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Unformatted text preview: Turbulent Mixing in the Microscale W.Dzwinel 1 , W.Alda 1 , M.Pogoda 1 and D.A.Yuen 2 1 University of Mining and Metallurgy, Institute of Computer Science, 30-059 Kraków, Poland 2 Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, USA Abstract Results of 2-D molecular dynamics (MD) method are presented for the mixing phenomenon in the microscale, where the length and time are measured in terms of microns and nanoseconds, respectively. Particle ensembles consisting of 0.7 to 3x10 6 particles in 1.3 to 5x10 5 timesteps were simulated. We focus on the temporal evolution of mixing layer between two superimposed Lennard-Jones particle systems in a gravitational field directed from the heavier to the lighter particle fluid, and compare its properties with those observed in the macroworld. It is shown that the bubble-and-spikes stage of mixing process is similar in both the molecular scale and in the macroworld. The mixing layer growth constant A, which can be estimated using MD, is approximately the same as that obtained for 2-D simulations in the macroscale, where the Navier-Stokes equations are used. For the closed particle systems, we show that the value A remains stable for changing physical conditions, as it is in the macroscale. For the open particle systems with a free surface A is 20% higher and reaches the value 0.07, i.e., the same as that obtained in laboratory experiments. The influence of fluid granularity on the speed of mixing can be observed at a very early stage. This start-up time is connected with spontaneous instabilities formation, which appears as the cumulative result of thermal fluctuations. The occurrence of Rayleigh-Taylor instability in the microscale, and its similarity to the same process in the macroscale, can also expand the scope of the term “turbulence” to micro-scaled flows on the molecular scale. Keywords: mixing in microscale, molecular dynamics, Rayleigh-Taylor instability, mixing layer growth constant 1. Introduction For many years the problems of turbulent mixing have been thoroughly investigated both theoretically and experimentally [1-5]. The classical experiments have been carried with the temporal evolution of mixing involving two superimposed fluids, with different densities under a gravitational field (the Rayleigh-Taylor instability) or in shock waves (the Richtmyer-Meshkov instability). Numerous computer simulations, which are based on the Navier-Stokes equations, reveal the complex nature of the phenomenon, enable the validation of theoretical ideas concerning the initial stages of the process occurring in linear regime, and explain new mechanisms and properties of mixing in both the non-linear and chaotic regimes. By combining the results from experiments, computer simulation and analytical solutions, semi-empirical rules were developed [1-2]. The most fundamental are those concerning with the growth of mixing layer for the Rayleigh-Taylor (R-T) and Richtmyer-Meshkov (R-M) types of instabilities . The models, which are based on the application of the(R-T) and Richtmyer-Meshkov (R-M) types of instabilities ....
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This note was uploaded on 09/16/2011 for the course ME 563 taught by Professor Staff during the Spring '11 term at Auburn University.
- Spring '11
- The Land