# Numerical Research on the NS-SDBD Control of a Hypersonic Inlet in Off-Design Mode

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Models and Methods

#### 2.1. Physical Models

_{r}= 7 ns and t

_{d}= 50 ns, respectively.

#### 2.2. Numerical Methods

_{c}and F

_{v}represent convective flux and viscous flux, respectively. Q is the source terms. t represents flow time. The flux terms are expressed as follows:

_{n}is the velocity normal to the surface of the control volume. E and H represent the total energy and total enthalpy, respectively. p is the static pressure. τ

_{xx}, τ

_{xy}, τ

_{yx}, and τ

_{yy}are shear stresses. Θ

_{x}and Θ

_{y}are heat transfer terms. P

_{th}is the energy source term. n

_{x}and n

_{y}are the components of the unit normal vector in the x and y directions, respectively.

^{−5}m, wall y

^{+}≈ 1. The second order dual time method was applied. The time-step size was 5 × 10

^{−9}s, iterating 20 times in each time step.

_{th}was provided by the phenomenological method:

_{t}represents the integral of spatial distribution function in the plasma zone. E

_{d}represents spanwise energy input per unit length. f(x), g(y) represents horizontal and vertical radiation intensity. t

_{d}is pulse duration. η represents the proportion of injected electrical energy used for gas heating. As is analyzed in reference [22], η ≈ 30%. The length of plasma layer l (unit: cm) is associated with voltage rising time t

_{r}(unit: ns) and peak voltage U

_{p}(unit: kV), and the thickness of the plasma layer h is 0.1 cm [23].

_{d}as well as distribution functions f(x), g(y) were fitted from the experiment data [24,25]:

_{d}is mJ/cm. f represents actuating frequency (unit: Hz), where f

_{0}= 10 Hz. Fitting coefficients a

_{i}, b

_{i}, c

_{i}, d

_{i}, m

_{i}, and n

_{i}are provided in Table 2.

#### 2.3. Verification of Methods

## 3. Results and Discussion

#### 3.1. NS-SDBD Control in the Starting State

_{∞}= 5, AOA = 5°) is shown in Figure 7. The incident cowl shock interacted with the boundary layer, forming a separation bubble and expansion fan. Since the forebody shock was away from the cowl, the inlet was in off-design state. This steady-state baseline flow was adopted as the initial value of the NS-SDBD flow control simulation.

_{d}is the input energy per unit spanwise length. S is the area of plasma region. In Case 1.2, the ratio of maximum increment of mass-flow weighted total pressure to total input energy intensity was 0.759 at the throat section. The ratio of total input energy intensity to mass-flow weighted total pressure (at the throat section) was 0.031.

#### 3.2. NS-SDBD Control in Unstarting State

_{∞}= 5, AOA = 5°) was used as the initial flow field, while the attack angle was increased to 6° in order to simulate the unstart process. As shown in Figure 14, the separation bubble generated by the adverse pressure gradient gradually moved forward from the shoulder point. At 5.15 ms, after the change of attack angle, the highest point of the separation bubble reached the cowl section, forming a normal shock wave, which led to a significant decrease in the mass flow rate coefficient and total pressure recovery coefficient. At this moment, the actuator was turned on for flow control.

## 4. Conclusions

- In the starting state of the inlet, the intersection of compression wave and cowl shock wave provide an increase in the total pressure recovery coefficient, and boosts the pressure ratio of the internal compression section as well. The maximum increments of total pressure recovery coefficient and pressure ratio are 2.37% and 11.6%, respectively;
- If the two actuators are placed closely (with a horizontal coordinate spacing of 4 mm), the intersection of compression waves generated by the two actuators will provide an additional increase in peak total pressure;
- Under the unstarting condition, the NS-SDBD actuation makes the separation point and reattachment point move forward, meanwhile decreasing the separation shock angle and recovering mass flow rate coefficient.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Rodi, P.E.; Emami, S.; Trexler, C.A. Unsteady pressure behavior in a ramjet/scramjet inlet. J. Propuls. Power
**1996**, 12, 486–493. [Google Scholar] [CrossRef] - Bauer, C.; Kurth, G. Importance of the bleed system on the overall air intake performance. In Proceedings of the 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, San Diego, CA, USA, 31 July–3 August 2011. [Google Scholar]
- Xie, W.; Luo, Z.; Hou, L.; Zhou, Y.; Liu, Q.; Peng, W. Characterization of plasma synthetic jet actuator with Laval-shaped exit and application to drag reduction in supersonic flow. Phys. Fluids
**2021**, 33, 096104. [Google Scholar] [CrossRef] - Wang, H.; Li, J.; Jin, D.; Dai, H.; Wu, Y. Effect of a transverse plasma jet on a shock wave induced by a ramp. Chin. J. Aeronaut.
**2017**, 30, 1854–1865. [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. AIAA J.
**2009**, 47, 168–185. [Google Scholar] [CrossRef] - Durasiewicz, C.; Singh, A.; Little, J.C. A Comparative Flow Physics Study of Ns-DBD vs Ac-DBD Plasma Actuators for Transient Separation Control on a NACA0012 Airfoil. In Proceedings of the AIAA Aerospace Sciences Meeting, Kissimmee, FL, USA, 8–12 January 2018. [Google Scholar]
- Kimmel, R.L.; Hayes, J.R.; Menart, J.A.; Shang, J. Effect of surface plasma discharges on boundary layers at Mach 5. In Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 5–8 January 2004. [Google Scholar]
- Shang, J.S.; Huang, P.G.; Yan, H.; Surzhikov, S.T.; Gaitonde, D.V. Hypersonic flow control utilizing electromagnetic-aerodynamic interaction. In Proceedings of the 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Dayton, OH, USA, 28 April–1 May 2008. [Google Scholar]
- Leonov, S.; Bityurin, V.; Savischenko, N.; Yuriev, A.; Gromov, V. Influence of surface electrical discharge on friction of plate in subsonic and transonic airflow. In Proceedings of the 39th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 8–11 January 2001. [Google Scholar]
- Leonov, S.; Bityurin, V.; Savelkin, K.; Yarantsev, D. Effect of electrical discharge on separation processes and shocks position in supersonic airflow. In Proceedings of the 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 14–17 January 2002. [Google Scholar]
- Leonov, S.; Bityurin, V.; Yarantsev, D.; Isaenkov, Y.; Soloviev, V. High-speed flow control due to interaction with electrical discharges. In Proceedings of the AIAA/CIRA 13th International Space Planes and Hypersonic Systems and Technologies, Capua, CE, USA, 16–20 May 2005. [Google Scholar]
- Bisek, N.J.; Poggie, J.; Nishihara, M.; Adamovich, I. Computational and Experimental Analysis of Mach 5 Air Flow over a Cylinder with a Nanosecond Pulse Discharge. In Proceedings of the 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Nashville, TN, USA, 9–12 January 2012. [Google Scholar]
- Nishihara, M.; Gaitonde, D.; Adamovich, I.V. Effect of Nanosecond Pulse Discharges on Oblique Shock and Shock Wave—Boundary Layer Interaction. In Proceedings of the 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Grapevine, TX, USA, 7–10 January 2013. [Google Scholar]
- Chen, Z.; Hao, J.; Wen, C.-Y. Control of supersonic compression corner flow using a plasma actuator. Phys. Fluids
**2022**, 34, 073605. [Google Scholar] [CrossRef] - Falempin, F.; Firsov, A.A.; Yarantsev, D.A.; Goldfeld, M.A.; Timofeev, K.; Leonov, S.B. Plasma control of shock wave configuration in off-design mode of M = 2 inlet. Exp. Fluids
**2015**, 56, 54. [Google Scholar] [CrossRef] - Zhang, W.; Shi, Z.; Zhang, C.; Geng, X.; Li, K.; Chen, Z. A study on flow control in a hypersonic inlet using a plasma synthetic jet actuator. Phys. Fluids
**2022**, 34, 106109. [Google Scholar] [CrossRef] - Poggie, J.; Adamovich, I.; Bisek, N.; Nishihara, M. Numerical simulation of nanosecond-pulse electrical discharges. Plasma Sources Sci. Technol.
**2013**, 22, 015001. [Google Scholar] [CrossRef] - Ahn, S.; Chae, J.; Kim, H.-J.; Kim, K.H. Numerical simulation of streamer physics in nanosecond pulsed surface discharges. Int. J. Aeronaut. Space Sci.
**2021**, 22, 547–559. [Google Scholar] [CrossRef] - Chen, Z.; Hao, L.; Zhang, B. An Empirical Model of Nanosecond Pulsed SDBD Actuators for Separation Control. In Proceedings of the 43rd Fluid Dynamics Conference, San Diego, CA, USA, 24–27 June 2013. [Google Scholar]
- Gaitonde, D.V.; McCrink, M.H. A Semi-Empirical Model of a Nanosecond Pulsed Plasma Actuator for Flow Control Simulations with LES. In Proceedings of the 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, USA, 9–12 January 2012. [Google Scholar]
- Li, Z.F.; Gao, W.Z.; Jiang, H.L.; Yang, J.M. Unsteady behaviors of a hypersonic inlet caused by throttling in shock tunnel. AIAA J.
**2013**, 51, 2485–2492. [Google Scholar] [CrossRef] - Popov, N.A. Fast gas heating in a nitrogen–oxygen discharge plasma: I. Kinetic mechanism. J. Phys. D Appl. Phys.
**2011**, 44, 285201. [Google Scholar] [CrossRef] - Chen, Z.L.; Hao, L.Z.; Zhang, B.Q. A model for Nanosecond Pulsed Dielectric Barrier Discharge (NSDBD) actuator and its investigation on the mechanisms of separation control over an airfoil. Sci. China Technol. Sci.
**2013**, 56, 1055–1065. [Google Scholar] [CrossRef] - Takashima, K.; Zuzeek, Y.; Lempert, W.R.; Adamovich, I.V. Characterization of surface dielectric barrier discharge plasma sustained by repetitive nanosecond pulses. In Proceedings of the 41st AIAA Plasmadynamics and Lasers Conference, Chicago, IL, USA, 28 June–1 July 2010. [Google Scholar]
- Nudnova1, M.; Kindusheva, S.; Aleksahdrov, N. Rate of Plasma Thermalization of Pulsed Nanosecond Surface Dielectric Barrier Discharge. In Proceedings of the 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, FL, USA, 4–7 January 2010. [Google Scholar]
- Ukai, T.; Russell, A.; Zare-Behtash, H.; Kontis, K. Temporal variation of the spatial density distribution above a nanosecond pulsed dielectric barrier discharge plasma actuator in quiescent air. Phys. Fluids
**2018**, 30, 116106. [Google Scholar] [CrossRef]

**Figure 12.**The flow parameter distribution at the throat section in Case 1.2. (

**a**) Pressure coefficient; (

**b**) Mach number.

Frequency | X Position of Actuator 1 | X Position of Actuator 2 | Peak Voltage | Input Energy | |
---|---|---|---|---|---|

Case 0 | No control | No control | 0 | 0 | |

Case 1.1 | 20 kHz | −0.01 m | −0.006 m | 14 kV | 0.2227 mJ/cm |

Case 1.2 | 40 kHz | −0.01 m | −0.006 m | 12.65 kV | 0.2227 mJ/cm |

Case 1.3 | 80 kHz | −0.01 m | −0.006 m | 11.36 kV | 0.2227 mJ/cm |

Case 2 | 40 kHz | −0.014 m | −0.01 m | 12.65 kV | 0.2227 mJ/cm |

Case 3 | 40 kHz | −0.01 m | −0.006 m | 15 kV | 0.3397 mJ/cm |

i | a_{i} | b_{i} | c_{i} | d_{i} | m_{i} | n_{i} |
---|---|---|---|---|---|---|

0 | 12.01 | 57.38 | 84.43 | 275.1 | 0.008365 | 7.991 |

1 | 0.06322 | 0.1244 | 0.001479 | −0.1264 | 2.476 | 0.2772 |

2 | 0.07158 | 0.3682 | 0.1396 | 0.4499 | 0.4585 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yan, Y.; Wang, J.
Numerical Research on the NS-SDBD Control of a Hypersonic Inlet in Off-Design Mode. *Aerospace* **2022**, *9*, 773.
https://doi.org/10.3390/aerospace9120773

**AMA Style**

Yan Y, Wang J.
Numerical Research on the NS-SDBD Control of a Hypersonic Inlet in Off-Design Mode. *Aerospace*. 2022; 9(12):773.
https://doi.org/10.3390/aerospace9120773

**Chicago/Turabian Style**

Yan, Yilun, and Jiangfeng Wang.
2022. "Numerical Research on the NS-SDBD Control of a Hypersonic Inlet in Off-Design Mode" *Aerospace* 9, no. 12: 773.
https://doi.org/10.3390/aerospace9120773