Week 2 - Flow over a Cylinder.

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

`S t = (f D)/ (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 coefficent(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 dra`.

The drag coefficient Cd is defined as

`C d = (2.F d)/ (ρ u^2 A)`

where:

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

ρ is the mass density of the fluid,

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

A is the reference area.

4. Co-efficient of lift:

The lift coefficient (Cl) 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.

5 .Vortex shadding:

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.

Reynolds Number (Re):

Reynolds number for a flow is a measure of the ratio of inertial to viscous forces in the flow of a fluid around a body.

Re = rho*V*d/Dynamic Viscosity

The range of Re values will vary with the size and shape of the body from which the eddies are being shed, as well as with the kinematic viscosity of the fluid. Over a large Re_d range (47<Re_d<10⁵ for circular cylinders; reference length is d: diameter of the circular cylinder) eddies are shed continuously from each side of the circle boundary, forming rows of vortices in its wake. The alternation leads to the core of a vortex in one row being opposite the point midway between two vortex cores in the other row, giving rise to the distinctive pattern shown in the picture. Ultimately, the energy of the vortices is consumed by viscosity as they move further downstream, and the regular pattern disappears.

A brief explanation to solve the flow over a cylinder

1. Geometry

Creating the geometry by sketching using the line and circle command, circle diameter of 2m and the dimensions having 20X60m and the circle is placed 20m from the inlet.

2.Mesh

After the geometry is loaded we should mesh it and here I used 0.19m as elemental size

Fluent details/procedure:

a. laminar model

b. fluid: Air

c. Method of discretization: Simple

d. Density/kinematic viscosity: 1/0.05

e. Creating a monitor point behind the cylinder by selecting point under surfaces in the results bar.

f. After creating the monitor point, create reports/plots for drag, lift, velocity wrt cylinder.

g. Create plots for the velocity at the monitor point to analyze the vortex shedding.

h. Use hybrid initialization for steady-state and standard for transient state simulations

(i) Simulate the flow with the steady case and calculate the Strouhal number for Re=100 and velocity 2.5m/s.

• Velocity and pressure contours

(ii) Simulate the flow with the unsteady case and calculate the Strouhal number for Re=100 and velocity 2.5m/s.

• Velocity and pressure contours

solver	Cd	CL	Strouhal number
steady-state	1.365	-0.13	0.01333
unsteady-state	1.3336	-1.179	0.1996

Result:

Drag and lift coefficient for different Re

Conclusions:

• In the first case, the 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.
• Necessary plots are plotted in order to observe that the flow is converged and the vortex shedding is happening.
• Contours are generated in order to observe the flow over a cylinder.
• By plotting Power Spectral Density vs Frequency, the Strouhal number is calculated.

• In the second case,
• 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.
• 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.
• 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.
• For Re=10, it is observed that there is no formation of vortex shedding and in the rest of the cases, it is clearly observed.
• As per the basic conditions and parameters, the results are validated from the literature.
• As we refine the mesh we need to run more iterations.
• From the above table, it can be concluded that the error percentage is less than 5%.