Taylor Instability Simulation using ANSYS FLUENT
SOME PRACTICAL CFD MODELS BASED ON RAYLEIGH TAYLOR WAVES:
1. The Richtmyer–Meshkov instability (RMI): The Richtmyer–Meshkov instability (RMI) occurs when two fluids of different density are impulsively accelerated. Normally this is by the passage of a shock wave. 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 Rayleigh–Taylor instability
2.The Kelvin–Helmholtz instability: The Kelvin–Helmholtz instability can occur 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 is wind blowing over water: The instability manifests in waves on the water surface. More generally, clouds, the ocean, Saturn\'s bands, Jupiter\'s Red Spot, and the sun\'s corona show this instability.
3. Potential flow models of Rayleigh Taylor and Richtmyer–Meshkov Bubble front:
In the model, which extends the work of Layzer [Astrophys. J. 122, 1 (1955)], ordinary differential equations for the bubble heights and curvatures are obtained by considering the potential flow equations near the bubble tips. The model is applied to two‐dimensional single‐mode evolution as well as two‐bubble competition, for both the Rayleigh–Taylor (RT) and the Richtmyer–Meshkov (RM) instabilities, the latter treated in an impulse approximation. The model predicts that the asymptotic velocity of a single‐mode RM bubble of wavelength λ decays as λt−1, in contrast with the constant asymptotic velocity attained in the RT case. Bubble competition, which is believed to determine the multimode front evolution, is demonstrated for both the RT and RM instabilities. The capability of the model to predict bubble growth in a finite‐thickness fluid layer is shown. Finally, the model is applied to the evolution of three‐dimensional modes with an initial rectangular geometry.
SIMULATION OF RAYLEIGH TAYLOR INSTABILITY:
GEOMETRY AND MODELLING:Two squares of Air(below) and Water(above).
dimension of each square: 20mm x 20mm
MESHING:
CASE 1: Element Size = 0.5 mm
CASE 2: Element Size = 0.3 mm
CASE 3: Element Size = 0.1 mm
PHYSICS SETUP:
Transient Implicit Setup
Gravity : in y-direction = -9.81 m/s^2
Phases : Air and Water
Multiphase Modelling With 2 eulerian phases with Volume of fraction Method
Patching done with initialization
iterations per time step: 20
Time step size : 0.005s
RESULTS:
CASE1:
https://drive.google.com/open?id=17wKWzcTeGRpQ_ljZFoReyKx8OpbWtq7W
CASE2:
https://drive.google.com/open?id=1KJRRb77_IEcLUaEbTibg0RRUdHOjzhvt
CASE3:
https://drive.google.com/open?id=1RazBqAdU3iMxzmVhyxfXBVnsfxgSpgPp
REASONS FOR NOT DOING STEADY STATE SIMULATIONS:
If we do steady state simulation , then we would not be able to observe the mixing behaviour of the two phases and just see the end result(which we already know).We are interested in observing mixing of a dense fluid with a light fluid with respect to time, hence a transient analysis is required
The Atwood number (A) is a dimensionless number in fluid dynamics used in the study of hydrodynamic instailities in density stratified flows. It is a dimensionless density ratio defined as
A=`(rho1-rho2)/(rho1+rho2)`
`rho1`: density of heavy fluid
`rho2`: density of light fluid
Atwood number is an important parameter in the study of Rayleigh–Taylor instability and Richtmyer–Meshkov instability. In Rayleigh–Taylor instability, the penetration distance of heavy fluid bubbles into the light fluid is a function of acceleration time scale`A*g*t^2`, where g is the gravitational acceleration and t is the time. This formula can be used to validate our simulation