Rayleigh-Taylor Turbulent Mixing Simulations

Abstract

We study the Rayleigh-Taylor mixing layer, presenting on simulations in agreement with experimental data. This problem is an idealized subproblem of important scientific and engineering problems, for example the gravitationally induced mixing in oceanography and performance assessment for inertial confinement fusion. Engineering codes commonly achieve correct simulations through the calibration of adjustable parameters. In this sense, they are interpolative and not predictive. As computational science moves from the interpolative to the predictive and reduces the reliance on experiment the quality of decision making improves. The diagnosis of errors in a multiparameter, multiphysics setting is daunting, so we address this issue in the proposed idealized setting. The validation tests presented are then a test for engineering codes, when used for complex problems containing Rayleigh-Taylor features. The Rayleigh-Taylor growth rate, characterized by a dimensionless but non-universal parameter and alpha, describes the outer edge of the mixing zone. Increasingly accurate Front Tracking/LES simulations reveal non-universality of the growth rate and agreement with experimental data. Increased mesh resolution allows reduction in the role of key subgrid models. We study the effect of long wavelength perturbations on the mixing growth rate. A self-similar power law for the initial perturbation amplitudes is here inferred from experimental data. We show a maximum ±5 % effect on the growth rate. Large (factors of 2) effects, as predicted in some models and many simulations, are inconsistent with experimental data of Youngs and co-authors. The inconsistency of the model lies in the treatment of the dynamics of the bubbles, which are the shortest wavelength modes for this problem. An alternate theory for this shortest wavelength, based on the bubble merger model, was previously shown to be consistent with experimental data. Turbulent mixing at the molecular level and turbulent combustion are remaining challenges for turbulent mixing studies. Theoretical studies suggest that convergence of numerical solutions, considered within an LES regime, is to a space time dependent probability distributions (Young measures). This point of view is proposed for the study of micro-observables, which describe the molecular mixing rate. New results comparing our simulations to experimentally observed molecular mixing rates are reported.