Week 2 - Flow over a Cylinder.

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

Objective:

PART-I

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

PART-II

1. 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)
2. 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 %]

Theory:

GOVERNING EQUATIONS AND THEORY:
Flow visualization is used to understand the flow past a long circular cylinder held with its axis normal to a steady stream. A
direct experimental method involves the introduction of colored fluid at select points upstream of the cylinder and
photographically records the motion of the particles.
As the flow velocity or the Reynolds number increases, changes are observed in the flow visualization mainly accounting to drag
vs velocity curve. At very low values of Reynolds Number (Re<<1), the lines indicating the paths of the fluid are shown in the
figure below. The pattern is symmetrical. The velocity of fluid decreases as it approaches the body and becomes zero at contact with
the cylinder. This point is called STAGNATION POINT. The velocity increases from A to B and is maximum at B, and later
decelerates to C (v=0), and accelerates further downstream.

Fig. 1 Flow over a cylinder at low Re

As the flow velocity and Re increase, the development of fore-and-aft symmetry is observed. Two small regions are formed just
behind the cylinder in which the fluid does not flow downstream as it does elsewhere, but whirls around in closed paths. These
regions of recirculating flows are called ATTACHED EDDIES. One consequence of this phenomenon is that the flow no longer
follows the contour of the body and is said to be SEPARATED. Another major effect that the increasing Re has on the flow
picture is the modification of the region of disturbance to the flow stream. The distributed region upstream of the body and on
its sides contract, while it elongates in the downstream direction. This region of disturbance downstream is termed WAKE.

Fig. 2 Attached Eddies formation at Re=40

As Re is further increased the size of the two attached eddies increases. These eddies make the flow unstable, and consequently,
when the Re exceeds a value (40) the eddies are shed from the surface and swept downstream. As the eddy shed and swept
away, new eddies are formed, shed, and swept downstream. The eddies on either side of the cylinder shed alternatively and
create an unsteady, albeit periodic, wake flow. The wake of such a flow, with a series of staggered vortices, shed from either side
of the cylinder and swept downstream by the flow is termed as KARMAN VORTEX STREET. It is noticed that for low values of
Re, the velocity at a fixed point varies almost sinusoidally, but as Re increases the periodicity is lost.

Fig. 3 Vortex Shedding at Re=100 and above

The lift coefficient is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the
body, the fluid velocity, and an associated reference area. A lifting body is a foil or a complete foil-bearing body such as a fixed-wing aircraft.CL is a function of the angle of the body to the flow, its Reynolds number, and its Mach number.

PRE-PROCESSOR AND SOLVER SETTINGS:
GEOMETRY:
The geometry is sketched in SpaceClaim. On the XZ plane, a D=2m diameter circle is drawn and enclosed with an inlet side at
10D upstream and outlet side 20D downstream. The symmetry condition used on the other two boundaries at 5D from the
center of the circle. After the geometry is drawn the circle part is deleted and the geometry is extruded outside to create a body.
This is done because, now all the fluid flow is being visualized in the body left, and that is what is required for the simulation.

MESH:
The Meshing tab is opened, and when Generate Mesh is used, a mixture of quadrilaterals and triangles is input in the mesh
domain. The Element size of Mesh is set to 0.25m. To create a uniform mesh, a New Method is inserted into the mesh and
The tetrahedron method is selected. To improve the sizing on the edge od the circle, the Sizing option is inserted in the Mesh and
the Number of Divisions is increased to 36 so that there exists one mesh element every 10 degrees of the circle's circumference.

Fig. 6 Uniiform Tetrahedron Mesh

An Inflation Layer is added into the mesh to better visualize the flow at the surface of the circle. The First Layer thickness is set
to, the number of layers to 6 and the successive percentage increase in thickness to 20%.

Fig. 7 Inflation Layers on the circumference of the cylinder (circle)

Later the respective sides are selected and named Inlet (upstream-left), Outlet (downstream-right), Wall (Circle circumference)
and Symmetry Boundary (Above and below the circle) accordingly.

SOLUTION:
PART I:
STEADY STATE (Re=100):

The simulation was run for 300 iterations. The convergence criteria established was the plot for Residuals. Even though the
continuity and velocity residual plots increased in magnitude as the vortex shedding started, they maintain a steady value and
show minimal fluctuations. Therefore, they can be considered as converged for the current simulation.

TRANSIENT STATE (Re=100)

PART II:

Comparing the steady flow with different reynolds number:
Density = 1kg/m^3
viscosity =0.02 kg/m.s
itertions =600(for 1,2,3,4,& 5 cases);
Case:1:
Re=10 ; u=0.1 m/s

From the above plots ,
We can conclude that the flow is steady and converged because curves in residuals reached the constancy.
At very slow flow in which we have neglected viscosity entirely. so there will be no separation of flow and no viscous wake
downstream of the cylinder

Case:2:
Re= 100 ; u=1 m/s

From the above plots,
We can conclude that the flow is steady and converged because curves in residuals reached the constancy.
A stable pair of vortices are formed on the downwind side of the cylinder. the flow is separated but steady and the vortices
generate a high drag on the cylinder.

Case:3:
Re= 1000 ; u=10 m/s

From the above plots ,
We can conclude that the flow is steady and converged because curves in residuals reached the constancy.
In this, the flow velocity is increased. The downstream vortices become unstable, separate from the body, and are alternately shed
downstream. The wake is very wide and generates a large amount of drag

Case:4:
Re= 10000(10^4); u=100 m/s

From the above plots,
We can conclude that the flow is steady and converged because curves in residuals reached the constancy.
The flow velocity is increased even more. The periodic flow breaks down into a chaotic wake. The flow in the boundary layer on
the windward side of the cylinder is laminar and orderly and the chaotic wake is initiated as the flow turns onto the leeward side
of the cylinder.

Case:5:

Re= 100000(10^5) ; u=1000 m/s

Flow is even increased at higher velocity. the boundary layer transitions to chaotic turbulent flow with vortices of many
different scales being shed in a turbulent wake from the body.

Conclusion
An increase in Reynolds number also increases the drag and lift values simultaneously.
DragonForce that is exerted by the following fluid on the cylinder depends on the Reynolds number of the flow.
With the increase in the Reynolds number, the flow is becoming more unsymmetrical.
increasing velocity eventually brings the turbulent drag up to and even higher than the laminar drag value.