Week 2 - Flow over a Cylinder.
Challenge No- 2 – Flow Over a Cylinder.
Geometry Creation: We have created the geometry by the geometry tools in the Ansys Space claim.
Circle Diameter – 2 Meter
Geometry length – 60 Meter
Geometry width – 20 Meter
After geometry creation, we have to make this geometry a solid plane. For this, we need to use pull tool in the user tool bar.
After plane creation, the geometry will look like this.
Operation in User Mesh: Apply the mesh to the geometry. After creation of the mesh, it is shown that the mesh is majorly looking like quadrilateral. But we need more triangular mesh for the CFD analysis
Triangular Mesh Generation:
For generating triangular mesh, we have changed the method of meshing.
Inflation Layer: Inflation layer is a function in Ansys fluent that allows you to create thin elements that can capture the normal gradient with minimal element. It is used to accurately analyses boundary conditions by creating a finer mesh near the wall or boundary
Creating named edge selection: Select the particular edge & named it as mentioned. Inlet, Outlet, Wall & Symmetry.
Final Mesh: Mesh element size – 0.25 m. Method of mesh – Triangl
Material Selection: For this material selection, we have made a user specific material and changed the dynamic viscosity of the user specific material due to this stmulation. Foe this selection, we have deleted the unwanted material already assigned in the material list.
While deleting the assigned material, Air is not getting deleting, as it is made default material by the ansys fluent data base. So, we have changed the default material from the cell zone editing & and change the default material name.
Assigning Boundary Condition: We have defined the boundary condition of the cylinder. As the inlet velocity of the air is defined as 1 m/s.
Boundary condition for the wall. As it going to be no slip boundary. We will go for the no slip boundary
Viscosity Model:
Reynolds number - Reynolds number is a dimensionless quantity that is used to determine the type of flow pattern as laminar or turbulent while flowing through a pipe. Reynolds number is defined by the ratio of the inertial forces to the viscous forces.
Reynolds Number – Density of medium x Velocity of Flow x Characteristic length = 1x1x2/0.02 = 100
Dynamic Viscosity.
For the first case, Reynolds number is 100. So, we can say that the flow will be laminar.
laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion. When the Reynolds number is below 1100, then it is said to be laminar flow.
Turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities. When the Reynolds number is above the 1100, then it is said to be turbulent flow.
As we have already calculated that the Reynolds number will be 100, fall in the laminar region. So, that the viscosity model is set to ‘Laminar’ Model.
Creating Monitor Point: For the analysis part, we have to create a common point, It should be at the 4 times at the distance of the diameter.
Creating Surface report:
Monitor Point velocity.
Report Name: Lifting coefficient, We will analyze the lifting coefficient near the wall.
Report Name: Drag Coefficient. We will analyze the Drag coefficient near the wall.
Creating initial condition of the cylinder: Create ‘Contours’. Before creating ‘Contours’ we have to initial initialize the hybrid initialization method before creating contours.
After hybrid initialization, we have created two ‘Contours’. One is pressure Contours & second one is velocity contour.
Pressure Contour:
Velocity Contour:
Solution method will be Simple:
Residual Monitors: As we have selected the residuals monitors, we have unchecked the convergence criteria. This was done, as we are wanting to run the solution till the iteration we have fixed. After uncheck the convergence, just click on ‘OK’.
Create Animation File: As we will run the solution, it will be very helpful to record this solution in a video format. So, it can be done by the creation tab in the Activity list. So, we have created the velocity animation.
What is Vortex Shedding: In fluid dynamics , vortex shedding 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 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 ‘Karman Vortex street’. The fluid flow past the object creates alternating low pressure vortices on the downstream side of the object. The object will tends to move towards the low pressure zone.
If the frequency of the vortex shedding matched the resonance frequency of the structure, then the structure can begin to resonate, vibrating with harmonic oscillation.
Vortex Shedding Governing Equation:
The frequency at which vortex shedding takes place for an infinite cylinder is relate to the Strouhal number by the following equation.
This is an dimensionless quantity.
St = fD/V (St – Strouhal Number, f – Vortex shedding frequency, D – is diameter of the cylinder, V – Flow velocity)
Karman Vortex Street: In fluid dynamics, a Karman vortex street is a repeating pattern of the swirling vortices, caused by a process known as the ‘vortex shedding. Which is responsible for the unsteady separation of flow of a fluid around blunt body.
Challenge Part -1 (a)
Challenge No-1 Part -B
Flow over a cylinder in transient manner. https://youtu.be/N-tHnuecv1w
From the above images following observations can be made.
1. In residual plot, the error value is neither changing not increasing from the set limit of 1e-3, that’s what it can be said that the solution is converged.
2. In velocity contour plot, the von karman vortex street can be seen, but it can be seen properly in the below animation file.
3. The drag coefficient value is constant after one point. The drag coefficient of the cylinder is calculated by the fluent around 1.33.
4. In pressure contour image, the low pressure field is changing alternatively. It can be seen by the blue area. The low pressure wake field is the primary physics to observe for this challenge.
5. In lift coefficient plot, the value is kept rising & falling because of vortex shedding phenomena. The lift coefficient data has been used in the fourier transform plot to plot the Strouhal number.
6. The Strouhal number is more in transient flow simulation as compared to the steady flow simulations with the same parameters.
There are multiple reasons behind this.
1. Unsteady Nature of Transient Flow: Transient flows inherently involve unsteady conditions with time-varying parameters. The variations in velocity and frequency can result in higher Strouhal numbers compared to the average values calculated in steady flow simulations.
2. Vortex Shedding Phenomenon: The Strouhal number is often associated with the shedding of vortices behind bluff bodies. In transient flows, the shedding of vortices might be more pronounced or occur at different frequencies compared to steady flows, leading to variations in the Strouhal number.
3. Time-Dependent Changes in Flow Characteristics: Transient flow simulations capture changes in the flow field over time, which can affect the Strouhal number. For example, variations in the velocity profile or boundary conditions during different time steps can influence the oscillatory behavior of the flow.
It's essential to note that the specific reasons for higher Strouhal numbers in transient flow simulations may depend on the details of the simulation setup, the characteristics of the flow, and the object under consideration. Analyzing the transient nature of the flow and understanding how it impacts the vortex shedding or other relevant phenomena will provide insights into the variations in the Strouhal number.
Raynolds No
Density ‘ρ’ – 1 kg/m^3
Viscosity ‘µ’ – 0.05 Kg/(m s)
Velocity of flow ‘U’ – 1 m/s
Characteristic Length ‘L’– 2 meters.
Re – ρ x U x L.
µ
|
ρ |
L |
U |
µ |
Re – ρ x U x L. µ |
|
1 |
2 |
0.25 |
0.05 |
10 |
|
1 |
2 |
2.5 |
0.05 |
100 |
|
1 |
2 |
25 |
0.05 |
1000 |
|
1 |
2 |
250 |
0.05 |
10000 |
|
1 |
2 |
2500 |
0.05 |
100000 |
Challenge No – 2
For Raynolds Number – 10
For Raynolds Number – 100
For Raynolds Number – 1000 https://youtu.be/KFxnA_QX32c
For Raynolds Number – 10000 https://youtu.be/NYwgBd971SI
For Raynolds Number – 100000 https://youtu.be/qF98hQWauPE
Discussion & Conclusion:
01. The time & resources consumed by the transient solver is far more than the steady state solver.
02. For the transient simulations, the simulation were running after the turning off the convergence criteria. In the transient mode, the more iteration are required to develop proper physics of the flow. Because of that the transient simulation has taken more iteration with smaller time steps compare to the steady state.
03. The drag coefficient for the Re above 1000, is start fluctuating but periodic after one point which can be seen from the results images. So statistically, it is constant.
04. The results of the simulation are the one we are expecting from the physics point of view.
The challenge of simulation flow over a cylinder has been carried out to study the vortex shedding phenomena & visualizing von Karman vortex street. The challenge has been divided into two parts. In first part, the steady & unsteady state simulations have been performed for Re 100 & Strouhal number has been calculated using analytical method & later compared with the fluent result. While in the second part series of the simulation has been carried out for various RE numbers in steady state condition. Vortex shedding & Karman vortex street was unable to visualize for Re 10 because these two phenomena doesn’t occur below Re 40. The drag coefficient & lift coefficient has been compare for all simulations.
Drag Coefficient vs. Reynolds Number
When designing a system that will move through a fluid, it is best to measure drag on the system or determine drag through a simulation. It is often helpful to regress the data back to an analytical model. The problem here is that one model does not normally describe all flow behaviour in both regimes and the transition region. Instead, the standard practice is to use measured or simulated data to determine models in each flow regime and then examine where these models intersect to determine a transition region.
In the following examples, the expressions for Cf consider both skin friction drag and pressure drag:
Laminar Example
The example below is a common model used to relate the drag coefficient vs. Reynolds number for laminar flow across a sphere:
Approximation for drag in laminar flow
This equation is known to be reliable for a broad range of Reynolds numbers in enclosed geometries. An important takeaway is the rough dependence of drag at low Reynolds number (Re < 36), particularly for incompressible or nearly incompressible flows—we find that the drag coefficient is a nearly linear function of velocity. This is the Stokes regime and it is often the starting point for understanding the effects of drag.
Eventually, the above equation will lose its predictive power as the flow transitions into the turbulent regime, and we need a new model to describe the turbulent drag coefficient vs. Reynolds number.
Turbulent Example: Prandlt’s Power Law
Turbulent flow, whether compressible or incompressible, requires a different model that is particular to the type of system being studied. One simple model relating the drag coefficient vs. Reynolds number is Prandlt’s power law. This simple model is defined below:
Prandtl’s
power law for turbulent flow
In general, the one-seventh power law described above is not applicable to every system, but it is applicable to a wide range of fluids in pipes or other enclosed systems. Drag exerted by turbulence may follow a more complex model with a different power defining the relationship between drag and turbulence. One article in the research literature that contains a review of models relating the drag coefficient vs. Reynolds number can be found below.
Where Laminar and Turbulent Flow Intersect
Eventually, as the flow rate increases, there is an intersection between laminar flow and turbulent flow, which we call the transition region. In the high Reynolds number regime, we eventually find that, although the drag coefficient is low, the total drag force is large and is a quadratic function of velocity. This is due to the flat profile of the drag coefficient vs. Reynolds number curve deep into the turbulent regime, as shown below.
Correlation of the Drag Coefficient vs. Reynolds Number | System Analysis Blog | Cadence