THE BetaCAP DESIGN
BetaCAP is a project that did evolve during the years, generating an high quality and diversified set of gas diluters. It was born about 20 years ago by some intuition immediately converted into drawings but just after long decantation converted into a prototype. It was different from the actual BetaCAP30, but it was possible to see the promises and the game become a work. Considering how much all the BetaCAP diluters series is known and used in Italy , but also how it’s generating interest (and some qualified User) in all the word, lets us to understand that we did match the performances technicians was waiting. All of this without a sales dept, just thanking the word of mouth and this web site. Our task is continuing that way, respecting our users requests and promoting the knowledge of BetaCAP advantages : as you will see it’s not difficult. Advantages list is:
- Using nearly equal capillaries
- Electronic pressures control
- Design and management of the diluter using the logical and analytical representation of the gas divider and associated capillaries physics
- Construction based on manifolds couples
Each ofthe above points participates in the achievement of reaching superior performances.
The range of gas dividers resulting from that project includes various models, each with specific functions and suitable for a defined user type. Now the family is growing again… you will see next.
EQUAL CAPILLARIES
Capillaries are very thin holes where fluids flow in laminar mode (without vortexes) and with repeatable flow value. Flows are induced by a differential pressure applied to capillary ends and are quantified by the Poiseuille formula. Other parameters influencing the flow are the physical dimensions and the fluid viscosity. A simpler image of the capillary can be got using the Electrical analogy : Replacing Differential pressure with Voltage difference, the fluid flow with current flow and the capillary with a resistor, it’s evident the analogy of Poiseuille formula and Ohm law.
In the title it’s used the words couple “equal capillaries” : we know that equality does not exist in real word : the project identifies the ways to arrive very near to the equality result. Purchasing the capillaries lot, departure is not the best with 0,015 mm tolerance over 0,1 mm (the specified capillary diameter). Unfortunately the consequent mean deviation on the flow induced by a constant pressure is about 0,028 over an expected value of 0,05 L/min (that result is due to the fourth power elevation of diameter ). Hopefully selecting nearly equal capillaries by measuring the flow is very easy :
a) Lot classification. A first series of flow measurements (one or two thousands of capillaries) is selected with better than 0,1% accuracy. Different classes are located in different containers at 0,2% distance in flow one each other
b) To build BetaCAP30 gas dividers it’s necessary to have 5 capillaries groups, 1, 2, 4, 8 and 15 capillaries each group, to reach a total of 30 capillaries. Using a self made tool that can receive 36 capillaries and filling it with 36 capillaries taken from a single compartment of classified capillaries we start extracting the 30 capillaries required to produce one BetaCAP30 :
The 1 capillary group is the “internal reference” for all the groups chain, where the proportion flow / capillaries number must be constant This single capillary is chosen with measured flow near to the mean value of flows measured in the selected capillaries class. The groups containing more capillaries are composed in a way that , combining scarce and abundant flows, the proportion “total group flow / capillaries number in the group” is strictly constant.
Applying a constant pressure, The flow measured on each capillary of the used class is “equal” to the others with 0,05% rel. accuracy. The groups including more capillaries are even more and more accurate : the flow is the sum of individual flows and the flow deviation is the mean value of combined capillaries flow.
It must be highlighted that whichever different technics cannot offer an accuracy near to 0,05% of the value. Similar values can be (not easily) achieved at the end of dilution range, but at 1/10 dilution the accuracy of flows is reduced 10 times and even more form higher ratios.
ELECTRONIC PRESSURES CONTROL
As shown in the functional diagram, Input pressures (gas to be diluted and diluting gas) and output pressure (Diluited gas) are measured. The electronic function (hardware and firmware) handling the pressures control operates on differences P(TG1)-P(OUT) and P(TG0)-P(OUT) and setpoints come from calculations This is another key point of the project : being known the logical-mathematic function behind the diluter device and capillaries physics, the diluter can be driven as a conceptual object. This allows reaching unexpected results, like viscosities compensation, certified deviations correction and, last but not least … the continuous dilution range covering ! This means that, without loosing accuracy, dilutions spece can be extended from steps to the continuous space between them-
MATHEMATICAL DESCRIPTION OF THE DILUTER
This subject is already mentioned in another section of this web site, but it’s so essential in BetaCAP project that we need to anticipate here some point. Dilution ratio is the target of the BetaCAP project function and it can be expressed in a numerical form as a flows ratio : gas to be diluted flow / total output flow.
Those contributions depends on capillaries partition in the diluter and from the physics of capillaries that we learned from Poiseuille. The resulting formula (one more equation is added to allow P(TG1) and P(TG0) calculation) shows us that, changing the capillaries partition in the range 1/29 to 29/1, always it exists a couple of P(TG1) and P(TG0) giving the wanted dilution.
- To get the better accuracy and an easy handling of the diluter, capillaries partition is set in the best way, mainly depending on the viscosities ratio (typically some more capillaries are moved to the more viscous side). When the user sets a target dilution, the equations solution starts to recover viscosities, to fix N (capillaries crossed by measurand gas) and then calculating P(TG1) and P(TG0) : calculated pressures become the setpoints of the automatic pressures control system.
- Certified deviations correction. In the metrological certificate, the gas to be diluted flow and the diluted output are measured and deviations are recorded for each of the main dilutions. Whichever dilution can be expressed as a ratio of gas to be diluted flows through some main capillaries group and the sum of all the main certified flows. This calculation gives the real dilution as measured by certifying body. The correction function moves the user dilution target in a direction opposite to the certified deviation in a way that this deviation restores the user dilution target.
- Extension of the step by step operating mode to the continuous uninterrupted mode typical of MFCs. Operating from the menu “Set Kdil.” we can just change the capillaries partition : in this case BetaCAP30 allows 31 different capillaries partition. If viscosities (η1 and η0) are very similar, P(TG1) is nearly equal to P(TG0) . We can imagine to increase P(TG1) : TG1 flow increase and the diluted concentration is higher. This is done basing on accurate measurements, than a control of all the dilution range is available.
MANIFOLDS TYPE CONSTRUCTION
A big amount of junctions between the 30 capillari alternately to the gas to be diluted or to the diluting gas and all the devices in the functional diagram (five 3 ways solenoid valves, two proportional pressures controllers, three pressures sensors and the connections to two inlets and one outlet, did force us to search a method different from tubes and fittings. We saw in the past some “Manifold type” circuit connection and we did apply. Did use a couple of parallelograms in a way that capillaries are hod part in one and part in the second with an o-ring between the two faces sealing all the ways requiring not to leack The two pieces are hardly kept together by 4 or more screws. The other components are placed and fixed in caves on external faces. This solution assures a total capillaries protection (never had 1 broken) and a module very compact, rugged and easily assembled.
