Flow over a cylinder

"FLOW OVER A CYLINDER."

"Simulating Flow over a Solid Cylinder."

1. Objective:-
2. To Run a baseline simulation and then calculate the Reynolds number.
3. Increase the Reynolds number by a factor of 20%, 40%, and 100% then run the transient flow simulation.

iii. Create animations for pressure-velocity for all the three Reynolds number.

2. Concepts:-

Before doing the simulation first we need to understand some basic terms related to the fluid flow over the body. the basic terms are as follows.

2.1 Basic Terms:

1. Stagnation point:

In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is Minimum (or) zero and static pressure acting on the body is maximum. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object.

ii Separation point and Wake Region:

The position at which the boundary layer leaves the surface of a solid body. It may occur with the laminar flow (laminar separation) or when the boundary layer is turbulent (turbulent separation). Separation is sometimes followed by reattachment of the flow.

The thickness of this layer is smallest at the stagnation point and increases towards the backside of the obstacle. However, at some point on the backside, the boundary layer separates from the obstacle's surface to form a vortex-filled wake whose transverse dimensions are similar to those of the obstacle itself. This phenomenon is known as boundary layer separation.

the flow separates from the surface and creating a highly turbulent region behind the cylinder called the wake.

iii. Vortex Shedding:

The boundary layer separates from the top to form a free and uncluttered shear layer. This layer of shear will eventually flow into the discrete vortex and then away from the surface (something called vortex shedding). Another type of fluid flow occurs as the shear layers drain from the top and bottom meet. They drain the other way from the cylinder and form a typical vortex pattern (Karaman vortex road) in the wake. Vortex depletion occurs at a discrete frequency and is a function of the Reynolds number. Unlimited frequency of vortex depletion, Strouhal depletion rate, St = f D / V, is approximately equal to 0.21 when the number of Reynolds is greater than 1,000.

2.2 Equations:

The type of flow is decided based on Reynold's number which is based on the density of fluid, Velocity of fluid, diameter and viscosity.

`[Re = (ρ*V*D)/μ]` .................(i)

Where:-

ρ = Density

V = Velocity

D = Diameter of pipe

μ = Viscosity

In our problem, we need the help of Reynold's number and increase it to 20%, 40% and 100% and then customize according to it. After that, We need to calculate the travel time and time. calculation of time based on the following formula.

`[Time=(Distance)/(Velocity)]` .................(ii)

Where:-

Time = flow-through time;

Distance = Length of the computational domain;

Velocity = calculated velocity for each case.

Other than These we need to understand some other basic terminology which is as follows.

2.3 Basic Terminology:

1. Computational Domain and its Dimensions:

Computational Dut is a simple visual form factor that is sufficient to look at geometry in measurement and to set boundary conditions.

this simple form should keep all the important aspects of the problem. by considering this as the nature of the system the boundary condition is given accordingly. here Cylindrical geometry. also, the size of the base provided for the computational domain is as shown below.

1. Transient Simulation:

temporary impairment is when the time from the other is reversed, so the maximum values ​​in the system can be employed at any given time but in a strict measurement of the situation, only the initial values ​​and fixed state values ​​can be obtained.

In this project, we are approaching a solution through a temporary simulation so that we can see the dynamics of each movement over time. this will also help us to look at the frequency of vortex spills in relation to the various Reynolds numbers.iii. Total Analysis time(TAT):- The total analysis time defines the physical time period until which the simulation will be run from its initial instant of time.

1. Flow-through time(FTT):-The time required for the flow to pass through the domain.
2. Output time steps(OTS):-Time step is used in transient solving which denotes the time interval for which the simulation will progress between each iteration/step. in our simulation the time step is 10 for each case.

3. Calculations:-

In All the Cases of simulation, we took the Diameter of the cylinder as 0.04m and length of the cylinder 0.05m. Also, the working fluid is air with density 1.225Kg/m^3 and viscosity as 18*10^-6 N.sec/m^2.

3.1 Baseline:

In the baseline simulation, we took the Velocity as 10m/s and doing the simulation with the total analysis time with 0.1sec and output time step 0.01sec. The calculation of the Reynolds number is as follows.

Reynold's number calculation:

from equation (i)

`Re= (1.225*10*0.04)/(18*10^-6)`

Re=27222.22Re=27222.22

After calculating Reynold's number for the baseline we need to increase it with a factor of 20%, 40% and 100% and calculating the velocity and effective time duration for the simulation as follows.

3.2 Increasing (Re) factor of 20 Percentage:

Increasing the Re:

Re=1.20⋅27222.22Re=1.20⋅27222.22

Re=32666.66Re=32666.66

Velocity calculation:

From Equation (i)

`32666.66= (1.225*V*0.04)/(18*10^-6)`

V=11.999 m/s

Time calculation:

from equation (ii)

`T=11.999/0.8`

T=0.067 sec

OTS=0.0067 sec

Similarly, We can calculate other Parameters for the remaining cases.

3.3 Increasing (Re) factor of 40 Percentage:

Increasing the Re:

Re=1.40⋅2722222

Re=38111.11

Velocity calculation:

`38111.11= (1.225*V*0.04)/(18*10^-6)`

V=13.999 m/s

Time calculation:

`T=13.999/0.8`

T=0.0571 sec

OTS=0.00571 sec

3.4 Increasing (Re) factor of 100 Percentage:

Increasing the Re:

Re=2⋅27222.22

Re=54444.44

Velocity calculation:

`54444.44= (1.225*V*0.04)/(18*10^-6)`

V=19.999 m/s

Time calculation:

`T=19.999/0.8`

T=0.0400 sec

OTS=0.00400 sec

Final Parameters Table:

Type	Reynold's Number	Velocity(m/s)	FTT(sec)	TAT(sec)	OTS(sec)
Baseline	27222.22	10.000
20% Factor	32666.66	11.999	0.067	0.133	0.0133
40% Factor	38111.11	13.999	0.0571	0.1142	0.01142
100% Factor	54444.44	19.999	0.0400	0.08004	0.008004

Where:-

FTT = flow-through time ; TAT = Total Analysis time ; OTS = Output time steps.

4. Procedure:-

After the calculation we move on to the next.

Step 1: Making a Cylinder 0.04m wide and 0.05m long at Solidworks.

Step 2: Setting the Wizard in flow simulation with the required data such as flow type, water type, precise velocity and more. Here we take an external study of dependence and time variability in relation to the calculated number of Reynold for each case. Also, the liquid flow of air and the velocity are in the x-direction position (different in each case) and the z-direction velocity is taken to be zero.

Step 3: Setting a Computational Domain As Discussed in Basic. i.e. 0.8m in good x-direction, -0.4m in non-x area, 0.25m in direct y direction, -0.25m in y-negative direction.

Step 4: Set Mesh by default. above the cylinder, we need a fine mesh to get a better result. therefore, to do that we are fitted with a local mesh with 3 refining valve.

Step 5: Place the Cut plan on the XY plane and turn it into the center of the cylinder.

Note: Here we are taken a strong guard.

5. Simulation & Analysis:-

5.1 Baseline:

In the baseline simulation, we took the Velocity as 10m/s and doing the simulation with the total analysis time with 0.1sec and output time step 0.01sec.

Pressure

https://youtu.be/EDMPFUCEqcY

Velocity

https://youtu.be/N0LGebOVSio

5.2 factor of 20% :

In the baseline simulation, we took the Velocity as 10m/s and doing the simulation with the total analysis time with 0.1sec and output time step 0.01sec.

Pressure

https://youtu.be/Z2UEvv1NW8o

Velocity

https://youtu.be/L8MfGwXfqL4

5.3 factor of 40%:

In the baseline simulation, we took the Velocity as 10m/s and doing the simulation with the total analysis time with 0.1sec and output time step 0.01sec.

Pressure

https://youtu.be/nhK-rITUrOg

Velocity

https://youtu.be/WFdi7AuoguE

5.4 factor of 100%:

In the baseline simulation, we took the Velocity as 10m/s and doing the simulation with the total analysis time with 0.1sec and output time step 0.01sec.

Pressure

https://youtu.be/4rVpSziOT80

Velocity

https://youtu.be/nNDmIHegjXE

6. Observation and Conclusion:-

Pressure View:

Velocity View:

Note:- Here we take a picture of only one case as a reference for the visual representation of basic understanding. because the view made here applies to all cases.

This recognition.

1. As Reynold's figure increases the velocity increase and the passage of time decreases in all cases. While in all pressures of compression, we can see that the pressure changes are very small.
2. In all cases the surface exposed on the side of the water flow encounters a high pressure indicated as a red cartoon area. the green area shows the low pressure on the cylindrical surface exposed where the liquid flows. the red area is shown to be small due to the small impact area while the green area is large due to the separation of water on the surface of the cylinder.

iii. Stagnation point: - In 'Pressure View', we see that the red area shown as 'Cut plan 1 Maximum' and 'velocity view', we can see the blue region above the cylinder exposed to the fluid flow described as 'base area 1 minimum'. These two circuits indicate the point at which the static pressure is higher and the velocity is lower. Therefore as we know that the point where the velocity is low (near zero) and the high static pressure is known as the stagnation point.

1. Division by region: - In the 'velocity view' we see that the point is indicated by the red domain name as the 'top area circuit' is the point at which the fluid (or) boundary layer of the boundary layer has begun. This is due to the magnitude of the width boundary affected by the pressure gradient and, the separation occurs due to the resistance (or) of the gradient pressure.

As we have seen on the balcony view the flow separates from the outside and creates a turbulent area behind a cylinder called a wake.

i.e: The separation point is different for different cases. also may have a different point of maximum and minimum velocities.

Reference:

http://ecoursesonline.iasri.res.in/mod/page/view.php?id=1080

http://www.eng.fsu.edu