Analysis of steady and unsteady flow behaviour over a cylinder using ANSYS Fluent module.

Objective: - To simulate the air flow over a cylinder at Reynolds number 100 i.e. viscous fluid flow inside the fluid domain in both steady and unsteady approach. The study of the vortex shading inside the fluid domain also carried out and calculating the strouhal number in case of unsteady flow simulation.

Introduction: A fluid is a substance that deforms continuously under the application of shear stress no matter how small the shear stress may be. There are many kind fluid flows i. e. steady and unsteady flow, uniform and non-uniform flow, rotational and irrotational flow, Laminar and turbulent flow, compressible and incompressible flow and one, two & three dimensional flows etc. In our study is mainly focused on steady and unsteady flows.

Steady flow: A flow is said to be steady flow, if the fluid properties (temperature, pressure and velocity) do not vary with respect to time at any given section.

Unsteady flow: A flow is said to be unsteady flow, if the fluid properties (temperature, pressure and velocity) vary with respect to time at any given section.

To determine the nature of flow we used generally a dimensionless quantity is called as Reynolds number. It is the ratio of inertia force to viscous force

Table 1: flow over cylinder at different Reynolds no.

Reynolds number	Nature of flow
Re<5	Regime of unseparated flow
5to 15<Re< 40	A fixed pair of vortices in wake
40<Re<150	Two regimes in which vortex street is laminar
150<Re<300	Transition range to turbulence in vortex
300<Re<3*105	Vortex street is fully turbulent
3*105 <Re< 3.5*106	Laminar boundary layer has undergone turbulent transition.
3.5*106 <Re	Re-establishment of turbulent vortex street

Vortex shedding:

when fluid (air or water) flows over a cylinder body at a certain velocity after passing the fluid it is oscillating along the direction of flow after some distance. Due to this it creates vortices at back of body and separate periodically and fluid develops low pressure at back of cylinder.

Effects: If cylinder is not fixed rigidly and frequency of shedding matches the resonance frequency of cylinder body. Then cylinder is begin to resonate and create harmonic vibrations, due to this it can damage or destroy the structure.

Strouhal number: it is a dimensionless quantity that is used for describing oscillating flow mechanism.

`St = (f.L)/U`

Where- St is strouhal number

f is frequency of vortex shedding

L is characteristic length

U is the flow velocity.

Methodology:

To achieve the objective of this study following steps are used;

Step 1: pre-processing:

• Modelling of geometry: In this step the geometry is created in space claim.

Dimensions: Diameter of cylinder is 2m.

Computational fluid domain size is 20*60m.

Figure 1: Geometry of cylinder with fluid domain

• Meshing:

Now model is to be meshed by using ansys mesher. The methodology used for meshing is triangular method with element size of 0.25m. After generating mesh 40642 elements and 20767 nodes are formed. In mesh if more elements is generated smoothly, results are to more accurate from previous simulations.

Figure 2: Meshed structure of fluid domain

Figure 3: Meshed structure of boundary fitted mesh

Figure 3 is indicating the boundary fitted mesh or inflation mesh at cylinder edges. To find out more specific physics or results around the cylinder, this method is more beneficial for the study.

Figure 4: Mesh metrics plot between number of element and element metrics

The mesh metric plot of element quality is shown in figure 4. It identified the elements as per their quality. From figure 4, we can say that elements have their high quality is shown in the range of 0.75- 1.0 and elements of lower quality is very less. Hence mesh is acceptable range.

• Name creation for boundaries:

Inlet --- left side edge,

Outlet --- right side edge,

Symmetry --- top & bottom edges,

Walls --- edge of cylinder

Step 2: Setup

1. Setting up physics

Solver – both steady state and transient state, pressure based used.

Model--- in this study we used viscous model for set up.

Material properties---Density=1 kg/m³ and Dynamic viscosity= 0.02 kg-m/s, Reynolds no. = 100.

Boundary condition---inlet velocity= 1m/s, outlet = 1 atm pressure

2. Setting up solution

Hybrid initialization in case for steady state simulation

Standard initialization in case for transient simulation

Step 3: Post- processing

In post-processing we saw the simulated results of plots, contours, and animations. In post-processsing we can also create the locations at which results are simulated. In this study we created a point i.e. called monitor point. At monitor point vortex shedding is going to started.

Results:-

The main aim of this study is to analyse the vortex shedding after passing over the cylinder in both cases of steady and transient simulations. Initially we started with checking mesh grid dependency test to check the effect of the fluid flow around the cylinder. When we decreased the element size from 1m to 0.25m, more easily visualize the fluid flow effects on the results. Due to this we can analyse the effect of vortex shedding in fluid domain around the cylinder. In second analysis we can check the effect of Reynolds number on vortex shedding generations. If we used Reynolds number more than 40 vortex shedding is formed. Below Reynolds no. 40 vortex shedding is not formed.

A. Steady state simulation:

In steady state simulation we found directly end results at monitor point. For study of convergence rate we generally analyse the residuals plot which is explained below in figure 5. From residuals representation we can say that there is no change in velocity (x & y components) after 500 iterations. Which shows that solution are going to converge.

1. Residuals plot: Figure 5: plot between residuals vs no. of iterations

2. Velocity plot vs iterations:

Figure 6: plot between averages of velocity magnitude vs no. of iterations at monitor point

Figure 6 is showing the vertex velocity average at monitor point. From this figure we can say that velocity is decreasing upto 120 iterations and further it was increased and after 500 iterations it is start oscillating along the direction of flow. These oscillations are called vertex shedding.

3. Velocity distribution contour:

Figure 7: Velocity distribution on flow over cylinder

Figure 7 is showing the contour of velocity distributions. From contour it showed that velocity is after passing the cylinder and after some distance it is varying and started oscillations.

4. Velocity contour animation:

The animation of velocity contour is shown in above video.

5. Pressure distribution contour:

Figure 8: Pressure distribution of flow over cylinder

Figure 8 is showing contour of pressure distributions. From contour we can say that pressure is decreased after monitor point locations. Due to these fluctuations, pressure is also decreased. And this regions fluid is circulating and centre region it creates void space.

B. Unsteady state (transient) simulation:

In transient case we analyse the results variations each and every time steps. We used 0.1 time step and no. of time steps are 500.

1. Residuals plot:

Figure 9: plot between residuals vs no. of iterations

Figure 9 is showing the scaled residuals plot for transient simulations. The number of iterations is 10000 for this simulation and showed that fluctuations of velocity is a pattern form and give the convergence indications.

2. Velocity plot vs iterations:

Figure 10: plot between averages of velocity magnitude vs no. of iterations at monitor point

Figure 10 is showing the vertex velocity average at monitor point in transient simulation. From this figure we can say that velocity is decreasing upto 5000 iterations and further it was increased and after 7000 iterations it is start oscillating along the direction of flow. These oscillations are called vertex shedding.

3. Velocity distribution contour:

Figure 11: Velocity distribution on extracted volume

Figure 11 is showing the contour of velocity distributions. From contour it showed that velocity is after passing the cylinder and after some distance it is varying and started oscillations.

4. Velocity contour animation in transient study:

The animation of velocity contour is shown in above video.

5. Pressure distribution contour:

Figure 12: Pressure distribution on flow over cylinder

Figure 12 is showing the pressure contour in transient simulations and it help in analysing the variations of pressure. In this case the low pressure region is showing just after the cylinder.

C. Strouhal Number calculations:

Strouhal no. is directly proportional on frequency of vertex shedding. In steady state analysis we cannot find out the frequency. So in the steady state case strouhal no. is not calculated.

In the transient case analysis, strouhal no. is calculated from FFT plot.

Figure 13: plot of strouhal no. – FFT on monitor point velocity

The above shown fig.13 is indicating the plot of magnitude vs. strouhal no. generated using FFT on monitor point velocity. With help of micro soft excel worksheet, we calculated the median values of strouhal number. And we found strouhal no. directly by this method. Its value in this case is 0.2267.

Conclusions: The following conclusions made from the above analysis:

Vortex shedding is depends upon the Reynolds number of the viscous flow.

Vortex shedding is generated in both steady and unsteady simulations.

If we increase the mesh quality, fluid flow behaviour is easily analysed.

strouhal no. is calculated in transient simulation because in transient study we can find flow time easily and calculate the frequency of oscillations and find strouhal no..