Steady Vs Unsteady flow over a cylinder

Title: Simulation of flow over a cylinder with the help of AnsysFluent.

1. Introduction

In this project, we are simulating the flow of fluid over a cylinder at different Reynold numbers with a steady and unsteady solver. Change in value of Reynold number would be done by a change in the value of viscosity at constant density, velocity, and Hydraulic length.

At certain velocity, fluid starts to flow in a reversed direction to streamline, and vortex shedding formed due to oscillation of flow takes place. This phenomenon is known as Karman vortex street.

The aim of this project is to compare convergence or the vortex shedding behind the cylinder at varied Reynold number. Also, to find Strouhal Number in steady and unsteady state at Reynolds number = 100.

Steady State flow – It is the property of fluid at a single point in a flow that is independent of time. Most, significant property is the mass flow rate, it remains constant over a time period.

Unsteady state flow – it is time-dependent flow. Also, known as transient flow. For example velocity and pressure of flow change with time.

Reynold number – It is a dimensionless parameter of fluid mechanics helps to analyze the flow pattern

Reynolds number (Re) = (ρVL)/μ

Where, ρ = Density of fluid

V = fluid velocity relative to the body

L = Internal pipe diameter of the body

μ = kinematic viscosity.

As shown in the figure below, are the flow pattern over a cylinder and formation of the vortex at different Reynold numbers.

Ref - https://myassignmenthelp.info/assignments/simulation-of-flow-past-cylinder-at-moderate-reynolds-numbers-907403/

Strouhal Number - it is a dimensionless parameter used to describe oscillating flow mechanisms.

St = (f * D)/U

where, f - vortex shedding frequency,

D - diameter of the sphere,

U - free-stream velocity.

2. Solving & Modelling approach

To perform a simulation of flow over the cylinder with the help of ANSYS Fluent. It is approached in two different sections. In the first section, Simulating flow with the steady and unsteady case at Re = 100, and in other parts of the simulation, the drag coefficient and lift coefficient would be calculated with different Reynold numbers using steady-state solver. which are performed as stated below.

Part 1 - Simulating flow with the steady and unsteady case at Re = 100

Case 1

• Steady-state solver.
• Reynold number = 100

Case 2

• Unsteady state solver.
• Reynold number = 100

Part 2 – calculate drag and lift coefficient with steady-state solver at different Reynolds number

• Reynold number = 10
• Reynold number = 100
• Reynold number = 1000
• Reynold number = 10000
• Reynold number = 100000

2.1 Geometry

As we are interested in capturing vortex shedding of a flow over a cylinder, we design the geometry in a SpaceClaim. We design a body in the shape of a cylinder. In this approach, we took a 2D geometry. The computational domain, we create is as shown below.

Fig.: Dimensions and final geometry of a computational domain

We took a larger distance = 20*D from the center of the cylinder to an outlet to capture vortex shedding effectively.

2.2 Meshing

After extracting the computational fluid domain from the model, the next step is to discretize the fluid domain. ANSYS meshing tool is used to generate a mesh in the model.

The method used for meshing in these cases is triangular mesh. Body sizing of 0.25 m is used to generate finite volumes. After normal meshing without the inflation layer, we get distorted surfaces of the cylinder. So, we have to create a smooth surface by dividing the surface into a larger number of edges. Here, we divide the cylinder surface into 36 divisions to get the accurate result from the simulation. Also, we make the finer layer of mesh around the surface of the cylinder using inflation to capture the flow pattern effectively.By applying these configurations, the number of elements generated is 40294.

Fig. : Final meshing in Computational Domain Fig.: Inflation Layers around the cylinder surface.

The name selection of the computational domain is as shown below.

Fig.: Name selection in Computational Domain.

3. Pre-processing and solver setting

The next step in the simulation after generating fine meshing is to set-up the physical properties for the case.

3.1. Part 1 - Steady-state simulation/Unsteady state simulation at Re=100

• Type of solver: Pressure-based
• Simulation method: Steady-state simulation/Unsteady state simulation
• Model – Viscous model (Laminar)
• Material properties of the fluid (User-defined material)

Density : 1 kg/m3

Viscosity : 0.02 kg/m-s

• Inlet velocity: 1 m/s (Inlet x is along the pipe axis).
• Outlet Gauge pressure – 0 Pa
• Body Walls: symmetry.
• Cylinder Wall: No-slip

Here in this part, to capture Strouhal Number and the frequency of vortex shedding. We need to locate the point at 10m away from the center in the outlet direction of the cylinder in direction of flow of fluid.

Part 2 – calculate drag and lift coefficient with steady-state solver at different Reynolds number

In this part, we ran the steady-state simulation using the same fluid and solver with different Reynold numbers. Reynold number value varied with respect to viscosity by taking other value constant. As shown below in the table we take the value of Reynold number and viscosity for simulation.

Reynold number	Viscosity	Density	Velocity
10	0.2 kg/m-s	1 kg/m³	1 m/s
100	0.02 kg/m-s	1 kg/m³	1 m/s
1000	0.002 kg/m-s	1 kg/m³	1 m/s
10000	0.0002 kg/m-s	1 kg/m³	1 m/s
100000	0.00002 kg/m-s	1 kg/m³	1 m/s

4. Results

After setting up a case and providing appropriate initial and boundary conditions, numbers of simulations are performed mainly for the comparison of results of convergence and Strouhal Number, for steady and unsteady state simulation. And also, Drag coefficient at different Reynolds numbers in steady-state simulation.

4.1 Results of Steady-state simulation/ unsteady state simulation at Re = 100

4.1.1 Results of Steady-state simulation (Re = 100)

The figures below show the residual plots and the plot of the Vertex average of velocity-magnitude at the monitoring point.

Fig.: Plot of Residuals of the steady-state solver for Re=100 Fig.: Plot of the Vertex average of velocity-magnitude at the monitoring point.

As can be seen from both the curves, We ran the simulation for 1000 iteration and we get converged solution around 500 iterations.

• Strouhal Number:

In the steady-state simulation, we ran the simulation based on no. of iterations instead of Time-step. Hence, it is not possible to calculate the frequency of vortex, which is required to calculate the Strouhal Number.

4.1.2 Results of unsteady-state simulation (Re = 100)

The figures below show the residual plots and the plot of the Vertex average of velocity-magnitude at the monitoring point.

Fig.: Plot of Residuals of the unsteady-state solver for Re=100 Fig.: Plot of the Vertex average of velocity-magnitude at the monitoring point.

We ran the simulation with a time step size of 0.1 s, with 2000 number of time steps. As shown in figure there are lots of fluctuations in the convergence of result due to time-based simulation.

• Strouhal Number

The Strouhal Number in this can be calculated as below:

St = (f*D)/U

Vortex shedding Frequency, f = No. of peaks of a Time range/ Time taken on that range

We take the time range from 120 to 200, because in this interval our solution gets converged.

We get 13 peaks in this time range.

So, f = 13/80

= 0.1625 Hz

Stouhal number, st = 0.1625 *2/1

= 0.32

4.2 Results of drag coefficient with steady state solver at different Reynolds number

4.2.1 Results of drag coefficient with steady state solver (Re = 10)

1) Residuals plot (Re = 10)

2) Drag coefficent (Re = 10) 3) Lift Coefficient (Re=10)

4.2.2 Results of drag coefficient with steady state solver (Re = 100)

1) Residuals plot (Re = 100)

2) Drag coefficent (Re = 100) 3) Lift Coefficient (Re=100)

4.2.2 Results of drag coefficient with steady state solver (Re = 1000)

1) Residuals plot (Re = 1000)

2) Drag coefficent (Re = 1000) 3) Lift Coefficient (Re=1000)

4.2.2 Results of drag coefficient with steady state solver (Re = 10000)

1) Residuals plot (Re = 10000)

2) Drag coefficent (Re = 10000) 3) Lift Coefficient (Re=10000)

4.2.2 Results of drag coefficient with steady state solver (Re = 100000)

1) Residuals plot (Re = 100000)

2) Drag coefficent (Re = 100000) 3) Lift Coefficient (Re=100000)

4.3 Comparison of simulation results from the different cases

From the above simulation, we can analyze the dependency of drag coefficient on Reynolds number. Drag coefficient decrease with increase in Reynold number as can be seen from the curve and table below.

Reynold Number	Drag coefficient (Cd)
10	3.32392
100	1.35519
1000	0.7569108
10000	0.6841709
100000	0.858982

ref.https://www.grc.nasa.gov/www/k-12/airplane/dragsphere.html

Fig.: Reynolds number vs Coefficient of Drag plot compared with experimental results

4.4 Post-processing

After performing all the simulations, to analyze the result it is very important for any CFD simulation to perform post-processing as it gives clear visualization of the results. This section provides a few post-processing results of the above-performed simulations.

4.4.1 Velocity and pressure contour for steady and unsteady state simulation(Re = 100)

1) Steady-state simulation

Fig – Velocity contour Fig – Pressure contour

2) Unsteady state simulation

Fig – Velocity contour Fig – Pressure contour

4.4.2 Velocity and Pressure contour for steady-state simulation for different Reynold number.

1) Reynold number = 10

Fig – Velocity contour Fig – Pressure contour

2) Reynold number = 100

Fig – Velocity contour Fig – Pressure contour

3) Reynold number = 1000

Fig – Velocity contour Fig – Pressure contour

4) Reynold number = 10000

Fig – Velocity contour Fig – Pressure contour

5) Reynold number = 100000

Fig – Velocity contour Fig – Pressure contour

5. Conclusion

After performing numerous simulations with different parameters and inputs for flow over a cylinder, we can few conclusions from this study of CFD simulations.

1. Flow is converging in both the steady and unsteady state simulations for Reynolds number=100. But, to effectively calculate the Straouhal Number Transient simulation is better as compared to steady-state as it gives a solution at every time step.

2. As the cylinder is a bluff body, from the contour of velocity we can conclude that flow remains separated after the cylinder.

3. For very low Reynolds numbers such as 10 in this case, Vortex does not get generated as viscosity is too high in that case.

4. From the Reynolds number vs Coefficient of Drag plot, we can conclude that drag is reducing as the Reynolds number is increasing. As the Reynolds number increases, the viscosity decreases, and for both a laminar and a turbulent boundary layer increasing Reynolds Number gives lower skin friction drag. Hence, the drag coefficient decreases with increase in Reynolds number.