Shock wave propagation in two-phase flow
by Michael James Weaver
A thesis submitted in partial fulfullment of the requirements for the degree of Master of Science in
Mechanical Engineering
Montana State University
© Copyright by Michael James Weaver (1986)
Abstract:
The frequency dependence of acoustic velocity in upward, vertical, two-component, two-phase flows
was experimentally investigated. The two fluids used were air and water in annular and annular mist
flow regimes.
Weak shock waves were introduced into the two phase flow by pressurizing the downstream (top) side
of a diaphram until the diaphram ruptured. As the pressure pulse propagated through the flow,
hydrophones, tangentially wall mounted, were used to record the wave form at two separate locations.
A spectral analysis was then performed on the waveforms.
In comparison to the single phase (still air) spectral (phase) sonic velocity, the lower frequency
components of the pressure pulse were slowed more than the higher frequencies as the air quality
decreased. SHOCK WAVE PROPAGATION IN TWO-PHASE FLOW
by
Michael James Weaver
A t h e s i s su bm itted in p a r t i a l f u l f u l l m e n t
o f the req u irem en ts f o r th e d egree
of
Master of S c ie n c e
in
Mechanical E n gin eerin g
MONTANA STATE UNIVERSITY
Bozeman, Montana
May, 1986
«*a»n Lie.
//3 9 ?
Lo
ii
' 2'
APPROVAL
of a t h e s i s subm itted by
Michael James Weaver
T h is t h e s i s h a s been rea d by ea ch member o f t h e t h e s i s
c o m m i t t e e and h a s been fou n d t o be s a t i s f a c t o r y r e g a r d i n g
co n te n t, E n glish usage, form at, c i t a t i o n s , b ib lio g r a p h ic s t y l e ,
and c o n s i s t e n c y , and i s r e a d y f o r s u b m i s s i o n t o t h e C o l l e g e o f
Graduate S tu d ie s .
Approved fo r th e Major
partment
S
Date
Head, Major Department
Approved fo r th e C o lle g e o f Graduate S tu d ie s
Date
Graduate Dean
iii
STATEMENT OF PERMISSION TO USE
In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l l m e n t o f th e
req u irem en ts f o r a m a ster's degree a t Montana S t a t e U n i v e r s it y , I
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r u l e s o f t h e L ib r a r y .
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P e r m is sio n fo r e x t e n s iv e q u o ta tio n from or rep ro d u ctio n of
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or in h i s / h e r
a b s e n c e , by t h e D i r e c t o r o f L i b r a r i e s w hen, i n t h e o p i n i o n o f
e ith e r ,
th e
purposes.
fin a n c ia l
p e r m is s io n .
proposed use
of
th e m a t e r ia l
is
for
sch o la r ly
Any copying or use of th e m a t e r ia l in t h i s t h e s i s for
g a in
sh a ll
n o t be a l l o w e d
w ith o u t
my w r i t t e n
V
ACKNOWLEDGMENT
The p resen t author w is h e s t o ex p r e s s h i s s i n c e r e thanks and
a p p r e c ia t io n to th e f o l l o w i n g fo r t h e i r c o n t r ib u t io n to t h i s
p roject.
B i l l M a rtin d a les my a d v is o r , fo r guidance and support
throughout t h i s
study.
My mom and dad f o r t h e i r p rayers,
spent h e lp in g c o l l e c t data.
encouragement,
and hours
We f i n a l l y made i t !
My b ro th er, Bob Weaver, who went way beyond my e x p e c t a t io n s
and dreams in c o n t r ib u t in g v a lu a b le support and in fo r m a tio n .
Harry Townes,
f o r h i s p a t ie n c e ,
knowledge,
and w i l l i n g n e s s
to h e lp g e t the computer programs working.
Dan Marsh, S c o t t Figg and th e r e s t in computer s e r v i c e s who
put up w it h my q u e s tio n s and h elp ed w it h my computer problems.
I r a j S a d ig h i, fo r h i s p r in t e r and knowledge o f computers.
Tom Reihman and Ron M ussulm an, f o r s e r v i n g a s c o m m it t e e
members and r e v ie w in g t h i s t h e s i s .
Pat
V o w e ll,
for
h is
in v a lu a b le
a ssista n c e
in
th e
c o n s t r u c t io n and m aintenance of the tw o-phase f lo w apparatus.
The M e c h a n ic a l E n g i n e e r i n g D ep a rtm en t o f Montana S t a t e
U n iv e r sity ,
for
fin a n c ia l
a ssista n c e
and
fu n d in g
of
th is
in v e stig a tio n .
And m o st i m p o r t a n t l y , J e s u s C h r i s t , my Lord, who g i v e s me
the s tr e n g th to do ev er y th in g through him.
vi
TABLE OF CONTENTS
Page
V i t a .............................................................................................................................
iv
Acknowledgment ......................................................................................................
v.
L i s t o f T a b le s
v ii
L i s t of F i g u r e s .........................................................................................................v i i i
N o m e n c la t u r e ..............................................................................
x ii
A b s t r a c t ......................................................................................................................... x iv
I.
I n t r o d u c t i o n .................................................................
I
II.
L it e r a t u r e R eview ....................................................................................
3
III.
Experim ental Apparatus andProcedure .........................................
29
Experimental Apparatus. . .........................................................
29
Experim ental Procedure.................................................................
35
IV.
A n a l y s i s .......................................................................................................
37
V.
R e s u l t s .......................................................................................................
45
VI.
C o n c l u s i o n ......................................................... - .................................
54
R e f e r e n c e s ...............................................................................................................
56
R eferen ces C i t e d ....................................
57
A p p e n d i c e s ...............................................................................................................
61
Appendix A - Flowmeter C a lc u la t io n s
62
. . ................... . . . . .
Appendix B - Program Source L i s t i n g s ..............................................
Appendix C - F ig u r es ................................................................
Appendix D - V e l o c i t y C a l c u l a t i o n s ..................................................
.
66
98
128
v ii
LIST OF TABLES
Table
Page
1
R eyn old 's Number v e r s u s K . ..................................................
2
A ir Flowmeter C a l i b r a t i o n ............................................................
57
59
v iii
LIST OF FIGURES
Figure
Page
1
D is p e r s io n ( p a r t i c l e s in a i r ) ...................................................
18
2
D is p e r s io n ( p a r t i c l e s in helium ) . . .................................
18
3
Two-phase, Two-component Sound Speed as a F unction
o f F r e q u e n c y ......................................................................... ....
:
20
Sound Speed as a Function o f Frequency in a Bubbly
Steam-Water M ixtu re............................................................ . . .
22
Sound Speed as a Function o f Frequency in a SteamWater D rop let M ix tu re.....................................................................
22
Sound Speed as a Function of Frequency in a SteamWater D rop let M ixtu re......................................................................
24
Comparison o f Data from V apor-continuous Two-phase
Media w ith Theory.......................................................................... ...
24
8
E f f e c t o f Flow Q u a lity on T h e o r e t ic a l Model...................
25
9
Comparison o f Experimental and T h e o r e t ic a l R e s u lt s .
25
10
Phase V e l o c i t y v e r s u s Frequency..............................................
27
11
Experimental Apparatus .................................................................
30
12
Hydrophone Mounting..........................................................................
33
13
Phase One Diagram. . . . . . .
^ ................... ...................
40
14
Phase Two Diagram....................... * ..................................................
40
15
Time Window fo r A n a ly s is .............................................................
43
16
Frequency Magnitudes in S t i l l A ir , Top and Bottom
Hydrophones. ..................................... . . .....................................
46
4
5
6
7
17
18
O r ig in a l and R econ stru cted P ressu re Pulse f o r Top
Hydrophone in S t i l l A ir , Burst P ressu re = 14 p s i g .
.
48
Normalized V e l o c i t y v e r s u s Frequency Index f o r S t i l l
A i r ...............................................................................................................
49
X
ix
LIST OF FIGURES (c o n tin u e d )
19
20
21
22
Normalized V e l o c i t y v e r s u s Frequency Index f o r Twophase Flow, A ir Q u a lity = 76.33%, Burst P ressure =
14 p s i g ......................................................................................................
50
Normalized V e l o c i t y v e r s u s A ir Q u a lity as a F unction
o f F r e q u e n c y ........................................................................................
52
Two-phase Flow, A ir Q u a lity = 93.13%, P ressure
P u lse fo r Top and Bottom Hydrophones, Burst P ressu re
= 14 p s i g .........................................................................
98
Two-phase Flow, A ir Q u a lity = 94.89%, Pressure
P u lse f o r Top and Bottom Hydrophones, Burst P ressu re
= 14 p s i g ..................................................................................................
99
23
Two-phase Flow, A ir Q u a lity = 87.82%, Pressure
P u lse fo r Top and Bottom Hydrophones, Burst P ressu re
= 14 p s i g .......................................................................................................100
24
Two-phase Flow, A ir Q u a lity = 82.30%, Pressure
P u lse f o r Top and Bottom Hydrophones, Burst P ressu re
= 14 p s i g ....................................................................................................... 101
25
Two-phase Flow, A ir Q u a lity = 78.14%, Pressure
P ulse fo r Top and Bottom Hydrophones, Burst P ressu re
= 14 p s i g .......................................................................................................102
26
Two-phase Flow, A ir Q u a lity = 76.33%, Pressure
P u lse f o r Top and Bottom Hydrophones, Burst P ressu re
= 14 p s i g .......................................................................................................103
27
Two-phase Flow, A ir Q u a lity = 73.13%, Pressure
Pulse for Top and Bottom Hydrophones, Burst P ressu re
= 14 p s i g .......................................................................................................104
28
Flowing A ir , P ressure P ulse fo r Top and Bottom
Hydrophones, Burst Pressure = 14 p s i g ..................................... 105
29
S t i l l A ir , P ressu re P ulse fo r Top and Bottom
Hydrophones, Burst P ressure = 14 p s i g ......................................106
30
Two-phase Flow, A ir Q u ality = 93.13%, Frequency
Magnitudes f o r Top and Bottom Hydrophones............................ 107
31
Two-phase Flow, A ir Q u ality = 94.89%, Frequency
Magnitudes f o r Top and Bottom Hydrophones............................ 108
X
LIST OF FIGURES (c o n tin u e d )
32
Two-phase Flow, A ir Q u a lity = 87.82%, Frequency
Magnitudes f o r Top and Bottom Hydrophones........................109
33
Two-phase Flow, A ir Q u a lity = 82.30%, Frequency
Magnitudes f o r Top and Bottom Hydrophones........................
HO
34
Two-phase Flow, A ir Q u a lity = 78.14%, Frequency
Magnitudes f o r Top and Bottom Hydrophones.............................. I l l
35
Two-phase Flow, A ir Q u a lity = 76.33%, Frequency
Magnitudes f o r Top and Bottom Hydrophones..............................112
36
Two-phase Flow, A ir Q u a lity = 73.13%, Frequency
Magnitudes f o r Top and Bottom Hydrophones. . . . . .
113
S t i l l A ir , Frequency Magnitudes fo r Top and Bottom
Hydrophones..............................................................................
114
37
38
Flowing A ir , Frequency Magnitudes fo r Top and Bottom
Hydrophones.................................................................................................. 115
39
Normalized V e l o c i t y v e r s u s Frequency Index f o r Twophase Flow, A ir Q u a lity = 9 3 .1 3 % , Burst P ressu re =
14 p s i g .....................................................................
116
Normalized V e lo c i t y v e r s u s Frequency Index f o r Twophase Flow, A ir Q u a lity = 94.89%, Burst P ressu re =
14 p s i g .......................
117
40
41
Normalized V e l o c i t y v ersu s Frequency Index f o r Twophase Flow, A ir Q u a lity = 87.82%, Burst P ressure =
14 p s i g . .......................................................................................................118
42
Normalized V e l o c i t y v e r s u s Frequency Index f o r Twophase Flow, A ir Q u a lity = 82.30%, Burst P ressure =
14 p s i g ............................................................................................................119
43
Normalized V e l o c i t y v ersu s Frequency Index fo r Twophase Flow, A ir Q u a lity = 78.14%, Burst P ressu re =
14 p s i g ........................................................................................................... 120
44
Normalized V e l o c i t y v e r s u s Frequency Index f o r Twophase Flow, A ir Q u a lity = 76.33%, Burst P ressure =
14 p s i g ............................................................................................................121
45
Normalized V e l o c i t y v ersu s Frequency Index fo r Twophase Flow, A ir Q u a lit y = 73.13%, Burst P ressure =
14 p s i g ............................................................................................................122
xi
LIST OF FIGURES (co n tin u e d )
46
Normalized V e l o c i t y v e r s u s Frequency Index fo r
Flowing A ir , Burst P ressure = 14 p s i g . . . . . . . .
123
47
Normalized V e l o c i t y v e r s u s Frequency Index f o r S t i l l
A ir , Burst P ressu re = 14 p s i g ................................................... 124
48
Normalized V e l o c i t y v e r s u s A ir Q u a lity as a Function
o f F r e q u e n c y ................................................... .... . ........................125
49
Top Hydrophone Frequency Response C h a r a c t e r i s t i c s .
50
Bottom Hydrophone Frequency Response
C h a r a c t e r i s t i c s ....................................................................................127
.
126
x ii
NOMENCLATURE
D e s c r ip t io n
A
a
C r o s s - s e c t i o n a l area
Thermal D i f f u s i v i t y
D rop let p r o je c te d area
Gas co n sta n t
Speed of sound
V ir t u a l mass c o e f f i c i e n t
Thermal damping c o e f f i c i e n t
Drag con stan t
O s c i l l a t i o n frequency
Frequency
A c c e l e r a t io n due t o g r a v it y
G r a v it a t io n a l con stan t
Newton's con stan t
P o ly t r o p ic gas co n sta n t
Wave number
Latent heat o f ev ap oration
Number o f p o in ts
D im en sion less parameter
D im en sion less parameter
D roplet d e n s it y
P ressure
U n iv e r sa l gas co n sta n t
Bubble ra d iu s
R eyn old 's number
D roplet ra d iu s
Temperature, where x r e f e r s to any phase
Time
V e l o c i t y , where x r e f e r s to any
;
phase
M odified Froude number
V e lo c i t y
Mass flo w r a t e
Speed of propagation
V olum etric f r a c t i o n
Expansion f a c t o r
P o sitio n
Void f r a c t i o n
Change in parameter Y = AZy / ac:
O
Bd pi
Symbol
cVM ■
D
Dc
F
f
S
Sq
gO
K°
k
L
N
nGuSM
nL
n
P
R
Rb
R0
r
Tx
Ux *
Vgs
V
W
W
X
Y
Z
a
Y
6
y
V
Px
P
TT
R atio of s p e c i f i c h e a t s , 5 = 1
c p/0 v
A bsolute v i s c o s i t y
Kinematic v i s c o s i t y
D e n s it y , where x r e f e r s t o a:
D en sity o f e q u ilib riu m s t a t e
P a r t i a l p ressure o f e q u i l i b r
x iii
NOMENCLATURE (co n tin u e d )
CT
ta
T
*x
S u rface t e n s io n
Angular frequency
Time delay
Phase, where x r e f e r s to which hydrophone
x iv
ABSTRACT
The f r e q u e n c y d e p e n d e n c e o f a c o u s t i c v e l o c i t y i n upward,
v e r t i c a l , t w o - c o m p o n e n t , t w o - p h a s e f l o w s w as e x p e r i m e n t a l l y
i n v e s t i g a t e d . The two f l u i d s u s e d w e r e a i r and w a t e r i n a n n u la r
and annular m is t flo w regim es.
Weak sh o c k w a v e s w e r e i n t r o d u c e d i n t o t h e tw o p h a se f l o w by
p r e s s u r i z i n g t h e d o w n strea m ( t o p ) s i d e o f a d iaphram u n t i l t h e
diaphram ruptured. As th e p ressu re p u lse propagated through the
f lo w , hydrophones, t a n g e n t i a l l y w a l l mounted, were used to record
the wave form at two s ep a ra te l o c a t i o n s . A s p e c t r a l a n a l y s i s was
then performed on the waveforms.
In c o m p a r is o n t o t h e s i n g l e p h a se ( s t i l l a i r ) s p e c t r a l
( p h a s e ) s o n i c v e l o c i t y , t h e l o w e r f r e q u e n c y c o m p o n e n ts o f t h e
p ressu r e p u lse were slow ed more than th e h igh er f r e q u e n c ie s as
th e a i r q u a l i t y d ecre a se d .
I
CHAPTER I
INTRODUCTION
C la ssic a l
flu id
m e c h a n ic s
b e h a v i o r o f m o t io n f o r
e ith e r
can be u s e d t o
d e sc r ib e
the
p h a se i n t w o - p h a s e f l o w ,
but
u n f o r t u n a t e ly t r y in g t o apply fundam entals,
such as th e N a v ier-
S t o k e s e q u a t i o n s , p r o v e s t o be a h o p e l e s s t a s k e x c e p t f o r t h e
most t r i v i a l tw o-phase m odels.
T h ere
are
several
fa cto rs
th at
in flu e n c e
th e
speed of
p ropagation o f a shock wave in tw o-phase f lo w , such as th e speeds
o f sound o f b o th p h a s e s , t h e d e n s i t i e s o f t h e p h a s e s , and t h e
volume f r a c t i o n o f the d i s p e r s e d p h a s e .
g a s-liq u id
A h o m o g e n e o u s ly m ix ed
( a ir - w a t e r ) tw o-phase flo w has a sound v e l o c i t y th at
i s s m a lle r than th e v e l o c i t y o f sound o f e i t h e r th e gas or li q u i d
component of th e m ixtu re because of th e high c o m p r e s s i b i l i t y of
the gas ( a i r ) and th e la r g e d e n s it y o f the l i q u i d (w a ter)* .
The p a s t t w e n t y t o t h i r t y y e a r s h as s e e n a c o n s i d e r a b l e
in c r e a s e in th e amount o f resea r ch and study in th e area o f tw op h a se f l o w b e c a u s e o f i t s many d i v e r s e a p p l i c a t i o n s . A c o u s t i c
prop agation e f f e c t s are im portant c o n s id e r a t io n s to s a f e l y design
th e v e s s e l ,
p ip in g ,
r e a c t o r power system .
flo w r a t e s ,
and s u p p r e s s i o n p o o l o f a b o i l i n g w a t e r
The p r e d ic t i o n o f e x i t choking,
c r itic a l
and c e r t a i n o s c i l l a t i o n phenomena in pipe f lo w s r e l y
on t h e v e l o c i t y o f p r o p a g a t i o n o f p r e s s u r e w a v es i n t w o - p h a s e
2
(liq u id -g a s)
flo w s.
The d e t e c t i o n
of
th e r m a l- h y d r a u lic
i n s t a b i l i t y in tw o-phase media and th e e x p lo r a tio n and p r e d ic t io n
of earth movements are a l l r e l a t e d t o th e speed o f sound in tw op h a se m i x t u r e s .
In t h e o r y , v o i d f r a c t i o n s
system s
f ree-gas
and
th e
co n cen tra tio n
in
d e t e r m i n e d by m e a s u r in g t h e s o n i c v e l o c i t y
m ixtu re.
in b o i l i n g w a t e r
liq u id s
can
be
in t h e t w o - p h a s e
This le a d s t o an i n t e r e s t i n g a p p l i c a t i o n in th e e a r ly
d e t e c t i o n o f gas bubbles a s s o c i a t e d w ith d ecom pression s ic k n e s s
( t h e "bends") i n d i v e r s ,
and t o a i d i n t h e t r e a t m e n t th ro u g h
m o n ito rin g th e c o n c e n tr a tio n of gas bubbles in the d iv e r 's body.
The
th e
purpose of t h i s study was t o e x p e r im e n ta lly i n v e s t i g a t e
frequency
dependence
of
a c o u stic
v e lo c ity
v e r t i c a l , tw o co m p on en t, t w o - p h a s e f l o w s .
A n n u lar
and
exp erim en t.
The m i x t u r e
upward i n a I 1 / 4 inch i n s id e d iam eter pipe.
a n n u la r
The
upward,
The tw o co m p o n en ts
u s e d i n t h e t w o - p h a s e f l o w w e r e w a t e r and a i r .
flo w e d v e r t i c a l l y
in
m ist
sh ocks,
flo w
w h ic h
reg im es
w ere
co n ta in e d
used
a la r g e
in
th is
range of
f r e q u e n c ie s , were induced t o t r a v e l downward th r o u g h t h e f l o w .
The shocks were produced by ru p tu rin g a la y e r of aluminum f o i l by
p r e s s u r iz i n g the downstream (top ) s id e u n t i l the diaphram b urst.
The shocks were recorded by two s ep a ra te hydrophones l o c a t e d one
f o o t a p a r t a lo n g t h e i n s i d e w a l l o f t h e f l o w p i p e .
A sp ectral
a n a l y s i s was performed on th e waveforms to an alyze th e data.
3
CHAPTER I I
LITERATURE REVIEW
The study o f a c o u s t i c c h a r a c t e r i s t i c s in tw o-phase media i s
a very d iv e r s e and co m p lica ted f i e l d because of th e la r g e number
f a c t o r s t h a t m u st be t a k e n i n t o a c c o u n t .
Some o f t h e f a c t o r s
t h a t i n f l u e n c e t w o - p h a s e s t u d i e s a r e : I ) The l a r g e v a r i e t y o f
f l o w r e g i m e s and i n t e r f a c i a l g e o m e t r i e s , such a s s l u g , b u b b ly ,
annular f l o w s , e t c .
d u r in g
p h ase
im p u r itie s ,
2) Nonequilibrium e v e n t s ,
change.
such
as
3)
The
fo a m in g
la r g e
ag en ts.
c o n f ig u r a t io n o f a t e s t a p p aratu s.
such as n u c le a t io n
in flu e n c e s
of
sm a ll
4 ) The g e o m e t r i c a l
Due t o t h e l a r g e number o f
v a r i a b l e s i n f lu e n c i n g tw o-phase media s t u d i e s ,
th e study o f tw o-
p h a se a c o u s t i c c h a r a c t e r i s t i c s h a s b een l a b e l e d an " in s e c u r e "
s c i e n c e by K enneth B o u ld in g ^ .
An "insecure" s c ie n c e i s d efin ed
as one which s t u d i e s a very la r g e u n iv e r s e w ith a v e r y s m a ll and
b ia s e d sam ple,
and th e a v a i l a b l e data on ly cover a s m a ll part of
t h e t o t a l f i e l d i n w h ic h t h e s t r u c t u r e s and r e l a t i o n s h i p s a re
e x t r e m e l y c o m p le x .
The dan ger h e r e l i e s i n t h e t e m p t a t i o n o f
c la im in g an a n a l y t i c a l p r e c i s i o n th a t i s g r e a te r than th e degree
t o which th e problem can be d efin ed .
W a l l i s ^ d e s c r i b e s s i x d i f f e r e n t m e th o d s o f a n a l y s i s , th e
most common o f which i s d e s c r ip t i v e - e x p e r im e n t a l .
in v e s tig a tio n
This method of
i n v o l v e s o b s e r v i n g and t r y i n g t o e x p l a i n w hat
4
happens.
m e th o d ,
S in c e
th e
in v e stig a tio n
th e f o llo w in g
of
th is
p ap er i s
d i s c u s s i o n w i l l be m a i n l y
of th is
lim ite d
to
p rev io u s i n v e s t i g a t i o n s o f the d e s c r ip t i v e - e x p e r im e n t a l nature.
The e x i s t e n c e o f an i n t e r f a c e in t w o - p h a s e f l o w c a u s e s a
w ide v a r i e t y o f flo w p a t t e r n s or flo w reg im es,
depending on the
flo w r a t e s and the p h y s ic a l p r o p e r t ie s o f the phases.
McQuillan
and Whalley^ d e fin e d four main flo w p a t t e r n s fo r upwards flo w in
v e r t i c a l tu b es.
annular f lo w .
They are bubble f lo w , plug f lo w , churn f lo w , and
Their paper d e a ls w ith a method f o r p r e d ic t i n g the
l i k e l y f lo w p a tte r n
m ixtu re.
in v e r t i c a l u p flow o f a g a s - l i q u i d tw o-phase
For an annular flo w regim e t o e x i s t :
vGs*> I
Where
vq
s*
i s a m o d if ie d Froude number, r e p r e s e n t in g a comparison
between i n e r t i a and g r a v i t y f o r c e s .
The c r i t i c a l v a lu e of u n ity
was e m p i r i c a l l y observed by H ew itt and Wallis"*
f o r an a ir - w a t e r
system .
A m ore c o m p r e h e n s iv e s t u d y on f l o w p a t t e r n s w as done by
M u k h erjee and B r ill* * .
T h e ir i n v e s t i g a t i o n d e r i v e d e m p i r i c a l
e q u a tio n s fo r p r e d ic t i n g flo w regim e t r a n s i t i o n s as a fu n c t io n of
the i n c l i n a t i o n an g le in the pipe fo r both upf low and downflow in
tw o-phase g a s - l i q u i d sy ste m s.
The i n c l i n a t i o n a n g le s ranged from
O d egrees ( h o r iz o n t a l ) to 90 d e g r e e s ( v e r t i c a l ) .
The t r a n s i t i o n from slug t o annular m is t f l o w was found to
be i d e n t i c a l f o r a l l h o r i z o n t a l and a l l u p f low and d ow nf lo w
a n gl es .
th is
The l i q u i d v i s o s i t y ,
tran sition .
As
the
p , has a s i g n i f i c a n t i n f l u e n c e on
liq u id
v isco sity
in crea ses,
the
5
t r a n s i t i o n from s l u g t o a n n u la r m i s t f l o w a c c e l e r a t e s .
The
t r a n s i t i o n i s d e fin e d by:
llGvSM ‘ 1 0 * * U .4 0 1 - 2 . SOTliv + 0.521NL t -3 2 9 )
where th e d im e n s io n le s s parameters;
nGv SM
nLv
= v SG^pI /
=
Pl O3 ) 1/4
and Vgg = s u p e r f i c i a l gas v e l o c i t y
Pjj = l i q u i d d e n s it y
a
= s u r fa c e t e n s io n
g = a c c e l e r a t i o n due to g r a v i t y
H i j ik a t a e t a l.* e x p e r im e n t a lly and t h e o r e t i c a l l y stu d ied
th e
h y d ro d y n a m ic a l
d ia m eter ),
flo w
b e h a v io r
of
a la r g e
b u b b le
(4
to
8 mm
su b je c te d to a shock wave in a homogeneous two-phase
c o n s i s t i n g o f s m a l l b u b b le s (.5 mm in d i a m e t e r ) .
They
d e t e r m i n e d t h e l a r g e b u b b le s w ere a d i a b a t i c a l l y compressed and
move w it h a v e l o c i t y
d i f f e r e n t from th e l i q u i d v e l o c i t y
behind
th e shock due to th e bubble's i n e r t i a f o r c e of th e v i r t u a l mass.
M a r t i n d a l e and Sm ith^ fou n d t h a t b o th s o n i c v e l o c i t y and
p r e s s u r e drop d a t a w e r e good i n d i c a t o r s
t r a n s i t i o n from annular to ch u rn -fro th f lo w .
v e l o c i t y d a t a show ed l i t t l e
of th e flo w
r e g im e
Because the so n ic
or no c h a n g e , t h e y a l s o c o n c lu d e d
t h a t i n t e r f a c e tra n sp o r t p r o c e s s e s such as h eat and mass t r a n s f e r
w e r e n e g l i g i b l e i n t h e s e p a r a t e d f l o w r e g i o n from 100 p e r c e n t
q u a l i t y down to th e q u a l i t y o f the t r a n s i t i o n between annular and
ch u rn -froth flo w p a t t e r n s and at t h i s r a t e o f wave p ropagation or
6
p ressu r e ch an ge.
The e f f e c t s o f a g a s - l i q u i d i n t e r f a c e and tube geometry on
pressure
wave
p r o p a g a tio n
were
e x p e r im e n ta lly
stu d ied
S u t r a d h e r e t al.® by u s i n g " tee" s e c t i o n s i n t h e p i p i n g .
by
They
concluded th a t momentum t r a n s f e r occurred a cro ss th e g a s - l i q u i d
i n t e r f a c e because of th e d i s t o r t i o n in th e p ressu r e d i s t r i b u t i o n
a c r o s s th e duct.
The geometry e f f e c t s caused by flo w through the
"tee"
sig n ific a n tly
se c tio n
en h a n ced
th ese
pressure
wave
p ropagation phenomena.
E v a n s, G o u s e , and B e r g l e s ^
r e p o r t e d t h a t w a l l mounted
p ressu r e tra n sd u ce rs do n o t m e a s u r e t h e c h a r a c t e r i s t i c s o f t h e
shock wave i t s e l f ,
t h e s h o c k w ave.
e x p la in
r a th e r th e l i q u i d boundary la y e r 's resp on se to
They came t o t h i s c o n c l u s i o n a f t e r f a i l i n g to
why t h e
shock p ic t u r e
from
th e
tra n sd u cers
had
c o n s id e r a b ly d i f f e r e n t c h a r a c t e r i s t i c s d ep e n d in g on w h e t h e r i t
was f lo w in g up or downstream.
Evans e t a l .
fo u n d t h a t l i t t l e
or no a c o u s t i c e n e r g y i s
capable of being t r a n s m it t e d in th e l i q u i d f i l m a t th e pipe w a ll
due to therm al con d u ction and v is c o u s drag.
The f lo w i s u s u a lly
t u r b u le n t w ith e x tr e m e ly h igh shear f o r c e s which cause a l l but
very high f r e q u e n c ie s t o be c o m p le te ly damped ou t.
The r e s u l t of
t h i s i s th a t th e p ressu r e s ig n a l propagates down th e core of the
f lo w .
T h erefo r e, th e core c h a r a c t e r i s t i c s govern th e propagation
phenomena.
Evans e t a l . were a b le to measure the p r e ssu r e s ig n a l
t r a v e l i n g down th e core of flo w a t th e pipe w a ll by t r e a t i n g the
i n t e r a c t i o n b e t w e e n p r e s s u r e d i s t u r b a n c e s i n t h e c o r e and t h e
7
w a ll
film
as the i n t e r a c t i o n of bulk flo w over a t h in boundary
la y e r
rath er
th a n
a c o u stic
phenomena.
T h is
situ a tio n
is
analogous t o s in g le - p h a s e boundary la y e r f lo w , w ith th e e x c e p tio n
o f e x t r e m e l y h ig h b oundary l a y e r d e n s i t y . By s u b t r a c t i n g th e
l i q u i d f l o w i n g a lo n g t h e p ip e w a l l from t h e t o t a l l i q u i d f l o w
r a t e b e fo r e c a l c u l a t i n g the v o id f r a c t i o n ,
v e lo c ity
d ata
c o lle c te d
by Evans e t
a l.
t h e mean a c o u s t i c
com pared w e l l w i t h
p rev io u s t e s t s done by Hinkle'*"®.
R a d o v sk ii11 d eriv ed an eq u ation fo r th e speed o f propagation
for
a d istu r b a n c e
of
an a r b i t r a r y
n atu re
in
a s lig h tly
n on eq u ilib riu m a d ia b a t ic tw o-phase flo w :
W2 - C2 -Y 1 CC2 - C2 ) - y 2 (C 2 - C2 J-Y 3 CC2 - C2 J
where
W = speed o f propagation
Y=
, J
ASjj
, change in parameter Cj , which c h a r a c t e r iz e the
.
' .
independent p r o ceses
c = speed of sound
and t h e s u b s c r i p t s d e n o t e t h e number
o f p r o c e s s e s t h a t a re
co n sid ered as "frozen", th e o th er p r o c e s s e s are e q u ilib r iu m ones.
An e x p r e s s i o n
to
p r e d ic t
th e
speed
of
p r o p a g a tio n
of
l o n g i t u d i n a l a c c e l e r a t i o n w a v es i n b u b b ly t w o - p h a s e f l o w s was
d eriv ed by Dobran
IO
.
W2 = (A1+ A2 )/A 3
where
W = speed of propagation
A1 = P icI ^ 2 + All^
+ ^2C2 ^ 1 + Al l^
8
Il
A3 =
C1 =
( J 1Cb Cp 2 + I 11) ■- P2 Cb CJ1 + A 11) ) 2 + SJ1J2CbCb Abi
GPl +
4I i t 5 I + P2 ) )
( S i Z S p 1) s i
11
<r"
(P1P2) Z ^ 1 + P2)
A
0
( S i 1ZSJ2) 82
TF = p a r t i a l p ressu r e o f e q u ilib r iu m s t a t e o f th e phase
( I or 2)
P = d e n s it y o f e q u ilib riu m s t a t e o f th e phase ( I or 2)
To s ee i f t h i s r e l a t i o n could be used to model th e speed of
p rop agation o f shock w aves,
Dobran assumed th a t
and C2 could
be approximated by aj and ag, th e speeds of sound in phases I and
2 r e sp e c tiv e ly .
The e x p r e s s io n f o r th e speed of prop agation of
shock w aves, W, became:
W /a g} ? ,2 '
where
« 1 1 B2/ 2 ) / B 3
B1 =Cpg Zpji) (I + ( x / ( l - x ) ) C ^ ) + (ag / a | ) Cpg/ p £) + Cm
B2 = ( ( P g / P £ ) ( l
+
Cvm X Z ( I - X ) )
-
( 4 / a g ) ( P g Z p £ + CVM) ) 2
4 x Z ( l - x ) ( P g Zp£ ) ( a £ Zag )C ^M
B3
= 2 ^ p g yfp^
+
Cv m C( x Z ( 1 - x ) ) ( p g Z P £ +
I))
CyM = .3 tanh ( 4 a ) V ir t u a l mass c o e f f i c i e n t
X = v o lu m e tr ic f r a c t i o n o f gas bubbles
p = d e n s it y
+
9
The
su b scrip ts £
and g r e f e r
to
th e
liq u id
and g a s
p hases
resp ectiv ely .
T here a r e tw o p h y s i c a l s o l u t i o n s f o r W.
i s independent of ct and
and
One s o l u t i o n , W^,
= A^. The second s o l u t i o n , Wg'
s t r o n g l y d ep en d s on CyM and i s much l e s s th a n e i t h e r a^ or 3g.
The v a l u e s o b t a i n e d from t h e e x p r e s s i o n a g r e e d w e l l w i t h t h e
ex p erim en ta l data o f Akagawa e t a l . ^
Cheng e t
v e lo c ity
of
a l.^
sound
homogeneous f l u i d
p resen ts
in
th e
and Miyazaki e t a l . ^
an e x p r e s s i o n
b u b b ly
flo w
for
reg im e
and c o n s id e r in g c o m p r e s s i b i l i t y
homogeneous "frozen" v e l o c i t y
of sound,
C^,
th e
" fro zen "
a ssu m in g
effects.
a
The
r e f e r s to th e s t a t e
o f th e f l u i d in which th e speed of sound i s bein g measured.
As a
s t e e p p r e ssu r e p u lse p a s se s through a m ix tu re, th e f l u i d does not
have tim e to a d ju st t o a new e q u ilib r iu m s t a t e and i s r e f e r r e d to
as "frozen".
The r e l a t i o n i s :
1/C2 = - ( ( l - a ) p £ +
where
apg) ( ( l - a ) / ( p £ C 2) + a /( k P g ) )
a = v o id f r a c t i o n
P = p ressure
p = d e n s it y
k = p o ly t r o p ic gas constant
C = speed of sound
S u b s c r ip ts A and g r e f e r to l i q u i d and gas phase r e s p e c t i v e l y .
The thermodynamic p ro cess ( a d ia b a t ic ,
flu id
u n d erg o es as th e
pressure
p u lse
is o t h e r m a l,
p asses
e t c . ) the
th rou gh
it
d e t e r m i n e s t h e m eth od u s e d t o c a l c u l a t e t h e s p e e d o f sound in
ea ch phase.
This model was extended to in c lu d e r e l a t i v e m otion ( v i r t u a l
10
mass) and v i s c o s i t y
effects
by C r e s p o ^ .
The r e l a t i o n s d erived
by Crespo p r e d ic t th e v e l o c i t y o f sound f o r l i q u i d in th e fro ze n
sta te,
i s o t h e r m a l s t a t e , or i s e n t r o p i c s t a t e d e p e n d in g on t h e
r a d i u s o f t h e g a s b u b b l e s , a s com pared t o v i s c o u s l e n g t h and
th e therm al d i f f u s i o n le n g th .
Vi
------- -- v i s c o u s l e n g t h
a) Rb
a g
----- = t h e r m a l d i f f u s i o n l e n g t h
m Rb
Sg= thermal d i f f u s i v i t y
Rb= bubble Radius
V = Kinematic v i s c o s i t y
to = angular frequency
The b u b b l e s b eh a v e i s o t h e r m a l Iy ( i . e .
k = I ) when t h e b u b b le
r a d i u s i s l e s s th a n t h e v i s c o u s l e n g t h w h ic h i s l e s s th a n t h e
therm al d i f f u s i o n le n g th .
C r e s p o 's r e l a t i o n a g r e e d w i t h t h e
r e l a t i o n d e r i v e d by Cheng e t a l . * When th e b u b b le r a d i u s i s
la r g e
when com pared t o
th e v is c o u s
le n g th ,
but
s m a l l when
com pared t o t h e t h e r m a l l e n g t h , t h e b u b b l e s w i l l s t i l l beh ave
is o t h e r m a ll y but do not move a t th e same v e l o c i t y as th e liq u id .
The s o n ic v e l o c i t y i s g iv e n by:
C2 = [ ( I + o i l - a ] / c VM) p £] / [ p £a ( l - a)]
where CyM = V ir t u a l volume c o e f f i c i e n t .
The r e s t o f th e symbols
and s u b s c r i p t s are th e same as in th e p reviou s eq u ation .
C resp o fo u n d t h a t when t h e b u b b le r a d i u s i s g r e a t e r th a n
b o th t h e v i s c o u s and t h e r m a l d i f f u s i o n l e n g t h s , t h e r e i s s l i p
b e t w e e n t h e tw o p h a s e s and t h e b u b b l e s b eh ave i s e n t r o p i c a l l y .
The v e l o c i t y o f sound i s g iv e n by:
11
C2 = ( ( I + 0 ( 1 - a ) / c VM) 6 P £ ) / ( p a ( l - a ) )
where S i s the r a t i o o f th e s p e c i f i c h e a t s in th e gas (Cp/Cv ).
For
C r e s p o 's
e q u a tio n
d e r iv e d fo r th e
c a s e when t h e
b u b b le r a d i u s i s g r e a t e r th a n t h e v i s c o u s l e n g t h b u t l e s s th a n
t h e t h e r m a l d i f f u s i o n l e n g t h , t h e f r e q u e n c y m u st be b e lo w t h e
b u b b le r e s o n a n c e
freq u en cy.
H enryk
in c lu d e d
a sim p lifie d
v i r t u a l mass term in h i s d e r i v a t i o n and assumed P^= Pg to take
i n t o account th e frequency r e s t r i c t i o n .
C^j,= ( ( I + o ( l - o)/CVM)k P £ ) / ( o ( l - o) P^)
For k = I ,
th e is o th e r m a l c a s e ,
t h i s eq u ation redu ces t o Crespo's
r e l a t i o n fo r is o th e r m a l b eh a v io r.
is e n tr o p ic
case,
th e
S i m i l a r l y , when k = 6 , t h e
above r e l a t i o n
isen tro p ic rela tio n sh ip .
reduces
to
C r e sp o 's
For th e case of homogeneous f lo w ,
— > 00J H e n r y 's r e l a t i o n
reduces
r e l a t i o n d erv ied Cheng e t a l
I C
Cy^
t o an a p p r o x i m a t i o n o f th e
.
By assuming th a t th e gas c o m p r e s s i b i l i t y term was a fu n c t io n
o f th e v o id f r a c t i o n
fa cto r
th a t
(k = k (ct)), Henry d e r i v e d a c o r r e c t i o n
was l i n e a r
in v o id
fr a c tio n .
He d e r i v e d
an
e x p r e s s io n fo r hom ogeneous, is o th e r m a l tw o-p h ase v e l o c i t y of
sound,
Cg^j,:
Cjjrj, - [ ( [ I - a IpjJ, + ctPgM [I - a ] / [ p ^ C 2 ] + ct/P ^) I
12
T h is r e l a t i o n a g r e e s w e l l w i t h e x p e r i m e n t a l d a t a f o r v o i d
f r a c t i o n s up to 0.5 and appears to a c c u r a t e ly d e s c r ib e both on eand two-component bubbly flo w momentum t r a n s f e r p r o c e s s e s .
By t r e a t i n g
th e
in te r fa c e
of
one p h ase a s
th e
e la stic
boundary o f the o th e r , Nguyen e t al.*** d eriv ed a r e l a t i o n fo r the
v e l o c i t y of sound g iv e n by:
Ch = .[( [I - a]p jj/2 + Ctp^2X t l - ct]/[pgC2] + ot/[pg Cg ] ) 1/ 2] -1
The r e s u l t s o f t h i s eq u a tio n a l s o agree, w e l l w it h o n e - and tw ocomponent sound v e l o c i t y data.
Van W ijn gaard en ^ p r e s e n t s an e x p r e s s io n in tw o-ph ase f lo w s
where l i q u i d forms th e continuous phase,
CQ, t h a t i s s i m i l a r t o C r e s p o 's .
fo r th e speed o f sound,
The f o l l o w i n g r e l a t i o n n e e d s
c o r r e c t io n when the v o id f r a c t i o n , a ,
i s e i t h e r c l o s e t o zero or
u n ity .
C2 = ( 6 P ) / ( p g a [ l - a ] )
where
P = p ressu re
Pg= d e n s it y o f l i q u i d phase.
L e v i c h ' s 2 ® m o d el f o r
c a lc u la tin g
th e f r i c t i o n a l
fo rce,
W,
e x p e r i e n c e d by a b u b b le in t w o - p h a s e f l o w was e x p e r i m e n t a l Iy
v e r i f i e d by van Wijngaarden.
The r e l a t i o n i s :
W = 12Try R (v-u)
where
V = v isc o sity
u = liq u id v e lo c ity
R = bubble ra d iu s
v = bubble v e l o c i t y
13
Nakoryakov. e t
a l.
OI
e x p e r im e n ta lly v e r i f i e d
t h e Landau
r e l a t i o n fo r th e speed o f sound, Cp in a v a p o r - li q u i d m ixtu re on
th e
sa tu r a tio n
lin e .
A ssu m in g
slo w
p ropagation due to phase t r a n s i t i o n ,
processes
and sound
th e r e l a t i o n i s :
C12 .= Lp2ZP12Cv B3T3
l i q u i d d e n s it y
where
p ressu r e
Cy = speed o f sound in vapor
B = gas con stan t
T = temperature
L = l a t e n t h ea t o f ev a p o ra tio n
A r e la tio n
b etw een
shock
stren g th
p rop agation (Uglioclt) fo r is o t h e r m a l,
tw o-ph ase
flo w
w as d e r i v e d
and
homogeneous
and e x p e r i m e n t a l l y
v e lo c ity
of
two-component
v e r ifie d
by
Campbell and P i t c h e r ^ .
U2
uShock
-
cI2
P1 O1 (I-C t)
w h e re t h e s u b s c r i p t s I and 2 s t a n d f o r c o n d i t i o n s i n f r o n t and
behind th e wave f r o n t ,
is
c a lc u la te d
from
and th e is o th e r m a l tw o-phase v e l o c i t y C1
th e
e x p r e ssio n
of
Cheng e t
a l.
for
d e term in in g the "frozen” v e l o c i t y .
Akagawa e t a l .
23
used a one-component,
tw o-phase h o r iz o n t a l
bubbly flo w to p r e d ic t the r e l a t i o n s h i p between th e magnitude o f
the p o t e n t i a l surge,
APpg, and th e propagation v e l o c i t y ,
APps = 0TP wI o pI
where
Wlo = s u p e r f i c i a l v e l o c i t y o f th e li q u i d
P1
= d e n s it y o f the l i q u i d
C^p.
14
E x p erim en ta l r e s u l t s
show t h a t t h i s r e l a t i o n h o l d s f o r t w o -
component tw o-phase flo w as w e l l as one-component tw o-ph ase flo w .
For a l i q u i d w i t h g a s b u b b l e s ,
fo u n d
th at
as
in c r e a se d ,
the
in cid e n t
wave p r e s s u r e
th e
dam ping o f
the
e x p e r im e n ta lly
d eterm in ed
th a t
d ecreased ,
Malykh and O g o r o d n i k o v ^
p u lse
as
of
th e
p u l s e was
in c r e a se d .
th e
v o id
They
a lso
fr a c tio n
was
th e speed o f wave propagation in creased .
Moody^S s t u d i e d a c o u s t i c a l dam ping i n l i q u i d - g a s s y s t e m s
c o n sid e r in g
o n ly
th erm a l
and
m e c h a n ic a l
i r r e v e r s i b i l i t i e s w ith o u t phase changes.
in te r fa c e
Thermal damping in tw o-
p h a se m i x t u r e s o c c u r when g a s b u b b le s undergo p r e s s u r e changes
and t e m p e r a t u r e v a r i a t i o n s due t o h e a t t r a n s f e r b e t w e e n t h e
l i q u i d and gas in a bubbly m ixtu re.
Mechanical drag d i s s i p a t i o n
r e s u l t s from th e r e l a t i v e m otion between l i q u i d d r o p le t s and the
surrounding gas in a d r o p le t m ixtu re.
Moody fo u n d t h e s p e e d o f sound i n a b u b b ly m i x t u r e , C^, t o
be:
cb
= [ x ( p /p g ) 2 / Cg 2 + ( I - X K p Zpl ) 2 /
cL2]
~1 /2
where:
p = d e n s it y
x = m ixtu re q u a l i t y
C = speed of sound
s u b s c r i p t s L and g r e f e r to l i q u i d and gas phases r e s p e c t i v e l y .
Moody d e r i v e d e x p r e s s i o n s f o r t h e a c o u s t i c p e n e t r a t i o n o f
sound w a v e s
in b u b b ly m i x t u r e s
and d r o p l e t
m ix tu res.
The
propagation in t o the f l u i d , P ( z , t ) , i s a f u n c t io n o f p o s i t i o n , z,
15
and t i m e , t .
P ( z , t ) = P 0e -aZ s i n w ( t - z / c )
For a bubbly m ix t u r e :
a - (D/Cb) [ ( [u)/D] ( [u /D ]2 + I ) 1 /2 - ( o>/D)2) / 2 1/2
C = Cb/ ( [ ( 1 + [D/ w] 2) 1 /2 + 1 ] / 2 ) 1/Z
For a d r o p le t m ix t u r e :
d = (m /Cg)[(C1-C2)Cz ZC4 I iz 2
d = CgZtCc1 + c 2) c 3 / c 4 ] 1/2
C1= ( [ I +(A3 ZtC2O)])2] [I +(A3 ZCC2O)D2 (PZpg ) 2] ) 1 /2
w ith
C2= I + (A3 ZtC2O)D2pZpg
<3= 1 + P g C g d - ag>/ ( P£C2ag)
C4= 2(1 + tA3 Z(CgO))]2)
A3= [goDcnCg ] / [ a g ( l - ag)p (1+ PgCg ( I - ag )Z(p C2ag) ) ]
where
D = thermal damping c o e f f i c i e n t
Ot = volume f r a c t i o n
Dc = drag con stan t
o) = c i r c u l a r frequency
g 0 = Newton's Constant
C = speed o f sound in
m ixtu re
. n = d r o p le t d e n s it y
16
P - p ressu r e
= speed of sound in gas
phase
I t can be determ ined from t h e s e r e l a t i o n s th a t h ig h e r f r e q u e n c ie s
p e n e t r a t e s h o r te r d i s t a n c e s , w h i l e lo w er f r e q u e n c ie s tend to
p e n e tr a te f u r t h e r w ith o u t a t t e n u a t i o n in b oth b u b b ly or l i q u i d
drop m i x t u r e s .
T h is e x p l a i n s why f o g h o r n s a r e u s e d t o warn
s h ip s in s t e a d o f w h i s t l e s .
An e x p r e s s io n f o r a c o u s t ic decay was form u lated by Moody to
be:
P ( z , t ) = P0e""Rt (c o s T t ) s in ( k z )
where
R = (CgK2) / ( ( (3Dc gQ) / (4agrp^ad) ) Cp/pg ) ) 2
F =
o s c i l l a t i o n frequency
K=
wave number
a^ =
r =
d r o p le t p r o je c te d area
s p h e r ic a l d r o p le t ra d iu s
By i n c r e a s i n g t h e wave number ( s h o r t e r wave l e n g t h ) , t h e sound
wave decays f a s t e r .
A lso la r g e v a l u e s o f th e d e n s it y r a t i o cause
f a s t e r decay.
Chug r ingout occurs when steam i s disch arged i n t o c o o l water
and t h e
su dden c o n d e n s a t i o n
a c o u s t i c d istu rb a n c e.
creates
a v o id
th at
causes
an
Moody d is c o v e r e d th a t therm al d i s s i p a t i o n
i n a f i n e b u b b ly m i x t u r e w as c a p a b le o f p r o v i d i n g t h e s t r o n g
damping a s s o c i a t e d w ith chug r in g o u t ,
and th a t f u r t h e r study i s
needed t o d eterm ine th e r e l a t i o n s h i p betw een the two.
The m a j o r i t y o f t h e s t u d i e s p e r f o r m e d on p r e d i c t i n g th e
17
p ro p a g a tio n
speed
of
w a v es
have g e n e r a l ly
been
lim ite d
to
p r e d i c t i n g t h e l e a d i n g ed g e v e l o c i t y o f l a r g e a m p l i t u d e w a v e s .
In e f f e c t ,
t h i s corresponds to p r e d ic t i n g th e s o n ic v e l o c i t y for
th e h ig h e s t frequency con tain ed in th e wave.
High f r e q u e n c y w a v es p r o p a g a t e a t a f a s t e r r a t e th a n low
f r e q u e n c y w a v e s b e c a u s e t h e r e i s l e s s t im e f o r t h e d i s p e r s e d
phase (w ater) and th e continuous phase ( a i r ) to reach e q u ilib riu m
w ith r e s p e c t t o m ass, momentum, and energy tra n sp o r t p r o c e s s e s .
T h is m eans t h a t
t h e number o f a c t i v e
r e d u c e d w h ic h r e s u l t s
in
26
d e g r e e s o f free d o m i s
an i n c r e a s e
in t h e
speed
o f wave
prop agation through th e media.
Of
th e
th ree
tra n sp o rt
processes
(m ass,
momentum and
e n e r g y ) , m a ss t r a n s f e r ( c o n d e n s a t i o n and e v a p o r a t i o n ) , may be
show n
to
be
th e
slo w e st
m ode
of
energy
d istr ib u tio n .
T h e o r e t i c a l l y , h igh frequency p ropagation in one-component media
should not d i f f e r from th a t in two-component m edia,
not e x p e r ie n c e mass t r a n s f e r ,
t r a n s f e r to occur.
which does
because th ere i s no tim e fo r mass
E xperim ental r e s u l t s support t h i s v ie w .
Zink and D e ls a s s o
s tu d ie d how sound v e l o c i t y as a fu n c tio n
o f frequency was a f f e c t e d in a gas w ith s o l i d p a r t i c l e s suspended
in i t . The ex p erim en ta l procedure in v o lv e d comparing th e o r i g i n a l
s ig n a l to th e s ig n a l a f t e r i t passed through th e tw o-ph ase media.
An o s c i l l o s c o p e was used to compare the s ig n a l s and measure the
m a g n it u d e and p h a se c h a n g e s .
They fou n d t h a t t h e change in
v e l o c i t y f o r low f r e q u e n c ie s was g r e a t e r than the v e l o c i t y change
in
th e
h ig h e r
fr e q u e n c ie s.
F ig u r e s
I and 2 sh ow
th e ir
18
x
EXPERIMENTAL
StC
----------------- TOTAL THEORETICAL
-----------------THEORETICAL VISCOSITY
-----------------THEORETICAL THERMAL CONDUCTIVITY
>
<
I OOO
3 300
9 200
6 200
IO 800
F REQUENCY
Figure
I. D ispersion
(p articles
in a i r ) ,
ref.
I EXPERIMENTAL
-----------------
O
TOTAL
THEORETICAL
---------------- T H E O R E T I C A L
VISCOSITY
---------------- T H E O R E T I C A L
THERMAL
I QOO
3 300
CONOUCTIVITY
9 zoo
6 ZOO
io aoo
FREQUENCY
F ig u r e 2. D i s p e r s i o n
r e f . 27.
(p articles
in helium ),
27.
19
e x p e r im e n ta l
and
th e o r e tic a l
r e su lts
for
so lid
p a r tic le s
suspended in oxygen and n it r o g e n r e s p e c t i v e l y .
A m od el w as d e v e l o p e d by M ecredy and H a m ilto n ^ -0 f o r t h e
speed
and a t t e n u a t i o n
of
a c o u stic
w a v es
frequency in tw o-p h ase, two-component media.
n on eq u ilib riu m
im portant.
in te r p h a s e h eat t r a n s f e r ,
a fu n c tio n
of
This model included
which was found to be
The model d erived fo r th e sound speed, C, i s
C = [ P /(c tp )]1 / 2 [ ( l + [a)/GS£ ] 2 ) / ( l +
where
as
[ l/ f i] Lw/ gS ^ ]2 )] 1/2
G& = in v e r s e tim e co n sta n t f o r h eat t r a n s f e r - l i q u i d to gas
P = p ressu r e
a = v o id f r a c t i o n
S = s p e c if i c heat r a tio
P = d e n s it y of two phase m ixture
( p= p^+ p^)
a) = frequency
Data c o l l e c t e d by Karplus2 ^ tends to agree w it h t h i s model
and can be s e e n i n F i g u r e 3.
Mecredy and H am ilton2® a l s o found th at th e wave speed has a
low frequency l i m i t ,
th e iso th e r m a l sound speed o f th e m ixtu re,
and a h ig h f r e q u e n c y l i m i t o f t h e a d i a b a t i c sound s p e e d o f t h e
m i x t u r e e v i d e n c e d by t h e f l a t • s e c t i o n s a t t h e lo w and h ig h
frequency ends of Figure 3.
L a t e r on M ecredy and Hamilton®® e x t e n d e d t h e i r work t o
in c lu d e one-component, tw o-phase media.
This model in clu d ed the
20
Socuxi S p « d rs. Frrqo+rtcy
Air frbfar
/ atm
Korptus' Data
O1-OS o
.tO a
.!5 v
.2! o
.J/ o
F i g u r e 3 . T w o - p h a s e , T w o -co m p o n en t Sound S p e e d a s a F u n c t i o n
o f F requency, r e f . 28.
21
e f f e c t s o f n o n e q u i l i b r i u m i n t e r p h a s e h e a t , m a s s , and momentum
transfer.
At low f r e q u e n c i e s , i t was found th at the wave speed,
C, approached
Iim C2 = (dp/dp)
oj-»-'o
= U / ( a p ) ] t ( u f(, / h fe. ) 2 ( l / p ) +
®
6
([PCvTlZ aK vf g Zhf g ) 2] " 1
where
Cv =constant volume s p e c i f i c h ea t - pure vapor phase
hf g = h ea t of v a p o r i z a t i o n
T
= temperature of mixture
uf g = change in i n t e r n a l energy upon evap ora tion
v f g = change in s p e c i f i c volume upon eva p o ra tio n
For t h e h i g h f r e q u e n c y l i m i t , t h e wave s p e e d was fou n d t o
have no h e a t , mass, or momentum t r a n s f e r between the l i q u i d and
vapor phases.
For bubbles in continuous l i q u i d ,
Iim C2 = [(SP)Z (ct p) ][ l + 2 a ( l - a ) 2Z( l + 2 a ) I
0J - > « P
For d r o p l e t s in continuous vapor,
Iim C2
(l)
CO
They fo u n d t h a t
[(Sp)Zp ] [aZ(a + [ 3 - 2a] [ I - a]Z[2a] )]
O
the
b u b b l e or d r o p l e t
radius
and
the void
f r a c t i o n or q u a l i t y were important in determining t h e frequency
a t which none qui lib ri um e f f e c t s become important.
F i g u r e s 4 and 5 c o n t a i n t h e r e s u l t s f o r sound s p e e d v e r s u s
f r e q u e n c y as a f u n c t i o n o f b u b b l e or d r o p l e t r a d i u s f o r s t e a m -
22
Sound speed vs frequency
s t e a m w a te r
P = - K . 7 psia
I = - 21 2*F
Void fr a c t Ion=O- 20
Case
io Kr io io io io
I
II
III
IV
V
CT
0.001
0.01
0.01
0.01
1.00
bubble radius
O-Olin
0 - 0316 in
0.01 In
0.00 316 in
0.01 in
F r e q u e n c y ps
F i g u r e 4 . S ound S p e e d a s a F u n c t i o n o f F r e q u e n c y i n a B u b b ly
S te a m -W a te r M i x t u r e , r e f . 30.
Sound sc o td in c sre c m -wc.'er droder m u rare
1600
ICQO
c - 0-80
I O-Ci Q-iQin.
I IL- OTDI iO-Cim
1200
ICOO
Frequency.
F i g u r e 5 . Sound S p e e d a s a F u n c t i o n o f F r e q u e n c y i n a
S te a m -W a te r D r o p l e t M i x t u r e , r e f . 30.
23
w a t e r m i x t u r e s i n b u bb ly and m i s t f l o w r e g i m e s r e s p e c t i v e l y .
Sound s p e e d v e r s u s f r e q u e n c y a s a f u n c t i o n o f v o i d f r a c t i o n i s
shown i n F i g u r e 6 , a l o n g w i t h sound s p e e d v s . f r e q u e n c y as a
f u n c t i o n o f q u a l i t y i n F i g u r e 7.
Firey,
Data c o l l e c t e d by En gland,
and Tr ap p^ was p l o t t e d along w i t h the theory deriv ed by
Mecredy
and Ham ilton ^® .
They
also
observed
that
at
high
f r e q u e n c i e s and low v o i d f r a c t i o n s , the wave a t t e n u a t i o n was very
large.
Kokernak and Feldman-3^ s t u d i e d the frequency dependence of
a c o u s t i c v e l o c i t y in a s i n g l e
component (R-12 r e f r i g e r a n t ) two -
p ha se m i x t u r e . The a p p a r a t u s u s e d by Kokernak and Feldman t o
m e a s u r e t h e s p e c t r a l ( p h a s e ) v e l o c i t y i n v o l v e d two p r o b e s . One
probe r e m a i n e d f i x e d ,
w h i l e t h e o t h e r prob e was f r e e t o move
a l l o w i n g m e a s u r e m e n t s t o be made a t
several
d ifferen t
path
l e n g t h s . The v e l o c i t y was c a l c u l a t e d by knowing the t r a n s m it t e d
frequency
and m e a s u r i n g
the
agreement
between
th eoretical
th eir
change
in
phase.
The
general
and e m p i r i c a l
resu lts
( F i g u r e s 8 and 9) i m p l i e d t h a t momentum t r a n s f e r and m u l t i p l e
s c a t t e r i n g c o n s i d e r a t i o n s such as b u b b le rad ius , f l o w q u a l i t y ,
and t e m p e r a t u r e o f m o d e l w e r e s i g n i f i c a n t i n d e t e r m i n i n g t h e
speed of sound.
Rather than us ing the most f r e q u e n t l y occu ring
bubble s i z e as the e f f e c t i v e bubble r a d iu s , they found th a t using
the l a r g e s t occuring bubble as the e f f e c t i v e radius gave a b e t t e r
agreement between the t h e o r e t i c a l and ex p eri m en ta l r e s u l t s .
No
c o n c l u s i o n s were formed about the r e l a t i o n s h i p between speed of
sound and the choked or maximum f l o w r a t e s , other than th a t more
24
Sound sp e e d in a
s t e a m w a t e r droplet
mixture
P = 14-.7 psia
CT=O-OI
Droplet radius=.0.0T in.
Id1MCTh id id 2 id 3 io h OMO5
F r e q u e n c y , cps
F i g u r e 6 . S ound S p e e d a s a F u n c t i o n o f F r e q u e n c y i n a
S te a m -W a te r D r o p l e t M i x t u r e , r e f . 30.
I SGOi
I
I
/
u
I/- 0 0
/7
/
-
fli a
OJ
•SI
>*
U
O
U
>
//
Ctb',»sia y/
1000 -
/a'=
//
/
soo-
Oa
»♦" Snymnd
a t si /?
---------- Theory s e p a r a t e d p h a s e s
----------Theory homogene ous p h a s e s
U
'c
a f7 -3>, <= .
O
CO 2 0 0
i
0
i
i
i
0.2 0.4 0.S 0.8 1.0
Q u a l it y ^ x
F i g u r e 7 . C o m p a r i s o n o f D a t a f r o m V a p o r - c o n t i n u o u s Twop h a s e M e d ia w i t h T h e o r y , r e f . 3 0 .
25
X-
1« IO
_1000
X • I . IO'5
10
IOz
IO5
frequency
10*
IO5
,0«
(cpI I
F i g u r e 8 . E f f e c t o f Flow Q u a l i t y on T h e o r e t i c a l
32.
M odel
1000
Frequency ( c p s )
F i g u r e 9 . C o m p a r is o n o f E x p e r i m e n t a l a n d T h e o r e t i c a l
R e s u l t s , r e f . 32.
ref.
26
s t u d y was n e e d e d .
T h i s w as due t o t h e l a r g e v a r i a t i o n o f sp eed
of sound w i t h frequency.
Cheng e t a l .
wave
number,
d er iv ed a f u n c t i o n a l r e l a t i o n s h i p between the
K,
and
the
angular
f r e q u e n c y , to .
This
wave
d i s p e r s i o n r e l a t i o n ta k es i n t o account t h e e f f e c t s of i n t e r f a c i a l
h e a t , mass, and momentum t r a n s f e r by u s in g a o n e-d im en sio n al twopressure,
t w o - c o m p o n e n t , t w o - f l u i d model.
The wave d i s p e r s i o n
r ela tio n is:
det
(WA-iC)-kB
=0
w he re A, B and C a r e m a t r i c e s c o n s i s t i n g o f t h e c o e f f i c i e n t s o f
= =
—
the l i n e r i z e d c o n se r v a tio n law s used in the d e r i v a ti o n .
The
r e s u l t s o f t h i s r e l a t i o n a g r e e w e l l w it h exp eri m en ta l r e s u l t s ,
and the d i s p e r s i o n r e l a t i o n has been used to a c c u r a t e l y p r e d ic t
the speed of both standing and propagating pressure waves in twop h as e m i x t u r e s .
The r e s u l t s can be s e e n i n F i g u r e 10.
N otice
th e s i m i l a r i t y between t h e s e r e s u l t s and Kokefnak and Feld ma n's ^
r e s u l t s i n Figur es 8 and 9.
OO
Rehman J e x p e r i m e n t a l l y measured the frequency dependence of
s o n i c v e l o c i t y u s in g low pass f i l t e r s i n a i r - w a t e r , annular m i s t ,
two-phase f l o w .
q u alities,
He found th at f o r low f r e q u e n c i e s (IkHz) at low
t h e s o n i c v e l o c i t y was l o w e r th a n t h a t f o r h i g h e r
frequencies
( IOOkHz
and
150
kHz).
The h i g h e r
frequencies
main ta ine d a con stant s o n i c v e l o c i t y equal t o the s o n i c v e l o c i t y
in
air
over
qualities,
the
range
of
q u a lities
he
tested.
At h i g h e r
the lower frequency wave s o n i c v e l o c i t y was c l o s e r to
27
Ph a s e veloci ty
VS.
FRECUEVCY
S 84 • io
WE-N 3U83LE RADIUS IR
iO'
F ig u re
O
1.92 x .0
I .98 x IO
C
2. CT x iO
A
2 . SC x IO
), m
IOz
IOz
FREQUENCY (He)
10*
1 0 . P h a s e V e l o c i t y v e r s u s F r e q u e n c y , r e f . 15.
28
th a t o b ta in ed f o r the h ig h er frequency waves.
that
th is
in d ica tes
that
the frequency
Rehman s u g g e s t s
dependence
of
sonic
v e l o c i t y i s suppressed when the gas phase i s dominant.
As e v i d e n c e d by t h i s r e v i e w ,
the f i e l d of tw o-phase flow
c h a r a c t e r i s t i c s i s v er y d i v e r s e , and s e v e r a l i n v e s t i g a t i o n s using
d i f f e r e n t a p p r o a c h e s ha ve b ee n p e r f o r m e d .
study i s
The p u r p o s e o f t h i s
t o e x t e n d t h e work done by M a r t i n d a l e and Sm ith '',
S h a nk ar a, S m i t h ,
and A r a k e r i ^ ,
and R eh m a n ^
in the area of
f r e q u e n c y d ep e n d e n c e o f a c o u s t i c v e l o c i t y in annular m i s t twophase f lo w .
29
CHAPTER I I I
EXPERIMENTAL APPARATUS AND PROCEDURE
Experimental Apparatus
O r i g i n a l l y , 23 1 / 2 f e e t o f 1.25 i n c h i n s i d e d i a m e t e r (I.D.)
extruded p l e x i g l a s s
p i p e w i t h a one f o o t
long
test
section
l o c a t e d s i x f e e t from t h e t o p was u s e d t o run t h e t e s t s .
The
extruded p l e x i g l a s s pipe d e v e l o p e d s t r e s s f r a c t u r e s and c r a c k s
t h a t c a u s e d l e a k s and i r r e g u l a r i t i e s i n t h e f l o w .
Therefore,
s e a m l e s s 6061 T6 aluminum w i t h a 1.25 i n c h I.D. w as u s e d t o
r e p l a c e a l l but a 12 f o o t s e c t i o n o f p l e x i g l a s s p i p e l o c a t e d 6
1/2 f e e t from the bottom of t h e apparatus ( s e e Figure 11).
The I f o o t t e s t s e c t i o n was l o c a t e d 19 f e e t from whe re t h e
f l o w o r i g i n a t e s so as t o insure th at the f l o w was f u l l y developed
when i t r e a c h e d t h e t e s t s e c t i o n .
A m a c h in e d " t ee " was l o c a t e d
11 inc hes above the t e s t s e c t i o n t o a l l o w f o r the f l o w t o exhaust
into
a drain
bucket.
The "t ee" was
sp ecially
m a ch in ed t o
e l i m i n a t e as many o f the sharp edges as p o s s i b l e and thus reduce
t h e amount o f n o i s e i n t h e f l o w .
Two p u r p o se s, w e r e s e r v e d by
having the f l o w exhaust through the "tee" to a bucket f i l l e d wit h
a drain hose.
The w a t e r e x i t i n g c o u l d e i t h e r be r e t a i n e d i n a
b u c k e t and u s e d t o c h e c k t h e w a t e r f l o w m e t e r s , or a l l o w e d t o
d r a i n back i n t o t h e main w a t e r s u p p l y .
A F a i r b a n k s s c a l e was
u s e d t o w e i g h t h e e x i t i n g w a t e r . L o c a t e d 41 i n c h e s downs trea m
30
m
SYMBOL
A
DESCRIPTION
P r e s s u r e ga ge
D i a p h r a n c h a mb e r
Top h y d r o p h o n e
Bottom h y d ro ph o n e
S e c t i o n of p l e x i g l a s s
pipe
Water i n l e t
Exhaust bucket
Drain to w a te r sup ply
Wa t e r f o l v m e t e r s
Wa t e r pvnap
O r if ic e taps
D ifferential pressure
transducer
Voltaeter
Air compressor
Water s u pp ly
B
C
D
E
F
C
H
I
J
K
L
M
N
0
O S
Air
line
valve
Slide valve
Fl aages
Gate v a lv e
N
D«
3
Globe v al v e
Thermocouple
F ig u re
11. E x p e r i m e n t a l A p p a r a t u s .
31
from t h e " t e e " was a s l i d e
s i t u a t e d behind the v a l v e .
v a l v e w i t h t h e diaphram chamber
The s l i d e v a l v e enabled the diaphram
t o be changed w i t h o u t h a v i n g t o s h u t o f f t h e f l o w .
Four win g
nuts were used to assemble and d is a s s e m b l e the diaphram chamber.
T h i s made f o r q u i c k and e a s y c h a n g i n g o f d ia p h r a m s a f t e r t h e y
were ruptured.
The diaphrams were ruptured by u sin g an a i r l i n e
to
the
pressurize
t o p s i d e o f t h e diaphram u n t i l
it
sending a shock wave propagating down through the f l o w .
line
was
equipped w it h
a pressure
regulator
p r e s s u r e ga u g e t o m o n i t o r t h e b u r s t p r e s s u r e .
burst,
The a i r
and a Bourdon
The a c c u r a c y o f
t h e p r e s s u r e ga u ge was c h e c k e d u s i n g an A m e t e k / M a n s f i e l d and
Green pneumatic dead weig ht model PK p res su re t e s t e r .
An I n ge rs ol l-R an d a i r compressor was used to supply a i r for
the
two-phase
d ia p h r a m s .
flow
and
A series
imm er se d i n
the
of
water
the
air
co p p er
supply
lin e
co ils
barrel
used
in the
and
to
rupture
air
served
line
as
the
were
a heat
e x c h a n g e r t o e n s u r e t h a t b ot h t w o - p h a s e c o m p o n e n t s , w a t e r and
a i r , were at the same temperature.
A d ifferential
air flow rate.
pressure transducer was used t o monitor the
A 12 v o l t Lambda r e g u l a t e d power supply su pplied
v o l t a g e to the p ressure tran sdu cer,
and t h e o u t p u t from the
t r a n s d u c e r was r e a d on a D i g i t e c 268 DC M i l l i v o l t m e t e r .
The
pres sur e transducer measured the pres sur e drop a c r o s s a Meriam
Tang P l a t e O r i f i c e i n s t a l l e d i n Meriam f l a n g e t a p s . The Tang
P l a t e had a c o r e o f .5127 i n c h e s i n d i a m e t e r and w as made of
sta in less
steel.
The d i f f e r e n t i a l
pressure
t r a n s d u c e r was
32
calibrated
using
calcu lation s
a U-tube
can be
seen
Meriam m erc ur y
in Appe nd ix A.
m an o m et er .
The
A Meriam mer cur y
barometer read the s t a t i c pr es s ur e of the a i r upstream from the
o r ific e taps.
A p res s u r e r e g u l a t o r l i m i t e d th e s t a t i c p r e s s u r e of a ir
e n t e r i n g t h e s y s t e m t o a maximum p r e s s u r e o f 18 p s i g . so a s t o
in su re no cracks d eve lo pi ng in the remaining 12 f o o t s e c t i o n of
plexiglass pipe.
A 55 g a l l o n o i l drum was f i l l e d w i t h w a t e r and a F l i n t and
Walling e l e c t r i c pump su p p li ed the w ater t o the two-phase system.
A s e r i e s of four Dwyer Flowmeters were used t o monitor the water
flow rate.
Water was i n j e c t e d i n t o the a i r fl o w s i x in ch es from
t h e b o t t o m o f t h e a p p a r a t u s . The w a t e r e n t e r e d t h e I 1 / 4 in ch
p i p e from f o u r e q u a l l y s p a c e d t a p s around t h e c i r c u m f e r e n c e o f
the pipe. This helped to ensure a f u l l y developed f l o w pa tt er n by
the t e s t
section.
T-type thermocouples were used t o monitor the temperatures
of the a i r , wa ter , and two-phase exhaust ( s e e Figure 11 f o r t h e i r
l o c a t i o n s ) . The thermocouples were wired to a Fluke 2165A D i g i t a l
Thermometer which gave a d i g i t a l readout of the temperature.
Shock w ave m e a s s u r e m e n t s w e r e made by two B r u e l and Kjar
m in ia t u r e hydrophones type 8103.
The h y d ro p h o n es w e r e l o c a t e d
one f o o t a p a r t on o p p o s i t e s i d e s o f t h e p i p e ( s e e F i g u r e 12).
and w e r e mo un ted f l u s h w i t h t h e i n s i d e p i p e w a l l
su rfa ce to
prevent f l o w i n t e r f e r e n c e . The frequency response c h a r a c t e r i s t i c s
f o r ea ch hy d ro p ho n e a r e i n c l u d e d i n A pp en dix C, F i g u r e s 49 and
33
Top
hydrophone
12 inches
F ig u re 12.
H y d r o p h o n e M o u n tin g
34
50.
I t was important to have the hydrophones mounted w i t h t h e i r
a c o u s t i c ce n t er in the pipe w a l l opening to ensure th at the f u l l
signal
s t re n g t h was read.
By mounting the hydrophones properly,
t h i s p rob lem can be a v o i d e d . F a i l u r e t o have t h e h y d ro p h o n es
mounted properly r e s u l t s
recorded.
in d r a s t i c a t t e n u a t i o n in the waveform
This l e d to the s u s p i c i o n th at maybe the two d i f f e r e n t
mounting l o c a t i o n s (top and bottom), might a f f e c t the wave form
recorded.
T h i s was c h e c k e d by making a p l o t o f t h e w a v e f o r m s
recorded by the hydrophones mounted in t h e i r o r i g i n a l l o c a t i o n s ,
and then comparing i t w i t h a p l o t o f the wave forms recorded by
the hydrophones a f t e r t h e i r mounting l o c a t i o n s were interchanged.
The tw o p l o t s w e r e f o r e q u a l s t r e n g t h s h o c k s , and t h e r e s u l t s
p ro ve d t h a t t h e two m o u n t i n g l o c a t i o n s d i d n o t a f f e c t t h e wave
form recorded.
A d u a l t r a c e Gould 1425 D i g i t a l S t o r a g e O s c i l l o s c o p e was
u s ed t o r e c o r d
o scilloscop e
t h e s h o c k w a v e s s e e n by ea ch h yd ro p h o n e.
had
d ig ita l
cap ab ilities
and
a
Zenith
The
Z-100
microcomputer was i n t e r f a c e d w i t h the o s c i l l o s c o p e t o r e c e i v e the
d i g i t i z e d waveform. _ The o s c i l l o s c o p e
s t o r e d 10.25 d i v i s i o n s per
t r a c e . Each d i v i s i o n was d i v i d e d by 100 e q u a l l y s p a c e d d i g i t a l
p o i n t s . A tim e s e t t i n g of I m i l l i s e c o n d per d i v i s i o n was used for
t h i s i n v e s t i g a t i o n . T h i s r e s u l t e d i n a 0.01 m i l l i s e c o n d t i m e
increment between data p o i n t s .
A program f o r d a t a a c q u i s i t i o n MJ2 . C ( s e e A p p en d ix A) was
used
to prompt the o s c i l l o s c o p e to send the d i g i t i z e d data and
35
read the data in t o a d is k f i l e .
The d i s k f i l e c o u l d l a t e r be
op en ed and t h e d a t a m a n i p u l a t e d and a n a l y z e d u s i n g r o u t i n e s t o
perform Fast Fourier tran sf orm s.
Experimental Procedure
Before opening the v a lv e to a llo w the compressed a i r in to
the system,
the s l i d e v a l v e was c l o s e d .
The compressed a i r was
then a ll o w e d t o f l o w i n t o the pipe and the water pump was turned
on.
The a p p r o p r i a t e g l o b e v a l v e was op ene d and w a t e r was f e d
i n t o the a i r stream.
A 5-10 minute warmup period was a ll o w e d to
l e t the f l o w r a t e s t a b i l i z e .
With t h e s l i d e v a l v e s t i l l
closed,
could be opened and a diaphram i n s e r t e d .
t h e diaphram chamber
The diaphrams c o n s i s t e d
of one l a y e r of aluminum f o i l . The burst pressure was maintained
at 14 p s i g .
Once the diaphram was i n s t a l l e d and the chamber c l o s e d , the
s lid e valve
was op en ed .
The t o p
(downstream)
side
diaphram was p r e s s u r i z e d u n t i l the diaphram ruptured.
of
the
The burst
pres sur e was read and recorded from the Bourdon pressure gauge.
As t h e sh ock t r a v e l e d down t h e p i p e t h ro u g h t h e f l o w , t h e
t o p h yd rop ho n e was u s e d t o t r i g g e r t h e o s c i l l o s c o p e .
A 25%
p r e t r i g g e r delay was used t o capture the e n t i r e wave form as seen
by each hydrophone.
The data a c q u i s i t i o n program,
into
the
Z-100
and u s e d
to
MJ2.C (Appendix A), was loaded
command t h e
oscilloscop e.
The
d i g i t i z e d w a v ef o rm from each t r a c e was s e n t t o t h e Z - 1 0 0 , and
36
s t o r e d i n sep arate d i s k f i l e s .
To d e t e r m i n e t h e mass f l o w r a t e o f t h e a i r ,
v o l t m e t e r readi ng was recorded.
the D ig ite c
This reading corresponded to the
pres sur e drop a c r o s s the o r i f i c e ta p s,
and the mass f l o w r a t e of
the a i r was c a l c u l a t e d according to the procedure in Appendix A.
The s t a t i c pres sur e upstream from the o r i f i c e taps was measured
u s in g a Meriam mercury barometer.
The t e m p e r a t u r e s of t h e a i r , w a t e r , and e x h a u s t w e r e re ad
and recorded.
The water l e a v i n g the system through the exhaust
t e e was d i v e r t e d from the drain system and c o l l e c t e d i n a bucket
over s p e c i f i e d i n t e r v a l s of tim e.
The w a t e r c o l l e c t e d d u r i n g
t h e s e i n t e r v a l s was weighed on the Fairbanks s c a l e to check the
Dwyer f lo w m e t e r s and determine the mass f l o w r a t e of
the water.
The a i r q u a l i t y fo r the p a r t i c u l a r two-phase flow was determined
from the mass f l o w r a t e s of the a i r and water.
A program c a l l e d HEAD:C (Appendix A) was used t o add t o the
d i s k f i l e co n t a in in g the d i g i t i z e d wave form a header co n ta in in g
the p e r t i n e n t f l o w c o n d i t i o n s , such as burst p res sur e, f l o w r a t e s ,
etc.
To chan ge t h e f o r m a t o f t h e d a t a i n t h e d i s k f i l e
so t h e
a n a l y s i s r o u t i n e s could be run, CF.C (Appendix A) was used. After
CF.C was
executed,
the
d a t a was r e a d y
t o be a n a l y z e d .
a n a l y s i s r o u t i n e s were w r i t t e n in Fortran computer code,
The
while
a l l of the other programs were w r i t t e n in "C" computer code.
The preceeding procedure was re pea te d t w e n t y - f i v e t im e s at
37
ea ch a i r q u a l i t y w i t h t h e b u r s t p r e s s u r e h e l d c o n s t a n t at 14
psig.
A t o t a l o f e i g h t d i f f e r e n t a i r q u a l i t i e s r a n g i n g from
73.13% t o 100% were t e s t e d along w it h s t i l l a i r .
38
CHAPTER IV
ANALYSIS
The d a t a was r e c e i v e d from t h e Gould o s c i l l o s c o p e i n t h e
form o f two d i g i t i z e d w a v e f o r m s .
stored in a separate d isk f i l e
Each d i g i t i z e d w a v e f o r m was
by t h e program MJ2.C.
l i s t i n g f o r a l l t h e p ro gra m s a r e i n c l u d e d i n A pp en dix B.
the p e r t in e n t
i n f o r m a t i o n such as f l o w r a t e s ,
So urc e
After
tem peratures,
q u a l i t y , e t c . was added t o ea ch d a t a f i l e by HEAD.C and t h e d a t a
was r e f o r m a t t e d by CF.C,
t h r e e F o r t r a n pro gra ms w e r e u s e d t o
analyze the data.
The f i r s t program, AVE.F, would take t w e n t y - f i v e data f i l e s
read by a p a r t i c u l a r hydrophone f o r a p a r t i c u l a r q u a l i t y ,
convert
t h e d i g i t i z e d w a v ef o rm t o t h e v o l t a g e v a l u e s i n d i c a t e d by t h e
oscilloscop e
hydrophone.
and
then
to
the
pressure
values
read
by
the
Next the t w e n t y - f i v e pres sur e p u l s e s were averaged.
T h i s was done i n an e f f o r t t o e l i m i n a t e random n o i s e from t h e
signal.
The r e s u l t i n g averaged p res su re p u ls e was p l o t t e d using
PLOT.BAS w r i t t e n by I ra j Sadighi.
Appendix C c o n ta in s f i g u r e s of
t h e r e s u l t s from AVE.F f o r each hy d ro p ho n e and a i r q u a l i t y .
It
s h o u l d be p o i n t e d o u t t h a t t h e p l o t s a r e p r e s s u r e v e r s u s t i m e ,
and t h e p r e s s u r e p u l s e a p p e a r s n e g a t i v e b e c a u s e f o r a p r e s s u r e
increase,
the hydrophones output a n e g a t i v e v o l t a g e .
The f a s t Fouri er tr a n s f o rm a t io n o f the pressure v a l u e time
39
s e r i e s was performed u s in g ANALM.F.
t r a n s f o r m a t i o n , from t h e
tim e
to
The r e s u l t s o f the Fourier
the
frequency
ou tp utt ed i n the form of magnitude and phase.
also
s t o r e d on a d i s k f i l e .
domain w er e
These r e s u l t s were
PLOT.BAS was u s e d
to
plot
the
magnitude o f the frequency spectrum.
By e x a m i n i n g t h e f r e q u e n c y m a g n i t u d e s p e c t r u m , a new f i l e
was c r e a t e d t o c l e a n up t h e f r e q u e n c y p h as e s p e c t r u m .
m ethod^ en ta iled creating
one's.
a new f i l e
c o n s i s t i n g of zero's and
Wherever a frequency magnitude had a " s i g n i f i c a n t " v a l u e ,
a one was
p laced
at
that
frequency
index
(wave number).
Otherwise a zero was placed at the frequency index.
used
T h is
to
determ ine
" significan t"
frequency
valu es
The method
w ill
be
d es cr ib ed i n the chapter on r e s u l t s .
MULT.F was used t o m u l t i p l y t h i s new f i l e w i t h t h e frequency
phase spectrum.
This cleaned up the phase spectrum so th at the
p h a se chan ge t h a t o c c u r r e d b e t w e e n t h e two h y d r o p h o n e s f o r a
p a r t i c u l a r frequency could be determined.
For a p r e s s u r e p u l s e p r o p a g a t i n g a d i s t a n c e , x, t h ro u g h a
medium in t i m e , t , the v e l o c i t y i s V = x / t . A d i s c r e t e frequency,
f , t r a v e l i n g in t h i s
p r e s s u r e p u l s e c o u l d m a t h e m a t i c a l l y be
d es cr ib ed by:
P = A sin(2irf + (j)^)
where
P = pressure
A = amplitude
= phase
f = frequency
Figure 13 c o n t a in s a p l o t o f t h i s f u n c t i o n .
40
A s i n ( 2 i r f + <(>,)
0 R ad ian s
F ig u re
F ig u re 14.
Phase
D ia g r a m
P h a s e Two D ia g r a m
41
As
the
pressure
p u lse
moves
through
the m edia,
i n d i v i d u a l f r e q u e n c i e s may e x p e r i e n c e a ph ase s h i f t .
the
The new
mathematical model:
P = A s i n ( 2 v f + Iji2 )
was i l l u s t r a t e d in f i g u r e 14.
The change in phase between the s i g n a l s in Figures 13 and 14
i s (^i - $ 2 ) ~ ~ 7r/ 4 . T h i s change i n phase was t h e r e s u l t o f a
chan ge
in
the
propagation
rate
for
the
d iscrete
frequency
component, f . The f o l l o w i n g procedure d e s c r i b e s how to determine
t h e new v e l o c i t y
f o r t h e f r e q u e n c y co m po ne nt ,
f . A pp en dix D
contains
calcu lation s
the
sample
for
calcu latin g
speed
of
propagation f o r i n d i v i d u a l fr e q u e n c ie s .
First,
p h a se
c a l c u l a t e the tim e de lay , t , caused by the change in
that
occurs
w hile
the
frequency
component
travels
a
d i s t a n c e , x.
T = U 1 -<f'2 ) / ( 2irf)
The t i m e
required
for
the
pressure
pulse
to
propagate
t h r o u g h t h e same d i s t a n c e , x , was t . T h e r e f o r e , t h e t o t a l t i m e
f o r t h e f r e q u e n c y component t o t r a v e l a d i s t a n c e , x , was ( t + t ) .
The speed of propagation f o r f was x / ( t + t ) .
By knowing the change in phase that occurred between the two
hydrophones,
the frequency i t
between the hydrophones,
occurred at,
and t h e d i s t a n c e
the change in s p e c t r a l
sonic v e lo c ity ,
C, s o m e t i m e s r e f e r r e d t o as p h ase v e l o c i t y , f o r t h a t f r e q u e n c y
was determined.
C = I / ( t + t)
42
where
x = d i s t a n c e between hydrophones was I f o o t
t = !/"group" v e l o c i t y
T = Ciji1 - ij>2 ) / ( 2irKAf)
K = frequency index or wave number
Af = frequency i n t e r v a l between data p o i n t s , sampling r a t e
Af was determined by the time increment between data p oi n t s
in the d i g i t i z e d data f i l e and the number of data p o i n t s used in
the f a s t Fourier tra n sf o rm a tio n . Although the o r i g i n a l data f i l e s
contained 1024 d i g i t i z e d data p o i n t s ,
u s e d so t h a t
only 512 data p o i n t s were
t h e p r e s s u r e p u l s e w o u l d be i s o l a t e d
from t h e
p r e t r i g g e r delay and the f l a t response f o l l o w i n g the p u ls e .
pressure
data f i l e
p r e t r i g g e r d el ay ,
(see
pressure
15)
co n sists
o f : I)
A 25%
the f l a t response at the beginning of the p l o t ,
2) The pressure p u ls e ,
sligh t
Figure
The
the s t e e p n e g a t i v e response f o l l o w e d by a
in crease
and f l a t
response,
and 3) Ano th er
pressure p u ls e caused by the r e f l e c t i o n o f the o r i g i n a l burst on
the diaphram chamber.
The tim e window ( s e e Figure 15) f o r u s in g 512 data p o i n t s was
5.12 m i l l i s e c o n d s .
The same t i m e window was u s e d
for
both
h y d r o p h o n e s so t h a t t h e same p a r t o f t h e p r e s s u r e p u l s e s i g n a l
would be analyzed from each hydrophone.
The f r e q u e n c i e s r a n g e d from 0 H e r t z (Hz) t o 1 0 0 , 0 0 0 Hz in
increments o f 195.31 Hz. The upper l i m i t on the frequency domain,
in
th is
case
1 0 0 , 0 0 0 Hz,
is
commonly known a s t h e N y q u i s t
43
TPI:
■Tim e window-
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v>
LU
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n
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h
[-
W
U
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IL
Top H y d ro p h o n e
,-.MVV-"' '''v AfAZVvv^i ' A ........
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use:]
«— Tim e w i n d o w -------*
LL
A
Ti
I
-
LU
L
A
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D
V)
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QC
T
J
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r
L
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I ;
I/
I'
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I TE !ffliEU B o tto m H y d r o p h o n e
F i g u r e 1 5 . Tim e Window f o r A n a l y s i s
44
f req u en cy -^ .
Appendix C
c o n t a in s graphs o f a normalized v e l o c i t y versu s
freq u en cy index fo r each a i r q u a l i t y .
The n o r m a l i z e d v e l o c i t y
was d e f i n e d as t h e " s p e c t r a l " v e l o c i t y d i v i d e d by t h e "group"
velo city .
The s p e c t r a l v e l o c i t y r e f e r s t o t h e v e l o c i t y
of a
p a r t i c u l a r f r e q u e n c y co m p o n en t, a l s o r e f e r r e d t o a s t h e phase
v elocity.
leading
The group v e l o c i t y
ed g e
of
t h e w av e.
r e fe r r e d to the v e l o c i t y
refers
to
In r e a l i t y ,
the v e l o c i t y
of
the
t h e g rou p v e l o c i t y
o f t h e h i g h e s t f r e q u e n c y component
cont aine d i n the wave as was d i s c u s s e d by Sbankara e t a l . ^
The
reason the group v e l o c i t y was used to n orm ali ze the v e l o c i t y was
t h a t t h e o r e t i c a l l y a l l o f t h e s h o c k w a v e s p ro d u ce d w e r e o f t h e
same s t r e n g t h and s h o u l d ha ve t h e same f r e q u e n c y s p e c t r u m s .
Therefore the same frequency would be propagating as the leadi ng
edge
in a l l
of the
test
runs.
T h is w ould g i v e
denominator between a l l of the t e s t runs.
v e l o c i t y may vary between t e s t runs,
a common
Even though the group
the v a r i a t i o n s were caused
by i n c r e a s i n g or d ec re as in g the m ixt ur e f l o w r a t e s which would be
r e f l e c t e d in the a i r q u a l i t y .
Als o a graph o f the normalized v e l o c i t y v e r s u s a i r q u a li t y
fo r seven d i f f e r e n t f r e q u e n c i e s was made t o pres en t a d i f f e r e n t
v ie w of the data.
45
CHAPTER V
RESULTS
To v e r i f y th at the apparatus and equipment were a l l working
properly,
s h o ck
introduced
in to
waves
still
at
air.
a
constant
burst
pressure
were
The s p e e d o f p r o p a g a t i o n o f
the
r e s u l t i n g pres sure p u ls e was determined from the two hydrophone
re c or d in gs and compared w i t h the t h e o r e c t i c a l l y c a l c u l a t e d speed
of
propagation
for
the
p u lse.
The r e s u l t s
of
the
son ic
v e l o c i t i e s w e r e w i t h i n one p e r c e n t o f ea c h o t h e r and i n d i c a t e d
th at the equipment and apparatus were working properly.
To
determ ine
which
values
of
the
" s i g n i f i c a n t " , frequency magnitude diagrams o f
still
air
(Figure 16) were cons tru cte d.
frequencies
a
were
shock wave in
The frequency magnitude
d i a g r a m s f o r a l l o f t h e t e s t ru n s w e r e i n c l u d e d i n A pp en d ix C.
Prom inent
p oin ts
that
were
maximum s when compared w i t h
n e i g h b o r i n g v a l u e s w e r e g i v e n a v a l u e o f o n e, w h i l e t h e r e s t o f
th e m agnitudes were a s s ig n e d the v a lu e of zero.
A total
t h i r t e e n " s i g n i f i c a n t " f r e q u e n c i e s ranging from 390.6 Hz
Hz were
of
t o 8789
used. The frequency magnitude diagrams were e s s e n t i a l l y
z e r o f ro m 9000 Hz on o u t t o t h e N y q u i s t f r e q u e n c y o f 100000 Hz.
T h i s e n s u r e d t h a t no "wrap-around" or a l i a s i n g o f f r e q u e n c i e s
g r e a t e r th a t the Nyquist frequency was occurring.
"Wrap-around" o c c u r s when f r e q u e n c i e s g r e a t e r
than the
46
.25
Sftl
MAGNITUDE
r
r
.15
.CS
Top H y d ro p h o n e
2V
Sfi2
36
46
FREQUENCY INDEX
56
66
70
MAGNITUDE
B o tto m H y d ro p h o n e
FREQUENCY INDEX
F i g u r e 16
F r e q u e n c y M a g n i t u d e s i n S t i l l A i r , Top and
B o tto m H y d r o p h o n e s .
47
Nyquist frequency are pres en t in the s i g n a l being analyzed.
The
r e s u l t s from the f a s t Fourier t r a n s f o r m a t i o n only g i v e magnitudes
for
frequencies
up t o
the v a lu e
of
the
Nyquist
frequency.
F r e q u e n c i e s g r e a t e r t h a n t h e N y q u i s t f r e q u e n c y "wrap-around"
t h e z e r o f r e q u e n c y and b e g i n a d d in g on t o t h e m a g n i t u d e s o f t h e
lower f r e q u e n c i e s causing a l i a s i n g .
A f t e r t h e p ha se f i l e was m u l t i p l i e d by t h i s f i l e o f z e r o ' s
and o n e ' s , t h e p r e s s u r e p u l s e was r e c o n s t r u c t e d t h r o u g h a f a s t
F o u r i e r t r a n s f o r m a t i o n back t o t h e t i n i e
co n t a in s the o r i g i n a l pres sur e
domain.
F i g u r e 17
p u ls e and the r e c o n s t r u c t i o n fo r
t h e t o p h yd rop hon e r e a d i n g i n s t i l l a i r . The d i f f e r e n c e s i n t h e
p u l s e s a r i s e from t h e f a c t t h a t a f i n i t e number o f f r e q u e n c i e s
w e r e u s e d i n t h e r e c o n s t r u c t i o n i n s t e a d o f t h e i n f i n i t e number
th at the wave i s a c t u a l l y composed o f .
The a n a l y s i s t e c h n i q u e f o r c a l c u l a t i n g t h e s p e c t r a l s o n i c
v e l o c i t y from the change in phase f o r a p a r t i c u l a r frequency was
p e r f o r m e d on t h e s t i l l a i r d a t a t o v e r i f y t h e p r o c e d u r e . F i g u r e
18 shows the r e s u l t s of the normalized v e l o c i t y v e r s u s frequency
index
in
still
air.
The
data
in d ica te
a straigh t
line
at
approximately a v a l u e of one f o r the normalized v e l o c i t y at a l l
v a l u e s of the frequency index. This i s what i s exp ected s i n c e no
change i n the speed of propagation of the pressure p u ls e would be
exp ected in s t i l l a i r .
The r e s u l t s
for
the
two-phase
data fo r
the n orm alized
v e l o c i t y v e r s u s frequency index i n d i c a t e a gen eral p a t t e r n l i k e
t h e one i l l u s t r a t e d i n F i g u r e 19. At l o w e r f r e q u e n c i e s ( l o w e r
48
SAl
o
e
: LU
U
LL
v v :
i
4
'I
'
5
-.5
Z'
L
i"'
I ,y,
O r ig in a l P u lse
U
LL
-
1.5
TlHE USES]
SAl
0)
.5
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IL
M, /
. W
A1
r
W
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a v,
! LL
'
1
4
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i/i
u
LL
CL
-.5
v
~ y
' TT
\ /VvW
'
R e c o n s tru c te d P u lse
-I
TlHE IibSECI
F ig u re 17.
O r i g i n a l and R e c o n s tr u c te d P r e s s u r e P u ls e f o r
Top H y d r o p h o n e i n S t i l l A i r , B u r s t P r e s s u r e =
14 p s i g .
I
I
I
l
l
I
l
I
U n c ertain ty
Band
-
-
L
I
I
O O
Oj
I
i
I
i
I
,1
O
O O
I
i
O
O
I .00
— ,
-
I O
I
I
I .0 4
-
i
SpectraI Velocity
I
I .O S
/
Gr oup V e l o c i t y
49
.9 6
-
-
-
-
.9 2
Frequency,
I
5
I
I
I
15
l
l
25
Frequency
F ig u re 18.
t
=
1 9 5 . 3 1 *N
l
l
35
l
45
Index, N
N o rm a liz e d V e l o c i t y v e r s u s F re q u e n c y Index
fo r S t i l l A ir.
!
!
I
!
!
I
!
r
U n c ertain ty
Band
\
I .04
—
-------
■ ■■
I
--------------- ---- --- ---
~
I'
I
O
I
=
^
I
f
I
I
O
.96
I
■ —^
I
—■ ■ — ' ■
I
O
I .00
°
O
I
Velocity
Spectral
!
I .08
/
Gr oup V e l o c i t y
50
.92
_0
Frequency,
I
5
I
I
I
15
l
l
F ig u re 19.
l
25
Frequency
I 9 5 . 3 1 *N
l
35
Index,
l
45
N
N o rm a liz e d V e l o c i t y v e r s u s F re q u e n c y In d e x
f o r T w o - p h a s e F lo w , A i r Q u a l i t y = 7 6 .3 3 % ,
B u r s t P r e s s u r e = 14 p s i g .
51
values
of
the freq u en cy in d ex),
d e c r e a s e d more t h a n
frequencies.
the
the s p e c t r a l
spectral
sonic v e l o c it y
sonic v e l o c i t y
at
higher
The normalized v e l o c i t y had v a l u e s l e s s than one at
lower v a l u e s of the frequency index and a s y m t o t i c a l l y approached
one as the frequency index in cr ea se d.
Appendix C c o n t a in s p l o t s
of. the no rmali zed v e l o c i t y v er s u s frequency index f o r a l l of the
t e s t runs.
Figure
20 p r e s e n t s
the
resu lts
in
a d ifferen t
format.
Normalized v e l o c i t y v e r s u s a i r q u a l i t y was p l o t t e d as a f u n c t i o n
of frequency.
to
Seven d i f f e r e n t f r e q u e n c i e s ranging from 390.6
Hz
8789 Hz were chosen from the t h i r t e e n f r e q u e n c i e s a v a i l a b l e .
A l l t h i r t e e n f r e q u e n c i e s w e r e n o t i n c l u d e d i n F i g u r e 20 so t h e
graph would not become c l u t t e r e d and m e a n in gl e ss . The u n c e r t a i n t y
band r e f e r s to the accuracy l i m i t a t i o n s o f the d i g i t i z e d waveform
r e c e i v e d from t h e o s c i l l o s c o p e . The graph i n d i c a t e s t h a t t h e
low er a ir q u a l i t i e s cause a g r e a t e r d ecre a se in th e s p e c t r a l
s o n i c v e l o c i t y t h a n t h e h i g h e r a i r q u a l i t i e s . In c o m p a r i s o n t o
the s i n g l e phase ( s t i l l
air,
Figure 18) s p e c t r a l s o n ic v e l o c i t y ,
as the a i r q u a l i t y was decreased,
of
the
pressure
pulse
we re
the lower frequency components
slow ed
more
than
the
higher
f r e q u e n c i e s . T h i s p a t t e r n was a l s o o b s e r v e d i n t h e g r a p h s of
no rmali zed v e l o c i t y v e r s u s frequency index f o r each two-phase a i r
q u a l i t y t e s t e d ( s e e Figures 39-47).
The r e s u l t s of Figure 40, two-phase fl o w wit h an a i r q u a l i t y
o f 94.89%, do n o t a g r e e w i t h t h e r e s t o f t h e r e s u l t s . The l o w e r
f r e q u e n c i e s show a v e l o c i t y i n c r e a s e a s op p os e d t o a v e l o c i t y
j e cIr a I V e Io c ity /
Group Ve l o c i t >
52
0 £=3 9 0 . 6 Hz
□ £=11 71.9 Hz
<> £=2 5 3 9 .1 Hz
# £=4 2 9 6 . 7 Hz
1 £=6 6 4 0 . 6 Hz
♦ £=7 81 2.5 Hz
X £=8 78 9.1 Hz
Uncertainty
Band
1.10
---- H -
I .00
_ X
.75
.80
.85
Ai r
F ig u re 20.
.90
.95
1.00
Quality
Norm alized V e lo c it y v e r s u s A ir Q u a lity as
a F unction of Frequency.
53
d ecrease observed
i n t h e r e s t o f t h e d a t a . The r e a s o n f o r t h i s
i s unknown, and th e s i t u a t i o n m e r i t s f u r t h e r i n v e s t i g a t i o n .
No d i r e c t comparison o f th e s e exp erim en tal r e s u l t s and th ose
of
p rev io u s
in v e s tig a tio n s
flo w
reg im es,
c a n be made b e c a u s e
range o f
q u a litie s,
of
th e
d iffe r e n c e s
in
range of
f r e q u e n c ie s ,
and components used in th e i n v e s t i g a t i o n s . However,
some g e n e r a l remarks can be made.
Mecredy and H am ilton-3u observed f o r one-component tw o-phase
flo w , th a t as th e v o id f r a c t i o n d e c r e a se d , th e s p e c t r a l so n ic
v e lo c ity
a l s o decreased.
No c o n c lu s io n s as to which f r e q u e n c ie s
slow ed f a s t e r were a v a i l a b l e .
Z ink and D e l s a s s o
' t e s t e d s o l i d p a r t i c l e s suspended in a
g a s . They fo u n d t h a t t h e s p e c t r a l s o n i c v e l o c i t i e s f o r lo w e r
f r e q u e n c ie s d ecreased more than th e s p e c t r a l so n ic v e l o c i t i e s for
h ig h e r f r e q u e n c ie s a t one p a r t ic u l a r m ixtu re q u a l i t y .
54
CHAPTER VI
CONCLUSIONS
This i n v e s t i g a t i o n chose to use an a ir - w a t e r (two-component)
tw o-p h a se flo w
t o a v o id e f f e c t s o f i n t e r p h a s e m ass t r a n s f e r
(ev a p o ra tio n or c o n d e n s a tio n ) t h a t o c c u r i n o n e -c o m p o n e n t t w o p h a se m i x t u r e s . T h is s t u d y was a l s o l i m i t e d t o f l o w r e g i m e s o f
th e a n n u la r -m is t and m is t p a tte r n s so no i r r e g u l a r i t i e s would be
c a u s e d by a change i n t h e f l o w
reg im e.
E ig h t a i r q u a l i t i e s
ranging from 73.13% t o 100% were t e s t e d .
T h i r t e e n f r e q u e n c i e s r a n g in g from 3 9 0 .6 H e r tz (Hz) t o 8789
Hz
were used to d e s c r ib e the p ressu r e p u ls e propagating through
t h e t w o - p h a s e m e d ia . The s p e c t r a l ( p h a s e ) s o n i c v e l o c i t i e s f o r
each o f t h e s e was measured f o r each a i r q u a l i t y t e s t e d .
As th e a i r q u a l i t y was d ecreased ,
t h e l o w e r f r e q u e n c y c o m p o n e n ts s l o w e d
th e s p e c t r a l v e l o c i t y at
m ore th a n t h e s p e c t r a l
v e l o c i t y at th e h ig h er frequency components in comparison t o the
s p e c t r a l v e l o c i t i e s measured in s t i l l a ir .
The s p e c t r a l v e l o c i t i e s
for
a ll
th e f r e q u e n c ie s approached
the corresponding s t i l l a ir s p e c t r a l v e l o c i t y as th e a i r q u a lit y
approached 100%.
The a i r q u a l i t y o f 94.89% did not f o l l o w th e tren d s observed
in the r e s t o f the d ata, and f u r th e r study at t h i s a ir q u a l i t y i s
recommended t o i n v e s t i g a t e t h i s phenomenon.
55
The a n a l y s i s tech n iq u e used in t h i s i n v e s t i g a t i o n i s unique
in th e area of stu d y in g frequency dependence o f a c o u s t i c v e l o c i t y
in tw o-phase f lo w s . I t recommended th a t f u r th e r r e fin e m e n t o f the
t e c h n i q u e and s t u d y be done i n t h e a r e a s o f i n c r e a s i n g t h e a i r
q u a l i t y range and expanding th e frequency spectrum.
56
REFERENCES
57
REFERENCES CITED
1. H i j i k a t a , K., M o ri, Y., N a g a s a k i , T., and N akagawa, M.,
"Structure o f Shock Waves in Two-phase Bubble Flows", Twophase Flow Dynamics. Japan-US Seminar, 1979, pp. 239-254.
2. B o u l d i n g , K.E, " S c ie n c e : Our Common H e r i t a g e " , S c i e n c e . V o l.
207, No. 4433, Feb. 1980, pp. 8 3 1 -8 3 6 .
3.
W a l l i s , G.B., " R e v i e w - T h e o r e t i c a l M odels o f G a s - L iq u id
Flows", Journal o f F lu id s E n gin eerin g. Vol. 104, Sept. 1982,
pp. 279-283.
4.
McQuillan, K.W. and W h alley, P.B., "Flow P a tter n s in V e r t ic a l
T w o -p h a se Flow", I n t e r n a t i o n a l J o u r n a l o f M u l t i p h a s e F l o w .
V o l. 1 1 , No. 2, 1 9 8 5 , pp. 1 6 1 - 1 7 5 .
5.
H e w i t t , G.F. and W a l l i s , G.B., " F lo o d in g and A s s o c i a t e d
Phenomena in F a l l i n g F ilm Flow i n a Tube", AERE-R 4 0 2 2 , 1963
( u n p u b lis h e d ) .
6.
Mukherj e e , H. and B r i l l , J.P., "Em pirical Equations to P re d ict
F low P a t t e r n s i n T w o-P h ase I n c l i n e d Flow", I n t e r n e t i o n a l
Journal o f M ultiphase Flow , Vol. 11, No. 3, 1985, pp. 299-315.
7.
Mart i n d a l e , W.R. and S m it h , R.V., " P r e s s u r e Drop and S o n ic
V e l o c i t y i n S e p a r a t e d T w o -p h a se Flow ", T r a n s a c t i o n s o f t h e
AS ME. Vol. 102, March 1980, pp. 112-114.
8 . S u t r a d h a r , S.C., Y o s h id a , H., and Chang, J .S ., "Shock Wave
Propagation in a H o r iz o n t a l S t r a t i f i e d G a s - L iq u id S y ste m i n
S t r a i g h t and "Tee" T u b es, Shock Tubes and Waves", 1 4 th
I n t e r n a t io n a l Symposium, Aug. 1 9 -2 2 , 1983, pp. 437-444.
9.
E v a n s , R.G., G o u s e , S.W. J r . , and B e r g l e s , A.E., " P r e s s u r e
Wave Propagation in A d ia b a tic Slu g-A nn u lar-M ist Two-Phase GasLiquid Flow", Chemical E ngineering S c i e n c e . Vol. 25, 1970, pp.
569-582.
10.
H i n k l e , W.D., Sc.D. T h e s i s , N u c le a r E n g i n e e r i n g D e p t ., M.I.T.,
May 1967.
11. R adovs k i i , I . S ., " P r o p a g a t io n S p e e d s f o r P e r t u r b a t i o n s i n a
Flow o f T w o -p h a se M ix tu r e " , T r a n s l a t e d from T e o l o f i z i k a
V v so k ik h T e m p e r a t u r e , V o l . 1 5, No. 2, M ar-Apr. 1 9 7 7 , pp. 3 5 9 361.
58
REFERENCES CITED (c o n tin u e d )
12.
D obran 5 F., "An A c c e l e r a t i o n Wave Model f o r t h e Speed o f
Propagation o f Shock Waves in a Bubbly Two-phase Flow", ASMEJSME Thermal E ngineering J o in t Conference P r o c e e d in g s. V ol. I,
1 9 8 3 , pp. 3 - 9 .
13.
Akagaw a, K., S a k a g u i c h i , T., F u j i i , T., F u j i o k a , S ., and
Sugiyama, M., "Shock Phenomena in Air-W ater Two-Phase Flow",
M ultiphase T ran sp ort, Vol. 3 , Hemisphere, New York, 1980, pp.
1673-1694.
14. M i y a z a k i, K., F u j i i - E , Y., and S u i t a , T., "Shock P u l s e s in a
Low P ressu re Steam-Water Medium", Journal o f Nuclear S c ie n c e
and T e c h n o l o g y , V o l. 11, 1 9 7 4 , pp. 1 9 9 - 2 0 7 .
15.
Cheng, L.Y., Drew, D.A., and L a h e y , R.T. J r . , "An A n a l y s i s o f
Wave D is p e r s io n , Sonic V e lo c i t y and C r i t i c a l Flow in Two-Phase
Flow", T op ical Report, J u ly 1983.
16.
C r e s p o , A., "Sound and Shock Waves i n L i q u i d s C o n t a i n in g
B u b b le s " , The P h y s i c s o f F l u i d s , V o l. 12, No. 1 1 , 19 6 9 , pp.
2274-2282.
17. H enry, R.E., G rohn es , M.A., and F a u s k e , H.K., " P r e s s u r e P u ls e
Propagation i n Tw o-Ph ase One- and Two-Component M ix tu r e s " ,
ANL-7792, 1971.
18.
Nguyen, D.L., W in t e r , E.R.F., and G r e i n e r , M., " S on ic
V e l o c i t y in Two-Phase Systems", I n t . J. M ultiphase Flow, Vol.
7 , 19 8 1 , pp. 3 1 1 - 3 2 0 .
19.
Van Wi j n g a a r d e n , L., "Sound and Shock Waves i n Bubbly
L iq u id s " , C a v i t a t i o n and I n h o m o g e n e t i e s i n U n d e r w a t e r
A c o u s t ic s ,
Proceed in gs o f th e F i r s t I n t e r n a t io n a l Conference,
J u l y 9 - 1 1 , 1 9 7 9 , pp. 1 2 7 - 1 4 0 .
20. L e v i c h , V.G., " P h y s i c o c h e m i c a l H yd ron om ics" , P r e n t i c e H a l l ,
1962.
21.
N a k o r y a k o v , V.E., P o k u s a e v , B.G., and S h r e i b e r , I . R.,
" P r e s s u r e Waves i n a L iq u id w i t h Gas or Vapour B u b b les" ,
C a v i t a t i o n and I n h o m o g e n e t i e s i n U n d er w a ter A c o u s t i c s ,
P roceedings o f th e F i r s t I n t e r n a t io n a l Conference, J u ly 9-11,
1 9 7 9 , pp. 1 5 7 - 1 6 3 .
22. C a m p b e ll, I . J . £and P i t c h e r , A.S., "Shock Waves i n a L iq u id
Containing Gas Bubbles", Proc. Royal S o c ie t y London, S e r i e s A,
2 43 , 19 5 8 , pp. 5 3 6 - 5 4 5 .
59
REFERENCES CITED (c o n tin u e d )
23.
Akagawa, K., F u j i i , . T., Ho, Y., H i r a k i , S ., K i t a n o , T., and
Tsubokura, S., "Shock Phenomena in a One-Component Two-Phase
Bubbly Flow", Thermal H yd rau lics o f Nuclear R e a c t o r s , Vol. I ,
J an . 1 9 8 3 , pp. 2 4 6 - 2 5 1 .
24.
Malykh, N.V. and Ogorodnikov, I .A., "Dynamics o f a Liquid w ith
Gas B u b b le s D u rin g I n t e r a c t i o n w i t h S h o r t L a r g e - A m p lit u d e
P u l s e s " , C a v i t a t i o n and I n h o m o g e n e t i e s i n U n d e r w a t e r
A c o u s t i c s , P roceedings of th e F i r s t I n t e r n a t io n a l Conference,
J u l y 9 - 1 1 , 1 9 7 9 , pp. 1 6 4 - 1 7 6 .
25.
Moody, F.J., "Interphase Thermal and Mechanical D i s s i p a t i o n of
A c o u s t i c D i s t u r b a n c e s i n G a s - L iq u id M ix tu r e s " , ASME-JSME
Thermal E ngin eerin g J o in t Conference Proceedings Vol. I , 1983,
pp. 1 1 - 1 7 .
26.
S h a n k a ra , J ., S m it h , R.V., and A r a k e r i , V.H., " S o n ic V e l o c i t y
i n T w o -P h a se F lo w s - A R eview " , D i v i s i o n o f M e c h a n ic a l
S c ie n c e s Indian I n s t i t u t e of S c ie n c e , January, 1985.
27.
Zink, J.W. and D e ls a s s o , L.P., "Attenuation and D is p e r s io n of
Sound by S o l i d P a r t i c l e s Suspended in a Gas", The Journal of
t h e A c o u s t i c a l S o c i e t y o f A m e r ic a , V o l. 3 0 , 1 9 5 8 , pp. 7 6 5 771.
28.
M e c r e d y , R.C. and H a m i lt o n , L .J ., "Speed A t t e n u a t i n g o f
A c o u s t i c W aves i n T w o - p h a s e , T w o - c o m p o n e n t M ed ia " ,
P r o c e e d i n g s o f t h e 6 t h S o u t h e a s t e r n S em in a r on Therm al
S c ie n c e s , A p r il, 1970, pp. 301-311.
29.
Karplus, H.B., "The V e lo c i t y o f Sound in a Liquid Containing
Gas B u b b le s " , Armour R e s e a r c h F o u n d a t io n , COO-248, Ju n e,
1985.
30.
M e c r e d y , R.C. and H a m i l t o n , L . J . , "The E f f e c t s o f
N onequilibrium Heat and Mass, and Momentum T ran sfer on Twop h a se Sound Speed", I n t e r n a t i o n a l J o u r n a l o f H eat and Mass
T ran sfer, Volume 15, 1972, pp. 61-72.
31.
E n g la n d , W.G., F i r e y , J.C., and Trapp, O.E., " V e l o c i t y o f
Sound M ea su rem en ts i n Wet Steam ", i/E C P roc. D es . Dev. 2 ( 3 ) ,
1 9 6 3 , pp. 1 9 7 - 2 0 2 .
32.
Kokernak, R.P. and Feldman, C .L ., " V elo city of Sound in TwoPhase Flow o f R -I 2", ASHRAE J o u r n a l. Feb. 1972, p p .3 5 -3 8 .
60
REFERENCES CITED (c o n tin u e d )
33.
Rehman, F., "Sonic V e lo c i t y in Two-phase Flow as a Function
o f F req u en cy" , M a s t e r ' s T h e s i s , W i c h i t a S t a t e U n i v e r s i t y ,
1983.
3 4. R a m ir e z , R ob ert W., "The FFT, F u n d a m e n ta ls and C o n c ep ts" ,
P r e n t i c e - H a l l, I n c . , Copyright 1985, p. 85.
\
61
APPENDICES
)
)
)
)
)l
62
APPENDIX A
FLOWMETER CALCULATIONS
P la t e Diam eter, d = .5127 in c h e s
I n s id e Pipe Diameter, D = 1 . 0 0 inch
A = d (830-5000 3 +
£ = d/D = .5127
= Rq/ 3
9000 S2 - 4200 g3 + 530/ ( D ) ^ 2)
= .5 1 2 7 ( 8 3 0 - 5 0 0 0 ( .5 1 2 7 ) + 9 0 0 0 ( .5 1 2 7 ) 2- 4 2 0 0 ( .5 1 2 7 ) 3 + 5 3 0 / 1 .0 )
= 3 0 5.68
Ke= .5 9 9 3 + .0 0 7 /D + (.3 6 4 + .0 7 6 / (D)1 / 2 ) ^ + . 4 ( 1 . 6 - l / D ) 5( 0 . 0 7 + 0 5 / D - 6 ) 5 / 2
- ( 0 . 0 0 9 + 0 . 0 3 4 / D ) ( 0 . 5 - g ) 3 /2 + (65/D 2 + 3 ) ( & - 0 .7 ) 5 /2
= . 5 9 9 3 + . 0 0 7 / l + ( . 3 6 4 + . 0 7 6 / l ) ( . 5 1 2 7 ) 4+ . 4 ( 1 . 6 - l ) 5( . 0 7 + . 5 - . 5 1 2 7 ) 5 /2
- ( . 0 0 9 + . 0 3 4 K . 5 - . 5 1 2 7 ) 3 / 2 + ( 6 5 / l 2+ 3 ) ( . 5 1 2 7 - . 7 ) 5/2
= .6367
K0 = Ke
106d
— ---------- = .6367
106d+15A
106 ( .5127)
— -------------------------------1 0 ° ( .5 1 2 7 )+ 1 5 (3 0 5 .6 8 )
= .6311
K = K0 (l+A/Rd)=K0 (l+AG/R0 ) = .6 3 1 1 (1 + 3 0 5 .6 8 ( .5 1 2 7 ) /R D
= .6311 + 9 8 .908/Rp
Dpv
Dv
Choose a v a lu e f o r Rp and c a l c u l a t e K from Rp= ------- = —
vi
- Table I .
Reynolds Number v s . K.
Rr,
—JJ
K
IO3
5x103
IO4
2 x l0 4
5x104
SxlO4
IO3
IO6
.730
.651
.641
.636
.633
.632
.632
.631
v
63
From Mechanical Measurements^^, Table D .4,
p . 679, fo r a ir at
60 F,
lbf
s
il = .374 x 10™° ----f t 2-
(■ I b f - S
70 F, y = .379 x 10™b ----ft2
(■ I b f - S
80 F, -u = .385 x 10“b ----- ft2
,
90 F,
I b f -S
u = .390 x 10"b ----- —
ft2
I inch o f Hg = .4898 p s i at 60 F .
From c a l i b r a t i o n
of o r i f i c e
flo w m eter,
u sin g a C u r v e fit
program, th e f o ll o w i n g r e l a t i o n was d erived :
Change in P r e s s u r e ( p s i) — >
P = -5.8654+ 10274 V
where V i s v o l t s .
t h e d a t a c o l l e c t e d t o d e r i v e t h i s e x p r e s s i o n i s l i s t e d in
ta b le 2.
From Mechanical Measurements, mass f lo w r a t e , W, i s
W=KA2Y [2gc P1 (P1- P 2 ) ] 1/2
where,
Y, the expansion f a c t o r , i s — >
Y=I - (A1+ . 35^) --------kPi
A2 = ir(d /2)2 = ir(. 5 1 2 7 /2 ) 2 = .2 0 6 5 i n 2 = . 0 0 1 4 f t 2
Ibm-ft
Sc
32.17
Ib c-s 2
64
TABLE 2 .
V oltage
(v o lts)
A ir flowm eter c a l i b r a t i o n .
Change in P ressure
(p si)
( in ch es o f Hg)
5.68
0 .0
0 .0
5 .9 0
0 .4
.1959
6 .1 2
0 .8
.3918
6 .4 3
1 .4
.6857
6 .5 4
1.8
.8816
6 .6 7
2 .0
.9795
6.86
2 .4
1 .1754
7.57
3 .9
1.9101
7 .7 8
4 .3
2 .1060
8 .0 6
4 .9
2.3999
7 .9 8
4 .7
2.3019
9 .5 3
7 .9
3 .8 6 9 2
8.71
6 .4
3 .1 3 4 5
9 .0 1
7 .0
3 .4 2 8 4
8 .1 0
5.1
2.4978
5.67
0 .0
0 .0
65
Pl
P1
RT1
lb f-ft
R = 53.34 ---------1V R
A computer program was used to s o lv e fo r the mass f lo w r a t e ,
W, o f t h e a i r .
The program prom p ted th e u s e r t o
in p u t t h e
v o lt m e t e r read ing which was converted to th e p ressu r e drop a cro ss
t h e o r i f i c e t a p s ; t h e a i r t e m p e r a t u r e and p r e s s u r e w h ic h w ere
u s e d t o c a l c u l a t e t h e a i r d e n s i t y ; and t h e a i r v i s c o s i t y w h ich
was used to c a l c u l a t e th e Reynolds Number. The exp an sion f a c t o r ,
Y, was c a l c u la t e d from th e f o l l o w i n g equation:
Y = 1-C.41 + .35x S4 ) -------k P1
Then a t r i a l and e r r o r p r o c e d u r e w as u s e d .
was:
T h is p r o c e d u r e
I ) Choose a v a lu e of the R eyn old 's Number.
/
2) C a lc u la te K.
3) S o lv e fo r W from th e Equation
W=
ZgcP1CP1- ^ ) ] ^ ^
4) Back out th e a i r v e l o c i t y from W.
5)
C a lc u la te
t h e R e y n o ld 's Number and com pare w i t h
th e
R eyn old 's Number chosen in I ) .
A l i s t i n g o f the program, Flow, c i s includ ed in Appendix C.
66
APPENDIX B
PROGRAM SOURCE LISTINGS
/*
Source: mj2 .c
Created by Mike Weaver on March 4 , 1986 and f o l l o w i n g to
send commands out the aux. port to an o s c i l o s c o p e , and to
r e c e i v e data back from the scope. The commands and the data
should both be echoed t o th e scree n . The data w i l l a l s o be
read in t o a b u ffe r and sto r e d in a f i l e .
Use f u n c t io n s aux_in and aux_out to do I/O.
M odified on Mar. 6, 1986 by MJW.
*/
/**************************************************************/
//in clu d e < s t d io .h >
# d e f ine CR OxOd
/**************************************************************/
m a in ()
{
char m s g [ 8 0 ] , ch;
in t i , j ;
unsigned count=0;
/*************************************************************J
/*****
*****j
P rin t th e menu.
menu();
J *************************************************************/
/** * *
****/
Send out a command a b yte a t a tim e to the scope and
echo i t t o the screen.
67
p r i n t f C1
What i s th e message to send ?\n");
p r i n t f ("The m essage MUST be in UPPER CASE c h a r a c t e r s ! ! !\n");
g ets(m sg);
p r in tf ( " W ) ;
i=0;
printfC" The command sen t out i s : ");
w h ile (m sg [i]!= '\0 '){
aux_out(mSg[ i ]);
/ * Send char o f command o u t.* /
p r i n t f ( " % c " , m s g [ i ] );
/ * P r i n t t h e char s e n t . * /
i f ( i I= 2 ) {
f o r ( j = 0 ; j < 1 0 7 0 0 ; j + + ) ; / ljLoop t o t a k e up t i m e . * /
i++;
>
e lse
i++;
)
/ * End o f w h i le loop. * /
aux_out(CR);
/ * Send a c a r r ia g e retu rn ou t. * /
p r in t f C " \n \n " );
/*****************************************************************/
/*
Read in the data coming from th e scope. This r o u t in e u ses
s o ftw a r e in t e r r u p t s to read data in through th e aux. port.
Data, i s read in u n t i l a c a r r ia g e re tu r n i s read which i s
assumed to be the end o f the f i l e . T herefore th e BL=O
which i s what th e scope wakes up in.
*/
char c h _ in ,b u ff [45000];
count=0;
w h ileC ( ch _in = au x^ in () ) ! =CR){
b u ff[cou n t+ + ] =ch_in;
/ * Data read i n t o b u ff array.*/
c o (c h _ in );
/* D a t a e c h o e d t o s c r e e n .
*/
}
/**********************************************************J
/* * *
Save the b u ffe r in t o a data f i l e c a l l e d b u ffe r .
***/
/**********************************************************J
s a v e b u f f ( c o u n t, b u f f );
>
/*****************************************************************/
/* * * End o f main. ***/
/*****************************************************************/
68
/*
I/O f o r t h e p o r t s i n C.
The f u n c t io n s aux_out and aux_in use s o ftw a r e in t e r r u p t s
to send and read ch a r a c te r s through the aux. p ort.
*/
/********************************************************j
/*
Function aux_out sends a ch a ra cte r out th e aux.
port u sin g s o ftw a r e in t e r r u p t s .
*/
au x_out(kar)
char k ar;
{
#asm
mov
d l , [bp+4]
reg iste r.
mov
ah,04h
i n t 21h
Move t h e c h a a r a c t e r i n t o t h e d l
; T his s e t s up the aux. port to send,
; The ch aracter in the d l r e g i s t e r i s
; s e n t t o t h e aux. p o r t .
#end asm
>
j ********************************************************/
/* * *
The aux_in f u n c t io n reads in one ch aracter a t a
tim e through the aux. port u sin g i n t 21h.
***/
a u x _ in ( )
{
#asm
mov ah,03h
in t 21h
xor ah,ah
#end asm
>
/********************************************************j
/*
end of th e port i / o r o u t in e s * /
/**********************************j
/***
***/
The sa v eb u ff f u n c t io n saves the b u ffe r co n ten ts in a data
f i l e c a l l e d b u ffe r .
sa v eb u ff ( c o u n t, b u f f )
unsigned count;
69
char * b u f f ;
{
char i d [80];
long count2=count;
FILE * f id , * f o p e n ( ) ;
p r i n t f ( " \n \n \n
Saving th e b u ffe r as a data f i l e .
W );
p rin tfC 'In p u t the name under which the data f i l e is\n " );
p r in tfC '
t o be saved.\n\n");
g e ts(id );
f id = f o p e n (id ," w " ) ;
p r i n t f ( " \ n \ n B u f f e r s i z e %D\n",count2);
p r in tfC ' E x it in g Data C o lle c t in g Program\n\n");
b u f f[c o u n t]= 0 ;
count=0;
w h ile C b u f f[ c o u n t ] ) {
i f ( buf f [ cou n t] I= ' , ' }
f p u tc ( b u f f [ c o u n t + + ] , f i d ) ;
else{
f p u t c C \ n ' ,f i d ) ; /* R e p la c e s th e commas w ith CR.*/
count++;
}
}
/ * End.of w h ile . * /
fc lo se (fid );
}
j *************************************************************/
/* * * Create a f u n c t io n c a l l e d menuO t o p r in t a d e s c r i p t i o n o f
th e program.
***/
menu( )
<
printf("%cE",Oxlb);
/ * C lears th e screen on Z-100. * /
p r i n t f ( ,,*****************************************************\n")•
p r i n t f ( "*****************************************************\n");
prin tfC '*****
* * * * * \n " );
p rin tfC '* * * * *
SOURCE: MJ2.C
*****\n»);
p rintfC '*****
* * * * * \n " );
p r i n t f ( ,,*****************************************************\n");
p r i n t f ( ,,*****************************************************\n");
p r in t f ( " \n \n " );
p r in tfC '
Created by Mike Weaver on March 4, 1986. T his
\n");
printf("program w i l l op erate th e Gould O s c illo s c o p e and store\n " );
p r i n t f ("the b u ffe r c o n te n ts in a data f i l e . This f i l e can
\n");
p rin tfC 'th en opened and the data m anipulated and a n alyzed .
\n");
70
p r i n t f (" ------------------------------------------------------------------------------------------- \n")
p r in t f ( " X n " ) ;
/* * * * * End of menuO.
*****/
/***************************************************************/
71
/***
Source: f lo w .c
March 28, 1986
Mike Weaver
This program c a l c u l a t e s the mass f l o w r a t e of the
a i r through o r i f i c e ta p s used on th e tw o-phase flo w
experim ent conducted by Mike Weaver fo r h i s t h e s i s
research.
***/
# i n c l u d e "stdio.h"
# in c lu d e "math.h"
y*************************************************************y
mainO
{
/* * *
D efin e the v a r i a b l e ty p es.
***/
char kar;
f l o a t a ,a 2 ,b ,b e t a ,d e n s ;
flo a t g c ,k ,p ,p l,r ,t l,v ;
f l o a t vel,w ,w m ,y;
f l o a t nu;
d o u b le v is ,b 4 ,r d ;
/* * *
I n i t i a l i z e some c o n s ta n ts .
***/
a = - 5 .8 6 5 4 ;
b = 1 .0 2 7 4 ;
a2 = .0 0 1 4 3 ;
b e t a = .5 127;
g c = 3 2 .1 7 ;
b4 = b eta * b eta * b eta * b eta ;
r = 5 3 .3 4 ;
/* * *
D isp lay th e d e s c r i p t i o n of th e program. ***/
p r i n t f ("% cE",0xlb);
p r i n t f ( llX n W ) ;
A**********************************************^") •
p r i n t f ("
***********************************************Xn1
1) •
p rin tfC '
**
**\n");
p r i n t f ("
72
p r in tf("
p rin tfC '
printfC"
p rin tfC '
p rin tfC '
printfC"
printfC"
printfC"
p rin tfC "
printfC"
p r in tfC "
/* * *
**
Source: f lo w .c
Mike Weaver
**\n")
**
**\n " )
**
This program c a l c u l a t e s the mass
**\n")
** f l o w r a t e of th e a i r flo w in g through an
**\n")
** o r i f i c e p la t e . The v e l o c i t y i s backed out **\n")
** o f the mass f l o w r a t e so th at th e Reynolds **\n")
** Number canbe c a l c u la t e d
andcompared
**\n")
** w ith the one assumed
t o s e l e c t K.
**\n")
**
**\n")
*********************************************** \ n")
***********************************************\n")
Prompt th e u ser fo r th e input o f the v a r i a b l e s .
***/
p rin tfC " \n \n
What was th e v o lt m e t e r read ing ? ");
scanfC"%f",&v);
p rintfC"\n
Input th e a i r tem perature in degrees F. ");
s c a n f C"%f" , & t l ) ;
printfC "\n
Input th e s t a t i c p ressu r e in p s i. ");
scanfC"%f",&pl);
printfC'Xn
Input the a i r v i s c o s i t y fo r %f F " , t l ) ;
scanfC"%lf" , & v is ) ;
/* * *
***/
C a lc u la te th e p ressu r e drop a c r o s s the o r i f i c e tap s.
p = a+Cb*v);
printfC'Xn
The p ressu re drop a c r o s s th e o r i f i c e
i s %f p si.\n " ,p );
/* * * Convert the p ressu r e drop and s t a t i c p ressure to I b f / f t^2
***/
p = p * 1 4 4 .0 ;
p i = p l* 1 4 4 .0 ;
/* * *
C a lc u la te th e d e n s it y in lb m /ft^3
***/
d en s = p l/C r *Ctl+460));
printfC'Xn The d e n s it y i s %f ",dens);
p r in tfC 'X n " );
/* * *
C a lc u la te the expansion c o e f ., Y .
***/
y = l- (.4 1 + (.3 5 * b 4 ))* (p /(p l* 1 .4 ));
p r i n t f C ' The e x p a n s i o n c o e f . , Y = %f",y);
73
P r i n t f ( llW ) ;
/* * *
Routine t o c a l u l a t e mass f l o w r a t e , w.
***/
check:
/* * *
***/
/* * * Label ***/
Input th e gu ess f o r K, which depends on Reynold's #.
p r i n t f ("\n
Input a v a lu e for K. ");
scanf("%f",&k);
/* * *
C a lc u la te th e mass f lo w r a t e of the a i r in Ibm/min.
***/
nu = 2*gc*dens*p;
w = sq rt(n u );
p r i n t f ( llX n W ) ;
w = w*k*a2*y;
wm = w*60;
/* * *
***/
C a lc u la te th e v e l o c i t y from the mass f lo w r a t e .
v e l = w /(dens*a2);
/•kirk
C a lc u la te the Reynold's Number.
•kirkj
rd = ( d e n s * v e l ) / ( g c * v i s ) ;
/* * *
P rin t out th e r e s u l t s .
***/
p r i n t f ("The m ass f l o w r a t e o f t h e a i r f o r avo I t a g e r e a d in g Xn");
p r in tfC
o f v=%f v o l t s i s ",v);
printfCXnXn
»»>
w=%f Ibm/min
< « « \ n \ n " ,w m ) ;
p r in tfC
The K v a lu e used was %f",k);
p r i n t f CXn
The a i r v e l o c i t y i s %f",vel);
p rin tf(" \n " );
p r in tfC
The Reynold's Number i s %e ",rd);
p r i n t f ( " \n \ n \ n " ) ;
/* * *
Check to see i f th e user wants to tr y another v a lu e
o f K.
***/
p r in tfC
Type ' I ' i f you w ish to tr y another v a lu e fo r K ");
p rin tfC X n o t h e r w is e h i t any key t o e x i t program. ");
p rin tfC X n X n ");
k a r= ci();
74
i f ( kar == ' I ' )
goto check;
else{
p r i n t f ("\n
E x it in g mass f l o w r a t e program.\n\n")
p rin tfC '
B y e!\n \n " );
>
/* * * *
End o f main. ****/
75
/* * *
Created by Mike Weaver.
March 11, 1986
Source: head.c
This program i s to add a header to a data f i l e so
th a t the p e r t in e n t in fo r m a tio n regardin g data
c o l l e c t i o n can be recorded. The header w i l l con tain
13 l i n e s .
***/
j ***********************************************************j
# in c lu d e < s t d io .h >
/***********************************************************j
m a in ()
{
/ ***
char
char
char
ch ar
D e c la r e
th e
* * *
v a r ia b le s.
f
i n c h a r , k;
x x [ 20] , y y [ 2 0 ] , b p [ 1 5 ] , d t [ 6 0 ] , z s [ 4 ] , s t [5 ];
t a [ 5 ] ,tw [ 5] , t e l [ 5] , t e 2 [ 5] , a f [10] ,w f [ 15] ;
v d [ 1 5 ] , t d [ 1 5 ] , z s [ 5 ] ,v w tlO ];
sta tic
sta tic
sta tic
sta tic
sta tic
sta tic
sta tic
sta tic
sta tic
sta tic
d a ta ." ;
sta tic
d a ta ." ;
sta tic
sta tic
sta tic
sta tic
sta tic
sta tic
sta tic
sta tic
char s o [4 0 ]= "Source: ";
char bu[30] =llBurst p ressu re = ";
char p s[10]= " psig";
char tmp[3 9 I=llTemperatures : ";
char f a r [3]=" F";
char a i [8] =llA ir = ".;
char wa[45]="
Water
char e l [48]="
Exhaust
char e2[48]="
Exhaust
char s t l [ 6 5 ] =llS T l , to p h y d rop h on e
n.
9
H.
I
If.
2 = ";
# 4 0 8 , w as u s e d t o c o l l e c t
char st2[65]="ST2, bottom hydrophone #439, was used to c o l l e c t
char
char
char
char
char
char
char
char
ii.
f i t 16] =llF lo w ra te s :
dd[60]=" Ibm/min";
it.
ww[30]="
Water
v o l 2 0 ] =lfVoltageZdiv. = i i .
2 0 ] = 1 v o lts/d iv isio n " ;
t o [ 4 0 ] ="Time/div. = ";
t t [ 1 9 ] = " m s e c /d iv is io n " ;
s z [4 0 ] =llZero s e t t i n g f o r t r a c e i s
>
w
l
If.
>
76
s t a t i c char v f [60]="
Q u a lity o f th e a i r
it.
9
FILE * f i d x x , * f i d y y , * f openO;
p r i n t f ( "%cE",Oxlb);
printf("NnXnXn");
p r i n tf ("***********************************************^@1')
p r i n t f ( "***********************************************\n")
p r i n t f ("**
Source: HEAD.C
By: Mike Weaver
**\n")
p rin tfC '**
**\n " )
p r i n t f ("**
This program i s to add to a data f i l e
**\n")
p rin tfC '* * a 13 l i n e header c o n ta in in g p e r t in e n t
**\n")
p r in t f C 1** in fo r m a tio n about th e data c o l l e c t i o n .
**\n")
p rin tfC '**
**\n " )
p rin tfC '**
A f t e r running t h i s program, th e SEE
**\n")
p rin tfC '** e d it o r can be used t o d e l e t e p r e - and
**\n")
p rin tfC '** p o s t - s i g n a l data. Then th e data must be
**\n")
p rin tfC '** re fo r m a tte d by u sin g program CF.EXE .
**\n")
pri n t f ( "***********************************************\n")
p r i n t f ( ,l***********************************************\n")
p r in tf(" \n \n " );
p r i n t f ("Input th e name of the data f i l e to add header to. ");
g ets(x x );
p r in t f ( " \n ln p u t th e new name to be g iven to th e f i l e . ");
g ets(yy);
p r in tf(" \n \n " );
f id x x = f o p e n (x x ," r " ) ;
fid yy= f open( y y , "w");
/***************************************************************/
/***************************************************************/
/* * *
C reating th e header fo r th e data f i l e th a t c o n t a in s the
p e r t in e n t in fo r m a tio n .
***/
j A**************************************************************/
/***************************************************************/
p r i n t f ("Creating th e header fo r f i l e
. / * F ir s t li n e ;
% s\n\n\n",yy);
c o n ta in s f id . * /
f p r i n t f ( f i d y y , "% s",so);
f p r i n t f ( f i d y y , "% s\n",yy);
/ * Second l i n e ; b urst p ressu r e and v o id f r a c t i o n . * /
77
p rin tfC '
What was t h e b u r s t p r e s s u r e in p s i g ?
g ets(b p );
f p r in t f ( f id y y ," % s " ,b u ) ;
f p r i n t f ( f i d y y , "%s",bp);
f p r i n t f ( f i d y y , " ^ s " ,p s ) ;
p r in t f ( " \n What was the q u a l i t y o f th e a i r ?
gets(vw );
f p r i n t f ( f i d y y , "%s",vf);
f p r i n t f ( f i d y y , "%s\n",vw);
");
/ * L in es 3-6; tem p eratu res. * /
p r i n t f ("Xn What
g ets(ta );
p r i n t f ("Xn What
gets(tw );
p rin tfC X n What
F ? ");
g e ts(te l);
p rin tfC X n What
F ? ");
g ets(te2 );
was th e a i r tem perature in d egrees F ? ");
was th e w ater tem perature in d eg ree s F ? ");
was the exhaust tem perature from Tl in degrees
was th e exhaust tem perature from T2 in d egrees
f p r i n t f ( f i d y y , "%s",tmp);
f p r i n t f ( f i d y y , " % s" ,ai);
f p r i n t f ( f i d y y , " % s",ta);
f p r i n t f ( f i d y y , " % s\n " ,fa r );
f p r i n t f ( f i d y y , "%s",wa);
f p r i n t f ( f i d y y , "%s",tw);
f p r i n t f ( f i d y y , " % s\n " ,fa r );
fp r in tf(fid y y ," % s " ,e l);
f p r i n t f ( f i d y y , "Xs11J t e D ;
f p r i n t f ( f i d y y , " % s\n " ,fa r );
f p r i n t f ( f i d y y , "%s",e2);
f p r i n t f ( f i d y y , " % s" ,te2);
f p r i n t f ( f i d y y , " % s\n " ,fa r );
/ * L in es 7&8; f l o w r a t e s . * /
p r i n t f CXnWhat was th e mass f l o w r a t e o f the a i r in lb/min?");
gets(af);
78
p r i n t f ("\nWhat was th e mass f l o w r a t e of the w ater inlb/m in");
gets(w f);
f p r i n t f ( f i d y y , "%s",f I ) ;
f p r i n t f ( f i d y y , "%s",a i ) ;
f p r i n t f ( f i d y y , " % s " , a f );
f p r i n t f ( f id y y , " % s \n " , d d ) ;
f p r i n t f (fidyy,"% s",w w );
f p r i n t f (fid y y ," % s" ,w f);
f p r i n t f ( f i d y y ," % s \ n " , d d ) ;
/ * L in e 9; v o l t / d i v . * /
p r in t f ( " \n
gets(vd );
What was the v o l t a g e / d i v . used I ");
f p r i n t f ( f i d y y , ' ^ s 111V o );
f p r i n t f ( f i d y y , l^ s ll1V d);
f p r i n t f ( f i d y y , "%s\n", w ) ;
/ * Line 10; t i m e / d i v . * /
p r in t f C ’Xn
g ets(td );
What was th e t i m e / d i v . used in m s e c /d iv . ? ");
f p r i n t f ( f i d y y ," % s " , t o ) ;
f p r i n t f ( f i d y y ," % s " , t d ) ;
f p r i n t f ( f i d y y , "%s\n", t t ) ;
/ * Line 11; sto ra g e tr a c e . * /
p r in t f ( " \ n \ n
What sto ra g e t r a c e did th e data come from ?");
p r i n t f ( " \ n Type ' I ' i f i t w as th eu p per t r a c e , t r a c e #1");
p r in t f ( " \n Type '2' i f i t was th e lower t r a c e , t r a c e #2\n");
k = c i();
i f ( k == ' I ' )
f p r i n t f ( f i d y y , " Z sX n " ,stl);
else
fp r in tf(fid y y ," % s\n " ,st2 );
/ * L in es 12&13; zero s e t t i n g and blank l i n e . * /
)
)
)
>
79
printfC'Xn What was the zero s e t t i n g fo r th e t r a c e ? ");
gets(zs);
f p r i n t f ( f i d y y , "% s",sz);
f p r i n t f ( f i d y y , " % s\n \n " ,zs);
/*******************************************************J
/* * *
End of header.
***/
/*******************************************************I
I***
Copy data from th e o ld f i l e to th e new f i l e . ***/
w h i l e ( ( in c h a r = fg e t c ( f id x x ) ) ! = ( char)EOF)
f p u tc ( i n c h a r , f i d y y ) ;
fc lo se (fid x x );
fc lo se (fid y y );
p r in tf(" \n \n " );
p r i n t f ("Done fo r m a t t in g data f i l e
printfC'Xn
Bye ! XnXn");
>
/* * * * *
End o f Main.
%s \n",yy);
*****/
80
/* * *
This program i s to convert the massaged data in 'C
form at to Fortran format by r e p la c in g th e ca rr ia g e
retu rn l i n e f e e d s w it h j u s t a c a r r ia g e retu rn . This
w i l l make the data f i l e appear as a lon g h o r iz o n t a l
s t r i n g o f data.
C r e a te d by Mike W eaver.
March 11, 1986
Source:
c f.c
M odified: March 20, 1986
***/
J***********************************************************I
# in c lu d e < s t d io .h >
J*********************************************************** j
m a in ()
{
/* * *
D eclare the v a r i a b l e s .
***/
char inchar;
ch ar x x [ 8 0 ] , y y [ 8 5 ] ;
char l i n e [ 1 2 ] [8 5 ];
FILE * f i d x x , * f i d y y , * f openO;
p r i n t f ("% cE",0xlb);
p r in t f (" \n \n \n " );
p r i n t f ( "***************************************************\n")•
p r i n t f ( "***************************************************\n");
p r in t f C 1*** Source: CF
By: Mike Weaver ***\n");
p rin tfC '***
* * * \n " );
p r in t f C * * *
This program w i l l read a data f i l e w it h ***\n");
p r in t f C * * * 13 l i n e s o f header and data in a v e r t i c a l ***\n");
p r in t f C * * * form at and c r e a te a new f i l e w ith the same ***\n")
p r in t f C '* * * header and data ex ce p t the data w i l l now be ***\n")
p r in tfC '* * * in a h o r iz o n t a l format sep arated by commas. ***\n")
p r in t f C '* * *
***\n " )
p r in t f C '* * *
The new f i l e can be read by ANAL. EXE,
***\n")
p r in tfC '* * * which w i l l perform a FFT on the d a ta .
***\n " )
p r in t f C '* * *
***\n")
p r i n t f ( "***************************************************\n")
pr i n t f ( ,l***************************************************\n.11)
p r in tf(" \n \n " );
81
p r i n t f ("Input data f i l e t o be reform atted ?
");
gets(x x );
p r i n t f (" \n ln p u t th e new name o f th e reform atted data f i l e ? ");
gets(yy);
p r in tf(" \n \n " );
f id x x = f o p e n (x x ," r " ) ;
f id y y = fo p en (y y ," w " );
in t i=0;
i f ( i <= 12 ){
f g e t s ( l i n e [ i ] , 7 1 sf i d x x ) ;
f p r i n t f (f id y y ," % s " ,lin e [ i] );
i++;
.
/ * This c o p ie s th e 13 l i n e s
/ * o f header from one f i l e
/ * to a n o th e r .
*/
*/
*/
>
p r in tfC '
S t a r t in g on n um erical data. \n\n");
/ * * * Change t h e f o r m a t o f
h o r z .* * * /
the d ata
in f i l e
from v e r t i c a l
to
i= l;
w h i l e ( ( i n c h a r = f g e t c ( f i d x x ) ) ! = ( char)EOF){
i f ( in c h a r ! = ' \ n ' )
f p u tc ( i n c h a r , f i d y y ) ;
else{
i f ( i <= 12 ){
/ * Leave header in o r i g i n a l * /
f p u t c ( ' \ n ' , f i d y y );
/* format.
*/
i+ + ;
>
else
f p u t c C ' , f i d y y ) ; / * Replaces \n w ith a comma.*/
}
}
I* End o f e l s e .
*/
/ * End o f w h ile loop. * /
fclo seC fid x x );
fc lo se C fid y y );
p r in tf(" \n \n " );
p r i n t f ("Done fo r m a ttin g data f i l e
p r in t f ( " \n
Bye I \n\n");
>
/* * * * *
End o f Main.
%s \n",yy);
*****/
S o u r c e : ANALM.F
A p r i l 22, 1986
By:
Mi ke We a v e r
file
is
modified
do p r e s s u r e
FFTCC,
data
files.
*****************************************************
Variable declarations.
o
FFTRC,
value
Required
o
subroutines:
to
o
This
o
o
o
o
82
FFT2C
*****************************************************
O
O
O
w
O
O
O
INTEGER NDPMAX.ND2
INTEGER I , J , N, IWK( 3 2 8 0 )
INTEGER B E , E D , F N , S T , YN
COMPLEX X ( 1 0 2 5 )
REAL V P , V S , ZS
PARAMETER ( NDPMAX=II OO)
PARAMETER ( V S = O . 2 )
CHARACTER*14 INFILE
CHARACTER*9 O EEADER( I S)
CHARACTER*I 4 NAME
CHARACTER*I 4 PRES
CHARACTER*14 MAG
CHARACTER*!4 AVE
CHARACTER*!4 PEA
REAL A ( 1 0 2 5 ) , B ( 1 0 2 5 )
REAL WK( 3 2 8 0 )
* * * * * ************************************************
A s k f o r t h e d a t a f i l e t o be a n a l y z e d .
*****************************************************
WR I T E ( * , 1 0 0 )
READ(*,1000)
*****************************************************
Open t h e d a t a f i l e t o b e g i n m a n i p u l a t i o n a nd a n a l y s i s .
*****************************************************
O
O
O
OPEN ( I ,
15
20
INFILE
F I L E = I N F I L E , STATUS =' OLD' )
* * * * * ************************************************
Re a d i n t h e d a t a p o i n t s i n t o a r r a y A( ) .
*****************************************************
R E A D ( 1 , * , E N D = 2 0 ) ( A ( I ) , I = I , N D P MAX)
N=I-I
O O O
83
* * * * * ************************************************
C a l l FFTRC t o p e r f o r m t h e FFT.
*****************************************************
WRITE( * , 6 5 0 )
CALL FFTRC( A, N, X, I WK, WK)
O O O
C o m p u te t h e r e s t o f t h e c o e f .
*****************************************************
I-*
* * * * * ************************************************
ND2 =N/ 2
DO 1 1 , 1 = 2 , ND2
X( N+ 2- l) =C0 NJG( X( l))
CONTINUE
O O O O
DO 1 2 , 1 = 1 , N
X(I)=X(I)/N
CONTINUE
O O O
Make t h e c o e f . l o o k l i k e R a m i r e z by m u l t i p l y i n g by
I / N, w h e r e N i s t h e n u mb e r o f d a t a p o i n t s .
*****************************************************
^
* * * * * ************************************************
* * * * * ************************************************
S a v e t h e FFT c o e f i c i e n t s t o a f i l e .
*****************************************************
O'
WRITE( * , 9 0 0 )
WR I T E ( * , 9 1 0 )
READ( * , 1 0 0 0 )
NAME
0 PEN( 2 , FILE=NAME, S TATUS='NEW')
DO 6 5 , 1 = 1 , N
WR I T E ( 2 , 1 2 0 0 ) X(I)
CONTINUE
O O O
WRI TE( * , 9 2 0 )
80
*****************************************************
C alc u la t e the magnitude of the frequency coef.
*****************************************************
DO 8 0 , 1 = 1 , N
A ( I ) = CABS( XXl ) )
CONTINUE
84
O OO
V
O
V
O
V
O
OOO
C
*****************************************************
F in d o u t w h a t p o r t i o n o f t h e f r e q u e n c y s p e c t r u m i s t o
be s a v e d i n a f i l e .
* * * * *************************************************
WRITE ( * , 1 5 0 0 )
READ( * , * , ERR= 9 5) YN
I F ( YN . EQ. I ) THEN
GOTO 96
ELSE
GOTO 98
ENDIF
WR I T E ( * , 1 4 0 0 )
READ( * , * , ERR=9 6 ) ST
I F ( S T . EQ. I ) THEN
BE=I
ELS EI FCST . EQ. 2 ) THEN
BE=N/8
ELSE I F ( S T .EQ. 3 ) THEN
BE=N/ 4
ELSE
BE= 3 * N/ 8
ENDIF
WR I T E ( * , 1 4 5 0 )
READ( * , * , ERR= 9 7 ) FN
I F ( FN . EQ. I ) THEN
ED= N/ 8
EL S E I F ( FN . EQ. 2 ) THEN
ED=N/ 4
E L S E I F ( F N . EQ. 3 ) THEN
ED= 3 * N/ 8
ELSE
ED=N/2
ENDIF
*****************************************************
Save th e m a g n i t u d e s in a d a ta array.
*****************************************************
WRITE(*,1300)
WRITE( * , 9 1 0 )
READ( * , 1 0 0 0 )
MAG
85
OPEN( 23 , FI LE = MAG, STATUS = ' NEW')
WRI TE( 2 3 , 1 3 5 0 ) ( A ( l ) ,
I =BE, ED)
C
C
C
*****************************************************
C l o s e t h e mag. f i l e .
*****************************************************
CL0SE( 2 3 ,
S TATUS = ' KEEP' )
GOTO 9 5,
98
CONTINUE
C
C
C
*****************************************************
Format s t a t e m e n t s .
*****************************************************
100
650
FOR MAT ( / 8 X 'T h is p r o g r a m c o m p u t e s t h e FFT o f p r e s s u r e
value'/
&5 X , ' d a t a . I n p u t t h e name o f t h e d a t a f i l e t o be
analyzed ? '/)
FORMAT( / 8 X , ' > > >
E n t e r i n g t h e FFTRC s u b r o u t i n e .
<<<' / / )
900
9 10
92 0
F OR MAT ( / 1 0 X , ' S a v i n g t h e FFT c o e f i c i e n t s i n a f i l e . ' / )
FORMAT( 8 X , ' Wha t do y o u w a n t t o name t h e f i l e ? ' )
FORMAT(/ / 8 X , ' D o n e s a v i n g t h e FFT c o e f i c i e n t s i n
f i l e 'A S//)
1000
FORMAT(A)
1100
FORMAT( IX, A7 7)
1110
FORMAT( I 5 X , A7 7 )
1200
FORMATd 5 X , ' ( ' F l 1 . 6 '
, ' F l l . 6 ' )')
1300
F O R MA T ( / 1 0 X , ' O p e n i n g a f i l e t o s a v e t h e f r e q u e n c y
m agnitudes.')
13 50
F OR M A T ( 1 0 2 4 ( 1 X , F 9 . 5 ) )
50
FORMAT( I I ,
Si I OX , '* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' /
StI OX, ' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' J
S tlO X ,'* * * * *
> S o u r c e : ANAL. F
<
* * * * * ')
51
FORMAT( I OX,' * * * * * ' , 1 4 X , '
* * * * * '/
Stl OX, ' **
T h i s program w i l l compute t h e F a s t
F o u r i e r * * '/
S tlO X ,'** T r a n s f o r m o f c o m p l e x and r e a l v a l u e d
s e q u e n c e s * * '/
Stl OX, ' ** o f d a t a .
* * ')
52
FORMATdOX,'*****',14X,'
* * * * * '/
St I OX, ' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' /
S tlO X ,'* * * * *
* * * * * '/
)
86
&10X,'**
By: Mi k e We a v e r
Mar. 1 3 , 1 9 8 6
* * ')
F OR MAT ( I OX, ' * * * * * ' , 1 4 X , '
* * * * * '/
& I OX, ' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ^- )
1400
F OR MAT ( / 8 X , ' A t w h a t f r e q u e n c y i n d e x do y o u w a n t
to s t a r t ' /
&5X,'saving c o e f f i c i e n t s ?
Type:'/
&33 X , ' " I " f o r b e g i n n i n g ' /
& 3 3 X , ' "2" f o r N / 8 ' /
&3 3 X , ' "3" f o r N/ 4 ' /
&3 3 X , ' "4" f o r 3 N / 8 ' )
1450
FORMATC/8 X , ' A t w h a t f r e q u e n c y i n d e x do y o u w a n t
to s t o p '/
&5X,'saving c o e f f i c i e n t s ?
Type:'/
&3 3 X , ' " I " f o r N / 8 ' /
& 3 3 X , ' "2" f o r N / 4 ' /
&3 3 X , ' "3" f o r 3 N/ 8 ' /
&3 3 X , ' "4" f o r N/ 2 ' )
1500
FORMATC / 8 X , ' D o y o u w a n t t o s a v e t h e m a g n i t u d e s ' /
& 5 X , ' o f t h e FFT c o e f .?
Type:'/
&3 3 X, ' " I " f o r YES & "2" f o r NO')
END
53
no
T h is program w i l l read a d ata f i l e t h a t has been
f o r m a t t e d by CF.EXE and c a l c u l a t e t h e a v e r a g e o f t h e
d a t a w i t h o t h e r d a t a f i l e s o f t h e s a me c o n d i t i o n s .
n o n
S o u r c e : AVE.F
A p r i l 29, 1986
n o n
87
By:
Mi ke We a v e r
*****************************************************
V ariable d ecla ra tio n s.
* * * * *************************************************
n o n
INTEGER NDPMAX,ND2, CH
INTEGER I , J , N9JMAX
PARAMETER (NDPMAX=II 0 0 )
CHARACTER*I 4 INFILE
CHARACTER*14 PRES
REAL A ( 1 0 2 5 ) , B ( 1 0 2 5 )
REAL V P 9V S 9ZS
PARAMETER ( V S = . 2 )
* * * * *************************************************
D i s p l a y th e program d e s c r i p t i o n .
*****************************************************
n o o n
vi
WRITE( * , 5 0 )
WRITE (*,■ 51 )
WRITE( * , 5 2 )
WRITE(*,53)
45
WRITE(*, 120)
READ( * , * , ERR= 5) JMAX
J=O
****************************************************
Need
t o know w h i c h h y d r o p h o n e w a s u s e d t o c o l l e c t
the data s i n c e they have d i f f e r e n t s e n s i t i v i t i e s .
****************************************************
WR I T E ( * , 5 0 0 )
READ ( * , * , ERR=45) L
I F ( L .EQ. I ) THEN
VP=4.36766
ELSE
VP=4.4 7 8 8 4
ENDIF
Ui
O O O
O'
O O O O
88
* * * * *************************************************
Check to s e e
setting.
if
the data f i l e s
a l l have the
same z e r o
*****************************************************
WRITEC*, 1 5 0 )
R E A D ( * , * , E R R = 6 ) CE
I F ( CE .EQ. I ) TEEN
WRITE( * , 6 0 0 )
READ( * , * ) ZS
ELSE
CONTINUE
ENDIF
* * * * ***************************************************
A s k f o r t h e d a t a f i l e t o be a n a l y z e d .
*******************************************************
WRITE(*,100)
R E A D ( * , 1 0 0 0 , ERR= 5 5) INFILE
O O O
J=J + 1
* * * * *************************************************
Open t h e d a t a f i l e t o b e g i n m a n i p u l a t i o n and a n a l y s i s .
*****************************************************
F ILE= I N F I L E , S TATUS = z OLD')
* * * * *************************************************
N3l->
Re ad i n t h e d a t a p o i n t s i n t o a r r a y A ( ) .
*****************************************************
READ( l , * , E N D = 2 0 ) ( A ( l ) , I = I , N DP MAX)
N=I-I
O O O O
O O O
OPEN Cl ,
****************************************************
Need t o i n p u t t h e z e r o v o l t a g e v a l u e f o r t h e t r a c e
b e i n g a n a l y z e d . R e a d s t h e v a l u e i n t o ZS.
****************************************************
7
I F ( CE .EQ. 2 ) TEEN
WRITE ( * , 6 0 0 )
READ( * , * , ERR=7 ) ZS
ELSE
CONTINUE
ENDIF
89
C
* * * * * ***********************************************
C
C
C
C on ve rt t h e d a t a v a l u e s v o l t a g e t o p r e s s u r e in pounds
p e r s q u a r e i n c h ( p s i ) and s t o r e i n a r r a y A ( ).
****************************************************
35
DO 3 5 , 1 = 1 , N
A(I)=VP* V S * (A (I)-Z S )* 3 5 ./1 000.
B(I)=B(I)+A(I)
CONTINUE
CLOSEd ,
STATUS='KEEP')
I F ( J .EQ. J MAX) THEN
GOTO 13
ELSE
GOTO 55
ENDIF
C
C
C
* * * * ************************************************
13
DO 3 3 , 1 = 1 , N
a ( i ) = b ( i ) / j max
CONTINUE
33
8
C a lc u la t e the average of the data f i l e s .
****************************************************
WRITE(*,300)
WRITE( * , 9 1 0 )
R E AD ( * , 1 0 0 0 , ERR=S) PRES
0 PEN( 2 , FILE=PRES, STATUS='NEW')
DO 3 6 , 1 = 1 , N
WRITE( 2 , 1 3 5 0 ) ( A U ) , 1 = 1 , N )
CONTINUE
C
C
C
1 00
120
1 50
)
)
)
)
300
****************************************************
Format s t a t e m e n t s .
****************************************************
F OR MAT ( / 8 X 'I n p u t t h e name o f t h e d a t a f i l e t o be
a n a l y z e d I' I )
FORMAT( / 5X, ' How many d a t a f i l e s do y o u w a n t t o
average?')
FORMAT ( / 8X, ' Do a l l o f t h e f i l e s h a v e t h e s a me z e r o
s e t t i n g ?'/
& 5 X , ' T y p e a "I " f o r YES a n d a "2" f o r NO. ' )
FORMATd I O X , ' O p e n i n g a f i l e t o s a v e t h e a v e r a g e d d a t a
values.')
i
I
90
5 00
600
910
1000
1350
50
51
52
53
1400
1450
1500
)
FORMAT(/ 8 X , ' Wh i c h h y d r o p h o n e w a s u s e d t o c o l l e c t t h e
files
YU
& 5 X , ' I n p u t a "I" f o r t h e t o p h y d r o p h o n e ( # 4 0 8 ) ' /
&5 X, ' o r i n p u t a "2" f o r t h e b o t t o m h y d r o p h o n e ( # 4 3 9 ) . ' / )
FORMAt C / / 8 X , ' I n p u t t h e z e r o s e t t i n g f o r t h e t r a c e . ' )
FOR MAT ( 8 X , 'Wh a t do y o u w a n t t o nam e t h e f i l e ? ' )
FORMAT(A)
FORMAT( 1 0 2 4 ( 1 X , F 9 . 5 ) )
FORMATC/ / ,
&I OX , ' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * • ' /
& 1 0 X ,' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' /
&I OX, ' * * * * *
> S o u r c e : AVE.F
<
* * * * * ')
FORMATd O X ,'* * * * * ', 1 4 X , '
* * * * .* ' /
&1 0 X , ' * *
T h is program w i l l compute th e a v e r s g e
of
* * '/
&1 0 X , ' * * any n u mb e r o f d a t a f i l e s and s t o r e t h e
r e s u l t s * * '/
&1 0 X , ' * * i n a new d a t a f i l e .
* * ')
FORMATd O X ,'* * * * * ', 1 4 X , '
* * * * * '/
& 1 0 X ,' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' / "
&1 O X ,'* * * * *
* * * * * '/
&1 0 X , ' * *
By: , Mi k e W e a v e r
Apr . 3 0 , 1 9 8 6
* * ')
FORMAT( I O X ,'* * * * * ', 1 4 X , '
* * * * .* '/
& 1 0 X ,' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' )
F0RMAT( / 8 X , ' A t w h a t f r e q u e n c y i n d e x do y o u w a n t t o
start'/
&5X,'saving c o e f f i c i e n t s ? Type:'/
&33X,' "I" f o r b e g i n n i n g ' /
& 3 3 X , ' "2" f o r N / 8' /
& 3 3 X , ' "3" f o r N / 4 ' /
&3 3 X , ' "4" f o r 3 N / 8 ' )
FORMAT( / 8 X , ' A t w h a t f r e q u e n c y i n d e x do y o u w a n t t o
stop'/
&5X,'saving c o e f f i c i e n t s ? Type:'/
&33X,' "I" f o r N/ 8 ' /
& 3 3 X , ' "2" f o r N / 4 ' /
& 3 3 X , ' "3" f o r 3 N / 8 ' /
&33X , ' "4" f o r N/ 2 ' )
FORMATC / 8X, ' Do y o u w a n t t o s a v e t h e m a g n i t u d e s and
phases'/
&5 X , ' o f t h e FFT c o e f . ?
Type:'/
&3 OX, ' " I " f o r YES & "2" f o r NO')
END
91
C
C
C
C
C
C
C
C
Source: M ult.f
A p r i l 5, 1 9 8 6
By:
Mi k e We a v e r ,
C
****************************************************
T h is program i s to prompt th e u s e r to in p u t two d a ta
f i l e s t h a t c o n t a i n FFT f r e q u e n c y d o m a i n c o e f . t h a w i l l
m u l t i p l i e d t o g e t h e r and s t o r e d i n a t h i r d d a t a f i l e .
T h i s t h i r d d a t a f i l e c a n t h e n be r u n r u n t h r o u g h
T f f t and t r a n s f o r m e d b a c k i n t o t h e t i m e d o m a i n .
INTEGER I , N , ND2
INTEGER B E , E D , F N 1S T 1YN
COMPLEX A( 1 0 2 5 ) , B( 1 0 2 5 ) , C ( 1 0 2 5 )
CHARACTER*!9 AIN
CHARACTER*!9 BIN
CHARACTER*!9 OUTFILE
CHARACTER*!9 PHA
PARAMETER ( NMAX= I l l O)
OO
C
* * * * * *********************************************** ■
P r i n t d e s r i p t i o n of program.
****************************************************
O O O O
WRITE( * , 5 0 )
WRITE( * , 5 1 )
W R I T E ( * , 52)
WRITE( * , 5 3 )
****************************************************
S e c t i o n to read in th e names of the two d ata f i l e s to
be m u l t i p l i e d t o g e t h e r .
****************************************************
WRI TEX*, 1 0 0 )
REA D ( * , 9 9 ) AIN
WRITE( * , 1 5 0 )
READ( * , 9 9 ) BIN
q
****************************************************
C
Re ad
C
10
the
data
into
complex
arrays
A(I)
& BCl ) .
****************************************************
0 P E N ( 1 , FILE = AIN,
STATUS='OLD')
R E A D ( 1 , * , END=I O) ( A ( I ) , I= I , NMAX)
N=I-I
ND2=N/ 2
92
O O O
DO 2 0 , I = I , ND2+I
C( I ) = A ( I ) * B ( I )
CONTINUE
O O O O
M
****************************************************
S e c t i o n to m u lt p ly the complex a rrays t o g e t h e r .
****************************************************
' S J I - 1
0 P EN( 2 ,
FI LE= BI N, STATUS='OLD')
R E A D ( 2 , * , E N D = I l ) ( B ( I ) , I= I , NMAX)
DO 2 5 , 1 = 2 , ND2
C(N+2-l)=C0NJG(C(l))
CONTINUE
****************************************************
S e c t i o n t o c r e a t e a new d a t a f i l e w i t h t h e p r o d u c t o f
th e two i n p u t t e d f i l e s .
****************************************************
w
WRITE( * , 2 0 0 )
REA D ( * , 9 9 ) OUTFILE
OPEN(2 1 , FILE=OUTFILE,
DO 3 0 , 1 = 1 , N
WRITE(21,300)
CONTINUE
O O O
WRITE(*, 3 5 0 )
STATUS='NEW')
C(I)
OUTFILE
****************************************************
C a l c u l a t e the phase s h i f t .
****************************************************
95
WRI TE( * , 3 7 5)
READ( * , * , ERR= 9 5) YN
I F ( YN .EQ. I ) THEN
GOTO 96
ELSE
GOTO 98
ENDIF
96
WRITE(*,380)
DO 4 0 , 1 = 1 , N
I F ( REAL( C( I ) )
B(I) = O
.EQ.
0)
THEN
93
ELSE
40
B(I)
ENDIF
CONTINUE
C
C
C
****************************************************
Save th e p h a se s in data f i l e s .
****************************************************
85
WRITE(*, 400)
READ( * , * , ERR=S5) YN
I F ( YN . EQ. I ) THEN
GOTO 97
ELSE
GOTO 98
ENDIF
97
87
= ATAN2 (RE AL ( C d ) ) , A l M A G ( C d ) ) )
WRITE(*,450)
WRITE(*, 460)
READ( * , * , ERR=8 7 ) FN
WRITE(* , H O ) FN
WRITE(*,500)
READ(* , 9 9)
PHA
OPEN(2 2 , FILE=PHA, STATUS='NEW')
WRI T E ( 2 2 , 6 0 0 ) ( REAL( B ( I ) ) , I = I ,
cl
os E( 2 2 ,
FN)
S t a t u s =^k e e p ' )
GOTO 85
98
CONTINUE
C
C
****************************************************
Format s t a t e m e n t s .
99
100
HO
FORMAT(A)
FORMATd/ I O X , ' I n p u t t h e f i r s t d a t a f i l e ? ' )
FORMATd 5X, ' The p h a s e f i l e w i l l c o n t a i n ' 1 4
point s ' / )
FORMAT( / 1 0 X , ' I n p u t t h e s e c o n d d a t a f i l e ? ' )
F OR MAT ( / / 1 0 X , ' O p e n i n g a new d a t a f i l e t o s t o r e t h e
product of th e'
&/ 7 X , ' a r r a y s . Wh a t do y o u w a n t t o n a m e t h e f i l e ? ' )
C
1 50
200
****************************************************
94
300
350
375
380
400
450
460
500
600
50
51
52
53
F0RMAT(15X'('F11.6'
,'F l I .6' )')
F ORMA T ( / / 5 X, ' D o n e s a v i n g ' , A l O )
FORMAT( / I 0X, ' Do y o u w a n t t o c a l c u l a t e t h e p h a s e
s h ifts of'/
& / 8 X , ' t h e FFT. T y p e "I " f o r YES a n d "2" f o r NO. ' )
F OR MAT ( / 5 X , ' C a l c u l a t i n g t h e p h a s e s h i f t s . ' / )
FORMAT( / 8X, ' Do y o u w a n t t o s a v e t h e p h a s e s o f t h e
FFT c o e f . ? ' /
& / 1 0 X , ' T y p e "I " f o r YES a n d "2" f o r NO ' )
F OR MAT ( / 8 X ,' The f i l e w i l l START a t a f r e q u e n c y
i n d e x o f "I"')
F0RMAT(/ / 8 X , ' A t w h a t f r e q u e n c y i n d e x do y o u w a n t
t o STOP ? ' )
FORMATC/1 0 X , ' O p e n i n g a f i l e t o s a v e t h e p h a s e s h i f t s .
Wh a t ' /
&8 X , ' do y o u w a n t t o n a m e t h e f i l e ? ' )
F OR M A T ( 1 0 2 4 ( 1 X , F 9 . 5 ) )
FORMATC//,
&10X,'**********************************************'/
&I O X ,' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' /
& 10X ,'* * * * *
> S o u r c e : MULT.F <
* * * * * ')
FOR MAT ( I OX,' * * * * * ' , 1 4 X , '
■ * * * * * '/
&10X,'**
T h is program prompts the u s e r to input
two * * '/
&I OX,' * * d a t a f i l e s c o n t a i n i n g c o m p l e x f r e q u e n c y
do main * * '/
&1 0 X , ' * * c o e f . r e s u l t i n g f r o m t h e ANAL.F r o u t i n e .
The
* * '/
& 1 0 X ,'* * p r o d u c t o f t h e t w o f i l e s i s c o m p u t e d and * * ' /
S i O X ,'** s t o r e d i n a t h i r d f i l e w h i c h c a n b e l a t e r
run
* * ')
F0RMAT( 1 0 X, ' * * t h r o u g h t h e TFFT
r o u tin e to transform
the
* * '/
S I OX, ' ** c o m p l e x d a t a b a c k t o t h e t i m e d o m a i n .
* * ')
FOR MAT ( I OX,' * * * * * ' , 1 4 X , '
* * * * * '/
& I O X ,
'* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 'f
S i O X ,'* * * * *
& 1 0 X ,'* *
By:
&1O X ,'* * * * *
Mi k e
We a v e r
April
5,
* * * * * '/
1986
* * '/
* * * * * '/
&I OX, ' A * * * * * * * * * * * * * * * * * ****************************'/
ox,'**********************************************")
END
97
^**********************************************************
****************
950 "
96 0 '
THIS IS THE EQUATION YOU HAVE TO USE
970
98 0 "
L I N E - ( ( X - X M I N ) *XE + I 2 8 , 1 8 0 - ( Y YMIN)*YE)
990 '
1000 '
PS ET ( ( X - X M I N ) *XE + I 2 8 , 1 8 0 - ( Y YMIN) *YE)
1010 '
1020
"* * * * * * * * * *************************************************
****************
1030
"* * * * * * * * * *************************************************
****************
1040
1050
1060
1070
1080
1100
1110
1120
1130
1140
1150
1160
1170
1180
1185
1190
1200
'
OPEN IRA$ FOR INPUT AS #1
X=O
I F EOF( I ) THEN 1 1 4 0
INPUT # 1 , Y
IF X=O THEN PSET ( (X-XMIN) *XE+1 2 8 , 1 8 0 - ( Y- YMI N) *YE)
LINE - ( ( X - XMI N ) *XE + 1 2 8 , 1 8 O- ( Y - YMI N ) *YE)
X=X+I
GOTO 1 0 7 0
PU T ( 1 0 , 1 9 0 ) , IRAJ #
I IRR$ =INKEY$ : I F IIRR$="" THEN 1 1 5 0
I F I I R R $ = "Y" OR II.RR$ = "N" OR I I R R $ = "y" OR I I R R $ = "n"
THEN 1 1 8 0
GOTO 1 1 5 0
P U T ( 1 0 , 1 9 0 ) , I RAJ#
I F IIRR$="N" OR I I RR$="n" THEN LOCATE 1, 1: END
I IRR$ = INKEY $ : I F I IRR$ = "" THEN 1 1 9 0
GOTO 1 1 4 0
95
10
REM PROGRAM TO CREATE A GENERAL GRAPH: SETTING UP
SCALING AND LABELING THE AXES AND TITLE.
2 0 DIM Z ( 2 4 1 , 7 ) , I RAJ# ( 1 0 0 0 )
3 0 PRINT "INPUT XMI N , XMAX1YMI N , YMAX, DELTA X LABEL1D-Y
LAB1X T I C 1YTIC"
4 0 INPUT XMl N1XMAX1YMrN1YMAX1XLAB1YLAB1XTI C1YTIC
50 PRINT "INPUT GRAPH TITLE":INPUT TITLE $
60 PRINT "INPUT X-AXIS LABEL":INPUT XAL$
7 0 PRINT "INPUT Y -AX IS LABEL":INPUT YAL $
80 PRINT : PRINT : INPUT " DATA FILE NAME ?";IRA$
1 4 0 CLS
1 5 0 LOCATE 1 , 1 : PRI NT " DO YOU WANT PRINTOUT ? ( Y ) OR ( N) "
1 6 0 GET(O1O ) - ( S O O 1I O ) 1 I R A J #
1 7 0 CLS
1 8 0 CLS
1 90 ZMAX=LEN( YAL $ ) * 8
2 0 0 I F Z MAX>2 4 0 THEN Z MAX=2 4 0
2 1 0 LOCATE 1 , 1
2 2 0 PRINT YAL$
2 3 0 FOR X%= 0 TO ZMAX
2 4 0 FOR Y%=0 TO 7
2 5 0 Z(X%, Y%)=POINT (X%,Y%)
2 60 NEXT Y%
2 7 0 NEXT X%
28 0 ZSTAR= 2 0 0 - ( 2 0 0 - Z MAX)/ 2
2 9 0 CLS
3 0 0 FOR X=O TO Z MAX
3 1 0 FOR Y=O TO 11
320
I F Z ( X , Y / 1 . 5 ) > 0 THEN PSET ( Y+1 0 , ZSTAR-X) , Z(X, Y / 1 .5 )
330
NEXT Y
3 4 0 NEXT X
3 50 LI NE ( O 1O ) - ( O S O 1O)
3 6 0 LINE - ( 6 3 9 , 2 2 4 )
3 7 0 LINE - ( 0 , 2 2 4 )
3 8 0 LI NE - ( O 1O)
3 9 0 XA=XMAX-XMIN
4 0 0 YA=YMAX-YMIN
4 1 0 X E = ( 57 5 - 1 2 8 ) / XA
4 2 0 YE=1 5 8 / YA
4 3 0 I F YMAX*YMIN>=0 THEN YLOC=ISO
4 4 0 IF YMAX*YMIN<0 THEN YLOC=YMAX*YE+22
4 5 0 I F XMAX*XMIN>=0 THEN XLOC=128
4 6 0 IF XMAX*XMIN<0 THEN XLOC=5 7 5-XMAX*XE
4 7 0 LI NE ( 1 2 8 , YLOC) - ( 575, YLOC)
4 8 0 LINE ( X L O C , 2 2 ) - ( X L O C 11 8 0 )
4 9 0 FOR X=XMIN TO XMAX+XLAB* .0 2 STEP XLAB
5 00 I X%=(X-XMIN)*XE+128
96
510
520
530
540
550
560
570
58 0
590
600
610
620
630
640
650
660
670
680
690
700
710
720
730
740
750
760
770
780
790
800
810
820
830
840
850
860
870
880
890
9 00
910
PSET (IX%, YLOC)
I F YLOC< 1 8 0 THEN PSET (lX%,YLOC+4)
LINE - ( I X % , YLOC-4)
SCREEN I
LOCATE YLOC/ 9 + 1. 5 , I X%/ 8 - 1
PRINT X
SCREEN 0
NEXT X
FOR X=XMIN TO XMAX STEP XTIC
I X%=(X-XMIN)*XE+128
PSET ( IX%, YL OC)
I F YLOC<180 THEN PSET (IX%,YLOC+2)
LINE - ( I X % , YLOC-2)
NEXT X
LOCATE 2 5 , 1
FOR Y=YMIN TO YMAX+YLAB* .0 2 STEP YLAB
I Y%=180- ( Y- YMI N) *YE
PSET (XLOC, IY%)
IF XL0 0 1 2 8 THEN PSET (XLOC-8, IY%)
LINE - ( XLOC+8, IY%)
SCREEN I
LOCATE I Y%/ 9 + 1 , XLOC/ 9 - 4
PRINT Y
SCREEN 0
NEXT Y
FOR Y=YMIN TO YMAX STEP YTIC
I Y%=180- ( Y- YMI N) *YE
PSET ( XLOC, IY%)
I F XL0 0 1 2 8 THEN PSET ( XL0C- 4, I Y%)
LINE -(XLOC+4, IY%)
NEXT Y
P=LEN(TITLE$)
R= ( S O- P ) / 2
LOCATE 2 , R
PRINT TITLE$
P=LEN(XAL$)
R=(60-P)/2
LOCATE 2 3 . R + 1 5
PRINT XAL$
LOCATE 2 5 , 1
REM P O I N T S MUST BE PLOTTED AT x = ( X - X M I N ) / ( X M A X XMIN) * 4 4 7 + 1 2 8 = ( X-XMIN) * XE+1 28
9 2 0 REM AND y = 1 8 0 - ( Y - Y M I N ) / ( YMAX- YMI N) *! 5 8 = I 8 0 - ( Y-YMIN)*YE
930
"* * * * * * * * * *************************************************
****************
940
r
98
APPENDIX C
FIGURES
TP! I
.5
<f>
d.
A
L
e
M
lZl-VV.
•
5
i
- -A-,. ^
13
-.5
U
i'
-I
Top H y d ro p h o n e
'f)
til
Z
C.
-1.5
-2.5
■1*1 CsSECi
TE 2 !
a
A,*.12
Vl
I
I
13
A
I
Ui
I cr
>/)
I V)
2
ti.
Boccom H y d ro p h o n e
f
-1.5
f.
I
-2.5
u
TiIiE (,SEC!
F ig u re 21.
T w o - p h a s e F l o w , A i r Q u a l i C y = 93.13% , P r e s s u r e
P u l s e f o r Top a n d Boccom H y d r o p h o n e s , B u rs e
P r e s s u r e = 14 p s i g .
- - A ,.
99
TPl 2
/v
.5
2
Vi
6
c.
U
-.5
/ \
L
ti.
p
t
r
_
— '—
?
|.0
/
|!
-I
C
Top H y d r o p h o n e
f
[
U
|V
L-
TF
/
Cl
D
^ 11 f ' ' 1" v-v
L
-1.5
Eh
I
L
-2
TIME in,SEC]
TP22
•5
^WVVvV.'
co
c.
6
6
'1
WAV.-,
........................................
f1
w
--5
I
,.I1
m
CO
LU
|V
-I
I
-1.5
B o tto m H y d r o p h o n e
/
,/
V
-2
TIME IftSECl
F ig u r e 2 2 .
Tw o-phase F low , A ir Q u a lity = 94.89% , P r e s su r e
P u ls e f o r Top and Bottom H ydrophones, B u rst
P r e s s u r e = 14 p s i g .
100
TP13
.5
a.
u
C£
v
BI
V)
_i________
/A vX
'
, -"^v 'y_________'
y
v a. .,
1 r%
•
/
'
,/
r
'
fy
r
-.5
Top H y d r o p h o n e
D
<0
‘S i
UJ
Cl
C.
■ I
-2
TIME [»SEC3
TF'23
.5
O
*—«
m
lL
!
I ..
-
B
f ''
,1- V W f W
1«
T
e.
u
Cl
='
i CO
/ •
t
" ‘
J
-
U
LL
CL
-
1.5
B o tto m
H y d ro p h o n e
I
.
IS l
V
-2
TIM E
Im SEC I
I
F ig u r e 2 3 .
Tw o-phase F low , A ir Q u a lity = 87.82% , P r e s su r e
P u ls e f o r Top and Bottom H ydrophones, B u rst
P r e s s u r e = 14 p s i g .
101
Top H y d r o p h o n e
TP24
.5
' 1'I'i'''V//.,*.,!-».:,\s .-..ViA1IV
0
:
:
!7
/
-.5
I
-i
J
B o tto m H y d r o p h o n e
-1.5
-2
I i H E tiiSEC]
F ig u r e 2 4 .
Tw o-phase F low , A ir Q u a lity = 82.30% , P r e s su r e
P u ls e f o r Top and Bottom H ydrophones, B u rst
P r e s s u r e = 14 p s i g .
102
Top H y d r o p h o n e
.5
.A,XV-VyA '
r
pL_
-.5
L
-i
r
1
■
/
IS
Zi
0'i
U'l
B o tto m H y d r o p h o n e
ii
U
; ^
<L
7
-1.5
TIME CaSECl
F ig u r e 2 5 .
Tw o-phase F low , A ir Q u a lity = 78.14% , P r e s su r e
P u ls e f o r Top and Bottom H ydrophones, B u rst
P r e s s u r e = 14 p s i g .
103
TPie
j_
A
.5
V --v->.
er
Vl
lL
-.5
-I
P
:
p
[
r
[
-1.5
_ ' _____ I
r
Top H y d r o p h o n e
\I
r
TIME L t E E : ]
TP2e
.5
:O
I-Av'-'.--'-
>.0
LL
I
iu
r
Ie
'
'liV P V v ' A'\\A'.A'r/
iy
Z
I
B o tto m H y d r o p h o n e
r
VI
U
OL
CL
-1.5
L
L
TIME [ , E E C ]
F ig u r e 2 6 .
Tw o-phase F low , A ir Q u a lity = 76.33% , P r e s su r e
P u ls e f o r Top and Bottom H ydrophones, B u rst
P r e s s u r e = 14 p s i g .
104
TPl ?
,5
o
U)
6
Il
U
-.5
12'
Z'
<:>
v,
U
LL
C-
L
i
E
f
.
1
U
-2
f
^ ^
TT
f
r
-1.5 c
T
Vv W v
x vW V ai i
[
I1
Top H ydrophone
I
TIME I itSECT
TP2?
•5
O
v)
0
I:
m
Iu
12
tt
8-
-i
-1.5
1
t
Z
I
J
' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
B o tto m
H ydrophone
I/
TIME [»SEC1
F ig u r e 2 7 .
Tw o-phase F low , A ir Q u a lity = 73.13% , P r e s su r e
P u ls e f o r Top and Bottom H ydrophones, B u rst
P r e s s u r e = 14 p s i g .
105
Ffi!
A
u . ,—
'Tl
e.
IE
Ii
-.5
r
r
I
7
5
-I
Top H y d r o p h o n e
-1.5
:
-2.5
TlflE I it EEC j
Ffi 2
'lV';ry'‘
'S i
(L
U
LL
-.5
-I
j.
f
'i/,r, f ^
:e
7 v
E
B o tto m H y d r o p h o n e
Z'
'."I
I/I
U
Cl
Cl
-1.5
V
-2
-2.5
T I K E t mSEO]
F ig u re 28.
F low in g A ir , P r e s s u r e P u ls e f o r Top and Bottom
H ydrophones, B u rst P r e s su r e = 14 p s i g .
106
Sftl
.5
I
,'-V'
LI
Il
O'i
r
/
-I
:
. k-i-- *1Y-Tl,
4
5
Top H y d r o p h o n e
. |V
Li
Vf
li
i_
I
3
-.5
3
UJ
I rI V
2
-1.5
H H E Iii. S EC j
.5
AMr
V)
I
■I
b
U
Il
-r v ^ - A . .1'
-.5
/V
-I
B o tto m H y d r o p h o n e
U
/
Il
Il
r /v x - v # /'
e
=I
'Si
'SI
.
-1.5
t/
-2
IIHE USECl
F ig u re 29.
S t i l l A i r , P r e s s u r e P u l s e f o r Top a n d B o tto m
H y d r o p h o n e s , B u r s t P r e s s u r e = 14 p s i g .
107
TPll
MAGNITUDE
Top H y d r o p h o n e
FREQUENCY INDEX
T P2!
MAGNITUDE
B o tto m H y d r o p h o n e
FREQUENCY INDEX
F ig u r e 3 0 .
Tw o-phase F low , A ir Q u a lity = 93.13% ,
Frequency M agnitud es f o r Top and Bottom
H ydrophones.
108
TPl 2
.25
MAGNITUDE
f
.2
.15
.1
Top H y d r o p h o n e
.65
6
- - X - e
i6
26
TP22
56
46
FREQUENCY INDEX
56
66
76
MAGNITUDE
B o tto m H y d r o p h o n e
FREQUENCY INDEX
F ig u r e 3 1 .
Tw o-phase F low , A ir Q u a lity = 94.89% ,
Frequency M agnitud es f o r Top and Bottom
H ydrophones.
109
.25
r
TP13
MAGNITUDE
.2
,!5
-
.1
Top H y d r o p h o n e
.05
-------
e
30
40
FREQUENCY INDEX
Tf'23
56
60
70
MAGNITUDE
B o tto m H y d r o p h o n e
FREQUENCY INDEX
F ig u r e 3 2 .
Tw o-phase F low , A ir Q u a lity = 87.82% ,
Frequency M agnitud es f o r Top and Bottom
H ydrophones.
no
TP24
MAGNITUDE
B o tto m H y d r o p h o n e
FREQUENCY INDEX
F ig u r e 3 3 .
Tw o-phase F low , A ir Q u a lity = 82.30% ,
F requency M agnitud es f o r Top and Bottom
H ydrophones.
Ill
TPI5
MAGNITUDE
.25
E
K
Top H y d r o p h o n e
. 65
S
26
TP25
36
46
FREQUENCY INDEX
56
66
76
MAGNITUDE
.25
.15
-\
.1
\
.65
B o tto m H y d r o p h o n e
F ig u re 34.
10
20
30
40
FREQUENCY INDEX
I
0
"
J0
50
60
70
T w o - p h a s e F l o w , A i r Q u a l i t y = 7 8 .1 4 % ,
F r e q u e n c y M a g n i t u d e s f o r Top a n d B o tto m
H ydrophones.
112
T Pl b
.25
MAGNITUDE
F
.15
hI
v
.05
Top H ydrophone
e
0
10
26
TP26
.25
30
40
FREQUENCY INDEX
50
66
76
MAGNITUDE
.2
.15
h
\
.1
: i
\
.65
:
:
\
B ottom
V .
H ydrophone
\
a
6
6
F ig u r e 3 5 .
16
26
30
46
FREQUENCY INDEX
56
60
70
Tw o-phase F low , A ir Q u a lity = 76.33% ,
Frequency M agn itu d es f o r Top and Bottom
H ydrophones.
113
TP17
.25
MAGNITUDE
.2
I
.15
.1
Top H y d r o p h o n e
.65
k
r . . . . . .
6
6
16
.
- — .A ._
26
TP27
36
46
FREQUENCY INDEX
56
66
76
MAGNITUDE
B o tto m H y d r o p h o n e
FREQUENCY INDEX
F ig u r e 3 6 .
Tw o-phase F low , A ir Q u a lity = 73.13% ,
F requency M agn itu d es f o r Top and Bottom
H ydrophones.
114
Sfi!
NfiGIIITlK' :
Top H y d r o p h o n e
20
38
48
58
66
76
FREQUENCY INDEX
Sn2
.25
HfiGNITUDE
.2
.15
[
fr
I
.1
.65
0
I
0
F ig u r e 3 7 .
B o tto m H y d r o p h o n e
vx
18
20
30
40
FREQUENCY INDEX
50
60
70
S t i l l A i r , F requency M agnitud es f o r Top and
Bottom H ydrophones.
115
Top H y d r o p h o n e
FREQUENCY INDEX
Ffil'
MAGNITUDE
B o tto m H y d r o p h o n e
FREQUENCY INDEX
F i g u r e 38
F low in g A ir , F requency M agn itu d es f o r Top and
Bottom H ydrophones.
!
r
I
~T~
I
!
I
I
I
I .08
U ncertainty
Band
<xx>
0
O
I
I
i
O
0
o
O
%
I
I
.96
I
I
I
I
-
h
I .00
I
I
I .04
.92
F r e q u e n c y , i = 1 9 5 . 3 1 *N
I
Sp e c t r a I V e l o c i t y /
Sr oup V e l o c i t y
116
»
I
5
I
I
I
15
l
l
25
Frequency
F ig u r e 3 9 .
l
_I _____ L35
Index,
45
N
N orm alized V e l o c i t y v e r s u s F requency Index
f o r Two-phase Flow , A ir Q u a li t y = 93.13%,
B u rst P r e s s u r e = 14 p s i g .
Spectral
V e l o c i t y Z Group V e l o c i t y
117
!
I
!
!
I . OS
U ncertainty
Band
I .04
»
____ 1 _
I .00
-
-o -o * *
.9 6
.92
Frequency,
5
15
25
Frequency
F ig u r e 4 0 .
i
= I 9 5 . 3 1 *N
35
45
Index, N
N orm alized V e l o c i t y v e r s u s F requency Index
f o r Two-phase Flow , A ir Q u a li t y = 94.89%,
B u rst P r e s s u r e = 14 p s i g .
Velocity
I .04
L
I
U ncertainty
Band
Spectral
Velocity
/
I .0 8
G roup
118
0
I .00
.96
O
.92
F r e q u e n c y , f = I 9 5 . 3 1 *N
I
5
I
I
I
15
I
25
Frequency
F ig u r e 4 1 .
I
I
35
Index,
I
I
45
N
Norm alized V e l o c i t y v e r s u s Frequency Index
f o r Two-phase Flow, A ir Q u a li t y = 87.82%,
B u rst P r e s s u r e = 14 p s i g .
I
I
!
I
!
I
I
I
-
-
I .04
U ncertainty
Band
-
I
I
-
I
Spectral
n r
I .08
*1
-
I .00
I
O o
%
r
Velocity /
Group V e l o c i t y
119
.96
O O
-O
-
.92
Frequency, f =
I
l
5
l
l
15
l
l
25
Frequency
F ig u r e 4 2 .
I 9 5 . 3 1 *N
-
_____ I______ I______ l _
35
45
Index, N
N orm alized V e l o c i t y v e r s u s Frequency Index
f o r Two-phase Flow, A ir Q u a li t y = 82.30%,
B u rst P r e s s u r e = 14 p s i g .
!
!
!
!
n
!
!
r
-
I .04
U ncertainty
Band
-
— Ij
I
I
I .00
I
0I
-
O
<
pec t r a l
!
I .08
O
O
Velocity /
Group V e l o c i t y
120
O
O O
O
.9 6
O
"O
Frequency,
.9 2
I
5
l
l
l
15
l
l
25
Frequency
F ig u r e 4 3 .
f
1 9 5 . 3 1 *N
=
I
35
I
I
45
Index, N
N orm alized V e l o c i t y v e r s u s Frequency Index
f o r Two-phase Flow, A ir Q u a li t y = 78.14%,
B u rst P r e s s u r e = 14 p s i g .
!
!
!
!
!
!
!
!
!
I .08
U ncertainty
Band
\
I .04
-
I
-
I
$
=
I
I
f
I
I
I
I
j o
o
I .00
I
^
.96
I
O
--------------o —
I
Spectral
Velocity /
Group V e l o c i t y
121
.92
_0
Frequency,
I
I
5
I
I
15
l
l
F ig u r e
44.
l
25
Frequency
1 9 5 . 3 1 *N
l
35
Index,
l
45
N
N orm alized V e l o c i t y v e r s u s Frequency Index
f o r Two-phase F low , A ir Q u a li t y = 76.33%,
B u r s t P r e s s u r e = 14 p s i g .
Spectral
"i
i
I
I
I
I
r
I
I
I .O S
-
U ncertainty
.
Band
-
O
O
I
I
h
I
O
O
. 9 6
L
O
I
k>
I
I
I
I
I
I .00
I
I .04
-
T T
Velocity /
Group V e l o c i t y
122
--------------- ------------------------ —
O
O
.92
F r e q u e n c y , i = 1 9 5 . 3 1 *N
I
l
5
l
l
15
l
l
25
Frequency
F ig u r e 4 5 .
_____ I_______ I______ I______
35
45
Index, N
N orm alized V e l o c i t y v e r s u s Frequency Index
f o r Two-phase Flow , A ir Q u a li t y = 73.13%,
B u rst P r s s u r e = 14 p s i g .
I
l
l
l
I
I
I
U ncertainty
Band
■
- J
I
I
<b
I
I
f>
i
4
o
I
'
I .00
'I
I
f o
I
I
I
I
-
,i
I .04
I-
Velocity
l
-
I
I,
Spectral
l
I .08
/
Group
Velocity
123
o
-
.96
.92
Frequency,
I
5
l
l
l
15
l
l
=
1 9 5 . 3 1 *N
I
25
Frequency
F ig u r e 4 6 .
f
35
Index,
I
I
45
N
N orm alized V e l o c i t y v e r s u s F requency Index
f o r F low ing A i r , B u r s t P r e s s u r e = 14 p s i g .
124
I
I
I
I
I
~T~
I
I
I .04
U ncertainty
Band
-
-O ^ o — O
O O
O O
O O
i
I .00
o
i
.9 6
,I
I
I
O
I
CO
I
I . OS
Io
pe c t r a I V e l o c i t y /
G r o u p Ve I o c i
x
Frequency, f
, 3
I
5
I
I
I
15
I
25
Frequency
F ig u r e 4 7 .
I
I 9 5 . 3 1 *N
=
I
35
Index,
I
I
45
N
Norm alized V e l o c i t y v e r s u s F requency Index
fo r S t i l l A ir.
O
□
O
$
f = 3 9 0 . 5 Hz
f = 1 17 1 . 9 Hz
f = 2 5 3 9 . I Hz
f = 4 2 9 6 . 7 Hz
H
♦
f = 6 6 4 0 . 6 Hz
£ - 7 8 1 2 . 5 Hz
f = 3 7 8 9 . I Hz
X
U ncertalnCy
Band
1.10
I .00
ec I r a l
Me I o c i t /
/
Gr o u p
Meloci t >
125
. /5
.30
.3 5
A ir
Figure
48
. 'PO
.95
I .00
Quality
N orm alized V e lo c it y v e r s u s A ir Q u a lity as
a Function of Frequency.
my ObjCiU
C alib ratio n C h a rt fo r
H y d ro p h o n e Type 8 1 0 3
Brtiel A Kjmr
P u lc iilio iiiv lv r
Serial N o. V / J - t V e i
Netun DuuiwX
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T e m p u ia lu ie I ie n s ie ii l S e n s iliv iiy . - 6 0 P a / vC
(ANSI S 2 I I 19 6 9 ). IiitidSUiciI Willi B S K C liaig e
P itidiuplilitii Iy p e 2 6 2 6 L lF 3 H f
Q -
A llo w a b le T o ta l R a d ia lio n D o s e . b« IO * H ad
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H o iu o n ia l D iiu c liv iiy 2 0 0 h H l
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ly p ical : 4 dB
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Figure 49.
Top H y d r o p h o n e F r e q u e n c y R e s p o n s e C h a r a c t e r i s t i c s
126
Q. iI
M O at
C h a n g e o l S e n s iliv iiy w ith S i a li c P i e s s u i e
3 - 1 0 - 'u B P e ( O O S d B Z e io )
F ieg u e n cy R e sp o n se .
Individual F in e Field F m g u en c y R e sp o n se C u iv e
e iia c h e d
D ele
ZQ*
O p e i e lin g l e m p e i e l u i e R a n g e .
4 0 “C Io . I ZOvC
4 0 F io . 2 4 8 - F
Briiel & Kjaer
C alib ratio n C h a rt for
H y d ro p h o n e Type 8 1 0 3
Serial N o.
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in c lu d in g 6 in m ie g ia l c ab le
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0 .1 Hz to 1 4 0 kHz : 2 d d
il D ire c tiv ity I
T e m p e ia tu r e T r a n s ie n t S e n s itiv ity . - bO P a C
(ANSI S 2 I I 1 9 6 9 , m e a s u r e d w ill, B S K Cl,,
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r
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3 * 1 0 - >dB- Pa ( 0 . 0 3 UB ate)
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F ig u re 50.
Bottom Hydrophone F re q u e n c y R esp o n se C h a r a c t e r i s t i c s
127
ILlO
C e p e c ite n c e (in clu d in g 6 in c ab le)
O p e r a tin g I e n ip e id iu i o R a n g e
—4 O0C io • I 2 0 , C
4 0 F to . 2 4 8 F
C h a n g e o l S e n s itiv ity w ith I e m p e i a l u i e
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C h a r g e S e n sitiv ity
D ate
MiJat
UB re I V Z p P a e e
cWz Zr UB ie I V p e i P a or
128
APPENDIX D
VELOCITY CALCULATIONS
The time between each d i g i t i z e d data p o i n t , At = .00001 seconds
The t o t a l number o f p o in t s analyzed from each f i l e , N= 512
T otal tim e, t t = NAt = .00512 seconds
T r a n s f o r m in g t h e t i m e dom ain sequence i n t o th e frgequency
domain r e s u l t e d in a change in frequency between each p oin t o f ,
Af = l/( N A t ) = 195.31 Hz
The number of p o in t s between le a d in g edges o f the pressure
p u lse i s Np
This corresponds t o a tim e of
t = NpAt. The group v e l o c i t y ,
V, i s t h e d i s t a n c e b e t w e e n h y d r o p h o n e s , I f o o t , d i v i d e d by th e
tim e , t.
V = 1 /t
The p h a s e s f o r t h e t o p and b o tto m h y d r o p h o n e s , <f>^, and <j>2»
were c a l c u la t e d by MULT.F.
The t i m e d e l a y , t , c a u s e d by t h e p h a se change o c c u r r i n g
between the two hydrophones was
T = ((J)1 - (Ii2 ) /(2nKAf)
The s p e c t r a l s o n ic v e l o c i t y was c a l c u la t e d by
c = l / ( t + 't )
EXAMPLE
Np = 89
Q1 = 2.94703
K= 6
<f»2 = 2.63458
129
Group V e l o c i t y , V = I / (8 9 * .0 0 0 0 1 ) = 1123.6 f e e t / s e c o n d
f = KAf = 6*195.31 = 1171.9 Hertz
T = (2 .9 4 7 0 3 - 2 . 6 3 4 5 8 ) 7 ( 2 * 1 1 7 1 .9 ) = .00004243 seconds
C = ! / ( . 0 0 0 8 9 + .00004243) = 1072.5 f e e t / s e c o n d
MONTANA STATE UNIVERSITY LIBRARIES
stks N378.W377
t
r, RL
Shock wave propagation in two-phase flow
3 1762 00512364 9
Tain
N778
W3T7
cop.2
DATt
Weav e r , Mic h a e l J.
Shock w a v e pro-carat ion
in t w o - p h a s e flow
IS S U E D TO
v R -r
9378
W377
COT).
2