8/18/2019 PSV Forces in Closed System
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PSV Forces in Closed System
I risk a long post on this subject. Maybe will help someone to
understand …what we are not ableto count and why our approach is
rather empirical.
Crosby manual says: "There are momentum effects and pressure
effects at steady state flow as
well as transient dynamic loads caused by opening" and in my
opinion this is !alid for eitheropen or closed systems. There is a
kind of similitude between "open" and "closed" #$%s
discharge piping handling gases& so a discussion may be
forced on both cases.
'orces that are affecting the #$s discharge piping are gi!en
by:
(. a free jet effect in steady state flow). unbalanced forces on
each "piping leg" due to transient flow.
(. The "free jet effect" is the *rd law of dynamics.If a free
jet is released in atmosphere or in a large !olume& the piping
system will recei!e areacti!e force. This is the force that (I
counts and is:
+eacti!e,'orce- mass flowrate/0jet,!elocity/1
p,jet/0area,jet/where
mass flow rate must be the actual !alue 2it is greater than the
designed flow rate& because theactual #$ orifice is larger than
minimum re3uired4
jet,!elocity is the critical speed when the jet gas flow has
Mach-5 feature 2it is not e6actly thespeed of sound calculated as
for a resting fluid& you may get some details in a fluid
Mechanicsbook on the critical speed and stagnation temperature
concept4 and is counted as jet,!elocity-s3rt270+0k0T8
22k1540M44& where notations are as in (I& + is the
uni!ersal perfectgasconstant & in #I is +-9*5.; ou may note
this is e6actly the (I formula& where the numerical coefficient
is s3rt270+4& in #I
units s3rt2709*5.;4-57?
This long preliminary discussion is useful because we can be
focused now on where this force canappear.
>ou ha!e this force e6actly where there is a '+@@ jet.That
means: in an open system& where really the free fluid jet is
released into atmosphere
in a closed system& at the header connection& presuming
your #$ is not pressuriAing theheader that is the header is counted
as a large !olume recei!ing the jet rather than a path for
flow…
(nd...despite the common opinion& the problem of the true
steady state force in the #$ is !ery3uestionable. In the #$ orifice
there is a flow at Mach-5 i.e a critical flow& but the jet is
radialreleased 2it e6ists thru a lateral cylindrical surface4 and
it%s not a "free jet"& because there isn%t abig !olume in the
#$%s body.
+oughly considering the steady state flow& there is a
changing in fluid momentum& initially is
radial compensated& after that there is an impact with the
#$ body on about 78* on the pathflow that generates a lot of
turbulence& etc. )y the other hand& we may consider a model
closed
to those proposed by )randmayer and =nebel& see the article
"#team 'low Through #afety !al!e$ent ipes"& based on an
onedimensional model of the shocked flow 2anindya stress has
had
the generosity to post it recently& thank you anindya
stress& it was !ery interesting and Iappreciate your courtesy
and your postsB4…
8/18/2019 PSV Forces in Closed System
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My opinion is& in fact& we ha!en%t a realistic model for
the steady state flow& e6actly here& in the#$ body&
where the flow is not onedimensional. robably is not a significant
!alue and e6actlyfor this reason& you cannot see& in (I;7
part II or )*5.5 figures& this force as horiAontallyapplied on
the #$ body& but for some safety reasons& the stress
tradition asks to count as thisforce e6ists& and I would say is
more a way to be conser!ati!e rather to be realistic…. of
course&this is just my opinionB
). The transient dynamic loads caused by opening.
I%!e ne!er seen a "rocess Department issued" transient
calculation for gas flow near or atMach-5& maybe you%ll be
luckier than me…
Ehat really we know: the #$ generates sonic wa!es because the
flow is at Mach-5 inside theorifice. These wa!es may be counted as
"normal" shock wa!es& in the terminology of 'luidMechanics. (
shock wa!e is an onedimensional wa!e so "hard" that the frontup
profile is!ertical. ractically& this wa!e has a Aero ramp time
and is a !ery special wa!e in fluid dynamics&being a
discontinuity in flow. This kind of shock appears in the supersonic
flight. >ou may think
it%s possible to ha!e it also along your #$s discharge
piping& so that means you%ll ha!e anunbalanced force at
magnitude of (I force or larger on each discharge piping leg&
because the
wa!e propagates thru all the piping. My opinion: if you consider
this scenario& you must considerthe same large force 2don%t ask
me how much…4 applied in e!ery piping leg& not applied only
on
the first piping leg& adjacent to the #$.
robably a more realistic scenario is to consider the wa!e as
described by @.C. Foodling in thepaper "#implified analysis of
steamhammer pipe supports loads".
CraigB has posted this paper 2please search for it in this
forumB4G the community really has !erygood reasons to thank
him& and )TE& I really thank you Craig) for all your posts
and for your
generosityB)asically& the Foodling scenario presumes there
is a sonic wa!e& but the wa!e profile is gi!en by
the !al!e%s closing or opening time. The Foodling%s paper is not
referring to #$s& but he waspresenting his paper as !alid for
both tra!eling wa!es of increasing and decreasing pressure.
(gain my opinion: it would be engineering satisfactorily to
consider such approach for eithere6pansion or compression wa!es.
Theoretically& it is !ery complicated to confirm or
in!alidateFoodling approach in 'luid Mechanics& the "classical"
+iemann model predicts the wa!e shapedoesn%t remain stable during
the wa!e propagation& but it%s also recogniAed that the
friction andheat gradient effects H not counted in the theory&
counteracts this tendency. @!entually& thetheory failed to
e6plain the real case. It remains the Foodling%s engineering
approach….and that%sall& you can trust it or not…et%s consider
the effects of this scenario. The idea is to count the unbalanced
force on each leg…
If the #$ opening time is .;s and the wa!e speed is *m8s you can
ha!e the ma6imumforce on #$ only if you ha!e 5; m or more distance
from #$ to the ne6t elbow. If you ha!e just
5.;m distance and you still consider the same ma6imum force&
that would correspond to anopening time of .; s and your procedure
is !ery conser!ati!e since you%!e applied a safetyfactor of 5.
(lternati!ely& you may follow the Foodling approach and to
count only the fraction of this force& corresponding to
the real opening time and to tyhe actual length of the leg.This
procedure& applied conser!ati!e or realistic as you wantB can
be applied leg by leg in atime history scenario& with the
notable e6ception of the last one where is more probable that
theforce is gi!en by the steadystate flow "free jet" effect&
e6actly as youJ!e obser!ed.
