Rayleigh-Benard convection in a fluid with Prandtl number near one | | Posted on:1996-04-25 | Degree:Ph.D | Type:Dissertation | | University:University of California, Santa Barbara | Candidate:Hu, Yuchou | Full Text:PDF | | GTID:1462390014987058 | Subject:Physics | | Abstract/Summary: | | | Studies of Rayleigh-Benard convection rotated about a vertical axis in cylindrical geometries with the shadowgraph imaging method are reported. The convection cells had radius-to-height ratios {dollar}Gamma{dollar} of between 23 and 52. The working fluid was CO{dollar}sb2{dollar} at 16 to 32 bar with Prandtl numbers ranging from 0.85 to 0.98. The results at zero rotation are presented first. For one of the cells ({dollar}Gamma{dollar} = 43), axisymmetric convection rolls were stable above onset up to {dollar}epsilonequivDelta T/Delta Tsb{lcub}c{rcub}-1=0.19,{dollar} where {dollar}Delta Tsb{lcub}c{rcub}{dollar} is the critical temperature difference. The amplitude of the center of the concentric patterns, the umbilicus, much larger near onset than that of the outlying region, grew as {dollar}epsilonsp{lcub}betasb 1{rcub}{dollar}, with {dollar}betasb1=0.27pm0.04.{dollar} Outside the umbilicus, the amplitude grew as {dollar}epsilonsp{lcub}betasb2{rcub}{dollar}, with {dollar}betasb2{dollar} = 0.48 {dollar}pm{dollar} 0.04. Pattern dynamics, wavenumbers, spatially-averaged roll-curvature, and sidewall roll-orientation as a function of {dollar}epsilon{dollar} are presented for a {dollar}Gamma{dollar} = 40 cell. As {dollar}epsilon{dollar} was increased, the skewed-varicose instability was first observed at {dollar}epsilonapprox{dollar} 0.09, and roll-nucleating sidewall-foci were seen for {dollar}epsilon sbsp{lcub}sim{rcub}{lcub}>{rcub} 0.15.{dollar} The average roll curvature remained relatively constant for 0.2 {dollar}sbsp{lcub}sim{rcub}{lcub}<{rcub} epsilon sbsp{lcub}sim{rcub}{lcub}<{rcub}{dollar} 0.5, contrary to general expectation of increasing curvature with {dollar}epsilon{dollar}. Spiral-defect chaos appeared at {dollar}epsilonapprox{dollar} 0.55. Coincident with the increase in spiral-defect activity was a decrease in the average wavenumber and a marked increase in the sidewall-foci roll-nucleation frequency and average roll curvature. The thresholds of the onset of spiral-defect chaos for {dollar}Gamma{dollar} = 28, 40, and 52 were all at {dollar}epsilonapprox{dollar} 0.55.; For rotating convection, pattern evolution at {dollar}Gamma{dollar} = 40 are described for dimensionless rotation rate {dollar}Omega{dollar} up to 20 and compared with observations at zero rotation. The Kuppers-Lortz instability was observed at the onset of convection at {dollar}Omegaapprox9{dollar} and co-existed with the skewed-varicose instability. For {dollar}Omega sbsp{lcub}sim{rcub}{lcub}<{rcub}{dollar} 11, the Kuppers-Lortz instability occurred via propagation of fronts initiated near the sidewall whereas at higher {dollar}Omega{dollar} fronts appearing spontaneously away from the sidewall became dominant. For {dollar}Omega sbsp{lcub}sim{rcub}{lcub}>{rcub}{dollar} 13, the Kuppers-Lortz angle was {dollar}60sp{lcub}circ{rcub}pm1sp{lcub}circ{rcub}{dollar}, and the time scaling of the pattern dynamics showed a power-law dependence on {dollar}epsilon{dollar} with an exponent of 0.6 {dollar}pm{dollar} 0.1. The threshold for spiral-defect chaos was depressed by rotation with spirals appearing at {dollar}epsilonapprox0.40{dollar} at {dollar}Omega{dollar} = 8.8. The preferential inward-winding direction of the spirals was the same as the direction of the system rotation. The average wavenumber at onset of convection agreed with theoretical calculations and decreased with increasing {dollar}epsilon{dollar}. Quantitative measurements of the sidewall obliqueness show a general trend of rolls ending less perpendicular to the sidewall with increasing {dollar}Omega{dollar} for {dollar}Omegaleq{dollar} 9. | | Keywords/Search Tags: | Convection, Sidewall, {dollar}omega{dollar} | | Related items |
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