
Verzonden: maandag 7 februari
2005 15:05
Hope you are
well. I have been reading your article on CMF stuff and I am not so
sure it is a sonic flow. First the kiss system of adding o2, it is
important that the flow drops as we go deeper otherwise the o2 added
would be too great with increasing depth.
For CMF to work
it has to be 2 x ambient for upstream IP to make the gas sonic,
"maybe" in a kiss valve the IP is typically set at 7bar (old
orifice) or
1011 bar (new orifice)
If the CMF rule
were to be true then the old orifice would cease to work at 25m and
the new one at 4050m. This of course does not happen (fortunately)
because what we DON'T want is a cmf flow! We need the o2 flow to
reduce in comparison with depth so the diver continuously receives
the correct number of o2 molecules. This slowing of the flow keeps
the amount of o2 that's is required by the diver constant in the
face of increasing pressure.
Now this is as I
understand it and that of course may be wrong :))))

 Original
Message 
From: "J.W.Bech"
<jw.bech@quicknet.nl>
Sent: Monday,
February 07, 2005 7:56 PM
Dave T sent me
this answer to the article. The KISS IP
Dave
mentioned
in my opinion is
not correct. The old ones 10 bar IP the new 12 bar IP.
What are your
thoughts about his statement?

Original
Message
Sent: 07
February 2005 21:48
To: jw.bech@quicknet.nl
Cc: dave.thomp@virgin.net
Subject: Re: cmf
Hi, JW and Dave,
I´ll try to
answer:
1. Any gas flow
is sonic (i.e. the speed at the critical section equals the local
sound speed) when the pressure ratio p0/p1>=cca 2 (in our case
p0=IP, p1=ambient press.) "cca" means it depends a little on the gas
whether mono or biatomic etc. So it has to be sonic when p0=7 bar
and p1= e.g. 3 bar (20 m). At about 25 m the flow starts to cease
with depth (becoming subsonic) and fully ceases when p1=7 bar (60
m). That´s simple.
2. In the KISS
RB the steady flow cca 0,8 lpm should be adjusted giving
hypometabolic flow of O2 in depths of use. It is adjusted adjusting
the p0 (=IP). The plug in the water inlet of the 1st stage ensures
the constant absolute IP in any depth. Reading the KISS manual find
in the table of adjustment of flow (for a 0.0035 = cca 0.09 mm diam.
orifice): p0=9bar: 0.5 lpm, 10 bar: 0.6 lpm, 11 bar: 0.7 lpm, 12
bar: 0.8 lpm, 13 bar: 0,9 lpm (calculations using the O2 flow
formula give 0.61, 0.68, 0.75, 0.82 and 0.89 lpm). In the manual 15%
difference is declared as allowable. I haven´t found values for 7
bar but the flow would be insufficient then (about 0.4 lpm).
3. Adjustment of
IP on 12 bar ensures the flow being sonic up to cca 50 m.
Then the flow
slowly decreases (my calculations give 0.82 lpmsonicin 50 m, 0.80
in 60 m, 0.75 in 70 m, 0.72 in 80 m, 0.62 in 90 m and then rapid
decrease in 100 m to 0,45 lpm and of course zero in 110 m). That
simply
means: going
deeper, over the sonic limit, you have to use the manual add valve
more often.
4. Even the
manual states: "The metering orifice flow rate will diminish as the
depth (ambient pressure) increases. How much it decreases depends on
the upstream pressure (regulator pressure setting) versus the
downstream pressure (depth). This is not a fault, it is physics."
(end of citate). The decrease of the flow when crossing certain
critical depth is not intentional, it is simply the matter of p0/p1
< cca 2.
5. Regarding the
"correct number of O2 molecules": remember that the flow
(0.8 lpm) is the
normal pressure volume pro minute in any correct depth (not ambient
pressure related volume) so the number of molecules in the dose is
always the same in any depth (statistically, of course:).
I hope my answer
is satisfying enough, if not, let me know why, guys.
Wishing clear
water around. Jan.
Well, during
writing this sentences I obtained your next emails. But I think
everything is explained in this answer. I’ve got my figures from the
new manual (for 0.08 mm orifice) as you can see. Regarding diving
deeper then to "sonic limit" see the upper calculations for 80
meters: the flow makes always 0.72 lpm which doesn’t differ much
from 0.82 lpm in 50 meters.
Compare also
with the plot of CMF in the article on mass flow.. The drop starts
at critical depth but is not very rapid except at the depths where
the ambient press. draws near to the IP.
Greetings.


Oorspronkelijk bericht

Verzonden: maandag 7 februari
2005 23:39

Aan: 'Jan Jahns'; jw.bech@quicknet.nl

Onderwerp: RE:
cmf


Ok I think I
understand most of that but one thing bothers me if I understand
your reasoning correctly and you were to plot the flow on a graph,
you would have a pretty straight line until the flow went subsonic
then it would curve off?


If that is
correct that is not what seems to happen in practise


I notice no
additional need to touch the add button when deep over when
shallow. An example, I need to set my IP to give a flow of 0.68lpm
(this matches my metabolic rate when diving) with this set and at
65m I did one hour on the bottom (the deck of a huge ship in nice
clear water) and I didn’t touch the manual add button once. The IP
set to give this flow is 10bar (according to my gauge) if your
theory/ maths is correct it should have gone subsonic at 40m, is
this correct?


Thank you for
your help and explanations



Original Message

Sent: 07 February 2005 23:35

To: 'David Thompson'

Cc: jahns@quick.cz

Subject: RE: cmf


Dave; Jan;


Greetings. Very interesting! Dave, when I look at the curve it
doesn't curve off. It seems almost flat until 80 meter.

I think what Jan supposed would be similar to your findings Your
VO2=0,68 and 70 m= 0.72 in 80 m= 0.62.(how many injections would be
needed for the 0,68 & 0,62 difference?) In my opinion that would
explain your findings.



This message reached me too:


"the orifice is a "sinthetic ruby" (actually is "sinthetic
corundum", Al 2O3, the red variety is "ruby", the blue variety is
"sapphire"), not a natural gem (it would cost too much to cut a
natural gemstone).


The use of corundum is due to the fact that it is the harder
material after the diamond in the Mohs scale and it is possible to
produce it industrially at a relative low price.

"

The person telling this is Gilberto Bonaga a geologist.


OK for now, good night;




I do wonder however if its not sonic but just simple physics "double
the pressure, halve the volume" type of stuff, we are just lucky
that it fits perfectly with our metabolic needs!!!


A couple of engineers I spoke to (who know far more about this than
I ever

will) also doubt the sonic flow of this type of gas addition


They argue that were it sonic you would see a large change in the
gas addition once the 2 x ambient upstream pressure diminished!!!


Anyway very interesting conversation guys


Best




Original Message

Sent: 08 February 2005 21:27

To: David Thompson; jw.bech@quicknet.nl

Subject: Re: cmf


Well, then


I´ve made some recalculations of the flow depending on depth
according to your low O2 consumption rate. I suppose you used
normal pressure gauge and your reading was 10 atm gauge, i.e. 11 ata
(absolute)^{
(1)}.
My calculations give about 0.61 lpm (for 0.08 mm orifice) then, but
let´s take your actually measured value 0.68 lpm as the base for
following calculations.

More exactly the calculated critical ratio p0/p1 = IP/(ambient
pressure) is not 2 but 1.9026^{(2)}
and 11/1.9026 gives 5.78 bar of the ambient pressure, i.e.

47.8 meters as the maximum depth in which the flow changes from
sonic to subsonic. At this depth the flow rate is always 0.68 lpm
and only then started to diminish. The calculated flow rates are
then: in 50 m the 3 th decadic place does not change giving always
0.68 lpm. At 55 m I obtained

0.676 lpm. In 60 m: 0.663 lpm and in 65 m: 0.645 lpm. Seems the
little difference (0.035 lpm) is not serious for your needs, Dave
:).

To calculate the subsonic flow is a little bit more complicated then
the sonic one but is not very difficult and your engineering friends
sure could do it as well.^{
(3)}
I use spreadsheet calculator to do the math but during the long
period of use I´ve built in much balast so it´s readable for me only
now.

Regarding your doubts about the sonic speed and precise mass flow in
the sonic region:

The gas expands adiabatically into place of lower pressure, cools
down and the speed of sound at this temperature is the critical one
which cannot be overcome in the critical section of the orifice
(usage of properly formed – so called “Laval – nozzle” can enhance
the speed downstream of the nozzle up to Mach 2). This speed is
maintained then even if the downstream pressure grows  (e.g. in
confined space) but only up to this given by the mentioned ratio
(calculations in the article). Only then it becomes subsonic.

The mass flowing out equals then (see Continuity Equ.:)
(crosssection) x

(speed) x (critical density). As all 3 variables are constant in the
sonic region also the mass flow is maintained constant.



Excellent, thanks for your help, that makes it more understandable
to my

non engineer mind :))


Best






13 Februari 2005

Oosthuizen Netherlands

11:17


 Jan:

 Reading all
this I still have three questions:

(Jan Jahns answers follow
directly in colour Red)

 ^{
(1)}
 So for the
calculations we use the ABSOLUTE pressure and not the measured
pressure on the IP gauge! I.e when a IP is measured of 16,7 bar as
Dräger stated in the technical manual the calculations should be
made with a absolute IP of 17,7 bar? (I
changed the values in the article).
http://www.therebreathersite.nl/01_Informative/orifices_in_rebreathers.htm Or
do they give the gasflow for a measured IP?

 I think Dräger IP
values are in bargauge for custom convenience, so 1 bar has to be
added to obtain the absolute pressure, really. There is only 1 place
in Draeger manual concerning the IP which I have found to be 240 psi/16.5
bar (not psig/ata!). During the check of your article I hold not in
mind these parameters and I supposed you used absolute pressure. In
my article I always mentioned it as well as in graphs.
 But really again:
Dräger allowed flow tolerances are 11% and the flow using either
values (16.7 bar vs. 17.7 bar) lies in 6 % tolerance (the flow is
proportional to IP). The calculated orifice diam. using 17.7 bar
changes from 0.156 to 0.162 mm. It makes only a little difference,
nevertheless it is methodically wrong if 16,7 is used in the
calculations.

 ^{
(2)}

 You stated that
in this case the
p0/p1 =
IP/(ambient pressure) is not 2 but 1.9026.
The values of the
inverted ratio p_{0} /p_{crit} =1/B
lie for the breathing gases in the range 1,90 2,05, i.e.
p_{0} /p_{crit } in average aproximately
equals 2.
 What factor(s)
determin this exact calculation? In other words, how did you
calculate the 1.9026 factor in Dave’s case?
 It´s simple: I took κ = 1.416 for O2
(which I use in my calculation spreadsheet) and inserting it to the
formula you can find 6 rows down I got B = 0,5256 which inverted
gives 1/B = 1.9025875, rounded 1.9026.

 Should
the flow velocity be sonic (equal the velocity of sound) we have to
put w^{2} =c^{2} and from equations derived
we obtain that for the ratio p/p_{0 } (i.e. for the
ratio of the outlet to inlet pressures) following condition has to
be fulfilled:

p_{crit}
/ p_{0 } =[2/(k
+1]^{ }^{
k/(k
1) }
=B
.^{
}
 Here
p_{crit} is the critical pressure in the critical
section of the nozzle and from the formula follows that if the
outlet pressure p is lower or equal to p_{crit }
, i.e. if p/p_{0}
£
B
holds in
the critical section the local sonic velocity w_{crit}
is achieved which can't
be
exceeded increasing the inlet pressure p_{0}.



^{
(3)}
 Could you
sent me an example of the subsonic flow calculation, using the
calculated examples you sent to Dave and me.


The calculated
flow rates are then: in 50 m the 3 th decadic place does not change
giving always 0.68 lpm. At 55 m I obtained

0.676 lpm. In 60
m: 0.663 lpm and in 65 m: 0.645 lpm. Seems the little difference
(0.035 lpm)


As I wrote it´s a problem: I wrote the programs
for myself so there are many odds which currently only I understand.
I have to rewrite some but it takes time. Nevertheless: (I prefer
using bigger Arial to make types in formulae beter readable). Using
asterix for multiplication sign.


D =
dV_{n} / dt
(normal liters pro minute) = 1/ρ_{n} * dM / dt =
1/ρ_{n} * S * w * ρ,

M

mass (kg), ρ – density (kg/m^{3}) in orifice, ρ_{n }
– normal density = 1.409 kg/m^{3} for O_{2} , S
= π * (d/4)^{2}^{ }–cross section of the orifice
and w – the velocity of gas in the orif. – now subsonic ! It
could be calculated by the help of
formula you can find some rows lower.
Insert IP (absolute) as p_{0} , ρ_{0}
= ρ_{n} * (p_{0}/p_{n} ), ρ = ρ_{0
}* (p/p_{0})^{1/κ} . Put all variables
in the above bold formula , do some algebra and you have the
right formula into which the correct figures can be inserted.

Notice: There are mostly ratios of pressures there, so mostly bars
could be used, only once in the √ you have to use 101300 (Pascals
) for p_{n} . Inserting d in mm you also have
to divide the result by 1000^{2 } (=10^{6}), then
multiplicate by 1000 (mm = 1 m) and by 60 (seconds in 1 minute).

 Jan thanks
for the efforts!

 Janwillem Bech

 You are welcome, JW

Jan Jahns

 Inserting
e.g. the value of
k
for biatomic gases gives the value B=0,528.
 The
values of the inverted ratio p_{0} /p_{crit}
=1/B lie for the breathing gases in the range 1,90 2,05,
i.e. p_{0} /p_{crit } in average
aproximately equals 2. It means again that the inlet pressure p_{0}_{
}being at least the double of p the outlet one the
velocity in the nozzle is sonic. But being lower, e.g. p_{0}_{
}=1.5 p the velocity would be subsonic.
 The
above reasoning implies following: holding the inlet pressure p_{0
} constant (independent of depth) and equal
10 bars
(absolute)
the velocity (i.e.also the gas flow as we´ll see later) is sonic up
to depth in which the ambient pressure is half of it, i.e. up to 40
meters, in which the ambient pressure is 5 bars. The velocity in the
nozzle of air whose inlet temperature has been 0°C is in each
depth up to 5 bars 303 m/s. But going deeper the velocity decreases
onto 230 m/s in 60 m

(according
w =Ö{
[2.k/(k
1)].p_{0}/r_{0}
.[1 (p/p_{0}) ^{(}^{k
1)/k}]}
), onto
105 m/s in 80 m and the flow would stop in 90 m (where p_{h}
=10 bar ºp_{0}).



