Department of Flight Physics and Loads AVFP Full Wave Analysis of the Contribution to the Radar Cross Section of the Jet Engine Air Intake of a Fighter Aircraft Pim Hooghiemstra Department of Flight Physics and Loads AVFP 10 April 2007

About NLR NLR = Nationaal Lucht- en Ruimtevaartlaboratorium (National Aerospace Laboratory NLR) Two residences (Amsterdam, NOP: Marknesse) Independent Technological Institute 700 employes 12/5/2018

Overview RADAR Governing Equations Finite Element Method Dispersion Analysis Present Solution Process Future Research OUTWASH Important feature of radar signature of helicopter is: HERM = Helicopter Rotor Modulation Similar to jet engine modulation ( reflection by rotating compressor fan) RCS has Doppler spectrum caused by rotating rotor blades and hub. Can be used for target detection, classification and recognition Spectrum determined by Shape of hub Shape and material of blades Number of blades Rotational speed of rotor Radar cross section computations based on asymptotic high frequency techniques: Physical Optics/ray-tracing and the Method of Equivalent Currents. Incorporation of landing gear, weapons and other protuberances would require (hybrid) full-wave modelling. Here quasi-steady analysis of seperated rotor and fuselage. Higher order effects to be included Electromagnetic blade-blade and rotor-fuselage interaction Deflection and/or pitch changes of rotor blades 12/5/2018

Radar Detection The platform is detected if the signal-to-noise ratio exceeds the minimum level of received signal 12/5/2018

Received power by enemy radar Radar Equation Received power by enemy radar Power of enemy radar Gain of enemy radar Wavelength of enemy radar Distance to enemy radar If the RCS is decreased by a factor 16, the maximum detection distance is decreased by a factor 2 only. 12/5/2018

Radar Cross Section (RCS) Measure of detectability assuming isotropic scattering. Radar excited on the front -> jet engine air intake (modeled as a cylinder) accounts for a great part of RCS for a large range of incident angles. RCS of total aircraft computed by subdividing the aircraft in simple geometries as flat planes and cones. For these simple geometries the RCS is known. RCS is computed in stead of measured since measurements are not always possible (expensive, not available or in development stage). Important feature of radar signature of helicopter is: HERM = Helicopter Rotor Modulation Similar to jet engine modulation ( reflection by rotating compressor fan) RCS has Doppler spectrum caused by rotating rotor blades and hub. Can be used for target detection, classification and recognition Spectrum determined by Shape of hub Shape and material of blades Number of blades Rotational speed of rotor Radar cross section computations based on asymptotic high frequency techniques: Physical Optics/ray-tracing and the Method of Equivalent Currents. Incorporation of landing gear, weapons and other protuberances would require (hybrid) full-wave modelling. Here quasi-steady analysis of seperated rotor and fuselage. Higher order effects to be included Electromagnetic blade-blade and rotor-fuselage interaction Deflection and/or pitch changes of rotor blades 12/5/2018

Computing the RCS Approximate the electric field on the aperture numerically Compute the far-field components of the electric field and the RCS, proportional to 12/5/2018

Maxwell’s Equations OUTWASH Important feature of radar signature of helicopter is: HERM = Helicopter Rotor Modulation Similar to jet engine modulation ( reflection by rotating compressor fan) RCS has Doppler spectrum caused by rotating rotor blades and hub. Can be used for target detection, classification and recognition Spectrum determined by Shape of hub Shape and material of blades Number of blades Rotational speed of rotor Radar cross section computations based on asymptotic high frequency techniques: Physical Optics/ray-tracing and the Method of Equivalent Currents. Incorporation of landing gear, weapons and other protuberances would require (hybrid) full-wave modelling. Here quasi-steady analysis of seperated rotor and fuselage. Higher order effects to be included Electromagnetic blade-blade and rotor-fuselage interaction Deflection and/or pitch changes of rotor blades 12/5/2018

Vector Wave Equation RCS computed for one frequency only. Introduce phasor notation and derive the wave equation for the electric field. 12/5/2018

Vector Wave Equation (2) To obtain a well-posed problem define a boundary condition on the cavity wall and a integral equation for the aperture. To analyse the vector wave equation in detail it is made dimensionless. 12/5/2018

Wave Number Wave number important number for the dimensionless vector wave equation. It is related to the wavelength by The product is characteristic for the RCS. An appropriate test problem should have this ratio in the same order of magnitude to obtain an equivalent problem. 12/5/2018

Finite Element Method – The Elements Tetrahedral elements are chosen for two reasons: They easily follow the shape of the object. They are compatible with the triangles used for the discretization of the aperture OUTWASH Important feature of radar signature of helicopter is: HERM = Helicopter Rotor Modulation Similar to jet engine modulation ( reflection by rotating compressor fan) RCS has Doppler spectrum caused by rotating rotor blades and hub. Can be used for target detection, classification and recognition Spectrum determined by Shape of hub Shape and material of blades Number of blades Rotational speed of rotor Radar cross section computations based on asymptotic high frequency techniques: Physical Optics/ray-tracing and the Method of Equivalent Currents. Incorporation of landing gear, weapons and other protuberances would require (hybrid) full-wave modelling. Here quasi-steady analysis of seperated rotor and fuselage. Higher order effects to be included Electromagnetic blade-blade and rotor-fuselage interaction Deflection and/or pitch changes of rotor blades 12/5/2018

Finite Element Method – The Basis functions Vector based basis functions are chosen to prevent spurious solutions to occur. 12/5/2018

Higher Order Basis functions Interpolation points on the edge and face for construction of basis functions (higher order, more points) Higher order basis functions are chosen for efficiency. This choice decreases the number of DoF. OUTWASH Important feature of radar signature of helicopter is: HERM = Helicopter Rotor Modulation Similar to jet engine modulation ( reflection by rotating compressor fan) RCS has Doppler spectrum caused by rotating rotor blades and hub. Can be used for target detection, classification and recognition Spectrum determined by Shape of hub Shape and material of blades Number of blades Rotational speed of rotor Radar cross section computations based on asymptotic high frequency techniques: Physical Optics/ray-tracing and the Method of Equivalent Currents. Incorporation of landing gear, weapons and other protuberances would require (hybrid) full-wave modelling. Here quasi-steady analysis of seperated rotor and fuselage. Higher order effects to be included Electromagnetic blade-blade and rotor-fuselage interaction Deflection and/or pitch changes of rotor blades 12/5/2018

The System of Equations Nonzero pattern for the discreti- zation matrix A. The matrix has a sparse and a fully populated part. The fully populated part consist of half of the total number of nonzeros. 12/5/2018

Dispersion (1) Assume a wave front entering a cavity. After reflection through the cavity, phase differences occur between different rays of the front. The strength of the electric field (needed for computing the RCS) depends on this phase difference. Due to the discretization the dispersion error is introduced which influences the phase difference. For a deep cavity this error accumulates and dominates the problem. 12/5/2018

Dispersion (2) Exact phase difference Dispersion error Computed phase difference 12/5/2018

Dispersion (3) Wave without error Wave with dispersion error 12/5/2018

Complexity Purpose: Minimize dispersion error and compute RCS accurately Dependence of matrix size on dispersion error element order 12/5/2018

Degrees of Freedom The total number of unknowns in the system is a function of the element order p, the error . It is observed that the total DoF decreases for higher order elements. 12/5/2018

Present Solution Method A direct method is used. Iterative methods with well known preconditioners (ILU, approximate inverse) were considered but not promising. Frontal solver Eliminate fully summed variables immediately Store active (front) variables only Benefits: Can be used to compute the RCS for multiple right hand sides and an answer is always obtained. Drawback: Takes a long time to compute accurate solution 12/5/2018

Ideas for Future Research Use efficient iterative method (GCR or COCG) Construct an effective preconditioner. Observed: ‘simple’ preconditioners do not work. ILU and approximate inverse are implemented and they are not efficient Idea: use the shifted Laplace operator as preconditioner. This works well for the Helmholtz equation, expected to work for vector wave equation. 12/5/2018

Questions and Suggestions Other Remarks? 12/5/2018