Fundamentals Of Constant Mass Flow Gas Systems

Fundamentals Of Constant Mass Flow Gas Systems
For Rebreather Scuba.
BY: Dan Dunfee

A clear understanding of sonic and mass flow fundamentals is essential to safe and effective use of Manually-Controlled, Closed-Circuit and Semi-Closed Circuit Rebreather ( mCCR and SCR ) diving rigs. This is especially true for divers who build or modify their own equipment.
Early Constant Mass Flow Rebreathers

In spite of many threads and extensive discussions on this subject, in this and several other Rebreather forums, there are still substantial mis-understandings of the basic functional inter-relationships in these system . The confusion sometimes includes:

• What actually constitutes an 'Orifice', or 'Sonic' and 'Mass Flow' conditions.
• Mass vs Volumetric Flow values, which are not synonomous.
• Volumetric values at-depth vs Surface Equivalent Volumes (SEV)
• Mass flow differences as a function of Upstream (intermediate) vs Downstream (at-depth ambient) pressures.

Much of the confusion is also caused by straying away from First Principles, co-mingling the First Order (primary) and Tertiary effects ( 3rd, and 4th order efffects, etc.), and treating or discussing them as if they were about co-equal in functional importance,… which they are not.

As an alleged rocket scientist and SCUBA designer, maybe I can outline the most basic issues more simply and clear up some of the confusion. I'll not delve into the physics, aerothermodynamics, or mathematics details. These fill whole technical books, design manuals, and articles and, if not well understood by the reader, can contribute to the confusion. The math formulae, presented in most rebreather documentation and forums are relatively simplified forms of the total equations anyway. I'll try simply to focus on the prioritized hierarchy of functional interractions.

Sonic Orifices


'Sonic orifices' can be of many types, shapes, materials, and complexities. These began with simple, circular, sharp-edged, holes in flat metal plates. From the beginning, many of the CCR and SCR orifices have been of these simple types. Most sonic orifices are circular, but they can actually be rectanglar, triangular, or other reasonable geometric shapes. Materials began with metals, and now include ceramics and synthetic jewels (rubies and sapphires). Recent technology improvements are opening new doors, including very inexpensive plastic orifices. Adjustable SCUBA metering valves (needle valves etc.) are typically run sonically. Similarly, 'pintled' nozzle designs for rockets are just much more complex sonic orifices which are adjustable during the rocket firings.

The next progression from circular, sharp-edged orifices in flat plates, involves chamfering, radiusing or tapering the entrance contour to increase the 'entrance flow coefficient'. Vena Contracta and the length of the orifice 'throat' can also have a significant influence. Such contouring can increase the mass flow of same-area orifices, with the same upstream / downstream pressure ratios, by up to 75%, when compared with circular, sharp-edged orifices in flat plates.


Much more complex are the 'multiple-stacked- orifice designs' as reflected in the LEE Company orifice literature, up to the 'Viscous' orifices, shown here and detailed in the URL below. The Divex SLS, Mk IV SCR uses a multiple-stacked orifice. These allow the use of much larger-diameter induvidual orifices, to avoid clogging…yet these larger 'stacked' orifices can produce the same controlled mass flow output as a single orifice that may be up to 20 times smaller.

Lee Company Orifices
These types of orifices have very complex aero-thermo-dynamic effects, some so great that they aren't accurately modellable, and the 'actual' orifice mass flow performance has to be be determined experimentally, over the specific range of use parameters.

Critical Pressure Ratio & Sonic Flow

Given a 'fixed' orifice design , the next greatest effect is the ratio of pressures Upstream (IP) and Downstream (ambient pressure at-depth) from the Orifice. As a generalization, a critical pressure ratio of about 2 is when the gas flow thru the orifice achieves sonic velocity, and stays that way at all at higher pressure ratios.

One of the most common mis-interpretations relative to sonic orifices is the notion that, once the orifice is 'sonic', the mass flow does not change with changes in either the upstream or the downstream pressure. That's only half correct… the facts are:

• Once sonic flow is achieved, and at all higher critical pressure ratios, the mass flow does not change with changes in downstream (ambient) pressure. That's principally why mass flow measurements made on the surface remain valid at depth.
• With sonic flow, at any given downstream pressure, the mass flow changes about proportionally with any changes in upstream IP , as shown in Marekm's Rebreather World data example for an .004 in. dia. metal orifice:

psig…bar..gas...flow(lpm)
50…..3.4....o2...0.38
70…..4.8....o2...0.45
90…..6.1....o2...0.53
110…..7.5….o2...0.58
150…10.2....o2...0.79

'Constant Mass Flow' (Cmf) Revisited

In Rebreather diving, the human body deals with most of the principal breathing gases, expecially Oxygen, on a Mass (number / weight of gas molecules), rather than a Volumetric (space ocupied by the No. of molecules), basis. The Mass and Volumetric terms are not synonomous and must not be confused. An idealIzed goal in mCCR and SCR regulator and orifice delivery systems is to achieve true CMFs. Precision of the mass flow control becomes especially critical relative to controlling Oxygen partial pressures in very deep diving where, at a depth of ~625 ft / 190 m fsw, or 20 ata, a difference of 1.0 % in typical, absolute SEV Oxygen content can mean a 50 % difference in Oxygen Partial Pressure. True CMF occurrs only when all the pressure, temperature, gas density, and flow conditions are also 'constant'. In diving, deeper and shallower, with varying gas supply tank pressures, and in different water temperatures, these parameters rarely stay exactly the same for very long, and changes in any of them changes the mass flow to 'some' degree....... whether that is to a large or small degrees is the key issue. To achieve relatively constant mass flows the challenge is to control as many of the major, first and 2nd order variables as one can..and not get hung up on the 3rd and 4th order effects.... especially in discussions on the subject.

First Stage Regulator & Intermediate Pressure

The next major effect is the type of 1st stage regulator used to provide the Upstream or Intermediate Pressure (IP) to the orifice. The 2 general types are 'Compensating' and 'Non-Compensating'. 'Compensating' is where the 1st stage changes the Absolute IP as a function of depth.. (ie IP= ambient pressure + regulator preload spring pressure + ambient water pressure at-depth). Most Open Circuit regulators are of this type. Azimuth and the Draeger Ray are of this type. With this type first stage, the IP & mass flow increase substantially with depth. 'Non-compensating' types, do not purposefully increase the Absolute IP & mass flow with depth ( ie IP=ambient pressure at the surface, nominally 14.7 psia + regulator preload spring pressure). Most military mCCR and SCRs, are of this type… also the civilian Draeger Dolphin and the Jetsam KISS. The Apeks DS4 regulator, shown above, can readily be converted from its original Compensating to a Non-Compensating mode simply by replacing the flexible Secondary Diaphram with a rigid 'Plug', which is sealed with an o-ring.

Manufacturers of 1st stage types claim advantages over one another. 'Compensating' ones typically use lower initial (surface) IPs and larger orifices, which are less succeptable to clogging, but at additional supply gas consumption rates. 'Non-Compensating' ones typically achieve mass flow rates that are considerably closer to truly 'constant' mass flows. This can be especially important where more constant and precise mass flows and minimal gas consumption are critical. Care must be taken to ensure that the Initial IP for non-compensating regulators is maintained at, or reset to at least twice the maximum intended dive pressure. The risk of clogging is greater with the smaller orifices and better filtration is required.

With either 1st stage type, variations in IP with tank pressures variations can also have significant effects on the constancy of delivered mass flow. Therefore, the repeatability and the linearity of the 1st stage IPs vs tank pressure becomes significant in the selection of 1st stages. This is especially true, for the 'non-compensating' types where, at 330 ft / 100 m, the en-situ volumetric flow is only about 9% of the original surface flow value.

Gas Constants

There can be up to~ 20% differences among the Gas Constants for Air, Oxygen, Nitrogen, Helium, and their mixes. The Gas Constants for the specific gas / mix to be controlled, can be significant in computing mass flow rates and selecting orifices for general equipment and diving scenarios. Once this is done, minor differences in gas mixes, per se, generally fall into the Tertiary effects category. Occasionally, on especially deep and critical dives, the Gas Constants may be brought back into play to define specific orifice sizing for specific dives and conditions. However this is not the norm.

Tertiary Effects

With changing diving depths, temperature, and other conditions, a number of tertiary effects, (ie gas temperature, density, the sonic velocity itself, etc ) come into play and make small changes to the orifice mass flow in both compensating and non-compensating IP system types. However, in most cases, these changes are negligible, and not subject to adjustment during on-site dive-prep or the dives.

Summary

The choices must rest with conscientious divers and homebuilders, to first ensure the adequacy of their own training and technical knowledge, as it applies to CCRs generally, and CMF gas flow systems specifically,… Then by carefully evaluate their diving needs and scenarios, before purchasing or building the respective mCCR or SCR diving rigs,… with their respective orifices, 1st stage regulators, and mass flow rates, and setting them up for diving.

I hope this helps clarify, rather than adding to the confusion.

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