Non-equilibrium Thermodynamics of Rayleigh-Taylor instability

27th IUPAP Conference on Computational Physics

物理学;计算机科学

Sengupta, Tapan K.^1 ; Sengupta, Aditi^2 ; Shruti, K.S.^1 ; Sengupta, Soumyo^3 ; Bhole, Ashish^1

High Performance Computing Laboratory, Department of Aerospace Engineering, I.I.T. Kanpur, U.P. Kanpur, India^1

Department of Engineering, University of Cambridge, Cambridge, United Kingdom^2

Department of Mechanical and Aerospace Engineering, Ohio State University, Ohio, United States^3

关键词: Boussinesq approximations;    Compressible Navier-Stokes equations;    Dispersion-Relation-Preserving;    Equilibrium thermodynamics;    Interface instability;    Non equilibrium thermodynamics;    Rayleigh-Taylor instabilities;    Temperature differences;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/759/1/012079/pdf
DOI  :  10.1088/1742-6596/759/1/012079

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

Rayleigh-Taylor instability (RTI) has been studied here as a non-equilibrium thermodynamics problem. Air masses with temperature difference of 70K, initially with heavier air resting on lighter air isolated by a partition, are allowed to mix by impulsively removing the partition. This results in interface instabilities, which are traced here by solving two dimensional (2D) compressible Navier-Stokes equation (NSE), without using Boussinesq approximation (BA henceforth). The non-periodic isolated system is studied by solving NSE by high accuracy, dispersion relation preserving (DRP) numerical methods described in Sengupta T.K.: High Accuracy Computing Method (Camb. Univ. Press, USA, 2013). The instability onset is due to misaligned pressure and density gradients and is evident via creation and evolution of spikes and bubbles (when lighter fluid penetrates heavier fluid and vice versa, associated with pressure waves). Assumptions inherent in compressible formulation are: (i) Stokes' hypothesis that uses zero bulk viscosity assumption and (ii) the equation of state for perfect gas which is a consequence of equilibrium thermodynamics. Present computations for a non-equilibrium thermodynamic process do not show monotonic rise of entropy with time, as one expects from equilibrium thermodynamics. This is investigated with respect to the thought-experiment. First, we replace Stokes' hypothesis, with another approach where non-zero bulk viscosity of air is taken from an experiment. Entropy of the isolated system is traced, with and without the use of Stokes' hypothesis. Without Stokes' hypothesis, one notes the rate of increase in entropy to be higher as compared to results with Stokes' hypothesis. We show this using the total entropy production for the thermodynamically isolated system. The entropy increase from the zero datum is due to mixing in general; punctuated by fluctuating entropy due to creation of compression and rarefaction fronts originating at the interface and reflecting from the walls.