High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Every fusor and fusion system seems to need a vacuum. This area is for detailed discussion of vacuum systems, materials, gauging, etc. related to fusor or fusion research.
Michael Bretti
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti » Wed Jan 31, 2018 11:25 pm

2.) CALCULATION AND COMPARISON OF SYSTEM CONDUCTANCES AND EFFECTIVE SPEEDS FOR MOLECULAR FLOW FOR VARIOUS PROCESS GASES

PART I – SYSTEM DESIGN V2

SECTION 1 – Design Overview
Based on the prior mentioned availability of a 2.75” CF inline valve, I decided to redesign V1. The design decision to move from V1 to V2 was made primarily due to part availability, and a basic knowledge that a linear path would provide better conductance compared with one of equivalent length with multiple bends. Up until this point no calculations were made influencing design decisions, which were based on limited general knowledge and intuition alone. Subsequent design iterations however were directly influenced by the calculation results from the molecular flow numbers derived from the system. Below is a rendering of the V2 design:

2.75 Conflat Multipurpose High Vacuum System V2.jpg

The new inline valve would allow for a more direct pumping path, and have a vertical topology. The main crosses were kept and just re-oriented to save functionality of the previous system. The third port on the KF25 cross was also decided to be dedicated for gas input and venting the system to atmosphere, and the remaining KF25 inputs stayed the same (thermocouple gauge and high vacuum gauge.) One downside to the valve however was that it was pneumatic – while cheap, it means that I have no control over the flow rate if needed, for example, for a fusor. This required the additional use of some sort of manual valve. After weeks of searching, I came across a 2.75” Conflat manual butterfly valve. This valve also had an additional bonus of being both a sealing and conductance throttle valve, and was found at a very low price. I have found it very difficult to locate similar valves since. The overall cost slightly increased from V1, however it made for a more convenient chamber to mount and work with physically, while allowing for better flow control and potentially better conductance along a more direct path to the chamber. The system was subsequently modelled in CAD to determine the best orientation of parts.

In order to further understand how system topology would affect high vacuum pumping behavior, I decided to start calculations on this design to determine its viability before I started investing in too many parts. Unfortunately I already bought some valves and parts due to the fast nature of things popping up and disappearing on eBay – some of which ended up being recycled to new designs, others are still unused due to further design changes. From V1 to V2 however, this design satisfies more of my initial requirements stated in the introduction and Section 1 of this post. I found though that some things had to be slightly sacrificed. Form factor, functionality, and control was gained, however at slightly higher cost. Conductances and speeds, as illustrated below, did not seem to be as good as I had initially hoped.

SECTION 2 – Calculations for Determining Conductance and Effective Speed in Molecular Flow
Below are the PDFs with the calculations performed on the V2 design to determine conductance and effective pumping speeds in molecular flow for the following gases: air, argon, deuterium, and water vapor:


In order to determine the effective speed of the system, both conductance and maximum pumping speed of the high vacuum pump are needed, given the gas load Q and the ultimate pressure P of the system are unknown. The equations and all of the definitions are in the PDFs for reference. As an important note going forward, effective speed IS NOT THE SAME as the speed of the pump. Effective speed is the total speed of the system accounting for the speed of the pump and the conductances of the pipeline to the chamber. Effective speed is practically always lower than the pump speed, never higher. The KEY LIMITING FACTOR of conductance in a system is dictated by the component with the lowest conductance – that component represents a choke point in the conductance where the total conductance and effective pumping speed WILL ALWAYS BE LOWER. Thus for a system based off of 2.75” CF hardware, you are always limited to the theoretical max limit of conductance for that size pipe, regardless of pump speed. Conductance drastically falls off for length, and for short pipes conductance counter-intuitively can come out lower than for long pipes due to correction factors required when calculating the numbers for such pipes and components.

The max speed of my pump is already known, at 600 L/s for air and 800 L/s for hydrogen, based off the datasheet (the pump is an Edwards EO4 diff pump.) This is represented in Section 1 of the above PDFs.

For calculating the conductance of the pipeline, one approach would be to find the equivalent conductance of a length of pipe for all the parts, assuming the internal diameter stays the same. However, a more accurate approach for finding the worst case conductance under ideal conditions would be to find the conductance of each individual component in the pipeline, and sum all of the conductances – note that series conductances for vacuum systems, when summed, are calculated like resistors in parallel. By finding the total conductance from all the sums, correction factors can be applied for each component, giving a worst-case scenario conductance for the system. In reality, the conductance may probably be higher since I calculated everything in the above PDFs using the largest correction factor numbers for the appropriate calculations as experimentally determined in literature on the subject.

The conductances are calculated in order of the component, from diffusion pump up to the chamber, which is the 5 way cross. Note that each part is calculated in multiple stages. First, the conductance is found using the general formula for a tube. However, since the L/D ratio for the components is less than 5, corrections must be applied. First, the equation for short pipes is calculated using the number for a long pipe. Then, a further error factor correction of about 12% max is factored in to the number, resulting in the final conductance for that part. This 12% is a correction factored applied based on experimental data observed in literature for air @20C, which provides the maximum deviation for the given L/D ratio. Other gases are approximated and estimated to give rough numbers using this correction factor.

Note that the choke point in the system is actually the inline valve, calculated in Section 3. Even though the valve is technically “linear” in fashion, it actually is not a full straight-through gate valve, and hence must be approximated with x2 90 degree bends in series, which cuts the original conductance of the valve in half. This is the limiting factor of the system. Inline valves such as this generally have lower conductance than an equivalent 90 degree valve, despite the fact it looks like the flow is straight through. One should note that motion in molecular flow is random, which plays a large factor in the behavior of gas flow in high vacuum systems, and does not behave as initially expected under non-molecular flows.

In Section 4, the butterfly valve is calculated, and the valve portion must be accounted for in the area of the opening. Even in the fully open position, it still adds impedance. The ratio of the equivalent area was found to be 65.8%, which was applied as an additional correction factor to the valve conductance.

The following sums up the total system conductance and effective pumping speed of the system in molecular flow for each of the gases, calculated in Section 6 of the PDF:

AIR:
Conductance – 8.737 L/s
Effective Speed – 8.612 L/s


ARGON:
Conductance – 7.440 L/s
Effective Speed – 7.349 L/s


DEUTERIUM:
Conductance – 33.137 L/s
Effective Speed – 31.819 L/s

WATER VAPOR:
Conductance – 11.078 L/s
Effective Speed – 10.877 L/s


As can be seen from the above numbers, the conductances and speeds of the system, despite having a very short and direct pipeline, are surprisingly small, except for deuterium. As expected, with all things equal, it can be seen that molecular weight has a direct result on the conductance of a system in molecular flow. The pump, starting with a speed of 600 L/s, has been effectively reduced by more than an order of magnitude, to around 10 L/s for the various process gases (much higher for deuterium). Although these numbers may be ok for deuterium, I wanted extra room for argon, in addition to being able to handle more loading from water vapor. Because of this, a new topology was designed and calculated in the same manner to compare numbers to see if these estimates could be improved. This will be seen in the next section covering design V3 for molecular flow. However, I will not know the actual gas handling load due to effective speed until after ultimate pumpdown pressure is calculated due to water vapor loading, and applying this number for gases involved at all pressures I will be experimenting at.

As a final side note on this section and going forward, I started the calculations on molecular flow since this is the very first step for figuring out the system when gas loads and ultimate pressure are unknown. These will be derived in later sections from these results. Also note that the low vacuum, roughing portion is not covered until later. This is due to the fact that the roughing pump parameters are not needed for the high vacuum calculations, and it is in the high vacuum regime that I will be primarily operating in. For the time being, the only parameter really required for the roughing pump is to make sure that it meets the backing requirements of the diffusion pump. This number is found from the datasheet, and set aside. For 600 L/s operation, a min displacement of 1.83 L/s is required of the two stage pump. However, due to the fact that during high vacuum operation it is clear that I will not see these speeds at the chamber, a smaller pump can be used. I still do want to benefit from the max pumping speed of the diffusion pump, which will have an effect on the effective speed still, and as such, a backing pump has been selected with a displacement of 2.83 L/s, much more than is required for this system with a good safety margin. This should allow me to still attain 600 L/s at the pump inlet, while having additional overhead. Because the actual gas load will be very small for my system, especially at high vacuum, this will be acceptable for handling gas flows during steady state operation for the systems I want to employ, given the limitations of max gas load for my system. Actual details of the roughing calculations however will be detailed in sections 3 and 5.

Michael Bretti
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti » Thu Feb 01, 2018 4:27 am

2.) CALCULATION AND COMPARISON OF SYSTEM CONDUCTANCES AND EFFECTIVE SPEEDS FOR MOLECULAR FLOW FOR VARIOUS PROCESS GASES

PART I/b – COMPARISON OF SYSTEM DESIGN V2 CALCULATIONS WITH ESTIMATES USING DUSHMANS TABLE

I have decided to include this brief Part b of the above section to illustrate the comparison using multiple calculation techniques, to help show the validity of the more intensive method presented. Let us assume that we are to calculate the conductance of System V2 using a very simplified estimate from Dushmans Table. This table is an empirically derived method for approximating conductances of tubes. Using this approach, we would assume the entire pipeline with all its elements are a single element of equivalent length with constant diameter. An example reference to this table can be seen here:

http://www.lesker.com/newweb/technical_ ... e_calc.cfm

This Table is pulled from the above source from the KJL website, and is shown below:

Dushmans Table - KJL.jpg

From System V2 measurements, we know the following parameters:

Total Effective Length = 26.244cm
Average Diameter of 2.75” CF Hardware = 3.556cm

The radius is then 1.778cm. Dividing the length by the radius gives the “L/a” ratio of 14.760, where “L” is length and “a” is radius. Following the table down the “a” column, we end up between rows 1.0 and 2.0. Following this over to the L/a ratio column, we lie somewhere between 12 and 16. This roughly approximates to a conductance value between the lower and upper bounds of 5.013 and 25.210. If we interpolate this data between these major bounds, and generate a table such as the one below,

Extrapolation Example - Dushmans Table, Design V2.jpg

we see that we get a closer approximation of the conductance between the bounds of 1.7 to 1.8 and 14 to 15, of a conductance between 18.571 and 20.784. This conductance is higher than those for air, argon, and water vapor, but less than that of deuterium - in fact, it is almost exactly in the middle of the two extremes between argon and deuterium. This shows that we are well within the expected ballpark for our original intensive calculations. The above method using Dushmans Table however does not account for temperature, molecular mass, or other correction factors for short pipes. Also note that this estimate was found using a straight length of pipe equivalent to length of the actual system, with no bends. If we included the bends in our estimation using the table method, this number would be much lower, and hence much closer to the values similar to air. Thus we can show within reasonable agreement and certainty that breaking down each individual component of a pipeline, applying correction factors, and summing the total for series conductance, is within the expected range, even when compared with very simplified methods of estimation.

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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Tom McCarthy » Thu Feb 01, 2018 4:25 pm

Michael,

This is great, thanks for going to the the time of typing it all up and presenting. I’m learning a lot.

One thing you mention - counter-intuitively, conductance for a short pipe can come out Lowe than a long pipe due to correction factors.

As you’ve said, this is counter-intuitive. Are you sure it’s correct? While I know little about these vacuum calculations, I appreciate that the correction factors used are necessary and presumably well worn. Can a short tube of same diameter have a lower conductance than a longer tube? It seems the maths says one thing, but physics would make you believe another.

Looking forward to seeing the rest of the posts.

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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti » Thu Feb 01, 2018 4:58 pm

Tom McCarthy,

Thank you for your comment and reply. Your question is a very good one, and I probably should have been more clear in my explanation, so I apologize if there is confusion on this point. The conductance for a short pipe is less when you apply the correction factors and equation for calculating the conductance of a short pipe with an L/D ratio less than 5 for an equivalent pipe. This results in a conductance that is much lower than one would initially expect for a short pipe. So for example, taking the first component in the above PDFs, from the example using AIR, the Diffusion Pump to 2.75" Conflat Plate Adapter, initially when the general equation is used to calculate the conductance, it comes out to 213.992 L/s. However, this equation is only valid for long tubes. When the equation for short tubes are used, this lowers the conductance to 74.649 L/s. Adding further worst case error correction factors, we end up with a final conductance of 65.691 L/s. However, if the tube was originally longer, let's say with a length now of 18cm, now making it with an L/D ratio greater than 5, using only the first equation for long tubes, would lower the conductance to 30.197 L/s, which is about half that of the short tube. No correction factors are needed since the long tube equation describes tubes more accurately that are long. So in reality, a short tube will still have higher conductance than a long tube, but it may be lower than one initially expects. In this example, despite the short pipe being 5 times shorter than the long pipe, the resulting conductance is only about twice as much.

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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Tom McCarthy » Thu Feb 01, 2018 5:35 pm

Ok, that clears things up. Thanks for the thorough explanation.

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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Richard Hull » Thu Feb 01, 2018 7:31 pm

Your efforts are much appreciated.

The emphasis on short pipe plumbing here is related to the fact that folk arrive here with 0.0000 vacuum experience. It seems the first thing they do is purchase a vacuum pump and put 2 or 3 feet of 3/8-inch bore vacuum hose on the pump to their first demo chamber, strangling the pump. Our first advice and response is to have them move the pump inlet inches from the chamber's outlet and use a larger bore tubing in a short run.

A professional vacuum system used in production or advanced research is a "must calculate system". The reason being that inefficiencies in such a system will decrease the net value of a very expensive undertaking, resulting in a slower pump down to the "ready condition". In a production situation, this can result in reduced production and, thereby, increased costs.

Here we are just trying to help newbies get better, very acceptable, but not necessarily perfect results in their first vacuum effort.

Richard Hull
Progress may have been a good thing once, but it just went on too long. - Yogi Berra
Fusion is the energy of the future....and it always will be
Retired now...Doing only what I want and not what I should...every day is a saturday.

Michael Bretti
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti » Thu Feb 01, 2018 11:03 pm

Richard Hull,

Thank you for your compliment and reply. If nothing else, hopefully these examples, and walking through this design process and my own mistakes and efforts might show the importance of at least planning a vacuum line/system and how things can affect it, even without rigorous math or analysis (which is still at best only a very rough estimate anyway.) It appears all too easy to completely kill conductance, especially when dealing with high vacuum and molecular flow. Fortunately, fusors do not operate under such strict restrictions around the micron range so, as you stated, it is much less critical for most efforts here.

Michael Bretti
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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti » Thu Feb 01, 2018 11:18 pm

2.) CALCULATION AND COMPARISON OF SYSTEM CONDUCTANCES AND EFFECTIVE SPEEDS FOR MOLECULAR FLOW FOR VARIOUS PROCESS GASES

SUPPLEMENTAL INFORMATION

For those who are interested in diving into the subject more deeply, below is a scanned photo of the original error curve I have used for reference in my calculations dealing with short tubes (usually 12% for most of my calculations). This was taken from (a rather excellent book on vacuum engineering, one of my favorites that I have read so far):

"Fundamentals of Vacuum Science and Technology"
Gerhard Lewand, Ph.D.
Plasma Physics Laboratory, Princeton University
Copyright 1965 by McGraw-Hill, Inc.

LD Error Curve.jpg

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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Jerry Biehler » Fri Feb 02, 2018 7:42 am

The cooled trap I got you is just to reduce backstreaming, it wont do much to help your ultimate vacuum, that will require a LN2 cooled trap which is installed on top of the other trap.

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Re: High Vacuum Engineering Design, Analysis, and Build of a Small-Scale Multipurpose System

Post by Michael Bretti » Fri Feb 02, 2018 1:49 pm

Jerry Beihler,

Thank you for your comment. However, the baffle should indeed help improve ultimate vacuum despite not having any cryotrapping principles. If we look to solve for the total gas load of a system, we need to account for the load of oil backstreaming, Q(backstreaming). Depending on the mode of operation for a diffusion pump, this could be non-negligible or trivial. For a pump with an optically opaque baffle above it cooled to at least 20C, backstreaming rates are reduced to near negligible levels, and can effectively be removed from the gas loading equation. Effective speed of the system can be easily calculated as shown above, and once the total gas load in known, or roughly estimated, then the ultimate vacuum can be determined. Since the load due to backstreaming is required in finding the total gas load of the system, this does have a direct impact on the ultimate vacuum level attained. I will post actual details of these calculations in coming sections. In my setup, since I am going to be using the water cooled baffle, I can effectively reduce the load due to backstreaming to 0, and this should have a small but noticeable effect on the ultimate vacuum achieved.

The other mode of operation to consider for the diffusion pump in regards to ultimate vacuum achieved is primarily related to the foreline pressure of the diff pump. Assuming a perfectly sealed system, the ultimate pressure that can be attained by the diffusion pump is governed by the medium used for pumping (various types of oils, mercury, etc), and the foreline pressure of the pump. This also greatly plays into backstreaming rates, which again contributes to ultimate vacuum. For diffusion pumps, if the foreline pressure is under 10^-3 - 10^-4 Torr, backstreaming is essentially reduced to negligible amounts. However, since the ultimate vacuum of my foreline will only be around 2x10^-2 Torr, or 20 microns, backstreaming will be noticeable due to the pump operating above the critical pressure which backstreaming rates are reduced to near zero. The ultimate vacuum of a diff pump itself also is largely determined by the backing pressure. A topology utilizing a diff pump backed by a secondary diff pump in series will allow the system to be pumped into the ultra-high vacuum regime, even with only a water cooled baffle, assuming the system has already been well prepared, outgassed, and baked. At least from reading through the forum so far, I do not believe I have seen anyone here utilizing a diff backed diff pump topology, which for fusor efforts is completely overkill and unnecessary. However it should be completely do-able to achieve much higher vacuum without cryo-trapping. This also depends on how I handle the gas loading due to o-rings in my system, which if a differential pumped concentric o-ring topology is used, or the o-rings themselves are chilled (experiments in literature show this to be around at least 6C or lower), then the gas load due to outgassing and permeation can be drastically reduced and allow the system to drop into the 10^-9 Torr regime. For my current system that is backed by a two stage refrigeration pump, I would not be able to reach ultra-high vacuum in the long run with just a water cooled baffle. In the following sections, I can mathematically show that even in an ideal scenario, my current setup should only in theory be able to peak into the upper 10^-7 Torr range. However, by using the proper oil (which I will be using DC705 equivalent), a diff backed diff pumped topology, the water cooled baffle, and differentially pumped concentric o-rings, higher vacuum is attainable without cryotrapping.

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