Week 2 - Flow over a Cylinder.
AIM: - Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street.
Objectives: -
1. Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.
2. Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000. (Run with steady solver).
Discuss the effect of Reynolds number on the coefficient of drag.
In both approaches, show that the flow has converged. That is, what quantities or plots need to be looked at to determine that the flow has converged?
Plots of the coefficient of drag and lift.
Plots to show vortex shedding behind the cylinder.
Solution:
The given problem is solved using ANSYS WORKBENCH using the Fluent project environment. The steps are as follows:
STEP 1: Creating the model geometry.
The model geometry is generated in SpaceClaim consisting of an infinite length solid cylinder of 2m diameter enclosed in an infinite length cuboidal control volume, as shown in the figures below:
STEP 2: Meshing:
In this step, the given geometry is meshed with global size of 0.25m with Triangular being the method.
The cylinder wall is meshed using 36 divisions through Edge Method.
The cylinder wall geometry is captured through body fitted mesh with the help of 6 Inflation layers, as shown below:
The mesh is then assigned with the names of the respective boundaries.
STEP 3: - Problem Setup
In this step the given model will be added on with the necessary boundary conditions, loading or flow conditions. The material media is added to the control volume of the given model.
The Inlet boundary is assigned with certain velocity depending upon the value of the Reynold’s number.
The Outlet boundary is assigned as the Pressure based boundary.
Control Volume domain is assigned with a User Defined material having absolute Viscosity equal to 0.05 Pa – Sec and the density as 1 Kg/m3.
The flow is set to be Laminar Flow and energy considerations are neglected in the problem.
The different outputs which are desired from this analysis are created and the specific output data of Drag and Lift Coefficients, Pressure and Velocity data at some specific reference location will be plot and the animations will also be obtained after successful completion of the analysis.
Initialise the model to see the initial pressure and velocity conditions in the control volume.
Before starting, the Check Convergence checkbox must be kept unchecked, so that the analysis can run for all the timesteps and not stops after the solution convergence is achieved.
STEP 4: - RESULTS:
1. Steady State Flow:
The Reynolds Number is given by
Re = ρ⋅V⋅D/μ
Viscosity = 0.05 Pa. Sec
Diameter = 2m
On substituting all data, the Re value is equal to:
Hence, for different values of Re, the flow velocity is known.
a) Re = 10.
For this Re value, the velocity is equal to 0.25 m/sec, substitute this as inlet velocity and run the analysis. Results are shown below:
Weighted Residual:
Coefficient of Lift:
Coefficient of Drag:
Probe Location Average Pressure:
Probe Location Average Velocity:
Probe Location Average Velocity Contour:
Probe Location Average Pressure Contour:
Pressure Animation:
Velocity Animation:
b) Re = 100.
For this Re value, the velocity is equal to 2.5 m/sec, substitute this as inlet velocity and run the analysis. Results are shown below:
Weighted Residual:
Coefficient of Lift:
Coefficient of Drag:
Probe Location Average Pressure:
Probe Location Average Velocity:
Probe Location Average Velocity Contour:
Probe Location Average Pressure Contour:
Pressure Animation:
Velocity Animation:
c) Re = 1000.
For this Re value, the velocity is equal to 25 m/sec, substitute this as inlet velocity and run the analysis. Results are shown below:
Weighted Residual:
Coefficient of Lift:
Coefficient of Drag:
Probe Location Average Pressure:
Probe Location Average Velocity:
Probe Location Average Velocity Contour:
Probe Location Average Pressure Contour:
Pressure Animation:
Velocity Animation:
d) Re = 10000.
For this Re value, the velocity is equal to 250 m/sec, substitute this as inlet velocity and run the analysis. Results are shown below:
Weighted Residual:
Coefficient of Lift:
Coefficient of Drag:
Probe Location Average Pressure:
Probe Location Average Velocity:
Probe Location Average Velocity Contour:
Probe Location Average Pressure Contour:
Pressure Animation:
Velocity Animation:
e) Re = 100000.
For this Re value, the velocity is equal to 2500 m/sec, substitute this as inlet velocity and run the analysis. Results are shown below:
Weighted Residual:
Coefficient of Lift:
Coefficient of Drag:
Probe Location Average Pressure:
Probe Location Average Velocity:
Probe Location Average Velocity Contour:
Probe Location Average Pressure Contour:
Pressure Animation:
Velocity Animation:
2. Transient State:
For the transient case, the Re = 100, thus, the flow velocity is 2.5 m/s.
With this, the setup for transient analysis is done and the required results are as follows:
Weighted Residual:
Coefficient of Lift:
Coefficient of Drag:
Probe Location Average Pressure:
Probe Location Average Velocity:
Probe Location Average Velocity Contour:
Probe Location Average Pressure Contour:
Strouhal Number:
Pressure Animation:
Velocity Animation:
STEP 5 Conclusions:
From the above analysis it can be seen that:
How the flow behaves as the fluid flows pasts the cylinder, the pressure waves are created alternatingly from the top and bottom regions of the rear face of the cylinder. As a result, the velocity in those regions is also fluctuating in similar fashion. This phenomenon is known as the Von karman Vortex shredding.
In Steady state analysis, the vortex shredding phenomenon is not occurring for the Re = 10 case and as the Re is increased the vortex shredding starts to appear with maximum capturing occurring for the Re = 100000 case.
The transient analysis captures the realistic results since it is observed that vortex shredding will occur as the Re goes beyond 40.
As the Re increases, the Lift coefficient is seen to increase and the wavelength is large, however the Drag coefficient also increases but the wavelength is quite small compared to Lift coefficient.