Week 2 - Flow over a Cylinder.

WEEK 2 CHALLENGE :DETAILED REPORT:

AIM:

Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street. Understanding the vortex shedding for different Reynolds numbers by changing the inlet velocities accordingly. Create a monitor point behind the cylinder at a distance 4 times the diameter which can be used to calculate and analyze the vortex shedding.

OBJECTIVE:

1. Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100

2. Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000. (Run with steady solver)

2. Discuss the effect of Reynolds number on the coefficient of drag. [ Results should be validated with any standard literature and error should be within 5 %]

3. In both approaches, show that the flow has converged. That is, what quantities or plots need to be looked at to determine that the flow has converged?

4. Plots of the coefficient of drag and lift.

5. Plots to show vortex shedding behind the cylinder.

6. Mention the preferred material at the end of the challenge submission page.

• THEORY:

1. Flow over cylinder:

In spite of extensive experimental and numerical studies almost over a century, flow around a circular cylinder still remains a challenging problem in fluid mechanics, where intensive investigations are continued even today to understand the complex unsteady dynamics of the cylinder wake flow. Cross-flow normal to the axis of a stationary circular cylinder and the associated problems of heat and mass transport are encountered in a
wide variety of engineering applications. Both experimental measurements and numerical computations have confirmed the onset of instability of the wake flow behind a cylinder beyond a critical Reynolds number, leading finally to a kind of periodic flow identified by definite frequencies, well-known in the literature as the Von Karman vortex street. In case of laminar flow past cylinders with regular polygonal cross-section, the flow
usually separates at one or more sharp corners of the cross-section geometry itself, forming a system of vortices in the wake on either side of the mid symmetry plane. On the other hand, for a circular cylinder, where the point of flow separation is decided by the nature of the upstream boundary layer, the physics of the flow is much more complex than what its relatively simple shape might suggest.

2. Strouhal number:

In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms.

For large Strouhal numbers (order of 1), viscosity dominates fluid flow, resulting in a collective oscillating movement of the fluid "plug". For low Strouhal numbers (order of 10⁻⁴ and below), the high-speed, quasi-steady-state portion of the movement dominates the oscillation. Oscillation at intermediate Strouhal numbers is characterized by the buildup and rapidly subsequent shedding of vortices.

The Strouhal number is often given as

St=fD/U

Where,

f= frequency of vortex shedding

D= characteristic diameter of the cylinder

U'= fluid flow velocity

3. Co-efficient of drag:

In fluid dynamics, the drag coefficient(Cd)">(Cd)(Cd) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation in which a lower drag coefficient indicates the object will have a less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.

The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag. The drag coefficient of a lifting airfoil or hydrofoil also includes the effects of lift-induced drag. The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag.

The drag coefficient Cd">Cd is defined as

where:

Fd">Fd is the drag force, which is by definition the force component in the direction of the flow velocity,

ρ">ρ is the mass density of the fluid,

u">u is the flow speed of the object relative to the fluid,

A">A is the reference area.

4. Co-efficient of lift:

The lift coefficient (CL">CLCL) is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity, and an associated reference area. A lifting body is a foil or a complete foil-bearing body such as a fixed-wing aircraft. C_L is a function of the angle of the body to the flow, its Reynolds number, and its Mach number. The section lift coefficient c_l refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.

where

is the lift force,

is the relevant surface area and

q is the fluid dynamic pressure, in turn, linked to the fluid density, and to the flow speed.

Vortex shadding:

vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff (as opposed to streamlined) 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 Von Karman vortex street. The fluid flow past the object creates alternating low-pressure vortices on the downstream side of the object. The object will tend to move toward the low-pressure zone.

If the bluff structure is not mounted rigidly and the frequency of vortex shedding matches the resonance frequency of the structure, then the structure can begin to resonate, vibrating with harmonic oscillations driven by the energy of the flow. This vibration is the cause for overhead power line wires humming in the wind, and for the fluttering of automobile whip radio antennas at some speeds. Tall chimneys constructed of thin-walled steel tubes can be sufficiently flexible that, in air flow with a speed in the critical range, vortex shedding can drive the chimney into violent oscillations that can damage or destroy the chimney.

Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street.

Opening Ansys Workbench and fluent

Opening Spaceclaim

Unit of length set into Metres

Circle with diameter 2Meter created

Computational domain created as per required dimesion

Geometry creation completed.

Opened in mesh interface

Quadrilateral mesh created by default

Quadrilateral mesh changed into triangular mesh.

Mesh refined near the cylinder and all over the surface

6 number of inflation layer added around the cylinder for capturing the flow phenomena

Number of inflation layer increased as 15 beacuse the size of outermost inflayer layer and size of free stream mesh should be almost similiar.

Opened in setup window

Mesh checking done

Setting physics for the problem

Adding customized material ad default material

Giving density and viscosity and therefore here Re=100.

Giving inlet boundary conditions.

Giving outlet boundary conditions.

Giving wall boundary conditions.

Giving symmetry boundary conditions.

Taking vertex average of velocity at monitor point

Hybrid Initialization done

Setting velocity contour

Setting pressure contour

Uncheking convergence criterias for running full number of iteration what we put.

RESULTS AND DISCUSSION:

Showing vertex average velocity at monitor point.

From this plot it is clear that velocity is continously reducing from 1m/s to 0.1m/s upto 100 iterations and then it is slightly increasing till 150 iterations. After 150 iterations we can see that velocity is fluctuating with almost constant frequency and this type of fluctuations in velocity will cause for vortex shedding.

Showing residuals.

Showing velocty contour and Vortex Shedding phenomena(Karman vortex street) can see here.

From this velocity contour it is clear that VonKarman Vortex Shedding(Karman vortex street) is happening in this case also we can understnd that velocity near to the cylinder wll is zero due to no-slip conditions and velocity just behind the cylinder also almost zero due to flow seperation.This flow seperation is heppening due to the adverse pressure gradient just behind the wall of cylinder and this adverse pressure gradient happening due to the force acting in the opposite direction of flow.

Vortex Shedding happens when high velocity flows passes over an object .The oscillating cross flow produces forces perpendicular to the flow.

Contours of pressure.

It is clear that pressure is very less just behind the cylinder and this is due to flow seperation.

PART-I (a)

1. Simulate the flow with the steady case and calculate the Strouhal Number for Re= 100.

So this is similar to the previous case therefore not posting the results again and here I am only calculating the Strouhal Number for Re=100

PART-I (b)

1. Simulate the flow with the unsteady case and calculate the Strouhal Number for Re= 100.

Giving transient condition

Giving time step and no of iterations

Hybrid initialization done

RESULTS AND DISCUSSION:

Showing Residuals

Showing Vertex Average of Velocity

Showing Velocity Contour

Here we can see the velocity contour and from thet it is clear that Vortex Shedding is happening here.

Showing Pressure Contour

From this figure it is clear that pressure just behind the cylinder is very less due to flow seperation.

Calculation of Strouhal Number:

Showing Strouhal Number

From this plot it is clear that Strouhal Number is 0.0798

Showing lift coefficient

Showing drag coefficient

PART-II

1 (a) Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10 (steady state)

Inlet velocity changed to 0.1m/s for getting Re=10

Hybrid Initialization done

RESULTS AND DISCUSSIONS:

Showing Residuals

Showing plot and value of drag coefficient.

From this it is clear that here the drag coefficient is 3.3008744

Showing plot and value of lift coefficient.

From this it is clear that here the lift coefficient is 0.0007469

PART-II

1 (b) Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number =100(steady state)

Giving inlet velocity as 1m/s for getting Re=100

Hybrid initialization done

RESULTS AND DISCUSSIONS:

Showing residuals.

Showing plot and value of drag coefficient.

From this it is clear that here the drag coefficient is 1.2934

Showing plot and value of lift coefficient.

From this it is clear that here the lift coefficient is 0.00290

PART-II

1 (c) Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number =1000(steady state)

Giving inlet velocity as 10m/s for getting Re=1000

Hybrid initialization done

RESULTS AND DISCUSSION:

Showing Residuals

Showing plot and value of drag coefficient.

From this it is clear that here the drag coefficient is 0.8027

Showing plot and value of lift coefficient.

From this it is clear that here the lift coefficient is 0.00297

PART-II

1 (d) Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number =10000(steady state)

Giving inlet velocity as 100m/s for getting Re =10000

Hybrid Initialization done

RESULTS AND DISCUSSION:

Showing Residuals

Showing plot and value of drag coefficient.

From this it is clear that here the drag coefficient is 0.51083

Showing plot and value of lift coefficient.

From this it is clear that here the drag coefficient is 0.00713

PART-II

1 (e) Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number =100000(steady state)

Giving velocity at inlet as 1000m/s for getting Re=100,000

Hybrid initialization done

RESULTS AND DISCUSSION:

Showing residuals

Showing plot and value of drag coefficient.

From this it is clear that here the drag coefficient is 0.53300

Showing plot and value of lift coefficient.

From this it is clear that here the lift coefficient is -0.0168

Values of Drag Coeffient from the Journal is given below:

Values of Drag Coeffient which I got by simulation is given below:

Si No	Re No	Drag Coeffient from Simulation	Drag Coeffient from Journal
01	10	3.3008744	3.30
02	100	1.2934	1.50
03	1000	0.8027	1.30
04	10,000	0.51083	0.89
05	100,000	0.53300	0.64

Reference link for Journal: Paper: https://www.researchgate.net/publication/305876539_A_Numerical_Analysis_of_Fluid_Flow_Around_Circular_and_Square_Cylinders?enrichId=rgreq-9a504361d3a4f3abb357b56fd06d5120-XXX&enrichSource=Y292ZXJQYWdlOzMwNTg3NjUzOTtBUzo0MTQ4NDk4NTIwMzUwNzJAMTQ3NTkxOTMyMDI5Ng%3D%3D&el=1_x_2&_esc=publicationCoverPdf

CONCLUSION:

1.When fluid flows over cylinder, wake region is formed next to cylinder due to decrease in pressure and recirculation of flow occures and hence flow separation occures.

2.he flow over a cylinder is simulated for both Steady and unsteady cases with Re=100, and with the results generated the phenomena of Von Karman Vortex Street are also observed.

3.Necessary plots are plotted in order to observe that the flow is converged and the vortex shedding is happening.

4.Contours are generated in order to observe the flow over a cylinder.

5.The Strouhal number is calculated.

6.Six different simulations i.e (Re = 10,100,1000,10000,100000,1000000) are simulated to observe the behavior of the drag and lift coefficients by changing the Reynolds number.

7.In order to observe the behavior of the drag coefficients for the simulations, the velocity of the flow is varied to change the Reynolds number and the rest of the parameters are kept constant.

8.As we know if the Reynold number is less than 2000, then flow in a pipe is Laminar. Hence we use the Viscous model = Laminar.

9.When Re number increases the drag coefficient is decreasing

10. Drag coeffients from simulation and Journal comapared .