t -. '. i · vortex tube. in his analysis, he assuned both a free and forced vortex reg- ion...
TRANSCRIPT
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DEPARTMENT OF MECHANICAL ENGINEERING AND MECHANICS SCHOOL OF ENGINEERING OLD D O M I N I O N U N I V E R S I T Y NORFOLK, V I R G I N I A
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EXPERIMENTAL AND ANALYTICAL STUDIES I N FLUIDS 73/64
BY
Gene L. Gogl ia, P r i n c i p a l I n v e s t i g a t o r
and
. Ado1 .-- Thrahim -e. -.. ....
Prepared f o r t h e N a t i o n a l Aeronaut ics and Space A d m i n i s t r a t i Langley Research Center Hampton, V i r g i n i a 23665
Under NASA Grant NSG-1177 R icha rd F. Hellbaun, Techn ica l M o n i t o r FCSD-Cockpi t Systems Branch
F i n a l Report F o r t h e p e r i o d ending August 31, 1984 .I
(NASA-CR-181242) B X P E B I B E I T A L Aa6D 887-2744 3 B l i B L Y I I C A L STUDIES 1% P L U I C S € i n a l Ereport, ~ ~ ~ i o d e n d i o q 3 1 Auq- 1584 ( C l d Dominion U r i v - ) 101 p A v a i l : 8 T l S EC AC6/W A01 Unclas
CSCL 20D 63/34 0093SC4
https://ntrs.nasa.gov/search.jsp?R=19870018510 2020-03-20T10:10:07+00:00Z
DEPARTMENT OF MECHANICAL ENGINEERING AND MECHANICS SCHOOL OF ENGINEERING OLD DOMINION UNIVERSITY NORFOLK, V I R G I N I A
EXPERIMENTAL AND ANALYTICAL STUDIES I N FLUIDS
BY
Gene L. Goglia, P r i n c i p a l I n v e s t i g a t o r
and
Adel I b rah im
F i n a l Report Fo r t h e p e r i o d ending August 31, 1984
Prepared f o r t h e N a t i o n a l Aeronaut ics and Space A d m i n i s t r a t i o n Langley Research Center ilampton, V i r g i n i a 23665
Under NASA Grant NSG-1177 R icha rd F. Hellbaun, Techn ica l M o n i t o r FCSD-Cockpi t Systems Branch
Submitted by t h e 01 d Dominion U n i v e r s i t y Research Foundat ion
N o r f o l k , V i r g i n i a 23508 h P.O. Box 6369
September 1984
TABLE OF CONTENTS
INTRODUCTION .................................................... EXPERIMENTAL EQUIPMENT .......................................... EXPERIMENTAL RESULTS ............................................ REGRESSION ANALYSIS ............................................. CONCLUSION.. .................................................... REFERENCES. ..................................................... APPENDIX........... .............................................
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LIST OF TABLES
Table Paye
I Vortex tube dimensions. .................................... 43
LIST OF FIGURES
F i gure
Flow r a t e vs. f requency response f o r sensor 1 w i t h t h r e e s w i r l e r s hav ing var ious diameters .......................... Flow r a t e vs . f requency f o r sensor 1 with t w o s w i r l e r s hav ing var ious diameters............. ...................... Flow r a t e vs. f requency f o r sensor 2 w i t h t h r e e s w i r l e r s hav ing var ious diameters ................................... Flow r a t e vs. frequency f o r sensor 2 w i t h two s w i r l e r s hav ing var ious diameters. .................................. Flow r a t e vs. frequency f o r sensor 3 w i t h t h r e e s w i r l e r s hav ing var ious diameters. .................................. Flow r a t e vs. frequency f o r sensor 3 w i t h two s w i r l e r s hav ing var ious diameters ................................... Flow r a t e v s . f requency f o r sensor 4 w i t h t h r e e s w i r l e r s hav ing var ious diameter .................................... Flow r a t e vs. f requency f o r sensor 4 w i t h two s w i r l e r s having var ious diameters ...................................
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TABLE OF CONTENTS - continued
LIST OF FIGURES - continued
Figure
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Flow r a t e vs. frequency for sensor 5 w i t h three swirlers having various diameters..... .............................. Flow r a t e vs. frequency for sensor 5 with two swirlers having various diameters.. ................................. Flow r a t e vs. frequency for sensor 6 with three swirlers having various diameters........... ........................ Flow r a t e vs. frequency for sensor 6 with two swirlers having various diameters. .................................. Flow ra t e vs. frequency for sensor 7 with three swirlers having various dimeters .................................... Flow ra t e vs. frequency for sensor 7 with two swirlers having various diameters ................................... Flow ra t e vs. frequency for sensor 8 with three swirlers having various diameters ................................... Flow r a t e vs. frequency for sensor 8 with two swirlers having various diameters.... ............................... Flow r a t e vs. frequency for sensor 9 with three swirlers having various diameters ................................... Flow r a t e vs. frequency for sensor 9 with two swirlers having various diameters ................................... Flow r a t e vs. frequency for sensor 10 with three swirlers having various diameters.......... ......................... Flow r a t e vs. frequency for sensor 10 with two swirlers having various diameters. .................................. Flow ra t e vs. frequency for sensor 11 with three swirlers having various diameters......... .......................... Flow r a t e vs. frequency for sensor 11 with two swirlers having various diameters ................................... Flow r a t e vs. frequency for sensor 12 with three swirlers having various diameters. .................................. Flow r a t e vs. frequency for sensor 1 2 w i t h two swirlers having various diameters. ..................................
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i i i
TABLE OF CONTENTS - cont inued
LIST OF FIGURES - cont inued
F i g u r e
25 E f f e c t o f var ious s w i r l e r diameters on t h e frequency, sensor 1. ..................................................
26 E f f e c t o f var ious s w i r l e r diameters on t h e frequency, sensor 2.. .................................................
27 E f f e c t of var ious s w i r l e r diameters on t h e frequency, sensor 3. ..................................................
28 E f f e c t o f var ious s w i r l e r diameters on t h e frequency, sensor ....................................................
29 E f f e c t o f var ious s w i r l e r diameters on t h e frequency, sensor 5...................................................
30 E f f e c t o f var ious s w i r l e r diameters on t h e freuency, sensor 4 . . .................................................
31 E f f e c t o f var ious s w i r l e r diameters on t h e frequency, sensor 7....... ............................................
32 E f f e c t o f var ious s w i r l e r diameters on t h e frequency, sensor 8.... ...............................................
33 E f f e c t o f var ious s w i r l e r diameters on t h e frequency, sensor 9.. .................................................
34 E f f e c t o f var ious s w i r l e r diameters on t h e frequency, sensor 10 ..................................................
35 E f f e c t o f var ious s w i r l e r diameters on t h e frequency, sensor 11 ..................................................
36 E f f e c t o f var ious s w i r l e r diameters on t h e frequency, sensor 1 2 ..................................................
37
38
39
40 E f f e c t o f t h e (P) l e n g t h on t h e frequency .................. 41 E f f e c t o f p i c k up s i g n a l p o i n t on frequency ................ 42 E f f e c t o f t h e s w i r l e r diameter on frequency ................
Ef fec t o f t h e sensor tube l e n g t h on t h e f requency .......... E f f e c t o f sensor tube diameter on the frequency ............ E f f e c t o f t h e nozz le l e n g t h on t h e frequency ...............
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TABLE OF CONTENTS - con ten ts
LIST OF FIGURES - cont inued
F i gure Page
43 E f f e c t o f sensor tube leng th increase on frequency.. ....... 86
44 E f f e c t o f increase o f sensor tube diameter on frequency 57 ..................................................
45 E f f e c t o f increase o f l e n g t h (P) on t h e frequency .......... 88
46 E f f e c t o f inc rease o f nozzle l e n g t h on frequency ........... 89
47 E f f e c t o f inc rease o f t h e pickup signal p o i n t
48 E f f e c t o f inc rease o f t h e s w i r l e r diameter on
l e n g t h on frequency 90
frequency 91
........................................ ..................................................
I
V
EXPERIMENTAL AND AiIALYTICAL STUOIES I N FLUIDS
Gene L. Gog
BY
i a l and Ade I b r a h im2
INTRODUCTION
A t t h e present t ime, t h e r e are two types o f a i rspeed i n s t r u n e n t s which
migh t be used on a i r c r a f t : t h e d i f f e r e n t i a l - p r e s s u r e t y p e and t h e t r u e
a i rspeed meter. The P i t o t - s t a t i c inst runent , which i s o f t h e d i f f e r e n t i a l -
p ressure type, i s however e x c l u s i v e l y used. T h i s i n d i c a t o r i s c a l i b r a t e d i n
terms o f a i rspeed a t a standard a i r densi ty. I n o rder t o o b t a i n t h e ac tua l
a i rspeed a t o t h e r d e n s i t i e s , a c o r r e c t i o n must be made. Fur ther , t h e
per fomance o f t h e P i t o t - s t a t i c tube i s a f f e c t e d by i n s t a l l a t i o n l o c a t i o n .
One must, there fore , f i n d . a l o c a t i o n f o r the P i t o t - s t a t i c openings t h a t w i l l
be f r e e from s t r u c t u r a l i n t e r f e r e n c e e f f e c t s .
The t r u e airspeed sensor i s t h e convent ional t y p e o f meter w i t h
r o t a t i n g surfaces, such as prope l le rs , which g ives readings independent o f
a i r dens i ty . The sensor i s u s u a l l y used i n making measurements o f a i rspeeds
i n t h e lower ranges. One k i n d o f t r u e airspeed sensor used by t h e Un i ted
Sta tes Navy on a i r s h i p s i s known as t h e commutator-condensor type.
The i d e a of des ign ing a t r u e airspeed sensor o r i g i n a t e d f rom the
d i s c o v e r y o f a vor tex w h i s t l e and t h e f l o w phenomenon-precession, which i s
d i f f e r e n t f rom t h a t of vor tex shedding. The understanding o f t h e o r i g i n o f
Eminent Professor, Mechanical Engineering and Mechanics Department, 01 d Dominion U n i v e r s i t y , Nor fo lk , V i r g i n i a 23508
Department, Old Dominion U n i v e r s i t y , Nor fo lk , V i r g i n i a 23508. 2Graduate Research Ass is tant , Mechanical Engineering and Mechanics
the sound o r whistle was studied by a few investigators [ l - 3 ] * from differ-
ent points of view. Also, the vortex shedding problems associated with the
aero1 ian tones and edgetones were studied and observed experimental ly by
many researchers. The project was maintained by a small s taff which worked
on the vortex whistle and precessional flow problems. Bernard Vonnegut [ l ]
in 1954 was the f i r s t t o discover and investigate the vortex whistle. In
his laboratory, he was conducting an experiment on a vortex creating housing
for a i rc raf t thermometers. D u r i n g the experiment, he observed a sound tha t
was generated when the r o t a t i n g a i r escaped from the open end of the tube.
He also found t h a t the frequency of th i s sound increased with increasing
rates of a i r flow. In addition, the frequency t h a t was produced decreased
as the- length of the tube in w h i c h the vortex rotates was increased.
Vonnegut suggested t h a t the vortex instabi l i ty leaving the tube caused the
whistle, and he developed an empirical formula describing t h i s performance.
In 1955, Irving Michelson [2] published a paper which was the f i r s t
analytical work.on the theory of a vortex whistle. He considered the flow
throughout the whistle t o be two-dimensional unsteady, inviscid and i sen-
tropic. He was able t o arrive a t linearized simultaneous equations. A
secular equation was then derived with one roo t of particular interest being
noted. From the solution and the secular equation, he noted the occurrence
of a frequency that was proportional t o the flow speed U . When he intro-
duced the isentropic flow relatiofiship, he was able t o express the frequency
in terms o f pressure d r o p and reservoir sound speed. Michelson's theory
compares favorably with Vonnegut's empirical formula.
In 1957, J. P. Nicklas [3 ] on his investigation o f a vortex tube acous-
t i c true airspeed sensor conducted a t t h e Cornel 1 Aeronautical Laboratory.
*Numbers i n brackets i nd icate references.
2
He i n v e s t i g a t e d t h e feas b i l i t y o f measuring t r u e a i r c r a f t a i rspeed b y mea-
s u r i n g t h e frequency of t h e sound produced i n a v o r t e x tube mounted on an
a i rp lane. Nick1 as, however, concentrated h i s e f f o r t s on t h e s i n g l e tangen-
t i a l nozz le v o r t e x tube. H i s d a t a revealed t h a t t h e f u n d m e n t a l sound
frequency o f a vor tex tube cou ld be considered a ' l i n e a r f u n c t i o n o f t r u e
airspeed i n t h e subsonic speed range. He i n d i c a t e d t h a t t h e a l t i t u d e and
temperature s e n s i t i v i t i e s of t h e vor tex tube cou ld be reduced by proper
design. In h i s conclusion, he a lso mentioned t h a t no s i g n i f i c a n t improve-
l e n t i n s i g n a l q u a l i t y was obta ined b y modi fy ing t h e tube shape. N i c k l a s
s t u d i e d t h e e f f e c t t h e angle of a t t a c k had on frequency response.
I n 1960, M. Suzuki s tud ied and i n v e s t i g a t e d t h e v o r t e x tube w i t h t h e
o b j e c t i v e of f i n d i n g a method o f e l i m i n a t i n g t h e w h i s t l e o c c u r r i n g i n t h e
v o r t e x tube. In h i s analys is , he assuned bo th a f r e e and f o r c e d v o r t e x reg-
i o n o f v e l o c i t y d i s t r i b u t i o n . Suruki, using t h e boundary c o n d i t i o n s a t t h e
w a l l and a t t h e i n t e r f a c e between f r e e and f o r c e d vor tex, der ived a l i n e a r l y
p r o p o r t i o n a l r e 1 a t i o n s h i p between the pecul i a r f requency and t h e a n y 1 ar
v e l o c i t y of t h e f o r c e d vor tex. I n h i s der iva t ion , t h e d e n s i t y and v e l o c i t y
components were separated i n t o mean and f l u c t u a t i o n terms. Suzuki i n t r o -
duced a nunber of assunptions and r e s t r i c t i o n s t o enable him t o o b t a i n t h e
Besse l ' s equat ion and i t s so lu t ion . Although Suzuki d i d n o t present e i t h e r
n u n e r i c a l o r q u a n t i t a t i v e r e s u l t s , he did, however, r e p o r t and d iscuss h i s
exper imenta l data. In a d d i t i o n t o t h e l i n e a r r e l a t i o n s h i p , Suzuki found
t h a t no sound was produced a t small f l o w r a t e s , and t h a t when t h e va lue o f
Lc /Dc Lc
was t h e l e n g t h o f c o l d tube i n h i s model, whereas t h e Dc was t h e diameter
of t h e o u t l e t .
was l e s s t h a n u n i t y , no d i s t i n c t f requency c o u l d be observed.
In 1963, Robert C. Chanaud [ 4 ] converted Vonnegut's d a t a i n t o Reynold's
3
and Strouhal nunbers, and found t h a t the a i r and water d a t a were almost
co inc ident , suggest ing t h a t dynamic s i m i l a r i t y m iqh t occur. The per turba-
t i o n o f a two-dimensional i n v i s c i d vor tex f l o w was inves t iga ted . Chanaud
d e r i v e d a 1 inear r e l a t i o n s h i p between p e r t u r b a t i o n f requency and f l u i d angu-
l a r v e l o c i t y f o r n e u t r a l l y s t a b l e o s c i l l a t i o n s o f an i n v i s c i d f l o w . H i s
r e s u l t s support t h e i n v e s t i g a t i o n s and conclusions repor ted b y Vonnegut and
Michelson. He conf i rmed t h a t t h e precessional f requency i s t h e same as t h e
sound frequency and t h a t t h e f l u i d angular v e l o c i t y i s s imp ly r e l a t e d w i t h
t h e precess ion frequency o f t h e unstable motion. I n h i s conclusion, he
mentioned t h a t "h igh speedll'was n o t necessary t o generate t h e wh is t le , as
v e l o c i t i e s o f f i v e f e e t per second were found s u f f i c i e n t . He, as o t h e r s
d id , expla ined t h a t t h e i n s t a b i l i t y which occurred was due t o t h e sudden
area change a t t h e tube e x i t . Chanaud's r e s u l t s show t h a t t h e ampl i tude o f
o s c i l l a t i o n w i t h i n t h e tube depends on how t h e area changes; a gradual area
increase permi ts l a r g e r ampl i tude f l o w o s c i l l a t i o n s whereas an abrupt area
. change reduces t h e magnitude o f t h e f l o w o s c i l l a t i o n w i t h i n t h e tube. He
mentioned t h a t t h i s may be t h e reason Vonnegut d i d n o t d e t e c t t h e sound w i t h
a f l a r e d tube. He a lso s t a t e d t h a t no q u a n t i t a t i v e i n f o r m a t i o n on t h e na-
t u r e o f t h e i n s t a b i l i t y had been obtained.
Powel l [5] i n 1964 pub l ished a paper d iscuss ing t h e o r i g i n o f t h e
sound. He showed and expla ined i n d e t a i l f rom a phys ica l p o i n t o f v iew how
aerodynamic sound i n an unsteady f l u i d f l o w was generated as a r e s u l t of t h e
movement o f v o r t i c e s , o r o f v o r t i c i t y .
I n 1965, Chanaud [8 ] publ ished a paper d e s c r i b i n g t h e exper imental
s tudy i n c e r t a i n s w i r l i n g f lows. One o f t h e s w i r l i n g f lows was s t u d i e d by
Talbo t . The exper imental r e s u l t s show t h a t t h e p e r i o d i c mot ion i n bo th a
v o r t e x w h i s t l e and a cyc lone separator can b e descr ibed i n terms o f a
4
hydrodynanic osc i l la tor where the frequency i s closely related t o the angu-
l a r velocity of the flow. Chanaud also mentioned tha t the two important
parameters, the Reynolds nunber and the Strouhal nunber, are both of such
magnitude tha t i t appears no important simplifications can be made i n the
equations of motion t o solve the problem analytically. The energy of the
osc i l la tor i s derived from the hydrodynamic in s t ab i l i t y of the f l u i d w i t h i n
a reversed-flow region on the swirl axis. No quantitative information i s
available on the condition of a steady reversed-flow region. Chanaud, how-
ever, mentioned tha t the experimental results suggest t ha t the two-dimen-
sional perturbation analysis may prove of some value i n describing the am-
p l i f i e r part of the osci l la tor .
Rodely, found tha t the osc i l l ative .motion began only beyond certain
Reynolds nunbers. He also observed that the osc i l la t ive motion was
accompanied by the reversal of f low near the t u b e axis. Gove and Ranz [ 6 ]
in the i r paper explained i n detail this reversal of flow. The reversal of
flow was caused by the sudden area enlargement at the t u b e exi t . In the
bet ter swirler designs the Rossby nunber could be h e l d constant for various
Reynolds nmbers. This indicates t ha t t h e frequency i s 1 inearly related t o
the flow ra te . However, below some Reynolds nunber, due t o viscous e f fec ts ,
there were deviations from the constant value.
Chanaud again i n 1970 [8] suggested that i n the aerodynamic whistle the
v i b r a t i n g system i s the a i r i t se l f . This i s i n contrast t o nonaerodynamic
devices such as a d run or loud speaker, where sound i s generated when a
mechanical system vibrates and disturbs the a i r . Chanaud showed tha t d u e t o
the ins tab i l i ty of the system a small disturbance i n the stream flowing
through the aerodynmic whistle was amplified, and tha t kinetic energy was
converted t o osci l la tory energy. Part of the energy of the amplified
5
d is tu rbance i s f e d back upstream, where the f l o w i s most unstable, and, i f
t h e r i g h t frequency and ampl i tude ex is ts , i t i n t e r a c t s w i t h t h e o r i g i n a l
d is tu rbance t o ma in ta in t h e process. A f t e r a few c y c l e s t h e feedback con-
t r o l s t h e i n p u t cunp le te ly . A w h i s t l e i s produced when t h e f l o w speed i s
h i g h enough and t h e frequency i s i n t h e audib le range.
As prev ious ly , mentioned, t h e r e i s one common f e a t u r e t h a t in t roduces
t h e concept o f "no moving p a r t s " i n f l u i d i c devices. In c o n t r a s t t o t h i s
concept i s t h e dev ice w i t h moving par ts . F l u i d i c devices have been w i d e l y
researched i n t h e past 19 years. Simp1 ici ty, r e 1 i a b i l i t y and easy mainte-
nance make f l u i d i c devices a t t r a c t i v e .
o f F l u i d i c Components, wor thy o f ment ion i s :
A quote f rom t h e t e x t Design Theory
Although present t h e o r y g ives r e s u l t s s iif f i e ien t : y aeeiir ate f o r eiig ineer 5 i ig design, i t i s n o t poss ib le t o j u s t i f y a l l t h e assunpt ions used. s c i e n t i f i c sense t h e theory i s n o t always s a t i s f y i n g , b u t i n an engineer- i n g design sense t h e theory does seem t o b e s a t i s f a c t o r y .
Thus i n 'a
In t h i s i n v e s t i g a t i o n f l u i d i c models were designed and then t e s t e d i n
b o t h water and a i r . Flow v i s u a l i z a t i o n t e s t s i n a water model were under-
taken i n o r d e r t o a c t u a l l y see t h e f l o w phenomenon o f precession. Smal ler
models were subsequently made f o r t e s t i n g w i t h compressed a i r and i n a wind
tunne l . An exper imental a n a l y s i s was provided i n t h i s s tudy. The p h y s i c a l
models were s imulated and used i n computer c a l c u l a t i o n . The n u n e r i c a l so lu-
t i o n s i n v o l v e d t r u e airspeeds up t o 321.89 km (200 mi les) per hour. S ix
d i f f e r e n t combinat ions of vor tex tubes and s w i r l e r s were used bo th i n cornpu-
t e r c a l c u l a t i o n s as w e l l as i n experimental t e s t s .
The o b j e c t i v e of t h i s study was two- fo ld . The f i r s t o b j e c t i v e was t o
analyze ana des ign a t r u e airspeed sensor which w i l l r e p i a c e t h e convention-
6
a1 Pi tot-s ta t ic pressure transducer for smal 1 commercial a i rc raf t . The
desired features of t h i s sensor should include the flow phenomenon-preces-
sion, vortex whistle and have no m o v i n g par t s . In addition, this sensor
should n o t be affected by temperature, density, alt i tude, and h u n i d i t y chan-
ges. The second objective was to obtain a nunerical solution and predict
the frequency response which i s generated by the vortex whistle a t a certain
airspeed. In .a previous study, Shen [ 151, theoretical resul ts were present-
ed quantitatively t o enable a comparison w i t h experimental data. That study
also prssented a general solution t o the problem and provided specific ana-
lyt ical resul ts for comparison purposes. A correction factor f o r viscous
e f fec ts was also introduced t o enable a correl ation between theoretical
resul ts and experimental d a t a .
The objective of the current investigation was t o continue previous
studies w i t h the intent t o develop a new technique of sensing. The new
technique would then be used to develop a true airspeed sensor.
E XP ER l?l ENTAL EQU I PM ENT
The equi p e n t used throughout these experiments essenti a1 ly consi sted
of an a i r supply, pressure regulators, a calibrated or i f ice plate flow
meter, a pressure transducer, an electronic condenser microphone and signal
conditioner, an oscilloscope, a frequency counter and a vortex tube sensor.
The a i r used f o r the experiments flowed from a stagnation t a n k and
ultimately passed t h r o u g h the sensor. A calibrated or i f ice plate flow meter
with a capacity of one cubic foot per minute was used t o measure the flow
rate . The differential pressure across the or i f ice plate was measured with
a pressure cap entrance pressure transducer. An electronic condenser micro-
phone and signal conditioner was used t o detect the whistle signals. Tne
7
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electronic
a gain of
signal from the microphone was directed t o an amp1 i f i e r which had
50. The amplifier signal was forwarded t o a comparator c i rcu i t
whose o u t p u t was connected t o an oscilloscope and frequency counter.
In previous investigations frequency measurements below 700 HZ were not
attainable. In the current investigation, however, signals t h r o u g h the 60
H Z noise level down t o 20 HZ were achieved. This was accomplished t h r o u g h
use of a particular combination of amplifier and comparator c i rcu i t .
The t rue a i r speed sensor t h a t was used in t h i s study consisted of four
blocks. The a i r flow was directed th rough an in le t cover block t o a swirler
block. Within the swirler block the vortex swirl was generated. The a i r
then flowed through a third block w h i c h housed the vortex tube, which in
r ea l i t y was a diverging nozzle. iJithin the swirler block was placed a small.
o r i f ice and microphone. The generated signal frequency which occurred a t
the sudden enlargement was the location a t which the whistle was detected.
In the side of the vortex tube by housing a small o r i f ice and microphone the
whistle noise could be observed. From the sudden enlargement the a i r then
flowed t o the cover block. Noise on i t s way t o the microphone was reduced
by instal l ing a pad of f e l t in the blocks.
EXPERIMENTAL RESULTS
The experimental data obtained from th i s investigation was arrived a t
t h r o u g h the use of twelve ( 1 2 ) vortex tubes with diameters ranging from
0.25 inches t o 0.093 inches and f ive ( 5 ) swirlers with diameters from 0.5
inches t o 2.0 inches. Experimental results were obtained f o r each vortex
t u b e r u n separately with each of the swirlers o r s i x t y (60) different
configurations.
, A primary objective i n conducting these experiments was t o determine
8
t
t
the effect that the sensor geometric parameters had upon the frequency pre-
cession.
A s t a t i s t i ca l technique, namely the regressional analysis, was used t o
determine frequency dependency upon sensor geometry. This analysis involved
each of the f ive (5) swirlers combined w i t h each of the twelve ( 1 2 ) vortex
tubes.
Figures 1 t h r o u g h 24 are flow ratio versus frequency g raphs f o r the
various combinations of vortex tubes and swirlers.
that the flow ra te i s linearly proportional t o the frequency.
I t i s readily observable
Figures 25 t h r o u g h 35 were plotted t o indicate the effect changes i n
swirler diameter had on the frequency. I t i s apparent from those plots t h a t
frequency decreases as the swirler diameter i s increased for the majority o f
the vortex tubes.
Figure 36 reveals that tube length i s l inearly proport ional t o fre-
quency response and also t h a t frequency decreases w i t h increase in tube
length. Similarly, Figure 37 shows frequency t o be l inearly proportional t o
the vortex tube diameter and frequency increase w i t h a decrease i n vortex
tube d i ameter . Figure 38 reveals the exit nozzle length is linearly proport ional t o
frequency and that the frequency increases with an increase in nozzle
1 ength.
Figures 39 and 40 show b o t h P and P-S t o be linearly proportional t o
frequency response.
Figure 42 enables one t o estimate t h e percentages decrease i n frequency
Similarly figure 43 enables corresponding t o a vortex tube length increase.
one t o estimate the percentage decrease i n frequency corresponding t o a
vortex tube diameter increase.
9
Figure 44 enables one t o estimate the percentage change i n frequency
due t o a change in the P parameter. Figure 45 enables one t o estimate the
percentage change i n frequency due t o a change i n the S parameter. Figure
46 enables one t o estimate the percentage change i n frequency due t o a
change i n the P-S parmeter. Figure 47 enables one to estimate the change
in frequency due t o a change in swirler diameter.
A1 though in previous investigations frequencies below 700 HZ were n o t
attainable, however, through modifications made to the sensor, frequencies
as low as 20 HZ are attainable. Specifically by using vortex tube nunber
four and either swirler two or three a minunum frequency precession of 20 HZ
i s attainable.
.
10
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REGRESSION ANALYSIS
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CONCLUSION
I The p r ,,icipal conclusions from t h i s investiga
f o l 1 ows :
ion can be sunrnarized as
1. Flow ra te measurements indicate tha t the vortex tube sound frequen-
cy i s linearly proportional t o t h e frequency response.
The vortex tube whistle frequency i s dependent upon the qeometrical 2.
tube paraneters t o such an extent t h a t : an increase i n vortex tube
length produces a decrease i n frequency response and that an i n -
crease i n the exhaust nozzle length produces an increase i n the
frequency precession.
3. An increase i n the vortex tube diameter produces a decrease i n
frequency precession.
An increase i n swirler diameter produces a decrease i n frequency. 4.
5. An increase i n the location distance of the microphone pickup s ig-
nal point from the inside edqe o f the exi t nozzle produces an i n -
crease i n frequency response.
The experimental resul ts indicate t h a t those parameters most signifi-
cantly effecting frequency are i n descending order of importance microphone
location, vortex tube diameter, ex i t nozzle length, vortex tube length and
swirl er diameter.
41
I REFERENCES I
I 1.
~
2. I
I
I 3.
, 4. ,
5.
6.
7.
8.
9.
I 10.
11.
12
13.
14.
15.
Vonnegut, Bernard: A Vortex Whist le. J. Acoust. SOC. Anerica, Vol. 26,
Michelson, I r v i n g : Theory of Vortex Whistle. J. Acoust. SOC. Pmerica,
Nicklas, J.P.,: I n v e s t i g a t i o n o f a Vortex Tube True Airspeed Sensor. Cornel 1 Aeronaut ical Labora tor ies . Report 1H-942-P-2, 1957.
Chanaud, R.C.,: Experiments Concerning t h e Vortex Whist le . J. Acoust. SOC. Pmerica, Vol. 35, No. 7 1963, pp. 953-960.
Powel 1, A1 an: Theory o f Vortex Sound. J. Acoust. SOC. Anerica, Vol . 36, No. 1, Jan. 1964 pp. 177-195.
Gove, R.W. and Ranz, W.E.,: Backflows i n Rota t ing F l u i d s Moving A x i a l l y Through Expanding Cross Sect ions. h e r . I n s t . Chem. Enq.
Bossel, Hartmut H.,: Vortex Breakdown F lowf ie ld . The Physics o f F l u i d s . Vol. 12 No. 3 March 1969 pp. 498-508.
Chanaud, R.C.,: Aerodynamic Whist les. Sci . Am., Vol. 222, No. 1, 1973,
Wilson, T.A.,: Experiments on t h e F l u i d Mechanics o f Whis t l ing . J. Acoust. Soc. h e . , Vol. 50. No. 1 ( P a r t 2) 1971 pp. 366-372.
Randall, J.D. and Leibov ich S.,: J. F l u i d Mech., Vol. 58, Par t 3, 1973
Kubo, I. and Gouldin, F.C.,: Numerical C a l c u l a t i o n s o f Turbulent - S w i r l i n g Flow. Transact ion o f t h e ASME. September 1975 pp. 310-315.
Bossel, H.H.,: S w i r l i n g Flows i n Streamtubes o f Var iab le Cross Sect ion. J. A I A A Vol. 1 September 1972 pp. 1161-1164.
L e t t e r To The E d i t o r : J. Sound and Vibrat ion, Vol 38, 1975, No. 1 pp.
C a l i f , B.,: Laminar S w i r l i n g Pipe Flow. J. Appl ied Mech. J u l y 1952. Paper No. 53 - AP!4 -24.
Shen, Y.C. and Goglia, G.L.,: Experimental and A n a l y t i c a l Studies i n F l u i d i c s . Progress Report, f o r NASA Grant NSG 1177, June 1978.
NO. 1 pp 10-20.
V O I . 27, NO. 5 pp. 930-931.
pp. 40-46.
pp. 495-515.
149-155.
42
Table 1. Vortex tube dimensions.
Vortex Tube
1
2
3
4
5
L S P P -s 0.403 0.472 0.490 0.018
0.403 0.472 0.500 0.028
0.631 0.494 0.497 .o. 002
0.641 0.484 0.500 0.016
0.26 0.582 0.615 0.033
0.269
0.533
0.543
0.601 0.600 .o. 001
0.592 0.612 0.020
0.582 0.600 0.018
D
0.25
0.25
0.25
0.25
0.125
0.125
0.125
0.125
0.093
0.093
0.093
0.093
9
10
11
12
~
0.206 0.605 <. 625 ' 0.226
0.200 0.610 0.639 0.229
0.522 0.603 0.625 0.544
0.534 0.512 0.613 0.635 I
1000
Swirl e r Diameter
0 2 "
0 1"
0 1.5"
800
600
400
200
0 0.1 0.2 0.3
FLOW RATE Q CFM
0.4 0.5
Ficlure 1. Flow r a t e 1:s. freqllency resuonse for s e l i w r 1 w i t h three swirlers havina v a r i o u s diameters.
44
Ll A
Swirl e r Diameter
0.75"
0.5"
200 -
1 0.1 0.2 0.3 0.4 0.5 0
Fiqure 2 . Flow ra te vs . frequency for senscr 1 w i t h two swirlers havinq various diameters.
45
1000
800
600
400
200
0 0 0
0 0.1 0.2 0.3 0.4 0.5
FLOW RATE Q CFM
Fiwre 3. Flow rate vs. frecyency for sensor 2 w i t h th ree # swirlers having various diameters.
46
1000
800
6 00
400
200
Swirler Diameter
0.1
0 l5 0.1 0.2 0.3 0.4
FLOW RATE (7 CFM
Fiaure 4 . Flow r a t e vs. frequency response for sensor 2 with three swirlers having various diameters.
47
1 ooc
800
600
400
200
FLOW RATE Q CFM
Swirler Diameter
Figure 5. Flow rate vs. frequency for sensor 3 with three swirlers having various diameters.
48
1000
800
600
400
200
Swirl er Diameter
A 0.75"
0.5"
0 0.1 0.2 0.3 0.4
FLOW RATE Q CFF:
I 0.5
1 I I 1 0 0.1 0.2 0.3 0.4
F i q u r e 6. Flow rate vs . frequency for sensor 3 with two swirlers having various diameters.
49
1000
8 00
600
N 1 L L
> 0 z 400 w
Swirler Diameter 0 8-3
0 2 "
0 1.5"
0 1"
.
200 c FLOW RATE 0 CFM
F iwre 7 . Flow r a t e vs . frequency for sensor 4 with three swirlers havinrl various diameter.
50
1000
800
0 E 400
L L
2 00
A n
8-5
/ S w i r l e r Diameter
9.75''
0.5"
.
J 0.1 0.2 0.3 0.4 Q.5
0.2 0.3 0.4
FLOW RATE Q CFM
F i g u r e 8. Flow r a t e vs . frequency f o r sensor 4 w i t h two s w i r i e r s having var ious diameters.
51
22
18
14
2
- 0 0
Swirl er Diameter Lid 2 'I
1.5"
I I I 0.4 0 .6 0.8 1 0.2
FLOW RATE Q CFM
Figure 9. Flow rate vs. frequency for sensor 5 with three swirlers h a v i n g various diameters.
52
20
16
12
8
Swirl er Diameter
A 0.75"
0.5"
/
Figure 10. Flow rate vs . frequency for sensor 5 w i t h t w ~ swirlers tiayi:ng Various diameters.
53
20
16
12
N 1 8 ld
LL
> V z w 3 CJ. w LL “ 4
0
F igu re 11. Flow r a t e vs. frequency fo r sensor 6 w i t h t h r e e s w i r l e r s having var ious diameters.
54
24
20
16
12
8
4
Swirl er Diameter
A 0.75"
0.5"
I
0.2 f I / I I 1
0.4 0.6 0.8 1 , 0 0.2 0.4 0.6 0.8
FLOW RATE Q CFM
Figure 12. Flow r a t e vs . frequency f o r sensor 6 w i t h two s w i r l e r s having var ious d iameters .
55
Swirl er Diameter
0 -0 0
FLOW RATE Q CFM
Figure 13. F l o w rate vs. frequency for sensor 7 w i t h three swirlers having va r ious diameters.
56
D A
Swirler Diameter
0.75"
0.5"
57
24
20
16
12
N I I
Y
LL
Swirl e r Diameter
0 0.2 0.4 0.6 0.8
I I e l 0.2 0.4 0.6 0.8
FLOW RATE Q CFM
Figure 15. Flow ra te vs. frequency for sensor 8 w i t h three swirlers having various diameters.
58
20
18
i 6
N
5 14
w t E ' 12
10
8
Swirler Diameter A 0.75"
/1 0.5"
0.4 0.5 0.6 0.7 0.8 FLON RATE Q CFM
Figure 16. Flow rate vs. frequency for sensor 8 with two swirlers having various diameters.
59
40
36
32
28
L L
20
16
- 0
m
Swirl er Diameter I /
I I / c ,
I I I I 1 0.4 0.5 0.6 0.7 0.8 1
FLOW RATE Q CFM
Figure 17. Flow rate vs. frequency for sensor 9 with three swirlers having various diameters.
60
Swirl er Diameter 38 A 0.75"
22
18
14
26
-
-
I U I
U
0.5''
A
u.4 0.5 0.6 0.7 ~~
0.8 FLOW RATE Q CFM
Figure 18. Flow rate vs. frequency for sensor 9 with two swirlers having various diameters.
0 .9
6 1
N I Y
L L
42
38
34
30
26
22
18
14
0 0 0
I I I I I O , 2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 FLOW RATE Q CFM
Figure 19 . Flow rate vs . frequency for seiisar 10 w i t h three swirlers having various diameters.
62
40
35
30
25
20
15
10
5
Swi r l e r Diameter
A 0.75"
0.5"
0 .2 0.4 0.6 0.8 FLOW RATE Q CFM
Figure 20. Flow r a t e vs . f requency f o r sensor 10 w i t h two s w i r l e r s having va r ious diameters .
63
N
42
38
34
30
26
22
18
14 0.
S w i r l e r Diameter
0 2"
0 1.5"
0 1"
FLOW RATE Q CFM
F igu re 21. Flow r a t e vs. frequency f o r sensor 11 w i t h t h r e e s w i r l e r s hav ing va r ious diameters.
64
40
35
30
0 z W 25
A L1
Sw i r 1 er D i ante t e r
0.75"
0.5"
/
20
1 I I I Ib 0 0.2 0.4 0.6 0.8
FLOW RATE Q CFM
Figure 22. Flow rate vs. frequency for sensor 4 w i t h two swirlers having various diameters.
65
40
35
30
25
N I lL LL
20 z
15
10
5
0 0 0
I 0 0.2 0.4 0.6 0.8
FLOW RATE Q CFM
Figure 23. Flow rate vs. frequency for sensor 12 with three swirlers having various diameters.
66
N I Y
LL
34
29
24
19
14
9 0
A n
S w i r l e r Diameter
0.75"
0.5" / /
I I I I 1 0.5 0.6 0.7 0.8 . 3 0.4
FLOW RATE Q CFM
Figure 24. Flow rate vs. frequency f o r sensor 12 with two swirlers havilig various diameters.
67
1 ooa
900
800
700 N I LL
=- 0 z W 3 0
LL a 600
500 0 0 .5 1 1.5 2
SWIRLER DIAMETER INCHES
Figure 25. Effect of v a r i o u s swirler diameters on the frequency, sensor 1.
68
ll0C
1000
900
800
700
600 0 0.5 1 15
SGlIRLER DIAMETER INCHES
2
F iqu re 26. E f f e c t of var ious s w i r l e r d iameters on t h e frequency, sensor 2.
69
800
750
700
650
600
550
500 - 0.5 1 1.5 2 0
SWIRLER DIAMETER INCHES
F igu re 27. E f fec t o f var ious s w i r l e r diameters on the frequency, sensor 3.
a
70
N I
1000
800
6oo t 500
0 c) . 5 1 1.5 2
SWIRLER DIAMETER INCHES
Figure 28. Effect of various swirler diameters on the frequency, sensor 4 .
71
14
13.2
12.4
11.6
10.8
10 0.5 1 1.5 2 0
SWIRLER DIAMETER INCHES
Figure 29. Effect of various swirler diameters on the frequency, sensor 5.
72
14
13.2
12.4
N I Y
LL
> 11.6
W 3 c w OL LL
10.8
10 -2 0.5 1 1 . 5 2
SWIRLER DIAMETER INCHES
Figure 30. Ef fec t of various s w i r l e r d iameters on t h e C - - - . . I I rquency, sensor 6.
73
SWIRLER DIAMETER INCHES
Figure 31. Effect of various swirler diameters on the frequency, sensor 7 .
74
N I Y
L L
14 -
13.2
12.4 -
11.6 -
10.8 -
10 1 0 0.5 1 1 .5 2 0.5 1 1 .5 2
10 I 0
SWIRLER DIAMETER INCHES
F igu re 32. Effect o f var ious s w i r l e r diameter on t h e frequency, selscr 8.
75
30
28
26
24
22
20 0 0.5 1 1.5 2
S N I R L E R DIAMETER INCHES
F i g u r e 33. Ef fect of va r ious s w i r l e r diameters on t h e frequency, sensor 9.
76
SWIRLER DIAMETER INCHES
Figure 34. Effect of various swirler diameters on the frequency, sensor 10.
77
30
28
26
N I Y
L
> 24
w
22
20 0 0.5 1 1.5 2
SWIRLER DIAMETER INCHES SWIRLER DIAMETER INCHES
Figure 35. Effect of various swirler diameters on the frequency, sensor 1 1 .
78
~
25
27
25
L L
=- V z -
23 W => c, W ai LL
21
19
SWIRLER DIAMETER INCHES
F i g u r e 36. Ef fect of va r ious s w i r l e r d iameters on t h e frequency, s e n m 12.
79
17
15
13
1 1
9
7
5 . 2 0.3 0.4 0.5 0.6
SENSOR TUBE LENGTH INCHES
Fiqure 37. Effect o f the sensor tube length o n the frequency .
80
24
20
16
12
8
4
0 0.05 0.1 0.15 0.2
SENSOR TUBE DIAMETER I N INCHES
0.25
Figire 38. Effect o f sensor tube diameter on the frequency.
81
3c
2E
2c
15
10
5
0 0.5 0.54 0.58 0.62
NOZZLE LENGTH IN INCHES
0.66
F igure 39. E f fec t o f the nozzle l e n g t h on the frequency.
82
28
24
20
16 N I Y
F igu re 40. E f f e c t of t he ( P ) length on t h e frequency.
[PI INCHES
83
95
80
65
N
l.L
L L
+ u z W =I 0 W
L L
L 50
oi 35
20
5
0.016 0.02 0.024 0.028 0.032
[P-S] INCHES
Figure 4:. Effect o f pick Up signal point on frequency.
84
J
0 0.5 1 1.5
SWIRLER DIAMETER INCHES
2
F igu re 42. Ef fect of t h e s w i r l e r d iameter on frequency.
85
3
Increment o f L
9.2 9.3 0.4 0.5 0.6
SENSOR TUBE LENGTH INCHES
Figure 43. Effect o f sensor tube length increase on frequency.
86
c- z w V ClZL W
LL
>
n
v z W 3 0 w ClZL LL
1
-24%
-20%
-1 6%
-1 2%
-8%
-4%
Increment o f ( D )
0 75%
0 50%
0 25%
.
0
0.1 0.15 0.2 0 0.05
SErJSOR TUBE DIAMETER INCHES
F igure 44. E f f e c t of increase of sensor tube diameter on frequency.
87
640'
560'
48 0
400:
320:
24 07
160% 0.
0 0
Increment o f (P)
75%
50%
25%
& \
DIMENSION (P) INCHES.
.
Figure 45. E f f e c t o f increase of l e n g t h (P) on t h e frequency.
88
I
-36%
-30%
-24%
-1 8%
-1 2%
0 - 0 0
Increment o f ( S )
75%
.
0.3 0.34 0.38 0.42 0.26
NOZZLE LENGTH INCHES
Figure 46. Effect of increase of nozzle length on frequency.
89
Increment o f ( p - S )
0 75% 0 50% -2404,-
-200:-
-1 6r14-
-1 2w-
-80% -
-40% 0.016 0.02 0.024 0.028 0.032
Fialrre 47. E f f e c t of increase the p i c k up s i g n a ? point lenath on frequency.
90
-6% I
Increment of (Ds) /
-5%
-4%
0 75% - 0 50%
-3%
-2%
-1 %
0
SWIRLER DIAMETER INCHES
Fiqure 48. Effect of increase the swirler diameter on frequency .
91
.
APPENDIX
+ V
-e
O! P
2 I / P 0
(Amp1 i f i e r O/P) - 3 n v
100 K n
4
0.75"
100 K R i
5
0.5"
Figure A . l Comparator c i rcu i t
93
r Com par a t or Circuit
1
- - Freq. Counter -. Osci 11 oscope Amplifier I
I /Pick u p Siqnal
Damper
I , I
- - Air
Press 1 Volt;;; read 1 1 Transducer
,
I I I
I
Test set u p 100 K R
I 100 52
Fiqure A.2 I n p u t Amplifier
94
D L s d I tern Sensor
1 0.375'l- 0.750" 0.380 0.0145
2 0.380
3 0.385
4 0.184 0.372
5 0.250 0.403 0.472 I 1
6 0.472 0.472
7 0.631 0.494 II
8 0.641 0.484
I 1 I1 II
II II II
II II
I1 I 1
ll
II I1
Figure A.3 Sensor dimensions
P
0.394
0.383
0.394
0.383
0.490
0.500
0.492
0.500
95