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Radar sensing of Wake Vortices in clear aira feasibility study
V. Brion* , N. Jeannin**
Wakenet workshop, 15-16 may 2013, DGAC STAC, Bonneuil-Sur-Marne
*Onera Paris**Onera Toulouse
3
Introduction
In-house collaborative project at ONERA : DoCToR
Detection and Characterization of Wake Vortices by Radar and Lidar in clear air
Part of the objectives :– Understand radar echo in clear air
– Review the litterature for WV
– Model the physics
– Calculate the Radar Cross Section (RCS)– Conclude on the feasability
� Fluid mechanics, radar and lidar teams involved
� Knowledge on vortex dynamics but little on clear air radar echo
4
Bibliography
Gilson experiments ("Aircraft wake RCS measurement", NASA, 1990)
- VHF, UHF, L, S and C bands- R = 100m – 1km
- Power = 0.025 to 7 MW
Nespor et al. ("Doppler radar detection of vortex hazard indicators", NASA, 1994)
- C band
- Power ~ 1MW peak- RCS ~ - 80dBm2
5
Bibliography
Shephard (GEC Marconi trial 1990)
- S and X band
- RCS ~ - 80dBm2
Thales , more recently, in rainy weather
- X band
- Orly & Roissy airports
6
Bibliography
Main conclusions
– Proofs of radar detection in the 90'
– RCS ~ -80dBm2
– However no duplication of the tests
– Reports importance of the met. conditions (stratification, humidity)
– Independence upon jet exhaust is surprising
7
Outline
1 – How does radar echo in clear air occurs ?� theory of dielectrics
2 – How can we model the physics?� The Navier Stokes and Maxwell equations
3 – How much is the Radar Cross Section of WV ?� Evaluation of the RCS with the fluid & ElectroMag numerical models
8
Illustration of the problem
ground radar
PtPr
R
wake vorticesin the far wake
> 10 wing spans
echo
radar - target
Pt: transmitted power
Pr: received power
9
Illustration of the problem
ground radar
PtPr
Simplified radar equation
22 44 R
A
R
GPP et
r πσ
π=
RCS of the radar cell
wake vorticesin the far wake
> 10 wing spans
transmitted power
Ae
Ae: antenna surfaceG: antenna gain
echoradar cell
radar - target
R
10
Origins of the radar echo in clear air
Sample of clear air
H2O (less than 1% in mass)
O2 (20%)
N2 (80%)
Main components
Humidity
� in the form of water vapor� characterized by Relative Humidity RH
satv
v
p
pRH 100=
pv partial pressure of water vapor
pvsat partial pressure of water vapor at saturation
� also specific humidity q
p
pq vv 622.0≈=
ρρ
−=
TTR
L
p
p
vsatv
satv 11
ln00,
11
Origins of the radar echo in clear air
Consider a molecule of O 2
+q-q
By symmetry , the centers of positive and negative charges are at the same location
q = electric charge
12
The capacitor model
Apply an electric field E 0
+q
-q
E0
++++++++++++++++++++++++++++
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
� the positive and negative charges shift in opposite directions, a distance d appart
d
13
The induced dipole moment
Apply an electric field E 0
+q
-q
E0
++++++++++++++++++++++++++++
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
� the positive and negative charges shift in opposite directions, a distance d appart
� A dipolar moment p results such that p=qd in magnitude and oriented upward
d p
14
The atomic polarizability αααα
Apply an electric field E 0
+q
-q
E0
++++++++++++++++++++++++++++
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
� the positive and negative charges shift in opposite directions, a distance d appart
� A dipolar moment p results such that p=qd in magnitude and oriented upward
d p
� In the case of linear dielectric, p is proportional to the electric field E0 : p=αE0
15
Case of an ensemble of molecules
E0
++++++++++++++++++++++++++++
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
For more than one molecule, the resulting density of dipole moment is P=SUM(pi)/Volume
P
p1
p2 p3
p4
pi
16
Case of an ensemble of molecules
E0
++++++++++++++++++++++++++++
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
'4 EP π−=
For more than one molecule, the resulting density of dipole moment is P=SUM(pi)/Volume
An opposite macroscopic electric field E' results, such that
P
p1
p2 p3
p4
pi
E'
opposed to the applied field E0
17
Case of an ensemble of molecules
E0
++++++++++++++++++++++++++++
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
E'
'0 EEE +=
EP eχ=
( )EE eπχ410 +=
εεεεis the dielectric constant
E
Total macroscopic field
The resulting field yields
applied inducedtotal
Introducing the electric susceptibility χe
EE ε=0
p1
p2 p3
p4
pi
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Connecting εεεεto the flow variables temperature and density
Connecting εεεεand αααα
1- for gases at normal density
αχ Ne =2- therefore
απε N41+=
3 - which can be recast into
ραπεM
N A41+=
General formula found in the litterature
TKKK v
vd
ρρρε 3211 +++=K1, K2, K3 are constants
ρd is the density of dry air (80% N2 + 20% O2)
ρv is the density of water vapor (gas)
* M is the molar mass and NA the Avogadro number
E'E0
19
Important remarks
Refraction index "n"
TKKKn v
vd
ρρρ '3
'2
'11 +++=
kgmK /10223 36'1
−×=
kgKmK /.74.1 3'3 =
kgmK /10299 36'2
−×=
21
0
=
εε
n
Limitations
� No dependence upon frequency, ~ true up to 22GHz (absorption ray of water)
� linear relationship between p and E : true if E no too strong
Values given by Thayer*
* Thayer, "An improved equation for the radio refractive index of air", Radio Science, 1974
20
Flow phenomena causing εεεεvariations
Additional effects– compressibility in the vortex cores
– turbulence (increased mixing)– jet exhaust
Atmospheric stratification– temperature, pressure
– humidity– mixing and transport by the wake vortices
21
Radar echo in clear – the full problem
One way coupling : NS � Maxwell through the formula for "n"
FLOW ELECTRO MAGNETIC RESPONSE
TKKKn v
vd
ρρρ '3
'2
'11 +++=
22
Simplifications
NS + Maxwell = too complicated
Simplifications possible since
� flow is low speed
� incompressible
� mostly 2D
� harmonic electric field
� radar far away from the target
� scattered field = weak
23
Flow problem
sectional plane
y
z
x
Atmosphere� stratification in ρ, p, T� humidity
U∞
- 2D- equal strength |Γ| opposite vortices
- separation bb
-Γ +Γ
24
Model for the flow
Boussinesq model
( ) 01 =udiv
( ) 1121111
Re
11ue
Frpuu
t
uzd ∆+−−∇=∇+
∂∂ ρ
11111
RePr
1. dzd
d euut
ρρρ ∆+=∇+∂
∂
( ) ( ) ( )txuxutxu ,, 10 +=
( ) ( ) ( )txpxptxp ,, 10 +=
( ) ( ) ( )txxtx ,, 10 ρρρ +=
Atmospheric state + dynamics associated to the vortices
incompressible
Momentum
Energy
Fr = Froude number Re = Reynolds number Pr = Prandtl number
NbFr
22πΓ= πν2
ReΓ=
pc
k
µ=Pr
N = Brunt-Vaisala freq.2/1
0
0
−=
dz
dgN
ρρ
Parameters
variable constant = 400 constant = 0.7 variable with Fr
NS
25
Numerics
Methodology- Finite element solver FreeFem++
- 2D computational domain
- Only half of the domain calculated- 2nd order time & space
Computational domain and mesh structure
vortex
∑ =
−Γ= 2
1 21
2
2
ia
r
ii
eaπ
ω
State of the Atmosphere- Standard atmosphere
- Vapour pressure : ∆pv = -0.35 Pa/m
Flow initialization
� 2 Lamb-Oseen vortices separated by a distance b
fine mesh
� Configuration = Airbus A340-600 �Γ and b, a/b=0.2
26
Flow configuration
initial altitude z0
z (m)
y (m)
(n-1) x 106
initial vortices
stratification
refractive index
b
Γ
ground
27
Illustration of the transport phenomenon, Fr=10
(n-1) x 106
refractive index
time increases
The WV become more visible with time
28
Illustration of the mixing phenomenon, Fr=10
(n-1) x 106
refractive index
The background stratification is mixed by the vortices
29
Effect of the stratification on the vortex dynamics
Fr=∞
Fr=5
Fr=1
no stratification
weak stratification
strong stratification
formation of a secondary wakeby the baroclinc torque
pure descent
damping of the descending motionand emission of gravity waves
( )pdt
d ∇×∇= ρρ
ω2
1
30
Radar Cross Section evaluation (RCS)
Setup
Scattered electric field E s
Hypothesis– Far field approximation– Born approximation E=Ei
– Spherical incident wave Ei
radar cell (∆θ,∆r)
∆y ~ 1000m
∆x ~ 2000m
∆θ = 1°
∆r = 5m
( ) ( ) ( ) ( )'
'
'exp''
4
2
dVrr
rrjkrrE
koorE
V rs −−
∆××−= ∫ επ
rrrr
backgroundrr εεε −=∆
vaccumε
ε
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RCS evaluation
���� Fourier transform of the ∆∆∆∆εεεεr radial distribution
(a) HR=0% at ground level, Fr=1, t=47s (b) HR=70% at ground level
∆∆∆∆εεεεr
32
RCS results in X band (10GHz)
RCS
(a) RH=0%, Fr=1, t=47s (b) RH=70%
� -130dBm2 < RCS < -95dBm2 depending on humidity
� less than experimental values found in the litterature
2
2
24i
s
E
ERRCS π=
33
Conclusion
Summary
– Litterature review
– Origins of the radar echo in clear air
– Model and numerical evaluation of the RCS
Feasability
– Strong dependence upon meteorological conditions (stratification, humidity), yet to
be better investigated…
– weak signal giving RCS ~ -95 / -130 dBm 2, less than experimental tests
– RCS(wake vortices) in clear air ~ RCS(1 droplet of water) !
– Such reflectivities are too weak to be measured by standard radars
– Need for high power transmitter and very sensitive receiver ≠cost and size…