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Title: Roles of bulk viscosity on Rayleigh-Taylor instability: Non-equilibrium thermodynamics due to spatio-temporal pressure fronts

Abstract

Direct numerical simulations of Rayleigh-Taylor instability (RTI) between two air masses with a temperature difference of 70 K is presented using compressible Navier-Stokes formulation in a non-equilibrium thermodynamic framework. The two-dimensional flow is studied in an isolated box with non-periodic walls in both vertical and horizontal directions. The non-conducting interface separating the two air masses is impulsively removed at t = 0 (depicting a heaviside function). No external perturbation has been used at the interface to instigate the instability at the onset. Computations have been carried out for rectangular and square cross sections. The formulation is free of Boussinesq approximation commonly used in many Navier-Stokes formulations for RTI. Effect of Stokes’ hypothesis is quantified, by using models from acoustic attenuation measurement for the second coefficient of viscosity from two experiments. Effects of Stokes’ hypothesis on growth of mixing layer and evolution of total entropy for the Rayleigh-Taylor system are reported. The initial rate of growth is observed to be independent of Stokes’ hypothesis and the geometry of the box. Following this stage, growth rate is dependent on the geometry of the box and is sensitive to the model used. As a consequence of compressible formulation, we capture pressure wave-packets withmore » associated reflection and rarefaction from the non-periodic walls. The pattern and frequency of reflections of pressure waves noted specifically at the initial stages are reflected in entropy variation of the system.« less

Authors:
; ;  [1];  [2];  [3];  [4]
  1. HPCL, Department of Aerospace Engineering, IIT Kanpur, Kanpur, UP (India)
  2. Department of Engineering, University of Cambridge, Cambridge (United Kingdom)
  3. Graduate Student, HPCL, Department of Aerospace Engineering, IIT Kanpur, Kanpur, UP (India)
  4. Department of Mechanical and Aerospace Engineering, Ohio State University, Columbus, Ohio 43210 (United States)
Publication Date:
OSTI Identifier:
22598827
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Fluids; Journal Volume: 28; Journal Issue: 9; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; AIR; APPROXIMATIONS; COMPUTERIZED SIMULATION; CROSS SECTIONS; ENTROPY; EQUILIBRIUM; GEOMETRY; INTERFACES; NAVIER-STOKES EQUATIONS; PERIODICITY; PERTURBATION THEORY; RAYLEIGH-TAYLOR INSTABILITY; REFLECTION; THERMODYNAMICS; TWO-PHASE FLOW; VISCOSITY

Citation Formats

Sengupta, Tapan K., E-mail: tksen@iitk.ac.in, Bhole, Ashish, Shruti, K. S., Sengupta, Aditi, Sharma, Nidhi, and Sengupta, Soumyo. Roles of bulk viscosity on Rayleigh-Taylor instability: Non-equilibrium thermodynamics due to spatio-temporal pressure fronts. United States: N. p., 2016. Web. doi:10.1063/1.4961688.
Sengupta, Tapan K., E-mail: tksen@iitk.ac.in, Bhole, Ashish, Shruti, K. S., Sengupta, Aditi, Sharma, Nidhi, & Sengupta, Soumyo. Roles of bulk viscosity on Rayleigh-Taylor instability: Non-equilibrium thermodynamics due to spatio-temporal pressure fronts. United States. doi:10.1063/1.4961688.
Sengupta, Tapan K., E-mail: tksen@iitk.ac.in, Bhole, Ashish, Shruti, K. S., Sengupta, Aditi, Sharma, Nidhi, and Sengupta, Soumyo. 2016. "Roles of bulk viscosity on Rayleigh-Taylor instability: Non-equilibrium thermodynamics due to spatio-temporal pressure fronts". United States. doi:10.1063/1.4961688.
@article{osti_22598827,
title = {Roles of bulk viscosity on Rayleigh-Taylor instability: Non-equilibrium thermodynamics due to spatio-temporal pressure fronts},
author = {Sengupta, Tapan K., E-mail: tksen@iitk.ac.in and Bhole, Ashish and Shruti, K. S. and Sengupta, Aditi and Sharma, Nidhi and Sengupta, Soumyo},
abstractNote = {Direct numerical simulations of Rayleigh-Taylor instability (RTI) between two air masses with a temperature difference of 70 K is presented using compressible Navier-Stokes formulation in a non-equilibrium thermodynamic framework. The two-dimensional flow is studied in an isolated box with non-periodic walls in both vertical and horizontal directions. The non-conducting interface separating the two air masses is impulsively removed at t = 0 (depicting a heaviside function). No external perturbation has been used at the interface to instigate the instability at the onset. Computations have been carried out for rectangular and square cross sections. The formulation is free of Boussinesq approximation commonly used in many Navier-Stokes formulations for RTI. Effect of Stokes’ hypothesis is quantified, by using models from acoustic attenuation measurement for the second coefficient of viscosity from two experiments. Effects of Stokes’ hypothesis on growth of mixing layer and evolution of total entropy for the Rayleigh-Taylor system are reported. The initial rate of growth is observed to be independent of Stokes’ hypothesis and the geometry of the box. Following this stage, growth rate is dependent on the geometry of the box and is sensitive to the model used. As a consequence of compressible formulation, we capture pressure wave-packets with associated reflection and rarefaction from the non-periodic walls. The pattern and frequency of reflections of pressure waves noted specifically at the initial stages are reflected in entropy variation of the system.},
doi = {10.1063/1.4961688},
journal = {Physics of Fluids},
number = 9,
volume = 28,
place = {United States},
year = 2016,
month = 9
}
  • The initial multi-mode interfacial velocity and density perturbations present at the onset of a small Atwood number, incompressible, miscible, Rayleigh-Taylor instability-driven mixing layer have been quantified using a combination of experimental techniques. The streamwise interfacial and spanwise interfacial perturbations were measured using high-resolution thermocouples and planar laser-induced fluorescence (PLIF), respectively. The initial multi-mode streamwise velocity perturbations at the two-fluid density interface were measured using particle-image velocimetry (PIV). It was found that the measured initial conditions describe an initially anisotropic state, in which the perturbations in the streamwise and spanwise directions are independent of one another. The evolution of various fluctuatingmore » velocity and density statistics, together with velocity and density variance spectra, were measured using PIV and high-resolution thermocouple data. The evolution of the velocity and density statistics is used to investigate the early-time evolution and the onset of strongly-nonlinear, transitional dynamics within the mixing layer. The early-time evolution of the density and vertical velocity variance spectra indicate that velocity fluctuations are the dominant mechanism driving the instability development. The implications of the present experimental measurements on the initialization of Reynolds-averaged turbulent transport and mixing models and of direct and large-eddy simulations of Rayleigh-Taylor instability-induced turbulence are discussed.« less
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  • A new model for the instability of a steady ablation front based on the sharp boundary approximation is presented. It is shown that a self-consistent dispersion relation can be found in terms of the density jump across the front. This is an unknown parameter that depends on the structure of the front and its determination requires the prescription of a characteristic length inherent to the instability process. With an adequate choice of such a length, the model yields results, in excellent agreement with the numerical calculations and with the sophisticated self-consistent models recently reported in the literature. {copyright} {ital 1997more » American Institute of Physics.}« less
  • The linear stability analysis of accelerated double ablation fronts is carried out numerically with a self-consistent approach. Accurate hydrodynamic profiles are taken into account in the theoretical model by means of a fitting parameters method using 1D simulation results. Numerical dispersion relation is compared to an analytical sharp boundary model [Yanez et al., Phys. Plasmas 18, 052701 (2011)] showing an excellent agreement for the radiation dominated regime of very steep ablation fronts, and the stabilization due to smooth profiles. 2D simulations are presented to validate the numerical self-consistent theory.
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