Week 2 - Flow over a Cylinder.

AIM

Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street.

PART-I

Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.

PART-II

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. [Results should be validated with any standard literature and error should be within 5 %]

Strouhal Number:

In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms. The parameter is named after Vincenc Strouhal, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding and singing in the wind. The Strouhal number is an integral part of the fundamentals of fluid mechanics.

The Strouhal number is often given as

Where f is the frequency of vortex shedding, L is the characteristic length (for example, hydraulic diameter or the airfoil thickness) and U is the flow velocity.

Reynolds number:

The Reynolds number (Re) helps predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent.

Geometry and Meshing:

Procedure:

Material

Steady State Simulations

Case-1: For Re=10; viscosity=0.02; velocity=0.1m/s

Case2: For Re=100; viscosity=0.02; velocity=1m/s

Case3: For Re=1000; viscosity=0.02; velocity=10m/s

Case4: For Re=10000; viscosity=0.02; velocity=100m/s

Case5: For Re=100000 viscosity=0.02; velocity=1000m/s;

Unsteady-Case: For Re=100 viscosity=0.02; velocity=1m/s;

Strouhal Number:

From this reference graph, take 2 reference points on the x-axis b/w 100 and 50. It’s pretty clear that we have 4 cycles b/w these two points.

Frequency = cycles/flow time

= 4/100-50= 0.08

St = Frequency*Length/velocity

= 0.08*2/1 = 0.016.

Observations:

For the low Reynolds number simulation you can clearly observe that there isn’t much phenomenon of vortex shredding which is visible to us. But, as the Reynolds number is increased you can observe vortex shredding coming into play here.

Another observation which we can make here is that as the Re is increasing the value of Cd comes down. This phenomenon is happening because of when Reynolds number get increased, it causes the boundary layer to break before the flow is separated hence amount of drag get decreases and lift increases.

This reduction in drag around the cylinder is exploited in golf. The purpose of providing dimples on golf ball is to trip turbulence in order to decrease drag. Bowlers in cricket, especially the ones that bowl swings would like to have one side of the ball shining than the other. The idea is to keep flow on one side of the ball laminar and the other one turbulent. The ball is to swing from the laminar to the turbulent side.

In the transient case, you can see that the Cl is oscillating and never actually converges. This is happening as the flow is time dependent and also because of the alternative nature of eddies or vortices which are being generated.

References:

• http://www.mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/introvisc/node11.html#:~:text=When%20the%20Reynolds%20numbers%20are,is%20increased%20this%20drag%20decreases.
• https://www.researchgate.net/publication/305876539_A_Numerical_Analysis_of_Fluid_Flow_Around_Circular_and_Square_Cylinders
• https://www.grc.nasa.gov/www/k12/airplane/dragsphere.html#:~:text=For%20most%20aerodynamic%20objects%2C%20the,large%20range%20of%20Reynolds%20numbers.&text=In%20all%20of%20the%20cases,to%20increase%20the%20Reynolds%20number.