Roles of bulk viscosity on RayleighTaylor instability: Nonequilibrium thermodynamics due to spatiotemporal pressure fronts
Abstract
Direct numerical simulations of RayleighTaylor instability (RTI) between two air masses with a temperature difference of 70 K is presented using compressible NavierStokes formulation in a nonequilibrium thermodynamic framework. The twodimensional flow is studied in an isolated box with nonperiodic walls in both vertical and horizontal directions. The nonconducting 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 NavierStokes 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 RayleighTaylor 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 wavepackets withmore »
 Authors:
 HPCL, Department of Aerospace Engineering, IIT Kanpur, Kanpur, UP (India)
 Department of Engineering, University of Cambridge, Cambridge (United Kingdom)
 Graduate Student, HPCL, Department of Aerospace Engineering, IIT Kanpur, Kanpur, UP (India)
 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; NAVIERSTOKES EQUATIONS; PERIODICITY; PERTURBATION THEORY; RAYLEIGHTAYLOR INSTABILITY; REFLECTION; THERMODYNAMICS; TWOPHASE FLOW; VISCOSITY
Citation Formats
Sengupta, Tapan K., Email: tksen@iitk.ac.in, Bhole, Ashish, Shruti, K. S., Sengupta, Aditi, Sharma, Nidhi, and Sengupta, Soumyo. Roles of bulk viscosity on RayleighTaylor instability: Nonequilibrium thermodynamics due to spatiotemporal pressure fronts. United States: N. p., 2016.
Web. doi:10.1063/1.4961688.
Sengupta, Tapan K., Email: tksen@iitk.ac.in, Bhole, Ashish, Shruti, K. S., Sengupta, Aditi, Sharma, Nidhi, & Sengupta, Soumyo. Roles of bulk viscosity on RayleighTaylor instability: Nonequilibrium thermodynamics due to spatiotemporal pressure fronts. United States. doi:10.1063/1.4961688.
Sengupta, Tapan K., Email: tksen@iitk.ac.in, Bhole, Ashish, Shruti, K. S., Sengupta, Aditi, Sharma, Nidhi, and Sengupta, Soumyo. 2016.
"Roles of bulk viscosity on RayleighTaylor instability: Nonequilibrium thermodynamics due to spatiotemporal pressure fronts". United States.
doi:10.1063/1.4961688.
@article{osti_22598827,
title = {Roles of bulk viscosity on RayleighTaylor instability: Nonequilibrium thermodynamics due to spatiotemporal pressure fronts},
author = {Sengupta, Tapan K., Email: 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 RayleighTaylor instability (RTI) between two air masses with a temperature difference of 70 K is presented using compressible NavierStokes formulation in a nonequilibrium thermodynamic framework. The twodimensional flow is studied in an isolated box with nonperiodic walls in both vertical and horizontal directions. The nonconducting 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 NavierStokes 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 RayleighTaylor 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 wavepackets with associated reflection and rarefaction from the nonperiodic 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 multimode interfacial velocity and density perturbations present at the onset of a small Atwood number, incompressible, miscible, RayleighTaylor instabilitydriven mixing layer have been quantified using a combination of experimental techniques. The streamwise interfacial and spanwise interfacial perturbations were measured using highresolution thermocouples and planar laserinduced fluorescence (PLIF), respectively. The initial multimode streamwise velocity perturbations at the twofluid density interface were measured using particleimage 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 »

Experimental characterization of initial conditions and spatiotemporal evolution of a small Atwood number RayleighTaylor mixing layer
The initial multimode interfacial velocity and density perturbations present at the onset of a small Atwood number, incompressible, miscible, RayleighTaylor instabilitydriven mixing layer have been quantified using a combination of experimental techniques. The streamwise interfacial and spanwise interfacial perturbations were measured using highresolution thermocouples and planar laserinduced fluorescence (PLIF), respectively. The initial multimode streamwise velocity perturbations at the twofluid density interface were measured using particleimage 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 » 
Rayleigh{endash}Taylor instability of steady ablation fronts: The discontinuity model revisited
A new model for the instability of a steady ablation front based on the sharp boundary approximation is presented. It is shown that a selfconsistent 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 selfconsistent models recently reported in the literature. {copyright} {ital 1997more » 
Selfconsistent numerical dispersion relation of the ablative RayleighTaylor instability of double ablation fronts in inertial confinement fusion
The linear stability analysis of accelerated double ablation fronts is carried out numerically with a selfconsistent 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 selfconsistent theory. 
Dynamic stabilization of RayleighTaylor instability: Experiments with Newtonian fluids as surrogates for ablation fronts
A previous theory on dynamic stabilization of RayleighTaylor instability at interfaces between Newtonian fluids is reformulated in order to make evident the analogy of this problem with the related one on dynamic stabilization of ablation fronts in the framework of inertial confinement fusion. Explicit analytical expressions are obtained for the boundaries of the dynamically stable region which turns out to be completely analogue to the stability charts obtained for the case of ablation fronts. These results allow proposing experiments with Newtonian fluids as surrogates for studying the case of ablation fronts. Experiments with Newtonian fluids are presented which demonstrate themore »