Flow over a cylinder
AIM:
To simulate the flow over a cylinder for the given conditions and to obtain the plots for velocity and pressure with respect to time.
INTRODUCTION:
Computational Fluid Dynamics (CFD)
CFD is the branch of Fluid Mechanics which uses numerical methods and algorithms to solve complex problems involving the fluid flow. This has facinated the users, as it is fast, accurate and reliavle method of analyzing the variations of hydrodynamic properties of the flow over the cylinder and with in the cylinder.
Reynolds Number
It is the dimentionless number that reveal whether the flow is laminar or turbulant. Usually any kind of flow depends on the surface roughness, flow velocity, geometry, surface temperature, and type of fluid etc.
`R_e = (rho*v*D)/mu`
where,
| `R_e`= Reynolds Number (Dimensionless) |
| `v` = Average flow velocity in `m/s` |
| `D` = Diameter in `m` |
| `rho` = Density in `(Kg)/m^3` |
| `mu` = Dynamic Viscosity in `Pa*s` |
OBJECTIVE:
Our objective is to analyze the fluid flow over the cylinder and calculate Reynolds number for the base line simulation and increase the calculated Reynolds number to a factor of 20%, 40% and 100% and perform the simulation for all the three values of the Reynolds number and create the animation for velocity-pressure.
3D MODEL:
| Dia of the cylinder = 40 mm |
| Length of the cylinder = 50 mm |
BASELINE SIMULATION PARAMETERS:
Initially, i considered the baseline velocity of the air to be as 10 m/s. On the basis of initial velocity the Reynolds number is calculated. The parameter are given in the table below.
| INPUTS | VALUES |
| Diameter | 40 `mm` |
| Initial Velocity | 10 `m/s` |
| Density | 1.225 `(Kg)/m^3` |
| Dynamic Viscocity | 18.14*`10^-6` `(Ns)/m^2` |
Re = rho*U_inlet*D/mu
- D = cylinder diameter
- mu = dynamic viscosity
- rho = density
- Re = Reynolds number
- U_inlet = Velocity
By substituting the above values we get baseline Reyonlds number,
Re = 27012.12789
Similarly, Reynolds number at 20%, 40% and 100% is calculated,
| At 20% Re = 32414.55347 |
| At 40% Re = 37816.97905 |
| At 100% Re = 54024.25579 |
Now we are conducting the baseline simulation and conditions are given below
| INPUTS | VALUES |
| Analysis Type | External Flow |
| Fluid | Air |
| Time Dependent | Total Analysis Time: 0.0833 |
| Output time step: 0.00833 | |
| Inlet Velocity | 10 m/s |
| Global Mesh level | 3 |
CALCULATING SIMULATION END TIME
| Velocity = Distance / Time |
| Time = Distance / Velocity i.e., Time = 0.5/10 = 0.05 sec |
| The length of the domain along the X axis is 0.5 m |
| When the velocity is 10 m/s for Re = 27012.12789 then the simulation end time = 0.1 sec |
| Given that the end time should be 2 times the flow through time |
| At Baseline For V = 10 m/s, Re = 27012.12789, simulation end time = 0.1 sec |
| At 20%, for V = 12 m/s, Re = 32414.55347, simulation end time = 0.0833 sec |
| At 40%, for V = 14 m/s, Re = 37816.97905, simulation end time = 0.0714 sec |
| At 100%, for V = 20 m/s, Re = 54024.25579, simulation end time = 0.05 sec |
| From this we can say that as the velocity increases the time decreases. |
RESULTS:
1. Flow over a cylinder at 20% of the Reynolds Number ( V=12 m/s )
Cut plot of Pressure contour
Animation for Pressure at 12 m/s
Animation:https://youtu.be/GY6VHdd6xA0
Cut plot of Velocity contour
Animation for Velocity at 12 m/s
Animation:https://youtu.be/E66cCwL3o78
2. Flow over a cylinder at 40% of the Reynolds Number ( V=14 m/s )
Cut plot of Pressure contour
Animation for Pressure at 14 m/s
Animation:https://youtu.be/_93JYf54xcg
Cut plot of Velocity contour
Animation for Velocity at 14 m/s
Animation:https://youtu.be/ljAyjUxcQw0
3. Flow over a cylinder at 100% of the Reynolds Number ( V=20 m/s )
Cut plot of Pressure contour
Animation for Pressure at 20 m/s
Animation:https://youtu.be/BXYRLW-g-i0
Cut plot of Velocity contour
Animation for Velocity at 20 m/s
Animation:https://youtu.be/FJjceTpcsW4
CONCLUSION:
- As the Reyonlds number increases the velocity increases and the flow through time decreases.
- The relative pressure variation does not varry to a larger extent for the Reynolds number taken.
- We can observe that high pressure is created on the surface of the cylinder where the inlet velocity is hitting.
- The velocity variation in the above animations has different velocity profiles, when the velocity is larger the velocity profile is longer behind the cylinder surface and it is approximately behind the cylinder surface where the inlet velocity does not hit.