Discuss Rayleigh Taylor Instability and run the simulations also understand the effect of Atwood number on instabilities using Ansys Fluent

Topic

Discuss Rayleigh Taylor Instability and run the simulations also understand the effect of Atwood number on instabilities.

A project

Submitted in partial fulfillment of the requirement for the award of the certificate

Of

Master Program

(CFD Masters)

By

Nitesh Negi

(Enrolment ID:3081)

Under the supervision of

CFD Team Leader Director of product

Pritam Goel Sarangarajan Iyengar

5th floor, Bristol IT Park
Main Rd, South Phase, Sathya Nagar, Gandhi Nagar, Chennai, Tamil Nadu 600032, +918939850851

CANDIDATE\'S UNDERTAKING

I, Nitesh Negi (Enrolment Id:3081) state that the contents and findings of the project entitled “Discuss Rayleigh Taylor Instability and run the simulations also understand the effect of Atwood number on instabilities using Ansys Fluent”, are original. To the best of my knowledge, the current project does not infringe upon anyone’s copyright nor violate any proprietary rights and that any ideas, techniques, quotations or any other material from the work of other people included in my project, published or otherwise, are fully acknowledged in accordance with the standard referencing practices. Even though later on in case of any complaint pertaining of plagiarism, I am solely responsible for the same and understand that as per norms.

ACKNOWLEDGEMENT

Primarily, I acknowledge this moment of time which has gone just forever but made up my mind to write the word for those who have been with me with their over-whelming gestures throughout this assignment. With deep gratitude, I express my earnest thanks to my respected guides Mr. Pritam Goel, CFD Team Leader, and Mr. Sarangarajan Iyengar, Director of product skilllync for his constant involvement, energetic efforts, and proficient guidance. Without his wise counsel and encouragement, it would have been impossible to complete the project work in this manner.

I would also thank to all the members of Ansys Fluent Skill-Lync what are app group members for support and express my gratitude.

ABSTRACT

Rayleigh Taylor Instability is frequently used for fluid mixing. Moreover, the mixing characteristics are of considerable interest, and numerous experimental studies and practical application have examined the question of optimal mixing. In this project, we discuss computer simulation of mixing of a fluid based on a 2D-dimensional flow code program utilizing the viscous model for volume of fluid. Comparison of the simulation results with different cases and appears to be a useful tool for predicting mixing. Not considering the temperature. Here we have reduced the restricted temperature, velocity, and mixing length with some combination in which we will perform the simulation. If we check by varying the mesh size shows the more accurate result with more simulation time.

The computational fluid dynamics (CFD) package FLUENT as a fluid flow analysis tool to solve the governing equations, prominently equations of continuity, motion and energy. Numerical results can be compared with experimental results and which was done by research scholar since due to model setup and lab constraints we will only compare the simulation results of different cases as per our objective. The mesh size is selected to do that the numerical solution is taken considering the computation time and simulation processing time.

Keywords: Mixing, numerical simulation, Fluent, CFD, viscous model, the volume of fluid

CONTENTS

Candidate’s undertaking i

Acknowledgment ii

Abstract v

Contents vi

List of figures vii

List of table’s viii

Nomenclature viii

Contents

CHAPTER 1: INTRODUCTION

-Introduction

-History

-Application

CHAPTER 2: LITERATURE REVIEW

- Introduction

- Review of Literatures

- Objectives

CHAPTER 3: METHODOLOGY

-Flow chart for CFD simulation

-Procedure/Steps for the CFD simulation

CHAPTER 4: RESULT AND DISCUSSIONS

CHAPTER 5: CONCLUSIONS AND FUTURE SCOPE

REFERENCES

LIST OF FIGURES

Figure (1):- Figure (8): Shows pictures, images, and plot for the simulation

LIST OF TABLES

Table(1): shows values of different parameters against the mesh size

NOMENCLATURE

Symbols Significance

⁰C Degree Celcius

CFD Computation Fluid Dynamics

RT Rayleigh–Taylor

CHAPTER 1

INTRODUCTION

The Rayleigh–Taylor instability, is the instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid with the effect of gravity.

Here we have prepared a model with two surfaces on over the above and considered one with light fluid a bottom phase and heavy fluid at top phases. here the potential energy of the configuration is lower than the initial state due to the movement of fluid due to gravity difference. Thus the disturbance will grow and lead to a further release of potential energy, as the denser material moves down under the (effective) gravitational field, and the less dense material is further displaced upwards.

The difference in the fluid densities divided by their sum is defined as the Atwood number, A. For A close to 0, RT instability flows take the form of symmetric \"fingers\" of fluid; for A close to 1, the much lighter fluid \"below\" the heavier fluid takes the form of larger bubble-like plumes.

The four main stages of RT instability are:-

Figure (1): The evolution of the RTI follows four main stages.

In the first stage, the perturbation amplitudes are small when compared to their wavelengths, the equations of motion can be linearized, resulting in exponential instability growth. In the early portion of this stage, a sinusoidal initial perturbation retains its sinusoidal shape. However, after the end of this first stage, when non-linear effects begin to appear, one observes the beginnings of the formation of the ubiquitous mushroom-shaped spikes (fluid structures of heavy fluid growing into light fluid) and bubbles (fluid structures of light fluid growing into heavy fluid).

In the second stage, the growth of the mushroom structures continues and can be modeled using buoyancy drag models, resulting in a growth rate that is approximately constant in time. At this point, nonlinear terms in the equations of motion can no longer be ignored. The spikes and bubbles then begin to interact with one another in the third stage.

Bubble merging takes place, where the nonlinear interaction of mode coupling acts to combine smaller spikes and bubbles to produce larger ones. Also, bubble competition takes place, where spikes and bubbles of smaller wavelengths that have become saturated are enveloped by larger ones that have not yet saturated.

This eventually develops into a region of turbulent mixing, which is the fourth and final stage in the evolution. It is generally assumed that the mixing region that finally develops is self-similar and turbulent, provided that the Reynolds number is sufficiently large.

History/Application[2]

We observe the development of the RTI whenever two matters of different densities are accelerated against the density gradients (Rayleigh 1883; Davies & Taylor 1950). Extensive interfacial material mixing ensues with time (Read 1984; Schneider et al. 1998; Ramaprabhu & Andrews 2003; Meshkov 2006). The turbulent mixing plays a key role in a wide variety of natural phenomena, spanning astrophysical to micro-scales, as well as in technological applications (Abarzhi 2008). It influences the formation of the ‘hot spot’ in inertial confinement fusion (ICF) (Gamaly 1993; Bodner et al. 1998; Mima 2004; Remington et al. 2006; Besnard 2007), limits radial compression of imploding Z-pinches (Ryutov et al. 2000) and controls non-equilibrium heat transfer induced by ultra-fast high-power lasers in solids (Barnes et al. 1974; Lukyanchuk et al.1993a,b; Perez & Lewis 2002). Rayleigh–Taylor (RT) turbulent mixing governs transports of mass, momentum and energy in mantle–lithosphere tectonics, ocean and atmosphere, interstellar molecular clouds, flashes of supernovae, and in flames and fires (Stone et al. 1996; Hillebrandt & Niemeyer 2000; Rosner 2003). Our ability to control the unsteady turbulent mixing is crucial for industrial applications in aerodynamics and aeronautics (e.g. Spalart & Wattmuff 1993; Gutman et al. 1995; Marmottant & Villermaux 2004), and in free-space optical telecommunications (e.g. Kaminow et al. 1996; Choi & Chan 2002). RTI is essential to occur under extreme conditions of high-energy-density (Zel’dovich & Raizer 2002; Remington et al. 2006; Drake 2009), but one can still easily observe it in everyday life when looking at how salted and freshwater mix or how wine flows out from an overturned glass.

Mathematical aspects of the dynamics of RTI and turbulent mixing reveal the intellectual richness of the theoretical problem (Abarzhi 2008). For instance, at atomistic and mesoscales, RT-induced material transport may depart from a standard scenario of Gibbs’ ensemble and quasi-static Boltzmann equation (Hoover 1991; Zhakhovskii et al. 2006; Kadau et al. 2007; Evans & Morriss 2008). On the other hand, at macroscopic scales singular character and similarity of the non-equilibrium dynamics are interplayed with the fundamental properties of three-dimensional Euler or Navier–Stokes equations and with the problem sensitivity to the boundary conditions at discontinuities and the initial conditions (Pumir & Siggia 1992; Baker et al. 1993; Tanveer 1993; Wu 2006). Furthermore, turbulent mixing is a multi-scale, anisotropic, non-local, and statistically unsteady process and its fundamental invariant properties depart dramatically from those in the classical Kolmogorov turbulence (Abarzhi et al. 2005). As in any turbulent process, the contribution of all scales into the flow dynamics induces randomness of RT mixing (Frisch 1995). Yet, because of the statistical unsteadiness and non-Gaussian character of fluctuations, capturing this randomness is a challenging task that necessitates further advancements of the methods of stochastic modelling (Abarzhi et al. 2007).

On the side of the numerical simulations, modeling RT mixing is a severe test, as the numerical solutions appear sensitive to the initial and boundary conditions as well as to the influence of unresolved small-scale structures on the large-scale dynamics and to the anomalous character of energy transport (Gardner et al. 1988; Youngs 1991; He et al. 1999; Cook & Dimotakis 2001; Young et al. 2001; Kadau et al. 2007). Addressing these difficulties brings up the issue of the predictive capability of the numerical models, their verification and validation as well as quantification of uncertainty of the solutions obtained (Calder et al. 2002; George et al. 2002). The synergy between theory, experiment, and simulations thus appears crucial for obtaining an integrated description of the phenomenon and for grasping its universality features (Dimonte et al. 2004; Abarzhi 2008). On the side of the experiments, RT flows are hard to implement and systematically study in a well-controlled laboratory environment, as their sensitivity and transient character of the dynamics impose high requirements on accuracy, Spatio-temporal resolution, and dynamic range of the flow quantities as well as on data rate acquisition. One of the primary concerns for RT experiments is the influence of an observer on the results of observation and data interpretation (Dimonte 2000; Waddell et al. 2001; Jacobs & Krivets 2005; Abarzhi 2008). To provide reliable and repeatable datasets, experiments on the RTI and turbulent mixing in fluids and plasmas employ the most advanced diagnostic approaches (Dalziel et al. 1999; Aglitskiy et al. 2001; Kucherenko et al. 2003; Meshkov 2006; Remington et al. 2006; Orlov et al. 2010).

CHAPTER 2:

LITERATURE REVIEW

- INTRODUCTION

To begin the proposed work it is required to make a review of research papers in order to discover what work has been done already about the related topic and which procedure or methodology has been adopted to perform the simulation/experiments and conclude the results.

A review of the various published literature on any specific topic is the first important step to be taken to get,

• Knowledge about the state of art.
• Familiarity with the established methods and procedures for conducting work.
• To stop duplication of work.

- LITERATURE REVIEW

There are several numbers of studies conducted by researchers regarding the Steady-state simulation on a TEE Geometry of Mixing fluid (air) from the turbulence model using Ansys Fluent, some of them are discussed below:-

1. Snezhana I. Abarzhi. (2010) [1] Review of theoretical modelling approaches of Rayleigh–Taylor instabilities and turbulent mixing.
2. Sharp, D.H. (1984). \"An Overview of Rayleigh-Taylor Instability\". Physica D. 12(1): 3–18. Bibcode:1984PhyD...12....3S. doi:10.1016/0167-2789(84)90510-4.
3. Jump up to:^{a b c d e} Drazin (2002) pp. 50–51.
4. David Youngs (ed.). \"Rayleigh–Taylor instability and mixing\". Scholarpedia.
5. https://gizmodo.com/why-nuclear-bombs-create-mushroom-clouds-1468107869
6. Wang, C.-Y. & Chevalier R. A. (2000). \"Instabilities and Clumping in Type Ia Supernova Remnants\". The Astrophysical Journal. 549 (2): 1119–1134. arXiv:astro-ph/0005105v1. Bibcode:2001ApJ...549.1119W. doi:10.1086/319439.

-OBJECTIVE

Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street.

1. What are some practical CFD models that have been based on the mathematical analysis of Rayleigh Taylor waves? In your own words, explain how these mathematical models have been adapted for CFD calculations.
2. Define the Atwood Number. Find out the Atwood number for this case and explain how the variation in Atwood number affects the behavior of the instability. How can we use the Atwood number to validate our simulation result?

PART-I

• Perform the Rayleigh Taylor instability simulation for 3 different mesh sizes with the base mesh being 0.5 mm. Compare the results by showing the animations( Attach them from your google drive). Also, explain why a steady-state approach might not be suitable for these types of simulation.

PART-II

• Perform the analysis for a refined mesh with water and oil. Find Atwood number for this case and discuss the effect of Atwood number & viscosity by observing the behavior of instabilities.

  Oil Properties:- Density= 400 kg/m³, Dynamic Viscosity = 1.06 kg/m-s.

CHAPTER 3

-METHODOLOGY

The complete methodology that has been adopted to conduct the present project work is shown in the form of the flow chart in figure 3.1

Figure 2: Flow Chart for Methodology

-Procedure for CFD simulation of Mixing Tee

Selection of material

The material property is not necessary for this simulation since we are not considering the heat transfer through the wall.

For multiphase fluid, we have considered a combination of water-air and water-oil.

Further, we will know that in this type of simulation we consider the surface generation and that is extracted using the Space claim tool.

Cad Model Preparation

Step1: Open the workbench & double click open Flow Fluent

Step2: Double click on geometry to open space claim> open the file from saved location.

prepare the surface by

Part 1

water-side (top) = (20 x 20) mm
air-side (bottom) = (20 x 20) mm

Part 2

water-side (top) = (20 x 20) mm
oil-side (bottom) = (20 x 20) mm

as shown below.

Figure (3): The evolution of the RTI follows four main stages.

Step4: Go to prepare the tab and select the surface generation tool and select the air and waterside one by one.

select both prepared surfaces one above another and use share >share topology> tick click and shared top done

Step5: Close space claim workbench and save files if required.

Preprocessing

Step6: Double click on Mesh from workbench>Generate Mesh by right-clicking the mesh icon and click generate mesh option and mesh will be generated; here you can change mesh size from element size option in the mesh tree.

Step7: Give a name to required parts by face section/edge selection>click update by right-clicking on the mesh>check the mesh metric matrix by select element quality should be not less than 5%.

CASE-1
Element Size = 0.5mm
Nodes = 4753
Elements = 4608
Mesh Type: Baseline mesh coarse

Element Quality

Aspect ratio

Skewness

Orthogonality

Figure (4): shows different parameters for .5 mesh size.

CASE-2
Element Size = 0.1mm
Nodes =115921
Elements = 115200
Mesh Type: medium

Element Quality

Aspect ratio

Skewness

Orthogonality

Figure (5): shows different parameters for 0.1 mesh size.

CASE-3
Element Size = 0.08mm
Nodes = 180901
Elements = 180000
Mesh Type: fine

Element Quality

Aspect ratio

Skewness

Orthogonality

Figure (6): shows different parameters for .08 mesh size.

Step8: close mesh module.

Setup/Processing

Step9: Double click on setup to open the workbench

Step10: select for Time -Transient solution, Solver Type -pressure-based solvers, Velocity Formulation - Absolute and Physics-none from the model.>select the laminar model for turbulent flow based upon the condition.

Properties:
Solver: Transient Pressure-based
Gravity: X = 0 m/s^2
Y = -9.81 m/s^2
Flow type: Laminar
Model type: Multiphase
Method: Implicit
Material: Air and Water-Liquid

Step11: setup the boundary condition as per the given data.

In the multiphase model select VOF i.e volume of fluid it is a widely used method. for simulation of multiphase flow>implicit >volume. fraction cut off.

select material air and water >specify primary phase =water>secondary phase=air for the first case.

select material oil and water >specify primary phase =water>secondary phase=oil for the second case.

Oil Properties:- Density= 400 kg/m³, Dynamic Viscosity = 1.06 kg/m-s.

perform standard initialization >patch >1 for water surface >0 for air surface for the first case.

perform standard initialization >patch >1 for water surface >0 for oil surface for the first case.

Time Step Size = 0.025

No. of Time Steps =1500 Iterations

Max. no. iterations per time steps=20

Post-processing/Results

Step12: Not required /the results. are the animation. file extract from the solution animation.

and the residual plot which gets generated along the simulation run and completes after settling of high-density fluid at the bottom.

CHAPTER 4:

RESULT AND DISCUSSIONS

The results of various Simulation tests conducted Rayleigh-Taylor instability as well as are calculated and explained with the help of different graphs and charts which are plotted by using Ansys Fluent & MS-Excel software. Comparisons of results are also done Case I and Case II. The compared results are summarized as the following:-

• What are some practical CFD models that have been based on the mathematical analysis of Rayleigh Taylor waves? In your own words, explain how these mathematical models have been adapted for CFD calculations.

Models used for Rayleigh-Taylor instability[2]

Plateau–Rayleigh instability:

Explains why and how a falling stream of fluid breaks up into smaller packets with the same volume but less surface area. It is related to the Ryleigh- Taylor instability. and is part of a greater branch of fluid dynamics concerned with fluid thread breakup. This fluid instability is exploited in the design of a particular type of inkjet technology. whereby a jet of liquid is perturbed into a steady stream of droplets. The driving force of the Plateau–Rayleigh instability is that liquids, by virtue of their surface tensions, they tend to minimize their surface area.

Kelvin–Helmholtz instability:

The theory predicts the onset of instability and transition to turbulent flow in fluids of different densities moving at various speeds. This instability occurs where there is a velocity shear or velocity difference between the interface of the multiphase fluids.

Richtmyer–Meshkov instability:

Instability occurs when there is an impulsive acceleration between the two fluids. This type of instability can occur when there is a shock at greater speeds. The development of the instability begins with small amplitude perturbations which initially grow linearly with time. This is followed by a nonlinear regime with bubbles appearing in the case of a light fluid penetrating a heavy fluid, and with spikes appearing in the case of a heavy fluid penetrating a light fluid. A chaotic regime eventually is reached and the two fluids mix. This instability can be considered the impulsive-acceleration limit of the Ryleigh- Taylor instability.

Rayleigh- taylor instability :

1. Define the Atwood Number. Find out the Atwood number for this case and explain how the variation in Atwood number affects the behavior of the instability. How can we use the Atwood number to validate our simulation result?

Atwood Number:

The Atwood number (A) is a dimensionless number in fluid dynamics used in the study of hydrodynamic instabilities in density stratified flows. It is a dimensionless density ratio defined as:

For water /air multiphase fluid
A = (1000 - 1.25) / (1000 + 1.25) = 0.9975

Atwood number is an important parameter in the study of Rayleigh-Taylor instability. For Atwood number close to 0, RT instability flows take the form asymmetric “finger” of fluid; for Atwood number close to 1, the much lighter fluid “below” the heavier fluid takes the form of larger bubble-like plumes.

The calculated Atwood number is close to 1 and from the simulation results, it is found that when high dense fluid i.e. water poured upon low dense fluid i.e. air under gravity, the formation of air bubble-like plumes takes place which travels towards the upward region in the form of waves and some gets trapped at the lower regions during the initial stages, which afterward try to move towards the upper region and at the end, both phases gets separated with some diffusivity left at the middle portion between them. Thus, the calculated Atwood number is validated for our simulation results.

PART-I

• Perform the Rayleigh Taylor instability simulation for 3 different mesh sizes with the base mesh being 0.5 mm. Compare the results by showing the animations( Attach them from your google drive). Also, explain why a steady-state approach might not be suitable for these types of simulation.

Plot for Base Mesh of 0.5mm

Residuals plot

Figure (7): shows residual values for 0.5 mesh size

Contour plot of volume fraction

Figure (8): shows after mixing volume fraction.

volume fraction. animation

Plot for Base Mesh of 0.1mm

Residuals plot

Figure (9): shows residual values for 0.1 mesh size

Contour plot of volume fraction

Figure (10): shows after mixing volume fraction at 0.1 mesh size.

volume fraction. animation

Plots for Base Mesh of 0.08 mm

Residuals plot

Figure (11): shows residual values for 08 mesh size

Contour plot of volume fraction

Figure (12): shows after mixing volume fraction at 0.8 mesh size.

volume fraction animation

PART-II

• Perform the analysis for a refined mesh with water and oil. Find Atwood number for this case and discuss the effect of Atwood number & viscosity by observing the behavior of instabilities.

  Oil Properties:- Density= 400 kg/m³, Dynamic Viscosity = 1.06 kg/m-s.

Images for Base Mesh of 0.1mm

Residuals plot

Figure (11): shows residual values for 08 mesh size

Contour plot of volume fraction

Figure (14): shows after mixing volume fraction o.1 mesh.

volume fraction animation