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Patterns in Rotating Patterns in Rotating Rayleigh-BRayleigh-Bénard énard
Convection at High Convection at High Rotation RatesRotation Rates
Presented by: P. L. MutyabaPresented by: P. L. [email protected]@clunet.edu
P. L. Mutyaba, Terri Kimmel, Janet D. ScheelP. L. Mutyaba, Terri Kimmel, Janet D. Scheel
California Lutheran UniversityCalifornia Lutheran University
Rayleigh-BRayleigh-Bénard Convection énard Convection (RBC)(RBC)
http://www.chemistrydaily.com/chemistry/upload/1/12/Convection_cells.png
Rotation,Rotation,ΩΩ
RRaa
Side View
Square Patterns in RBCSquare Patterns in RBC
BulkBulkSquareSquare
PeripheryPeripheryTraveling waveTraveling wave
Overhead View
Previous ResearchPrevious Research ExperimentsExperiments
Rotation ratesRotation rates170170
Cylindrical cellsCylindrical cellsAspect ratio 5 and 3Aspect ratio 5 and 3(radius to depth ratio)(radius to depth ratio)
Bajaj et al.(1998)Bajaj et al.(1998)
Previous ResearchPrevious Research Numerical SimulationsNumerical Simulations
Aspect Ratio 5 and 3Aspect Ratio 5 and 3 ΩΩ = =274 274
Aspect Ratio 3Aspect Ratio 3 ΩΩ = =180180
ObservationsObservations Traveling wave affects bulkTraveling wave affects bulk SSáánchez-nchez-ÁÁlvarez et al.lvarez et al.
(2005)(2005)
Current ResearchCurrent Research
GoalsGoalsAccurately simulate experiments Accurately simulate experiments
Investigate interaction between the traveling wave Investigate interaction between the traveling wave
and bulkand bulk
Study effect of centrifugal forces on square pattern Study effect of centrifugal forces on square pattern
formation formation
Methods Boussinesq Equations
Code written by Paul Fischer (Argonne) Experimentally realistic boundary conditions
No slip for the velocity
0u
u
uuuu
and ,)(
r,ˆ2ˆ-p
-)(
2
22
t
t zzg
Periodic Cell Periodic Cell Random initial Random initial
conditionsconditions
ParametersParametersAspect Ratio is 5, Aspect Ratio is 5,
ΩΩ = 274, = 274, εε==0.020.02
Oscillating RollsOscillating Rolls
KKL InstabilityL Instability90 °90 °
Periodic Cell Periodic Cell Non-random initial Non-random initial
conditioncondition Super-imposed Super-imposed
rolls, fade in and rolls, fade in and
outout
Not a transient Not a transient
statestate
Traveling wave is Traveling wave is
not necessary. not necessary.
ResultsResultsAspect Ratio = 5, Aspect Ratio = 5, ΩΩ=170, =170, εε=0.09=0.09
Coriolis and Coriolis and centrifugal forcescentrifugal forces
ResultsResults
Coriolis force onlyCoriolis force only
Aspect Ratio = 5, Aspect Ratio = 5, ΩΩ=170 , =170 , εε =0.09 =0.09
DiscussionDiscussionThe inclusion of the centrifugal and Coriolis The inclusion of the centrifugal and Coriolis forces provides better agreement with forces provides better agreement with experiment. (Aspect Ratio = 5, experiment. (Aspect Ratio = 5, ΩΩ=170, =170, εε=0.09=0.09))
Bajaj et al.(1998)Bajaj et al.(1998) Coriolis and Coriolis and centrifugal forcescentrifugal forces
Coriolis forceCoriolis force
DiscussionDiscussionThe inclusion of the Coriolis force only provides The inclusion of the Coriolis force only provides better agreement with other numerical better agreement with other numerical simulations. (Aspect Ratio = 5,simulations. (Aspect Ratio = 5,ΩΩ=274,=274,εε =0.004, =0.004, εε=0.02=0.02 ) )
SSáánchez-nchez-ÁÁlvarez et al.lvarez et al.(2005)(2005)
Coriolis and Coriolis and centrifugal forcescentrifugal forces
Coriolis forceCoriolis force
The oscillating rolls may be KThe oscillating rolls may be Küppers-üppers-
Lortz Instability with a switching angle of Lortz Instability with a switching angle of
90 °.90 °.
The centrifugal force should be included The centrifugal force should be included
in order to numerically model the RBC in order to numerically model the RBC
experimentsexperiments..
ConclusionConclusion
The effects of the fictitious forces on the growth The effects of the fictitious forces on the growth
rates of the modes are necessary to understand rates of the modes are necessary to understand
pattern formation.pattern formation.
The cause of the square patternsThe cause of the square patterns
The oscillation of the square bulkThe oscillation of the square bulk
Future WorkFuture Work
AcknowledgementsAcknowledgements Dr. Janet ScheelDr. Janet Scheel
Terri KimmelTerri Kimmel
Sam WaltonSam Walton
Katelyn WhiteKatelyn White
Dr. Michael CrossDr. Michael Cross
The Swenson FamilyThe Swenson Family