isothermal choked flow
isothermal choked flow
(OP)
What is mass flux?
I'm looking for the derivation or basis for choked ISOTHERMAL FLOW from a large reservoir thru a nozzle. Friction should be neglected.
I'm looking for the derivation or basis for choked ISOTHERMAL FLOW from a large reservoir thru a nozzle. Friction should be neglected.





RE: isothermal choked flow
RE: isothermal choked flow
M = (rho)V*n
where M is mass flux, rho is mass density, V is the velocity vector, n is the surface normal vector (dimensionless unit vector) for the surface of interest, and * denotes a vector dot-product. This is a point value equation.
An "average mass flux over the exit area" calculation would have you calculate the surface integral the above term over the area of intestest, and divide the result by the area.
RE: isothermal choked flow
Sorry, my question should have been, "What is choked mass flux for isothermal frictionless flow thru a nozzle"?
RE: isothermal choked flow
Or, surf to here:
http://www.potto.org/gasDynamics/node128.php
and click "next" to follow the derivation through to where he provides a table and some following examples. Essentially, the choked mass flux depends on the upstream conditions and length of pipe vs. heat flux parameter (the 4fL/D parameter).
RE: isothermal choked flow
This is not exactly on topic and you may have looked at it already, but FAQ1203-1293: A Simple Numerical Method for Gas/Vapor Flow in a Safety Valve answers the same question, except for isentropic, not isothermal, flow. You may be able to use that as a guide and make isothermal assumptions and get to the answer you seek.
Good luck,
Latexman
RE: isothermal choked flow
I am looking at exact solutions (or near to that as possible. For example, isothermal flow (even with friction)for a perfect gas has an exact solution.
Regards
RE: isothermal choked flow
Good luck,
Latexman
RE: isothermal choked flow
Po = 100 psia
To = 25 C
MW = 29 lb/lb.mole
k = 1.4
dnozzle = 1 inch
Pn = 52.0 psia
Tn = -25.8 oC
rn = 0.316 lbm/ft3
Sum(DP/rave) = -118.439 lbf.ft3/(in2.lbm)
Gn = 330.699 lbm/(ft2.sec)
w = 6493 lbm/hr
and for isothermal it's:
Po = 100 psia
To = 25 C
MW = 29 lb/lb.mole
k = 1
dnozzle = 1 inch
Pn = 60.0 psia
Tn = 25.0 oC
rn = 0.302 lbm/ft3
Sum(DP/rave) = -101.432 lbf.ft3/(in2.lbm)
Gn = 292.940 lbm/(ft2.sec)
w = 5752 lbm/hr
Good luck,
Latexman
RE: isothermal choked flow
Pc= e^[.5 - (u1^2RT)] and G = P/sqrt(2RT)
P is pressure at throat.
G is mass flux
RE: isothermal choked flow
Good luck,
Latexman
RE: isothermal choked flow
Also note my typos where I should have a division sign.
Crititcal press ratio, Pc is
Pc= e^[.5 - (u1^2/RT)] and G = P/sqrt(2RT)
P is pressure at throat.
G is mass flux
USA UNITS
Pc= e^[.5 - (u1^2/gRT)] and G = P/sqrt(2RT/g)
Regards
RE: isothermal choked flow
G = P/sqrt(2RT/MWg)
Good luck,
Latexman
RE: isothermal choked flow
USA UNITS
Pc= e^[.5 - (u1^2/gRT)] and G = P/sqrt(2RT/g)
With USA units, say for air, I would use R=53.3 ft/deg
g=32.2 ft/s/s P #/ft^2
RE: isothermal choked flow
Good luck,
Latexman
RE: isothermal choked flow
G = 60*144/sqrt(2*53.3*537/32.2) = 205 lbm/ft2.sec
I got 293 lbm/ft2.sec
Something is not right. ???
Good luck,
Latexman
RE: isothermal choked flow
I got 293 lbm/ft2.sec
Something is not right. ???
Why is something wrong?????
RE: isothermal choked flow
Good luck,
Latexman
RE: isothermal choked flow
Is it a coincident the answers differ by about 1/sqrt(2)?
Good luck,
Latexman
RE: isothermal choked flow
(w/A)*sqrt(T0)/P*1/sqrt(MW) = sqrt{kg/R')*M*sqrt(1+(k-1)/2*M2)
For isothermal (T = T0), choked flow set k = 1 and M = 1 to get (w/A)max:
(w/A)max*sqrt(T)/P*1/sqrt(MW) = sqrt{g/R')
Rearrange:
(w/A)max = P*sqrt{gMW/R'T)
R = R'/MW:
(w/A)max = P*sqrt{g/RT)
Notice there's no 2 in the equation.
Good luck,
Latexman
RE: isothermal choked flow
My Shapiro is in storage and I don't have access to the description of use of eq. 4.11. If my memory serves me correctly, is it possible that the equation is applicable to only adiabatic flow?
Please note that for isothermal flow in ducts and I believe isothermal flow in a nozzle, choking occurs NOT at M=1,but M=1/sqrt (k).
Regards
RE: isothermal choked flow
Good luck,
Latexman
RE: isothermal choked flow
Good luck,
Latexman
RE: isothermal choked flow
Again, my Crane is also in storage, but there are curves with fl/d for isothermal flow (and pv=RT) in the handbook.
My application is to apply a similar approach with real gas.
In reality heat flow will be difficult to maintain. However, with theoretical adiabatic flow, can we believe that at M=1, there is not heat transfer?
Regards
RE: isothermal choked flow
Agreed, neither model is perfect.
Good luck,
Latexman
RE: isothermal choked flow
dU^2/2)+dH=dQ energy
TdS+ VdP=dH combined 1st and 2d law
adding and considering reversible process
dU^2/2+VdP=0
Neglecting upstream velocity to make my calc easier
U^2/2 + int VdP=0 G, mass flux U=GV
G^2V^2/2 +int VdP=0
isentropic process
substitute V from PV^gamma=PoVo^gamma
subscript o for upstream
standard isentropic critical pressure and choked flow will be obtained by taking derivative of G wrt P
For isothermal
dU^2/2+VdP=0 do same as isentropic but substitute V=RT/P with T=constant R=unive R/mol
Isothermal choked flow results will be obtained.
Regards
RE: isothermal choked flow
MY ERROR, ANOTHER CORRECTION-NOTE THE 2UNDER U1^2
USA UNITS
Pc= e^[.5 - (u1^2/2gRT)] and G = P/sqrt(2RT/g)
With USA units, say for air, I would use R=53.3 ft/deg
g=32.2 ft/s/s P #/ft^2 J=778
For heat transfer BTU per pound flowing is
(Ut^2/2 -U1^2/2)/gJ or
[Runiversal/mol*T/2 -U1^2/2]/gJ
RE: isothermal choked flow
Good luck,
Latexman