Challenge

Steady Vs Unsteady flow over a cylinder

SSuhail Shaikh9 Jun 2020

Title: Steady VS Unsteady flow over cylinder

Aim:

To simulate the flow over a cylinder
To explain the phenomenon of Karman vortex street
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. (with steady solver)
To discuss the effect of Reynolds number on the coefficient of drag.

Introduction:

Phenomenon of Karman vortex street:

Karman vortex street is a repeating pattern of swirling vortices, caused by a process vortex shedding,

which is responsible for the unsteady separation of flow of a fluid around the blunt bodies.

Fig: Karman vortex street

Formula:

This formula will generally hold true for the range 40 < Re_d < 150

where:

f = vortex shedding frequency.
d = diameter of the cylinder
U = flow velocity.
St=Strouhal number

Vortex Shedding:

It is an oscillating flow that takes place when a fluid such as air or water flows past a bluff

body at certain velocities , depending on the size and shape of body.

Simulation Procedure:

GEOMETRY

Dimensions of Geometry:

Diameter of cylinder wall= 2m

Dimensions=10D*30D

Fig: Geometry

MESH GENERATION

Fig: Mesh Generation

Mesh Element size=0.2m

PART - 1 :- Simulating the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.

CASE - A :-Steady flow with Re 100.

We are simulating the flow with the reynolds number of 100 so we need to caliculate the flow velocity required to carried out so from the equation we had ,

Re = ( [ ρ*u*D ] / μ )

We knew Re = 100 , ρ = 1 , D = 2 , μ = 0.05. From the above values we get the Flow velocity as 2.5 (m/s).

So we run the simulation and capture the velocity, pressure contours along with the Drag Coefficient , Lift Coefficient and for having to identify the vortex shedding we need to first add the monitor point at the particular distance so that it helps in getting the vortex shedding frequencies. Here we are using the material as User manual because we are adding the values of the density and dynamic viscosity values manually.And flow type as laminar.

Results :

Fig: Residual Graph Fig: Coefficient of Drag

Fig: Coefficient of lift

Fig: Velocity Contour Fig: Velocity Plane

CASE - B : Unsteady flow with Re = 100.

So we run the simulation to capture the velocity, pressure contours along with the Drag Coefficient , Lift Coefficient and for having to identify the vortex shedding we need to first add the monitor point at the particular distance so that it helps in getting the vortex shedding frequencies. Here we are using the material as User manual because we are adding the values of the density and dynamic viscosity values manually.And Viscous type as laminar. Here we are going to use Turbulent.

Fig: Residual Graph Fig: Coefficient of drag

Fig: Lift Coefficient Fig: Vertex average of velocity magnitude

Here the flow gets converge 55 iterations this makes the flow into steady frequency state.

Fig: Velocity Contour

we can find the strouhal number from the frequency plot,

Sr = ( [0.4 * 2] / 2.5 ) = 0.32

PART 2:-Calculating the coefficient of drag and lift over a cylinder with Steady Solver

Range of Re - 10,100,1000,10000,100000.

CASE 1 :-Steady flow Re 10.

Fig: Drag Coefficient Fig: Lift Coefficient