All Courses
All Courses
Courses by Software
Courses by Semester
Courses by Domain
Tool-focused Courses
Machine learning
POPULAR COURSES
Success Stories
Objectives: 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. Perform the Rayleigh Taylor instability simulation for 2 different mesh sizes with the base mesh being…
Surya Naidu
updated on 19 Jan 2021
Objectives:
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.
Rayleigh Taylor instability:
From the Newtons law of viscosity, we know that even the fluid cannot resist the slightest shear force. Density is one of the main property of the fluid which the shear force can incorporate with it.
Depending upon the density we have lighter fluid like water etc and denser fluid like mercury, oil, honey etc.
Lord Rayleigh observed that when two liquids i.e lighter and heavier fluids are mixed together where the deser fluid is top on the lighter fluid, due to the gravity and the density variation the interface of the liquid is not stable. (i.e) water suspended on the oil .
So, the instability of the interface between the different densities of fluid when the lighter fluid is accelerated towards the heavier fluid is knowns as Rayleigh Taylor instability.
Types of Instability and some practical CFD models that have been based on the mathematical analysis of Rayleigh Taylor waves:
Ritchmyer-Meshkov instability:
The Richtmyer-Meshkov instability arises when a shock wave interacts with an interface separating two different fluids. It combines compressible phenomena, such as shock interaction and refraction, with hydrodynamic instability, including nonlinear growth and subsequent transition to turbulence, across a wide range of Mach numbers.
Plateau–Rayleigh instability:
The Plateau–Rayleigh instability, often just called the Rayleigh instability, explains why and how a falling stream of fluid breaks up into smaller packets with the same volume but less surface area. 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.
Kelvin–Helmholtz instability:
can occur when there is velocity shear in a single continuos fluid, or where there is a velocity difference across the interface between two fluids. An example is a wind blowing over water: The instability manifests in waves on the water surface. More generally, clouds, the ocean, Saturn's bands, and the sun's corona show this instability.
Practical CFD models:
SPH method(Smoother particle hydrodynaics)
Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows.Smoothed-particle hydrodynamics is being increasingly used to model fluid motion as well. This is due to several benefits over traditional grid-based techniques. First, SPH guarantees conservation of mass without extra computation since the particles themselves represent mass. Second, SPH computes pressure from weighted contributions of neighboring particles rather than by solving linear systems of equations. Finally, unlike grid-based techniques, which must track fluid boundaries, SPH creates a free surface for two-phase interacting fluids directly since the particles represent the denser fluid and empty space represents the lighter fluid.
SINGLE-FLUID MODEL
A typical approach used for the analysis of two-phase flows is a mixture model, i.e. the individual fluid phases are assumed to behave as a flowing mixture described in terms of the mixture properties. The applied single-fluid model is a five-equation model consisting of the mass, momentum and energy equations for a vapor/liquid mixture, and two equations describing the formation and growth of the liquid phase.
TWO-FLUID MODEL
In the two-fluid model, separate sets of the governing equation for the vapor and liquid phases have been used. The interaction between the droplets and the heat exchange between the liquid phase and the solid boundary are not modelled here as well. Additionally, the velocity slip between vapor and the liquid phase is in this model taken into account.
Turbulence model
Turbulence models are needed to predict the average mixing behaviour in flows that are on average one- or two-dimensional. The approach to the construction of tile turbulence model is guided by the experimental behaviour.The equations governing turbulent flows can only be solved directly for simple cases of flow. For most real life turbulent flows, CFD simulation use turbulent models to predict the evolution of turbulence. These turbulence models are simplified constitutive equations that predict the statistical evolution of turbulent flows.
2.Perform the Rayleigh Taylor instability simulation for 2 different mesh sizes with the base mesh being 0.5 mm. Compare the results by showing the animations( Attach them from your google drive). Observe the differences in the animation and explain the effect of mesh size on simulation. Also, explain why a steady-state approach might not be suitable for these types of simulation.[ Choose Air and Water for this simulation]
Rayleigh Taylor Instability Challenge:
Geometry:
Air:20mm*20mm(Bottom)
Water:20mm*20mm(top)
Meshing:
Case 1
0.5mm Element Size
Nodes:3321
Elements:3200
Transient and pressure based solver
Laminar flow.water and air are multiphase fluid domains
time step:0.005
No of time steps:1500
Solver set-up:
Step 3: Solving using Fluent
Solver - Pressure based , transient solver with Absolute velocity formulation with Gravity of value 9.81 ms2.
Viscous model - Laminar.
Material properties of air, water and user-defined material.
Results:
Residuals:
Animation:
Case 2
0.35mm Element Size
Nodes:6670
Elements:6498
Transient and pressure based solver
Laminar flow.water and air are multiphase fluid domains
time step:0.005
No of time steps:1500
Results:
Residuals:
Animations:
Case 3
0.25mm Element Size
Nodes:13041
Elements:12800
Transient and pressure based solver
Laminar flow.water and air are multiphase fluid domains
time step:0.005
No of time steps:1500
Results:
Residuals:
Animations:
Observation:
In the above cases, the simulation starts with the state of hydrostatic equilibrium and the Rayleigh Taylor instability is observed at the interference when a lower density fluid pushes a higher density fluid due to which formation of shock waves at the interface takes place. Formation of air bubbles starts taking place, which compresses the heavy fluid around it, due to which shock waves of multidimensional fashion generates and it gets more stronger as it moves upward.
It is observed that the more we refine the mesh, the more the simulation results get smoother about the irregularities that take place at the interface of the two fluids. As higher density fluid replaces lower density fluid, the formation of air bubbles and vortex takes place, which travels towards the upward region with time.
In case-3, we can see the more detail results about the formation of waves and the formation of some air bubbles that get trapped at the lower region during the initial stage and then they travel towards the upper region, generating shock waves. At the end of the simulation, it is to be observed that the two phases get separated from each other though, we can see some diffusivity between them which is a volume fraction of air and water.
why a steady-state approach might not be suitable for the above types of simulation?
The difference between the steady and transient is that you can't see the small-time variation of instability. The steady-state simulation is performed if we are concerned more about the final state results or the equilibrium state. In RT-Instability CFD models, we are more concerned to learn about the transition of the irregularities that starts developing when we pour high dense fluid upon low dense fluid under gravity effect so, by using transient solver along with refined mesh of the model, we can compute the smooth transition of irregularities that takes place at the interface of the fluids. The final state results for both the steady-state and transient state will be the same.
In this probleem we are observing the instabilities when it is occuring so we are not concerened about the final answer because steady state is more into caapturing the final results but by transient we can see the behaviour of the solution and every instant such that capturing bubbles,vortec and shockwaves. so this is reason why transient is more suitable than steady state model.
3.Run one more simulation with water and user-defined material(density = 400 kg/m3, viscosity = 0.001 kg/m-s) for refined mesh.
Meshing:
0.25mm Element Size
Nodes:13041
Elements:12800
Transient and pressure based solver
Laminar flow
time step:0.005
No of time steps:1500
Results:
Residuals:
Animations:
4.Define the Atwood Number. Find out the Atwood number for both the cases and explain how the variation in Atwood number in the above two cases affects the behavior of the instability.
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:
A=rho1-rho2/rho1+rho2
where,
rho1=density of heavier fluid
rho2=density of lighter 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 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 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.
For above cases
case 1:
heavier fluid(water)
density 1=998.2 kg/m^3
lighter fluid(air)
density 2=1.225 kg/m^3
Atwood number(A) =(density 1-density2)/(density 1+density2)
Atwood number(A)=0.996
case 2:
heavier fluid(water)
density 1=998.2 kg/m^3
lighter fluid(user-defined material)
density 2=400 kg/m^3
Atwood number(A) =(density 1-density2)/(density 1+density2)
Atwood number(A)=0.427
variation in Atwood number in the above two cases affects the behavior of the instability.
For Atwood number close to 0, RT instability flows take the form of symmetric fingurs of fluid.
When Atwood number close to 1, the much lighter fluid below the heavier fluid takes the form of larger bubble like plumes.
Therefore, from the value of Atwood number it is seen from the simulations that air forms larger bubbles when water is poured down the air pushes through and forms large bubbles. Therefore, the results can be validated by obtaining the value of Atwood number.
Atwood number is an important parameter in the body 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 acceleration due to gravity and 't' is the time.
Atwood number effects on the instability of a uniform interface driven by a perturbed shock wave and Rayleigh Taylor instability :-
The evaluation of a uniform interface subjected to a perturbed shock wave has been experimentally studied over a range of atwood numbers 0.22 <= A <= 0.68 and mach numbers 1.2 <= M <= 1.8 using a vertical shock tube. The perturbed shock wave is produced by diffracting a planar insident shock over a regid cylinder. The wave patterns of the perturbed shock are captured by high speed shadowgraphy while the evoluation of the shock interface is captured by planar Mie scattering. Besides the formation of a cavity and two steps, an apparent counter rotating vortex pair emerges on the shock interface due to the baroclinic vorticity deposition, as both the atwood number and mach number increase, Quantitatively it is interesting to note that the amplitude growth rae of the shocked interface decreases with increasing the atwood number, which is fundamentaly different from the results related to the classical RM instability. This notable features is explained by the approximation of an oblique shock hitting a uniform interface. For weak shock, a suitable time scaling is employed to collapse experimental data irrespective of the Atwood number difference.
Leave a comment
Thanks for choosing to leave a comment. Please keep in mind that all the comments are moderated as per our comment policy, and your email will not be published for privacy reasons. Please leave a personal & meaningful conversation.
Other comments...
Assignment 7-Side Pole Crash Simulation Challenge
AIM :- To create a deck setup for the Neon side crash -BIW and requst for TH (Time History) plots OBJECTIVES:- Check unit system and either follow[Mg mm s] or [Kg mm ms]. Create appropriate interface ,friction 0.2 and recommended parameters. Make sure of no penetrations and intersection,Correct rigid bodies if any issues.…
14 Jul 2021 07:08 AM IST
Assignment 6-Frontal Crash Simulation Challenge
AIM:- To create a deck setup for the FRONTAL CRASH OF CAR BIW and requst for TH (Time History) plots OBJECTIVES:- Check unit system and either follow[Mg mm s] or [Kg mm ms]. Create appropriate interface ,friction 0.2 and recommended parameters. Make sure of no penetrations and intersection,Correct rigid bodies if any issues.…
13 Jul 2021 06:18 AM IST
Assignment 4-RADIOSS Material Laws Challenge
Objective – Run the given Models in Radioss as per the required parameters and compare them using the plots and animations. Given model – impact of a rigid ball on sheet of metal, for all these cases the material laws are changed for the sheet. Case 1 – Law 2 with EPS Max Failure and Failure…
31 May 2021 01:34 PM IST
Assignment 5-RADIOSS Interfaces & Study of Effect of Notches Challenge
OBJECTIVE: The main objective of this challange is to understand the concepts of interface contacts and its application. Also apply the same to the given model by making some changes as given below and study the effects. Create the mesh for bumper assembly,mesh size should be 6mm. Run the crash tube model as it is. Change…
30 May 2021 01:01 PM IST
Related Courses
Skill-Lync offers industry relevant advanced engineering courses for engineering students by partnering with industry experts.
© 2025 Skill-Lync Inc. All Rights Reserved.