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Q2D Turbulence by Rayleigh-Taylor Instabilities. Xi Li and Vincent H. Chu Dept. of Civil Engineering and Applied Mechanics McGill University 4 th International Symposium on Environmental Hydraulics December 15, 2004. Objectives and Method.
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Q2D Turbulence by Rayleigh-Taylor Instabilities Xi Li and Vincent H. Chu Dept. of Civil Engineeringand Applied Mechanics McGill University 4th International Symposium on Environmental Hydraulics December 15,2004
Objectives and Method • Experimental study of the Rayleigh-Taylor instabilities by sudden overturning a tank of stably stratified fluid of two layer • Interfacial mixing is determined accurately by measuring the tracer dye concentration using a video imaging technique • Provide the data for the development of LES (Large Eddy Simulation) model
h1 h2 1800 T L Overturning a Tank of Two-Layer Fluid
Late Stage Development when d >> h1 d = a(2gAh1)1/2 t (1) where g = gravity constant, h1 = initial depth of the upper layer, A = (r1 - r 2)/( r 1 + r 2) = Atwood number, and 2gAh1 = total buoyant force associated with the upper layer
General Development: s = fn (t, g’, h1) Length scale = h1Time scale ts= (h1 /g’)1/2 where g’ = reduced gravity, h1 = initial depth of the upper layer, s = layer thickness
Quadratic in the Initial Stage and Linear in the Late Stage of Development Length scale = h1Time scale ts= (h1 /g’)1/2
Mixing Thickness by Gaussian Profile (2) whereC= mean tracer dye concentration determined by the video imaging method, Cm = maximum of the mean, d = mixing layer thickness defined by concentration profile
Fittingdata with d = a(2gAh1)1/2 t a = 0.13
The coefficient a __________________________________________________________________________________________________________________________________________________________________ Time (s) depth d (cm) coefficient a ________________________________________________________________________ 9 6.1700 0.13 10 7.1947 0.14 11 7.6056 0.13 12 8.5235 0.13 13 9.2586 0.13 14 10.2756 0.14 15 11.2919 0.13 _________________________________________________________________________ The coefficient a = 013 based on the tracer dye concentration measurements is significantly smaller than the value of 0.38 obtained based on the visual inspection by Voropayev et al. (1993).
Large Eddy Simulation (LES) Simulation uses the four-third-power interpolation formula in the modified Smagorinsky model proposed by Babarutsi, Nassiri and Chu (2004):
If then If then Modified Smagorinsky Viscosity
Largrangian Block Method (LBM) The LBM is a highly accurate numerical scheme that is relatively free of numerical diffusion and unphysical oscillations. Similarly successful simulations of highly turbulence interfaces have been obtained by the method using the method for a variety of the turbulent flows (see, e.g., Chu and Altai 2002).
Conclusion • Successful simulation of a highly irregular turbulent interface due the Rayleigh-Taylor instability has been obtained using the Lagrangian Block Method. • The results are highly consistent with the laboratory data obtained from an overturn experiment. • The LBM is positive definite and relatively free of the numerical oscillation and diffusion. It is shown in the present investigation to be suitable for simulation of highly complex turbulence interfaces.