Flow over a Cylinder.
Title :- Flow over cylinder
Aim :-
- To Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.
- To Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000.
- To Discuss the effect of Reynolds number on the coefficient of drag.
Theory :-
Ansys is a very important tool in CFD domain, Ansys fluent facilitates for modelling flow, turbulence, heat transfer and chemical reactions. With Ansys we can accomplice more in less time and with less training. In this study we will create Karman vortex street by simulating flow over cylinder.
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. Karman vortex street is a repeating sequence of swirling vortex, caused by a process known as vortex shedding, which is responsible for the unsteady separation of flow of a fluid around blunt bodies.
Reynolds Number – it is a non-dimensional number, which is used to predict fluid behaviour, whether fluid is steady or unsteady.
Re=ρ⋅v⋅dμ">Re=ρ⋅v⋅dμRe=ρ⋅v⋅dμ
ρ">ρρ = density of fluid(kg/m^3)
v">vv = velocity of fluid(m/s)
d">dd = characteristics length(m)
μ">μμ = kinematic viscosity (Kg/m*s)
Strouhal Number – it is non-dimensional number, used to describe oscillating flow mechanism.
St=fLV">St=fLVSt=fLV
f = frequency of vortex shedding
L = Characteristic length
V = fluid velocity
Drag – it is resistance offered by fluid. This force applies acting opposite towards the motion of the object which is moving submerge in a certain fluid
D=12⋅ρ⋅A⋅V2⋅cd">D=12⋅ρ⋅A⋅V2⋅cdD=12⋅ρ⋅A⋅V2⋅cd
V = relative velocity
A = cross section area of body
Rho = fluid density
cd">cdcd = coefficient of drag
Lift – lift is a force generated perpendicular to the direction of travel for an object moving through a fluid. It is a vector quantity.
L=12⋅ρ⋅A⋅V2⋅cl">L=12⋅ρ⋅A⋅V2⋅clL=12⋅ρ⋅A⋅V2⋅cl
V = relative velocity
A = cross section area of body
Rho = fluid density
cl">clcl = coefficient of lift
Procedure & Results :-
Part 1 :-
Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.
Pre-Processing :-
Geometry setup :-
A two dimensional cylinder and fluid zone is created.
Fig. 2D cylinder and fluid zone
Meshing :-
Fig. Meshed Model
Mesh type - Triangular
Element size – 0.5
Number of inflation layers near feature- 6
Number of elements - 10540
Solver Setup :-
Solver setup will be same for steady state and transient simulation.
Solver type – Pressure based
Solver model – Viscous-Laminar
Material – user defined
- Reynolds number = 100
- density = 1Kg/m^3
- Viscosity = 0.02 Kg/m-s
Boundary conditions –
- Inlet velocity = 1m/s
Post-Processing :-
Steady State -
Fig. Residuals
Fig. Velocity Magnitude
Fig. Von Karman Vortex Street
Strouhal Number –flV">flVflV
l = 2m
f= 520">520520 = 0.25
V = 1m/s
St = 0.25⋅21">0.25⋅210.25⋅21 = 0.5
Unsteady state
Fig. Residuals
Fig. Velocity Magnitude
Fig. Von Karman Vortex Street
Strouhal Number – flV">flVflV
l = 2m
f= 1.510">1.5101.510 = 0.15
V = 1m/s
St = 0.15⋅21">0.15⋅210.15⋅21 = 0.3
Part 2 :-
In this part we need to find coefficient of drag and lift for different Reynolds number. To adjust Reynolds number, we will change viscosity and remaining setting will be same as used in part 1.
|
Reynolds Number |
10 |
100 |
1000 |
10000 |
100000 |
|
Viscosity |
0.2 |
0.02 |
0.002 |
0.0002 |
0.00002 |
Results -
Reynolds Number = 10
Fig. Residuals
Fig. Velocity Magnitude
Fig. Coefficient of Drag
Fig. Coefficient of Lift
Fig. Velocity Contour
Reynolds Number = 100
Fig. Residuals
Fig. Velocity Magnitude
Fig. Coefficient of Drag
Fig. Coefficient of Lift
Fig. Von Karman Vortex Street
Reynolds Number = 1000
Fig. Residuals
Fig. Velocity Magnitude
Fig. Coefficient of Drag
Fig. Coefficient of Lift
Fig. Von Karman Vortex Street
Reynolds Number = 10000
Fig. Residuals
Fig. Velocity Magnitude
Fig. Coefficient of Drag
Fig. Coefficient of Lift
Fig. Von Karman Vortex Street
Reynolds Number = 100000
Fig. Residuals
Fig. Velocity Magnitude
Fig. Coefficient of Drag
Fig. Coefficient of Lift
Fig. Von Karman Vortex Street
Effect of Reynolds Number on Coefficient of Drag :-
The Reynolds number expresses the ratio of inertial forces to viscous forces and skin friction drag depends directly on viscous interaction of the object and the flow. So, every time increase or decrease in Reynolds number will affect drag and its coefficient. Our study proves it, we increased drag and generated drag coefficient. We can see drag coefficient is decreasing with increasing Reynolds number except the last case. This is happening because with increasing Reynolds number the boundary layer gets thinner which results into lower drag.
Reference - Reynolds' Number - an overview | ScienceDirect Topics
Conclusion :-
Ansys is very important tool in CFD domain and it makes task easy, by simulation with accuracy over 90%. In this we simulated flow over cylinder, understood, what is vortex shedding and how to simulate it in Ansys fluent. We make statement about how the Reynolds number affects coefficient of drag.