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 and till this date the research is still going on to study the unsteady behavior caused by the flow. 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. Considering any other object compared to cylinder most of them cause boundary layer detachment due to the effect of geometry feature like sharp edges but in the case of cylinder this point of separation is very complex and depend upon nature of upstream boundary layer and other flow parameters.

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. As the flow in the wake region may be have periodic motion hence can have certain frequency over which it resonate. If this frequency gets match with structural frequency of object, then it may cause phenomenon called resonance. This frequency of motion can be given by another dimensionless number called strouhal number which is used to determine frequency over flow rate. 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. In steady state simulation the varying Reynolds number will be taken into consideration by maintaining fluid property constant. The 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 to capture boundary layer detachment from the surface of cylinder. As it is stand to perform the unsteady state simulation this project will incorporate special method to solve the problem with traditional method and NITA method i.e. non iterative time advancement. 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.

For steady state solver SIMPLE interpolation scheme will be used to calculate results in neighboring volume. Unsteady state simulation will be done using two interpolation scheme one is SIMPLE and other one is PISO with NITA. To check for convergence of solution we will create some plots which have vertex average velocity 8m behind the cylinder which will be used to plot strouhal number later using FFT option in FLUENT. After that lift coefficient and drag coefficient will be calculated on the cylinder wall.

To check for vorticity only in FLUENT we will create a custom function which called as Q-criterion this is the one of the way of qualifying the wake vortices. The formula for Q-criterion is given by:

The Reynolds number calculation is done by given governing equation:

Where,

Re = Reynolds number

ρ = Density of Fluid

V = Velocity of Fluid

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

µ = Dynamic viscosity.

The coefficient of drag and lift are the function of respective lift and drag force with density of fluid and velocity with exposure area in front. The equation for coefficient of lift and drag is given as:

Where,

Fd and Fl are drag force and lift force respectively.

ρ = Density of Fluid

V = Velocity of Fluid

A = Frontal Area.

CASE – 1: - Simulation over cylinder with steady and unsteady solver for Reynolds number 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:

Geometry: -

In above geometry sketch we can see cylinder of 2m diameter which is immersed in the fluid domain of 20 x 60 m dimension. The inlet of domain is 20m left from center of cylinder and outlet is 40m right from center of cylinder. There is no thickness provided to the geometry as it is a 2D simulation. After providing the details the geometry will be:

Meshing: -

The meshing involves the creation of small discrete domain for calculation of governing equations. 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. It is important to capture flow around cylinder as flow separation seizure. To capture the flow near cylinder the inflation layer is need to be used. Inflation will create hexahedral mesh near the cylinder which makes solution convergence and will provide accurate solution.

Before inflation layer creation it required to capture the boundary of cylinder by using edge sizing local meshing method. For edge sizing mesh size or number of layers can be used as user input. For this case mesh size near the boundary is taken as 0.01m. The inflation layer property is first layer thickness in which height of first layer is 0.05 and amount of layer are 9 for capturing more area near the cylinder with growth rate of 1.2. After applying this value to the geometry the mesh will look like:

The mesh near the cylinder is seen as:

The mesh having both tetrahedral element and hexahedral element with 1^st order degree of accuracy. The mesh quality which need to checked are skewness and orthogonal quality of elements. The skewness quality should have most element near to 0 which shows better element quality and opposite to skewness, orthogonal quality should have more element near to 1 which represents better quality of elements.

Skewness quality

Orthogonal Quality

To make sure FLUENT read the boundary condition from workbench named selection should be provided according to flow parameters. The problem has velocity inlet and pressure outlet boundary conditions. The cylinder is considering as wall and other two edges are considering as symmetry boundary conditions.

 

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: - 0.02 kg/m-s

Solver setting: -

The main important setting for the simulation is reference value setting in the FLUENT. It will change the value with respect to the reference frame from previous value of updated value.

The method which is used for simulation of steady state and unsteady state simulation will be SIMPLE interpolation scheme. Later for the same unsteady state simulation we will be using NITA algorithm to faster the solution time compared to SIMPLE method. It is important to create the report to check for the convergence of simulation.

The first report will be vertex average of velocity which will be taking data from 8m from center of cylinder in X-axis. This data will later use to generate strouhal number from this report. Later report which will be required to generate are force report in which coefficient of drag and lift are need to be generated. For coefficient of drag wall should be select as cylinder and there should be 1 in x-axis for drag and respectively 1 for y-axis to calculate lift coefficient.

As a steady state solver does not have time as parameter, then to check the animation of flow as it gone past the cylinder, the contour animation plot need to be generated. This can be done after making initialization of solution first, after that solution animation is used as tool to create contour as solution progresses.

From the above image it can be seen that interior surface need to be selected on which velocity magnitude has to be seen as contour. Similar to it we can also make animation of report of vertex average, residual and coefficient of drag plot.

 

Result – Steady State Solver for Re = 100

After initialization of solution we run the simulation for 1200 iteration. Here convergence is not mainly important parameter to consider rather than that flow has to be stabilize for longer period so as to capture vortices in the wake region of flow domain.

1) Residual

2) Coefficient of Drag

3) Coefficient of Lift

4) Vertex average

5) Velocity Contour

 

6) Pressure Contour

Result – Unsteady State Solver with SIMPLE Pressure Velocity Coupling.

1) Residuals

2) Coefficient of Drag

3) Coefficient of Lift

4) Vertex Average

5) Velocity Contour

Result – Unsteady State Solver with NITA solver.

The NITA solver as discuss earlier is much faster with respect to simple pressure velocity coupling solver. This solver only accessed by using PISO solver in which further down non-iterative time advancement method is provided. In this method the transient formulation is selected as Bounded second order implicit which is 20% more faster. The setup for NITA is given below

1) Residuals

2) Coefficient of Drag

3) Coefficient of Lift

4) Velocity Contour

5) Strouhal Number

The strouhal number is calculated by going into plot option in FLUENT in which FFT option has to be choose. In FFT option Y axis function should be Magnitude and X axis function should be strouhal number. After that we need to provide the file of coefficient of lift from simulation and fed to the window to calculate the FFT of lift coefficient which further provide strouhal number. In above case of Unsteady state simulation, the strouhal number is 0.168 which is correct and near to the experimentation result provided by Eric Williams et.al it his paper ‘Simulation of cross flow Induced vibration”

 

Conclusion: -

• After running both the simulation respectively for steady state and unsteady state simulation it was found that unsteady state simulation provides the result near to the experimentation value validated from the research paper.

Solver	Coefficient of Drag	Coefficient of Lift	Time Taken
Steady State Solver	1.48	0.05	7 min 23 sec
Unsteady State solver (SIMPLE Method)	1.31	0.048	21 min 02 sec
Unsteady state solver (NITA Method)	1.43	0.06	13 min 56 Sec
Experimentation value	1.30	0.045

• If we compare the velocity contour from both steady state simulation and unsteady state simulation, there was more realistic vortex generation is shown in transient simulation as compare to steady state. Hence to capture the flow phenomenon effectively it is better to go with transient solvers.
• To make the comment about convergence, it can be seen that from steady state solver the solution gets converged after 600 iterations and after that it shows similar fluctuations. But in case of transient simulation it very hard to predict the convergence from residual, hence we need to take a look at vertex average plot to get the convergence idea.
• The q-criterion vortices generation plot was not seen in case of Re = 100 because of, this case still providing vortices in periodic nature in wake region.
• To save the time it was good practice to use Non-Iterative Time Advancement method provided in PISO pressure-velocity coupling method. As it has drastically lower the time of solution compared to SIMPLE pressure-velocity method.

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

1) Velocity Contour plot 

Re=10

Re=100

Re=1000

Re=10000

Re=100000

2) Coefficient of Drag

Re=10

Re=100

Re=1000

Re=10000

Re=100000

3) Coefficient of Lift

Re=10

Re=100

Re=1000

Re=10000

Re=100000

Comparison Table of Reynold number with Coefficient of Drag & Lift

Reynolds Number	Coefficient of Drag	Coefficient of Lift
10	3.37	0.0011
100	1.31	0.048
1000	1.08	0.433
10000	1.18	0.562
100000	0.85	0.672

 

Conclusion: - 

1) If we compare the data in the table, it is seen that as Reynolds number is increasing the coefficient of Drag is decreasing and coefficient of lift is increasing. This data is compared with research paper given for reference and another research paper titled as "Simulation of Cross flow Induced Vibration" by Eric Williams et. al.

This phenomenon is happening because of when Reynolds number get increased the surface friction between fluid and cylinder is also increasing which casue the boundary layer to break before flow seperated hence amount of drag get decreases and lift get increases.

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.

4) It can be seen that the steady state solver are more time friendly compared with transient one but Non-iterative Time Advance method can provide better opportunity to solve same trasient problem with less number iteration and time also.