Steady Vs Unsteady flow over a cylinder

Definition:

To simulate the steady and unsteady flow over a 2D cylinder. The problem domain is rectangular and has a circular hole in it. To simulate for different cases, we opt to change Reynolds number by changing the velocity of the flow

unsteady flow :

In this type of flow, we are interested in calculating vortex shedding frequency, i.e., Strouhal number and also the lift and drag coefficients for the cylinder.

Geometry :

the geometry was created in Ansys SpaceClaim using pull command

mesh details :

element order - linear

element size - 0.2m

no of elements - 63667

For capturing the boundary layer formed on the cylinder due to the flow of fluid over it, inflation layers are used on the cylinder wall.

orthogonal quality of elements is shown below, and the majority of the elements are above 90%

setup details :

solver - pressure-based (as Mach number is less than 0.3)

time - transient

viscous model - laminar (as Reynolds number is 100)

material properties - density - 1kg/mt3

viscosity - 0.02 kg/mt-s

Boundary conditions - inlet velocity - 1mt/s

outlet pressure - 0Pa

reference values - area - 2 mt2 (projected area in the direction of fluid flow, i.e., the diameter of a cylinder)

density - 1kg/mt2

length - 2mt (diameter of the cylinder)

viscosity - 0.02kg/mt-s

Results :

as the simulation is transient, 3000-time steps were calculated with time step size as 0.02sec

and the residual plots are as below

The velocity graph of a point, created at a distance of 10m from the center of the cylinder is used to conclude whether the flow is converged or not as residual plots don’t converge but follow a trend

a monitor point is created at a distance of 10m from the cylinder, and a velocity plot is obtained.

From the plot, we can see that the flow is converged after 90 seconds as the fluctuating velocity lying between two bounds is same for the rest of the time

from this, we can conclude that the simulation is converged

The coefficient of lift in the plot seems to fluctuate between 0.35 and -0.35. coefficient of drag seems to have a constant value, which is less than 0.2

and the plots of the coefficient of lift and drag are as follows

calculating strouhal number :

For calculating the strouhal number, an FFT plot of the coefficient of lift with Y-axis as magnitude and x-axis as strouhal number is performed and is imported to an excel sheet.

The value corresponding to the max value of magnitude is taken, and the obtained value for this simulation is 0.171

below is the FFT graph of magnitude vs. strouhal number

The above phenomena occur when the rear flow becomes unstable, and the vortex begins to oscillate in an up-down direction. The fully formed vortex is carried away on the surrounding mainstream, and a vortex subsequently occurs on the other side. The vortex then expands before finally dissipating and departing, leaving the circular cylinder. And, every pair of upper and lower vortices behind the cylinder is stored on an alternative array of form twin rows of vortices. These vortices are called the Von Karman Vortex Street.

And vortex shedding is a phenomenon that occurs when these pairs of stable vortices are exposed to small disturbances and become unstable at Re greater than 40. For these values of Re, the boundary layer over the cylinder will separate due to adverse pressure gradient imposed by the divergent geometry of the flow environment at the rear side of the cylinder, and it occurs at a certain frequency which is called as vortex shedding frequency

steady flow :

Geometry: same geometry used in unsteady flow

Mesh: used the same as in unsteady flow.

Setup details (except for case-5):

solver - pressure based

time - steady

viscous model - laminar

materials - air (density- 1kg/mt3 and viscosity - 0.02 kg/m-s)

Boundary conditions - inlet velocity - 100mt/s

outlet pressure - 0Pa

reference values - area - 2 mt2 (projected area in the direction of fluid flow i.e diameter of cylinder)

density - 1kg/mt2

length - 2mt (diameter of cylinder)

viscosity - 0.02kg/mt-s

results of flow patterns corresponding to reynolds number obtained by varying velocity:

	case-1	case-2	case-3	case-4	case-5
Reynolds number	10	100	1000	10000	100000
viscosity(kg/m-s)	0.02	0.02	0.02	0.02	0.02
velocity(mt/s)	0.1	1	10	100	1000

case-1 : Re =10

case-2 : Re=100

case-3 : Re=1000

case-4 : Re=10000

case-5 : Re= 100000

for this case, the k-epsilon model is used to remove the disturbances caused due to high velocity of fluid and

momentum is changed to first-order upwind for convergence of the velocity

comparison of Cd in different cases :

case	Re	Cd
case-1	10	3.3327
case-2	100	1.3788
case-3	1000	0.7688
case-4	10000	0.5762
case-5	100000	0.4624

comparison of velocity contour plots:

By observing these plots, we can say that an increase in Reynolds number caused a transition from a laminar vortex street to turbulence in the wake and then to a wake, which is entirely turbulent. From Re=10000, there is no more creeping in flow, but a separation of the laminar boundary layer. Which resulted in a narrower wake.

comparison of pressure contour plots:

Effect of Reynolds number on the coefficient of drag :

As we observe from the graph, as the Reynolds number increases, the coefficient of drag decreases.there is a drastic drop when Re changed from 10 to 1000, and after that the value of Cd becomes constant