Week 2 - Flow over a Cylinder.
Aim:
To simulate the steady and unsteady flow over a cylinder and understand the phenomenon of Karman vortex street.
Theory
Create Geometry in spaceclaim:
1. choose circle of diameter= 2 m
2. rectangular flow domain across the circle, with inlet at 10 D distance from centre, outlet at 20D distance from centre and symmetry walls at 5D distance from centre on both sides
3. after that use pull tool to create surface on rectangular geometry and delete circle from it and also contruction lines
mesh:
1. mesh element type as triangles
2. insert mesh method as automatic, select element size as 0.5 m
3. insert edge sizing to smoothen the mesh around circle, select no. of divisions as 36
4. provide inflation layers as 6 on the cirlce to obtain body fitted mesh
5. define boundaries as inlet, outlet, cylinder wall and symmetry
fluent setup :
PART 1 : Re = 100 - steady state flow
1. solve for steady state, pressure based solver and select laminar in viscous model.
2. create a monitor point at 10 m from centre of circle to study the velocity and vortex formation at that point
3. define a user material with density - 1 kg/m3 and dynamic viscoicty = 0.02 kg/ms to get Re= 100
4. define boundary conditions- inlet velocity = 1 m/s, outlet pressure - 0 Pa, wall = no slip and symmetry boundary condition on the top and bottom lines of the rectangular flow domain
5. define vertex average for velocity magnitude at monitor point
6. define force report to calculate drag coefficient anf lift coefficient plots
7. hybrid initialization and set no. of iterations
8. define solution animation for velocity
9. define contours for velocity and pressure
Results :
1. convergence
it is understood from residual plots of momentum and continuity
it can be seen that solution has reached steady state at around 200 iterations
2. monitor point velocity
it can be seen that vortex formation starts around 100th iteration and vertex average of velocity magnitude at monitor point is 0.504 m/s
3. velocity contour
vortex shedding can be seen at Re= 100 in laminar flow at steady state
4. pressure contour
5. drag coefficient
cd becomes constant after certain iterations at a value of 2.13
6. lift coefficient
significant oscillation seen in lift coefficient and at the end of iterations, value is -0.11
7. strohaul number
in steady state, flow velocity is contant hence there is no time dependant parameter to calculate vortex frequency hence strouhal number cannot be calculated
PART 1 : Re = 100 - unsteady state flow
1. repeat the above procedure with transient simulation
2. time step size = 0.1 s, total time steps = 500
RESULTS
1. convergence
flow is converged after around 1000 iterations
2. monitor point velocity
vertex average of velocity magnitude at monitor point is 0.21 m/s. vortex formation starts at around 45 sec.
3. velocity contour
velocity contour at the end of 50 sec. vortex shedding can be seen in it
4. pressure contour
5. drag coefficient
drag coefficient becomes constant very quickly at a vlue of 2.04
6. lift coefficient
lift coefficient oscillates and value at the ned of 50 sec is -0.0037
7. Strouhal no.
average is 0.25
CONCLUSION FOR PART 1 OF CHALLENGE
| flow type | Re | drag coefficient | lift coefficient | vertex avg of monitor point velocity, m/s | strouhal no. |
| steady state | 100 | 2.13 | -0.11 | 0.504 | -- |
| transient | 100 | 2.04 | -0.0037 | 0.21 | 0.25 |
PART II OF CHALLENGE
perform the above all steps for steady state solver with different values of Re = 10, 1000, 10000, 100000 and plot all the results and compare the values.
(DUE TO LARGE FILE SIZE, IMAGES ARE NOT GETTING UPLOADED, HENCE ONLY TABULAR VALUES PROJECTED HERE)
| Re | inflow velocity, m/s | drag coeff | lift coeff | vertex avg of monitor point velocty, m/s | effect of Re on vortex shedding and drag coeff |
| 10 | 0.1 | 0.054 | -0.04e-6 | 0.051 | no vortex formation |
| 100 | 1 | 2.13 | -0.11 | 0.504 | vortex formation seen |
| 1000 | 10 | 167.12 | -61.13 | 6.89 | vortex formation seen |
| 10000 | 100 | 16319.93 | -7377.95 | 73.01 | vortex formation seen |
| 100000 | 1000 | 1451647 | -181989.23 | 756.95 | vortex formation seen |