Thermische Aspekte von Rebreather-Entwerfen,
wenn Sie über die Vorteile von Rebreathertauchen eins der ersten Sachen, die Sie
sind ungefähr das warme hören, feuchte Atmengas hören. Wenn Sie Tauchen Oc-
anstelle von Rebreather-SCUBA Sie ein Gas inhalieren, das eine Feuchtigkeit nah
an null hat und ziemlich kalt ist. Doppel-Schlauchregler liefern ein Gas, das
fast zur Temperatur des umgebenden Wassers aufgewärmt wird, andere Regler
liefern es ziemlich kälter, z.B. mit -10°C (14°F). das Atmengas so aufzuwärmen
kann ein bemerkenswerter Faktor "der Arbeitsbelastung" für den Taucher sein,
weil, egal was er inhaliert, er mit 100%humidity an ungefähr 36°C ausatmet.
Lassen Sie uns die Situation für 3 typische Tauchensituationen, alles Tauchen im
warmen Wasser 10°C (50°F) und alle atmen25 liter/minute vergleichen. Beobachtung
(oder Dekompression) im einfachen Tauchen 6m (~20ft) in der wissenschaftlichen
Erforschung 30m (~90ft) 100m (~300ft) (atmenheliox mit dem 10%-Sauerstoff)
approximierte heizende Energie wenden durch den Taucher zu Atem 25 L Gas pro
Minute auf (zwecks den 1bar*l-/minsauerstoff verbrauchen):
6m 30m 100m "- 10°C"-Regulator 40 W + 44.8W 100W + 44.8W
Doppel-Schlauch 205W + 44.8W (+10°C) 22.5W + 44.8W 56W + 44.8W 116W + 44.8W
Kondensation-Art Rebreather (10°C, Feuchtigkeit 100%) 22.5W + 35.4W 56W + 35.4W
116W + 35.4W thermisches NullRebreather (36°C, Feuchtigkeit 100%) 0 W 0 W 0 W
Rebreather laufen gelassen an 46°C, Feuchtigkeit 100%, die der Taucher 8.65W +
31.5W empfängt, der Taucher 21.6W + 31.5W empfängt, der Taucher 44.5W + 31.5W
empfängt
Thermal Aspects of Rebreather-Design
When you hear about the advantages of rebreather-diving one of the first
things you hear about is the warm, humid breathing-gas.
When you dive OC- instead of Rebreather-SCUBA you inhale a gas that has a
humidity close to zero and is quite cold. Dual-hose Regulators deliver a gas
that is nearly warmed up to the temperature of the surrounding water, other
regulators deliver it quite colder, for example with -10°C (14°F).
So warming up the breathing-gas can be a remarkable factor of "workload" for
the diver, because no matter what he inhales he exhales with 100%humidity at
about 36°C.
Let's compare the situation for 3 typical dive-situations, all diving in 10°C
(50°F) warm water and all breathing 25 liter/minute.
- Observation (or decompression) in 6m (~20ft)
- Easy dive in 30m (~90ft)
- Scientific exploration in 100m (~300ft) (breathing Heliox with 10% Oxygen)
Approximated Heating Power spend by the diver to breath 25 l gas per minute (in
order to consume 1bar*l/min oxygen):
| |
6m |
30m |
100m |
| "-10°C"-Regulator |
40 W + 44.8W |
100W + 44.8W |
205W + 44.8W |
| Dual-Hose (+10°C) |
22.5W + 44.8W |
56W + 44.8W |
116W + 44.8W |
| Condensation-Type- Rebreather (10°C, 100%
humidity) |
22.5W + 35.4W |
56W + 35.4W |
116W + 35.4W |
| Thermal neutral Rebreather (36°C, 100% humidity) |
0 W |
0 W |
0 W |
| Rebreather run at 46°C, 100% humidity |
The diver receives
8.65W + 31.5W |
The diver receives
21.6W + 31.5W |
The diver receives
44.5W + 31.5W |
Thermal
capacity:
Cp( Air ) ~ 0.79*Cp(N2) + 0.21*Cp(O2) ~ 1.298
Watt*sec/(bar*Liter*Kelvin)
Cp(Heliox10) = 0.9*Cp(He) + 0.1*Cp(O2) ~ 0.9705
Watt*sec/(bar*Liter*Kelvin)
6m ~ 1.6bar : 1.6bar*Cp(Air) * 25Liter/60sec ~ 0.8653
Watt/Kelvin
30m ~ 4 bar: 4bar * Cp(Air) * 25Liter/60sec ~ 2.163
Watt/Kelvin
100m ~ 11 bar: 11bar * Cp(Heliox10)*25Liter/60sec ~ 4.448 Watt/Kelvin
Evaporation (100% relative Humidity, Liter here measures the volume of
Breathing-Gas):
ppH2O(+10°C) ~ 0.0123bar this means 0.00998g/l or 22.5 Joule/l (Breathing-Gas)
ppH2O(+36°C) ~ 0.06 bar this means 0.04772g/l or 107.5 Joule/l
ppH2O(+42°C) ~ 0.082 bar this means 0.06592g/l or 148.5 Joule/l
ppH2O(+46°C) ~ 0.1 bar this means 0.08123g/l or 183 Joule/l
1Joule = 1Watt*sec
107.5Wsec/l * 25l / 60sec ~ 44.8W
0.04772g/l*25l/min*60min ~ 72g/h which means 0.072 Liter Water per Hour
This means during an OC-Dive you loose 0.1 Liter Water per 1.4 hours because of
Evaporation, when you breath 25 l/min.
Evaporation-balance (breathing 25 l/min for an oxygen-consumption of
1 l/min):
| |
Dehydration/hour |
Condensation/hour |
| OC-Dive |
-0.072 Liter |
exhausted |
| Rebreather, inhalation-temperature 10°C |
-0.057 Liter |
0.107 Liter |
| Rebreather, inhalation-temperature 42°C |
+0.0273Liter: Hydration |
0.023 Liter |
| Rebreather, inhalation-temperature 46°C |
+0.05 Liter: Hydration |
Zero |
That Calculations assume that the CO2 is absorbed by breathing-lime and the
reaction-product water leaves the lime as steam (if the gas is warm enough).
Hydration means that the diver does not loose water by breathing, he gets 'water'
because he breaths a quite humid warm steam.
So, what do all those figures mean?
They show what
- using a proper designed rebreather means a serious way of thermal
protection for the diver.
- rebreather-divers have fewer problems with Dehydration.
- diving a rebreather in water what is colder or deeper than the engine was
mainly designed for means additional condensation-water and so can cause the
need of shorter dives as well as earlier change of breathing-lime.
(The more cooling by colder Input-Gas or by more thermal Capacity (for
example by higher Pressure of the "Cooling-Gas") per CO2 Mol the more Problems
with slower Reaction by lower Temperature plus by Condensation-Water drowning
the Scrubber arise.)
VO2 = (Qs (FsO2 -
FiO2 )) / 1 - FiO2
FiO2 = ((FsO2 * Qs) -
VO2) / Qs - VO2
VO2 =
Oxygen metabolic rate
FiO2 =
Inspired oxygen
Qs = Flow rate in lpm
FsO2 = supply oxygen percentage
Equivalent Air Depth
EAD = ((FN2 / .79) * D / 33) - 33
FN2 - Fraction of Nitrogen
D - Depth
Memory Aid for;
Pg = P * Fg P = Pg /
Fg Fg = Pg / P
Pg - Partial Pressure of
the gas i.e. PO2
P - Pressure in ata
Fg - Fraction of the gas i.e. FO2
Ambient
pressure
( P / 33 ) + 1
P - Pressure in ata
Flow through a sonic
orifice
Flow (lpm) = 11Pbar
* D2
P = pressure in bars
D = diameter in mm
|
INSPIRED OXYGEN CHART |
|
O 2
supply |
|
Flow Rate
5.8 lpm
7.6 lpm
10.7 lpm |
|
% |
| |
VO 2--->>> |
0.75 lpm |
1lpm |
1.25 lpm |
.75 lpm |
1 lpm |
1.25 lpm |
.75 lpm |
1 lpm |
1.25 lpm |
| |
|
|
|
|
|
|
|
|
|
|
|
60 |
|
0.54 |
0.52 |
0.49 |
0.56 |
0.54 |
0.52 |
0.57 |
0.56 |
0.55 |
|
59 |
|
0.53 |
0.50 |
0.48 |
0.55 |
0.53 |
0.51 |
0.56 |
0.55 |
0.54 |
|
58 |
|
0.52 |
0.49 |
0.46 |
0.53 |
0.52 |
0.50 |
0.55 |
0.54 |
0.52 |
|
57 |
|
0.51 |
0.48 |
0.45 |
0.52 |
0.50 |
0.49 |
0.54 |
0.53 |
0.51 |
|
56 |
|
0.49 |
0.47 |
0.44 |
0.51 |
0.49 |
0.47 |
0.53 |
0.51 |
0.50 |
|
55 |
|
0.48 |
0.46 |
0.43 |
0.50 |
0.48 |
0.46 |
0.52 |
0.50 |
0.49 |
|
54 |
|
0.47 |
0.44 |
0.41 |
0.49 |
0.47 |
0.45 |
0.51 |
0.49 |
0.48 |
|
53 |
|
0.46 |
0.43 |
0.40 |
0.48 |
0.46 |
0.44 |
0.49 |
0.48 |
0.47 |
|
52 |
|
0.45 |
0.42 |
0.39 |
0.47 |
0.45 |
0.43 |
0.48 |
0.47 |
0.46 |
|
51 |
|
0.44 |
0.41 |
0.38 |
0.46 |
0.44 |
0.41 |
0.47 |
0.46 |
0.45 |
|
50 |
|
0.43 |
0.40 |
0.36 |
0.45 |
0.42 |
0.40 |
0.46 |
0.45 |
0.43 |
|
49 |
|
0.41 |
0.38 |
0.35 |
0.43 |
0.41 |
0.39 |
0.45 |
0.44 |
0.42 |
|
48 |
|
0.40 |
0.37 |
0.34 |
0.42 |
0.40 |
0.38 |
0.44 |
0.43 |
0.41 |
|
47 |
|
0.39 |
0.36 |
0.32 |
0.41 |
0.39 |
0.37 |
0.43 |
0.42 |
0.40 |
|
46 |
|
0.38 |
0.35 |
0.31 |
0.40 |
0.38 |
0.35 |
0.42 |
0.40 |
0.39 |
|
45 |
|
0.37 |
0.34 |
0.30 |
0.39 |
0.37 |
0.34 |
0.41 |
0.39 |
0.38 |
|
44 |
|
0.36 |
0.32 |
0.29 |
0.38 |
0.36 |
0.33 |
0.40 |
0.38 |
0.37 |
|
43 |
|
0.35 |
0.31 |
0.27 |
0.37 |
0.34 |
0.32 |
0.39 |
0.37 |
0.35 |
|
42 |
|
0.33 |
0.30 |
0.26 |
0.36 |
0.33 |
0.31 |
0.38 |
0.36 |
0.34 |
|
41 |
|
0.32 |
0.29 |
0.25 |
0.35 |
0.32 |
0.29 |
0.37 |
0.35 |
0.33 |
|
40 |
|
0.31 |
0.28 |
0.24 |
0.33 |
0.31 |
0.28 |
0.35 |
0.34 |
0.32 |
|
39 |
|
0.30 |
0.26 |
0.22 |
0.32 |
0.30 |
0.27 |
0.34 |
0.33 |
0.31 |
|
38 |
|
0.29 |
0.25 |
0.21 |
0.31 |
0.29 |
0.26 |
0.33 |
0.32 |
0.30 |
|
37 |
|
0.28 |
0.24 |
hypoxic |
0.30 |
0.27 |
0.25 |
0.32 |
0.31 |
0.29 |
|
36 |
|
0.27 |
0.23 |
hypoxic |
0.29 |
0.26 |
0.23 |
0.31 |
0.29 |
0.28 |
|
35 |
|
0.26 |
0.21 |
hypoxic |
0.28 |
0.25 |
0.22 |
0.30 |
0.28 |
0.26 |
|
34 |
|
0.25 |
hypoxic |
hypoxic |
0.27 |
0.24 |
0.21 |
0.29 |
0.27 |
0.25 |
|
33 |
|
0.24 |
hypoxic |
hypoxic |
0.26 |
0.23 |
hypoxic |
0.28 |
0.26 |
0.24 |
|
32 |
|
0.23 |
hypoxic |
hypoxic |
0.25 |
0.22 |
hypoxic |
0.27 |
0.25 |
0.23 |
|
31 |
|
0.22 |
hypoxic |
hypoxic |
0.23 |
0.21 |
hypoxic |
0.26 |
0.24 |
0.22 |
|
30 |
|
0.21 |
hypoxic |
hypoxic |
0.22 |
hypoxic |
hypoxic |
0.25 |
0.23 |
0.21 |
Analysis of sonic flow through an orifice
Sonic flow through an orifice is usefully used on
chemical process plants in:
- restriction orifice : used to limit the
flowrate during equipment depressurisation.
- critical flowmeter : a simple meter in which
it is only necessary to measure the upstream pressure.
The discharge coefficients are reviewed in
Sonic flow
through orifices, nozzles and venturis.
When gas flows from a vessel through an orifice
to another vessel, it is well known that as the downstream pressure is reduced,
the mass flowrate steadily increases until the velocity at the orifice reaches
sonic velocity. If the downstream pressure is further reduced, the mass flow is
unaffected and the excess pressure is dissipated in shock waves downstream of
the orifice.
The ratio of the up and downstream pressures when
sonic velocity is just reached is called the critical pressure ratio. It is also
well known that for a gas with Cp/Cv = 1.4 the critical pressure ratio is just
greater than 0.5.
The analysis refers to the locations in the above
figure and is in three stages:
- contraction from upstream conditions (station
1) to vena contracta (station 2)
- flow rate at the vena contracta (station 2)
- expansion from vena contracta (station 2) to
downstream conditions (station 3)
1) Contraction from pipe to vena contracta of
orifice
It is assumed that the acceleration of the gas to
sonic velocity is isentropic. This is reasonable for a contraction if the actual
physical layout allows a smooth acceleration of the fluid from rest to the
orifice.
We now have the pressure and temperature (P2 &
T2) at the vena contracta when the flow is sonic for an adiabatic, isentropic
transition from station 1.
2) Flow rate at the vena contracta
The vena contracta is the place where the highest
velocity will occur, and it is the easiest place to consider the mass flow rate.
Assuming the discharge coefficient is equal to the contraction coefficient:
The flow through the vena contracta is caused by
the difference in pressure between stations 1 and 2. Reducing the pressure at
station 2 causes more and more flow until sonic velocity is achieved. The
discharge coefficient then takes its sonic value (Cd*). The mass flow is then
obtained by substituting sonic velocity and the pressure & temperature at the
vena contracta into equation E4:
3) Expansion from vena contracta to downstream
conditions
Consider the case where the flow in the vena
contracta is subsonic:
| |
If the (sub-sonic) expansion
downstream of the vena contracta were accomplished in a carefully designed
diffuser, the losses could be small and it might then be realistic to
calculate the expansion as an isentropic transition. |
| |
|
| |
In practice, there are always
expansion losses. Where the flow area of the orifice is small compared to
that of the downstream pipe, the expansion is the same as for flow into a
reservoir. As explained earlier (Flow at Enlargements and Contractions), the
losses then exactly balance the pressure rise that would occur if the
expansion was isentropic. The pressure at station 3 is then the same as the
flowing pressure at station 2. |
| |
|
| |
Whilst the flow is sub-sonic, reducing the
pressure at station 3 is therefore the same as reducing the pressure at
station 2 and this induces more flow through the orifice. |
Then consider the limiting case when sonic flow
just occurs :
| |
The pressure at station 3 is still the same
as that at station 2. Assuming the velocity at station 1 is low, equation E3
can be simplified and rearranged to give the pressure ratio between stations
1 and 2: |
| |
 |
| |
The critical pressure ratio predicted by
equation E5 is then also the ratio of pressures between stations 1 and 3
when sonic flow just occurs. |
| |
|
| |
Note that if k = 1.4 then P2/P1 = 0.528.
This is why it is usually said that the downstream pressure must be less
than half the upstream pressure for sonic flow to occur across an orifice. (The
significance of this for flow from the end of a pipe is discussed in section
E.3.) |
Finally, continue to reduce the pressure at
station 3 :
| |
Once the velocity at station 2 has reached
sonic, any further reduction in pressure at station 3 cannot be transmitted
upstream through the shock wave to station 2 to increase the driving force
and hence the flow rate. The pressure at station 2 then remains constant (at
the value given by equation E3) and the flow has reached its maximum value.
The difference in pressure between stations 2 and 3 is dissipated in shock
waves downstream of the vena contracta. |
- See Also
-
Flow at enlargements and contractions
Enlargements : sub-sonic flow
Contractions
Sonic
velocity
Choking
pressure
Sonic flow
through orifices, nozzles and venturis
Sonic flow from the end of a pipe
Ideal
program action if supersonic velocity is predicted
Real program action if supersonic velocity is predicted
Copyright ©
1999 Optimal Systems Limited
| 
