Week 2 - Flow over a Cylinder.

1. Flow over cylinder:

In spite of extensive experimental and numerical studies almost over a century, flow around a circular cylinder still remains a challenging problem in fluid mechanics, where intensive investigations are continued even today to understand the complex unsteady dynamics of the cylinder wake flow. Cross-flow normal to the axis of a stationary circular cylinder and the associated problems of heat and mass transport are encountered in a
wide variety of engineering applications. Both experimental measurements and numerical computations have confirmed the onset of instability of the wake flow behind a cylinder beyond a critical Reynolds number, leading finally to a kind of periodic flow identified by definite frequencies, well-known in the literature as the Von Karman vortex street. In case of laminar flow past cylinders with regular polygonal cross-section, the flow
usually separates at one or more sharp corners of the cross-section geometry itself, forming a system of vortices in the wake on either side of the mid symmetry plane. On the other hand, for a circular cylinder, where the point of flow separation is decided by the nature of the upstream boundary layer, the physics of the flow is much more complex than what its relatively simple shape might suggest.

2. Strouhal number:

In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms.

For large Strouhal numbers (order of 1), viscosity dominates fluid flow, resulting in a collective oscillating movement of the fluid "plug". For low Strouhal numbers (order of 10⁻⁴ and below), the high-speed, quasi-steady-state portion of the movement dominates the oscillation. Oscillation at intermediate Strouhal numbers is characterized by the buildup and rapidly subsequent shedding of vortices.

The Strouhal number is often given as

`St=fD/U'`

Where,

f= frequency of vortex shedding

D= characteristic diameter of the cylinder

U'= fluid flow velocity

3. Co-efficient of drag:

In fluid dynamics, the drag coefficient(Cd)">(`Cd`)is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation in which a lower drag coefficient indicates the object will have a less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.

The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag. The drag coefficient of a lifting airfoil or hydrofoil also includes the effects of lift-induced drag. The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.

The drag coefficient `Cd` is defined as

`Cd=2.Fd/rhou^2A`

where:

`Fd` = is the drag force, which is by definition the force component in the direction of the flow velocity,

`rho` = is the mass density of the fluid,

`u` = is the flow speed of the object relative to the fluid,

`A` is the reference area.

4. Co-efficient of lift:

The lift coefficient (`Cl`) 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. C_L is a function of the angle of the body to the flow, its Reynolds number, and its Mach number. The section lift coefficient c_l refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.

where

is the lift force,

is the relevant surface area, and

q is the fluid dynamic pressure, in turn, linked to the fluid density, and to the flow speed.

OUTPUT OF RESULTS AND SOLUTION

There are 2 cases to solve.

In which CASE 1:

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

Where we calculate Reynolds number by using

• = the free stream flow speed
• = a characteristic length parameter of the body or channel
• = the free stream kinematic viscosity

We have 2 parts to this case,

PART 1 :

STEADY-STATE:

PROCESS

GEOMETRY :

All the units are in meters

The diameter of the circle is 2 m, the total length of object being 60x20m, and the distance from the midpoint of the circle to the breath end being 10m.

MESHING:-

• the method used is triangular
• The element size of the mesh is 0.25
• Edge sizing is used around the circle with 36 'number of divisions'
• And inflation used is around the circle with a first-layer thickness of 0.005 and the number of layers is 6
• mesh consist of 20697 nodes and 40502 elements

mesh inflation layers

SETUP
Solver Type	Pressure Based
Velocity Formulation	Absolute
Time	Steady
Viscous Model	LAMINAR
Material	Fluid type: User-defined Where viscosity = 0.05(kg m s) and density = 1(kg/m^3)
Cell zones ff_surface	Fluid type: User-defined
Boundaries	Inlet (velocity inlet) Velocity Magnitude 2.5m/s Temperature – standard(288.16) Outlet x (Pressure outlet) Gauge Pressure – 0 pas. Wall - wall Symmetry - symmetry

scalar residuals :-

vleocity plot

co-eff of drag

co-eff of lift plot

velocity contour

pressure contour

UNSTEADY STATE

PROCESS

SETUP
Solver Type	Pressure Based
Velocity Formulation	Absolute
Time	transent
Viscous Model	LAMINAR
Material	Fluid type: User-defined Where viscosity = 0.05(kg m s) and density = 1(kg/m^3)
Cell zones ff_surface	Fluid type: User-defined
Boundaries	Inlet (velocity inlet) Velocity Magnitude 2.5m/s Temperature – standard Outlet x (Pressure outlet) Gauge Pressure – 0 pas. Wall - wall Symmetry - symmetry

scalar residual polt

co-eff- lift plot

co-off drag polt

velocity contour

pressure contour

PART 2

in this stage we need to calculate the co-efficient of drag and lift for the reynolds number 10,100,1000,10000 & 100000.

For Reynolds number = 10 number of iteration done is 1000

SETUP
Solver Type	Pressure Based
Velocity Formulation	Absolute
Time	Steady
Viscous Model	LAMINAR
Material	Fluid type: User-defined Where viscosity = 0.05(kg m s) and density = 1(kg/m^3)
Cell zones ff_surface	Fluid type: User-defined
Boundaries	Inlet (velocity inlet) Velocity Magnitude 0.25m/s Temperature – standard Outlet x (Pressure outlet) Gauge Pressure – 0 pas. Wall - wall Symmetry - symmetry

scalar residulas

velocity contour

co-eff-lift plot

co-eff-drag plots

velocity monitoring point

pressure contour

For Re = 1000 number of iteration done is 600

SETUP
Solver Type	Pressure Based
Velocity Formulation	Absolute
Time	Steady
Viscous Model	LAMINAR
Material	Fluid type: User-defined Where viscosity = 0.05(kg m s) and density = 1(kg/m^3)
Cell zones ff_surface	Fluid type: User-defined
Boundaries	Inlet (velocity inlet) Velocity Magnitude 25m/s Temperature – standard Outlet x (Pressure outlet) Gauge Pressure – 0 pas. Wall - wall Symmetry - symmetry

scalar residulas

velocity contour

co-eff-lift plot

co-eff-drag plot

velocity monitoring point

pressure contour

For Re = 10000 numbr of iteration is 500

SETUP
Solver Type	Pressure Based
Velocity Formulation	Absolute
Time	Steady
Viscous Model	LAMINAR
Material	Fluid type: User-defined Where viscosity = 0.05(kg m s) and density = 1(kg/m^3)
Cell zones ff_surface	Fluid type: User-defined
Boundaries	Inlet (velocity inlet) Velocity Magnitude 250m/s Temperature – standard Outlet x (Pressure outlet) Gauge Pressure – 0 pas. Wall - wall Symmetry - symmetry

CONCLUSION:

Reynolds Number	`Cd`
10	3.3370620
100	1.3933155
1000	1.2805548
10000	0.92382776

Validation of Cd value obtained for Re=100, with respect to any standard literature: Cd value from the literature for 2-D = 1.4

Cd value obtained from the simulation for Re 100 = 1.393

Percentage of error = [(1.4-1.3933)/1.3353] X 100 = 0.4888%

From the above results following can be observed:

• As the Re increases the coefficient of drag decreases accordingly.
• The increase in Re leads to the shedding of vortices from the upper and lower cylinder surface at a particular frequency. At lower Re=10, there is no formation of vortices. Vortex shedding takes place at higher Re like 100, 1000,and 10000 from the above results obtained from simulation.
• The transient model is appropriate for the Vortex Karman Street phenomenon as it is time-dependent.