# Numerical Optimization of Electromagnetic Performance and Aerodynamic Performance for Subsonic S-Duct Intake

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Computational Methodology

#### 2.1. Verification

#### 2.2. Mesh Independence Study

^{+}values ranged from 0 to 10.

#### 2.3. Orientation Characteristics of RCS

## 3. Method and Results of Optimization

#### 3.1. Correlation Parameter

_{n}, a

_{1n}, and a

_{2n}. The position and angle of any middle section vector are determined by the center line function of the diffuser.

_{n}is an X-axis coordinate of the nth section center. y

_{n}could be a Y-coordinate of the nth section center or one of the three section shape parameters, including S

_{n}, a

_{1n}, and a

_{2n}. To ensure the continuous variation of section parameters, there are four boundary conditions:

_{s}, the short axis length control variable of the upper semi-ellipse in middle section A

_{1}, and the short axis length control variable of the lower semi-ellipse A

_{2}.

#### 3.2. Efficient Model and Error Analysis

_{a}is the average RCS value in the vertical direction with horizontal polarization, while R

_{b}is the average RCS value in the vertical direction with vertical polarization. According to the table, there is a positive correlation between the TPR and the mass flow rate to some extent. The TPD has a greater impact on engine performance than the mass flow rate M. In order to improve the optimization efficiency, the maximum TPD index DC60 and the average RCS value R were taken as the main optimization objectives, with the constraint of M > 35 kg/s. DC60 could be calculated using Equation (6).

#### 3.3. Pareto Front and Verification

#### 3.4. Optimization Effect

_{a}value of model C decreased by 2.39, the SC60 value increased by 0.09, the M value increased by 2.6 kg/s, and the DC60 value decreased by 0.24, indicating that aerodynamic performance and electromagnetic performance of S-duct intake were improved after optimizing.

#### 3.5. Verification at Off-Design Conditions

_{r}= 9.72 − 1.08j was coated on all surfaces of the model except on the outlet section. The frequencies were set as 3 GHz and 10 GHz.

## 4. Conclusions

- The S-duct diffuser can effectively reduce the electromagnetic echo intensity of the intake but generally results in the loss of aerodynamic performance. The backflow, the second flow, and the local shock wave occurred in the diffuser due to the unsuitable design, decreasing the mass flow rate and the total pressure loss while increasing the total pressure and the swirl distortion;
- By determining the five parameters with the quartic polynomial functions, a definite S-duct intake model could be constructed, causing the optimal design to be feasible. According to the samples selected with the Optimized Latin Hypercube method, four effective models based on the Kringing model were established, with satisfactory accuracy for the aerodynamic performance parameters and available accuracy for RCS. By using the global multi-objective optimization algorithm, five solutions were obtained and verified to be feasible, with one of them set as the optimal result;
- By the optimal design stage, the two performances of the S-duct intake were both improved, with the area of the low-speed zone decreasing, the intensity of the local shock wave reduced, the second flow suppressed, and the average RCS decreased by 2 db. Compared with the straight intake, the electromagnetic performance of the optimized S-duct intake was obviously improved and the aerodynamic performance was similar except that the SC60 value was increased by 0.05. After verification, the optimized intake also has both applicable aerodynamic and electromagnetic performances at various off-design conditions.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Lee, C.S.; Lee, S.W.; Chou, R. RCS reduction of a cylindrical cavity by dielectric coatin. In Proceedings of the International Symposium on Antennas and Propagation Digest, Philadelphia, PA, USA, 8–13 June 1986; Volume 1, pp. 305–308. [Google Scholar]
- Syberg, J.; Koncsek, J.; Surber, L. Performance variations in high aspect ratio subsonic diffusers due to geometric constraints in supersonic tactical aircraft inlet installations. In Proceedings of the AIAA/SAE/ASME 16th Joint Propulsion Conference, Hartford, CN, USA, 30 June–2 July 1980. AIAA-80-1106. [Google Scholar]
- Little, B.H.; Trimbol, W.S. An experimental investigation of S-duct diffusers for high-speed prop-Fans. In Proceedings of the AIAA/SAE/ASME 18th Joint Propulsion Conference, Cleveland, OH, USA, 21–23 June 1982. AIAA-82-1123. [Google Scholar]
- Ball, W.H. Experimental investigation of the effects of wall suction and blowing on the performance of highly offset diffusers. In Proceedings of the AIAA/SAE/ASME 19th Joint Propulsion Conference, Seattle, WA, USA, 27–29 June 1983. AIAA-83-1169. [Google Scholar]
- Kitchen, R.A.; Sedlock, D. Subsonic diffuser development of advanced tactical aircraft. In Proceedings of the AIAA/SAE/ASME 19th Joint Propulsion Conference, Seattle, WA, USA, 27–29 June 1983. AIAA-83-1168. [Google Scholar]
- Goldsmith, E.L.; Seddon, J. Practical intake aerodynamic design. Aeronaut. J.
**1994**, 98, 323. [Google Scholar] - Fiola, C.; Agarwal, R.K. Simulation of secondary and separated flow in a diffusing S-duct using four different turbulence models. Aerosp. Eng.
**2014**, 228, 1954–1963. [Google Scholar] [CrossRef] - Xiao, Q.; Tsai, H.; Liu, F. Computation of transonic diffuser flows by a lagged k-oturbulence model. J. Propuls. Power
**2003**, 19, 473–483. [Google Scholar] [CrossRef] - Lefantzi, S.; Knight, D.D. Automated design optimization of a three-dimensional S-shaped subsonic diffuser. J. Propuls. Power
**2002**, 18, 913–921. [Google Scholar] [CrossRef] - Zhang, W.L.; Knight, D.D.; Smith, D. Automated design of a three dimensional subsonic diffuser. J. Propuls. Power
**2000**, 16, 1132–1140. [Google Scholar] [CrossRef] - Bae, H.; Park, S.; Kwin, J. Efficient global optimization for S-duct diffuser shape design. J. Aerosp. Eng.
**2013**, 227, 1516–1532. [Google Scholar] [CrossRef] - Gan, W.B.; Zhang, X.C. Design optimization of a three-dimensional diffusing S-duct using a modified SST turbulent model. Aerosp. Sci. Technol.
**2017**, 63, 63–72. [Google Scholar] [CrossRef] - Zhang, Z.K.; Lum, K.Y. S-shaped inlet design optimization using the adjoint equation method. Aerosp. Sci. Technol.
**2017**, 63, 63–78. [Google Scholar] - Crispin, W.J., Jr.; Maffett, A.L. Estimating the radar cross section of a cavity. IEEE Trans. Aerosp. Electron. Systems
**1970**, 6, 672–674. [Google Scholar] [CrossRef] - Chung, S.S.M.; Tuan, S.C. Shadowing a small size but large radar cross dection object with a large size but small radar cross section object. In Proceedings of the 2020 IEEE Asia-Pacific Microwave Conference (APMC), Hong Kong, China, 8–11 December 2020; pp. 1051–1053. [Google Scholar]
- Vogel, M. Radar cross section of aircraft with engine inlets including fan blades. In Proceedings of the IEEE International Symposium on Antennas and Propagation, Fajardo, PR, USA, 26 June–1 July 2016; pp. 1369–1370. [Google Scholar]
- Chung, S.S.M.; Tuan, S.C. Efficacy of an S-shaped air inlet on the reduction of front bistatic radar cross section of a fighter engine. Prog. Electromagn. Res. B
**2021**, 92, 193–211. [Google Scholar] [CrossRef] - Herrmann, C.D.; Koschel, W.W. Experimental investigation of the internal compression of a hyper-sonic intake. In Proceedings of the 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Indianapolis, IN, USA, 7–10 July 2002. AIAA-2002-4103. [Google Scholar]
- Song, J.; Lu, C.C.; Chew, W.C. Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects. IEEE Trans. Antennas Propagation
**1997**, 45, 1488–1493. [Google Scholar] [CrossRef] [Green Version] - Anastassiu, T.H.; Volakis, J.L. The mode matching technique for eletromagnetic scattering by inlets with complex terminations. J. Electromagn. Waves Appl.
**1995**, 9, 1363–1391. [Google Scholar] [CrossRef] - Chou, R.C.; Lee, S.W. Modal attenuation in multilayered coated waveguides. IEEE Trans. Microw. Theory Tech.
**1988**, 36, 1167–1176. [Google Scholar] [CrossRef]

**Figure 5.**Results of RCS calculation and experiment. (

**a**) Horizontal polarization (

**b**) Vertical polarization.

**Figure 9.**RCS calculation results of model S. (

**a**) Horizontal polarization (

**b**) Vertical polarization.

**Figure 20.**RCS of inlet coated with low scattering material. (

**a**) Vertical detection-3GHz (

**b**) Horizontal detection-3GHz (

**c**) Vertical detection-10GHz (

**d**) Horizontal detection-10GHz.

Variable | Value | |
---|---|---|

Inlet | Area S_{1}/m^{2} | 0.55 |

High H_{1}/m | 0.5 | |

Sweep angle/° | 12.43 | |

Outlet | Area S_{2}/m^{2} | 0.64 |

Diameter D_{2}/m | 0.9 | |

Length of S-duct diffuser/m | 2.5 |

Parameter | Point Coordinates | X/mm | Y/mm |
---|---|---|---|

Throat height h: 15 mm | 1 | 0 | 0 |

Total length: 400 mm | 2 | 45.7 | 18.0 |

Second compression angle δ_{2}: 21.5 | 3 | 75.0–145.0 | 18.0 |

Lip angle δ_{3}: 9.5 | 4 | 35.0 | 29.0 |

Expansion angle δ_{4}: 5 | 5 | 58.9 | 33.0 |

Variable | Value |
---|---|

Cavity diameter/m | 0.286 |

Cavity length/m | 0.3 |

Cylinder diameter/m | 0.16 |

Cylinder length/m | 0.16 |

Mesh Type | Whole Mesh Number | Inner Mesh Number |
---|---|---|

Mesh-A | 1.04 million | 0.58 million |

Mesh-B | 2.06 million | 1.23 million |

Mesh-C | 4.03 million | 3.07 million |

Mesh Type | Total Pressure/Pa | ||
---|---|---|---|

Maximum | Minimum | Average | |

Mesh-A | 32,249 | 25,123 | 30,113 |

Mesh-B | 32,126 | 25,076 | 30,106 |

Mesh-C | 32,150 | 25,068 | 30,120 |

Model | Average RCS/dbsm | |||
---|---|---|---|---|

H-V | H-H | V-V | V-H | |

S | 12.814 | 2.609 | 11.86 | 2.317 |

K | 12.508 | 2.551 | 12.504 | 1.935 |

P | 12.779 | 3.116 | 11.943 | 2.874 |

Variable | Maximum Value | Minimum Value |
---|---|---|

K | 2 | 0 |

Y | 0.25 | 0.15 |

As | 3 | −3 |

A1 | 3 | −3 |

A2 | 3 | −3 |

Y | K | A_{s} | A_{1} | A_{2} | DC60 | R_{a} (dbsm) | R_{b} (dbsm) | M (kg/s) | TPR | |
---|---|---|---|---|---|---|---|---|---|---|

1 | 0.1791 | 1.747 | 2.772 | 1.861 | 1.633 | 0.5676 | 12.81 | 11.86 | 31.392 | 0.9191 |

2 | 0.2411 | 0.506 | −1.861 | −1.177 | −2.241 | 0.2776 | 12.51 | 12.08 | 37.462 | 0.9470 |

3 | 0.212 | 1.241 | −1.785 | −3 | −1.481 | 0.4428 | 14.38 | 15.57 | 33.557 | 0.9287 |

4 | 0.1728 | 0.43 | −0.342 | 0.797 | −3 | 0.3590 | 12.80 | 15.14 | 37.748 | 0.9479 |

5 | 0.1652 | 0.506 | 0.494 | −2.392 | −2.392 | 0.2772 | 12.29 | 13.86 | 36.664 | 0.9384 |

6 | 0.1956 | 0.127 | −1.481 | −1.253 | 2.165 | 0.3114 | 11.40 | 15.15 | 37.567 | 0.9456 |

7 | 0.2361 | 0.329 | 2.089 | 1.633 | 1.861 | 0.2369 | 12.38 | 14.59 | 37.282 | 0.9430 |

70 | 0.1627 | 0 | −1.101 | −0.722 | −0.494 | 0.3747 | 13.26 | 13.48 | 37.067 | 0.9526 |

71 | 0.1513 | 1.342 | 1.937 | −2.089 | 1.177 | 0.5574 | 12.14 | 11.39 | 33.312 | 0.9273 |

72 | 0.1741 | 0.684 | −2.468 | −2.468 | 0.266 | 0.2934 | 14.39 | 12.48 | 36.736 | 0.9411 |

73 | 0.1614 | 1.418 | −1.709 | −1.937 | −2.013 | 0.4540 | 15.58 | 13.93 | 34.723 | 0.9310 |

75 | 0.1753 | 0.785 | 2.62 | 0.342 | −2.468 | 0.3106 | 13.51 | 14.07 | 37.363 | 0.9460 |

Sample | Y | K | A_{s} | A_{1} | A_{2} |
---|---|---|---|---|---|

1 | 0.1935 | 0.4546 | 1.9230 | 0.1030 | 0.2277 |

2 | 0.1797 | 0.6054 | 1.4740 | −0.2675 | 0.1318 |

3 | 0.1737 | 0.7093 | 1.3335 | −1.0590 | 0.1974 |

4 | 0.1833 | 0.8524 | −0.9254 | −1.7582 | 2.8266 |

5 | 0.1687 | 0.8850 | 2.2570 | −0.4626 | 0.4221 |

DC60 | M (kg/s) | R (dbsm) | TPR | SC60 | ||||
---|---|---|---|---|---|---|---|---|

Actual | Predicted | Actual | Predicted | Actual | Predicted | |||

1 | 0.2039 | 0.2056 | 37.26 | 37.19 | 12.17 | 11.76 | 0.9511 | 0.0858 |

2 | 0.2128 | 0.2156 | 36.98 | 37.65 | 12.16 | 11.34 | 0.9484 | 0.1269 |

3 | 0.2516 | 0.2487 | 37.61 | 37.29 | 11.56 | 10.64 | 0.9537 | 0.1247 |

4 | 0.2976 | 0.2699 | 37.59 | 37.72 | 11.31 | 9.28 | 0.9531 | 0.0646 |

5 | 0.3084 | 0.2855 | 37.16 | 37.96 | 10.44 | 9.17 | 0.9510 | 0.0665 |

Model | R_{a} (dbsm) | R_{b} (dbsm) | DC60 | M (kg/s) | TPR | SC60 |
---|---|---|---|---|---|---|

A | 17.523 | 15.637 | 0.3810 | 37.11 | 0.9498 | 0.0394 |

B | 14.45 | 12.64 | 0.4410 | 34.64 | 0.9177 | 0.1739 |

C | 12.06 | 12.27 | 0.2039 | 37.26 | 0.9511 | 0.0858 |

Frequency | 3 GHz | 10 GHz |
---|---|---|

V-V | 4.70 | −3.33 |

V-H | −2.82 | −7.75 |

H-V | 2.99 | 2.17 |

H-H | −8.39 | 1.97 |

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**

Wang, B.; Wang, Q.
Numerical Optimization of Electromagnetic Performance and Aerodynamic Performance for Subsonic S-Duct Intake. *Aerospace* **2022**, *9*, 665.
https://doi.org/10.3390/aerospace9110665

**AMA Style**

Wang B, Wang Q.
Numerical Optimization of Electromagnetic Performance and Aerodynamic Performance for Subsonic S-Duct Intake. *Aerospace*. 2022; 9(11):665.
https://doi.org/10.3390/aerospace9110665

**Chicago/Turabian Style**

Wang, Bin, and Qiang Wang.
2022. "Numerical Optimization of Electromagnetic Performance and Aerodynamic Performance for Subsonic S-Duct Intake" *Aerospace* 9, no. 11: 665.
https://doi.org/10.3390/aerospace9110665