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 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.

Ultrasound Triggering of Rayleigh-Taylor Instability: Solution of Compressible Navier-Stokes Equation by a Non-Overlapping Parallel Compact Scheme

“…The term given by, ω ∇ • V , is due to compressibility, and RTI should justifiably depend upon bulk viscosity as noted from the constitutive relation between stress and rates of strain tensors. Equation (1) demonstrates the need for predicting RTI using the compressible flow formulation along with the bulk viscosity contribution, as has been reported in [12,14], and the same formulation is also used here. Thus, without using the Stokes' hypothesis, the linear regression model for the bulk viscosity based on acoustic dispersion and attenuation experimental data of Ash et al [15] is utilized here also.…”

“…In the present case, the box is considered to be thermally insulated, which enables it to be viewed as an universe, without any mass, momentum, and energy transfer with the outside. The ensuing RTI upon removal of the partition enables one to view the process as one of non-equilibrium thermodynamics, as reported for a two-dimensional (2D) flow in [14,20,21] and a three-dimensional (3D) flow with A t = 0.2, due to initial temperature differential of 149K. In Read's experiments [22], two geometrical setups were considered with the purpose of providing results for 2D and 3D flows.…”

“…In practice, there is no need to impose any length scale as there are many 2D and 3D direct numerical simulations (DNS) where the initial interface is purely taken as planar [12,14,20,21,27] to replicate the experiments reported in [17,22,28] where the fluid interface is initially plane and the onset of RTI has been shown to originate from the edges and corners of the initial interface [12].…”

“…The above discussion indicates that the onset of RTI and associated length scales are still not unambiguously resolved. We have already noted that high accuracy compact schemes used for solving compressible NSE without the Stokes' hypothesis enable one to track the onset of RTI to be from the edges and corners of the interface [14,20,21] for 2D RTI problem. The authors in [29] used a 2D multi-physics simulation package, HYDRA [31,32] with a spatial resolution of the order of 3µm and time steps of the order of 100ps.…”

Comment on “Roles of bulk viscosity on Rayleigh-Taylor instability: Non-equilibrium thermodynamics due to spatio-temporal pressure fronts” [Phys. Fluids 28, 094102 (2016)]

“…There was no such publication. However, we did report the data that were employed in Figure 7 of that article, 5 as part of a NASA contractor report, 1 and that may explain the error. This author believes that Sengupta et al have identified an important non-equilibrium effect, but they should have been more thorough in reviewing the underlying non-equilibrium physics literature.…”