Flow over a cylinder

AIM:

Simulate the flow over a cylinder

OBJECTIVES OF THE PROJECT:

Run a baseline simulation and then calculate the Reynolds number. Then increase the Reynolds number by a factor of 20%, 40%, and 100% then run the transient flow simulation. Create animations for pressure-velocity for all the cases.

FORMULA USED:

A way of combining the factors to determine a number that can be used to indicate the presence of turbulent flow. It can be in as a variable expression as:

`Re=(ρVD)/μ`...(1)

Where Re is Reynolds number,

`rho`is the density

V is mean velocity

D is cylinder diameter

And `μ` is the dynamic viscosity,

Reynold's Number thus is:

(1) Determined mathematically from velocity of flow, radius of tube, density and viscosity of gas

(2) A unitless number

(3) Indicates that turbulent flow occurs when Re> 2000

(4) Reynold's number increases if there is an

(a) Increase in linear velocity of gas, density of gas, or radius of tube

(b) Reduction in viscosity of gas

INTRODUCTION:

Air Flow Patterns: -

The rate at which air moves from point of higher pressure to point of lower pressure a function of the

• Magnitude of driving pressure
• Resistance to gas flow in communicating pathway (influenced by radius, shape of pathway)
• Density and viscosity of gas

Formula for calculating resistance to flow in the airway:

`R=(p_1-p_2)/(V ̇)` ,Resistance in the airway is equal to the difference in pressure (also called pressure gradient) divided by the flow.

Properties of laminar flow of gas

Smooth unobstructed flow of gas and few directional changes, slow and steady flow.

Double flow by doubling pressure as long as the flow pattern remains laminar.

Properties of Turbulent flow of gas

Rough with much eddy current formation

Generated by sudden changes in direction or acute reduction in diameter

90% of turbulent flow in the airways occurs in the nose and trachea

Gas advances along tube at the same velocity at the centre as at the periphery

Driving pressure to produce given gas flow proportional to the square of volumetric flow rate

Double flow by fourfold increase in pressure

Development of Boundary Layer

• Laminar Boundary Layer:The boundary layer can be termed as laminar when there is no cross flow of air particles between the layers.

• Turbulent Boundary Layer:The boundary layer can be termed as turbulent when there is cross flow of air particles between the layers. Due to lose of energy, flow first becomes wavy in transition and then grows into turbulence.

The above Fig Shows that when a fluid (air or water) flows around an object certain phenomenon occur. For this discussion it is turbulence that is important. It represents the consequences of the boundary layer breaking away from the surface of the object. That turbulence is drag resistance and produces forces in the direction of the fluid flow. Such turbulence usually is invisible in air. However, the eddies that comprise the turbulence in water create random light refraction causing a milky white "substance" often called "bubbles".

Pressure and Velocity Relation:

Pressure and velocity are inversely proportional to each other. If pressure increases, the velocity decreases to keep the algebraic sum of potential energy, kinetic energy, and pressure constant. Similarly, if velocity increases the pressure decreases to so as to keep the sum of potential energy, kinetic energy, and pressure constant.

BODY OF THE CONTENT:

In this Case we have to create an obstacle as a cylinder (Dimensions: 0.02 Diameter, 0.05m length) over which the flow simulation has to be performed,

After creating the cylinder, now performing the flow simulation

• Creating new wizard, as it is a transient flow depends upon the time in this case setting up the time as 0.4 secs, and split up time can be set according to the precision we need or the fps we required for creating the animation.
• Fluid is Air at 293.2 K or 20⁰C and 1atm.
• The initial velocity is set to 1m/s in the x-direction.

(NOTE: As the simulation is set up for 0.4 secs and the velocity is 1m/s , therefore while setting up the computational domain, in x-direction setting the negative value to be 0.05m and positive to 0.15m in total of 0.2m, therefore the flow through time is 0.2 secs, and 0.4 secs is double of that.)

(NOTE: In all other case studies the computational domain will remain the same while flow through time will be changed in every case)

Now creating the cut plots for pressure as well as velocity and the global mesh is set to be automatic at level 3 with Advanced Channel refinement checked in.

After creating the animation saving the results Now calculating the Reynolds Number for this case and for other 3 cases as well.

Program to calculate the Reynolds Number, above table value is used for the calculation

close all
clear
clc
%% calculating the fisrt reynolds no.
Initial_velocity=1;      %vlocity of (m/s)
rho=1.204;              %density (kg/m^3)
D=0.02;                 %diameter (m)
mu=0.00001852;          %dynamic viscocity 1.852 * 10^-5 (kg/m-s)

Re_1=(Initial_velocity*rho*D)/mu;

%% calculating other three Reynolds Number
Re_2=1.2*Re_1;
Re_3=1.4*Re_1;
Re_4=2*Re_1;

disp(Re_1);
disp(Re_2);
disp(Re_3);
disp(Re_4);

Results

As the Reynolds number is directly proportional to the Velocity, the other three velocities were kept to be 1.2 m/s ,1.4 m/s and 2 m/s for the remaining cases.

As computational domain is set to be same for all the cases the flow through time is calculated according to which the simulation time is being set to be double of that.

VELOCITY(m/s)	FLOW THROUGH TIME(s)	SIMULATION TIME(s)
1.2	0.1666	0.3333
1.4	0.1428	0.2857
2	0.1	0.2

For each case we have to create a new wizard and in configuration save it as new.Procedure for creating the animation is same for all the cases.

OBSERVATIONS:

• From the animations created it can be seen that the velocity profile (in terms of magnitude) created is lesser in the front and the back region of the cylinder while greater in the case of edges.
• Pressure and velocity profiles are inversely proportional to each other, the region where the velocity is more the pressure generated is less and the region where the velocity is less the pressure generated is more.
• With the increase in the velocity the velocity profile of higher magnitude reduces in size and more turbulence starts to occur in frontal area.

CONCLUSION:

SolidWorks file for this project in given below in link.

https://drive.google.com/drive/folders/1uxYf5EffUwwrQhko5L__4lPAwp3a7iXs?usp=sharing

(NOTE: Run the calculation part for each case study, as results big files to upload, the mesh grid level can be increased for getting the finer results.)

The animations created is given below: