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Lehigh UniversityLehigh Preserve
Theses and Dissertations
1969
A compressible and incompressible flow analysis ofthe air-lift pumpKenneth A. SchoeneckLehigh University
Follow this and additional works at: https://preserve.lehigh.edu/etd
Part of the Mechanical Engineering Commons
This Thesis is brought to you for free and open access by Lehigh Preserve. It has been accepted for inclusion in Theses and Dissertations by anauthorized administrator of Lehigh Preserve. For more information, please contact [email protected].
Recommended CitationSchoeneck, Kenneth A., "A compressible and incompressible flow analysis of the air-lift pump" (1969). Theses and Dissertations. 3743.https://preserve.lehigh.edu/etd/3743
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A COivlPRES!~IBL.6 AND INCO~lPRESSIBLB .
PLOW ANALYSIS OF
TlIB AIR-LIPT PU)lP
-- ----·---------;----- --~-- ~--,,.~ ---
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-------.- -- : . -- --~-- -- - - ----·- - -------. -,---------
by
·~ ·:1"- :,_ --Kenneth A. Schoeneck
{
A Thesis
Presented to the Graduate Faculty
of Lehigh University .. ,-:s,
in Candidacy for the Degree of
Master of Science
y
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Lehigh University
1969
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. . ~ - ~ , ···This theSis is. accepted. and approved, in. partial. ful------~---~--;_,_~"'-~~_-~,.,---~--- ~--'---' '-''•'-~1-•. -_1::._..,, •~--~-~'"" -~-•-; __ c·· • •
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f~11ment of the requirements for the degree of Master of Science.
,
date·
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Chairma:n of Department"
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. ·-~
The author would lilte to thank Dr. Alan H. S.tenning, ~-- ..... ..., . ,, . -
Professor of Mechanical Engineering, for supervising this . .
study .anct providing helpful suggestions during the course
of the program. ':d1e help of members of the Mechanical
Engineering Department is gratefully· aclcnowledged. ·· · #&~ ·
The writoer is indebted to the Ingersoll-Rand Company
and his supervisors for their aid and assist.ance. Tl1anks
· are d11e to ~lessrs. Arthur F. Stahl, Analyst, and Chester
L. Koppenhat1ver, Analyst, Systems Development, for for
mula ting the computer program •
Special gratitude is due to the author's wife, S~San,
who shouldered all domestic pr·oblems to permit time to be .
spent on graduate study.
:,-• • • • '• A • --;; ,.,,. 0• - • • 0 -, .... .. •
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• - · TABLE OF CONTENTS
,, ... ·.
·, ··-~ ·.
ABS-TR>\CT SY~lBOLS
1. · INTRODlJCTION I ..
. . !
-· _________________ ,-,·:,&._ ... -·-=;.::·:·._. '·'···- -··-· ·-· -·=:.--·- ···-·- .,..:._ ----r• .· ·,
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....
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.1 2 #, . 4 r --
· 2~~ -BXPERI~lENT.A.L PROGWt . . - .. - . . ~~O ~-~, -- ·-·--_---·~. -~._----
,•.
4.
s.
The i1odel TI-IEORETICAL Ai~ALYSIS ..
. 3.1. Derivation of the Differential Pressure Gradient Equation Assuming Compressible Gas Flow in the Eduction Pipe ·
· 3 .2 ~'letl1od of Using Differential Pressure Gradient Equation in a Numerical
·Analysis _ 3.3 _Application of the Incompress.ible Flow
Equation for Calculating l"laximum
RESULTS 4.1 4.2
Theoretical· Isotl1ern1al Ef_f iciency
Tl1e Experin1ent Comparison of Incom-pressible Theory and Experiment
4.3 Compnrison of Compressible Theory and Experimental Data
.,4. 4 Su f!}m a r_y., DISCUSSION ~ "
5.1 Conclusions --·-····----·--·--·-------------------- _ _ ___ __ _ _ 5. 2 Sug:ge st io_ns for Pu ture ____ ,~_Qr_~ _____ -- .. ---~---- ... -------~, ______ _
FIGlJRES
•
Q -~ "
..
APPENDIX I. Computer Program II. Sample Print-Out
REFERENCES VITA
___ ... _. ________ ·-------·----
••
.;;.., ......... :
...
• l.V
.6 7 . 7
11
16 · 16 18
21
23 26 26 26 28-43 44 44 48 53 54
--- ·-···--·
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·-·-· ···------- - -. ____ :.·,_ .. --_,_-' ---;-·:'-·.:.:__. ___ : _ _:_ ___ ~: ____ _;;:_· ___ ·C;c-,.,: .. -__ ___ - -.- .
•· .. - ·_; ___ ,. __ ·.,. .. - ·-=---'..---------·---.-- . .:.: ..
. If .. '
... . ; i, - ~~ ;, 6 -~ . ~ ·---· -~ . ~_:_~_:_.~~- :_~ .... ·. ~e,_;e_. • ,". ".. .. . . .. - :, '. . . i··
. ·.·. ~-· t.L::: . . :·-~_·.·• .. :· ... ,. . -:· ..
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m-,.
G·
r··- ·t .·. ·. ..
-. 4" . ' . _·. ~ LIST OP FIGURES ·----·•:
-~ .. - ·. ' . ' ·. . /"
------------~=--..:.:.-~..--~-~~--· -- ·-~~ _...,,.__.,_.~~~~-~--·-- -.'--' -- - -"'- .,:c - =-.... --~--- . .__ -- . ,-------""--- • . • . -
:. ' \#"
. .r -
. 1. The .~lode! Air-Lift· Pump
2. p·erf ormance of itodel .Air-Lift Pump·
-Pages
28
29 ·. .. - -·-··· ··- ·-~~~--_Jc.___~
'
3. Comparison·of Theoretical and Actual Outputs
-4. · Comparison between Compressible and Incom- · · pressible Theories
s.
6.
·7.
s.
9.
10-12.
Comparison of ~lode! Pumt> Performance and Theoretical Output · ·
·..,.
The Efficiency Curves
Comparison of Theoretical and ~laximum Eff ici·encies for 1 and 2 Inch Eduction Pipes ·
Comparison of ·T11eoretical and Actual Friction . Factors
Comparison of Theoretical and Actual Slip Ratios
Comparison of Theoretical and Actual Outputs, \\farcl and Kessler Test Data
I
30
31
32
33
34
35
36
37-39
;.
---------··· ·-------------1-3-16-. ·- Comparison of Theoretical and Actual. Outputs·, --- --- --- -- 40-~43·· ···----------·-······-· ·· P. Pickert Test Data
l '
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; ', .... . ,--·--i
-. ABSTRACT . -~· ... .... ' ·.. •. . - ..
··- -. "'"·' ·-·-~-··--.-- --.- __ __:__,...._~--.. ~--- __________ ____:_.......;.:.__----;-_--"-~-------- _.----.-,,...,.·-=+----~---'"''_:,:..,.~,._;__. --~- --~----_·.· __ .. -.. _,-,.--:-,-~_~----.---·'· . ,./
•' I •
Th_e operation of an· air-lift- pump, 14 ft. high- and -
2 inches in diameter, has, been studied. The resul t-s · show
tt1a t a present theory based on in-compressible flow and iri-_• , ·
eluding the effec,ts of friction and slip between tl1e gas .
and liquid acc.urately predicts· the performance character-
istics of these devices in shallow· submergence applications.
· ~leasurements of two-phase friction and sl~p haye been - ~
. "' ' "'
made. an(l correlations are presented._
A theoretical treatment of the pump operation in
deep submergence applications, takinginto account the
change i_n volume of the expanding air -is also presented •. . '
' -.. I I
As a first ·approximation, constant values of. slip and friction
factor have been assumed to exist in the eduction pipe.
Good correlation \\Fas f 011nd bet\'leen the compressible theory
-·-·---· -- ------------;-;--_-" _____ - and experimental data upto the point of maximum liquid flow.
'
),.. . ' -
(T . ' '
. "---~-~
•
The assumptions of constant slip an<l friction factor prove
to be invalid beyond this p9int. No significant improve
ment is gained over the incompressible analysis unless point
values of slip and friction factor are used.
Suggestions for modifying the present comp~ter program
are included •
.-~:
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. . . . . . . ,
·"". : . -' .... - : . . . . .
. . . . . - ·.· . . '.·. . . .· · ; . '._._i,~. _-.:_,_~-.:.._.·:,,,:::.·:·.-. .'.~!- ,: ,. .. ,.,.,,.-,, .... · ;., _. ,_.,._ ,~ • ~·a: . .',...:'-.,,· ...... :., ... ,i·:-··,.-:··--· ... ··~---·'·---"·_,r·•··~•,-,_.·~-_ . .-., _ _.,.~_ .. ,-,.,•··· ,-:r-"·;·o.•_-•.
. -:- ·.-· .
STilBOLS . . . , .. ,·. • • • ·v
. . . ---··"-----~e,__- -~---------·-----t··. --- --~ ~:- . . , -. ,_, ---~ ----. --- .,~-~--'-A- --Pipe cross · section .. ,area (f t2) • I • - - - -~- - • 1·-·-~-----.---
'·, '· -:· .. ,_ . ·- .. ,' '. :;
,, ' .
b Pipe circumference (ft) ----.e_....~~-...:.__:_------:-------:---~~~
(~) L,1
, ____ .,.
- . '
--~--
a-.. •
•la-.----·--~-~--~· .. _.,_
D , Pripe diameter (ft)
. f Friction factor (dimensionless) ,
g Acceleration of gravity (32.2 .fps2)
gc Newton's _Law constant (32.2.lbm ft/lbf sec2)
H Submergence ~epth (ft)
'
K Friction coefficient (dimensionless) (K= 4fL/D) ~
L· Pump length (ft) 1''
-----• ~lass f 10\-/ (lbm/sec) . m rate
P Pressure (psf)
Q Volume flow rate (cfs).
S Slip ratio (dimensionless)
T. Titne (sec)
•
;r' Stress at fluid surface (psf)
·7.., 1iall shear stress (psf)
\/ Volume (ft3)
V Velocity (fps)
_____ W .\\'eight (lbf) ----------
~ Density (lbm/ft3)
Subscripts
0 Pump inlet
1 Leaving injector
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2 ~(· . r---------'·c-- --. . . . - ---·'·;·, . ·--···-- ····· ., ,- . -·-·
Point down.stream of injector·
. Liqttid
- ·-Vector· ·guariti ty··
.· s Pipe· .surf ace
g Gas at average pump pr~'¥ure
ATM Atmospheric condition
·M i·Iomentum
n Final integration po.int
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•· t.
ln 1966 work was· started at Lehigh ·University to exam,irie h ' ...
. · ·. r:_._,,_._ ... :-.-·-·.-·._ . _,._ ..
- · :··. ; - · thoroughly the fundamental principles of the air-lift pump.
'·
,,
'. .. : ·' ;., · .
. .,
- .,,. - . . - ..... _._ .. .
-a·"\-... ·· -J j
. -- __ .,,.-·-"
Th:rougb the applicatio~ of basic fluid mechanics, ~n equation-
was derived which accurately predicted the performance
characteristics of these devices in shallow submergence·
applications [1] [2] • -The only limitation was that suit-·
•ble values for the slip· ratio and wail frictio_n factor had - - . ~
to be found before the ·eqtlation could-·be solved. Experiment~·
al. tests performed on a model pump, 14 ft. high and 1 inch·
in diameter, provided enough data to substantiate an existing
theory for calculating the slip ratio but did not provide
a· suitable means for predicting the friction factor.
This work is intended to extend that originally done
by ~1artin in two different ,-rays. Th~ first part of the
- ·. :, .
):
- ..... - ;_ ----;,-· ·- ..
program is concerned with rebuilding the existing model
air-lift pump using a 2 inch diameter eduction pipe. By
rebuilding the pump, additional experiments could be carried
------·····----------------out using submergence ratios from 0.692 to 0.478 to determine~--
n-"_, V· .J
if the present theories for calculating pump performance,
slip ratio, and friction factor were still valid or invalid
for a pump t,.,ice the size of the original model. The ·
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. ···•·. +7 l ... Cf.··~. --~=-··-=·-·--,-~:·,.-·------ ----·--·- - . --· .. , •. : __ : __ ; ___ :_----·,----~:--·-'-"- -·· -- ----····---- -----·.·· -----=-·.,;,,.,_-~_,,,..:;;_ :,,.;.,.,_----__ . ~.---_ --,=-="'-.;;;;;,,.;_·...;._,..;,,..,· ___ -=,,m. :=----=---=-=-----·,...· -~. ·=-----~----==:=· --""':"---=-----=---=-----=""': =-.----- -
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numerical procedur~ for calcul~tfng pump performance -in
deep submergence.applications •. Under these circumstances,
it becomes nec~_ssary to account for, the change· in volume .
of the expanding air inside the eduction pipe. A comput~t'
program has been generated which performs the required '\ . . ,
·numerical integration while maintaining fixed values of the
slip ratio and friction factor as a first approximation •
Output from.the computer program is compared against avail
·able test data from previous authors.
. , ..
'
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- ---------- .. --,.------·- ............ ~ ·~·.,..,µ__!""~-_,_-,.._· __ ~.0.,·.-···-· . .-.·~---~:z .... 7' .. L··=,--.-- ,··-·-·-----._
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' ' . ' .. . '-• "·~----· 0 - -~~-" _ _:_ ___ .,._:____ ---,-~- '2·,t ····.·· liXPBR !MENTAL PROGR..Ut• ..•...•.. · -·": · --. · · .· ---~~.:~-,----~-;:·--~--,~-··c.-,~:~~-,~--.. -·-~~---,~~:--:-·"; ,· c--.- -
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. The ~1odel . ~
• .1'
· -- J·A sketch of the model· air-lift pump t·ested appears .
in Figure (1). The inj.ect~r allows air ·to pass into the '
dis·char$?e pipe thro1-tgh .56-7 /32'' diameter holes. The L/D
ratio of the apparatus was constant at 83.593 whereas the
H/L ratio could be varied from Oto 0.692. A rounded
entrance cone and large cross section area ·exit· elbo,1 were
used to minimize the losses iri these areas. The various
two-phase flow regimes of bubble, slug, and froth were
observed throu~h a 32'' length of plexiglass pipe located
near the discharge end of the model. A Vol-0-Flo meter
with~ scale range of Oto 10 CPM was used to read air
flow downstream of the pressure regulator. Air flow rates
up to 33 CPM were recorded through the use ·of a pressure
gauge and control valve downstream of t~he. f lO\\T meter.
i;.water flow was measured with the use of flow nozzles placed
in the bottom of ·the orifice tank. Both the air and water
- ------- --···-·---· ------ ··- - flow measurements were estimated to have .! 2% accuracy. .
1,
. .· 1-·_.;
'
f .,
.....
•,
. . .
' . i - --··· . -·- ---- . . ~
. I i f
.. I • f
l
. r ' (
. ' I l I
I I' t I 1·
. ,1 i f.
[ )"
i/ ·1· j.• :~:
. ,,
!I l1 .. r.::~··,
'/ti1 ,i1.1,,i l,l.11. wt 'I': t.::.-.
..
I
. , •·· ..
... ··. - - .-~~-· ... -·._._ .·.·.-~···-_ ·.,~.·c.:_.~. _ . .,,...-_· ___ .. ;-_,.,.;-._~----·----,......-;·-.
: . :·· --
.3. -.-,.--.CC_.C ,-C·.-_. .. ~.-·-~ ,0----·--- .... C-.--,-• .---• .-- ---,•-- •.. -- .... -..-.--".
\fllen. attempting to pre;_dict the_ pecf ormance of an -· . air-i'if t pump for suhmer~enc~epths exceeding 30 ft.,
-. .
..
--- --'·- -- . ' ..
.... '-, i- .
..J.
'I
- . ', .
-it.-be,comes pecessary to account for the variation in gas volume throughout the pumr,. Since isothermal flow is assumed to exist, the volume of,gas-in any given length of eduction pipehcan.he calculat~d providing the average pressure in that length is known. This section presents
.~ ... , .. _ .. -•~.-~ ... -.~-the derivation of ·a differential .. pressure equation ,1hich -can be used for analyzing the ope.ration of_ an air-lift pump through the.use of a step-by-step numerical computation •
)
Average pressures and pressure drops are calculated for any given finite length provided certain boundary conditions are satisfied.
•
_ 3.1 Derivation of the Differential Pre~sure Egu~.tion As.suming ComRressible Gas Flow in th~ Eduction Pipe The mathematical formu·lation of the conservation of -
· linear momentum for a material volume can be written as . ···------~----- - -- ~
- -----~
·· ·c1> where e_ is the fluid density, y the fluid velocity, and 'f the material volume being analyzed. The forces acting on ,
. '
,, •
1:1 1' •. ,I I
. ./': .
- .. %
-· ' .
,
·"
1'. .... . . ~--:-·· -\; ..
.,. ··- ., -·. ~ - . "
r
. , ........ _{:
. a'·,··,
. '·: :,, .•.. , .. --_,.J;- . ."., .• _.:. ,, .. p;.;,,_.,,: •.. .: •.•• _ ..... .. ":';,.
. . .- .
. . .
. ~the~-m-aterial vol'ttine can be cfividecl into t~o .gr:oups' ·the . -• ____ :~~--·-- . ~--·-'--:_.'.:.·'.·_,. --~.·: ........ ---· ~·- _: -·- .. .
... • . ,. • •. ,... . .. .. .. ...... c .. :-: .... ~,•-·->-··-·•· I r ., .... ,·>-•·•·-,
-surf ace forces .arid-- the body forces.· After making. -this . . .
6 . .
distinction_ between forces ~nd applying the Reynolds· .. · • • r-'- ·••••• ; -··•·•
Transport theorem to the left hand side, of (1) ,. the.
'principle of conservation of li-near momentum, when applied
to a control volume,·can be written [3] . _,,
(2) s s ~
,1here, f ·~denotes· the extraneous force per unit n_i3.Ss o't the -fluid, 1.., the wall shear stress, arid 1' the stress at the ·
fluid surface. A and A represent the pipe cross section s ,) p
area an<l wall shear stress area respectively.
In order to continue the· analysis, the following
assumptions are made: (1) steady flo\", (2)· one dimension-·
al flo\\1', and (3) changes in the linear momentu,n of thP
fluid are neglected. l\.pplying these assumptions to (2)
and substituting P the fluid static pressure for'\, the
momentum equation for a differential volume becomes
p~ + ~tegrating (3) yields
. . ~ ·, -
.•-
-s-• \ l , ·,
(4)
.
··-
/\
! .
. . • • l !
I !
'• j
•••. ('"' ·r., .......
• I ~ ·---------·--------· . -~
• • -• < r. ;·- ..• ,,---. ····,-•.·-••--;-· --:.--· ,~,_-.... ---·
0~ .' _,.,
..... _,_ ______ ,------- --
. \ ..
;.. .... .I . ,_
. . a
... •, . \
··":" '.
. . ' '••'-•·' -.•-,•-~•-•-'•·+ • ... ,.: .,__.;L,>•'•o''<.~-••,•-• •, .... ,.<oe,- ••--'~.---'+r •.. _, .. ,., .. _,_,,: •· •• ,_~,·---r-•,"C.,,;.-·, ~--· •,•,,;,,•'~.--.'.•-•-•'-
. . .
~ . .
·-~----·-·····--······. ··---···•>-"'•"'" --,·---···--·. . . ...... , wner·e· b i-s- tlie~ \,ret-tecr~,,-e-rimeterof ___ .the~--pipe~--and·-aw~·tne·-- -- ---_~--'. -" -- __ ·-_-- -- -·-
·-·' - . '--~---~-----~------....,.,...·-------·--··-·· ---·--- ---··-·-······ .
weight of the fluid in the differential volume~
The weight of the mixture in the pipe is the sum of
the weight of the gas a~~ the liquid~ . . ~
•I,(' dw :: dL °i ~~ Ai + {~ A.~ ·<s>·
~here A is the effective flow area of the gas, Af is the g
effective flow area of the liquid, and e~ the density of •
the gas. ~ince the gas and liquid do not rise with the
same velocity, the ratio of the average gas velocity Vg,
l
to the average liquid velocity Vf, is called the sl,lp ratio.
Also
• .i
(6)
.I
(7)
(8)
' \
•,
where Qf is the liquid volume flow rate and Qg the gas
volume flow rate. Suhstituting (6), (7), and (8) into ... . . ' -- ---·-- -- __________ ,.. ·-
(5) and neglecting the gas density in comparison with the
liquid density
_,
-9-
_J
_, ,,., . . . -- . ·-· -·---. ---· ·--··-· :···-·--- ·- - - . ·: . ... - -----. ·--"'----. . ... ---·-·
l --·-·-·------··---------·---------- ----·-·. -- ··---------- .. ·-- - - -··-··-·-------------~------ --··-··-·· . .
' .
.. . . : .. _ t, ..
. ... :·· - ,. . ~ ,.,
·-.;-. •'
. :_ :.,,:i:I · ... : i '~.
. '··. ~- •... • ·•. -- .•• ·'1- • .. ..
' .... ,' ·"';"
·@ .. ··
. .. . ...... -~,. . . . ~ \.·, .. ,.
"'~. ,.,._ .. l ·, . . ' -\~f .i;. . . . . . -~~ .
' . . ~ - . . ..... •, ':->. --~ ,; ' -. : ... ~
. . .. ··.< I
,.-_ . \'.-:~.,,' ·. ~ . .
·. · .... : ,-
, . . .. • . r,,:. ,·· '
- -~---~ ---r~ --~ ------- - ---- ------ -- -----:-i- - • --- - - - --- - -- -- -·- -
' . - --- --- ·· · --- --- -~ -- --Jw ~, dl e~ ~ . . ' .
1'.. -
~,.
. cs_·_·_·· __ ·· ~\
. .
•--~---- --· .
I ..
11- ~:.().\. .. ( 9)
··,_ . v~ where S is the slip ra t10 V+ •
· Following the analysis of [2] and [ 4] aqd assuming ·
the wall shear stress to be a function of the shear stress
for a single phase flow of liquid, tQe recommended expression
f o_r ~ becomes
+ e - .. ~ 'rw- -. 2~c. (10)
where f is a friction factor which can be evaluated using
the 1',loody Chart or equi val en t information •
With the aid of equations (9) and (10), equation
(4) can be rearranged and rewritten to yield an expression
for the pressure gradient at any point in the upper portion
of the pump
= ~ ~"'" + 4+ '4 v/· \ + o~ ~c. \+ ~ 1) 2!h. Q~
~Q~
dP --d\_ (11)
Examination of (11) shows that the pressure gradient can
be evaluated providing the slip ratio S, friction factor f, - ·
and gas volume flow rate are known at any point for a given
liquid flow rate.
,,
-10-
\
- . . '"" .'' .
', ..
-,
..
.' )
... , ...
---_.,.~----- ----- _ _. __ :._ ___ :;~:;;;:;:-~-=-= \.-.-. ~-:-:. -----· --.. ·->-:---· --·-- ----------·-------"~ - _"··- -·:_ ---~· -- . - ·:-- .----------·--- . ~-- . --· --- ---- _--- ---···-------·-·--·--·----·--·---·- ---~----- - - '-·- - --- --- --·--· -- ... __ : . ---- ·-- -----· --- -- --- --- -----··· -···--., ··- ----. -·---- - . ----- .. ---- --·----·--- .. -·--·----------- ----------·-------·------ ·--------------------------- ·------- ----- ------ -- -- -----· -----·--------
. \ t '. ' ' • . ~ • I
t·· l
l
_; _,__ .
fD .... _ ...
•
: .·. '
... -... , .
. \ ,- ..
--1.
_.,.;,_;. .
. ·• ~--
• _P
' . . /
---L-·•·•.3e2 · · Methoa of us~ing Oiff erential Pres.sure, Gradient c81fuat;1-on ~~- ~:::-.<-in ,a Nttpi~rical= Ahalysis
The analysis of Ste~~ing lind Martin [2] ~ showed that
. : the :pressure downstream of the _injector has. tl1e f_9rm
I _ 4~ VoQ~o
~ C. 'ti CI (12).
Although eqt1ation (12) was derived assuming incompressible
flow, it is sti-11 sui tahle for use _in a compressible gas ' aµalysis since the pressure dt6p across a n6rmal injectcit -
. ' is small compared to the pump inlet pressure. Thus, for
assumed gas and liquid flow rates at the pump inlet, the~ ./
_pressure and pressure gradient can be calculated at the
injector discharge provided the slip ratio Sand friction ..
factor fare known at this point.
As a first approximation, constant values of Sand f
can be assumed to exist at all points along the eduction
pipe. Appropriate S and. f values can be obtained for any
given suhmergence ratio and eduction pipe diameter by
extrapolating the combined results of .Martin [1] and the
experimental data contained in tl1is thesis. -
I '
Once the values of S an<l f hav·e been determined, the
-pressure gradient at the injector dischar~e and the absolute
pressure at some finite distance above the injector can be
-11- ·.;
·, .. ~ .
------=-.-·~, ... -~-~~- --- -- ,--~ ·-- ----·, ·--
I '•
-
-----------------------------~~-··. ~1
----:-------------------1!111_ !l!!!l[l! __ ~_ !!!l!IJ!I_ .... _._··--~-~~---"'---·-·--·--, ·-·--··---...• .,. ·-·-·-··--·-~---.. --•---~~~~~~~~~===!!= = .------- - ···---,-,.--:"----~---·---..:;_:_ ·-- .C-.- •• .- •.
- • - -· -- --- ··-. ..:.._· ___ -- ••• -. • ....c --- -- - -·- ·- ---- ------~- ------,----·--~- ' -----~ ------·-------·----·- ... ---- --------·-·------------·-----· - --- ---- ----·-··-·.!_ _________ ~----- ___ .:_ _____ _.,;_~----~--. -·------------- ---· . · _____ . ---·-·--· -·--------------~---------·-·- -·-------·.---·------·----------·--------------- -- -- ------· ·---------~- . -- -·- ---···--··· ·--- ----- --------------- -----·------- ------· -- - -······-----·-··· - -
. · .. ' ~
. '
. ·.· .
. . ~ . -· - - ..
. ,i -.
. . - . -' . . .
. '. . ' • - (j. ___ · '. - .. _ ----··------------- ______________ ;......_ _____ .:_.__ ____ .:..... _____ :.:..,...:__~-.'..----. ...:.....---------.-
- --'- ----- •••- ·-==· •• --~=----.~-.-~:-e-alcltl-a-ted ti-sing• -an·· ·.Bu-i.-er.~·c:au chy- me tli-od· of•- riume·:r-i-c-al • .. , .. C •••• ·'-· ::~.:,~··-c·•-c--,•'c •- .· , ,, --:• • -• • . - . .
··integration [s] • The gas volume flow r-ate at the first
. . : - . . . . . -point Q~ is simply the . flow rate injeccted in to the bottom -~ a .
of the pump multiplied by the pressure ratio. between the -~.-·--~---·.--,- ., , .- ,-·-····~--~---·--. - ~----'-- -~ - .. -· --- ----····-·-------'e-·~------__:____,.: --------------·, .
- # \
·~ - --- -------· - ... _--·--- .. -~- .
,-~,.; ~., ..__.,
•
·inject6r.discharge and the first point. Og~ then becomes
the proper_.value _to suhstitute into (11) when calculating
the pressure gradient at the first point. r~
The
for any
step-by-step ~
finite. numbe.r ' ' "l.
integration procedure can be repeated
of steps n along th·e complete 1·ength . .
of the eduction pipe.. At the p11mp exit, the calcul,a ted
discharge pressure shbuld equal atmospheric pressure
plus a pressure drop correction for the overall change in
momentum of the fluid. In mathematical terms
wher~
. - - -- -
and
:..
I ,--
V. - 4{ ~~"";- Q+) ~- ~ oi
•
Vo = 4( Q~o+ ~)
-tr O l
•
-12-
'·
(13)
(14)
., -·,t.
.. 1 ·1 --~ . \
•.
-------- a.--'~
.. -~---·-·~-~. ···----- '":- -:·-----~~------------ _ :_._., ,·--:~----- -- - ": .
, . . ' . . -- ·-·----- -·- -·----,- ------------··-·:---..:.c...:: .. ....:_· __ :-····----·----- -~--;-'·_---···· ·- ·--·-····--···---------------~----:----:------:. _______ :: __ . _ _:_~-----·-·_---- .......!..----~--'------- -- - .---- ------------ - -------·----·. ------~---· --·------------·--------··-----··-·---=-··------·-···-·--·--·--· -- ·•·---· ·----·-··----------,-----·--·--·--·-··-·····•··-•·•···--• ----•--· - -·-··-- ........ ···--- -----· ----·--a··--·--··-·------- - --- -- .. • ..
. -~--.
;,,;,
- · · · · · .. If· the ca\culated · f .:illai-discharge Pressure does not ;~tj_;fy .· ·• ' · ··-···.·· l ..
. '. ·.- - . ,, ' .
~' \....L;-
. . . (13), the complete step-by-step calculation is repeated.'.
using a different -value of Qf• ·: The Ilew value Of Qf is a -·. :·· . - ·. .
function _·of .. the magni tud~ and algebrai·c value·--of ... PERROR . -- ,. "-~-----_-. -· ---- ··---···-·--·-· - ----,,-- -~.- - .-- .~ ,.· .,.._-.., .---·-- ~--~~-'"--'-'
· · Where PBRROR is defined· as ;,
P •• ,o~ = P"" - PA'f"" - t:. P"' ~ (15)
A continuous curve of liquid pumped Qf vs. free air
~~ed_Q~~can be generated by. satisfying equation (13) .for.·. . .
the pump inlet. J
. . ·' ·_I
- ··~"'·v--= •.•;_ .. . ~ .. ,;
., .. ·,-'t ... '.:,~ ~-1:·.'.·
·_ .. {,· . ' ...
.. .. ,.
any number or' Q{ and Qg0
combinations at.
··Appropriate initial values of Qf and Qg0
can be-obtained --- - r "·" ••' -· ·---~~,
by .solving.the Stennin~ and Martin flow equation for
selected value.s of Q /Qf ratios •. The submergence ratio, g •
slip ratio, .friction factor, and pipe diameter to be used
in the compressible analysis should also be· used when solving
for the initial Of and Qg0
values.
Pigu~e (4) shows the comparison between a compressible
and inco~pressible analysis for a hypothetical pump operating I .
with a submergence of 150 ft. Figures (10-16) show results
f·rom the compressible and incompressible theories along
with Warc1 and Kessler [s] and P. Pickert [6] test data.
Tl,e effect of accot1nting for changes in the gas density ; '.
while maintaining fixed values of slip and friction factor
-13-..
. --:r .. -.
I '•
!--~~-. ' .. ·,______;____ .·----------~- . t --. ·-·----- -. . . -.---~' ·, ·,---.-·-~--. ··-~--~· . . . '-..• .__c...· _. ----
1... -- ---- · .. -- . __ -- . - . -- -•---. • - ---- ---- .. - - ·- - -··-· --- . --· ·- ---- •
. .
. . . . ·: -- . ·.
- ...• t!: ·,
-·--·-~·---····-·,-----~--·······---·--- -~---··~----- -·~~~--~-< -.. __ . ~- - ·-~ . . . .
. . ' . . - - . . . . .
- ' . . . ~ -- . -- . . . ... -~.~ . . ~ -.. - . -- -~. -~. ---·--··.----·--·- ---------- ·------------·-.-------·-----;:------
. -- . -- . ·- ---- ~...:. ,.-~,. ·. ,j:·-· :
· ..... . . . .
. ' ,:·· . '. ;, ·-:,·.
- --- OOes nC>t appear to yield results \1hich differ. ·signifiC8,11!~Y - .·. ·.-· . . - .. ""·· p~· -- -;'-- ' ... . . . . .
······-··---- --- - '--·-···-----··-· -·-·
-----/·.
..
' .
-- -- ···-·- - - -·----- ---- --
from tl,ose of the 1·ncompressible a.pproach. I . .,
All of the calcula"tions for·· the compressible gas
anafysis \'1ere. performed on an IB1vl 360/30~_digi tal computer. ,._ . . I --- J
'The, program was ,irri t ten in FoXra~ IV l~~uage and run /----~ .
.:using o.o.s. The computer program and a sample calculation· . ~
· using F. Pickert field data [6] are included in the Appendix •
3.3 Application, of th.e .Incom2ressible Flo1vv1. Equation for • C '
Calcula:ti ng .. ~l~ximum T}l.e.or.eti cal .Is.otl1e,rr.1al ~f f i ci~ncy
The efficiency of an air-lift pump is defined as the
ratio of the useful '"ork done on t11e \tater, VIL, to the energy .
available as. a result of the isothermal expansion of the .
gas from the injection pressure down to atmospheric pressure,
B • g
(16)
Bxa.mina tion of (16) sho,-1s that for a given set of opera ting
conditions, the highest efficiency is obtained \'lhen the
-· . . ·- ---- ---
, -~--------·---- .
... ~. ~-------- -· ____ ratio of Qf /Q ,.,"'\ is a maximum. -- - ---· ---·-·-------- - __ ,
J .
j . L...
(I\ • I .,
I "
. (
..
The flow equation for incompressible flow (17) can be
used to predict the perf orman,cc of an air-lift pump [2] •
•
(17)
·- ,
-14-
Q'· '
- . .'. _. ___ ... · ---·. - ·---' . . ~
.• .
. . --· ~---- ---,- ~ . - --:.,- -_- . -- -- - : ------ ,--· ________ :"" ---·--:;.---·-------=:;----~---------·----·-:----:- -----·-:----------~ -· ----- ------- -·---;----
·····-···--.~ --~---- : __ · ,,,: __
... : . . ;· ----- ·- : ... _ ·-· ..
r .,
~ -' . . '~ .. : -
. ; . . .
. . .
. !!'. . .... ·-~ .... -· .. ,: -. - .. --- --··.:
,
.. .' ·, ..
r. ·•: • . .
, : ... .-"where K.~.is,. called .. tt1·e friction coefficient .. · .. ., ··---- ------ ----- ... _ - ... -~------ ,. ___ .. ------· - ----·-· - ... - _, -- ---- · .. -·
K = 4.t\.. A 0
• , • : I
.. I ':
.,,, · ·An analysis of equ,ation (1.7)
,,
shows that the theory .predicts .:.,
-maximum-Qg/9r and hence maximum efficiencies at zero .
. liquid flO\\f rate. This is not in a·greement with experiment~l.
results, which show a ma.ximum Qg/Qf at .;_ finite flow rate
Figure (3). The analysis does not predict a meaningful
m·aximum efficiency point and. is .def ic~ent iri this respect. . . .
It- cottld nott'· be .expected to give good agreement wi tla
experimental ·data at low air and water flow rates.
:-; . /I'
:~
/
.. , .
•. .,
.•-_:,
-r---i
·-· '-·- - --·-- -: ---- -.- .---:----~. ;. --··- . ,r- . - ' - .. ,_ - -- --~----~-- -
•
,,\
' I
-15-*'
...
·1.:
:;• :, .f.
; _ C • ,;, ; ~\<,.f ·.!!~
I ~ .;,.-· ·: . ...:. . . .·. . . ' --- ___ ,.,,..,.,_,,_..,.. _ _,, ___ ,-........, .. ~--·-·--. -.~..,_...--~--· · ........ _, ___ _._. --·· . ·.· ' ·,.-·' ',·: - ·. -. . : .. .. ·.··········-···-·-··-· -- .. , ,·.~.-, .... ·. -;. ----~·- ~.-......- - .... ~ ........ · -----·---.·-· ... .
-·.:._-;-... ---- - - ----~ -- ----- --------------~ - --....-- ----------··------·--····-·-·--·---- ·:::__ ______ _ --------------_ - ---------- . - ~----- - ----·--·--·----------------·-,_ ------------------~--- ----- - _.· ........ _. . . ' - ; ...... .
. . : C ·--·'-··· • • -- - - - - • - --- • . ···--------·-- . . ... - c:.·c..;cc---- - ·-;;-
' .- ·-, .. ·.
'<- -· ·, ... '., -, ' ·,··.,:--:. - f
. . •'"- . . . - >:_r·:;-· -_ -.: _-- - . '.', ., .. •. '
' . • __ ...• ,.,••··,,._:••j••·:;•••'-'•AO,>·,•,.c.,.
_,. ----- ---------····-·---·-----· -·--- --- .. ,. -."--.- :.... ---- .. .:.. ... --____ : ... ·'.--·-·· -·---·---· ··-~,·.-.·- : --- ' -,--··· - - :..... ____ --: - ----··· .. ____ - -·- . -- - ---·--·--- ·------------ -- -
- .
· ..
I -
. 4.1 T],e -·Experiments _ · ~ '
The results of_ the experimen-ts are presented graphically
in Figures. (2-9). Pumping experiments \iere carried out at
air injection rates ranging from 0-32 ft. 3/min. of free
·air. For each value of tl,e submergence ·ratio H/L, as the
rate of air injection was increased, the flow of water also
increased until a poi~t of maximum water flO\\f \'las attained.
The point of maximum water flow \\fas more clearly defined
at higher values of the submergence ratio.
As in the case with a 1 '' diameter eduction pipe, the
two-pl1ase flow regimes of bubble, slug, and froth flo\1
developed in the pump discharge line [1]. During the
experiment it was noted that the emergence of the various
flo\'I regimes occurred in a sequence consisting of the
following parts:
(1) A regime in which a small amount of air
could be bubbled through the pump with
- ' ------ . --- - _ .... , .. - ·-·. ~---- -- - - --· -· - -- --- -
no resulting liquid flow.
(2)
•·
A regime in which the air injection rate
was 10\.\1 and there \'las a small flo,-1 of
liquid. The air rose through the liquid in
the form of large slugs.
. .. :.;,, .....
•16-·
--·· ------~ -- - - -·-· . . . . . -- . --.) ..... ,. ........... .
/
~--f .
i
~ - - ---~------~-==------·-----'-'-== -----:---:-~---~-~-=--=---~----=---=-·-=-----=-=~--=··=·-=--=-=="=· ====
• <:::, -
I ; -
~ . ~----- -- ---~ ----------- ------ ---- -. ' -~-.·_··->--~-~-··-- -~:· __ :· ·: - - -- ~ - - - - - - - -- - - - _________ '.'. __ .· - .. ·:. ·:· --.-··_·_' '·, _________ ----------·----- ---- -~-~-~-------
_,. ' • ~ ... __ _,,_::___', --- ·1 - J •• - - •• ......... __ :· •• -.:·•,"-·-----~··-'··:._~:_._,. __ , ·-···,--:~·,.---, ••• •.:-:.,.'--·
. . . · ··- ... : .. ~r.:-.::c.·' ... ?~:-~~=~--:-:_;---·~~---~--- __ (3) 'A regime .in \\Thic'h the water···-- f lO\i" in .. -
- I - - ·-·' '• .--·-, e' <. .: • ••• ;_- ,.'._,_,l,_'_, -•·· ."
-- '---,- . ,---· -
'.
. c-
CD
.... ;.... -
.,o-·_1,1.·,,._-· _·. -. ,\ ..
............
•.~·,, - .,. -•• I· •',L"" '.,•_:,._•,,.,> 1 ••••- -,• .":\. ,- _:_
(4)
..
creased rapidly for small changes in ait .·. .
f 10,i rate •. -The slugs of air ,,,~;e greatly
redttced in -size and the flo,1 became a _)
·~ J .,
combination of slug _and annular with
·increased leakage along the inside diameter.
of tl1e pipe. \
The pump experienced smooth
operatidn during· this regime \'ll1ich lasted ..
almost to the -point of - • liquid gow. max1mum
A high air f lov, regime containing the
point of maximum water fl0\'1. The flow
pattern in this • froth and regime was
difficult to observe.
·, .
' .. . ':...
···-
, Figure (2) is a graph of tl1e test curves for submergence
ratio values of .692, .619, .543, and .478. Submergence
ratios·greater than .692 or less than .478 could not be
obtained due .) tl1e physical limitations of tl1e pump. The
general shape of the test curves or1 both sides of tl1e
maximum point is in ap,reeme11 t '"i th results produced by
previous experiments [1] [6] .
1.
. '
Figt1re (3) displays tl1e test data in tl1e dimensionless
form suggested hy the Stenn:ing and Martin flow equation (17). ·
When presented in this form, the initial portion of each
-11-.. ;
.,
·:- ·, ~ < -, · .. .-.,· ~--_. .. ·-···--·--·- ·- -. ·--·····-·····-·-·-
. . - =· ===----------- -· --- ------··---·---·----------·-- .. -=---------· -------·-----···---·------------~----------- - ---- li . - --- --- - ----:··-,-=-~- . . -"· _: - --: -- ; . -·.- ~ -. -.-· ---- -- ... -- ·----- -. -- -------------- --·- . - ------ ------ ----------- ----------------- ----_,--· - . -· ---- ----- ·-------------- -- -- -- ···--· - ----·-·'·----•-- --- -·----··-· ----'-·- ----- . -c-\ ---···--·· ·-·--.-·--·---·---·-----·--------·--··-·-·-·--- ·-------·-· --- --·------·--·-:··---- ···-·-··----·--- --··--··--·--·-··---------·-··-- ·---'··· --·-···- -·· -- ... ,.. . . ,-{
·} . ~
. li - f
111
. .r
. -· .. ···~< . . I . I . • .
. .. ,.·
·,.
....... ----·-·---·----·-- ~ --------- . · __ · __ · .. . _: .. :.._. ' --:--:-----.---
. ' .' ") . ---~--~. --· .. - ,·-
'. ' ,• .·:
~ r
~~- ·.- . .-.: .. ·.··,.c.-,:.. · .. -~ . . ' . - ., .. ·--"------.--,~----,~------:-'··--·-- '1·'
. . . .. ." .- .·· ' . . . . .- ~:/: - .-. ;,.,.,. ... ..,.· -· .. ·- : ... -• .. • • •••" .... • • ._ ••• i •. <-•
0
• Ao-,·_,._ .. • • • • /. ii• f \'
t I' i
. ' ll
. .. . · · cut".v_e __ t_ends to have a .negat;i.ve.sloi,e •. _T.hiS indicates tha.t-.. __ :· ---~----c· . I --- ----· --- -:,-----·-_-/-,·-·- ---; -. / h - --.: -: -·t
i"
. ~- ;--· -·
a :. ,
.Y
· the efficiency of_ the pump increases sharply to a _maximum .. f I
. . . and·th~n decreases at a more· gradual tate.
Figure (3) also indicates that for a give~ set of __../
.operating conditions, a theoretical analysis taking irito
acco11nt the com_p.ressi bili ty of the gas/Should al,..,ays pro~uce
a lO\'t'er peak liquid flow rate than th.e incompressible theory. "---- . . ~ . .
.---·~ressibiU, ty causes the bQttom of the pump to operate ~ '
at. ],.ow Qg/Qf r_atios and the upper portion to operate at
high Q /Qf ratios. The resulting mean value of Vo· will g "e~\..
always be lower than that predicted by the incompressible
flow ~quation (17).
4.2
'
Comparison of Incompressible Theory and Experin1ent
Figure (5) sho,is a direct comparison bet\\1een the test
data taken using a two inch eduction pipe and theoretical
pe··rformance curves drawn using the flow equation (17).
The values of S- and K used in drawing the theoretical
curves were calculated using the actual test data and the
Stenning and Martin max~mum flow equations. This method
yields Sand K val.ues which theoretically should only be
used for predicting the maximum point of the test curve.
However, as Figure ·(5) clearly illustrates, the specific I
-18·
!'
.I ,.. - . ~
. ., .,
·\.o. ..••
-~---------------· -·--- --- - ·- . . .
---- -.: -- ___ ___.:___; __ _ . .
-----'-- ----~---· __ . -~.------~~------~--~, --~-~-~-~----~r--· --------~--~~---·---~ ----~-~--~----••• ----~--~---- _·. - ••. , -.-_- _------- .------ .. --~----. - -------------------- _____ '_- ___ ---- --- - -----·--------··· --·--- .-.- ••• • --·----~ .• --0· ----·· ••.• - ---.--- - ----- - .... --,- -=- - ,. - -- --- . ---,--- - ------------
; . '
. _"I. _/, ·- ..
. . ..... --- .. ----._.
- . ., ' . .
. . . - . ' ~- ~-(' ···---~---· '• : . . --- a,-·--'..,.. ___ · - _- . -- . . -- . ---~---_ -.-----------------------~~- -- -- --- - -~-~-- - - -- -- :_' -. - - - -" -~- -
- . ~ - .- -.- __ _. .... ,•', - •• • -· ~~~~----- -=?--~-'----- - =----,----·-- -~--~.,.-~-~=..,.,,..,._,.=_..,,,,,.._...,.._~--=~--~---- .• .. ...,.,,~~~---··. . -- . -~--=,,., .. =-.#:- - .-·- ·- ···--·-- -----·---=--·--·-- '=-1==-rn=. ~--- :=-:"?7~~==~-=---.-- ··-- -- ----- -..
- ,__-__.__.._. .. ______________ _
•
accurat~ly predicts the complete shape and range of the
pump performance cur·ve in shallow submergence applications.
Deviation betweert,.:theory ·and· exper·i·nient is less than 1% . ' '
• ' - J_ --- -·· - - - - ........ -,- • -·· -··· . - -·- .. - - ... __ ,.
~ .. . -/--· ·-'--··- ---- ~-----··--·· ··- ~ ·------- -····--······ ···- - -·--·-·-·- ··-·----·'-···-- .. ·----¥--. -J·-·-·-·----~---·---~~"---J-.--.-~-'"---~~ ------~----·---'~~--~.-------~-----~------'-------,.......:...----~------
---------~~~-
0-..... r.__r;
~,,.o_ ·_- ·-.~
<..!., . I
._.,/
for all value~ of tl1e submergence,-ratio H/L. · . .
' .
As the air flow is reduced belo,i that req~~red for
maximum liquid flow, the efficiency of the ,pump increases
until a point with infinite slope is reach~d. Figu.re (6) • I
;. ' _; __ -.-, .. ,.'._ ...... - - . -·--...... ··---·---·--·--· ~-~----
"I;·
shows ~he maximum ~ff iciency ohtaii:ied qt1ring th~ experimen_t
for each of the foltr H/L settings~ For comparison purposes,
a second ·c11rve ·shov,ing the efficiency at the maximum· f 10,-1
point is als·o included. The '"ide variation in efficiency
between the two points is clearly noted.
Curves showing the maximum theoretical and experiment
al efficiencies for one and two inch diameter eduction
pipes are illustrated in Figure (7). The theoretical
efficiency points for each curve were calculated using the
flow equation (17) and Sand K test values for each sub
mergence ratio. ft.taximum efficiencies on the order of 53-
57% are predicted by tl1e· present' theory. Agreement between
the theoretical and experimental optimum conditions was
good for low val11es of H/L and poor for high values of H/L. 1
---Th is indicates equation (17) usin~ constant values of S
·.•
..
'
..
... -~ .
___ I ~ -- L ~ -~- ---~r-'---~ -~----- -~=•=--'~-~ .. . . ... ..... -~=-~---~-=···-····-.-~- -········--··--·-·-"·--r ~-~- -~~,.----~~-~:--:-····-···--···· ·'..:.:···· ... ·•
.· - . · .• ;.,.,,-,.y..·
' :· ,-- .. · .' -~./ . - .
.· . -: . l ,,,.,--•. , . : • . . : . . . '. . ..
,\,j·' J.,,, ·J... . ] . I :y;,£:' :';-c . C ••• _d _c..c~ ~ -~ .. :, . -· :~ ... :: - -~- -.--;....:..· __ ._ --··--·· .. ·---·· .. ~-:-... ~·-, .. ,_:.:.,..~ - .. ,: .. :.:.,.~,.,_ .. ·.~ -----~~---~-:,.. ..... ·-- .. .
' - -··· --- - ' - :.,'_ -~- ----·- ----- . --- .
---·-··--·-·---------- ___ ~~-· __ and K--Wi-1-1-----nGt----pr-edi-ct·--th-e·---~i:n ft·i-a.1···- po·r·t-i'on ·--of·--th·e-~ ac t·u-al _· . ·-- -<-· . -~~=~-------~- ~--------~-·./'
...... ··- ··--·--2·:--··c·· ~--·-· '··---···-···. .. . .. • .
perf orrnance curve or its maximum efficiency in this area,
. ----------~--~- -...... ____ u,.
. .
------ ···-----------~
particularily for submergence ratios above 50%. Since the ; \ '
flow is very unsteady along the initial portion of the • . . • .ff'J
curves~- it is possible ~hat agreement between theoretical
and experimen t_al op'timum conditions could be achieved if
refinements are made to the air and .liquid flow measuring ·
systems. ----- . _ __: ·--~--- - ----- --
The present theory and the test d~ t~,- ~<?th show
-· - -·---- ----r----··-·
a decrease in optimum efficiency ·as the ~duction.pipe
diameter increases.
The value off yielded hy the maximized equations
does not agree '"i th tl,at derived from '"all shear stress ~
calculations assuming a Single phase flow of water having~
a volume flow rate (Qf+Qg)• Figure (8) indicates errors
of 40% in t·his assumption. Since the resttl ts for the two
inch diameter eduction pipe show no.substantial improvement
over those reported by Martin [l] , it appears that a
• ~ -'.J
..
more basic approach than that of.a single phase approximation
must be used when calculating the friction factor.
Fip,t1re (9) illustrates the excellent agreement ob
tained ben1een the tDeoretical value of slip as calculated
by the Gri(fith equation [7] and that calculated from the
test data using the maximized equations. Deviations of less
. -
..
--20-
,
,: .. :,.:··
,.-
------- ---------t-~-------· -- ------------:--~·-_ -- ----- ------ -- ------------ - -------- ·- -- -----c..·.a.c:.-•-'------'----.- • -- - - " ---- -- -- - ~--------~-=-~~=:--_:_~~---:-:::-:-_-;-:-:::::_~ --=---==------ -----=---_:--~ ·- - -------- ----. ----- -----· ~ .:.'-·.
. .. '-._j . - _. __ -.. _ ·- _ ·; ~ _
- ·,. - - ~' - 1,;<- -~ ••
•a.,1 · .. :,· .• ·,_ . :
- ----,---, -----:-·- - --~-- - - --~----t - _.__'___-l-~-- . ... ,.
-~~----- '. : ;--~,. , - ,__ . ·--- - --- - .. _ ·-~-'.-: ... -,--·--........ -·--; - -' .-----'. - " ,. - . . . . - ·- ---- . -!-' -en·, I
• ~ •. .J . ,
, -
. ,-- :__ ·-- ::..;~ - - . ,...; . --- ,; ..
(~L:.-·j'_··. -· · .• __ -_._ ------ -- .. ·--· ... ~,.. . --- . -,~-~-- ~- ·: "" ~ ,.·. - -.. --_· ;-- .. ·-· ----- ·-' . ---- --·- ··:·-·-· . - ' • . • i . -~-- • ---- ' ••-" -·" ·-~·--·-••"--• ~~ .~._..__. ..... r~=-~•• - . . -· -~- ··"'= -r."-<=,- -- ·= ---- - -~=--·'-- =-.==··=·-s,=·~~-c·-::-·-''""'~~-""''
. .
...... '
. •'
. - - ..
. - than 5% betw(?~Il !h1
eQ;y a.rtCl e~per,iment were rec0-rded--f'~:r--al-l-· --~~-'---_ -. -~~--.. _··--~----~~a~e·_________ ... ····-·-···---- ---- -- -,---,
_· test points.
•.
I '
•
.. These results substantiate those reported by
Martin and:indicate the Griffith equation tO be a'Valuable ··, ·\.
tool for calculating the average or lotal value of the slip
4.3 Com arison of Com ressih1e Theor and
Data erimental
................ , .'. , , .. , .. ~ '"' , , , , ....... r
., ___ --- ----~-------~
.. The results of the ancl.lysis' t.i.1(-illg ,into account the.
· ... · . change in volume of the expanding air are shm'V'n in Figures j ' .
-.~,
(10-16). Output from the computer program described in
the Appendix.was compared against available data fr~
previous experimenters.
as follows: Input for the program w~.s obtained
(1) Slip ratios were derived by extrapolating
the combined data of ~Iartin for l'' ID I
eduction pipes and t~e experimental data
presented in this thesis for 2'' ID eduction
pipes. A straight line was drawn between
the two points and extended to include larger
diameters.
(2) Theoretical friction factors were evaluated
by substituting Qg and Qf f~~m the exper
imental maximum liquid flow points into
...
- -• - _. • ,__,:,,r.,.
';I.,,,. ,,
-. .. .. ---~- •• .. ····.,;:•••'! ,I
•. . ·-- . -. ,:~-.. ···-·-·
. . . . ., . . . .... - ··-·T- •-• -•a•-· ·------ -·· '' ,_. --- -- -- '··-·: ... ,,. ---- --:-··-·';.··
' ,' - . " . .. . ·;, .· '• • • . • -, •: . •- .. . ,':· .::~~-.-.--. • .• :.,,.-_~- '.=••,'.: ...... ~~. - ~. • ""-.· ... ,.m,"&-~n:e_,~-~-,,;...;,.::;·,•~~~-~~.,_;,.~_-..;,.'<=~~--~-,:.,~.T.-c=-• __ : __ . ,." =='=· - _f ·-. -==-~-----------::....~~~:- __ . --:-·=-~~=-==~~-. '~~~~ -:=.:=~ -~ .· ', ---0=:L.' . ·--=--~--_:
- .. ..:-.._
. . 'JJ ·- . . . ' ; .
" · -<· --~ - -~---.·_ · ~-::-~~--~_.___ --.. · ,--.-~--equation~~-(--1~8?·--.· ___ : .... . , ... ·: - . '.··'-· ~' ... :.;~ --- .:: .... - - . --. . ·----;- -· ___ ; -·--
. . r: -~--'-·-'-~-.. -~ ... -:. _··:. ----·~- .. _-· . -· _ ...... _. ~------···--·--- ·___ .. · ~-:_,__:__._;--~~-.:.-c·:_· -~-. .;.,._..· . -~~~~----...,--
' ·• . .' • '. .,:. l
--.,- ' ... ~- -- .. -~ .... ______ . -~,·---------·--··-·---,---.--
. '. ' . " . __ ,... ___ .__· _____ .____. ---· --- --- _· . , , ---- -- .... ·. --- .---;·_ :.- ' ·---· - -.. . • c, ·:, .. -· '-: - .- - ........... ,. ·.' .... ~ .: ----~~--- .: .... ~~- .. -~ .. ·. ',-.!.'.': -·c·~. ·· ___ -~,,·_ -·
I - . ' . . . . , .. •_ ...
- . .
. 0: '· t' .1-,, .
• I ---- -~- - ·---·- - - -·-····
. !' ' . ;_,;,
• t •
(18)
· The :theoretical values ~ere t~en ·multiplied' · · . . '. ,- . , ; .
_,.· ,. . .
' .
·by a·correc.tie>n f~ctor C?f ·1;.6. The correction :· -. - • - • .. .., •••• - - _, -.:c- -· ·• ··~
. ~ .. . .. .. _ ... _J .
factor ,,,as· derived from.· an examin.ation of the ' . ..
test data for ·1'' D and 2'' D eduction pipes. . ··-~ .'--"
(3) _Values_ of H/L, D, Og0 , and Of were obt_ain_e~---~--::--,---'---~-- . . . - ··- ----··-----·--- ··- .\.. .. ------ ···-··· -----.----·---------------------.............. -----r-~- . '> (;..,.L.__!. --'-'-' . ~·. ,..___~--- ,, ____ -- •
0~ -
· . from the rep<?r1;ed -r·e~11l ts of other experi~en t~ • . . -· ...
· ·.sttooi·er~-:e~ce depths gre_at~r than 160ft. were not considered
as the expansion ratios for the air became too large and
a slug flow regime could not be maintained over the ~ntire
eduction pipe lengt~.
Figures (10), (11?, and ( 12) compare output from the com-
puter program against experimental results reported by Ward
and Kessler [a] . The results sho\m are for a 2.5 inch
diameter eduction pipe \'Ii th s-t1bmergence depths ranging from
32 ft. to 46 ft. Excellent agreement was obtained over the
limited range of data presented.
.-- .. - ... ··-··-·----~-···. -· ------.. -.---- .. Figttres (13), (14), (15), and (16) compare the com-. .
OJ
pressil)le tl1eory rcst1l ts a~ai11st expcri1nental data rer,orted
by P. Pickert· [6] • The Pickert data was particularly
interesting since it v1as the only data found ,1hich presented
.. a complete ptunp performance ct1rve, including the maximt1m
-22-•
:i:
•
. r:
I}
(. . •.
;; . ~
' 0 .
-.--.- - ----:- .-.c.~-- .--, .-- ... • .. -_. - .. - ' --- -- -_ - .· - ... '.:""'' .. - .
_ I. ./ .
',: . : . . . . ' . - ; ,, ' . - .... . ....... · --,-~---,._,_ -.--· ---· .- ---~--- .'··_·:···:'·_--.-·~.:-"., ·,::= ·:. _·- .. :,..~~·~~--· ... ..,..: . .,., .. _ .,., . ~ ......... __ -· -___ ·· ... ----. . ·_· ,. :,;:·· :· . :. ' -. '
· .... J_ . :· .· ' ..
- ------- - liquid flo,\1 point. - The t'esul ts, shO\\'Il are for· ·a 3.937 inch _ --C.·--··--- --- ·- .. , ··: . .
from 62 ·ft. to 91 ft. Good ap,reement betw"een theory and .
experiment \'7as. found to ~,xist· up to the point .--of' maximum~ ~_, __ c ____ ·_ :
- ... ---~--------...,----1 i quid flo~. _ As the air v~lume· flow rate increased beyond
this-_ point, ho,'1'ever, large _deviations between .. tneory and
experiment were recorded. The errors occurred because the
·ori~inal assumptions· of constant slip and friction f actox:s, ~----·------ ------------ . -~· LL----............-':~-----~----------·
' . I . ' _;
. ' ....
~
particular_ly cons t-~n t s·li p factors , 1_ .. PrQ_Ye_g .. to_~ __ be i_nva.lid _ ........ ---------- ----,=:·~=~-~~~--~----
at·the larger gas flo,\1 r~ates~ Iri a11· cases, __ the assumption-----------------~-
of a· negligible mom en tt1m pres-s-u-r-e- -d-rop---,\J'a-s----a-cceptable-...... - - ---·- ---------- ·------·.
a
'
Calculated valu~s of A~ ,-rere al,'lays less than 1.5%~of the
overall pressure drop occurring in .·the pump.
4.4 Sum~ary \ .
The results of the experimental and theoretical work, "' as illustrated in P'igures (2-16), can be summarized as fallows:
(1) The ·\\TOrlc of Stenninp, and ~lartin has been
extended to incl tide 2'' diameter eduction
pipes in shallow submergence applications.
:a"'Ccellent agreement \·1as obtained bet\,,een
the performance predicted by the flow .
equation (17) and tl1at obtained from the ~ •
model air-lift plunp. sho\,rn in Figure (1).
',
I. '
• t,
-- . -- --"--~ ,._,. - . -.. -- ._ --" - --~-- -· -- - ... -- .
" . . . ' ' ·, -- •· ••• --·--- ··-- ·-- ---~---,-,-,.~-~---·~.,..._,,,,.. __ fC < ~....... .:cc: ... ·-----·-:-- c..-~---·· '' --.-. .;;-'..; .. :~~ ,.-::.:L2...:.~..:.C:;~ ·'
' . I·'.. •<•. ~ ,' . • • . - ,.._ . ~-. . ~. , • r ' ~ " •.. ;·· ·. , :." .: ·•·
·· .. ,· ..... -,
' ,, .. '
__ ,. '.
r ~:,- • ' ' • .· .• • ./ ~ ' ' ; .
..... ,,· ... ··.,.
. 41:i~f._ . / ,;,,l., ., .· ,. ~1.. ' ' .,
\~; . d1. . .· :;,-_ .
. ..... - -··,;. .. ~' .
.. ;, ..
.. -, .,_,. ' .. . . .. · -----.- .. --------._·_-----. . . . --·. ---.1.'"~'.-~-~~·--:~~,--.---:--,_-:-:·"·7·:...:...---·-:~- ----· .... --·.-·-'-'·----,- -.--- ~ """:'.;---:--· .. ----· ------- --· --· I"''' '.-,r;i--,-----:~--- c--,.-_-·-_, .
{)' . . . .
. - ,. . . '' _:..____ ______ ....;.__ '--~ ----- .~:1 .. .- .• '" .- .
. ·- .. I .
·' . . '
• • ! - --- ·- .•
- - -- - - -. . - .- - - -- . -- ,- - ·. - - - --- -- - - ---- --
· (2) . Accurate values of . sli_Q__J:~l'LJ?e_"O btaine.d~-• -. -~-__ -,--_.·, ____ . _ ~"· ·- ________ . ------~---- - - - --- ·- - ------ -- . - - - - - --·--.. ·········--·- .---· -----·--- . ----·------~·-·---...-:---------~-..-- . - ... , .....
··· -- .. --- -·
. . from theoretical calculations-. . I
(3) Use of single phase data to calculate a· . -
- .. --:- --- ~'--:. - ____ ....'l.. ·--~ -- - - •• -- ·-- -
- . -·-friction tactor;·y:i.eids ·results \\1h1ch do not . .. t..·
agree with experimental data~
,·: ... (4) · A theoreticai-arialysis taking into account 1
'
tl1e cha11ge in volume of the exp~nding air
~_:___:___~~_..;.;.;..:_~--~::_;·, -----'-----:-----· -:---.. M.-tt-uUroS~t~--a-1:s-t'.r pr OVid-e f Or 1 o-c-a1:--·· Ch art g es1n--t fie
........... - -. '·- -~
•'
slip ratio and friction fac:tor·~· . '
(5) · A compressible gas approach yi~lds no signi-·-··· --- - , .. ·- .
' J .
f'icari t improvement over the incompressible
analysis of Stenning and Martin unless point • . ...
values of slip and friction factor are ,1sed •
- .... , -~~- -·~- ·- ............ .
l''· .
. . - . •. -. . .. - ..
_ .. -- ''"""<---; . ··-- --·--a~·'"'.,-•----· .... -·•~ ..... ·-•,. .- •
·I
- ---··- -· ---.- -~ . ·-·.-·:-- -~---= .. ,_._ ... --
..
By combining the experimental results of Martin with those I
presented • this thesis, these additional observations be 1n can
made: ~J -,v -.. . /
-· (6) The efficiency o_f an air-lift pump de-'
. __,---. ·creases as the diameter of the eduction
• • p1pe increases. ·-- - --- - -- -- --. -------- -- . --~ --- ---- ---- --( 7 ) '
,~i th constant suhmergence ratio, tl1e slip
ratio increases as the eduction pipe ' ,·
. \,,
diameter increases.
(8) With constant submer8ence ratio, the friction
Q. .. ••
-24-J ~· ·.
'"-\~•-------. It. I ·.r » . ., .. .c- ·-----~
·-
(
--~~·-. - ·----·· -~--~-= . .=_ ---· ---··=· ·=·· ·=· =· ~· ----- -- ----
. (9)
·. - ··-- .. :.·
,. --~ --- -,;• ~
..
•
·.;.,
y. ,·; ..j ........... ...,.
•
L_. -=-=-=-=--_;=es
__ -_____ -~· - . ·- ------· .... -- ·---- ----·,-···--· ...
... ____ .~, ------ ... .~ . . .
--- . ·-~ . -·: :.:..
- . · ...... ' ; --.... •
factor deer-ease$ as 'the -eduction pipe. ---'---'-,----'-~-----··--------" .·-·-.· --·----~------···· - ---·------ --·- ----·-------·-····--''-'····~·-·--·-~----·-- ·-·--··---···----·--,·-,.·--~------~-- . --·------ -- . __ _____:__ -- - ----·
diameter increases •
For submergence. depths below 30. ft., the . --,
of constant s and K values • the use 1µ. . '<-'---"'-., I
fl0\\1 equation ~c 11) will result • '-.... j
1n an
accurate predictioh of the pump performance
characteristics.
~ .... ' .. - . :.,_'. ..• :.-,_ . . :.. .... -
·,',.
.,
..
~ .....
,· .;.
. . ·,
-2s ..
--------·.' - ,._ ___ . ___ -· - -------;,--·-,,----
,····
_ .
.. __ , ... --- --· ------.. -----· - . --· - -·---- -------·---·· - -·----- -------- ----. -- ------------ ---- -- -- ---- -.; _______ _li_ ____ -------------h~- y -,----~------------~---·------.-···------ --------~-----· - -------······----------------·- -·-···--------·------·------····- -·--·-·------ -- ·-·-------------------
. -.--~- -.;-· ... . ·-- -·--··· ----·--·- - ·-------- . - --- ---- - - -- - - - - - -- - -- .. ·----- ... - ---- . - ·-· ·----· - -
- . '. ,· . 1t . • . . J ._ ~. ·- .,'<.i'!'-·_-,t : . . .
·-~--' > ;-.· t . ·, -. '
. ~ . . ~-.
~----· .:. ... ----~---------.--···- ----:·-·-····.::·
....
.· ~ . . ;. :_·,
- •-.-- '": ___ ..,. __ ' .... - -- . - . -- - -----. ------- - --- -------~~--- --.-.-------- -,----- ----------·--··· ... ' ... ~ - .
· · S. -DISCUSSION - .. ,. .
. ~.t~ .. J. C
~'-----. . ' . - .. ___:__.......;._ ____ -,:........-_..,..:-__ ~-,----,..----:----,-~:----·-·----------
'. ' J - - ... -· - ---- - - ·-_:_ . .,_ --·-·--·-·- __ ·_._: ·- ·-·- -- -s.1 Conclttsions
. f - -- - - - -- - .. - -------- -- - - - -- - -~ . '
. -.··- --·-,·---·--- -~~--- - ___ ..,.._ ---- - -- -----:.~-- ---------- - - - - -
. '
The results- of tl,e air-lif-t pump experiments sub-
- ·. ·-··---·-·--- ~---- --·-:·-,----- ~-•,--- ----stantiate the fact that the ·flo~ equation (17), used in
- .,.~... . ......
conjunction with constant slip an~ frict_ion factors, can ·be-,"',.·. "+
' - - -, - r
,.
used to theoretically predict the performance characteristics 0
of these devices in shallow submergence applications. Local -
· or average _ y~ t!J.~_§ ____ 9f.. ~.l..ip ___ J~_~ __ n_ __ be ac -~u_r_a t_e_l y_,~ .. c.alcu_l __ at e_d __ _u_s __ ing__,__. _______ ~------..
t~e ~q¥ation suggested by Griffith. Values of the. two-· · · · -·~-- ..... -----
phase friction factor, l1owever, cannot be calcµlated using _____ - --
- - ....... -- ... - --- -- ---------- - - single phase approximations.
...... :
r\", u_,·
J . ,
--
' . , lthen attempting to theoretically calculate the pump
characteristics in deep submergence applications, it is
insufficient to acco11nt only for the changes in volume of
the expanding air~' Local cl1anges in the slip ratio and
friction factor must also be considered. Figures (13),
(14), (15), and (16) show the resulting deviation between
theory and experiment when constant Sand f values are used
in deep submergence calculations.
s.2 Sttggest.ions for Ft1ture \\Tork
The present computer program as outlined in the Appendix
should be modified to include a local calculation of Sand£
-26-
.. .:.,-
' ••·t',
l ' ....
"\ r
'i
---·-------······--·-·---··- -. :. ---· --·-~--·-·-·-_.._., ----·-----·--.--
. -- --····-·---- -··---- ----- --·----- ---~----'-- ---·-·---·--·-- ._
Ir •.• ,.
' . .. . . . . .
. . ' ·.. -·-:;---:- ,'
. , ..... . # ...
. . ~-.
. . . -.· :. ,•: .. : ,, . ~
.. : .. ·-- --.·-_<:'··::·.c.,;,.-- :;" --; .-. .· .. ·. . >., .:- ' .• , . '. . .. ' . ':--s. : .. :_ ,·. ;,: : .. :.:_:·,., . ~ ·, --- -. - --.··. - . ,.,.. . . j ·-· • -- ~-· - - •.• . : . , ,' ~::
. . . ' ... .. _:__ -~: . .'' .. . ' ,,./- ... ~·.· ' ..
. ~ ... -:-:.,. . . -
. --~ . " - . ' ...
-----····· -·"·.---.C...:...·. -- ·~-1-0-c·al:--·vai-u-e-s--;of-~. s--and----f·--s1iotI1d-~-:--then-1:nt-·-u-s--e<1--wh-e-n'."--me ........ : ... , '.... ·- .... · · .. ·· ..... -·-----·--··-· - -=------···--· - ___ :_- _____ __:_. __ : __ ·-·- ----- - --------- ··-·· . -.-------- ... : ________ ---
presst1re gradient dP/dL is calculated at· each of t·he n ~-
points· along the length of the eduction p~pe. \~lhile the . . . . . .. . ~ l . .
. _:__ , .-, . equaitii:m sugr,'ested .by .. ,Griffith could be used to calculate '
the individual slip ratio values, more:work ~ust be done
before accurate friction factors .can be predicted •
.....
" -~·-·•>a-···· -- --~ --·· --- -~--- - - .... -· . - -.· ·: ' --., 1· ..• . ·r·· _J ·- _ _. •• -,_ • •• -~--, -·'-: _ .... .., ' . '···"--.--- - ··-···-- ·--···-·-·-·
. ·, • --- ....• ··-· -- • ~- - ~--c-' ....... -"' :- ·-- -- ·--· • - -- ·----'--' ~ -.,,.,........ ~-- --- . :~ . ~--. -- ------~ ,,-.-..-~ ~---~ --~~- ~ ~·--· -- _,, ____ , __ --....
.. . ..
:~.
•. ·.,.
'.•
.,
'.• .. '
~- -=-
. : o=, .•
-21-..
j.
- r. - ,.._ ;. • • r . .,__ ··--·-· •. ·-q -- ._ .......... .,....._._ •r-•·-"""'-C..• ,. -
: . -...... ·. [•.- 'f'
. •. . i • ·, ·. ·· ... · .. · £ ' c •· ; C ... ,. ;;-:: ,. '-s' •. ••'
I '.' ~ •'
0.~ .•... . ----·- _ .... ·· --~==~~~--~-·, ·····--·- -.... ---~~---. - . ·.·. -, ··--·:;· ..
(.· - .
i. ,.-.·._· ..
i i·:,:.-- ·. I' ·.·
._····o_-···_· __ ······ . . fil< ,.,
I ':' • 'j
\._.:)
.... -.'.~-------~----·------- .. -
. .--•- ··-·····--.------- ------. .:._ _____ ,_ ·---- ·.-------- -
. : . . - '~-=--- . : .. _ - ···- . ------------··---------~ ·----. . . . --· -- . · .. -- ·~~:- ·.· .. ··.···· ···.· .·
. . ~.
. . . "-~---~
--3 '' . ID . PIPE-----... ) I •
ORIFICE TM1K WITH SIGIIT GLASS --..... . . - ·--············. ----~-----· --~----·-· : ______________ .... ·•··· -~ ~---------- " ---· -- ---- .:. . -- ,--- - ----~------- -· --~·-······-· ... ---- ~- -·- •····• -- ......••.•. .., ..... ---- ------· .·. ··-· .. ··- .. ---·· - ·____ ----- ·_ ... ··-":
·-----------·-_·-····-· _···.···----3 ... 2" LENGTH OP CLEAR PLEXIGLASS PIPE ... J . . .... . - .
. '•,-- ·- ~·----~ ·-· ·····~--- -~ -~,~~- -' ... -,--~--- .. -..--~·-· -- _...._ __ ,, ... ____ ,_ -,- ·---~ .. _, ._.,.,. ...... ·-····,~- -~----·--···· -
---~--- I ""•
( )._ ..• ;
' ,f .._.
. -.
___________ WAT.BR SUPPLY----!.. --...
LM-1INAR 1YPB AIR FLOWMBTER-----...
' .
-{JI-'' .
AIR SUPPLY--__,
. PRESSURE REGULATOR _ __,
)
¥,-,.~·~+-·-··-- --'~~-- -~--'-'--·J-__ ,, ...... _,•,•.• -"~-•-.L.'>•••-•..--.,,-._.,. __ ,,, -~'•"-••.••• •.. •·-·- ·'••~---"•••-••-• • -•~ •-••-, .~. •• • • ~ .• ·-••.•• '•-••• > ••~"c• '"·••-· •.•
PRE_SSURE GAGE -----.1 ·- .
TH.ER~lO~lETEo--· __ _,
CONTROL VALV~----__,
OVERFLOW-------
1!1' ID AIR PIP~---_,
2'' ID DISCHARGE PIPE (D)
J\IR INJECTOR 56, 7 /32'' · D HOLE
'
4''
, . . ... ··- --··- -·-·-----
I :.. --·
167''(L)
... • •
l15''(H)
.. :-,---_.,__.... __ .._
•
-w---+---._t-+,.+.· .
ROUNDED ENTRANCE CONE----_:__+--__..,..
DRAIN---"
FIG. 1 THE t,lODEL AII{-LIFT PUJ\lP
-28-
•
• - f ..... -·.. -~- :,0 O
I ~
'° I
LJ __ .. ·· (~, ,.... ,,·
J-1 ,-... Cl)
rx. 0 '-"
Pit E-f
~ ~
6 H ~
~ ....1 0 :> ~ ~ 8
~
0.10
0.08
0.06
0.04
0.02
FIG. 2
I
0.1
I •
I "-..
0 ~- - o:_.
~-e
0.3
AIR VOLID1E FLO\v RATE (.CFS/) Q g
PERFOR!vIANCE OF IvIODEL AIR--LIFil' PUMP
. ' . ' i
0--0. . . 4:"---
o.5 o.6
'
\ ;)17 ,·
I
' .
I i
. i .
..
. · ·o-----._·.· __ -:_·· __ .. CC•;•, . ! ,•
. .'\~:. -·-·" ...
)• .. . l. .• . .
. ' . ,· ·, - . ,' . . ,. ..4,.... ·: .
i . .
.·· . :. -; . • I
• I
-, .
j ; . '"9
,,
~
; .
·" . ·... '.,. - ~- ~---· ...... .
'"~---
.. ·.·~.--.. > .. ·.,·:' -··'i~ ... r
. ,·. :. ... ~ ... ·.. . . ' -~.;..·_·-~.-~..:___ _______ _ ··--------:r----,---.. ------- ~------- ... ----· --- ---· ,.,. --, -- --- - ,
':·,,• .·, . .' -- . - . . .- ~- ._ ..... "
·".'··
. i:1
. f,l j( 1 hi, . /(,, (,f . p
. , . . . '! ~: . ' ;;J-,· '•\. . ... ··--· ·- -·-·· .- @ - ..• . . . . ii
... ·J. ;
' ( • . 1~:
. ····-···- -··--· -··-- ---~ ·' . --=,,· . : ... .:.~~·· . ·~-~-····---~,-'...-.... :...... .. ~--~-··---·-·. ·---. ----. ·-·-·. ····---~-------··------··--·~· --·-~--,·-----------·--··--·-·-'---···------····-··~-'-~---··-~--------__:_,, _____ ,.····----..,--·------·-------··--.!'::'.:_. -··- ~ --·---· -. ........._. . ·- -- --- ... l . . . --·-- --· ··-··-- -... -.~ ____ ~ ..... ~ __ --- . 0 .15 . . . . -.. ------ ~ . .
1'
0 .12 . .-· -----1----1f----------+--~iro--_.., _____ ,,1.-______ _.
. ' .! .
V2~t -· .---··-----·----- . -- -- -
,---., o.o.6 ()_·• ()
6 . '
t) 0
6 0
o.o. H/L DAT/\. THE RY
,_ ..
0.692 0 S= 1.956 T}"_ 2.115 ....... -0.619 6 S= 2.244 K= 2.127 0.543 0 S= 2. 72
.,. ,. 1.902 ~=
0.478 0 S= 3.05 K= 1.826
6.0 9.0 12.0 15.0 . ,,.
0 3.0
Og Qf
•. I
·• PIG. 3
,- '
C0~1PARISON OP THEOllETICAL AND ACID,\L OUTPUTS
.. 30.
I
I
H '·- I
~
f2 0 ~
M E-t
~ ~
I 0 w H ..... µ:., I E:J
f3 ..:I -0 > tr: µ:t 8 ~ ~
·., ·.
. J
- ' - I - - r
, I -l \ I
i ; I
0. 8 ----------------,-------;--~-.-----~---~-------, i
0.4
0.2
FIG. 4
,r-
5.o
:
. }
-------, -~
~-
CO}IPRESS BLE THEORY --INCOI·ll'RE SIBLE THEOR,
S= -2.45 C
f= 0.005 2 D= 0.333 FT.
10.0
•
15.0
0
FREE AIR VOLlTI1E FLO\v RA-TE (CFS) 1
l I C
i
20.0
COMPARISON BETWEEN COMPRESS!BiLE AND I
INCOJ\1PRESSIBLE THEORIES/
' .
i ) I J i ,
i ( ~ .
l
. '
' i i ' i
i 'I I I : ;
i '! ! I I
! i
'I • . i
25.Q .. I!
'. '' .; ;
I: I I I: ii
Ii : j·
' i ! . , I ', i :- : : I -
L ! .
-,
(.
I •
't. .
- \
~ ....-._
en ti. 0 ..._...
~ E-i
~ I
e5 w w I a-l
Ji.
~ H 0 > Cl:!
~ ~ .,_;-
0.10
0.06
0.02
0 0
FIG. 5
!UL DATA
(i) 0 .692 0 S= 1.956 0.619 6 S= 2.241+ o.(i~3 0 S= 2.72 o. i 8 D S= 3.0., .
0.1 0.2 0.3
AIR VOLUME FLOW RATE {CFS) Qg
cor~IPARISOli OF MODEL PIDfP PERFORI',IltNCE AND THE01-illTICAL OUTPUT
j.
y
K= 2.115 K= 2.127 K= 1.902 K= 1·.a26
I
o.6
(
i
' j '(7 . • ·.
, I .-
·, .
T I • i •
. ;. . . :,
--·o· --·:· ,·' ~:···. ·:· :·. ' . . . . . '' :
. ::•.;; . ·P· , ·-.- ... ; J .·
·~··.. . \._:..!
.1
. I
i·
- I
. 1
. l.~ ; If
l-, .
I
-, e•'
. I
ffl •. :: t ewren·1arrn---·
/ f
··---·.-·--- -~- .... -:., ·....:....;.:
so
: ,,. '
' .d .
40
'. ~ .. ,
l >4 -~-0
.. fa H
·.30 . '· $
0 H
t ·~\ E-t -
~
fa 20 i,.;
0
0~' fa \
-- ~
E FJ
-
10
FIG. 6
'·-- ··-,· ... ·,·--··-'-·---·---,.-..-.~·- ------ ---·--.
. _· __________ ...,._' _. ___ ..
. ..
,.
.. ,, - : -· ..
. ' ' - "' -,.;;~
·----- - -----' ... '-------.. . --~
: ; ..
' .. . ' -- ·- -·· ---·----- .-- ·-· ··-·-- ·-~ --~----.. --' -·--,
"
'. ~ CURVE o: : I
. / .. ...
J\t}\X I ~1U~1 •. ~·
____ f.IlFI-C.I-E~ ~CY-z--o- --·---.- --·--- . ------ -·~--- ---- ---~-~~--~-~-
·- ' ' . . .. .. . . .
.. . , ... - -
j • ..
"-.. . ...
·•.-· - -
,._ -- - -- -- - - -- -- ----·-'
:FICIE1~CY n.T ~ l:\ XI i1 U~1 ------ .
,,
·-,Olv POINT ti
-0 ,.,
~ I
-- - -~--- -- ---- -
\. ..
I
.
•
-•
20 40 60 80 100
PERCENT SU l3~lERr.:Ei~CE
-- .. ---------~-------------------· _, ___ ,_ ______ ._ . .,._.
THE EFFICIENCY ClJH.VES
~ -· I.
-33-,,
,· /
•
I·'
I I ~:i
•I
,i
I
f! Ii!
I
I
.. . .......
~ ·-•-'·--·-···-·-:···--·c·.·-·--··.~c-:--.----,··-,·----···-.··~·-·-.-c=_·"c·c--.,.-;,-••,---·-···,-···.···-··.-·.····-·--·--··.-·w·,,--- .c, -·-.·=--··•· •-,. - _---- ,(' .____-_,--. _ . - -• . _ -~ > •., • ,; '' , ' .-.•."••··-·"-•' ·-·-···--·-·--••-······-·~'--··-··· ' ··----·--- - -- - . -- --- --- -- ~ - --· --- -·- --- - -- - - ----- -
, ____ ,,' . . ·.· .. '. ~ ...
. ·c-
. ..., '{"':
· · zi· . .· .:· .
·r·~ . .. , .. , .... _:. : ...
I . r-.· __ ··"_ .. _ .. _-_.· __ i. ·.
\i;'_~, __ ' '~~ ·.· . . /-·, '/-~-- '
' :w - .
. ~ -~ . .. t.. • 4 .. -· ..
~ . . '. ·,., .-· _.:.._· ·._ .,· .
. . . . ,~ . --.-:' .
·. ___ -~n . . ~~~~~~~-_:_~ ____ .:_____:_,..:__.:....,__ ___ ~_:._~___:._-~~~-....::__--:-~~~--~-~~~;-· ~~
: ,, • . -· .• ,· ·1· __ •· ··-, .· ,. ~ .. -· ... -··--··· .• ·. ·.- ..• -···-·-·····.·--··. ·-.·-•• -"" ---·· -- .·.------- -,------ --------· ·--------··-----~---·· • ---------------·-. • I . . • .' . • :· .- ... .' • .. ·
. ··.. . . . . . . . . . - - - .. . - ·- - -· - - ·--------------.--·· ·~--'-- - - ----- . -- - .... - . ;-.' .. ·- .... · ... . ;_ :, . . . . . . . ' . . . . : '
. . .
60..---------,.......--~--------,.----------..---...;...-----.--------~
,.'
--'-~ •• - .......... ~·-,_____.;.._-~~ ........... ~ ~ - .~---,-,.···-.-··• .a• ...• •-•••--•-• --•• .,~--<'," - ··~-·· -, + ______ -~- - '""", ca· - + ···•- ·'• -.w- -~·-•••:._·_-• -•-•~ •---•.----~·····••• •.•· I i-·•-' .... - .,, __ -·.-- -- .---·--- -.. .· ...
. .
-•-· -·----~ ........ •.. .
..
'
.. , ..
.,.
Ci~,
' _.:
,, .. "
...
/ /o
b 111
' . ' -lj
. ~-' ·:-_ --:·
• l\ ..... -•. -· ..... . •. - .. , .. : - _; _,... - . ,._ -- ... -· . - ----
- --·- " -·- .. - -_ _,._., .. -~-· ,·. '---- -
,· - -· - -------- ·-·· --·--- ····-- -- - -- --·-- .. ----- - ··-
HEORETICA MAXIMUM FFICIENCY ERI}IENT ·L MAXI!1UM EFFICIENC -0-
10 t---~-+------h-----'"------'--------'
···FIG 7 • ,ii
{·:
20 • 40 60 ( i
PERCENT SUBMERGENCE
00?-IPARISON OF THEORETICAL AND Y.u\.XII'1u11 EFFICIENCIES FOR
l AND 2 INCH EDUCTION PIPES
.. 34_
. - ·----- -·- --------- ----.
0 100
---------·-- -·-·--.. --- .. _.
. !
.11
ir.
-r.J . ....... ' '· ' ' ·._,I
---·-· ------- --~---~·--- . ~-~-- - ·-· _. ___ ,_ -·_,_- . . -------· ·-- ---·
--~--.._-. '~~-..,__...,~-~-~-~~.- - ._.'_ .... ~-~- -···-~--~-- _____ . )--~-·~--_,:....-. ..:'......- · _ _:., __ ,_ .. _____ ... -... ·- . . .
.. 1 •.
. •I Q, ·., '/ ~
0.010
.. o.ooa
0.006 ..
f---
0.004 "
0
0.002
FIG. 8
·.'
.,
l.-' ..
•·
-•
-
EXT BRI~,1ENT.t\.T~ V . .\LUES
THI,ORETI C.-\I~ \ l\IJJES FlJT r.Y nEV.EI..OI ED Fl.OW
0.2 0.4 H I:"
.---
-.-o-
0.6
CO~'ll)_,\1lI SON OP 'TflEO!tETIC.'\L .t\CTUAL FRIC1,ION F,\CTOllS
..;35_
I
0.8
.'\ND
·--·---------,,,-----~-----
1.0
. ...
,1,
. , - I ,
4.0 , .u •. x .• ··------=---~, --~- ,.,,.,_~•-· ..... ,.· --~'--T~---,c'-------·--....,,_,.~ -·-····:-:-·'-- --
,
S 2.0
------ -- ------·-- -- -- --
(l-~"'-. ' ' :1 . .
~ .. ,.,____, -1. 0
-··
~---··
,o .. _.··_· .... ,:.,
' i-.. .......
. ' . ~
-~ .•.• 1 •. · .
. ~-:-
-· .. '·
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.. I
.. -
'
C ~ . . (~- ' ol .--r· .. \ ·-- ..
~ ·• ..... ---!...._ 1--
- ~ ---- ~~~---- ---·-· ----·--·---· -------~·~ - ···~--- .__ ·--·- -· -----·------- - ---- -.................. ____
.
- .
-o-
'
FIG •. 9
-~
~ i/rlt ~ , ..
'
'U
- . ' . ·- ·- . .. -
' .EX1 >ERI~lENTAL VAI.lJES
Tl-l ~:ORETI C.t\L , r ,'\Ll JES ~
FU1 .LY DEVELO~ >Ei) FLO\·: . ..
'\
0.2 0.4 0.6 0.8
....
H r
C0~1PARIS0N OF TJlEOH..ETIC1\L AND ACTUAL SLIP RATIOS
..
-36-
~
----. ----- .. -
'
;-l
--- - .... - ···------
--~--------· --
-- ··- -----·
1.0
·'
'· -: .
... I -- I - - - .,;_ - -,. --·. '. -·.· ':. _> _; ;-·.;-·;~; -: -'. 'c-;_·,- _! ,::.-.·-'\-·-'::· ,-:,_;- ''.'-: ··-:-; ;-:·:,s,;;. ~ ·.;-::.,·,;.-,:. :·~- .. -,: : -_ .. > ·>; .
' -'----'--------- 1 n
.r --'--'·~-~--• -.~ •.. • C·'-'-.- •• --:.~- ,•,a>,<u<,.._----',,_o·~·"'·'..
00 .·:~_.. ..... ,~•.,r-,hC ~ ,•;•··••~---·.·••~. '' . • . · -• •••- C- • • · • -. •. •·. •.,· .• C ·--,• • • -•• -~·-·---c"'·. ...:----=c--c--··-··. -~-----~·,-,.. ----.,...... - .. -~-- =,· ~----~-- -~-'-'-""~--'-----~---'-- '""'----- . "C;-··--.c.· - ---- ·---- ·.' ·-- ·a.-c,...~-.c.---- : .• : .... ·. - . - --~---- - .. :· . ·- -· ..•. • ... --·-----··-·'·:-" .-........ . --·· - -- - -- • _:_ ------. - --- • "- •• ·--- •• ·...:.....;:c ••. ···-· •
,-
<},> .
- . ... ''· ...,, .. -.· .. - ...... ~ ~. . . . '
.- · ... . . . . -
-. '~ , ', .,·:
. ·~ ~- .. . . _.,_· . --.. ,-·_ - •• _,·· .. t _;:; .:: - .. ....: '. ".•.' ·- - '. -·-·' _:_:.· __ -~,--.---
.. -. :
·- -- ·-: • - '; --....... , ,.- -- - - .. . ·,-·- - A.. "' -
. '. .· - .,· : . ·--'---~--· . . . . . . . . ,- -
. __ ,_ .. _____ _
:( . ' ~ - .· .- ' ' -
. ' ,_ ~--~--~----=-~------""=-""--='=".......,---~---=-=""'--~--~--"=--=--= === - ---==--::::---=------=-:-~, -_----::: __ -.==----:::=-r-_-_--:_·__ _- '-:="":::·:::--.=.~:::':·~=--.,_::·-=-:---:-.=--=:-=:-~~~- . -~·--~~- ~.~.~---·· ~--- - .· _____ ,:_~:~~__:._ ... --~·~:-- ··-·--·- ·------- . --· ----------------~--. ' '
• ·-;··1 .~
.
; ·o .12 ------..------.,........-----,.-----.,....------,
\iARD ·& KESSLER D TA :0 -/ 0.10 ~~H-=--3-2-.-.J-r--FT---+;,~---+---------+---------1----~-------,
. -
L= 60. 8 FT. D= 0.2 833 FT.
0
0
--··-·-- +.- - --------·-·
"-. . . •.· .. .~· - .-~., .
- "'"' . - - -- - . . -·
- . ··- --~-- ------·-·
- . ~ . -------------------- ----------. --- ------------- ------0-- - ---
- ~ __,o .06 "------4-----+--H-----+-----,..---~-, . rxt
~
B r~
0 .... ...: ~
0 ~->
0.04
0.02:
0 0
FIG. 10
ro
0
0.1
I!fC QivIP. ~ SIB LE T !1PP~SSIBTJE THE
S= 2. 70 f= 0.004 5
0.3
FREE AIR VOLUME FLOW RATE (CFS)
COMPARISON OF THEORETICAL AND ACTUAL OUTPUTS
-37-
-··-
o.s ). .
•--·•-•c, ....... - ., .• --·~--~...,._.~ ,-.••.'··-·····-··•-~ ~-
·'·
- - ,.~---
OJ· . I '· ~ ' .· ' ·, '_,/
·'
I
•
. ' .. ------------ --··-···---~---------'"·--··-·--....-.--.-..-- ....... __.._......_~·- fi~._.,._--,~--.-.:c,.,·v_;.;~-~--- .-.;·;;;.·'.'-·;_ __ -:_; -_ .- __ ._, ... -_ · --~~;i.--, · ,-·. ~-----·;,z ... --~-~7_. ·
. -·----:--.. ·· .. ---"'·.
- .. . ----~-' ___ :.
-- ·-- -. - -
o.16
~
-~~~--~- ----··
e 0.12 fil
.8 - ------ - ~-- .- -----~ ----- ....
,_.,.-1,
"
. ' • •
' . . . ==~•=,,·•·-=• ~·=••,'-'••~•• =~~===f=~'==~='==~=~=~=~~-'-'-'~~: ,.~~·-> ___ ~-~ ··-.-~·---~-,.-·-·-:•····.··c-O-:~
--~-~--------- ------ - --·--- ,. ,. - - ----- ~------~--- . -. ------------~-- - - -
·-"··---~· .. ·· .. ··-· .. ....:.·;....;......-:.
WARD&.
H= 3_7.88 L='· 60 e88
SSLER
FT. FT.
0
-------~--------- -
0 0 .,,_..---
~---. -·-·:·---------· -------·- ---- ----------- -----------
0 ---------------·~·-----
~ 0.08
0 .04- .
0 0 0.1
• cv· Q . •
S= 2.2 t= o.o
SSIBLE T
0.2 0.3
ORY-··-
FREE AIR VOLUME FLOW RATE. :(CFS)
FIG. ll
.I
·O
COMPARISON OF THEORETICAL AND ACTUAL OUTPUTS
-38- •
-.
.. ·
...
. . . .:. . -- .. ___ . ------- -·--'--
---p-~-· ....... ~-·- .· . -. ' .. ___________ .,'-.,:..
----J----~ ... ~-~ ---~------ ·-- -- --
.-...,
(i· • , .
. . ' • :. 'q •.
' . . ---·- - -·· --- ,.··-· - . - --·---'-- ·- . . -· ........ · .. -- ·-·' ·-. '. . ,,-,---- ···-·-----· .._.
~:}J '·
. I
. . , .\J - ·. . .·.. . ,' I I ---· _-....._ ___ -c....:.....,...:..;;. --- --- ·. ·-~-----··,---------:--·---· • • , • ~~ -----~-------' ------------- -- ------------ -....: ----~--------··-----------~..:.:.. .. .___--'-'--' ___ ..:.:...~-_-'-:.:.. __ ·--?--':-~ .... -~.:...it..~- . .L~---·~_ .. ___ ~~· ·. -.... ~=-=:...~· ~ ------~---~-------------------~---- ---- - - ··---.-·-··.--------· ·------------ /--------._------·· ------ ------· -..------------ -__ · -~-.--- --0~ i6- -~--:_~-- --- -- -- -- ------- -/ ·---·· ..... -.-- .-·--·--· ,-.-:
O·~ • -\
J
- ---···-------
CT·
I'
l
· 1 ··-
0.88 FT' .20833 T.
0
O·
. - --------····--··--··· I
. __ ...,. __
o.12t--------..-------+--------+-------~'------~--------4
. ~ 0.10. E-t
~
0.06
0.04.
0.02 0
---r---~---- - -· .
,
-FIG. l2
'
•
·"
- -·- ------ - -·-- - --- -- ---- --- ---- ---- - -- -----~- --------·-- - ----------
0
•
,. I
I! cor1PRES IBLE T ORY-··c 11PRESSI LE THEO Y
-------- .. --
0.08 0.12 0.16 0.20 0.24 FREE AIR VOLUME FLO\v RATE (CFS)
C0?1PARIS0I~ OF TlIEORETICAL Al~D ACTUAL 01.JTPUTS
-39-
•
~
C/l r:r. t) ...._,
µ:1 8
~ I ~ ~ H 0 I
rx. E=1 E? ...:t 0 :>
ffi E-1
~
0.3
0.1
-
F PICKER DATA -O
H= 62.24 · • L= 137.8 T • D= 0.3280 FT.
I / \
(,..-....._' . I .·~· \ )
1.0 2.0
9-1 __
INCOMP SSIB:tE THEO COI·iPRES~ IBLE: THEORY
S= 4;30 _ · r= o.ooi 74
4.0
FRRE AIR VOLUI·lE FLOW RATE ( CFS)
o __ -----
., -··-
FIG. 13. cor-IPA11IS0!{ OF TIIEOIIBTICAL AND ACTUAL OUTPUTS
• •
•. j
-o . I • I
,. i
s.o -~. - ....
. I;<
·1 ' •.. ' '.
; ' :1-, ·' .:.
• . i . ·.
"
.y ·; . t
f
. /
\
' ·. !
I
I .
. ' . .
•
\
'" ' . \
I ~ ~ I
\ \ \
\
•
,...., Cl) ~ 0 """' M 8
cZ ~ 0
~ ~ p H 0 > ~ µl E-• ~ ~
F. PICiillRT DA A-O-
H= FT.
0.3
0.2
0 ', )
---o--+-~ o-- .0~1 --0 -t-- __ _
--0
INCOI\iIPRESSIBLE I-IEORY -··cor-fPRESSIBLE T ~ ORY
o.1 t--~~~..,:...-~~~-4--~~~~~~~--+-s~,=~2-=--.~~~~~-+-~------------~i f= 0.00494 I
I i I-
i i I .
. . . i
Ol ..
- ..
- ' f
0 o.___ _______ 1_ • ..__0 _______ 2_ ...... o-------3---'o.._0 _______ 4Jo. ,l
FRc;E AIR VOLffi,IE FLO\v RATE !(CFS) ,· ,
t
'
FIG. J.4 C0!:1PAnIS01I OF TIIEORETICAL AlID ACTUAL OUTPUTS
,
• I . i I
; I
:· J
I I I
I , I
I I I
i . . ' . .
i ' . -
' . . .
: " \
I . '
·i
l .
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• ! .
•
........_
E2 0 ~
~ 8
~
I 6
-~ ~ ~ N I ~ s
...:I 0 > P:: µq
~ ~
l ! ! ' . . }
4
o.5 F PICKE~ D TA 0- . . _,,,,,,,,-
I
0.4 IF= 137.8 Fr. D= 0~32808 F •
0.3 -o 0- 0 -0
. .{
. 0.2
INCO}!PRESSIBLE -··-0.1 .-~~7?-~~~~--t--~~~~~~~-1~========:::::;:========.=i=======:.....:...~-----.l..J,
i
FIG. 15
1.0
S= 2~70 i
:f= 0.00504
2~0 " \
i
RATE/ ··(CFS) I.
' ! .. ~
3.0
cor-1PARIS0N OF THEORETICAL AND ACTUAL OUTPUTS
i I
I .
. ..,
I
i I
. I
I
1 .. ·1. .
~o l - I I j I
I I 1 '
I I J I .·
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, I
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·. t· ! < . :,. . . I . r ....
. -•.:. ~_.-.-.-·· , t .
i
...
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.. .·. l 11' .. '
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. .
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. '.
- 1 ·
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o.5 . F,
(
,-... H= Cl) rx.. 0.4 0 .__., D=
µ::t E-i
~ 0.3 ~....: b
I ....:l
.b. ~ w t) I ... ,_.
~ :::t
0.2
0 ::> er:: fit
~ ~
FIG. 16
PICKEl?I' DArA
91.38':F[r. • •
0.32808 FT.
o-
n. ·~)
~ 0
~
o----4)
l .
I I
. I .
INCOI'1PRE SIBLE THEORY-.- .. _ 7
C OI'·IP RESS LE THEO RY
1.0 2.0 3.0
FREE AIR VOLID·IB FLOW RATE (CFS)
C0}1PARISOli OF THEORETICA·L AND ACTrrAL OUTPUTS
. i
I I I
I
!
•· t· ..... 1-
· 1 · · .· 0 ·· I. :. ·t )•·;·.•····
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t .
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-·: . . - ·' -~ :'• .·.·.;;: + • '
. '.. - _... - ·. .
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;--·,. ·-.~~:-. _--;..:_-:._-~ ... _ -·---·---"-•-:--·~,.-· · ...... :- .i·· /.-: .. . :...:._ ... :_(·-:--~- :./'-: __ ;-_- -~·~~~ /"-' ' v .. · .. · ~ ... _: . ~-.--·-.--· ----- -··.
L
- • --- - - • , - - - .~ C • ) ~ - - - • - ~ -. - <- ·· -~ -_ ; -r- •- . · -·· · -. . -1
.. ·~· .. -- -- ·~·~·~ .. -.. ~·-·---·~·--·-~~---:-~· ··~-·~APP:BNBI-X--- · --~-· · ~~ ~·. -..... · .... · .. ·· · ·:·' . . · ... ····-· ·---·~ ..... . . . ~~ ·--·-·-·- -------.-·------·-.-··--·····--·,--.4-----.. ~- . ··... - - ----1
I. Computer Program ' .
---· ····--·-- A· For t ran . c ompute-r----pr-~r ~-m-:-~~as---·wr-i t,-ten · t~pe-r-fo-rn·-~- ____ :.,_ ... ~_,._,,·~~-~--- .·. __ . ____ ~ _ ~ _
required numerical integration for the-·6ompressible gas
solution. The .. fallowing data was used as input:
a. Run identification
b. Submergence depth, H
. ~
,•,
~---------·- ------, -- ---- --- ---~. --
c. Pump length, L •.
·-··--
. .
d. Pump diameter, D .,· .. -· ·-;-- ····-;-· ~ ·- -
----------------------~-----e ... _____ Ac·celer.ation_ o.f __ gravity __ (32._~ fp~ 2)
... ..
.,·
- .. - ·- - - -·- - --- .. . . :· ---- ---- ' - ------ --- -
f. _Pluid density,~ f
g. . \'o i
Gas constant, R \ ~ ! b"' ·( ',',
-h. Fl11id temr,erat,1re, 0 R
i. Atmospheric pressttre
j. Number of integration stops, n
k.' Number of Q , Qf combinations to be cal c11J a ted g 0
1. Damping factor (normally 0.30)
m. Tolerance .(normally 12 psf)
n. Nt1mher of different diameter pipes making up edt1ction pipe
...
o •
.•
-44- ,
0
•.
·, , . , ...
. .
'·>iii
a::1.11 eer::c12··MW• • ;=m*'~·&tm u·,. ·,J - n, -- ;;. --~---~~~;:;::::::::=::::::::::::_=-=4 ::::::::~~~~-~-----~--~-·--~--... ~-'-... ___ ----......... ~~~~~-P£~Ei,..,¥~-·~~~~~~~ - . -----· ------ ----- -··-- -------··----·---------------·---~---------_ ------~- --- --- -----·-·----- ·- - - -- -- -- - - - - - - ' ' - - - --- _- - - - -·- - -- . --- - - - - - . . ~
i - -- - . • - . - -· - - -- ' ' -- - - - - -,~ - . • j: i~~-~-~·~~-~ ~·":~ ---••• -~- -- .,.... . ... ., .... ---~~~,.~---_-~"'r·"•·-~=-,--=c -, =•~~ - . ·-c:-- .-- ·":'-'-v~ .. ,--._ .... ,,---.,":.-~- - -- -•••···-·-·•·--•'---C.•--·-·····''··--·---~••--•-~•--------·-'-•••···-:·"··:••••··.-···•••••: __ ,,_.,, .. _.,'.'.,···t
- - - - D I SK O P E RA T I I\ G S 't. S T E tJ. 13 6·0 F GR T RA f\ -3 6 C l\ - F C -4 51 3 l - - - ; o • - - , , - - - - - • , I
. .
-_ _:__~-.--e -------'~--------~---~-K-E-N---S-€r.-(lEN:E~K -PRG GRA!'1- --- - - - ------ --- --- ~
DI~ ENS ION XL. E i\ { -10-l, -- 0 I-A(-lC-)--,--·---1-S l E-P--l--10) , PRESS ( l O) --_ .,_ -- --·-:' f . ·_ D I M E f\ S I ON X S < l O O > , X F < l C O ) , . Q G Z E Ra ( l O CJ , . C F I NC < l CC J , - l I y· LE ( 2 O > - f
- - 9999 FCRfv.AT(8.FlOo0) ~- __ - ____ '. ______________ .·- \ -_ 9998 FOR~AT(2IS, 2Fl0.0,I5) - - - t - · 9 9 9 7 - F C R r' AT ( 4 F 1 0 a O ) ,. -~-·
. .. . ' . -~~~~- ,, . ,. ·-· -·-· . -- -- -- . ···-,·- .. __,,' ---·-· --- ·-~- ·------·-·---:\-
·-·· --=~~-~==~-. --===~'J9-'l6- FO R M A T ( 2 0 ~ A -) - --- ------ ----------------- -- -------- --~ --- ----- ··· -- -- --- ,-- --~~---------~----------- --- -------"'":----------~------ -----------'--------,'--:·---------~ --'·:--: · 9995 FCR~AT ('l',T8,20A4) ~
9 9 9 4 F G R ~ AT ( T 2 , • NC • 0 F • , T 16 , • Na-. C F ' , T 3 0 , ' NO • CF ' , T 4 5 , • BO T TC M • ,~r 5 7 , 1 D I . 1SC~Al{GE',T71,'LIQU10') . .. _ .
:.:. - 9993FCRMAT (//TlO,'S = •. -,El_C.__~5_,_1_3c~_!£_.· = _ _t__,_no_.__s__,_rn_,___!_l-~CO~. CF= •_,ElO_~ --"'-·-·-···--------- · 1 • s / -,- ---- --- --- -~- ----------- - . -9992 FCRMAT (/T5,'CGZERO = ',ElC.5,T35,'QF = ',El0.5,T59,'P~ = ',El0.5,
-.. l / T 9 , ' Q N -= ' , E l O • 5 , T 3 2 , ' C E X I T = • , E l O • 5 ,· T 5 3 , ' D E L-T A P ~ = • ·, E l O • 5 / / 16 -2 , • e CT TO tJ. ,p RESS URE = ., , E 1 C. 5 , T 4 5, ' NO. CF I TERA TIC f\ S = • , I 3 )
q 9. ~ l -· F C R fJ AT ( / ' L E N G TH • , I 2 , • - : , E l 2 • 5 , ' D = ' , E 12 • 5 , ' ~ C • S T E P- S = 1 , I 3 ) g990 .FC~r-'AT( 2Fl0.0, I5 )" 9 9 8 9 F C R ~ A T t '.O I NT E R M E D I A T E P R E ·s SL R E S = • , E 1 2 • 5 , / ( 2 6 X ,. E 1 2 • 5 ) ) CJ q 8 8 F C R f\/, A T ( / / / T l C , ' L · = 1 , E 1 0 • 5 , T 3 t , ' H = ' , E l C • 5 , T 6 C , 1 D = 1 , E l O • .. 5 ) g997 FCR~AT (T8,'RCF = ',ElC.5,T36,'R = •,ElC.5,T60,'T = •,El0.5)
-~-~-·----------·- g9_a6 FCR~AT (T2, 'N~ •. STEPS = ',1·3 ,T3C, 'DAM'P ING -- = ·, ,Fc.4 ,T5E, 1 TCL = 1 ,,F4. 1·0) - ..
9985 FCH~AT (TlO,'G = ',ElC.5,T33,'PATl-4 = ',.ElC.5) ) g 9 8 4 F C R ~ AT ( T 2 , ' C Y CL ES ' , T l i.e , ' C I A M E T E R S '· , T 2 7 , ' I ~ TE G RA T I C ~ S 1 , T 4 4 , 1 P R-E S Su
lRE', T56, •PRESSURE•, T72, 'FLO\.\ 1 )
-------- ------------ 9 9 8 0 -F C R fl A T ( I 5 , T l 5 , I 5 , T 2 g , I 5 , T 4 3 , F 8 • l , T 5 7 1 F 8 • l , T 7 0 • F 8-. 5 ) _ -- 10 REAC(l,9g<;6)TITLE
C.
C
REAC(l,ggsg)XLEN(ll,H,CIA(l),G,ROF,R,l,PAlM -REAC(1,ggse)ISTEP(l),~Q,OA~P,TOL,~DIAS REAC(1,ggg7)(C~GZEROCI), QFit\C(I), XS(I), XF(·I), I=l,N,> WRITE(3,9SS5)TITLE . WRITE (3,g988) XLEN(l),~,CIA(l) WRITE (3,Sg87) ROF,R,T WRITE (3,S~86) ISTEP(l),DAMP,TOL WRITE (3,gg95) G,PATM
IF(~DIAS-1)45,50,40 45 NCIAS = l
GC TO 50 1
40 REAC(l,gqgc)(XLEN( I),ClA( Il,ISTEP( Ir,I=2·,f\0IAS)
~ ... -
49 wRITE. (3,~ggl)(I,XLEN(I),CIA(l),ISTEP(I) ,1=2,NOI~S)
50 ABCT = .?e~ilDIA{l)iiOIA(l) AT C P = • 1 E 6 * 0 I A ( ND I AS ) ~ C I A ( l\ C- I A S ) AAVG - ( ATCP + A~OT) * C.5 Xf\STEP - C
C C 4 7 I = l , r,~ C I A S ·47 X~STEP = X~STEP +ISTEP(l)
.....
DC 1000 I = ltN~ 51 S = XS(I) 52 F = XF ( I) 5 3 0 f = t~ F I N C ( I ) 54 WRITi(3,9S03)S,F,QF
WRITE (3,c;C,<;4)
•
';I: .. -.....
~45-
' •
4
-,,.
.. ··.
I I.
. .
.12./16/68 FCRTMAIN· . . .
·· WRITE (3,9984)
··: ''
N·CCYC = 0- . . .
ER R C L = 0 • . -- - . · -~ · ··"·r·-··-··--· ,._; .... _._.~.-- ··.·-·--~. ----~--- . --- - -- ---- -- ~-:--. -.. .n, '.
.'.- -._:_., . ·_ .. .
,· ·;;.:·;··:.--":, ",".p,"• ,, '.-' .. · .
,. - . ., . -- - . - _____ ,.. __ - -- -~ -- ~- - ~ . --- .. - -
DC . 7 8 3 IR= 1, l C : · ·
-~-i-=:-~~.-: __ 7 __ 6_3~. ____ PHESS (_IR l ;::C .• Q~~--.. _~··-__c_·~·.·_ =~:__•·~-··_··-·~~~.'.._. ~=====~~-:::-·:........:....····~·---:-· ._._. _· --:-:..C--_-~~~~···-··_····-~,=-··=--··=_--~ --·~·-=,,.·=-~·-=_;·=· ·=='~·-;-· _:.~,-:--·:'·=· --=·:::•--:::·~---·~;'·-,-'. ·.~>---·~· ··· .. _··. _-:_:~:~----~
~...:..___.:.__~-----~f\E w - = C .-· .. NOIAN =l
J=O : ·-· •. ·' .• r
100 QG =· CGZERO( I)
:,-... -·- ''-,---·-·- .-.. -·.·-- .. -:--w-R--I-T--E----"(--3:-,-y<,-e-e). N_Qg_v~~--'---~_C_JAN,, .. ~t.P_R~~_§J ! l, PNE.~_,Q_F ___ ----~--------~-=~----~.--- >'· · ~ . _ . .~- ... NDIAN =l
:NOCVC ~ NCCYC + l 110 V = CF/ABCT
. ' '
111 P = PATM + ROF•G/32.174•H - RCF•V•V/64.348 -lABGT
RCF .. V•CG/32.174/ . I
PRESS(l)·=· P 114 X~CCtG = (RCF•H + PATM)•QG/R/T 115 X~DCTL = ROF• QF I'
TGTSTP = C ----~-·--1·1·2----Ns·r-E·J)S = IS TEP ( ND I AN>
113 D E L T A L =. ·· X L E N < ND I AN ) /' I S T E P ( f\ D I A .f\() ... D = DIA(NCIAN)
C .......
116 OC 150 J = .l,~STfPS --------- ------11·1-· ---o PC L l = - : -G *RO F / 3 2. 1 7 4 / ( l • +C GI s1-cF r ---- ------··---------~------~--~------. -. ,--.. ,·.·., -- '' .· .. - ..... ~.
DPCL2= 4.•f*ROF*V*V/C/f4.348•(1. +QG/QF) .
J
IQ'._ ... ,: ...
·-,; - '
•
C
DPOL = -CPCLl -OPDL2 118 Pl\Eh .= P + CPCL*DEL TAL 119 QG = P/PNEW*CG 805 IF(PNEh)l25,15C,150 125 XJ = TCTSTP -1. + J
QF=CF•XJ/Xr\STEP GC TC lCO
150 P = Pt\EW
155
160
TGTSTP = TCTSTP + ISTEP(NCIAN)
IF(NCIAS-~CIA~)l60,l6C,155 NCI/lN = NCIAN +l PRESS(NCIAf\) ; P GC TC 112 V~ = (CF+CG)/AAVG
",i.
- 161 162 163 164 200
Vlt:RC = (C:GZERO(I) + CF)/AAvG
DtLP~ = (XMCOTJ -~ XMDCTL)*(VN - VZER0)/32.174/AAVG PERROR = P - ~ATM -DELP~ IF(ARS(PERR[R)-TOL )2CC,2CC,25C QEXIT = QGZERC(I)*(ROF*h+PAT~)/PAT~
C
210
WRIT~ (3,SSS2) CGZERU( I),CF,P,QG,CEXIT,DELPM,PRESS(l),~CC~C IF(~CIAS -l)lCOC,lC00,210 WRIT£ (3,S~R~) (PRESS(K),K=2,~CIAS) GC TO lCOC
250 IF(ERRCL)26C,3CC,260 260 QF~E~ = .9•(QFLAST - QF)•PERRCR/(PERRCR -ERROL) +,F
GC TC 4CO
--46-
.. .
.,
•
.. ,.
-·--.~-,·--·-- -.····---- - .. ::·· ,-•· ..... ... , .. :.·. -~---,., .... ~·--···~-·-··:&,;.:>·····,d,c.-.-·.,_, __ . , ... _· ____ .:.·....,_ ·.3~::~;__;-~--
·-~..---=-'--··"' •··· .-..=-=-:., •.• .-_,.•,.,.,...-c,,_ .,=.,·,-,--•. ·.~ ....•..• ;.. .. ,--:-,-, -'.C ..• , .••.•• -.,-.•• c,_.,
--~·12 /18/ 66 FORTMAIN
300 CF~ ROF*H/P~T~/CAMP QF···t\ EW -- } / C PA l M + D ,E l. P M ) l CF >: . . .
400 QFLAST = CF QF - QFNEW •
ERR C L = P E R·R OR. '·: ·; ....... ~ . ';..
GC TO 100 •·· - ··.-· ... ___ ...;:.:__. -· -------·-------·-----'-'--·-. -1-o-e·o--=c~e:1~1~~fN{JE··--~--:_.: ____________________________ ._. ______ . __ -__:_~---~·· •·__.._. ---- .. · ...... -·-·. --·--- ·- ·~-· ... · .. --· - ·.·. · ·-:~. ·, · ·-.---. ·. · · ·~- · · .. ·· · ·.. · .- ---------.---•"'"
1500 GC TO 10 CCt\TI~UE Et\ C
'"------~---,--,...--,-----~------------------..
\·
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. -·c····-···-':~-:~-----~-'---:.· ___ .·., .· . - ·_ ~--.. ·.··-~-~---· __ ··.' ___ :..·-~~--~------------, . _·:..·: .:~--1~ ---
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\ _; = -~,- ___ •- •···'--·-·· . ._ -~.......::l..'t" -•-•-• S:amgl~. · Pr in:t:--&t : . _ :.... __ ---.. -·· · ~ __ • -·~-: _;_ ·• . _ _ _,-:.. :.... ~ _,.__;___....:..:..:._.~.:-.:::.. _..'.:....:...,. _______ -- _: ----:...C---. ---:--._:_ ____ ·:----·:-~ -~::--: .. -"· . ' ·. . . . . . . - . . . . . . .
i :_ ' ;•
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;:·- .. . .
't . . '
' ,·
... · 'I . The following is a sample print~Out comparing F. Pickert· • I
l · .. _ test data: agains;t the present theory. Thif data included in r., :_._- - - :__ ~'...;_-~~·,--.. -·-:--------_,:;~~~-,;.........._ _______ .. __ ···-·-····· .----···- ...... --- ....... .
1~,:, this print-011t was used._ to dra.\-t ~igure (14). Additional . . -1:;: ..
r·:·· ··: ,.. ' : :i: _,; . t- ... ·: r , l . . t, .
• i I ! . } i' f
i
' . ' ) ' .
' L r .
/
inf·6rmation in th~ print-out.includ~d: §f
a. ~Pressure at injector discharge (bottom piessure).
b.
- ----~-- -- -- ·- C •
i'lomentum pressure drop (AP~).
Number of times- the prcrgram ·'t-ecalcul ated the same
point hefore an answer was obtained which was within
the allo,'-'able tolerance. ' - -- - . ---- ---- --- - -- -------·· - -- --· -------·-----~-------·- --------------· -
!:,..;._.
-~ ....
- - - - ' .. ._r, ·-·-·-·- _ .......... ,. .••
• . :· . ~ .
-~
(J .... ,._ ., .
' ''_/,j
-48-
' ·. ~ .
., \:~.::-. ·'.-'--,:---;~C;-:.;_~=-:-··:~;~:-:=;:~:x_Z:: {~:;-=~r~=--_:,;~=~~-:-7.,_~-:--.~-<r~"."'"".'.:'.:/;;~-::-~--~~2~----'-,.:;-~7i..--__ _.:~::r.:.:--_.::a:2:.-·-:.1:----;~-~-~~~--~~:;:-_-,----·-z-: --,,..,·---~-.·--":'°::!-___ .~-.·---1~-----.~---.:-~_ ,-_ -i..~---..,."',.,.,....-..:....,.., -~~--..:..:::~-_=-=_. ___ -~=-:--""·-~-,.-·'-'-'c'---.:.---=-------~-,.-__ '. ;--.,-_, ---·-----!!!!!!· -· -~~--~. _!'l!!!!!! __ !II!!!! ___ ,.- -~!!!!!!:!!!!~~!!!!!!!!!!!!:==:;;;;;;;;;;~;;;;;1115_ . , -~ - -- ~ ----"'-~ --~-- ---.-.--.-- ...... ~-- __ __.,_,..,_ -- ..... ~.~-~-------··-··>·· --_,._ - ------·-·-·------- ___ _,;;..._~--~--v-~v:-:···.·;;::::;;:·'::-,.;:.:.\..;:.~~-.,,-.:r;·.~:..;::_·:0;~.-..:_--,-.. ,:
I - • • • ••• --· --- -· - ••.. - -
! __ ~-~-~---~ -_ ,,_,,,--c;- - ,__ -,---~-__ : __ ~ -~~·- ---~-~~"~-'~~~~~~,,~~--- --,--- ------·----.-~----,------ ----,-,~,-~=--~~--------------- --- -- - -----~-=--=
F PICKERT DATA ·s-uBfi'ERGENCE RATIO c.5736 SET 7 - - .
. . :.. ..... -.:.... .. ·---- -··- -- -- -· '-·--·--·- ~- -----'~ --~--- :_____ -----~--- ~.., ·---- . .. ---- ,, __ , _____ -··---·-. . .. . -
L = ·• 13800E 03 - H = • 7903<;E C2 - .. - ' '.
RG,F--~---,.6240CE -02 .' R = '.5363CE C2 . - D = .32808E CC ' T -= _ e 53CCCE C3 -
NO. '.:TQL=l8. STEPS = 138 '_', -- DAMPING,: 0.30CC , _I_ - - - , , ,
G = .32200E 02 '_ PATM =---~ __ Z__O_J_~~--E __ C't ,_,-__ -__ ·-""------· -,.,_ _____ -- _- - - - ~----~--------- ----- ------------=---~~~---------------~-----,
-.. _ ·. . . --~----.-.---~-•-·--·------- ------- .... -- ' - . -. -·-·· . ' . - . . ..
- -- -- - ---·---· ··-·-· -... ,. -- - .
. :: ... -..
- ' -~--. - ',, ' ' s = .2asooe or. F = .. • lt94CCE-02 ·1NCO~P QF· = . • 263COE 00 '~
·Ne. OF , , NC •. o F -NO-•. OF - ea 1 TOM o I SCHARGE ~: ____ , [.,. ~··: ... :e·v-et:E s·- .. ··_------~- .,..'., _____ O'l'A MET e·R:s· -~-~~--~'-l~N-T:E,GRlfTIO,NS -- . ---- ---·~PRE s Sl:R E ,-- ------ ------- -.--P'r~e-ss lfR E
L-ICUlO' -, ----~ ---------
- F LC k ,-·,'
0 - l O · o.o o.o C.26300 C.26'189 C.31166 C.31779
L .... _ , , _ , -l --~---_ -~-- - · :/" l 1 3 8 t: 9 c 1 • 3 2 5' a 4 • a -: -' 0 2,, ', - i 138 ~q5c;.1 2531.3 ·() '-,-' - 3 ' ' l - 138 c95C.3 2226.6
r··-·-----·-·-,· . ~.-.... ·- - , , , ' ' · CtZERC = .54700E- 00 1-.
~; QN = .l7400E 01 ~ - - . .
QF = .3177<;E CC QEXIT ~ .1848C~ 01
_ 'PN =· ,.2l843E 04 DELTA PM= .10343E 03
8GTT0f' PRESSURE =· .69488E 04 NO. OF ITERATICNS = 4 .'Q
~"Q_·· l . -~~-~--1\J O. 0,-F-
S· = .28500E 01
0 I"\'\
''J/
C Y CL c S 0 l 2, 3
--N-G • -~- 0-f--D I AME TE RS
l ' l l
·l
CGZERG- = .62660E 00 Q.~, = .19677 E 01
F · , = _ • 4 9 4 C C E- C 2 I NC C tJ P Q F = , • 2 6 5 lt OE C O - . " ..
-------NC-. ---0 F- -- --- -,------------·--B-O-f-T-O-M -. ----- -·- -- -{Jf-S CH A-R-G 1:--- ,- -- -------<--·t-I--Ctrtc--.------------INTEGRATIONS
0 138 138 138
PRESSLRE c.o
6'155.0 fg52.1 6'138.4
QF = .34027E CC. QEXIT = .2ll7CE Cl CELTA
PRESS~RE G.O
2757.5 2681.9 2268.3
F LO~ C.26540 C.275CO C.33156
. C.34C27
.22C8cE 04
.12455E 03
BCTTC~ PRESSURE~= .69361E 04 NO. CF ITERATICNS = 4
1,,, •
S = .28500E 01
NC. GF NC. C,F CYCLES DIAMETERS
- . ('' -- . - - --. -
l
,-, ( ~ ,.,_,,
. ···----- -------.. ---~---·- ---- .. - '. -· - ~ --- -
C l l l 2 l 3 l
,GZERC = .6607CE 00 CN = .2063SE 01
F = .~94CCE-C2 INCC~P QF = .266~0E CO
NC. OF BOTTOM DISCHARGE LICUIC INTEGRATIONS PRESSLRE .. --- -·- -·--· - PRESSLRE c-- FLC~ . ~ . -- - --
a c.o o.o C.266go 138 6<;52.2 2819.4 C.27150 138 c c; 4 <; • 5 2735.6 C.33S22 138 t933.3 2283.6 C.34872
QF = .34d72E CC PN = .2218~E C4 QEXIT = .22322E Gl DELTA PP= .1335~E 03
BCTTC~ PRESSURE= .69307E 0~ NO. a~ ITERATICNS = 4 - ...
S = .28500E 01 F • .~940CE-C2 INCO~P QF = .26070E CC I
NO. OF I
NC. OF 801 TOM DISCHARGE LICUIC \
' -49-•
··-~
- -·--- . .. .. --· .. - - ' .. - -~-·~· · · • .;....:...c: •..• c,'--=..-::..::;:":::.:::s;:c:•.:;...~,c:;_~.;.;, ... ~ -· ~""=--~~ ttc-=-_,._,.;_,=~-~=c~i,=; 'a<i5ri:;,;;;-ow·.,~;·:---~ .-..::;:;-;,:;:_~ · . _ ~~~~------ ----·--- -~---· ··-- ____ ..... , .· ... c __ . --- ---~ -·-····-'" '-· - ··- ..... . :. __ .. . . . --..,
- ------~-~--~-~ _ -~,..,.~,~-~,~~~=••-=="-•- --~~ .. ~a~~-a ... ·~a• .. ~.••-•~~""'·'··-·- ~-.~--. . -··· . = -.. - .. • . .. . . ·•· ~-=-':=--~--·····-~·-···- . • - • i
, ---~-"'C~-c~~S - . DIAMETERS' ~TEGR/.ITIONS PRESSLRE ·.. PRESSLRE FLCI-,
) ( · · ~ ·. -,. i 13 ~ C <; 4 ~: g. · 3 C 5 ~ : ~ . g: ~ ~ ~; ~ !l --· - -- ~--2 --~_ . - - ---1 . · · ....... •~ · rsa i- ·c , ........ -:§CJ 4 3 • l 2 9 4 0 • 9 C • 3 5 5 6 9 lil !{). __ .· 3 .· l. . , . 138 -- 6?19.,~ .Ji'; 2337 .5 C.36873
j.~.L ···.: .•. · CG)ERC : .756?0E ... 00 .... ·. QF = · .3.6873E oc ·. PN = .22472E 04 --i . · . · . f '1 N - • 2 3 2,o ~E_.O_L.~~---~- -·· .- .. -.. · --C-~-1-~T~ ·=-. ·•· i-5-5-1tl-E-~-1---·---=~e,_"T4----p~--=--.·~--1-~·e:,1)-~~=-~C--3~--~~, _ .. '.c ........ _
\:;-. =~=== ~-ac;'T~-" ~PRe;Su~ e- ~~ :~~-i-;1 E~4 -·- --- --·- No. o F- I TE RAT I c N s = 4 . _,, .. _ . .......... , '
,t ~: . . ' . ,._., .
- :' ~ ..... ~ .
---~-· .N·o.- OF NO. OF .
_ ....... , .. CYCLES ... DIAMETERS 1
NC. OF · · l-N-ft GR Af-1-e-N-S-- ------ · -
. BOT TOM . DI SC.HAR GE · l-I QUI C PRESSLRE ----: PREs·s-c-R·E- -- -- ----~-------~--- -
FLC\.t . ' i \.,f.,...,' .
.,-~. -
':"--'
)'1 0 .
l .... ~
·3 '
l l l
C 138 138 1·38
c.o. a.a 693g.6 3147.2 c934.q 3019.4 69C7.2 2361.4
C.26610 ·, C.28173 C.36960 C.38300
CGZERC = .83740E 00 _Q_E __ ~~-----183.CCE CC • •, ~ ----~--..-+----....-- -~ ---·-- . _,_ ---- ----- --:-·-- --- - Q N = • 2 5 4 9 0 E O l Q E X I T = • 2 8 2 <; 1 E -C l · - .. -PN = .22675E. C4 ' ~ .-. ' DELTA PM= .17Sl7E 03 { ··• ·._. ..
(' • I
\... .... --
- -t-· .
\..
.,,-..,
L
BCTTCf' PRESSURE = .6902SE 04 ,, . '
t\O. CF ITERATICNS· =
---~-Sv-......... =----..~8-5-e-e-E---e-t
NC.- GF CYCLES
0 l 2 3
NO. 0 F ' DIAMETERS
l 1 l l
CGZERC = .10750E 01 QN = .31?42E 01
-- ---------· ----------· ---- ---·-·------· .--··------ --- - -- --·-·--·-~-,--,--~-----· ---~---==--:··-~-4 9 4 CC E- 'C 2 I NC at' P Q F = - • 2 5 l 2 OE ·c 0 - .. ---- - --·--------
NC. OF I-NT E_G RA.TI ONS
0 138 136 138
BOTTOM PRESSLRE'
c.o 6'127.9 c92C.l
· t874.0
QF = .41'115E · CC QEXIT = .36319E Cl
0 I SCHA•RGE PRESSLRE
o.o 3589.3 34C4. 8 2455.5
LIC:UIC FLC~
C.25120 C.27259 C.39358 C.41115
PN = .23254E 04 DELTA PM= .23c28E 03
BCTTC~ PRESSURE= .6866qE 04 NO. CF ITERATICNS = 4
•
NO. OF CYCLES
0 l 2 3
S = .28500E Ol
- · NC. CF 0IA~ETERS
l 1 1 l
'CGZERO = .1034CE 00 Cf\= .34743E 00
•
NC. OF I ~ T E G r< A T I ON S
0 138 138 138
BOTTOM PRESSLRE
c.o 7CC7.o 7CC6.9 70C6.5
~ QF = .e1g24E-Cl CEXIT = .3493~E CC
DISCHARGE PRESSLRE
o.o 2 316. l 2293.4 2114.5
lICUIC FLC~
C.C7C66 C.C7168 C.C8C38 C.Cdl92
PN = .2CE5CE C4 CELTA F~ - .54~41E Cl
BCTTC~ PRESSURE= .70064E 04 ~a. CF ITERATICNS = 4 . ~-·
S = .28500E 01
"
F = .49~CCE-C2 I~CC~P QF = .98l~OE-Cl
-so-
·. . . 1' _['1
}- 1 - < -- -~- - ----·<-·· =- -·:-~: -=-· - ~--·-~-=.:..~_ --~~ · ·--.,··=-·-=--~-_=-- - -=~-~--. ----- -- .. ---- ·· -----~--,--.~-~ ~ ·-- -~---·--·--·- -----~---,,--~- -~"' -- -~- -· ·-- -----~- --,.-.-----.-. .,.-~ .. ----·-~---~~- -·------~--.,---·~---" -· -----~----,--. -~~ t;,I i ...... .
I - -
NG. GF "DI At' ET ER S ·
·l l . l
NC. OF · -- I t~ T E G R A T I ON S .
0 138 138 .
~OTTCM. PRESSLRE _
. . : ______ .. c·C e O • ---. 70C5.l
7CC5.2 .. ·
0 I SCt1ARGE PRESSLRE
.. , .. · .a 0 o .. 2021.1·
. 2026.8 _
LICUIC FLC"'
. C.09S.l4 .... C.09778
·_ C.09468. __
. ti
. Vi . • . . i'. ~ . '.!~·:··•-.'·····---~·., .. ,•.-, .. ---~---·_-.,,.-:"'!'o<·t;,J····-.· \ . - ~ '·(:
--, ..... : _______ ,_.:....._ _____ J;.GZ.E.8.Q __ _:_;; __ ... lJ..9.4-0-E----00 . ~C.....,-:;;~.S.4 6-S--lE-~-O-l-~-- P-N---~----.-2--G 7-&5 E---04--------~-- ----- -ti .,.., . . . 1,,
-- l~:./- . ----- -- ----- --.-·- ---------ON· -:::. · .40 2 71-E- --GG-- ---------~------- -- -~- QE-X I l-·:--~ --.-4-0 3 3 c; E -0-0- - ------C E-l TA-- PM-- =- --.1-3-G-6-l-E---01----- -·--· -- · -- 1 .. H
. > • . ,.. . . ··'·'' .. ' ••'· . .··· .;i ~-' .--~'' ' · ... '. . .· < . . ,. ., . ' .
BCTTC~ PRESSURE= .70053E 04· NO. OF ITERATICNS = 3 \·
. r·_ ~--. ,,,. ·:.: ... ;·s ~-: ..• --2as0Cie oi-- ._ ....... -.. - .---·----···,=···;c~,.~;~_4:94CC:E-C2 INC-Ot'P QF = . ,-:.\ C ,
• 208COE CO . fo.14'1" ' .
_;_~;:--:;:·:--N.O~.-- '.o f~~~ .: NO. CF DIAMETERS .....
l 0 CYCLES
0 l
. ·r---·"'- .•. ' "
2 J
:~· 1 . l
~-~~-' ~GZERG = • 24270E 00 QN = .81097E 00
0
NC. OF INTEGRATIONS
0 138 138
BOTTOM PR es·sLRE .
c.o t;gc;c.1 e:c;c;c.s
. DISCHARGE PRESStRE
a.a 1855.7 1881.5
LICUIC FLCh
C~20SCO C.20482 C.18C6l
Q-F ·= ;··1aC6lE cc PN .= .2C'i2eE C4 QEXIT = .el~~6E CC DELTA PM·= .27~5EE C2
BCTTC, PRESSURE= .69933E 04 NO. CF ITE~ATICNS = 3
C
0 -NG. OF NG. CF NC. OF BOTTOM DISCHARGE LICUIC ()'1 CYCLES DIAMETERS ;:~,;;, 0 l
C ~ ----~i 1-) , ~
...
INTEGRATIONS PRESSlRE PRESSLRE FLC~ 0 c.o o.o C.22770 .
138 cCJS4.8 lC,44.0 C.22532 13-8 ~~65.l 1962.4 C.20810 ..
0 QGZERO = .28850E 00 . CJF - .2081CE CC PN = .2lC16E 04 -QN = .959l5E 00 QEXIT - .g74c<iE CC OELTA p~ - .38C24E C2 - -r --· .. -
' ..
BCTTC~ PRESSURE= .• 69875E 04 ~a. CF ITERATICNS = 3
.,-, \_)
0
C
0
. ··") I ,........ ·i , i - ~
: ' ·'· i ~~,,, ,, .,....
NO . ._ OF CVCLES
C l 2
S :s .28500E Ol
--r··-- NO. CF OIA~ETERS
l 1 l
~GZERC·= .36410E 00 Cf\= .11916E 01
F = .49~CCE-C2 INCO~P QF = .24330E CO
NC. OF BOTTCM DISCHARGE LI,UIC INTEGRATIONS PRESSLRE PRESSLRE FLCY\
C c.o C.G C.2433C 138 6 CJ 1.7. 6 2154.'1 C.2436g
• 138 t:.<;77.5 2151.9 C.24634
QF = .2463LtE cc PN - .213l1E G4 -CEXIT - .123ClE Cl CELTA Pt-' - .5556CE C2 - -
BCTTC~ PRESSURE= .69771E 04 ~a. CF lTERATICNS = 3
NC. OF
S • .28500E Ol
NO. OF NC. OF
Fm .494CCE-C2 INCO~P Q~ = .25120E CO
BOllCM DISCHARGE LIC:LIC
-s1-
. -& . ~-. !l
. w . ~i,-
. . I • . .
i.:: f
. CY C .L E S · 0 I A M ET E R S - 1 N T E G RA T I ON S 0 · . l _. . 0
l. l · - 138 C • · 2 . · 1 · : . 'l 38 ·
i . :. 3 . 0 • • ••
0
• • • • • • : ' • • l - . . 1 ·3 8
PRESSLRE Co O ,.·· ·
6<l11o5· •- 6CJ7lo0 _ ·._-
- ~: -; -c)<)c7~ l -· · ··
PRESSLRE C. 0 -
. : 234405 2320.l 2168. 9.
fLCL\ C.25120 C.25435_
· ·C.-27468 c.21132 , ~ct· .. , . . . .
· C:GZERG = .4-3360E. 00 . QF = .27732E CC PN = .2150CE 04 .· . . . .· .' . ' .. ·· .. · .. QN = • l4049E ot .•. · .. · .. QEXIT = • l4l:49E Cl ··. DELTA PM = • 73A38E C2 ..•. ·· ·---r~~-.-. ;__-----'-~~".'."~:------'-----· ------------c.:, .. :.._ _______ . ________ ----· ''-··----;-~:---:---~------·---------------:-------··--·--:---- - - ----.=..-------- - - :..:--. -- -~.,;.'._:_~-~\--~_....._-____ . _. . --~------- --------,::-.-,.--~-----~----------'--.. _____ --'--·--~---------~~~--:-..:.C.....------'-------_ ---~-------- --,-----:-··- ... · ________ .. ______ ------------------'-~----- ------'-:·-:· .· ~~--.. _ -·~--~-~~----:
..... -1,_,_-···.• . . ·-- - .. --· - - -- ----- ·---- -- - - ------·. -------- -··-----·----- - ··- - -- - - - _____ _:_ ____________ ------ ---------~---- ------- --- - ---- --·----· .. ._ - --- --·- --------4-~-- -~---- - . ..
.. BCTTC~ PRESSURE= .69666E 04 ~
NO. Cf llERATICNS = 4
S = .2S.5-00E Ol f. = .• 494CCE-C2 INCQr,,p 9-f. = .25 1HOE GO , •• ·•·,- - !' -•••.' H ·-·~· • .,· . _ _,., . • •· .- • • ·0s•·-•-··. • - •: ' •. • - . ·-· · • .-.:.,-·-·.-;;:-· •·-• ...... •··-- • -···· ...... - ... ---··· • ._ ,. ...... _, __ ,__.:.. • ..:._s,_.._:_______ . .. ...... ··-···•·••·· -- ... . ............. ·····.·,· • .... ,,.. .. -· •· ............... • ...... ·-·----,..-· ...... _., •·-·•·· .. ,_ - ""°" ... -•• •. , ..
' . . ,.,·
-~~-
NO. OF .· CYCLES . ·
. 0 1 2
tr~:"·• .... ~.-- •. - ... --- l. 3 - ,-\
\. . --
·. NO. OF DIAMETERS
l l l l
NC. OF ,,
. <}. INTEGRATIONS 0
138 138 138
"BOTTOM - DISCHARGE LICUIC PR-ES SLRE , PRESSLRE FLC~
C;. 0 o.o C.25'il0 c'1t 7. 2 ·2411.6 C.26330 t9t6.4 237CJ.4 c.2ac;5g c9t1.o 2166.7 c.2q314
~"·'·'.
CGZERC = .47420E 00 . QF = .29314-E CO--_ -. ON---= .-152076·--0-h-· --~ ---- -·-QEX l T- -= .1602 lE--C 1
PN = .2lcl7E C4 . · . . DELTA PM= .-S413SE Cl .t . -·- ·-
0 -~. ~- ....... ,7 ,. -·-." -· ..
BCTTC~ PRESSURE= .69603E 04 l\ 0 • CF . IT ER A·T ·tc NS = 4
C:· · .. 1Jl2l9I • . '' .
_____.__ ---------·----- ---~ • 1; •
~-. . .. - . . . . -~ ------------~ .---·-. -- . --· -· -- ·----·-·-
('\
- ·-. -- -·- - ..... -·- -- . , -•- -·-· . • -- - ~- ·-·-. • • ,.,. -s~--
\....,.: I •
. 1:Q. ~! ..... \~~ ,.
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0
. ."".: .. - ....
0 ,_. --., .· . ,._ •-. - r ...,.
-·-. -~---·~-·- -~- -- ..._.. ____ , ___ -··--,...--...--~-- .------... ·-------. ~·-· .. -·--·.·--·-·-'.·--:···· ·----- .--~---. .
"- . .. - --- .. ,.~ ,. __ ..
0 .. -. ·~-- ,_,,,-
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:'.: l ...
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~: ., ' ' . ... ...... ~
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r'-or I _( .. ' . \ "' •. ·::, ..... .•,
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~-lartin, C. 'B. ''A 'J.wo-Phase Flo~ -Analysi~ · of the AirLift Pump.'' ~1.s. ··Thesis~ 1'iechanical, Engineering, Lehigh
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··~-·--·-··--·---- ----·-----~. ~--- .---~····---- ___ University, ... 19 67. .. ------ __ . __ :_: __ ·--------~ -~:_~-----·- -- --. : ·.· .. '· '! ·_-.:.,·
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. . 2. Stenning 9 Ao Ho and i1artin, C. B. ''An Analytical and Experi1nental Study of Air-Lift Pump Performance,'' J. of Pol'V'er, ·Trans$ ASlv1E, April 1968, PP• 106all0.
. 3. Owczarek, J. A.· Fundamentals .Qf Gas Dynamics. Scranton, ·Pennsylvania: Intern a tiona1· Textbook_ co·., 1964.
-------~----·-4-~ ____ Griffith, P. and \'lalli&, G. B. ''Two-Phase Slug Plow,'' . J. of Jieat Transfer, Trans. AS]w1E,- Vol. 83, August 1961,. pp. 307--320-.
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s. Golomb, M. and Shanks, M. Elements of Ordinary Differential. _ Egt1ations. Ne\\' Yorl<: i'lcGra\·i~Hill, Inc., 196.S. _________________ --. ____________ .: .. : _____ ··_
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6. Piclcert, F. ''The Theory of the Air-Lift Pump," Engineering, Vol. 134, 1932, pp. 19-20.
7. Griffith, P. ''The Prediction of Low .Qt1ality Boiling Voids,'' J. of Heat Transfer, Trans. ASf.IB, Vol. ~6, Augu~t 1964, pp. 327-333.
8. \\Fard, C. N. and Kessler, L. H. ''Experimental St1.1dy of Air Lift Pumps and Application of Results to Design," Bulletin of the_jlniversi ty of Vlisconsin, Engineering Series, Vol. IX, no. 4, Madison, 1924.
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Born in Chicago, Illinois,- on J\1ay 26, 1941, Kenneth ' .. : . ) ;._-·\ .···.
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Alleri·· Schoeneck is the son of ~-Ir.· and Mrs. Kenneth Otto.---~---· .. _::.-______ ---···· .. --··-····· - . -- . .--~-~:.:·.,-,-.•.. '- ' . ·--: -·.,--:---:--·--- .-----··-----
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'• C "\ •..;, • Scl,oeneck. / He attended grammar school in Illinois. and was graduated· from Dubuque Senior 1-Iigh Sct1ool in 1959.
~lr. Schoeneck· attended Iowa State University as an . , ·-•r,; . ·•. · undergraduate from September, 1959 to July, 1964, \-then he
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. -- -- ----- --~ :,~ ._. ____ ___,.....---'~-· --t--e,-Geived a Bach·elor -of -Scien·ce De-gree in Mechanical
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.Engineering- .and a Bachelor of· Scie11ce Degree in Industrial Engineering. I-Ie is a member of the Gamma Epsilon Sigma
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'· honor society. 'I
In August, 1964, Mr. Schoeneck went to work for the Ingersoll-Rand Company, Phillipsburg, New Jersey Plant. He is employed as a Project EnP,ineer, Turbo Products Engineering Depart~nt, where his functions include the
· design and development· of s~ngle and multistage centrifugal compressors and hot gas expanders.
He is married to the former Susan Burrowes and they - ' have one child, Kenneth Allen, Jr.
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