Electromagnetic and Mechanical Modeling of Large Phased Arrays of Structurally Embedded

100 Pages·2017·16.4 MB·English

Electromagnetic and Mechanical Modeling of Large Phased Arrays
of Structurally Embedded Waveguides
Nicholas J. Albertson
Thesis submitted to the Faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
Master of Science
in
Aerospace Engineering
Robert A. Canfield, Chair
Mayuresh J. Patil
Majid Manteghi
December 18, 2017
Blacksburg, Virginia
Keywords: SWASS, structurally embedded antennas, multi-fidelity modeling, phased arrays
Copyright 2018, Nicholas J. Albertson
Electromagnetic and Mechanical Modeling of Large Phased Arrays
of Structurally Embedded Waveguides
Nicholas J. Albertson
(ABSTRACT)
Use of Slotted Waveguide Antenna Sti↵ened Structures (SWASS) in future commercial and
military aircraft calls for the development of an airworthiness certification procedure. The
first step of this procedure is to provide a computationally low-cost method for modeling
waveguide antenna arrays on the scale of an aircraft skin panel using a multi-fidelity model.
Weather detection radar for the Northrop Grumman X-47 unmanned air system is consid-
ered as a case study. COMSOL Multiphysics is used for creating high-fidelity waveguide
models that are imported into the MATLAB Phased Array Toolbox for large-scale array
calculations using a superposition method. Verification test cases show that this method
is viable for relatively accurate modeling of large SWASS arrays with low computational
e↵ort. Additionally, realistic material properties for carbon fiber reinforced plastic (CFRP)
are used to create a more accurate model. Optimization is performed on a 12-slot CFRP
waveguide to determine the waveguide dimensions for the maximum far-field gain and sep-
arately for the maximum critical buckling load. Using the two separate optima as utopia
points, a multi-objective optimization for the peak far-field gain and critical buckling load
is performed, to obtain a balance between EM performance and structural strength. This
optimized waveguide is then used to create a SWASS array of approximately the same size
as an aircraft wing panel using the multi-fidelity modeling method that is proposed. This
model is compared to a typical conventional weather radar system, and found to be well
above the minimum mission requirements.
Electromagnetic and Mechanical Modeling of Large Phased Arrays
of Structurally Embedded Waveguides
Nicholas J. Albertson
(GENERAL AUDIENCE ABSTRACT)
Antennas used in military and commercial aircraft have traditionally been designed inde-
pendently from the aircraft structure. Increasingly, e↵ort has been made to integrate these
processes, in order to create more e�cient, dual-purpose structures. Slotted waveguide an-
tennas, hollow rectangular tubes with slots cut in one face, are commonly used to create
arrays for aircraft on-board weather radar. A type of structurally embedded antenna, slot-
ted waveguide antenna sti↵ened structures (SWASS), consists of slotted waveguides that are
sandwiched between two layers of a composite material. This sandwich structure can be used
in place of the conventional structure used for aircraft skin, allowing the slotted waveguides
to function not only as antennas, but also as part of the aircraft’s load-bearing structure.
Because of the geometric complexity of the slotted waveguides, generating accurate mod-
els of the antenna performance can be di�cult and requires a great deal of computational
power. This thesis presents and validates a method for reducing the complexity of modeling
the antenna performance of SWASS arrays. Additionally, optimizations are performed to
improve both the waveguide’s performance as an antenna and as a load-bearing part of the
aircraft structure. Finally, the optimized SWASS array is compared to the actual mission
requirements of the Northrop Grumman X-47 unmanned aircraft, and is found to perform
above the required levels.
Dedicated to my wonderful wife Lyndsey, without whom none of this would have been
possible.
iv
Acknowledgments
I would like to thank Dr. Canfield for his support of me throughout my graduate career
from the very beginning. He signed on to be the advisor for a student who was a novice to
the electrical engineering to work on a project that deals heavily with antennas. Though
neither of us was an expert, he guided me through the di�culties of jumping into a wholly
unknown field to expand the boundaries of my multidisciplinary design capabilities.
I would also like to gratefully acknowledge Mr. Robert J. Hanley, Director, USN & USMC
AirworthinessandCYBERSAFEO�ce,AIR-4.0P.Thisresearchwasfundedinpartbyprime
contract #HC1047-05-D-4005, purchase order APSC01797, clearance statement A10160-
S166-PR01. Additionally, special thanks are given to Katie Hauck and Doug Pennock of the
NAVAIR Radar and Antenna Systems Division (4.5.5.2) and to Rick Ryan of the NAVAIR
Tactical Aircraft Strength Division (4.3.3.1) for their technical advice.
v
Contents
List of Figures ix
List of Tables xiii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 The State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 EM Modeling of Large Phased Arrays of Structurally Embedded Waveg-
uides 10
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Waveguide Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 RF Model for WR90 Slotted Waveguide Antenna . . . . . . . . . . . 19
vi
2.2.3 Array Gain Calculation Using Superposition . . . . . . . . . . . . . . 21
2.2.4 Verification With Realistic Material Properties - CFRP . . . . . . . . 25
2.2.5 Waveguide RF Performance Optimization . . . . . . . . . . . . . . . 29
2.2.6 SWASS Panel Evaluation . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.1 Superposition Verification . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.2 CFRP Material Properties Verification . . . . . . . . . . . . . . . . . 39
2.3.3 Waveguide EM Optimization . . . . . . . . . . . . . . . . . . . . . . 40
2.3.4 Large Array Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.4 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 Structural Design Methods for SWASS 50
3.1 Waveguide Structural Performance Optimization . . . . . . . . . . . . . . . . 51
3.1.1 Coarse Optimization Proof of Concept . . . . . . . . . . . . . . . . . 51
3.1.2 High-Fidelity Optimization . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Multi-Objective Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 SWASS Panel Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4 Results 60
4.1 Waveguide EM Optimization (Chapter 2 Review) . . . . . . . . . . . . . . . 60
4.2 Waveguide Structural Performance Optimization . . . . . . . . . . . . . . . . 61
vii
4.2.1 Coarse Optimization Proof of Concept . . . . . . . . . . . . . . . . . 61
4.2.2 High-Fidelity Optimization . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Multi-Objective Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4 SWASS Panel Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5 Conclusions & Summary 75
5.1 Summary of Technical Contributions . . . . . . . . . . . . . . . . . . . . . . 79
5.2 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . . . 80
Bibliography 81
viii
List of Figures
1.1 Examples of aircraft antennas. (a) Mechanically steered slotted waveguide
antenna array under a radome [19], (b) externally mounted blade antenna
[20], and (c) Airborne Warning and Control System (AWACS) antenna[21] . 3
1.2 Northrop-Grumman X-47 with embedded SWASS array[1] . . . . . . . . . . 4
1.3 Waveguide design variables [8] . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Four SWASS design concepts for highest strength-to-weight ratio[8] . . . . . 9
2.1 Northrop-Grumman X-47 with embedded SWASS array [8, 12, 22] . . . . . . 14
2.2 Waveguide design variables [8, 13] . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Far-field gain pattern of a four-slot waveguide . . . . . . . . . . . . . . . . . 19
2.4 Four-slot waveguide CAD model (a) and its mesh (b) . . . . . . . . . . . . . 20
2.5 Four-slot waveguide shown with simulation domain . . . . . . . . . . . . . . 21
2.6 COMSOL high-fidelity model of a single waveguide element [8, 13] . . . . . . 23
2.7 COMSOL high-fidelity model of a three-element waveguide array . . . . . . . 23
2.8 Nine-element waveguide array . . . . . . . . . . . . . . . . . . . . . . . . . . 24
ix
2.9 COMSOL high-fidelity model of a long waveguide array . . . . . . . . . . . . 25
2.10 Single waveguide far-field gain (dB). COMSOL high-fidelity (a) front and (b) side
views. (c) Front and (d) side views after importing to MATLAB. . . . . . . . . . 35
2.11 Threewaveguidearrayfar-fieldgain(dB).(a)COMSOLhigh-fidelityand(b)MAT-
LAB superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.12 9-Waveguide array far-field gain (dB). (a) Superposition of three 1x3 arrays and
(b) superposition of 9 single elements. . . . . . . . . . . . . . . . . . . . . . . . 37
2.13 Single long 12-slot waveguide far-field gain (dB). COMSOL high-fidelity (a) front
and (b) side views. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.14 Genetic Algorithm Convergence Plot . . . . . . . . . . . . . . . . . . . . . . 41
2.15 Waveguide geometric configurations (a) before and (b) after genetic algorithm op-
timization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.16 Far-fieldgainpatternsbeforeandaftercoarsegeneticalgorithmoptimization. Waveg-
uide with nominal dimensions (a) front and (b) side views. Waveguide with EM-
optimized dimensions (c) front and (d) side views. . . . . . . . . . . . . . . . . . 46
2.17 Nelder-Mead Convergence Plot . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.18 Waveguidegeometricconfigurations(a)beforeand(b)afterNelder-Meadoptimization 47
2.19 Far-field gain patterns before and after high-fidelity Nelder-Mead optimization.
Waveguide with nominal dimensions (a) front and (b) side views. Waveguide with
optimized dimensions (c) front and (d) side views. . . . . . . . . . . . . . . . . . 48
x