikovskii, A.Y. Flow Separation Control by Plasma Actuator with Nanosecond Pulsed-Periodic Discharge. In Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 7–10 January 2008. [Google Scholar]
- Durasiewicz, C.; Singh, A.; Little, J. A Comparative Flow Physics Study of Ns-DBD vs. Ac-DBD Plasma Actuators for Transient Separation Control on a NACA 0012 Airfoil. In Proceedings of the 2018 AIAA Aerospace Sciences Meeting, Kissimmee, FL, USA, 8–12 January 2018. [Google Scholar]
- Sevant, N.E.; Bloor, M.I.G.; Wilson, M.J. Aerodynamic Design of a Flying Wing Using Response Surface Methodology. J. Aircr.
**2015**, 37, 562–569. [Google Scholar] [CrossRef] - Huber, K.; Schutte, A.; Rein, M. Numerical Investigation of the Aerodynamic Properties of a Flying Wing Configuration. In Proceedings of the 30th AIAA Applied Aerodynamics Conference, New Orleans, LA, USA, 25–28 June 2012. [Google Scholar]
- Xu, X.; Zhou, Z. Analytical study on the synthetic jet control of asymmetric flow field of flying wing unmanned aerial vehicle. Aerosp. Sci. Technol.
**2016**, 56, 90–99. [Google Scholar] [CrossRef] - Han, M.; Li, J.; Niu, Z.; Liang, H.; Zhao, G.; Hua, W. Aerodynamic performance enhancement of a flying wing using nanosecond pulsed DBD plasma actuator. Chin. J. Aeronaut.
**2015**, 28, 377–384. [Google Scholar] [CrossRef] [Green Version] - Yao, J.K.; Zhou, D.J.; He, H.B.; He, C.J.; Shi, Z.W.; Du, H. Experimental investigation of lift enhancement for flying wing aircraft using nanosecond DBD plasma actuators. Plasma Sci. Technol.
**2017**, 19, 11–18. [Google Scholar] [CrossRef]

**Figure 9.**Variation of instantaneous power and energy at different actuator lengths. (

**a**): comparison of instantaneous power; (

**b**) comparison of energy.

**Figure 10.**Variation of instantaneous power and energy at different actuator voltages. (

**a**): comparison of instantaneous power; (

**b**) comparison of energy.

**Figure 12.**Lift, drag, and pitch moment coefficient curves of the small flying wing at different dimensionless frequencies (U

_{∞}= 30 m/s, FL-5). (

**a**): Lift coefficient curves; (

**b**) Drag coefficient curves; (

**c**) Pitch moment coefficient curves.

**Figure 13.**Lift, drag, and pitch moment coefficient curves of the large flying wing at different dimensionless frequencies (U

_{∞}= 75 m/s, FL-51). (

**a**): Lift coefficient curves; (

**b**) Drag coefficient curves; (

**c**) Pitch moment coefficient curves.

**Figure 14.**Lift coefficient increment at different dimensionless actuation frequencies in incoming flow velocities of 30 m/s and 75 m/s.

**Figure 16.**Time-averaged flow field of measured cross-section 1 of the small flying wing (U

_{∞}= 30 m/s, FL-5).

**Figure 17.**Time-averaged flow field of measured cross-section 2 of the small flying wing (U

_{∞}= 30 m/s, FL-5).

**Figure 18.**Time-averaged flow field of measured cross-section 3 of the small flying wing (U

_{∞}= 30 m/s, FL-5).

**Figure 19.**Time-averaged flow field of measured cross-section 1 of the large flying wing (U

_{∞}= 75m/s, FL-51).

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xie, L.; Liang, H.; Han, M.; Niu, Z.; Wei, B.; Su, Z.; Tang, B.
Experimental Study on Plasma Flow Control of Symmetric Flying Wing Based on Two Kinds of Scaling Models. *Symmetry* **2019**, *11*, 1261.
https://doi.org/10.3390/sym11101261

**AMA Style**

Xie L, Liang H, Han M, Niu Z, Wei B, Su Z, Tang B.
Experimental Study on Plasma Flow Control of Symmetric Flying Wing Based on Two Kinds of Scaling Models. *Symmetry*. 2019; 11(10):1261.
https://doi.org/10.3390/sym11101261

**Chicago/Turabian Style**

Xie, Like, Hua Liang, Menghu Han, Zhongguo Niu, Biao Wei, Zhi Su, and Bingliang Tang.
2019. "Experimental Study on Plasma Flow Control of Symmetric Flying Wing Based on Two Kinds of Scaling Models" *Symmetry* 11, no. 10: 1261.
https://doi.org/10.3390/sym11101261