Week 2 - Flow over a Cylinder.

Aim :

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

Objective :

Part-1 :

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

Part-2 :

• 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 %]

Introduction :

Vortex shadding:

vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff (as opposed to streamlined) body at certain velocities, depending on the size and shape of the body. In this flow, vortices are created at the back of the body and detach periodically from either side of the body forming a Von Karman vortex street. The fluid flow past the object creates alternating low-pressure vortices on the downstream side of the object. The object will tend to move toward the low-pressure zone.

If the bluff structure is not mounted rigidly and the frequency of vortex shedding matches the resonance frequency of the structure, then the structure can begin to resonate, vibrating with harmonic oscillations driven by the energy of the flow. This vibration is the cause for overhead power line wires humming in the wind, and for the fluttering of automobile whip radio antennas at some speeds. Tall chimneys constructed of thin-walled steel tubes can be sufficiently flexible that, in air flow with a speed in the critical range, vortex shedding can drive the chimney into violent oscillations that can damage or destroy the chimney.

Reynolds Number (Re):

Reynolds number for a flow is a measure of the ratio of inertial to viscous forces in the flow of a fluid around a body.

`Re=(rho*v*d)/mu`

where

rho = density

v = velocity

D = diameter

mu = dynamic viscosity

The range of Re values will vary with the size and shape of the body from which the eddies are being shed, as well as with the kinematic viscosity of the fluid. Over a large Red range (47

Strouhal number (St):

Strouhal number is a dimensionless number describing oscillating flow mechanisms.

The Strouhal number is often given as

`St=(f*d)/u`

Where

f = frequency of vortex shading,

d = diameter

U = flow velocity.

Flow over a 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.

Co-efficient of drag :

In fluid dynamics, the drag coefficient 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 is defined as

`C_d=(2*F_d)/(rho*u^2*A)`

where:

`F_d` =  drag force.
`rho` = mass density of the fluid.

`u` = speed of the object

A = area.

Co-efficient of lift :

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. The section lift coefficient cl refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.

`C_L=(2L)/(rhou^2S)`

where

L = lift force

S = relevant surface area 

`rho` = density

Explanation :

• Creating the geometry by sketching using the line and circle command, circle diameter of 2m and the dimensions having 20X60m and the circle is placed 20m from the inlet.

• After the geometry the part is loaded.

• 
• we should mesh the loaded part.

• But in the meshing nodes, the shape is more quadrilateral than the triangle so we should this by changing the method to the triangle in the insert option

• After changing the node's shape into triangles we should improve the mesh around the cylinder by sizing in the mesh which is used to control precisely the mesh.

• Then we should add inflation which is used to create body-fitted mesh.

• Then ew should add inflanation which is used to creat body fitted mesh.

• Before opening the set up we should update the mesh. Then we should change the viscous flow to laminar.
• Open Materials and create a fluid that is to be used for the simulation for this case, it is air and also inputs the density and kinematic viscosity values.

PART-1 :

Case 1 :

SOLVER TYPE	PRESSURE BASED
VISCOSITY FORMULATION	ABSOLUTE
TIME	STEADY
VISCOUS MODEL	LAMINAR
FLUID TYPE	USER-DEFINE
VISCOSITY	0.05(kgm/s)
DENSITY	1(kg/m^3)
INLET VELOCITY	2.5(m/s)

RESIDUAL PLOT :

VERTEX AVERAGE OFVELOCITY MAGNITUDE PLOT :

COEFFICIENT OF DRAG PLOT :

COEFFICIENT OF LIFT PLOT :

VELOCITY CONTOUR PLOT :

 PRESSURE CONTOUR PLOT :

 Case 2 :

SOLVER TYPE	PRESSURE BASED
VELOCITY FORMULATION	ABSOLUTE
TIME	UNSTEADY
VISCOUS MODEL	LAMINAR
MATERIAL	USER-DEFINE
VISCOSITY	0.05(kgm/s)
DENSITY	1(kg/m^2)
INLET VELOCITY	2.5(m/s)

RESIDUAL PLOT :

VERTEX AVERAGE OF VELOCITY MAGNITUDE PLOT :

COEFFICIENT OF DRAG PLOT :

COEFFICIENT OF LIFT PLOT :

VELOCITY CONTOUR PLOT :

 PRESSURE CONTOUR PLOT :

 PART-2 :

Case 1 : REYNOLDS NUMBER = 10

SLOVER TYPE	PRESSURE BASED
VELOCITY FORMULATION	ABSOLUTE
TIME	STEADY
VISCOUS MODEL	LAMINAR
FLUID TYPE	USER DEFINE
VISCOSITY	0.05(kgm/s)
DENSITY	1(kg/m^3)
INLET VELOCITY	0.25(m/s)

RESIDUAL PLOT :

VERTEX AVERAGE OFVELOCITY MAGNITUDE PLOT :

COEFFICIENT OF DRAG PLOT :

COEFFICIENT OF LIFT PLOT :

VELOCITY CONTOUR PLOT :

 PRESSURE CONTOUR PLOT :

Case 2 : REYNOLDS NUMBER = 100

SLOVER TYPE	PRESSURE BASED
VELOCITY FORMULATION	ABSOLUTE
TIME	STEADY
VISCOUS MODEL	LAMINAR
FLUID TYPE	USER DEFINE
VISCOSITY	0.05(kgm/s)
DENSITY	1(kg/m^3)
INLET VELOCITY	2.5(m/s)

RESIDUAL PLOT :

 VERTEX AVERAGE OFVELOCITY MAGNITUDE PLOT :

COEFFICIENT OF DRAG PLOT :

COEFFICIENT OF LIFT PLOT :

VELOCITY CONTOUR PLOT :

 PRESSURE CONTOUR PLOT :

Case 3 : REYNOLDS NUMBER = 1000

SLOVER TYPE	PRESSURE BASED
VELOCITY FORMULATION	ABSOLUTE
TIME	STEADY
VISCOUS MODEL	LAMINAR
FLUID TYPE	USER DEFINE
VISCOSITY	0.05(kgm/s)
DENSITY	1(kg/m^3)
INLET VELOCITY	25(m/s)

RESIDUAL PLOT :

VERTEX AVERAGE OFVELOCITY MAGNITUDE PLOT :

COEFFICIENT OF DRAG PLOT :

COEFFICIENT OF LIFT PLOT :

VELOCITY CONTOUR PLOT :

 PRESSURE CONTOUR PLOT :

Case 4 : REYNOLDS NUMBER = 10000

SLOVER TYPE	PRESSURE BASED
VELOCITY FORMULATION	ABSOLUTE
TIME	STEADY
VISCOUS MODEL	LAMINAR
FLUID TYPE	USER DEFINE
VISCOSITY	0.05(kgm/s)
DENSITY	1(kg/m^3)
INLET VELOCITY	250(m/s)

RESIDUAL PLOT :

 

VERTEX AVERAGE OFVELOCITY MAGNITUDE PLOT :

COEFFICIENT OF DRAG PLOT :

COEFFICIENT OF LIFT PLOT :

VELOCITY CONTOUR PLOT :

PRESSURE CONTOUR PLOT :

Case 5 : REYNOLDS NUMBER = 100000

SLOVER TYPE	PRESSURE BASED
VELOCITY FORMULATION	ABSOLUTE
TIME	STEADY
VISCOUS MODEL	LAMINAR
FLUID TYPE	USER DEFINE
VISCOSITY	0.05(kgm/s)
DENSITY	1(kg/m^3)
INLET VELOCITY	250(m/s)

 RESIDUAL PLOT :

VERTEX AVERAGE OFVELOCITY MAGNITUDE PLOT :

COEFFICIENT OF DRAG PLOT :

 COEFFICIENT OF LIFT PLOT :

VELOCITY CONTOUR PLOT :

 PRESSURE CONTOUR PLOT :

 RESULT :

REYNOLDS NUMBER	`C_d`	`C_L`
10	3.332	0.001
100	1.362	-0.048
1000	0.758	0.173
10000	0.832	0.556
100000	0.728	0.286

CONCLUSION : 

• When fluid flows over cylinder, wake region is formed next to cylinder due to decrease in pressure and recirculation of flow occures and hence flow separation occures.
• This phenomenon is happening because of when Reynolds number get increased the surface friction between fluid and cylinder is also increasing which casue the boundary layer to break before flow seperated hence amount of drag get decreases and lift get increases.
• As the Reynolds number increase in value the wake region behind the cylinder is also increasing which results in bigger domain capturization for further simulations.
• For lower Reynolds number the vortices are bit symmetrical in nature but as Reynolds number get increase it start to deviate more.
• It can be seen that the steady state solver are more time friendly compared with transient one but Non-iterative Time Advance method can provide better opportunity to solve same trasient problem with less number iteration and time also.
• And i reffered R.K.Bansal material.