Week 2 - Flow over a Cylinder.
AIM:
The aim of this assignment is to simulate a user defined material over the cylinder with different Reynold's number and explain the phenomenon of Karman vortex street.
INTRODUCTION:
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.
- Flow past a cylinder and two circular cylinders in tandem configuration are common occurrences in many engineering applications, such as mooring lines, riser, and bundled cylinders at offshore installations, bridge piers, and tube bundles in heat exchangers.
-
Describing in exhaustive way the flow around cylinder with all of its flow properties opens the way of studying further more complex shapes like hulls of the ships and submarines.
REYNOLD'S NUMBER:
`Re = (rho*V*D)/mu`
where,
`rho` = Density of the fluid
`V` = Velocity of the fluid flow
`D` = Diameter of the cylinder
`mu` = Dynamic Viscosity of the fluid
STROUHAL NUMNBER:
`St = (fL)/V`
where,
`f` = frequency of the Vortex Shedding
`L` = Characteristics Length or Hydraulic Diameter
`V` = Velocity of the fluid flow
DRAG COEFFICIENT:
`C_D = (2*F_D) / (rho*V^2*A)`
where,
`F_D` = Drag Force
`rho`= Density of the fluid
`V` = Velocity of the fluid flow
`A` = Reference area
LIFT COEFFICIENT:
`C_L = (2*F_L) / (rho*V^2*A)`
where,
`F_L` = Lift Force
`rho`= Density of the fluid
`V` = Velocity of the fluid flow
`A` = Reference area
VORTEX SHEDDING:
- In fluid dynamics, 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.
OBJECTIVE:
The objective of this assignment is to:
- Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.
- Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000. (Steady solver)
- Discuss the effect of Reynolds number on the coefficient of drag.
- Plots showing velocity at a particular point.
- Plots showing the coefficients of drag and lift.
- Pressure and Velocity contour plots.
- To see the Vortex Shedding.
- To calculate the Strouhal Number.
METHODOLOGY:
We will be solving the above problem in Ansys Fluent.
PART - 1:
CASE 1:
- Using Steady state solver
- Using user defined material for varying the Reynold's Number
- Density = 1 Kg/m^3
- Velocity = 1 m/s
- Diameter of the cylinder = 2m (constant)
- Dynamic Viscosity = 0.02 Kg/(m-s)
- Reynold's Number = 100
GEOMETRY:
We need to create a closed flow region inside which the fluid will flow and a create a cylinder in between the 2D space region.
MESH:
We need to create a very fine mesh with edge sizing and inflation layers.
SETUP:
RESULTS:
RESIDUALS:
VELOCITY MONITOR POINT:
LIFT COEFFICIENT:
DRAG COEFFICIENT:
VELOCITY CONTOUR:
PRESSURE CONTOUR:
STROUHAL NUMBER:
The value of Strouhal number is 0.0852.
VALUES:
CASE 2:
- Using Transient state solver
- Using user defined material for varying the Reynold's Number
- Density = 1 Kg/m^3
- Velocity = 1 m/s
- Diameter of the cylinder = 2m (constant)
- Dynamic Viscosity = 0.02 Kg/(m-s)
- Reynold's Number = 100
GEOMETRY:
We need to create a closed flow region inside which the fluid will flow and a create a cylinder in between the 2D space region.
MESH:
We need to create a very fine mesh with edge sizing and inflation layers.
SETUP:
RESULTS:
RESIDUALS:
VELOCITY MONITOR POINT:
LIFT COEFFICIENT:
DRAG COEFFICIENT:
VELOCITY CONTOUR:
PRESSURE CONTOUR:
STROUHAL NUMBER:
The value of Strouhal number is 0.109.
VALUES:
TABULATION:
| SOLVER | REYNOLD'S NUMBER | DRAG COEFFICIENT | STROUHAL NUMBER |
| STEADY STATE | 100 | 1.3356022 | 0.0852 |
| TRANSIENT STATE | 100 | 1.3715761 | 0.109 |
PART - 2:
CASE - 1:
- Using Steady state solver
- Using user defined material for varying the Reynold's Number
- Density = 1 Kg/m^3
- Velocity = 0.1 m/s
- Diameter of the cylinder = 2m (constant)
- Dynamic Viscosity = 0.02 Kg/(m-s)
- Reynold's Number = 10
GEOMETRY:
We need to create a closed flow region inside which the fluid will flow and a create a cylinder in between the 2D space region.
MESH:
We need to create a very fine mesh with edge sizing and inflation layers.
SETUP:
RESULTS:
RESIDUALS:
VELOCITY MONITOR POINT:
LIFT COEFFICIENT:
DRAG COEFFICIENT:
VELOCITY CONTOUR:
PRESSURE CONTOUR:
VALUES:
CASE - 2:
- Using Steady state solver
- Using user defined material for varying the Reynold's Number
- Density = 1 Kg/m^3
- Velocity = 1 m/s
- Diameter of the cylinder = 2m (constant)
- Dynamic Viscosity = 0.02 Kg/(m-s)
- Reynold's Number = 100
GEOMETRY:
We need to create a closed flow region inside which the fluid will flow and a create a cylinder in between the 2D space region.
MESH:
We need to create a very fine mesh with edge sizing and inflation layers.
SETUP:
RESULTS:
RESIDUALS:
VELOCITY MONITOR POINT:
LIFT COEFFICIENT:
DRAG COEFFICIENT:
VELOCITY CONTOUR:
PRESSURE CONTOUR:
VALUES:
CASE - 3:
- Using Steady state solver
- Using user defined material for varying the Reynold's Number
- Density = 1 Kg/m^3
- Velocity = 10 m/s
- Diameter of the cylinder = 2m (constant)
- Dynamic Viscosity = 0.02 Kg/(m-s)
- Reynold's Number = 1000
GEOMETRY:
We need to create a closed flow region inside which the fluid will flow and a create a cylinder in between the 2D space region.
MESH:
We need to create a very fine mesh with edge sizing and inflation layers.
SETUP:
RESULTS:
RESIDUALS:
VELOCITY MONITOR POINT:
LIFT COEFFICIENT:
DRAG COEFFICIENT:
VELOCITY CONTOUR:
PRESSURE CONTOUR:
VALUES:
CASE - 4:
- Using Steady state solver
- Using user defined material for varying the Reynold's Number
- Density = 1 Kg/m^3
- Velocity = 100 m/s
- Diameter of the cylinder = 2m (constant)
- Dynamic Viscosity = 0.02 Kg/(m-s)
- Reynold's Number = 10000
GEOMETRY:
We need to create a closed flow region inside which the fluid will flow and a create a cylinder in between the 2D space region.
MESH:
We need to create a very fine mesh with edge sizing and inflation layers.
SETUP:
RESULTS:
RESIDUALS:
VELOCITY MONITOR POINT:
LIFT COEFFICIENT:
DRAG COEFFICIENT:
VELOCITY CONTOUR:
PRESSURE CONTOUR:
VALUES:
CASE - 5:
- Using Steady state solver
- Using user defined material for varying the Reynold's Number
- Density = 1 Kg/m^3
- Velocity = 1000 m/s
- Diameter of the cylinder = 2m (constant)
- Dynamic Viscosity = 0.02 Kg/(m-s)
- Reynold's Number = 100000
GEOMETRY:
We need to create a closed flow region inside which the fluid will flow and a create a cylinder in between the 2D space region.
MESH:
We need to create a very fine mesh with edge sizing and inflation layers.
SETUP:
RESULTS:
RESIDUALS:
VELOCITY MONITOR POINT:
LIFT COEFFICIENT:
DRAG COEFFICIENT:
VELOCITY CONTOUR:
PRESSURE CONTOUR:
VALUES:
TABULATION:
|
REYNOLD'S NUMBER |
COEFFICIENT OF DRAG | COEFFICIENT OF LIFT |
| 10 | 3.324157 | 0.000932039 |
| 100 | 1.3356022 | -0.04756705 |
| 1000 | 0.72393504 | 0.24208664 |
| 10000 | 0.76135553 | -0.25792059 |
| 100000 | 0.75462316 | 0.37194198 |
VALIDATION:
|
REYNOLD'S NUMBER |
THEORETICAL COEFFICIENT OF DRAG |
ACTUAL COEFFICIENT OF DRAG |
ERROR (%) |
| 10 | 3.4 | 3.324157 | 2.23 |
| 100 | 1.4 | 1.3356022 | 4.6 |
CONCLUSION:
- From the comparison between steady state analysis and transient state analysis for flow over a cylinder it can be concluded that steady state simulations are performed to get the final result we cannot get the solution between it, so any intermediate solution that we get is not time accurate.
- Transient state analysis is time dependent and are performed to get the intermediate solution for any time interval.
- From the comparison between Reynold's Number we can say that for Reynold's Number 10 no Vortex Shedding is present and for Reynold's Number more than 100 we can see the Vortex Shedding phenomenon.
- Also, from the above we can conclude that Drag coefficient is inversely proportional to Reynold's Number as the Reynold's Number increases Drag coefficient decreases.
REFERENCE:
- https://www.sciencedirect.com/science/article/pii/S0307904X08000243
- https://www.researchgate.net/publication/274309261_Computational_analysis_of_the_flow_around_a_cylinder_and_of_the_drag_force
- Book - FLUID MECHANICS BY FRANK M. WHITE
- Book - FLUID MECHANICS BY PHILIP J. PRITCHARD