Week 2 - Flow over a Cylinder.
- AIM:
The main aim of the project is to simulate the flow over cylinder for steady and unsteady cases and calculate to the strouhal number for Re=100.
- 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.
- 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.
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:
`Re=(rho*v*L)/mu`
v = 100*0.02/1*2 = 1 m/s
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.
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 6 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 walls :
- 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 Settings:
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,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.
INLET VELOCITY:
STEADY-STATE SIMULATION OUTPUT(RE=100):
After initialization of solution we run the simulation for 350iteration. 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.
Residual:
Coefficient of Drag:
Coefficient of Lift:
Vertex Average:
Velocity Contour:
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.
Lift and Drag coefficient:
UNSTEADY-STATE SIMULATION OUTPUT(RE=100):
Residual:
Drag coefficient:
Lift Coefficient:
Vertex Average:
Velocity countour:
Drag and Lift coefficients:
Strouhal Number:
COMPARISION:
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 | DRAG COEFFICIENT | LIFT COEFFICIENT | STROUHAL NUMBER |
| STEADY-STATE | 1.31 | 0.102 | 0.029 |
| UN-STEADY STATE | 1.23 | -0.00091 | 0.172 |
| EXPERIMENT VALUES | 1.33 | 0.179 | 0.156 |
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.
CASE-2 SIMULATION OVER CYLINDER WITH STEADY STATE SOLVER FOR REYNOLDS NUMBER OF 10,100,1000,10000,100000:
RESIDUAL:
LIFT COEFFICIENT:
DRAG COEFFICIENT:
VERTEX AVERAGE OF VELOCITY MAGNITUDE:
VELOCITY COUNTOUR:
- CONCLUSION:
| REYNOLD'S NUMBER | COEFFICIENT OF DRAG |
| 10 | 3.35 |
| 100 | 1.31 |
| 1000 | 1.30 |
| 10000 | 1.31 |
| 100000 | 0.97 |
If we compare the data in the table, it is seen that as Reynolds number is increasing the coefficient of Drag is decreasing. 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.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.For lower Reynolds number the vortices are bit symmetrical in nature but as Reynolds number get increase it start to deviate more.
- REFERENCES: