domingo, 5 de maio de 2013

Comparing Velocity Plot from Simulation's Result Against Analytical Equation

We have several ways of comparing the data. So ... my comparison is only based on mean values. If you want something deep you should look for some statistical book regarding data analysis.

Taking the last graphic and rearranging the data to be fitted on the radius together with the analytical solution we can see the following result:
Graph generated using QtiPlot

Using the "eye" we can see that the simulation was very good, but taking into account velocity's mean value we have a small difference of 0.45% between analytical solution and the simulated one.

Remember this is a weak data analysis but we are paving the road to a broader area.

Right know I must prepare myself to embark, so, the next post regarding of how to get the simulation done and the graphics is going to take a little longer.

Usually, my embark rotation takes 28 days and will try to post something from the rig, but don't expect too much ... maybe some sunset pictures.

Cheers and see you in some few days!!!!

sexta-feira, 3 de maio de 2013

Using Icofoam to Solve Annular Flow

It took me a while to solve this problem. More than expected in fact.

I was able to run the problem since the beginning but the values were too away from what I expected and I thought the problem was related to something behind Icofoam ... not the code, far from that ...  but, my problem setting.

The values were wrong due to two things a coarse mesh and , I believe, floating number precision. I had to produce a finer mesh to see the actual results and increase the tool's length. I came with the following conclusion: we need to evaluate how the tool's length is going to affect the results previously. Took me a while to simulate everything.

This steady, laminar flow with Newtonian fluid has an analytical solution and can be easily derived from Navier-Stokes equations. Obs: For this time I will not consider the gravity.

Velocity profile is given by the following equation:

And the pressure drop on an annular section of length l would be:


p  → pressure
ρ  → density
ν  → kinematic viscosity
r outer wall radius 
ri   inner wall radius
v→ average annular velocity  

All units are in SI.

From the dimensions in we will change the tool's length to 10m , ν = 7.27e-5 m2/s, ρ = 1.10e+3 kg/m3 and vm = 1.66 m/s we will have a Reynolds number of 1159 and we can safely assume that the flow is laminar. So, Δp/ρ is assumed to be 22.43 m2/s2,  Δp = 24.67 kPa.

We have the pressure drop and the velocity profile. Taking the results from the simulation we can see the values agree with minor error (we still have space to increase the mesh definition). You can see that in the graphics the "no-slip" condition on the walls are obeyed.
Pressure divided by density

Velocity magnitude contour

Velocity vector over velocity contour

Velocity plot against cells. 
For a next post I will compare simulated velocity plots against its analytical solution and solve another exercise.