CFD MODEL OF A SPINNING PIPE GAS LENS

SAIP

Dr Andrew Forbes

July 2006

G Snedden1, A Forbes2, C Mahlase1, C Mafusire3 and MM Michaelis4

1CSIR DPSS, PO Box 395, Pretoria

2CSIR National Laser Centre, PO Box 395, Pretoria

3University of Zimbabwe, Mount Pleasant, Harare

4University of Kwazulu-Natal, Durban

Page 2 © CSIR 2006 www.csir.co.za

Spinning Pipe Gas Lens

Page 3 © CSIR 2006 www.csir.co.za

Focal 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 20Pipe Speed,w (Hz)

Foc

al L

engt

h, 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)

Page 4 © CSIR 2006 www.csir.co.za

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 20Radial Distance, r(mm)

Ref

ract

ive

Inde

x, n

(r)

78 C 104 C

125 C 153 C

Poly. (78 C) Poly. (104 C)

Poly. (125 C) Poly. (153 C)

Gas Dynamics

Page 6 © CSIR 2006 www.csir.co.za

Cold Air

WarmAir

Cold Air

WarmAir

WarmAir

Tube Rotation

Heater tape

WarmAir Opposing Vortices

Guess at the gas dynamics

Page 7 © CSIR 2006 www.csir.co.za

Density Profile

Page 8 © CSIR 2006 www.csir.co.za

Density Profile

Page 9 © CSIR 2006 www.csir.co.za

Flow Profile

Page 10 © CSIR 2006 www.csir.co.za

Rosby Waves

Page 11 © CSIR 2006 www.csir.co.za

Rayleigh–Taylor Instabilities

Future Work

Page 13 © CSIR 2006 www.csir.co.za

Instabilities near the boundary

Page 14 © CSIR 2006 www.csir.co.za

3/5

0

2

= rDNnmnmσ

)6/23()6/17()6/5()3/14()1()1(15337.0

2 +ΓΓ−ΓΓ+−=

−

nnn

Nmn

nm

∑∑∞

= =

+=Φ0 0

)],(),([),(n

n

m

mn

mn

mn

mn VBUA θρθρθρ

∫ ∫ Φ+=π

θρρθρθρπ

2

0

1

0),(),(

1)( ddUn

mKA mn

mn

∑−

=

−−+ −−

−−=2

0

2

22 )!()!(!)!()1(

)(

mn

k

kn

mnmn

kmn kkk

knR ρρ

3/5

220

max

min

)(423.0

−

= ∫

h

hn dhhCkr

3/112033.0)( −= κκφ nC

Wavefront Measurement & Control

Page 15 © CSIR 2006 www.csir.co.za

Adaptive optics for turbulence correction

• SLM acts as an adaptive optic• Measure wavefront distortion,• Feed result back into SLM to create conjugate

phase,• Propagate conjugate phased beam through

medium.

Control Loop

Page 16 © CSIR 2006 www.csir.co.za

Conclusion

• CFD model of gas lens• Shows Rosby waves and Rayleigh–Taylor instabilities

• Propagation model in preparation• Full Fresnel propagation through GRIN system

• Future work• Adaptive optics theory and experiment

Questions