FLOW OVER A CYLINDER
AIM
To stimulate a transient flow over the cylinder using Soildworks.
OBJECTIVES
- To calculate the Reynolds number by running a base line stimulation.
- The Reynolds number is then increased by a factor of 20%, 40% and 100% and then the transient flow stimulation is carried out.
- To create Velocity and Pressure animations for all three Reynolds number.
THEORY
The flow of the fluid is transient or unsteady if its flow parameters such as velocity and pressure are dependent not only on the position in the coordinate system which is used to describe the field of flow but also time.
REYNOLDS NUMBER
Reynolds number is a dimensionless quantity which is used to determine the type of flow in any situation. It depends upon the viscosity of the fluid, density of the fluid and dimensions of the channel through which the fluid is flowing.
Reynolds number can be defined as the ratio of inertial force to viscous force.
`R_(e )= ρvD⁄μ`
Where
`R_(e )` is the Reynolds number
`ρ` is the density of the fluid in `kg⁄m^3`
`v` is the velocity of the fluid in `m⁄s`
`D` is the diameter of the pipe in `m`
`μ` is the dynamic viscosity of the fluid in `Ns⁄m^2`
Laminar flow occurs at low Reynolds number and the turbulent flow occurs at higher Reynolds number.
The physical properties of air at standard atmospheric pressure is given below
CALCULATION OF REYNOLDS NUMBER AND THEIR CORRESPONDING VELOCITY UNDER DIFFERENT CONDITIONS
For baseline stimulation, the following parameters are considered
Air is the fluid considered for carrying out the transient stimulation.
Velocity of the fluid `v= 10 m⁄s`
Density of the fluid `ρ = 1.204 kg⁄m^3`
Dynamic viscosity of the fluid `μ =〖1.82*10〗^(-5) Ns⁄m^2`
Diameter of the pipe `D =0.05 m`
% clear all
% close all
% clc
% Input Parameters
v = 10 % Velocity of the fluid
D = 0.05 % Diameter of the cylinder
rho = 1.204 % Density of air
vis_d = 1.82*10^-5 % dynamic viscosity
% Calculation of Reynolds number
Re = (rho*D*v)/(vis_d) % Formula to calculate the reynolds number
Re_20 = Re + 0.20*Re % Reynolds number is increased by a factor of 20 per cent
Re_40 = Re + 0.40*Re % Reynolds number is increased by a factor of 40 per cent
Re_100 = Re + Re % Reynolds number is increased by a factor of 100 per cent
RE = [Re_20 Re_40 Re_100]
% Calculation of velocity
V = (RE*vis_d)/(rho*D) % Velocity calculation for varying Reynolds numberTherefore,
Reynolds number for baseline stimulation is 33077
Reynolds number increased by 20% is 39692 and their corresponding velocity is `12 m⁄s`
Reynolds number increased by 40% is 46308 and their corresponding velocity is `14 m⁄s`
Reynolds number increased by 100% is 66154 and their corresponding velocity is `20 m⁄s`
CALCULATION OF FLOW THROUGH TIME AND END TIME
The time taken by the fluid to flow from inlet to the outlet in the computational domain is known as flow through time.
End time is the total time for which the stimulation has to be carried out. Generally, the end time should be twice the flow through time.
`Distance=Velocity ×Time`
`Time= (Distance )/(Velocity )`
The velocity is said to flow in x-direction and distance of the X-axis in computational domain is considered for the calculation. The computational domain length is set as 0.45m in x-direction.
% To calculate the flow through time and end time
clear all
close all
clc
d = 0.45 % Distance in x-direction
v = [12 14 20] % Velocities in m/s
flow =(d)./(v) % formula to calculate flow time
et = 2.*flow
|
`Velocity (m⁄s)` |
Flow through time (s) |
End Time (s) |
|
12 |
0.0375 |
0.075 |
|
14 |
0.0321 |
0.0642 |
|
20 |
0.0225 |
0.045 |
PROCEDURE
- Create a cylinder of diameter 50mm in the front plane.
- Under features, extrude it upto 150mm.
- Save the drawing.
3D MODEL
FLOW STIMULATION SETUP
- Click on Solidworks Add-Ins and Select flow stimulation.
- Click on Wizard to create a new project.
- Specify the name for the project and click Next.
- Specify the unit system and click Next.
- In Analysis type select External flow Click on time dependent stimulation and specify the Stimulation time and Time of Step and select next.
- In Default fluid dialog box, specify the fluid as air and click Add and click Next.
- In Initial wall conditions specify the inlet velocity in x-direction as `10 m⁄s` and click finish.
- Click on Global mesh and specify the initial level of mesh. 6 is the global mesh size used in this project.
- Click on Cut-plots and specify the contour as pressure and velocity and place the cut plot in the desired location
- Run the stimulation.
- Once the stimulation is completed animation for pressure and velocity profile can be done with the help of Animation wizard.
- The procedure is repeated for different inlet velocities.
The following are the results obtained from the stimulation
BASELINE STIMULATION
MESHING
Velocity profile
ANIMATION
Pressure profile
ANIMATION
The following are the velocity profile and pressure profile for 20% of the initial Reynolds number
Velocity Profile
ANIMATION
Pressure profile
ANIMATION
The following are the velocity profile and pressure profile for 40% of the initial Reynolds number
Velocity Profile
ANIMATION
Pressure profile
ANIMATION
The following are the velocity profile and pressure profile for 100% of the initial Reynolds number
Velocity Profile
ANIMATION
Pressure profile
ANIMATION
PART DRAWINGS
https://drive.google.com/file/d/136iXMUPZcCQIsGVHkrSz8wQjKBMDFg2X/view?usp=sharing
https://drive.google.com/file/d/1Mh6G7meOfy9MHFs_zAKiOrFcIlKE2XbT/view?usp=sharing
https://drive.google.com/file/d/1pctKlkYT4_cEC7n9KsDD1fJN16_Qb3FL/view?usp=sharing
https://drive.google.com/file/d/1Ue9xL2f3VH9EOpPTCFQVFTzZbXq8A2kG/view?usp=sharing
RESULTS
- The animation for pressure and velocity profile for a transient flow is carried out successfully.
- As the Reynolds number increases, the flow velocity also increases and the flow time decreases.
- High pressure is created on the surface facing the inlet velocity.
REFERENCES
https://www.ksb.com/centrifugal-pump-lexicon/transient-flow/328110/
Wikipedia