Challenge

Steady Vs Unsteady flow over a cylinder

CChinmaya Bhakta12 Aug 2020

# Aim of the challenge as follows:

1. To run steady and unsteady state simulation for flow over a cylinder at Re = 100 and hence calculate the strouhal number.

2. Calculate the drag coefficient for flow over a cylinder (steady state) at different reynolds number and to study the effect of reynolds number on drag coefficient.

# Introduction

* Flow over cylinder is a classic study in fluid mechanics. When fluid flow past a cylinder at certain reynolds number we can observe repeating pattern of swirling vertices in the wake of the cylinder this is called von karman street and this happens because of a process known as vortex shedding.

Study of vortex shedding is of due importance because it has its own implications. As an example consider a distribution pipe (circular cross section) which distributes oil/gas, these distribution pipes when subjected to fluid flow externally there is a chance that this external fluid flow can cause vortex shedding, because of the vortex shedding the pipes will start vibrating and if the vibration reaches the threshold frequency it will break. Hence the study and understanding the vortex shedding phenomena and measures to reduce the same are of due imprortance.

Vortex shedding can be measured in terms of a dimensionless number called strouhal number, which is given as

`str = ((f*L)/V)`

where f - frequency (Hz).

L - characteristic length (Diameter of pipe or sphere).

V - Flow velocity (m/s).

Larger the vortex shedding larger will be the frequency and hence larger strouhal number. A typical illustration of von karman effect is as shown below.

#Simulations:

In this challenge we are carrying out a 2D simulation the set up for the same is as shown below

# Meshing and geometry preparation:

* First the type of mesh is changed from type quadrilateral to triangular using the method option. Updated mesh will look as follow.

* If we observe the edge of the cylinder in the above screen shot it is clearly visible that the edge is not smooth, to make it smooth so as to capture the flow parameters properly at the edge we can use the sizing option. Selecting the edge and and applying a total number of 10 divisions makes the edge much smoother. a grab of the same is as shown below,

* Since in this simulations we are concerned about the flow around cylinder, it will be better if we take care of the cells around the cylinder and hence inflation layers are introduced near the edge. Inflation layers are also called as body fitted mesh and it helps in capturing the normal gradients with minimal number of cells.

Inflation layers are added using the inflation option and further selcting first layerthickness and inserting maximum layers 6, when generated we get the mesh around the cylinder as follow,

At this point the mesh generated is good and hence we can proceed to run the simulation.

# Simulations:

* Steady and unsteady state simulations for Re = 100 and calculating the strouhal number:

1. Steady state

Inlet velocity = 1 m/s.

User defined fluid material is used:

density, `rho = 1 (kg)/m^3`

Dynamic viscosity, `mu = 0.02 (kg)/(m*s)`

Plots:

* Contour plot:

* Residual plot:

* Vertex average of velocity plot:

This plot is taken at a distance 4 times the diameter of the cylinder from the centre of the cylinder , in this simulation it is 8 meters

* Lift coeffciient plot:

* Strouhal number plot:

* from the above residual and vertex average plots it is clear that the solution is converged, from the vertex average plot we can observe that after 400 iterations same kind of plot pattern is repeated and hence we can conclude that the solution converged at 400 iterations.

* Strouhal number plot is obtained through FFT. FFT is also called as fast fourier transform, it converts a time dependent function into frequency dependent function. So in our simulation once the solutions are converged, the lift coefficient data (time dependent) is given as input file to FFT, as output we can get strouhal number (frequency dependent). But in steady state simulation the lift coefficent data that we obtain is not time dependent because steady state simulations are time independent. This can be clearly observed from the lift coefficient plot wherein lift coefficient is ploted against No.of iterations rather than time. Hence the strouhal number plot obtained is not correct.

2. Unsteady state:

Inlet velocity = 1 m/s.

User defined fluid material is used:

density, `rho = 1 (kg)/m^3`

Dynamic viscosity, `mu = 0.02 (kg)/(m*s)`

* Plots:

* Contour plot:

* Residual plot:

* Vertex average of velocity plot:

* Lift coefficient plot:

* Strouhal number plot:

* Observing the vertex average plot it is clear that the solution is converged at flow time of 100 s, here the input file provided to FFT to calculate srouhal number is time dependent lift coefficient hence the outpt obtained from this is frequency dependent strouhal number. Its difficult to get the stouhal number from the above plot.

* Hence it is calculated manually from the vertex average plot,

`str = ((f*L)/V)`

from the above vertex average plot it can be observed that between 100 and 120 sec flow time there are 3 oscillations,

hence frequency, f = 3/20 = 0.15

from the same vertex average plot we have velocity corresponding to the oscillations from 120 to 140 sec, V = 0.775 m/s.

therefore, Str = (0.15*2)/0.775 = 0.387

* Steady state simulation at different reynolds number, understanding the effect of reynolds number on drag coefficient:

1. At Re = 10. we have Inlet flow velocity, V = 0.1 m/s.

to obtain the correct drag and lift coefficient it is necessary that we set the reference values exactly, a grab of the same is shown below,

Area is set to 2 m^2 , since this is a 2D simulation there is no width along z direction hence the area of the face covering the cylinder the mentioned area

Density value is the same density value of the user defined fluid material is used.

Depth is by default given 1 m,

Length it is the characteristic length, here it is the diameter of the cylinder.

Velocity , V =0.1 m/s it is velcity obtained at Re = 10

Viscosity is the same as that of the fluid material,

setting up the temperature value has no significance since we are not solving the energy equation.

For all further simulations for different reynolds number in the above reference values only the value of velocity is changed.

* Contour plot:

* Drag coefficient plot:

* Lift coefficient plot: