Flow over a cylinder
AIM:
To simulate the fow over a cylinder with fluid by increasing the reynolds number by 20%, 40% and 100% and simulate the pressure and velocity variation with respect to time.
INTRODUCTION:
First, we have to run a simulation with baseline reynolds number. Then, we can calculate the corresponding velocity with the help of the following relation:
After calculating the velocity of the baseline reynolds number, it was then increased by 20%, 40% and 100% and then, the entire simulation process was repeated again for the three new cases.
For the cylinder for which we are performing the simulation, its diameter is defined as 50 mm(outer diameter). Hence, we can easily calculate the velocity for a particular reynolds number for our simulation.
THEORY:
Reynolds number is a unitless value that defines the nature of the fluid flow. It is simply defined as the ratio of the inertial force to the viscous force of the fluid. This value is very helpful in observing the nature of the fluid flow. The data that can be inferred are as follows:
Re<2000, represents laminal flow
2000<Re<4000, represents transitional flow
Re>4000,represents turbulant fluid flow
The value of the velocity can always be calculated corresponding to a particular reynolds number which can be very helpful while defining the nature of the fluid flow.
CALCULATION:
baseline flow:
let us assume the baseline flow to occur at a velocity of 10m/s. So, by applying the equation, we can find the value for the corresponding reynold number by using the following values for air at 25 degree celcius as:
dynamic viscousity = 1.81 × 10-5 Pa·s
density = 1.2754 kg/m³
used diameter = 0.05 m
baseline velocity = 10 m/s
so, baseline reynolds number = 33765.15
similarly, by increasing the reynolds number by the given percentage, we can also calculate thee values of their velocities.
20% increase:
velocity = 12m/s
Re = 40518
40% increase:
velocity = 14m/s
Re = 47271.21
100% increase:
velocity = 20m/s
Re = 67530.3
simulation end time:
For the given study, the simulation end time shoud be set as twice as the total flow time. The total flow time is the time it takes for the fluid to cross the computational fluid domain.
Since the length of our computational fluid domain is 450 mm and the velocity of the fluid is set at 10m/s, the total flow time is,
flow time = 0.45/10 = 0.045s
so, simulation time = 2(flow time) = 0.9s
similary, the simulation time can be calculated for the different reynolds numbers.
for v=12m/s :
flow time = 0.45/12 = 0.0375s
so, simulation time = 2(flow time) = 0.75s
for v=14m/s :
flow time = 0.45/14 = 0.0321s
so, simulation time = 2(flow time) = 0.642s
for v=20m/s :
flow time = 0.45/20 = 0.0225s
so, simulation time = 2(flow time) = 0.45s
SIMULATION:
To perform the flow simulation over the cylinder, we have to first create a cylinder which can be simply done by sketching a circle and extruding it to a length of 80 mm. That was all about the modelling part.
Now, we have to save the current part and create a new project wizard from the ribbon menu of the SOLIDWORKS flow simulation tab. We set the following settings:
unit system to SI unit
flow type as external time dependent(as our is external and depends on time)
the total analysis time to 0.1s and output timestep to 0.1s which means that we would get 10 steps throught the time.
added air as our flowing fluid
and finally, added a velocity of 10m/s to the X- direction, since we need to observe the fluid flow over that direction only.
After creating the new project from the wizard setup, we get to see that our cylinder is enclosed in a computaional fluid domain. This means that, the fluid flowing will only be observed inside the specified domain. We can always increase the size of the fluid domain according to our needs but we dont need to, for the given case study.
Then, we view the mesh setting by selecting local mesh. We can see that the default mest is appropriate for our study. So, we leave it as it is.
Finally, we hit the 'run' button to let the CPU calculate the results for our simulation. After its complete, we insert a cut plot at the cross- section (lateral) to visualise our results.
velocity cutplane for baseline simulation:
similary, the cutplanes for the pressure can also be obtained for the same simulation.
pressure cutplane for baseline simulation:
Now, to visualize our results with the variation of time, we need to animate the results with respect to the derived cut plots. It can be done by inserting an animation from the results drop-down. Then, we create a new animation wizard with selecting scenerio mode. After the wizard is complete, we allign the playback keys and run the play button.
YOUTUBE LINK FOR THE PRESSURE VARIATION ANIMATION:
https://www.youtube.com/watch?v=SSuzHIhttAQ&feature=youtu.be
YOUTUBE LINK FOR THE VELOCITY VARIATION ANIMATION:
https://www.youtube.com/watch?v=vLYgEMb6vBk&feature=youtu.be
Now, the above procedure can be repeated to simulate the fluid flow for different reynolds number by changing the value of velocity along X-axis.
20% increase, v=12m/s, Re = 40518:
cutplane for the pressure:
YOUTUBE LINK FOR THE PRESSURE VARIATION ANIMATION:
https://www.youtube.com/watch?v=rbGYgjsHIFg&feature=youtu.be
cutplane for the velocity:
YOUTUBE LINK FOR THE VELOCITY VARIATION ANIMATION:
https://www.youtube.com/watch?v=nw4MiRjtxN0&feature=youtu.be
40% increase, v=14m/s, Re = 47271.21:
cutplane for the pressure:
YOUTUBE LINK FOR THE PRESSURE VARIATION ANIMATION:
https://www.youtube.com/watch?v=0_U7qCouMiE&feature=youtu.be
cutplane for the velocity:
YOUTUBE LINK FOR THE VELOCITY VARIATION ANIMATION:
https://www.youtube.com/watch?v=MKMr2LpTWnw
40% increase, v=20m/s, Re = 67530.3:
cutplane for the pressure:
YOUTUBE LINK FOR THE PRESSURE VARIATION ANIMATION:
https://www.youtube.com/watch?v=YwcZw1Y6dro&feature=youtu.be
cutplane for the velocity:
YOUTUBE LINK FOR THE VELOCITY VARIATION ANIMATION:
https://www.youtube.com/watch?v=twGjwMnZDEA&feature=youtu.be
All the simulations for the cases were run for the calculated period of time, ie - the end time simulation. The end time was set by using the playback keys in the animation window.
OBSERVATION AND CONCLUSION:
Thus, form the abovr simulations, we can observe that the velocity and reynolds number go hand in hand. Almost all the cases lie at the turbulant side. With increase in velocity, the turbulant nature of the flow increases and we can observe that the flow gets quite distorted behing the cylinder, or after the fluid crosses the cylinder.
But, even though the velocity drastically increases with the reynold number, the pressure variation is very minimal and it shows very little change. This is because, the velocity and the reynold number are directly related.