Pressurization Time (Nitrogen)

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1. Jan 28, 2015

Lee Chong Chi

Hi All Expert....

I have a question need help.

I have a part with internal volumme 24.5mm^3 at enviroment pressure 1.01325bar.

When I feed it with 1.14bar (nitrogen)...with a inlet Dia. 0.05mm

How can I calculate the pressurization time for the internally volumme up to 1.12bar

assume the initial condition at
1.01325bar & 20°C

I try to use solidworkd CFD to do simulation, and the result show is 0.36msec
And in actual, the part take update to 20msec

Thanks in advance for all the help.

2. Jan 28, 2015

Staff: Mentor

It will depend on the inlet. How do you get 0.36ms in the simulation? A very rough estimate gave me 12ms. Being wrong by a factor of 30 would surprise me.

3. Jan 28, 2015

Lee Chong Chi

Hi Mfb...

0.36ms get from solidworks CFD simulation.
at 1st i thought my CFD simulation is wrong. Becuase I always get below 1ms.
Then I send my 3D to my Solidworks CFD expert, they run it thru CFD and get 0.36ms (attached the plot i get from the expert)

Possible I know how you get 12ms. I aspect your calculation is close.
Actual 20ms I didn't exclude the sensor respond time and valve respond time.

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4. Jan 28, 2015

Staff: Mentor

Let's calculate a lower limit:
Energy conservation gives an upper limit on the gas speed, this is given by $\frac{1}{2} \rho v^2 = \Delta p$. Using the largest available pressure difference and the smallest relevant density, I get v=141m/s. Note that the pressure difference and therefore the speed will go down over time.
Neglecting temperature changes and the small difference between nitrogen and air, you need a mass of $V\rho \frac{\Delta p'}{p_0} = 3.34\mu g$ flowing in. With the given cross-section of $\pi \cdot (25\mu m)^2$, the speed of 141m/s from above and the density of nitrogen at 1.14 bar (~1.4 kg/m^3), this takes at least 8.6ms.

This value is wrong for two reasons that go in opposite directions:
- I used the maximal pressure difference. Pressure difference will go down, so the inflow will reduce significantly over time which means the whole process takes more time.
- I did not take into account that compression is probably adiabatic (?) or at least not completely isothermal. Filling in 5% additional gas could give of the order of 5% higher temperature (didn't calculate it precisely, some parts are expanding some get compressed), which would lead to the 10% pressure increase you are looking for. So the gas volume that has to flow in can be significantly lower. This is not a factor of 25, however, it is more like a factor of 1.5 to 3.

Your simulated pressure exceeds 1.14 bar and continues to rise afterwards. Do you have an explanation for that? What happens if you run the simulation even longer? In principle oscillations could lead to a higher pressure, but the timescale does not look that long earlier in the process.

Can you get measured times for other pressures? That would help to see how long those times are.

To get the 12ms I used a guess of 100m/s for the velocity and 0.1 for the delta p/p ratio instead of the real numbers.