Dissipation in a flow driven by precession and application to the design of a MHD wind tunnel experi

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Dissipation in a flow driven by precession and
application to the design of a MHD wind tunnel
experiment
5-th International PAMIR Conference, Ramatuelle,
16-20 september 2002

• J. Léorat, F. Rigaud, R. Vitry and G. Herpe
• Observatoire de Meudon- France

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Introduction

• Experimental MHD flows Rm 60
• Critical Rm for known dynamos Rm50-100
• Flows at Rm gtgt Rm are interesting for study of
  dynamos non-linear saturation and fully
  developped MHD turbulence
• gt question What is the largest Rm reachable
  in an experimental flow ?

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Obstacles towards large Rm ?

• ?Using liquid sodium (large conductivity s)
• Rm µs?LV 10 L (m) V (m/s) 10 -5 Re
• If Rm 100, Re 107 non linear dynamics
• Power turbulent dissipation P k Rm3/L
• Example L 0.5m, P100 kW, Rm60
• If Rm 3 and L3, then P9 not realistic
• Strategyfind driving configurations with smaller
  k
• Flow forcing at largest available scales? moving
  container walls. precession of container

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About "precession motion"

• Fast rotation around the container axis
• Slow rotation around y ("precession")
• Coriolis acceleration (volume force) in the
  precessing frame
• Solid bodygt gyroscopic torque ( TG ?P L)
• Fluid gt axial circulation

TOOLS
- Num. simul. up to Re5000 (lattice Boltzman
code, P.Lallemand)
-large Re flows and turbulence water exper.
,"ATER" (E 10-6)
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Influence of precesssion rate and Reynolds number
on poloïdal and toroïdal flow components
Re500 to 5000 Around precession rate 0.1, rms
azimuthal speed is comparable to rms axial
speed, 1/3 container speed
Note that the strong decrease of azimuthal energy
with precession rate is plausibly related to the
viscous driving by the walls. More efficient
inertial driving is possible using baffles fixed
to both ends of cylinder.
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A step towards ATER experiment
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A little step further
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Overview of container driving
container
r3
rotation axis
precession table
r2
r1
p1
p2
1/5
R
P
precession axis
transmission p128 , p2 98 r1 39 , r298,
r3 98
ratios preces.5p2/p1 17.5 rot. r3/r1
2.51 coupled5r1/p16.96
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Example of tilted vortex flow
Rotation rate 10 Hz, precession rate 1 Hz / Air
bubbles are used as tracers of pressure minima
FILM
click here for quicktime version
click here for animated gif
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Related precessing flows

• "Poincaré flow" (1910), cf also Busse (1968)
• Uniform vorticity vector w in the plane of the
  two axis (rot,prec)
• Streamlines in parallel planes
• Experiments Malkus (1968), Vanyo et al,, J.
  Noir et al (2000)

Precessing spheroïdal container
Precession (slow)
w
rotation
Infinite precessing cylinder
Streamlines in parallel oblique planes
Stability analysis cf Vladimirov
Tarasov Kerswell, experiments
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MEGATER a mechanical design for a large scale
facility
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MEGATER size, speed, Rm

• Cylindrical container (constraints
  transportation, experim. room) L diameter
  length 3m
• Liquid sodium mass about 27 tons
• Rotation (constraint acoustic noise)
• wall speed 100 m/s (10 Hz)
• Precession frequency lt 1 Hz
• Flow speed V 30 m/s (possibly greater using
  radial blades)
• Rm 10 (30 m/s) 1.5 m 450 (possibly close
  to the Earth's)
• Centrifugal pressure V2 50 atmospheres
• NB power dissipation is assumed here not to be a
  technological constraint this has to be
  confirmed using ATER !!!

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MEGATER
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Conclusions

• Two flow regimes according to the precession
  rate laminar "tilted vortex" or turbulent
• Precession looks interesting to drive flows at
  large Re and Rm ( gt 400 ?)
• N.B. driving power and scaling to be confirmed
  with a water model (cf friction in ATER)
• Critical Rm to be obtained numerically using a
  kinematic dynamo code and the averaged flow
• Possible contribution to the design of a large
  scale facility

(click here for Megater pictures)