Week 5 - Rayleigh Taylor Instability

AIM: To study the rayleigh taylor instability

Rayleigh taylor instability is defined as the mixing of two phases of different density materials, which are earlier is in the position such that, higher density material lies at the top of the lower density materials, and once we initialte the simulation, under the effect of gravity we had observed the mixing of phases, such that, lighter density material rushed into the zone of heavy density material, and at the end of the simulation, the lighter density material settled at the top, while the lower density material settled at the bottom.

Examples:

• Water suspended above oil
• Atmospheric nuclear explosion
• Supernova explosion (core gas accelerated into denser shell gas)
• Nuclear explosion
• Volcanic eruption

 CASE I: Base mesh 0.5mm

Procedure:

• Initially we create the required surface of 20x20 (two slabs), and after pulling the geometry, an sub-named into component we share the topology.
• asd

Fig: Model View

Following are the mesh view:

Mesh details are:

Element Size: 0.5mm
Total Nodes:3321
Total Elements:3200

Fig: Indicating name selection

In solver type, we had used, pressure based, transient study,

Under the setting up physics tab, we had used the multiphase, implicit function for simulation.

following are the materials which we had used for simulation:

Fig: Indicating air properties

Fig: Indicating water properties

After that, we patch the phases, via volumefraction as variable assigned as 0 for air, and 1 for water;

Fig: Indicates patching (before starting of simulation)

 Google Drive Link For The  Animation:

https://drive.google.com/drive/folders/11KlqnYX4192_5LvIvNFOJz8GpKwCbHZL?usp=share_link

 CASE II: Finer Mesh:

Fig: Indicate Mesh View

Details of mesh are as follows:

Element Size: 0.3mm
Total Nodes:9180
Total Elements:8978

Material properties are same as Case I, that is , air & water.

G-drive link for the animation:

https://drive.google.com/drive/folders/1PCb_g-Ok4MsYCkDRNf7Pmca6Iy9po7pN?usp=share_link

CASE III: Finer Mesh (0.3mm, with material as water & user defined)

mesh view is same as case II, the only difference from case II is the material properties, in this case I had take water and user defined material;

the property of user defined material are as follows:

G-drive link for the animation is:

https://drive.google.com/drive/folders/1nzgl7agMQ-PJT3KXWagqOud3Ls6hrh6n?usp=share_link

 
ATWOOD NUMBER:

it is a dimensionaless number, which is generally used to analyse the hydrodynamic instabilities,

the mathematical formula of the such are:

AN=(p1-p2)/(p1+p2)

where, p1= density of heavier fluid, p2= density of lighter fluid.

significance of atwood number:

when it is close to zero, it indicate the Rayleigh taylor instability of asymetric finger kind of fluid

while when it is close to 1, it indicate the rayleigh taylor instability takes the large bubble formation knd of fluid,

the following are the value of above cases:

CASE	STATE	MESH SIZE (mm)	PHASE	DENSITY OF PHASE 1	DENSITY OF PHASE 2	ATWOOD NO.	FORMULA
II	TRANSIENT	0.3	PHASE 1 WATER & PHASE 2 AIR	998.2	1.225	0.998	(p1-p2)/(p1+p2)
III	TRANSIENT	0.3	PHASE 1 WATER & PHASE 2 USER-DEFINED	998.2	400	0.42

Thus, it is evident from the above analysis that, as the value of atwood number is close to 1, it gives large bubble formation, prior to the formation of mushroom head shape (assymetrical in nature) at an accelerating rate leads to non linear growth, while when the atwood number is close to 0, it gives formation of bubble and mushroom head relatively in symmetrical manner, and they are in linear form Conclusion: Finer mesh gives bubble formation and vortices formation more accurately the reason why I didn't use the steady state for simulaton is that, beacause during simulation we are interested in the variation of model on the basis of time (iterative form), if we use the steady state, the state of model will constant wrt to time, and we get the only end result, which is not the requirement of the simulation. Practical CFD Models based On RTI: Ritchmyer-Meshkov instability: in such model mainly interaction between two fluids leads to the generation of shock waves, which are generally non linear in nature, and as a result, hydrodynamic instability occurs, Ex: Supersonic combustion in scramjet, hypersonic missile, etc. Ritchmyer-Meshkov instability: In such model, the fluid breaks into smaller version, as a result, the volume before and after splitting were same, but the surface area were less as compared to earlier case. Ex: Ink Jet Technology Turbulence model: It is generally used for the average mixing of fluids for 1D and 2D analysis, for CFD simulation system generally uses the turbulence model, to predict the turbulence behaviour of fluid.