CFD MODEL OF A SPINNING PIPE GAS LENS
SAIP
Dr Andrew Forbes July 2006
G Snedden 1 , A Forbes 2 , C Mahlase 1 , C Mafusire 3 and MM Michaelis 4
1
CSIR DPSS, PO Box 395, Pretoria
2
CSIR National Laser Centre, PO Box 395, Pretoria
3
University of Zimbabwe, Mount Pleasant, Harare
4
University of Kwazulu-Natal, Durban
Spinning Pipe Gas Lens
Page 3
© CSIR 2006 www.csir.co.zaFocal Length
78 C:f = 94.655w-1.1388 104 C:f = 138.94w-1.4796 125 C:f = 79.151w-1.3439 152 C:f = 197.55w-1.7476
0 1 2 3 4 5 6 7 8 9
6 8 10 12 14 16 18 20
Pi pe Spe ed,w (Hz )
Focal Length, f (m)
T =78 C T =104 C T =125 C T =152 C Power (T =78 C) Power (T =104 C) Power (T =125 C) Power (T =152 C)
Refractive Index
1.0002 1.00021 1.00022 1.00023 1.00024 1.00025 1.00026 1.00027 1.00028 1.00029 1.0003 1.00031
-20 -15 -10 -5 0 5 10 15 20
Radial Distance, r(mm)
Refractive Index, n(r)
78 C 104 C
125 C 153 C
Poly. (78 C) Poly. (104 C) Poly. (125 C) Poly. (153 C)
Gas Dynamics
Cold Air
Warm Air
Cold Air
Warm Air Warm Air Tube Rotation
Heater tape Warm
Air Opposing Vortices
Guess at the gas dynamics
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© CSIR 2006 www.csir.co.zaDensity Profile
Density Profile
Page 9
© CSIR 2006 www.csir.co.zaFlow Profile
Rosby Waves
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© CSIR 2006 www.csir.co.zaRayleigh–Taylor Instabilities
Future Work
Page 13
© CSIR 2006 www.csir.co.zaInstabilities near the boundary
3 / 5
0
2
= N
nm D r σ
nm) 6 / 23 (
) 6 / 17 (
) 6 / 5 ( ) 3 / 14 ( ) 1 ( ) 1 ( 15337 .
0
2
Γ +
Γ
− Γ Γ
+
= −
−n
n N n
m n nm
∑ ∑ ∞
= =
+
= Φ
0 0
)]
, ( )
, ( [
) , (
n n
m
m n m n m
n m
n U B V
A ρ θ ρ θ
θ ρ
∫ ∫ Φ
= +
πρ θ ρ θ ρ ρ θ π
2 0
1
0
( , ) ( , )
) 1
( n U d d
m K
A
nm nm∑
−
=
−
−
+
− −
−
=
2−
0
2 2
2
)! ( )!
(
!
)!
( ) 1 ) (
(
m n
k
k n m
n m
n k m
n
k k k
k
R ρ n ρ
3 / 5 2
2 0
max
min
) ( 423
. 0
−
= ∫
h
h
n
