Week 2 - Flow over a Cylinder.

Flow Over a Cylinder

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

PART-I

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

PART-II

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)

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 %]

Theory:

Vortex Shedding is the phenomenon that occurs when a fluid (air or water) flows past a blunt body (such as a cylinder) at certain velocities, depending on the size and shape of the body. In this oscillating flow, vortices are created at the back of the body and detach periodically from the sides of the body forming a “von Karman vortex street”. The fluid flow past the object creates alternating low-pressure vortices on the downstream end of the object. The object will tend to move toward the low-pressure zone. Furthermore, von Karman vortex street is a repetitive pattern of vortices, caused by a process called Vortex Shedding, which is responsible for the unsteady separation of flow of a fluid around blunt bodies.

Strouhal Number is a dimensionless number used to describe oscillating flow mechanisms. The Strouhal number is given as:

where f is the frequency of vortex shedding, L is the characteristic length (for example, hydraulic diameter or the airfoil thickness) and U is the flow velocity.

Procedure:

1. In Ansys Workbench, drag and drop Fluid Flow (Fluent) into Project Schematic.
2. Open Spaceclaim to create the 2D drawing of the apparatus. An infinitely long cylinder of dia D = 2m is placed in an otherwise undisturbed uniform crossflow. The boundaries on either side are placed at a value of 10D and 20D from the center of the circular cylinder, respectively.
3. In Spaceclaim, covert the above drawn figure into a surface by using “Pull” command. Delete all sketch lines and exit Spaceclaim when completed.
4. Open Mesh generation module. Create Named Selections for Inlet, Outlet, the two long edges of the surface will be “symmetry” and Wall for the edge of the hole.
5. Assign appropriate element size (0.225m in this report) as per grid-dependency test and generate triangular mesh. Ensure that the element metrics/quality is not lower than 5%. Edge sizing is given for the hole. (No. of edge divisions =36).
6. 6 inflation layers at a distance of 0.005m from each other are assigned for better mesh quality around the hole. Exit Mesh module.
7. Set the following data in Fluent Module for the simulation of Flow over a cylinder.

Part 1: Steady flow vs Unsteady Flow for Re = 100

Tab	Criteria	Parameter	Value
Domain	Units	Distance	m
Physics	General	Solver	Pressure-Based
		Time	Steady
		Velocity formulation	Absolute
		2D Space	Planar
	Models	Viscous Model	Laminar
	Materials	Create/Edit Material	Create New Material - "User Fluid" Density = 1 kg/m^3 Viscosity = 0.02 kg/ms (Subject to change)
	Zones	Cell Zones	Replace "Air" with "User Fluid" as simulation fluid
		Boundary Conditions	Inlet Velocity = 1m/s Outlet Gauge Pressure = 0 Pa Stationary Wall; No Slip Wall Condition
Results	Surface	Create Point	Create a "Monitor Point" at (8,0,0) from the centre of hole
	Graphics	Contours	Create Contour animations for pressure and velocity at "Monitor Point"
Solution	Solution	Methods	SIMPLE Scheme
	Reports	Definitions	New Surface Report-->Vertex Average Field Variable= Velocity & Velocity Magnitude Surfaces = Monitor Point Check Report Plot and Report File
			New Force Report-->Lift At wall Check Report File and Report Plot
			New Force Report-->Drag At wall Check Report File and Report Plot
	Initialization	Method	Hybrid
		Initialize
	Run Calculation	No. of Iterations	500

Note: The above set-up is done for Steady flow at Re=100. For unsteady flow the setup remains the same as above except for the following changes:

1. Physics-->Time-->Transient
2. Solutions-->time step size-->0.1
3. Solutions-->No. of iterations-->750

Part 2: Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000. (Steady flow)

• Lift and Drag Coefficients are plotted as shown in the above table.
• Reynolds Number (Re) =

Where ρ = Density of fluid, V = velocity of fluid, d = diameter of cylinder and µ= Dynamic Viscosity

Case 1: Re = 10, Viscosity = 0.2 kg/ms, Density = 1 kg/m³, Velocity = 1 m/s, Diameter = 2 m

Case 2: Re = 100, Viscosity = 0.02 kg/ms, Density = 1 kg/m³, Velocity = 1 m/s, Diameter = 2 m

Case 3: Re = 1000, Viscosity = 0.02 kg/ms, Density = 1 kg/m³, Velocity = 10 m/s, Diameter = 2 m

Case 4: Re = 1000, Viscosity = 0.02 kg/ms, Density = 1 kg/m³, Velocity = 100 m/s, Diameter = 2 m

Case 5: Re = 1000, Viscosity = 0.02 kg/ms, Density = 1 kg/m³, Velocity = 1000 m/s, Diameter = 2 m

Results: The results are shown in the images below:

Conclusion:

• When Re increases Cd decreases.
• When Re > 4000, flow is turbulent and therefore laminar flow is small, leads to lower skin friction drag.
• When Velocity increases, Cd increases.
• When Re = 10, no vortices are seen as the velocity is low and only boundary layer separation occurs. The Cd, also increases.
• In Unsteady flow for Re = 100, the vortices can be seen and shedding frequency calculated.
• Strouhal number (For unsteady flow, Re = 100) can be seen below.

Measure to avoid Vortex Shedding:

To prevent Vortex Shedding and unwanted vibrations of tall cylindrical structures, a longitudinal fin can be fit on the downstream end, which, given it is longer than the diameter of cylinder, will prevent the formation of eddies. Helical projections are placed at the top of tall cylindrical structures, such as chimneys (as shown above). They are helical because wind can blow from any direction. Another measure to prevent vortex shedding in tall cylindrical structures is to vary its diameter with height, such as tapering. This prevents the entire structure being driven at the same frequency.