Steady Vs Unsteady flow over a cylinder

Steady Vs Unsteady Flow Over a Cylinder

AIM:-

To simulate the flow over a Cylinder with using steady and Unsteady solver and to explain the phenomeno of the Karman Vortex street.Also to calculate the co-efficient of drag and lift over the cylinder by varying the Reynold's Number and discuss it effect on it.

INTRODUCTION:-

In fluid dynamics, a Kármán vortex street (or a von Kármán vortex street) is a repeating pattern of swirling vortices, caused by a process known as vortex shedding, which is responsible for the unsteady separation of flow of a fluid around blunt bodies a Cylinder.This type of vortex street will form only at a certain range of flow velocities, specified by a range of Reynolds numbers (Re), typically above a limiting Re value of about 90. The (global) 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 or in a channel.In this case, potential flow around a circular cylinder is a classical solution for the flow of an inviscid, incompressible fluid around a cylinder that is transverse to the flow. Far from the cylinder, the flow is unidirectional and uniform. The flow has no vorticity and thus the velocity field is irrotational and can be modeled as a potential flow. Unlike a real fluid, this solution indicates a net zero drag on the body.

THEORY:

ANSYS CFD solvers are based on the finite volume method,

• Domain is discretised into a finite set of control volume.
• General conservation equations for mass, momentum, energy, species, etc. are solved on this set of control volumes.
• Partial differential equations are discretised into a system of algebraic equations.
• All algebraic equations are then solved numerically to render the solution field.

Initially the process involves three major Categories,

Pre-Processing

• Geometry
• Mesh
• Physics
• Solver Settings

Solve

• Compute solution.

Post Processing

• Examine results.

SOLVING:-

There are two parts in solving the Probelm;

Part-1:-

For this part we will be comparing the simulation between the steady and unsteady flow over the cylinder for Reynolds Number 100.

Part-2:-

To calculate the co-efficent of drag and lift over the cylinder by using steady state solver and to discuss the effect of reynolds numberon co-efficient of drag.

MODELING:-

• Initially to design the desired object we are starting up Space Claim.
• After starting the space claim, the 2D representaion is drawn according to the given dimensions.

• First keeping the origin as centre in postive Y axis a circle is drawn for 2m of Diameter.
• Then using construction lines from the centre of the circle 2 lines are drawn horizontally at 20m and at 40m respectively.
• Then keeping the inlet length at 20m a rectangle is drawn with length 60m and breadth 20m.
• Then remove the construction lines to get the required figure.
• After that using Pull option a surface is created.
• Then the circular object (i.e.the cyindeler) is removed to show the required surface.
• This Completes the modeling of the required 2D surface.

MESHING:-

• After completing the 2D model next step is to generate the mesh.
• Intially Ansys generates the mesh Using Quad Dominant mesh.
• But to get a clear simulation we are using Triangular shape mesh.
• After generating the triangular mesh we need to get a perfect circle or smooth circle or else the simulation result may vary.
• To get that Body Fitted Mesh we are selecting the circular edge and we are chang in the type to number of divisons and type in the value 36(i.e. we are assaigning a division for every 10 degrees because circle has 360 deg).
• To refine the surface of the cyinder more we are adding 6 more inflation layers to refine it even further to get a clear shape, the first layer thickness of inflation layer is set to 0.005m.
• Thus generating the required mesh.
• After Generating the mesh we should name various components such as Inlet,Outlet,Cylinder walls and Symmetry Boundary condition.

Intially Generated Mesh Mesh after adding inflation layers

6 Layers of Inflation

Final Mesh with element size of 0.5m

SETUP:-

• After Meshing next step is to setup the Fluent.
• We will be doing two case scenarios,
• 1) Compare Steady and Unsteady FLow over cyinder for RE=100.
• 2) To perform and to find the co-efficient of drag and lift over cyinder for various reynolds number and compare it.

PART-1

• Intially the setup is done for steady state with preassure based absolute solver with keeping viscous at Laminar
• We are keeping viscous at Laminar beacuse Reynolds number is minimum and set at 100.
• To get the Required Reynolds number We are creating a new user defined element based upon Air by altering the density and viscousity of the fluid in respective of The Reynolds number.
• Reynolds number can be calculated by:-
• Kinematic viscosity = dynamic viscosity/fluid density
  
  Reynolds number = (Fluid velocity x Internal pipe diameter) / Kinematic viscosity
• To get the required Reynolds number 100 we are assaigning; Viscosity of fulid = 0.02 kg/m-s Fluid density = 1 kg/m3

Inlet velocity = 1 m/s

• We also set a monitor point to observe velocity towards the rear of the cylinder.
• After selecting the required plots,contours and animation we then Intialize.
• We will be choosing Hybrid Intialization to proceed with the solution.
• Then we run for 600 iterations and the simulations results of steady state is given below.

Scaled Residules of Steady State at Re=100 Monitor Point Velocity of Steady state at Re=100

Animation for velocity of fluid over a cylinder under steady state

Now we are going to do for transient flow over cylinder with Re=100

• Similarly we are using the same conditions but the solver is changed to Transient solver.
• Then we intialize the step.
• The given time step is set to 0.1 and upto 600 time step.
• The results of the simulations are as follows.

Scaled residule for Transient condition Monitor point velocity for Transient condition

Animation for velocity of fluid over a cylinder under Transient state

Strouhal Number:-

where L is a characteristic length (equal to the diameter D in case of a circular cylinder or tube in cross flow) and U∞ the freestream velocity .

Strouhal Number=0.198(1- 19.7/100)

=0.198(0.806)

Strouhal Number for Reynolds Number 100=0.158994

The Best Material Tht can be used is the fulid air with density=1kg/m3 and Viscosity=0.02kg/m-1.