Project

Steady vs Unsteady Flow over a Cylinder

PPradeep Bandaru20 Apr 2020

Title:- To run both steady and transient flow simulations of flow over a cylinder.

objectives:-

Part-l

Simulate the flow with a steady and unsteady case for Re=100.
To calculate the strouhal Number for Re=100.

Part-ll

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 must be with 5%).

Given data:-To vary the velocity of the flow to change the Reynold\'s number.

Expected Results:-

In both approaches, show the flow has converged that is what quantities or plots can be used to determine that the flow has converged?
Plots of Coefficient of drag and lift
Plots to show vortex shedding behind the cylinder.
Mention the referred material at the end of the challenge page.

To simulate flow over a cylinder:-

karman Vortex street:-

In fluid dynamics, a Karman Vortex street(or a von Karman 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. It is named after the engineer and fluid dynamicist Theodore Von Karman and is responsible for such phenomena as the \"singing\" of suspended telephone or power lines and the vibration of a car antenna at Certain speeds.

A 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 and may be defined as a nondimensional parameter of the global speed of the whole fluid flow

Formulae used:-

Reynolds Number:- It is a dimensionless number which measures of ratio of Inertia Force to Viscous Force in the Flowfield.

It is defined as

2. Strouhal Number:- It is a dimensionless number describing the oscillating flow Mechanisms.

St=(f*L)/u

where f=vortex shedding frequency

L=Characteristic length over which the flow takes place

u=Free stream velocity of the flow

Vortex shedding frequency (f)=No of cycles/Time for cycles.

Procedure:-

Geometry :-

2-D geometry which is used for simulation is as shown

Meshing:-

Element size:- 0.25

Element type:- Triangular

Sizing:- Circle edge sizing

No of divisions=36

Inflation:- First layer thickness

First layer height = 5mm

Number of layers =6

Growth rate =1.2

Statistics:- Nodes = 20687

Elements=40482

6 layers-inflation layer

using the same mesh for all the cases

Named selections:-

Top and bottom are symmetry

Setup and Results:-

Setting up physics - Steady/Transient(requirement), pressure-based solver.

Viscous model - Laminar.

Material details - Fluid as user-defined (density=1 kg/m^3,viscosity=0.02 kg/m.s).

Boundary Conditions - Velocity inlet =1 m/s.

Pressure oulter= 0 pas(gauge).

Wall = No slip and stationary

Solution Method - Simple

Part-l

Simulation of flow with Steady and Unsteady case

Given data:-

Reynolds number (Re) = 100
Inlet Velocity = 1 m/s.
considering Material density = 1 kg/m^3 (for Re to be 100)
Considering Material viscosity = 0.02 kg/m.s (for Re to be 100)

Steady flow Unsteady flow

(NO of iterations=350) (Time step size=0.1 & No of Time steps=800)

Residual Plot

Here the Residual Plot helps to monitor the change in each and every convergence criterion for every iteration/time step and plot those values for every iteration/timestep.

The continuity, X-velocity, Y-velocity, Z-Velocity, Energy, Turbulence related variable are all the quantities or plots which can be used to determine that the flow has converged.

Here in steady-state, the solution ran for 350 iterations and after 250 iterations we can see that plots are becoming constant So from that we can say that the solution has been converged

In transient state after 12500 iterations, we can see that the plots are following the same pattern and its values are being repeated from that we can that solution has been converged.

VERTEX-Average of Velocity

Here in the VERTEX-Average of velocity in steady-state, from about 125 iterations we can see that the solution is starting to oscillation ie the vertex shedding is taking place.

Where as in case of trasient state the vertex shedding is happening from 26,000 flow-time(s).

In a transient simulation, we solve equations with respect to time so each and every time we solve equations accurately and we can actually trust that result.

Drag Coefficient

Here we can observe that the drag Coefficient is same in both Steady and Unsteady cases Re=100

Lift Coefficient

Here the lift Coefficient remains the same for both types of cases for Re=100

Vortex Shedding- Contour Plot

These are the contour plots for Steady and Unsteady cases for Re=100

To Calculate the strouhal Number for Re=100

Vortex Shedding frequency is a measure of the peak to peak oscillations to the time taken to complete those oscillations in a cycle.

Vortex Shedding frequency (f)=Number of cycles/Time for cycles

Considering No of cycles=3 & Time for cycles=20 sec (approx)

f=3/20

=0.15

Strouhal Number St=(f*L)/u

where f=Vortex shedding frequency

L=Characteristic length (Here L=d=2)

u=inlet velocity

St=(0.15*2)/1

=0.3

Part ll

To Calculate the Coefficient of drag and lift over a Cylinder for different Re(In steady solver)

Setup details are the same mentioned above and varying Re by changing the inlet velocity.

Material Details:- Density = 1kg/m^3

Dynamic viscosity = 0.02 kg/m.s

Case :(1) Re=10 , u=0.1m/s

1) Residual Plot 2) VERTEX-Average of Velocity