Aircraft Radome Characterization via Multiphysics Simulation

Eamon Whalen

Eamon Whalen

Application Engineer at Altair
Eamon Whalen works as an Application Engineer at Altair Boston, where he supports Finite Element Analysis (FEA) and optimization software. His interests include multi-disciplinary optimization (MDO), design exploration, and machine learning. Eamon received a Bachelor’s degree in Mechanical Engineering from the University of Michigan in 2016.
Eamon Whalen

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This post is from a white paper written by Altair’s Eamon Whalen, Gopinath Gampala, Katelyn Hunter, Sarthak Mishra, CJ Reddy

Figure 1. The electromagnetic, aerodynamic, and structural performance of a nose cone radome can be characterized by computational simulation, allowing for early design concept validation and reducing the dependence on physical testing.

Radomes protect antennas from structural damage due to wind, precipitation, and bird strikes. In aerospace applications, radomes often double as a nose cone and thus have a significant impact on the aerodynamics of the aircraft. While radomes should be designed not to affect the performance of the underlying antennas, they also must satisfy structural and aerodynamic requirements. In this paper, we demonstrate a multiphysics approach to analysis of airborne radomes not only for electromagnetic (EM) performance, but also for structural, aerodynamic, and bird strike performances, as depicted in figure 1. We consider a radome constructed using composite fiberglass plies and a foam core, and coated with an anti-static coating, paint, and primer. A slotted waveguide array is designed at X-band to represent a weather radar antenna. The transmission loss of the radome walls is analyzed using a planar Green’s function approach. An asymptotic technique, Ray-Launching Geometric Optics (RL-GO), is used to accurately simulate the nose cone radome and compute transmission loss, boresight error, and sidelobe performance. In addition to EM analysis, Computational Fluid Dynamics (CFD) analysis is used to predict pressures resulting from high air speeds, which are then mapped to an implicit structural solution to assess structural integrity using the Finite Element Method (FEM). We also demonstrate damage prediction due to a “bird strike” impact using an explicit structural FEM solver. The multiphysics simulation techniques demonstrated in this paper will allow for early design validation and reduce the number of measurement iterations required before a radome is certified for installation.

I. Introduction

A radome (radar dome) is a rigid, thin-walled structure used to protect a radar antenna. Ground-based antennas, such as those used in anti-missile defense, are typically protected from wind and precipitation by a large, spherical radome [1]. Vehicle-based antennas, such as those mounted on maritime vessels and aircrafts, also make use of radomes to protect the underlying antenna from wind, precipitation, and bird strikes – though these vehicle-based radomes typically feature a streamline shape that is more aerodynamically favorable. A radome will inevitably affect the electromagnetic (EM) performance of the underlying antenna. Common metrics for quantifying a radome’s effect on a signal include transmission loss, boresight error, and change in sidelobe levels. Several factors can affect the EM performance of a radome, including the material composition and thickness of the radome wall, the antenna type, and the operating frequency [1]. Radomes should be designed to be as transparent as possible to the underlying EM signal.

An aircraft radome must also satisfy several aerodynamic and structural requirements. As aircraft nose cone radomes have a significant impact on the aerodynamics of the vehicle, aerodynamic performance is the dominant factor in determining a radome’s shape. A radome must also survive the wind pressure loads that occur during flight. The radome should be designed such that these aerodynamic loads do not significantly deform the structure or cause it to buckle. One of the most common causes of aircraft radome failure is collisions with birds. Bird strike occurs most frequently during takeoff and landing, when the aircraft is at lower elevations. The Federal Aviation Administration (FAA) dictates acceptable levels of damage to various components of the aircraft as the result of a bird strike. The collision of a 4-lb bird should not inhibit the successful completion of an airliner’s flight [2]. Accurate bird strike damage prediction is the first step in determining whether the flight may be continued.

An aircraft radome should be designed to minimally attenuate the EM signal while satisfying all structural and aerodynamic requirements. Currently, physical testing of these requirements is the primary method of design verification. We present computational simulation as a complementary approach to physical testing. Simulation has several advantages over physical testing, including reduced cost and time, the ability to verify before fabrication, and compatibility with parametric optimization. Previous work to simulate radome EM performance, aerodynamic performance, and bird strike has been done individually [3][4][5][6]. This paper takes a multiphysics approach to radome design validation.

II. Simulation Models

A generic airliner nose cone radome was selected as the base model for the following simulations. The radome wall consists of a fiberglass composite with foam core (A-Sandwich configuration). Five unidirectional fiberglass plies make up the laminate on either side of the foam core. The stacking sequence is shown in figure 2. The radome is coated with an anti-static coating, primer, and paint. An X-band weather radar antenna was modeled as a slotted waveguide array operating at 9.4 GHz. A rectangular waveguide feed is mounted on the back and spans the diameter of the antenna.

Figure 2: The generic airliner nose cone radome (left) and radome wall composition (right) used in the subsequent simulation models.

The thicknesses and material constants for each layer were selected to be characteristic of real world applications. These values are listed in Appendix A. Note that only the relevant material constants to each simulation were included in the models, for example, the coatings were omitted from structural analysis because their thicknesses and stiffnesses are negligible.

A. Radome Wall Transmission Loss

Radome walls should be designed to minimize transmission loss at the operating frequency to ensure successful signal transmission. Planar Green’s function with Method of Moments (MoM) is a common and computationally inexpensive way to predict transmission loss in a radome wall. The wall was modeled as an infinite multilayer substrate, composed of isotropic dielectric layers. A single fiberglass ply acts as an orthotropic dielectric due to the distinct material properties of the fibers and the matrix; however, when several plies of varying fiber orientations are combined they act as a single isotropic layer. For this reason, the fiberglass plies in this model were assumed to be isotropic. A 9.4 GHz plane wave source was applied to the radome wall at 1° increments between 0°-90°. The resulting transmission coefficients were computed using the commercial EM simulation tool, FEKO [7] (figure 3).

Figure 3: The simulated transmission coefficient of the radome wall across different incident angles.

The planar Green’s function approach is computationally inexpensive, solving in 3 seconds on 4 cores. The model predicts that transmission coefficients for the radome’s wall will be less than -2 dB for incident angles below 82°. Multiple “what-if” scenarios can now be evaluated by making changes to the wall composition and re-running the analysis.

B. Full Radome Far-Field Analysis

Radomes should be designed to minimally attenuate and distort the signal of the underlying antenna. The objective of the full radome far-field analysis is to predict the radiation pattern of the antenna with and without the radome, from which the signal attenuation and distortion can be inferred. The characterization of the radome wall performed with a planar Green’s function, while computationally efficient, does not take into consideration the shape of the radome. We used an alternative method which considers the radome’s shape and composition in the radiation pattern prediction.

The slotted waveguide antenna was modeled as a perfect conductor operating at 9.4 GHz. A waveguide port was placed at the center of the feed guide, exciting the fundamental mode of the antenna. Far fields were requested at 1° increments in every direction. The slotted waveguide is electrically large with a longest dimension of 0.34 m (10.6 λ). The problem was solved using the Multi-Level Fast Multipole method (MLFMM) – a full wave solution that is more efficient in time and memory than MoM for electrically large problems.

Figure 4: The radiation pattern of the slotted waveguide antenna was predicted using the Multi-Level Fast Multipole Method (MLFMM).

The simulation solved in under 5 minutes on 24 cores. The maximum directivity of the antenna was predicted to be 21.2 dB and the maximum sidelobe level was predicted to be 8.35 dB (figure 4). Once characterized, the antenna’s radiation pattern was written to a file to be used as an equivalent source for radome analysis. This saves computational time by eliminating the need to re-analyze the antenna geometry with each new simulation. The simulation was repeated with the radome placed over the equivalent source. The radome wall was again assumed to behave as an isotropic layered dielectric. Due to the radome’s size (113 λ) Ray Launching Geometric Optics (RL-GO) was employed as the numerical method. RL-GO is an asymptotic, ray-based technique well-suited for dielectrics that exceed 20 λ in size. The maximum number of RL-GO ray interactions was set to 3. Far field patterns were requested, and the results were compared to those of the antenna in free space (figure 5).

Figure 5: By comparing the antenna’s far-field patterns with and without the radome, it can be shown that the radome’s effect on the EM signal is negligible.

The model solved in under 3 minutes on 4 cores. The antenna’s far-field is nearly unaffected by the presence of the radome. The maximum transmission loss was found to be 0.25 dB. The radome did not significantly affect sidelobe levels. The model predicted a boresight error of zero, which implies that the actual boresight error is less than the requested far-field resolution of 1°. This simulation could be repeated with a finer far-field resolution if a more accurate boresight error prediction is desired. It can be surmised that the radome has a negligible effect on the antenna’s signal.

C.   Aerodynamic Load

A primary purpose of an aircraft’s radome is to protect the underlying antenna from damage due to high wind speeds. The first objective of this model is to confirm that the radome does not buckle under this aerodynamic pressure. Due to the cyclic nature of aircraft takeoffs and landings, a second objective is to determine composite stresses in the radome, which can be used to predict fatigue failure. A third objective is to verify that the deformations resulting from aerodynamic load are negligible in EM analysis.

A 3D Computational Fluid Dynamics (CFD) model was used to predict the pressure profile that forms around the radome during flight. The model consists of the front half of an airliner fuselage suspended inside a virtual wind tunnel. Full vehicle CFD models are very computationally expensive. As only the pressures around the radome were of interest, the wings and rearward half of the fuselage were replaced by a simple cone structure, significantly reducing the computational complexity of the problem. The walls of the wind tunnel were assigned a slip boundary condition, and the inlet initial condition was set to 283 m/s (Mach 0.96), which approximates the maximum operating airspeed of a commercial airliner. The steady state solution was computed by AcuSolve [7] (figure 6).

Figure 6: The air pressure profile of an airliner at cruise altitude and maximum operating speed. A steady state Computational Fluid Dynamics (CFD) model was used to compute these pressures, which were then mapped onto a structural model of the radome to predict deformation and stress.

The simulation completed in 2 hours and 15 minutes on 8 cores. The pressure profile obtained from the CFD model was mapped onto a structural FEA model to predict the radome’s deformation under aerodynamic load. The structural model consisted of 2D shell elements defined by a laminate composite property. The fiberglass plies were modeled as a thin orthotropic material (with Young’s Moduli E1 ≠ E2, E3 = 0) and the foam core was modeled as an isotropic material. The coatings were ignored as their structural stiffness is negligible. Nodes around the base of the nose cone were constrained in all six degrees of freedom to represent the brackets that join the radome and fuselage. The linear static solution and the first 10 modes of the linear buckling solutions were solved using OptiStruct [7], employing the Lanczos method for eigenvalue computation (figure 7).

Figure 7: The normal stress in the fiber direction for each of the radome’s 10 fiberglass plies. Note that stress concentrations are highly dependent on fiber direction. Results from the core are not shown.

The simulation completed in 10 seconds on 4 cores. The first buckling mode was found to have a buckling factor of 1.80, indicating that buckling will not occur at maximum speed. Normal stresses in the fiber direction of each ply ranged from 6.7 MPa in tensile regions to -15 MPa in compressive regions. The maximum deflection was found to be 0.8 mm, indicating that shape change due to aerodynamic load is negligible in EM and CFD models. In future work this analysis could be repeated for different maneuvers such as takeoff and landing where the pressure profile differs from the one above.

D.   Bird Strike

Bird strike is a highly dynamic event, resulting in large deformations at high velocities. A structural explicit model of the radome was built using three layers of solid hexahedron elements for the foam core and a single layer of 2D shell elements on either side for the fiberglass plies. A core of solid elements allows for the consideration of out-of-plane compression effects – critical in damage models like bird strike. The fiberglass plies were set to fracture at a tensile strain of 0.07. All material stiffnesses were assumed to be strain rate dependent. The coatings were ignored. As in the aerodynamic load model, nodes around the base of the radome were constrained in all degrees of freedom to represent the brackets that fix the radome to the fuselage.

The bird was modeled using Smooth Particle Hydrodynamics (SPH) – a mesh-free Lagrangian method well-suited for applications involving extremely high deformations. A 1.81 kg (4 lb) validated bird model was selected as this is one of the standard masses used in Federal Aviation Administration (FAA) regulations [2]. Most bird strikes occur during takeoff and landing. An initial speed of 67.1 m/s (150 mph) was applied to the bird at an angle of 15° above the horizontal, simulating a strike during takeoff. A total of 60 ms of physical time was simulated using Radioss [7] (figure 8).

Figure 8: The ability of the radome to withstand a bird strike was modeled with an explicit structural model utilizing SPH particles.

As the stability of explicit solutions depends on having a sufficiently small timestep, explicit models are often more computationally expensive than implicit models. The bird strike simulation solved in 22 minutes on 72 cores. The maximum tensile strain in the fiberglass plies was determined to be 0.027 and thus fracture did not occur. It should be noted that bird strike is a stochastic event – a wide range of velocities and impact points are possible, upon which the results may be highly dependent. A proper assessment of bird strike damage may involve a Design of Experiment (DOE) exploring several of these potential scenarios; however, the intent of this section is to demonstrate the modeling of a single bird strike event and thus a DOE involving multiple simulations is out of its scope.

III. CONCLUSION

A multiphysics approach to aircraft radome design validation has been presented. Planar Green’s function with Method of Moments (MoM) was used to predict the transmission loss of the radome wall. The Multi-Level Fast Multipole Method (MLFMM) was used to characterize the radiation pattern of a waveguide weather antenna, which was then compared to a Ray Launching Geometric Optics (RL-GO) radome model with equivalent source to more accurately assesses the EM performance of the radome. Computational Fluid Dynamics (CFD) was used to predict the wind pressures during flight. A structural implicit model used these pressures to compute the deformation of the radome under aerodynamic load and resulting stresses in each composite layer. Lastly, a structural explicit model was used to predict bird strike damage using Smooth Particle Hydrodynamics (SPH). These simulation techniques allow for early design concept validation of aircraft radomes, as well as reduce the need to perform physical testing. Now that the performance of the radome has been predicted, future work may entail a model-based optimization of the radome wall to reduce weight while satisfying performance criteria across all models.

References
  • Griffiths, “A fundamental and technical review of radomes,” Microwave ProductDigest, May 2008.
  • FAA Federal Aviation Regulations (FARS 14 CFR) Section 25.571, “Damage tolerance and fatigue evaluation of structure,” January 2011
  • Piche, G. P. Piau, C. Bernus, F. Campagna and D. Balitrand, “Prediction by simulation of electromagnetic impact of radome on typical aircraft antenna,” The 8th European Conference on Antennas and Propagation (EuCAP 2014), The Hague, 2014, pp. 3205-3208.
  • Paris, “Computer-aided radome analysis,” in IEEE Transactions on Antennas and Propagation, vol. 18, no. 1, pp. 7-15, Jan 1970.
  • Kumar, P. Honguntikar, “CFD analysis of transonic flow over the nose cone of aerial vehicle,” International Journal for Scientific Research & Development, vol. 3, issue 07, 2015
  • Jun, L. Yulong, G. Xiaosheng, Y. Xiancheng, “A numerical model for bird strike on sidewall structure of an aircraft nose,” Chinese Journal of Aeronotics, vol. 27, issue 3, June 2014
  • Altair Engineering Inc. HyperWorks Solver Suite, “FEKO, AcuSolve, OptiStruct, Radioss”, Version 2017.2 https://www.altairhyperworks.com/solvers-optimizaton
Appendix A. Radome wall thicknesses and material constants

The thicknesses and material constants used in the described models are listed in table A1. Only the material constants that are relevant to the simulation models are listed.

Table A1: Thicknesses and material constants used in simulation models. The values are representative of real engineering materials but should not be used in place of actual test data.

 

Eamon Whalen

About Eamon Whalen

Eamon Whalen works as an Application Engineer at Altair Boston, where he supports Finite Element Analysis (FEA) and optimization software. His interests include multi-disciplinary optimization (MDO), design exploration, and machine learning. Eamon received a Bachelor’s degree in Mechanical Engineering from the University of Michigan in 2016.