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 beastieboys6 May 3, 2012 02:42

How to get a uniform showerhead?

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Hi, everyone. I'm simulating the flow field of a showerhead-like structure within a low pressure chamber (operated at 1 Torr). I did the work with Fluent and I already had a convergent result. However, I did not how to explain the result and might need some help from you.

Fig. 1 (see the attached file) shows the showerhead-like structure. It's basically composed of several perforated metal tubes. My main objective is to obtain a uniform gas distribution, which means the velocity at the outlet of each hole must be the same.

Fig. 2 shows the flow field inside the showerhead-like structure. As you can see, the velocity is higher near the gas inlet. At first, I expected that the velocity distribution of the holes must follow the same pattern. Nevertheless, the results showed that the velocity are identical at each hole outlet. I went back to check the pressure and found that the pressure is also uniformly distributed among the holes. I've done some research and found that the key to get a uniform showerhead is to achieve a uniform pressure inside the flow channel. I guess I can imagine the pressure as a "push force". When the pressure is uniformly distributed, the velocity at different holes would also be the same. But how to explain it in a more accurate way? What is the principle or governing equation for this phenomenon?

Moreover, I'm quite confused about the non-uniform velocity (Fig. 2) but uniform pressure distributions inside the showerhead-like structure. What is the correlation between velocity and pressure in this case?

 julien.decharentenay May 3, 2012 19:13

Hi,

Your explanation of the pressure force that pushes the gas (or liquid) through the hole is correct. I will rephrase it in my own words:

The holes are significantly smaller than the metal tubes and therefore act as a pressure "barrier": the gas is driven through the holes by the pressure in the metal tubes that can be considered as pressure vessel.

The non uniform velocity is puzzling you. The velocity plot is a plot of velocity magnitude (the velocity of the gas in the tube). At each hole, the fluid in the tube is loosing a little bit of mass to the hole (the velocity through the hole). So the quantity of mass going from one hole to the next decreases slightly up to the middle holes where the velocity is near zero.

Try plotting the velocity magnitude at the center of tube from the left to the right in 2D and the velocity distribution will be close to linear.

Notes:
1) the two extreme tubes are not as well served by the fluid than the middle tubes. This can be attributed to the additional pressure loss at the end corner (in my opinion). You could use a curve in place of a sharp bend to improve.

2) If you have a bit of time, you could try aligning your gas inlet with one of the tube. It will drastically change the distribution of fluid in the tube, where the tubes that are aligned with the inlet will have more fluid than the others.

Hope it helps.

Julien

 beastieboys6 May 3, 2012 22:29

Hi, Julien. Thanks for your reply. Your comments defenitely help a lot. Now I have a better understanding of my simulation results. I have one more questions, though.

1. If I reduce the diamater of the gas inlet tube while keep the other parameters fixed (I'm simulating gas flow. In reality, the inlet gas is controlled by a mass flow controller, which means the mass flow inlet is a constant in this case), will it help to build up a higher pressure inside the metal tube? My guess is yes. And the reason is that the pressure drop at the gas inlet tube will be higher. This will help the gas flow further into the metal tubes and improve the velocity distribution of the holes. Am I correct?

Notes:
1) the two extreme tubes are not as well served by the fluid than the middle tubes. This can be attributed to the additional pressure loss at the end corner (in my opinion). You could use a curve in place of a sharp bend to improve.
Thanks for the tip. It's very helpful.

2) If you have a bit of time, you could try aligning your gas inlet with one of the tube. It will drastically change the distribution of fluid in the tube, where the tubes that are aligned with the inlet will have more fluid than the others.
And it will be more difficult to build up a pressure inside the metal tube. So the velocity distribution of the showerhead-like structure will be less uniform. Is that right?

 julien.decharentenay May 5, 2012 06:48

Hi,

I disagree with your guess. The driver for the pressure in the metal tubes is the size of the holes. The holes are the smaller orifices through which the gas has to flow through and will therefore control the pressure in the metal tubes. If you want a higher pressure in the metal tubes, make the holes smaller.

Making the gas inlet smaller will increase the pressure drop in the gas inlet. It will result in a higher pressure at your mass flow inlet (i.e the pump will have to work harder) - but the pressure increase will be negligible compared to the pressure loss through the holes.

You need to keep in mind a couple of aspects in these types of simulation:
1) The pressure level is driven by the pressure outlet. Reduce the pressure outlet by 1000 Pa and all pressures within the flow will be 1000Pa less (neglecting compressible effects if you are simulation compressible flows);
2) The CFD simulation is mass conservative. The gas you put in will go through the openings you model and only the openings you model. In real life, your tube arrangement will have seal and joint. If the pressure builds up too high, the seals/joints will be more prone to leaks.

In regards to my suggestion number 2: if a metal tube is aligned with the gas inlet, the flow will dominantly go through the aligned metal tube as this will be the path of least resistance. In the model scenario, the gas inlet is facing a wall. At the wall the gas velocity will be converted into local static pressure. This ensure a "reasonable" distribution of the gas within the metal tube. My advice is: you are running CFD models. Just try and investigate (it does not cost much apart from time - this being said if you are a consultant: time is money, but so if knowledge).

BTW: little tip if it takes too long to run, you can reduce the size of your case by 1/4 by using symmetry.

I am happy to keep this discussion alive, but would like to get the dimension and nature of the gas so I can run simulations to improve the discussions.

Kind regards,
Julien

 beastieboys6 May 9, 2012 22:16

Hi, Julien. Thanks for your comments again. I really learned a lot from your comments. I have a couple of new questions now.

1. Does the inlet flow rate influence the pressure inside the metal? If I can get a unifrom showerhead with a flow rate, say 1E-05 kg/s, is the velocity distribution of holes still be unifrum for any gas flow rate above 1E-05 kg/s? I think the answer is yes but then again I have to deal with the possible downsides you mentioned in your last reply.

2. One of my colleagues once argued with me that if I want to get a uniform showerhead, I have to make sure that the total area of gas outlets (in this case, the holes on the metal tubes) must be smaller than that of the gas inlets. In this case, the total area of gas outlets is much larger (400% larger). Apparently, the ratio of area is not a good indicator. I know the pressure or velocity distribution depends on a number of factors (in this case, e.g. the position of the gas inlets, the size of holes and so on). Let's assume that the configuation of a showerhead-like structure is okay (e.g. the gas inlets are not aligned with the metal tubes in this case), is there any parameter that can can be used as a quick estaimation to examine my design?

I disagree with your guess. The driver for the pressure in the metal tubes is the size of the holes. The holes are the smaller orifices through which the gas has to flow through and will therefore control the pressure in the metal tubes. If you want a higher pressure in the metal tubes, make the holes smaller.

Making the gas inlet smaller will increase the pressure drop in the gas inlet. It will result in a higher pressure at your mass flow inlet (i.e the pump will have to work harder) - but the pressure increase will be negligible compared to the pressure loss through the holes.
You are right about the influence of gas inlet dimater. I decreased the gas inlet diameter from 7 mm to 2 mm and found that the velocity and pressure distribution at the holes are the same. The only difference is that the pressure at the smaller gas inlet is higher.

2) The CFD simulation is mass conservative. The gas you put in will go through the openings you model and only the openings you model. In real life, your tube arrangement will have seal and joint. If the pressure builds up too high, the seals/joints will be more prone to leaks.
Thanks for telling me the answers to the question that I wanted to ask in my last reply. I was thinking about the downsides of high pressures inside the metal tubes.

 julien.decharentenay May 10, 2012 06:45

It will be a quick answer:

1) Yes, the mass flow rate will have an impact on the pressure in the tubes. Think of the pressure in the tube as a total pressure (= static pressure + velocity component). If you reduce the flow rate, the pressure in the tube will be reduced. Reduced pressure means (IMO) that it is more likely to have difference in flow rates through the holes.

2) I do not have a design guideline for you. How much would you/your company pay for one? In a nutshell, you could (by physical and numerical experience, or just aging experience) probably derive a relationship between the pressure drop through the holes and the likelihood of a bad distribution of flow through the hole - which can be easily estimated based on the mass flow rate and size of the holes.

 beastieboys6 May 11, 2012 05:48