# 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 »

- 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; 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. Thu .
"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 = {Thu Sep 15 00:00:00 EDT 2016},

month = {Thu Sep 15 00:00:00 EDT 2016}

}