CEM Workshop Lectures (5/11): Best Practices in RCS Prediction

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Best Practices in RCS
Predictions
Good practices evolved for solution in reasonable
accuracy and time

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©ZeusNumerixPvtLtd:ConfidentialDocument
Contents
 Introduction
 Assumption
 Grid Generation
 Basics of Electromagnetism
 Basics of RCS
 RCS of Simple Shapes
 Boundary conditions & scattering
 Post-processing
 Overview
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28-Sep-2012 Best Practices in CEM

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Best Practices : Introduction
 Before using the software, you should know
 Basics of Electromagnetism and RCS
 Aim of the problem – near field, far field or RCS?
 Accuracy vs. time available
 Hardware limitations
 No blind trust on the software. Every problem is unique in some sense or the other.
Can we validate the software and the simulation process on a similar problem?
 Recommend new users solving for canonical shapes first and interpret the results
 It is good to solve as many problems as possible, before attempting the real life problems
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Assumption
 Simulation engineer
 Has a reasonable background on electromagnetism and RCS
 Knows the basic steps in the simulation
 Has some idea about numerical method being used
 What one should do in each step
 Grid generation
 Setting up solver
 Post-processing
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Grid Generation
 Importance of grid generation
 Good grid is half CEM done; Inferior grid is full CEM repeated
 Grid must respect the physics
 Higher the frequency, finer will be the mesh. To satisfy Nyquist criterion, at least three mesh
points per wavelength are required.
 For Gaussian pulse, mesh points based on highest frequency
 Requirements change with problem. Waveguide requires resolving 3D field; RCS requires
resolving surface currents
 Position of outer boundary
 At short distance, it may produce a spurious reflected wave of considerable strength
 If it is a large distance, solution is costlier.
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Grid Generation contd…
 Topology of blocks affects global grid density
 If possible, use O-O-O topology for multi-block structured meshes.
 Clustering
 It is good to have more mesh points where field is expected to change rapidly; but too much
clustering slows down the progress of solution
 Cluster the mesh points near sharp corners, bends and areas of large curvature
 What mesh size is adequate ?
 Carry out grid convergence studies
 Make a fine mesh and coarsen it, till you get 2 meshes with reasonably identical results
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Grid Generation contd…
 Mesh quality
 Skewness - included angles should be close to 90 degrees
 Smoothness - volume changes must not be abrupt
 aspect ratio - hexahedrons should be close to cuboid
 A mesh good for one incidence may not be good for all incidences.
 Mesh generation is incomplete till
 BCs are assigned
 Proper labels are given to various surfaces
 The volume occupied by the scatterer is deleted
 Note that sizes and linear dimensions are in SI units
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Basics of Electromagnetics
Electromagnetic waves
Frequency : f = c/ , Wave number : k = 2/,
Poynting vector S = E x H (watts /m2) Polarization : direction of E
 EM waves have two fields: Electrical field and Magnetic field
 The fields are perpendicular to each other
 The direction of electrical field dictates the polarization
 Energy density = energy / volume = ( E2 +  H2) Joules / m3
 Flux of energy S = E x H watts / m2
 Power ~ (amplitude)2
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Basics of Electromagnetism
 RCS depends up on:
 Relative size of the object wrt. to wavelength of wave
 Shape of the target
 Orientation of target with respect to source of radiation
 Orientation of the receiving radar with respect to target
 Material of the surface. Here we are using surface as PEC
 If there is no absorption or transmission, RCS reduced in one direction, it will
necessarily increase in some other direction
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Basics of RCS
Incident power
scattered or reflected power is
collected by different antennas
Bi-static Configuration
Mono-static Configuration
scattered or reflected power is
collected by the same antenna
Rst
Rtf
Rst
Incident power
scattered power
Transmitting and also receiving antenna
Transmitting antenna
receiving antenna

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Basics of RCS…
 Contribution to RCS, energy received from the target comes from three mechanisms:
 Reflection
 Diffraction
 Creeping waves
 Mono-static radar RCS :Energy scattered towards the source is called backscattered energy
 Bi-static RCS: Energy scattered in any other directions
 RCS (normally denoted by ) is defined as 4 (Ps /Pi); where,
 Ps scattered or reflected power per solid angle (w/sold angle) and
 Pi incident power density (w/m2)
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RCS of Simple Shapes
RCS of flat plates
 This is mostly reflection (or specular reflection)
 RCS with incident wave making an angle  is
  = (L2/)(kw cos() sin(kw sin())/kw sin())2
 k = wave number = 2/
 at  = 0, RCS,   L2w2/2
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RCS of a cylinder
 Reflected energy is not restricted in the backward direction, however maximum
scatter is in the backward direction
 There can be considerable scattering at angles other than 90 degrees
 For a cylinder, the reflected signal is proportional to kaL2/
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RCS of a sphere
 Reflected energy is not restricted in the backward direction, however maximum
scatter is in the backward direction
 There can be considerable scattering at angles other than 90 degrees
 For a sphere, the reflected signal is proportional to r2
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RCS of Sphere

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Back Scattering from Different Shapes

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Boundary Conditions & Scattering

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Boundary Conditions & Scattering

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BCs for Scattered Field from PEC
 Escattered_n = - Eincident_n Escattered_t = Eincident_t
 Hscattered_n = Hincident_n Hscattered_t = - Hincident_t
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Reflections
 EM waves may reflect several times causing secondary reflections
 Multiple reflections may produce
 Constructive interference
 Destructive interference
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Diffraction
 Diffraction is scattering from edges and vertices
 Since the normal is not defined on PEC, it is very difficult numerically calculate the
effect of diffraction
 Diffraction obeys the law angle of incidence = angle of re-radiation cone
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Travelling and Creeping Waves on PEC
 For smooth surfaces such as ellipsoids, EM waves hardly get reflected
 Almost all the energy is carried parallel to the target surface with speed of light as
 Creeping wave – travelling in shadow region
 Traveling wave – incident + reflected wave in the illuminated region
 Energy is scattered from the farthest point form the transmitter
 Variation of E and H in creeping wave can be found out based on
 The governing equations and
 Boundary conditions on PEC
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Travelling and Creeping Waves on PEC

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Manifestation of Multiple Reflections,
Travelling and Creeping waves on PEC
 For an arbitrary body, there can be multiple reflections and traveling & creeping
waves
 EM waves need to be given path and time for these effects to manifest themselves
and change the results
 The simulations must be of adequate size so that reflected waves travel fully through
computational domain
 The simulation must be carried out for a longer so that RCS does not change and
contribution from these effects is affected
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Post-processing
 Use surface colour plots
 Confirm that BC is satisfied. At any instant
 Total magnetic flux must be zero on the surface
 Total electric flux must be constant on the surface
 Confirm that there is a sinusoidal variation of scattered field
 Sinusoidal incident will generate sinusoidal scattered field as the Maxwell’s equations being solved are
linear
 Do we have adequate surface meshes?
 Distance between two neighboring maximas (or minimas) for a component of E or H should be 
 Distance between two neighboring maximas (or minimas) for surface current must be 
 Distance between two neighboring maximas in |E| (or |H|) should be equal to /2. Here value for
minima must be close to 0.
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Post-processing Results
 Movement of scattered wave
 Scattered wave is the response of the PEC to the incident wave as a result of the boundary
condition.
 The scattered E field will have the same sign as incident wave
 The scattered H field will have the opposite sign as incident wave
 The scattered wave locally moves along outward normal
 Is the variation of scattered field following reasonable trend for
 Face directly illuminated by the incident wave
 Shadow region
 Is there a creeping wave expected?
 Is it correct near vertical and horizontal edge?
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General Overview
 Better to use standard format like CGNS for interoperability
 It is well known that a lot of time is wasted in converting and rewriting files in different
formats.
 Use good naming conventions for files.
 In real solutions are required in reasonable time. Estimate the time required as
accurately as possible before starting the simulations
 It is better to acquire suitable computing resources, than using existing resources
hoping that results with acceptable accuracies will be generated
 Usually engineers make a mistake in routine simulations due to over confidence
 More engineers doesn’t mean faster results; reverse possible
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www.zeusnumerix.com
+91 72760 31511
Abhishek Jain
abhishek@zeusnumerix.com
Thank You !

CEM Workshop Lectures (5/11): Best Practices in RCS Prediction

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CEM Workshop Lectures (5/11): Best Practices in RCS Prediction