Week 2 - Flow over a Cylinder.

Aim: - Vortex shedding simulation over a cylinder in Laminar flow.

Objective: -

• To setup case of steady state and Unsteady state simulation.
• To calculate Reynolds number and its significance over cylinder flow.
• To calculate lift and drag force over the cylinder region.
• To calculate the strouhal number and plot accordingly.
• To use Non-iterative time advancement method to lower the calculation time.

Introduction: -

Flow over a cylinder is one of the basic simulation in the CFD domain. The flow over cylinder study is very complex and periodic flow pattern are seen at lower Reynolds number and after achieving critical Reynolds number value, the flow gets change in the wake region and this wake formation can be studied using literature of Von karman vortex street.

Laminar region to turbulent region is govern by the dimensionless number called Reynolds number which is ratio of inertial forces to viscous forces. This number is measure of different flow criteria over the region can be calculated from density of fluid flow, flow speed, characteristic linear dimension depends upon geometry and dynamic viscosity of fluid. The relationship between Reynolds number and strouhal number can be used to determine the time step for the simulation as for specific Reynolds number, strouhal number is provided in many literatures.

The vortex induced vibration is one of the key aspect which may lead to study of vortex shedding in real life applications such as bridges, aircraft control surfaces, heat exchanger and many others. The vibration caused by the vortex phenomenon due to flow dynamics is need to be studied for the design and development of product at very good scale. The strouhal number is also used with other number in axial flow turbine to determine the frequency of blades over the flow period.

Solving & Modelling Approach: -

The main aim of the project is to study the behavior of Reynolds number on the flow over cylinder. To capture the flow with every regime it is important to have more flow domain and less mesh size to capture every possible vortex in wake region.The problem is divided in two group in which both steady state and unsteady state simulation will be carried accordingly.he simulation will be running for 10,100,1000,10000 and 100000 Reynolds number and accordingly other parameter will be studied.

• The problem will start with 2D geometry of flow field and mesh afterwards.
• It is important to have less mesh size to capture every little details from flow domain.
• The inflation layer will be added near the cylinder.
• This solver is more toward solving time marching problem with greater ease and with less number of iteration.
• The boundary conditions will be simple as velocity inlet and pressure outlet with symmetry wall type condition.
• The cylinder will be also considering as wall type on which coefficient of lift and drag will be calculated.

The Reynolds number calculation is done by given governing equation:

Re=VDρ/μ

Where,

Re = Reynolds number

ρ = Density of Fluid

V = Velocity of Fluid

D = Characteristic length in case of cylinder it is Diameter.

µ = Dynamic viscosity.

CASE 1 :- Simulation of the flow over cylinder with the steady and unsteady case and calculate the Strouhal Number for Re= 100

This simulation involves both steady state solver and unsteady state solver. The solver will be pressure based for both simulations. The velocity required for calculation of Reynolds number of 100 is given as: Re = (VDrho)/mu

Re = 100, D = 2, Density = 1, Viscocity = 0.05

SO, by calculating the equation we get Velocity = 2.5 m/s.

Geometry :-

Meshing :-

• The mesh should be fine enough to compensate for every changes that will create during simulation.
• Mesh size which is used for the steady state and unsteady solver will be same which is 0.25m for overall domain.
• growth rate of 1.2. After applying this value to the geometry the mesh will look like:-

As we have used inflation layer 6

Quality criteria :-

Skewness :-

Material Selection: -

The fluid which is used for the simulation is air with constant density and constant dynamic viscosity. To get required Reynolds number only inlet velocity has been changed respectively. The properties of air are given below:

• Density of Fluid: - 1 kg/m^3.
• Dynamic Viscosity: - 0.05 kg/m-s

Result – Steady State Solver for Re = 100

After initialization of solution we run the simulation for 350 iteration .

Drag coefficient :

Vertex average :

Velocity contour :

Unsteady State Solver for Re = 100

Residual :

Drag coefficient :

Vertex average :

Velocity contour :

Strouhal Number :

Conclusion : It was found that unsteady state simulation provides the result near to the experimentation value.

CASE – 2: - Simulation over cylinder with steady solver for Reynold number of 10,1000,10000,100000

For Re = 10 inlet velocity = 0.25 m/s

Drag coefficent :

Velocity contour :

Re = 1000 inlet velocity = 25 m/s

Drag coefficient :

Velocity contour :

Vertex average :

Re = 10000

Inlet velocity = 250 m/s

Vertex average :

Velocity contour:

Re = 100000

Inlet velocity = 2500 m/s

Drag coefficient :

Velocity contour :

Animation of velocity Contour for Re = 10

Re = 100

Re = 10000

Re = 100000

Comparison Table of Reynold number with Coefficient of Drag & Lift

Conclusion:-

1. It is seen that as Reynolds number is increasing the coefficient of Drag is decreasing and coefficient of lift is increasing.
2. As the Reynolds number increase in value the wake region behind the cylinder is also increasing which results in bigger domain capturization for further simulations.
3. For lower Reynolds number the vortices are bit symmetrical in nature but as Reynolds number get increase it start to deviate more.

Reference Research Paper:- https://www.sciencedirect.com/science/article/pii/S0307904X08000243