Blowdown Flow (Choked flow help)

[jproj]

I am trying to design a flash tank, but instead of giving us the inlet flow rate, our client only provided the flash tank pressure (2 psig), boiler operating pressure (500 psig), tank size, and blowoff line size (2&quot, and I'm not sure how to handle choked flow of a flashing liquid (fluid dynamics was a long time ago and choked flow was glossed over).

Can someone please help me out with an equation or a web reference? From a previous post here, I found the following website, but I'm not sold on the given equation:

http://www.air-dispersion.com/usource.html

I tried the "Discharge Of Flashing Saturated Liquid" equation: Q = 0.1597D2P[ln(P/14.696)](TB/T)(T/cp)^0.5(T-TB)^-1

and came up with a flow of 93.14 lb/s, but I'm concerned with the units. It says Q should be in lb/s, but (T/cp)^0.5 gives units of lb^.5/BTU^.5, which are never resolved.

Any help is much appreciated!!!

jproj

 

[zdas04]

jproj,
Units never work in made-up empirical equations. You just have to take it on faith (what a nasty word) that the units of the constant cover all of the other sins.

I always approach this sort of problem using relief valve arithmetic. It is a bit messy, but it works. First calculate Cm

Cm = 520*{k[2/(k+1)]^[(k+1)/(k-1)]}^0.5

Then mass flow rate (m) is (you have to just assume that the constant in "Cm" has the right conversions to get this mess into lbm/hr):

m(lbm/hr) = (pi/4)*d(inches)^2*Cm*P(psia)*K(total)*[MW/(T(R)*Z)]^0.5

k is the ratio of specific heats.

P(psia) is the upstream pressure. As long as downstream pressure is less than P(crit) then you will have choked flow. The multiplier is generally just greater than 0.5.

P(crit) = P(psia)[2/(k+1)]^[(k)/(k-1)]

K(total) is a series of adjustments for non-standard conditions multiplied together. A good default value is 0.975.

MW is molecular weight of the mixture.

With 500 psig, your P(crit) (using k=1.28) is 267 psig which is considerably above your tank pressure so the equation is valid. With a 2-inch Sched 40 line into the tank, your "relieving rate" is 103,000 lbm/hr (20 lbm/s).


David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

 

[tonycola]

I recommend the methods detailed in API-520-2000 part 1, paragraph D.2.2

Have fun!