Flow over a cylinder using SOLIDWORKS | Flow Simulation Study
SIMULATION OF THE FLOW OVER A CYLINDER WITH DIFFERENT REYNOLDS NUMBER.
THEORY:
COMPUTATIONAL FLUID DYNAMICS: CFD has fascinated researchers, as it is a fast, accurate, and reliable method of analyzing the variation of hydrodynamic properties of the flow over and within a body. Computational Fluid Dynamics (CFD) is a branch of fluid mechanics that uses numerical methods and algorithms to solve complex problems involving fluid flow.
REYNOLD'S NUMBER: Reynolds number can reveal whether the flow is laminar or turbulent. The transition from laminar to turbulent flow depends on the surface roughness, flow velocity, geometry, surface temperature, and type of fluid, among others. Formula to calculate the baseline case Reynolds number.
`Re = (ρ*u*D)/μ`
where
- D= cylinder diameter in
- = dynamic viscosity in
- = density in
- u= inlet velocity in
GEOMETRY OF THE MODEL:
A cylinder with the following dimensions is created in SOLIDWORKS.
- Diameter = 40mm
- Length = 50mm
- Surface roughness is taken as zero.
- Gravity is not considered.
AIR IS THE WORKING FLUID IN OUR SIMULATION.
- The density of air approx. 1.225 [according to ISA (International Standard Atmosphere)].
- Dynamic viscosity of air is Kg/ms at temperature 300 k pressure 1 atmosphere.
The computational domain has a length of 300mm. Thus, the flow-through time is given as the time taken for the velocity to reach the end of the computational domain. The end time is taken as twice that of flow through time.
THE CALCULATIONS ARE AS FOLLOWS FOR THE ‘VELOCITY’, ‘FLOW THROUGH TIME (FTT)’ AND ‘END TIME’
For Re_20:
We know,
`Re = (ρ*u*D)/μ`
For Velocity,
`u = (Re*μ)/(D*ρ)`
And for FTT (Flow-Through Time),
`FT T= (Len g t h o f domai n)/(V e locity)`
Now,
`u= (20 * 1.81*10^(-5))/(1.225 * 0.04)=0.0074 m/s`
And,
`FT T= (0.3)/(0.0074)=40.54 s`
For Re_40:
We know,
`Re = (ρ*u*D)/μ`
For Velocity,
`u = (Re*μ)/(D*ρ)`
And for FTT (Flow-Through Time),
`FT T= (Len g th of domai n )/(Velocity)`
Now,
`u= (20 * 1.81*10^(-5))/(1.225 * 0.04)=0.0148 m/s`
And,
`FT T= (0.3)/(0.0148)=20.27 s`
For Re_100:
We know,
`Re = (ρ*u*D)/μ`
For Velocity,
`u = (Re*μ)/(D*ρ)`
And for FTT (Flow-Through Time),
`FT T= (Leng th of domai n )/(Velocity)`
Now,
`u= (100 * 1.81*10^(-5))/(1.225 * 0.04)=0.0369 m/s`
And,
`FT T= (0.3)/(0.0369)=8.13 s`
And, the End time is twice of FTT, Therefore
- For Re_20 End Time is:`40.54*2=81.00 s`
- For Re_40 End Time is:`20.27*2=40.54 s`
- For Re_100 End Time is:`8.13*2=16.26 s`
Therefore, As per the calculations we have:
- Velocity in x-direction, For Re 20, 40, 100 respectively:
- 0.0074 m/s
- 0.0148 m/s
- 0.0369 m/s
- Flow-through time is, For Re 20, 40, 100 respectively:
- 40.54 s
- 20.27 s
- 813 s
- End time which is needed for the plots and calculation of simulation, For Re 20, 40, 100 respectively:
- 81.00 s
- 40.54 s
- 16.26 s
While conducting the analysis in the simulation wizard the total analysis time is equal to the end time obtained. The variable pressure and velocity for the respective Reynolds number are shown below.
FOR RE=20
PRESSURE PLOT
VELOCITY PLOT
FOR RE=40
PRESSURE PLOT
VELOCITY PLOT
FOR RE=100
PRESSURE PLOT
VELOCITY PLOT:
ANIMATED VIDEO OF ALL THE PLOTS SUBMERGED INTO ONE:
Click here to watch the video...
OBSERVATIONS
- Inlet velocity in x-direction increases with the increase in Reynolds number, thus increasing the flow of air over the cylinder.
- The Relative pressure variation does not vary to a large extent for the Reynolds numbers taken.
- It is observed that the high pressure is created on the surface facing the inlet velocity.
- 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 zero nearer to the cylinder surface [The surface which is not in contact with inlet velocity]. For higher values of the velocity, waves are created behind the cylinder.