Hey gang,
It took longer than expected but here is a summary opinion for consideration
regarding INP and freezing.
Jarrod,
Intermediate pressure: how it affects second stage performance
First define adiabatic expansion (ideal case in which no work or heat is
transferred):
The product of the temperature (in degrees Kelvin) and pressure elevated by
the exponent (1-gamma)/gamma, where gamma is the ratio of specific heats
(specific heat at constant pressure over specific heat at constant volume)
is the same before and after the expansion. Hence, since the pressure during
the expansion decreases, so will the temperature. Gamma for nitrogen oxygen
mixes is approximately 1.4.
Note that this is a very ideal case, representing the maximum possible
cooling. In reality, due to heat exchange the actual amount of cooling is
significantly lower. Still, this is a good way of estimating the maximum
possible cooling due to the expansion.
Lowering intermediate pressure has the following effects:
1) in the first stage: it increases cooling due to higher adiabatic
expansion. Effect is negligible since the pressure ratio hardly changes.
Example: expansion from 200bar to IP of 10bar at 40m, vs expansion from
200bar to IP of 9bar at 40m, starting at 20 Celsius
a. T2=293*(200/14)**(-0.286)=137K=-136C
b. T2=293*(200/13)**(-0.286)=134K=-139C
2) in the second stage:
a. due to adiabatic expansion: decrease in cooling due to the lower
adiabatic expansion. More noticeable effect than in first stage due to the
initial and ending pressure being closer in value, but not by much. Example:
expansion for an IP of 10 or 9bar at a depth of 40m, assuming again an
initial temp of 293K:
i.
T2=293*(14/5)**(-0.286)=218K=-54C
ii.
T2=293*(13/5)**(-0.286)=222K=-50C
b. due to reduction of positive pressure during inhalation: less
fluttering of exhaust valve hence less likelihood of water droplets entering
into the second stage
All in all, the lowering of the IP should have little or no effect on first
stage, whereas even one degree temperature difference might be of importance
in the second stage. Still, what isn¹t there cannot freeze.