Mixing in thermal convection

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Viscoelastic RT turbulenceFluid model:Boussinesq+Oldroyd-B⎧∂ tu + u ⋅ ∇u = −∇p + νΔu − βgT + (2νη / τ p)∇ ⋅ σ⎪⎨∂ tT + u ⋅ ∇T = κΔT⎪∂ σ + u ⋅ ∇σ = (∇u) T ⋅ σ + σ ⋅ (∇u) − (2 / τ )(σ − 1)⎩⎪t pPolymer conformation tensorσ ij =/R 02Coil-stretch transitionE = P + K + Σ = −β g zT + 1 2u 2+ νητptr(σ ) − 3Scales in RT turbulencerL~t 2polymers become stretched(and active) when ∇u > 1 / τ pi.e. when τ pWi = > 1τ ηr L ~t 1/2η~t -1/4tLumley scaleτ p /τ(r L )=1Weissenber number grows as Wi≈t 1/2
NewtonianviscoelasticTwo effects induced by polymers:- faster thermal plumes: acceleration of mixing layer growth (“drag” reduction)- small scale turbulence reduced: heat transfer enhancement
Page 2: Rayleigh-Taylor turbulence: a toy m
Page 9 and 10: Equation of motion and setupSingle
Page 11 and 12: Fermi’s model (Fermi and von Neum
Page 14: Numerical simulationsNumerical inte
Page 19 and 20: Evolution of the mixing layert=1.4t
Page 22 and 23: From geometrical to dynamical quant
Page 24 and 25: Effects of polymers onthermal conve
Page 28 and 29: Acceleration of the growthof mixing
Page 30 and 31: Heat transfer enhancementNu is larg
Page 32: ConclusionsRayleigh-Taylor turbulen

Mixing in thermal convection

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