rt instability

ANS 1 ; Some practical applications of the rayleigh taylor instabilities are;

1) supernova explosins

2) atmospheric nuclear explosions

3) volcanic eruptions

4) plasma fusion instability reactions

5) inertial confinemnet fusion

The mathematical model of the rayleigh taylor instability is a differential equation that can be modelled for the above cases now for obtaning the solutions in CFD we divide the domain in several parts for solving the differential equation , thus the differetial equation is converted ta a linear equaation and the solution gets converged as the errors keeps on reducing. Thus for the above cases certain assuptions would be used for obtaining a solution.

ANS 2 ; Rayleigh taylor instability is analysed by placing the heavier density fluid at the top and lighter at bottom. Letting the fluid to flow under influence of gravity.

CASE 1:

number of elements : 3200

size of elements : .5 mm

# GEOMERTY

two squares of side 20 mm are drawn

#MESH :

#FLUENT :

Heavier fluid is patched as 1

1) physics

pressure based

transient state

absolute velocity

mutiphase ( implicit, volume based )

gravity is also enabled ( 9.8 m/s2 )

number of iterations : 1500

timestep : .05

2) residuals

3) contour of volume fraction

CASE 2 :

number of elements : 80000

size of elements : .1 mm

#Same geometry

# MESH :

# FLUENT :

same physics is applied

number of iterations : 1500

timestep : .001

1) residuals

2) contour of volume fraction

CASE 3:

number of elements : 320000

size of elements: .005 mm

# Same geomerty

# MESH

# FLUENT :

same physics

number of iterations : 1500

timestep : .0003

1) residuals

2) contour of volume fraction

CONCLUSION :

Thus from the above analysis it\'s clear that the finner the mesh the better we capture the mixing of the two fluids and also the better we see the rayleigh taylor wave in the begining , followed by the formation of the spear as the denser fluid comes in and at last the formation of the cloud like structure and thus the mixing takes place.

ANS 3 : Atwood number is the ratio of the difference of the densities to the sum of the densities . `(rho1-rho2)/(rho1+rho2)` where , rho 1 is the density of the heavier fluid and rho 2 is the density of lighter fluid.

Atwood number : .997

the instability grows with tim as the atwood number increases

we can see that our instability has increased in finner mesh and thus the atwood number explanation fits in