Turbulent Rayleigh-Bénard
Convection
Katelyn White
Dr. Janet Scheel
Rayleigh-Bénard Convection
COLD
h=1
d=1
Cylindrical Cell
HOT
Top of cell cool,
bottom warmed
Rayleigh Number ~
Temperature Difference
Turbulence
Plume
Mean Wind
Chaotic System
Appearance of plumes:
- super hot /cold
volumes of fluid
Diameter, d = 1
Thermal
Boundaries
Major Change Observed in the
Dynamics of the Cell
Prior Work:
Present Study:
Rayleigh Number 1×106
Rayleigh Number 3 ×107
Purpose of Study
• Find parameters for good simulations
• Compare boundary layer thickness to
Rayleigh number
• Compare Nusselt number to Rayleigh
number
Data for Simulations
Goal: To find the correct combination of parameters to run
a computer simulation (blue)
System Dynamics
Closer Look at the Boundary Layer
• Top Boundary
Layer
h = 0.98
• Bottom
Boundary Layer
h = 0.02
Main point #1: Motion in opposite directions provides
evidence of mean wind!
Boundary Layers
Temperature (Co)
Low
Temperature
Mean
Temperature
High
Temperature
Boundary Layer
thickness
Mean
Temperature
z
High
Temperature
Distance from Plate, z
Ra = 1.07 × 1010
Goal: To measure the thickness of the boundary layers
Boundary Layers (cont’d)
Low
Temperature
Distance from Center of Cell
f
Boundary Layer
thickness
Mean
Temperature
Boundary Layer
thickness
Low
Temperature
Temperature
Mean
Temperature
High
Temperature
High
Temperature
Ra = 1 ×107
Goal: To measure the thickness of the boundary layers for data
Boundary Layer Double Log Plot
Slope:
-0.206 ± 0.017
log(Boundary Layer Thickness)
log(Rayleigh Number)
-1.2
6
6.5
7
7.5
8
-1.3
-1.4
-1.5
-1.6
-1.7
y = -0.2062x - 0.0669
R2 = 0.9564
-1.8
Goal: To determine magnitude of power law coefficients
for best fit
Ra = 7 ×106
Nu = 13.26
SD = 1.11
Nusselt Number
Nusselt Data
Time
Goal: To find the average heat transport in the cell
log(Nusselt Number)
Nusselt v Ra Double Log Plot
1.6
1.4
1.2
y = 0.3028x - 0.9473
2
R = 0.9982
Slope:
0.303 ± 0.004
1
0.8
6
6.5
7
7.5
8
8.5
log(Rayleigh Number)
Goal: Determine whether a 1/3 or 2/7 power law fits
the data better
Results
• Increased Rayleigh number
– More Turbulence
– Thinner boundary layers
– Higher Nusselt number
• Analysis comparable to experiment
– 2/7 coefficient vs. 1/3 coefficient
References
Johnston, Hans, and Charles R. Doering. ”Comparison of
Turbulent Thermal Convection Between Conditions of Constant
Temperature and Constant Flux.” Physical Review Letters 209
(2009). (2009): 301-304.
Sun, Chao, Yin-Har Cheung, and Ke-Qing Xia. “Experimental
Studies of the Viscous Boundary Layer Properties in Turbulent
Rayleigh-Bénard Convection.” J. Fluid Mech. 605 (2008): 79113.
Verzicco, R., and K. R. Sreenivasan. ”A Comparison of Turbulent
Thermal Convection Between Conditions of Constant
Temperature and Constant Heat Flux.” J. Fluid Mech. 595
(2008): 203-19.
Thanks to:
Dr. Janet Scheel (Technical guidance)
Dr. Paul Fischer (Numerical code)
Swensons (financial support)