Flow Through a Cylinder
AIM:
To simulate the flow over a cylinder for the conditions shown in the video, increase the Reynolds number by 20%, 40% and 100% and create animations for Pressure and Velocity variation.
THEORY:
Internal and External Flow: The flow of an unbounded fluid over a surface is treated as ‘external flow' and if the fluid is completely bounded by the surface, then it is called as ‘internal flow'. For example, flow over a flat plate is considered as external flow and flow through a pipe/duct is internal flow. However, in special cases, if the duct is partially filled and there is free surface, then it is called as open channel flow. Internal flows are dominated by viscosity whereas the viscous effects are limited to boundary layers in the solid surface for external flows.
Steady and Unsteady Flow: When there is no change in fluid property at point with time, then it implies as steady flow. However, the fluid property at a point can also vary with time which means the flow is unsteady/transient. The term ‘periodic' refers to the kind of unsteady flows in which the flow oscillates about a steady mean.
One/Two/Three dimensional Flow: A flow field is best characterized by the velocity distribution, and thus can be treated as one/two/three dimensional flow if velocity varies in the respective directions.
Compressible and Incompressible Flow: The flow is said to be ‘incompressible' if the density remains nearly constant throughout. When the density variation during a flow is more than 5% then it is treated as ‘compressible'. This corresponds to a flow Mach number of 0.3 at room temperature.
Reynolds' Number: The Reynolds' Number is defined as the ratio of inertial to viscous forces. The Reynolds' Number is a dimensionless number used to categorize the fluids system in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid.
Mathematically, the Reynolds' Number is defined as
Re= (rho*V*D)/Mu
where rho= density of the fluid flowing (kg/m^3)
V= velocity at which fluid is flowing (m/s)
D= Diameter of the container in ehich fluid is flowing (m)
Mu= Dynamic Viscocity of the fluid ( N-s/m^2)
PROCEDURE:
For simplification, we take a flow through the computational domain only in the X-Direction.
Diameter of the cylinder D= 0.04m
Velocity of Air V1= 10m/s (in the X-Direction)
Density of Air= 1.225 kg/m^3
Dynamic Viscocity of air at 20 deg C= 18.13 X 10^-6 Pa-s
Re1 = (rho*V1*D)/Mu
= 1.225*10*0.04/(18.13 X 10^-6)
= 27027.02703
Flow through time = 0.4/10= 0.04 secs.
End time= 0.04 x 2= 0.08 secs
We have to increase the Reynolds' Number by 20%,40% and 100%. rho,D and Mu will remain the same. Only V will vary. Knowing the new Re, we can find out the new V.
Case 1: 20% Increase
Re2= 32432.434
V2= Re2*Mu/(rho*D) = 12 m/s
Flow through time = 0.4/12= 0.03333333 secs.
End time= 0.033333 x 2= 0.06667 secs
Case 2: 40% Increase
Re3= 37837.83784
V3= Re3*Mu/(rho*D) = 14 m/s
Flow through time = 0.4/14= 0.0285714 secs.
End time= 0.0285714 x 2= 0.0571428 secs
Case 3: 100% Increase
Re4= 54054.05406
V4= Re4*Mu/(rho*D) = 20 m/s
Flow through time = 0.4/20= 0.02 secs.
End time= 0.02 x 2= 0.04 secs
1)Open SolidWorks. Select "Create New Part".
2) In the Top Plane, sketch a circle of radius 0.02m. Exit sketch. Extrude the circle by 0.05m.
3) Using the Shell command, make the cylinder hollow with thickness 0.001m.
4) Click on the Flow Simulation Tab and select the "Create Lids" option. Select the two ends of the cylinder as the two lids.
5) Click on the Wizard option. Enter the project name.Select SI system. Under Analysis Type, select External Flow. Under Physical Features select Time-dependent simulation. Total Analysis time should be 0.08 seconds and output step time should be 0.01 seconds.
6) Under Fluid to be selected, choose air.
7)Under Velocity Parameters, enter Velocity in X direction as 10 m/s. Click Finish. Computational Domain is created.
8) Select the Computational Domain. Make its length as 0.4m.
9) Run the simulation. After Running, Go to Results----> Cut Plot---->Insert Cut Plot.
10)Under Plane to be selected, select Top Plane. Under parameter, select Pressure.
11)Create another cut plot in the Top Plane, this time parameter being Velocity.
12) Select Animations.
13)Insert Control Point for both the lines representing the two cut plots.
14)Move the second line such that the second animation starts when the first gets over.
15) Play The animation.
16) Repeat these steps for the other cases.
RESULTS:
When Velocity is equal to 10m/s: https://www.youtube.com/watch?v=IH0G7GkswPs&feature=youtu.be
When Velocity is equal to 12m/s (20% Increase) : https://www.youtube.com/watch?v=sBLSX1Ug-ZU&feature=youtu.be
When Velocity is equal to 14m/s (40% Increase): https://www.youtube.com/watch?v=AXQXhGHI5gw&feature=youtu.be
When Velocity is equal to 20m/s (100% Increase): https://www.youtube.com/watch?v=tuHiz6AK2II&feature=youtu.be
INFERENCE:
The pressure distribution doesn't seem to vary much when velocity increases from 10m/s to 20m/s. Average Pressure increases from 101330 Pa to 101380 Pa.
Velocity Distribution: When Vx= 10m/s The Computational domain starts with a brown colour(Velocity approximately equal to 11.5 m/s) but with the passage of time a dark green region begins to form (Velocity= 7.5m/s).This is followed by a blue region(low velocity region) which signifies that air is leaving. When the Reynolds' number increases by 100 %, the region is first dark green (Velocity= 16m/s), but with the passage of time a brown region begins to form (Velocity= 23m/s) with a red region near the Curved surface area of the cylinder(Velocity=25m/s). This is followed by a blue region(low velocity region) which signifies that air is leaving. This shows that average velocity increases with increase in Reynolds' number.