Rayleigh Taylor Instability
OBJECTIVE-Perform the Rayleigh Taylor instability simulation for 3 different mesh sizes with the base mesh being 0.5 mm.
Case-1:Rayleigh Taylor instability simulation with mesh size 0.5 mm
Case-2:Rayleigh Taylor instability simulation with mesh size 0.35 mm
Case-3:Rayleigh Taylor instability simulation with mesh size 0.25 mm
Rayleigh Taylor instability:
The Rayleigh–Taylor instability is an instability of the interface between two fluids of different densities. Examples include:
1. The behavior of water suspended above oil in the gravity of Earth.
2. Volcanic eruptions and atmospheric nuclear explosions supernova explosions in which expanding core gas is accelerated into denser shell.
3. Gas instabilities in plasma fusion reactors and inertial confinement fusion.
The equilibrium in all these cases is unstable to any perturbations or disturbances of the interface. If a parcel of heavier fluid is displaced downward with an equal volume of lighter fluid displaced upwards, the potential energy of the configuration is lower than the initial state. Thus the disturbance will grow and lead to a further release of potential energy, as the more dense material moves down under the gravitational field, and the less dense material is further displaced upwards.
CFD Models based on Rayleigh Taylor instability:
1. Kelvin–Helmholtz instability - Occurs when there is velocity shear in a single continuous fluid, or where there is a velocity difference across the interface between two fluids.
An example of this is wind blowing over water.
2. Richtmyer–Meshkov instability- Occurs when two fluids of different density are impulsively accelerated. Normally this is by the passage of a shock wave.This is seen 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.
3. Plateau–Rayleigh instability- This model 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 Rayleigh–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 ink jet technology whereby a jet of liquid is perturbed into a steady stream of droplets.
Steps involved in the simulation
- Geometry
- Mesh
- Setup
- Solution
- Results
Case-1:Rayleigh Taylor instability simulation with mesh size 0.5 mm
Geometry-A 2d geometry was created with two surfaces for water and air,water being the denser fluid at the top.The information for the two surfaces was shared with share topology option
Mesh-
Element size-0.5 mm
No of nodes-3321
No of elements in Mesh-3200
Setup-
Solver Type-Pressure Based Solver
-Transient State
Gravity=-9.81 y axis
Model-Viscous laminar
-Multiphase-ON
Material properties- Fluid-Water-Density=998.2 kg/m3
Air-Density=1.225 kg/m3
Method- SIMPLE
Initialization- Standard initialization with patch
Solution-
Residual plot:
Results-
Contour of Volume fraction
Animation-
Case-2:Rayleigh Taylor instability simulation with mesh size 0.35 mm
Mesh-
Element size-0.35 mm
No of nodes-6670
No of elements in Mesh-6498
Setup-
Solver Type-Pressure Based Solver
-Transient State
Gravity=-9.81 y axis
Model-Viscous laminar
-Multiphase-ON
Material properties- Fluid-Water-Density=998.2 kg/m3
Air-Density=1.225 kg/m3
Method- SIMPLE
Initialization- Standard initialization with patch
Solution-
Residual Plot:
Results-
Contour of Volume fraction
Animation-
Case-3:Rayleigh Taylor instability simulation with mesh size 0.25 mm
Mesh-
Element size-0.25 mm
No of nodes-13041
No of elements in Mesh-12800
Setup-
Setup-
Solver Type-Pressure Based Solver
-Transient State
Gravity=-9.81 y axis
Model-Viscous laminar
-Multiphase-ON
Material properties- Fluid-Water-Density=998.2 kg/m3
Air-Density=1.225 kg/m3
Method- SIMPLE
Initialization- Standard initialization with patch
Solution-
Residual plot:
Results-
Contour of Volume fraction
Animation-
Why a steady state approach might not be suitable for these types of simulation?
Steady state approach is not useful because we want to see the behaviour of instability with time and we are not interested in seeing the end results.So a transient simulaion is performed.
Atwood Number-Atwood number is a dimensionless number to study hydrodynamic instability in fluid flows.
`A=(rho_1-rho_2)/(rho_1+rho_2)`
where `rho_1`=density of heavier fluid
& `rho_2`=density of lighter fluid
Atwood number in this simulation
`A=(rho_1-rho_2)/(rho_1+rho_2)`
=`(998.2-1.225)/(998.2+1.225)=0.997`
In this case Atwood number is 0.997.
In case of Atwood number close to 0 the instability looks like symmetric fingers.And for Atwood number close to 1 the instability looks like bubble plumes.
In this case Atwood number is 0.997 which is close to 1 and we can observe bubble like plumes which can validate the results.
Conclusion:
By refining the mesh the instability was noticed more prominently and the interfaces were seen clearly.