FLOW OVER A CYLINDER
1.AIM :
TO PERFORM A TRANSIENT FLOW SIMULATION OVER A CYLINDER FOR VARIOUS REYNOLDS NUMBER
2.OBJECTIVE :
- To perform transient flow simulation over a cylinder using Solidworks flow simulation.
- To calculate Reynolds number for the baseline case.
- To increase the baseline case Reynolds number by a factor of 20%, 40%, and 100% and perform transient flow simulation for the same.
- To create cut plots and animations for pressure and velocity for all the Reynolds number.
3.INTRODUCTION :
Flow simulation over a cylinder can be performed through computational fluid dynamics (CFD), a powerful and convenient tool to perform CFD is Solidworks flow simulation.
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions.
In simple words to perform CFD following steps are performed in order:-
- A computational model is made using computer aided designing and the domain of fluid is extracted.
- Further the domain is divided into discrete cells called mesh.
- Next the Boundary conditions are defined, which is specifying the fluid behaviour and properties at all bounding surfaces of the fluid domain.
- Next the calculations are performed and the equations are solved iteratively till the convergence is achieved.
- Finally the analysis and visualization of the calculations performed can be seen.
The CFD analysis to be performed for the fluid domain can be either steady state or transient.
The steady state simulation computes a solution that does not change with time whereas transient simulation calculates the value in each time for each quantity, which leads to steady state simulation giving results faster than transient but are less accurate.
Here in this work the transient flow simulation over a cylinder is performed for an assumed air velocity of 10 m/s and the Reynolds number is calculated for the same. Further the value of Reynolds number is increased by a factor of 20%, 40% and 100% and the transient flow simulation is performed for all these 3 values obtained.
The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities.
`"Reynolds number, Re "= "inertia force"/"viscous force" = (ρ *V* D)/µ`
Where, ρ is mass density
V is average velocity of flow
D is diameter of cylinder
µ is dynamic viscosity of flowing fluid
Based on the values of Reynold’s number (Re), different flows are classified as :
i. Re<2000 - Laminar flow
ii. Re>4000 - Turbulent flow
iii. 2000< Re < 4000 - Transitonal flow
4.CALCULATIONS :
The diameter of cylinder is taken to be, D = 0.05 m
The height of cylinder is taken to be, H = 0.05 m
`Re = (ρ* V* D)/µ`
We know that
Kinematic viscosity, `nu = mu/rho`
`=> Re = (V* D)/nu`
The fluid flowing is taken as Air
Density of Water, `rho = 1.225 "kg/"m^3`
Kinematic viscosity of Air @ 293 K, `nu = 1.516 " x " 10^-5 m^2"/s"`
The study is divided into 4 cases, the first case is the baseline case in which the reynolds number is calculated using the velocity of air assumed and further the reynolds number obtained is increased by a factor of 20%, 40% and 100% and the velocity of air corresponding to each reynolds number is calculated and used for simulation.
CASE 1
Baseline case
Assumed air velocity = 10 m/s
`"Reynolds number, Re = "(V*D)/nu = (10*0.05)/(1.516 " x "10^-5 )`
`Re = 32981`
CASE 2
Increasing value of baseline reynolds number by 20%
New value will be
`Re= (1+0.2)*32981`
`Re = 39578`
Corresponding velocity of air
`39578 = (V*0.05)/(1.516 " x "10^-5 )`
`V = 12 m"/s"`
CASE 3
Increasing value of baseline reynolds number by 40%
New value will be
`Re= (1+0.4)*32981`
`Re = 46173`
Corresponding velocity of air
`46173 = (V*0.05)/(1.516 " x "10^-5 )`
`V = 14 m"/s"`
CASE 4
Increasing value of baseline reynolds number by 100%
New value will be
`Re= (1+1)*32981`
`Re = 65962`
Corresponding velocity of air
`65962 = (V*0.05)/(1.516 " x "10^-5 )`
`V = 20 m"/s"`
Calculation for simulation time
The simulation time is taken as 2 times the flow through time of air across the computational domain.
The length of computational domain taken is L = 0.45 m.
CASE 1
Flow through time = `L/V = 0.45/10 =0.045 s`
Simulation time, `T=2 *0.045 =0.09s`
CASE 2
Flow through time = `L/V = 0.45/12 =0.0375 s`
Simulation time, `T=2 *0.0375 =0.075s`
CASE 3
Flow through time = `L/V = 0.45/14 =0.032 s`
Simulation time, `T=2 *0.032 =0.064s`
CASE 4
Flow through time = `L/V = 0.45/20 =0.0225 s`
Simulation time, `T=2 *0.0225 =0.045s`
| CASE | VELOCITY (m/s) | REYNOLDS NO | SIMULATION TIME (sec) |
| 1 | 10 | 32981 | 0.09 |
| 2 | 12 | 39578 | 0.075 |
| 3 | 14 | 46173 | 0.064 |
| 4 | 20 | 65962 | 0.045 |
5.PROCEDURE :
1) First the model of a cylinder with dimensions is created using Solidworks
Diameter = 0.05 m
Height of cylinder = 0.05 m
2)Using the wizard option a new project is created. The analysis type selected is External and a time dependent analysis is chosen.
3)Further the air is selected as fluid.
4)The velocity of air and ambient conditions are entered and the project is created.
5)The global mesh created with settings can be seen in the snapshot below.
6)Finally the simulation is run for different velocities and pressure-velocity plots and animations are made.
6.RESULTS :
The cut plots and animations for pressure & velocity for all the cases are shown below:-
CASE 1 (@ 10m/s)
Cut plot for pressure contours
Animation for pressure variation
Cut plot for velocity contours
Animation for velocity variation
Explanation
When the air encounters cylinder surface due to the circular cross section of the cylinder the air diverges and it leads to increase in pressure and velocity in that region but at the front and back portion in the linear direction the amount of air reaching decreases and the pressure and velocity decreases.
This large region formed due to flow seperation is created wake region.
In wake region the flow is highly unsteady and large eddies are formed which leads to high turbulence and producing drag.
CASE 2 (@ 12m/s)
Cut plot for pressure contours
Animation for pressure variation
Cut plot for velocity contours
Animation for velocity variation
Explanation
When the air encounters cylinder surface due to the circular cross section of the cylinder the air diverges and it leads to increase in pressure and velocity in that region but at the front and back portion in the linear direction the amount of air reaching decreases and the pressure and velocity decreases.
This large region formed due to flow seperation is created wake region, this region increases in size comparitive to the 10 m/s velocity case.
In wake region the flow is highly unsteady and large eddies are formed which leads to high turbulence and producing drag, with increase in velocity the turbulence also increases and so does drag.
CASE 3 (@ 14m/s)
Cut plot for pressure contours
Animation for pressure variation
Cut plot for velocity contours
Animation for velocity variation
Explanation
When the air encounters cylinder surface due to the circular cross section of the cylinder the air diverges and it leads to increase in pressure and velocity in that region but at the front and back portion in the linear direction the amount of air reaching decreases and the pressure and velocity decreases.
This large region formed due to flow seperation is created wake region, this region increases in size comparitive to the 12 m/s velocity case.
In wake region the flow is highly unsteady and large eddies are formed which leads to high turbulence and producing drag, with increase in velocity the turbulence also increases and so does drag.
CASE 4 (@ 20m/s)
Cut plot for pressure contours
Animation for pressure variation
Cut plot for velocity contours
Animation for velocity variation
Explanation
When the air encounters cylinder surface due to the circular cross section of the cylinder the air diverges and it leads to increase in pressure and velocity in that region but at the front and back portion in the linear direction the amount of air reaching decreases and the pressure and velocity decreases.
This large region formed due to flow seperation is created wake region, this region increases in size comparitive to the 14 m/s velocity case.
In wake region the flow is highly unsteady and large eddies are formed which leads to high turbulence and producing drag, with increase in velocity the turbulence also increases and so does drag.
7.CONCLUSION :
Due to large flow seperation at the interface there is a highly turbulent region formed called wake, this region increases with increases in velocity which implies with increase in velocity the turbulence increases and more drag in produced.
8.REFERENCES :