Transcript Patterns in Rotating Rayleigh-Bénard Convection at High Rotation

Patterns in Rotating
Rayleigh-Bénard
Convection at High
Rotation Rates
Presented by: P. L. Mutyaba
[email protected]
P. L. Mutyaba, Terri Kimmel, Janet D. Scheel
California Lutheran University
Rayleigh-Bénard Convection
(RBC)
Rotation,
Ω
Ra
Side View
http://www.chemistrydaily.com/chemistry/upload/1/12/Convection_cells.png
Square Patterns in RBC

Bulk
 Square

Periphery
 Traveling
wave
Overhead View
Previous Research
 Experiments
 Rotation
rates
170
 Cylindrical
cells
Aspect ratio 5 and 3
(radius to depth ratio)
Bajaj et al.(1998)
Previous Research

Numerical Simulations
 Aspect

Ω =274
 Aspect

Ratio 5 and 3
Ratio 3
Ω =180
 Observations

Traveling wave affects bulk
Sánchez-Álvarez et
al.(2005)
Current Research

Goals
 Accurately
simulate experiments
 Investigate interaction
between the traveling wave
and bulk
 Study
effect of centrifugal forces on square pattern
formation
Methods

Boussinesq Equations
( t  u  )u  -
p

 2u - gzˆ  2zˆ  u   2 r,
( t  u  )   2 , and
 u  0


Code written by Paul Fischer (Argonne)
Experimentally realistic boundary conditions

No slip for the velocity
Periodic Cell

Random initial
conditions

Parameters
 Aspect
Ratio is 5,
Ω = 274, ε=0.02
 Oscillating Rolls

KL Instability
 90
°
Periodic Cell

Non-random initial
condition
 Super-imposed
rolls, fade in and
out
 Not
a transient state
 Traveling wave
not necessary.
is
Results
Aspect Ratio = 5, Ω=170, ε=0.09
Coriolis and
centrifugal forces
Results
Aspect Ratio = 5, Ω=170 , ε =0.09
Coriolis force only
Discussion
The inclusion of the centrifugal and Coriolis
forces provides better agreement with
experiment. (Aspect Ratio = 5, Ω=170, ε=0.09)
Bajaj et al.(1998)
Coriolis and
centrifugal forces
Coriolis force
Discussion
The inclusion of the Coriolis force only provides
better agreement with other numerical
simulations. (Aspect Ratio = 5,Ω=274,ε =0.004,
ε=0.02 )
Sánchez-Álvarez et
al.(2005)
Coriolis and
centrifugal forces
Coriolis force
Conclusion

The oscillating rolls may be KüppersLortz Instability with a switching angle of
90 °.

The centrifugal force should be included
in order to numerically model the RBC
experiments.
Future Work

The effects of the fictitious forces on the growth
rates of the modes are necessary to understand
pattern formation.

The cause of the square patterns

The oscillation of the square bulk
Acknowledgements

Dr. Janet Scheel

Terri Kimmel

Sam Walton

Katelyn White

Dr. Michael Cross

The Swenson Family