Behavior of nozzles and acoustic liners in three dimensional acoustic field

Daniel, B. R.

Smith, A. J., Jr.

Zinn, B. T.

English

NASA Technical Reports Server

NASA 2! N(;L 11.42485 
BMAWOR OF NOZZLES AND ACOUSTIC LINWS W 
SIONAL ACOUSTIC FIELDS 
Quaster%Jr Report for Period 1 Segtember 1970 to 31. Rovember 1976 
Prepared by: Ben T. Zinn, Principal Xnvestfgawr 
A U a n  J. Smith, Jr., Project agineer 
B. Robert Dmiel, Beseeseh Engineer 
Sehool sf Aersqwe mfneer i r4  
Georgia Institute of T e e h l o ~ a r .  
At lmka,  ksrgiea. 
https://ntrs.nasa.gov/search.jsp?R=19710005167 2020-03-12T00:01:25+00:00Z
The analytical investigations associated td th  t h i s  program have 
been devoted t o  the development of techniques for  the optimization of 
&crophone location; the adaptation of a nonlinear regression technique 
t o  the reduction of exgerimental nozzle admittance data obtained a t  a 
given frequency; and the refinement of the stat; istical curve-fitting 
routine used t o  correlate the nozzle admittmce data over a range of 
frequencies. 
Six t e s t s  have been conducted and analyzed during th i s  report 
period and the nozzle admittance resul ts  obtained i n  ttro of these t e s t s  
are discussed i n  th i s  report. An alternative method for  determining 
admittwces xras at temted but found to be unreliable. 
Be Theoreticjl Studies 
The majority of vrorlr: associated with the analytical aspects of 
th i s  progrw has been devoted t o  the optimization of microphone loca- 
t ion, the adaptation of a nonlinear regression technique t o  the re- 
duction of nozzle admittance data obtained a t  a given freqnency, and 
the refinement of the s t a t i s t i c a l  curve-fitting routine used t o  
correlate the nozzle sdmittsxlce data over a range of frequencies. 
I n  addition the efforts  msociated v i t h  the prediction of the a u k -  
t m c e  values of ntszzles ~ 6 t h  rapidly-converging ~ m l l s  have been 
continued. 
The opt idzat ion  of  microphone location effort presented i n  
Reference 1, approached th is  subject by conducting a computer- 
oriented parametric study. One significant result of that stuw 
p r a s  the isbservation tha t  i n  order to obtain good data the sound 
presslase %eve$ of' "ehe  trmsctucers c a o t  be the  sme.  me use 0% 
the above-mentioned pGwme%ricr: atu* t o  obtain addi t ional  a d  mre 
general rules bas; been h q e r e d  by the  bsrsk;l-~eepi% msociated ~ntk  the 
vast qumt i ty  sf conlputer output* GsnsequentPy, an al ternate  grssedwe 
of exmining the es1alyticaP e q r e s s i s n s  has been in i t ia ted .  The r e su l t  
of t h i s  current study i s  expected t o  provide valuable &crophone loca- 
t ion cr i te r ion  tha t  t r i l l  be incoqorat;ed in to  the experimental phase 
of th i s  progr~un. Additionally, these same cr i te r ion  may provide guide- 
l ines  for the proper instrumentation of unstable rocket motors. 
As a prelude t o  the discussion of why a nonlinear regression 
technique is  being enployed by th i s  program, i t  i s  necessary to  reviev 
some of the character is t ics  of the analyt ical  expression that describe 
the amplitude of the standing wave pressure dis t r ibut ion within a 
chamber. 'Ilhis analyt ical  expression depends on three unknown variables - 
two of which describe the nozzle admitt,mce - and numerous lcnoxrn vari-  
ables tha t  are determined by chamber geometry, chamber operating 
conditions, frequency of the osci l lnt ion,  and the location trhere the 
pressure i s  measured. Consequently, the use of data obtained from 
pressure measurements taken a t  three different  chamber locations 
together 'trbth the above-mentioned a n d y t i c a l  expressions resu l t s  
i n  the derivation of three algebraic equations tha t  could be used to 
solve fo r  the unlcnotsn variables; t ha t  is, the nozele admittance etnd 
the standing wave pressure dis t r ibut ion over the en t i re  lengtla of 
the chamber, 
To improve the accuracy of the data f ive  presswe measurements 
w e  taken a t  each t e s t  condition instead of' three measurements. This 
procedure provides redundant admittance data a t  each of the t e s t  
conditions. That i s ,  f ive transducers provide ten different  combina- 
t ions of s e t s  of three; consequently, each t e s t  point w i U  ykeld t en  
values of the nozzle admittance, If the e a e r b e n t a l  technique and 
the data reduction procedure m e  flavrless, then a31 Len vdues of the 
a W t t a n c e  t r i l l  be equrxl, kfd~iever, due %s emesimntal inaccurae$es 
8-e data sca t te r  5s encounkered and the iavest igatsr  rnugt use a 
h;$a%istiea% correla$icrn technique ( e  .g . , averwe, me=, or medfura 
value) i n  "e;e presentation of his data. 
It i s  e q e c l e d  that  the qua l i ty  o f  the  data obtained by use of 
the above-mentioned teelnnique may be imroved by use of a nonlinear 
regression technique. The nonlinear regression technique, developed 
i n  Reference 2, has been extended to  f i t  the objectives of  t h i s  program, 
In  t h i s  case, each s e t  of three pressure measurements r e su l t s  i n  a 
standing wave pressure d i s t r ibu t ion  tha t  agrees trith the measured 
r e su l t s  of the  selected pressure transducers but may not necessari ly 
agree trith the other t t o  transducers. Inasmuch as  there is  a possi-  
b i l i t y  of producing ten d i f fe ren t  standing rrave pressure dis t r ibut ions ,  
the problem i s  t o  determine a pressure d i s t r ibu t ion  tha t  is a "best 
f i t "  for  a l l  of these dis t r ibut ions  . The nonlinear regression technique 
employed i n  t h i s  program provides the 'bes t  fit" for the pressure 
d i s t r ibu t ion  and the nozzle admittance for  t ha t  t e s t  point .  
The analyt ical  e f f o r t  associated tritli the s t a t i s t i c a l  curve f i t  
of the nozzle admittance dcta as a function of frequency i s  aimed a t  
ref ining the exis t in8 curve-fi t t ing procedure. Whereas the nonlinear 
regression technique determines the "best" nozzle admittance value 
a t  a given Crequency, the s t a t i s t i c a l  curve-f i t t ing scheme determines 
the var ia t ion of the nozzle admittance over a range of frequencies. 
This rmrk is  s t i l l  i n  p r o p e s s .  
Additional e f fo r t s  associated trith the ana ly t ica l  investiga- 
t ion  of three- dimensional s tandin@ \rave behavior i n  chambers ~ r i  th  
l ined ~raLls as trell  as the prediction of the admittance values of 
nozzles arith rapidly-converging xraU-s have continued during t h i s  
report  period; ho~rever, the studies have not progressed to  the poin% 
where s ign i f ican t  resu l t s  can be reported. 
Six t e s t s  hme been csnciucted and analyzed d w i n g  th i s  repor& 
period, The nozzle ahd i t tmce  resul ts  of t ~ r o  t e s t s  u e  discussed 
herein,  The other Pow tests  did  not  produce a&lt$mee data due to 
After the i n s t d l a l i o n  and checlcout of the new tape recorder 
system, t e s t s  were conducted to  measuse the a h i t t m c e s  of the ttm 
nozzles shotrn i n  Figure 1. The first nozzle has an entrance Mach 
number of 0.08 m d  a convergent half  -angle of 15' . The small half - 
angle of t h i s  nozzle i s  i n  agreement with some of the a s s w t i o n s  
made i n  exis t ing nozzle admittance theories3; hence data obtained 
from t e s t s  conducted -with t h i s  nozzle can be used t o  check the 
appl icab i l i ty  of  t h i s  theory. The second nozzle has an entrance 
Mach number of  0 .l6 and a convergent half-angle of 30' , which i s  
more typ ica l  o r  rocket motor nozzles. 
Figure 2 sho~rs a tl;ypical sound pressure l eve l  t race  taken 
from a transducer located 49 inches upstream of the  nozzle. The 
t race represents the output of a tracking f i l t e r ,  which has a tuneable 
center frequency and a frequency bandwidth of 1.5 Hz a t  the  -3 db 
point and 6.0 Hz a t  the -60 db poin t ,  This  very narrow bandwidth 
permits excellent resolut ion of the  data. For exanlgle, the first 
t a n g e n t i d  mode is  the first h i g h - w l i t u d e  peak observed on the 
graph a t  approximately 670 Hertz. B?o Hertz t o  the r i g h t  i s  the 
Location of the  f i r s t  three-dimension& wave, the combined first 
tangent ia l - f i r s t  longitudinal mode, These f i ne  resolutions a r e  not 
possible with standard f i l t e r s  such as l/3 octave bandtrridth f i l t e r s .  
Because of the  mult ipl ic i ty  of admittances at each t e s t  point, 
I t  averagef' points  have been presented on t h e  f igures tha t  follow. 
Some of the  points  are  indicated as "singular value" because multiple 
admittances were not available for  a var ie ty  of reasons. Data s c a t t e r  
i s  indicated by ve r t i ca l  l i ne s  tha t  are  connected to  the sJmibol. Zate 
absence of aw external symbol mark in^ indicates tha t  the data s c a t t e r  
i s  ~ d t h i n  the confines 0% the symbol. 
P i m e s  3 m d  4 present the  rave-nwdber-dependence sf the  real 
and Imaginary p a r t s  of the emeuimentdiy determined gzwttanees fir 
the M = 8.08 mzz le .  The tlaeore"cica1 predictions m e  presented in. 
the  upper l e f t h m d  corner of the graph. It can be seen tha t  there is 
a minimu mouat of data s c a t t e r .  The very f i r s t  point i s  %he f irst  
tangential  mode and the next point i s  the combined f i r s t  tangential-  
f i r s t  l o q i t u d i n d  mode, 
m e  r e a l  p a r t  of the admittance i s  shown t o  agree with the 
theore t ica l  predictions over most of the trave numbers. Exceptions 
occur i n  two regions, with the most serious departuxe a t  a/c = 6. 
This exceptionally high value indicates tha t  a substant ia l  por t ion 
of the acoustic energy i s  b e i q  transmitted out of the system. The 
imaginary p a r t  of the admittance is  seen t o  be decreasing over most 
of the o/c-range. 
Figure 5 and 6 present the complex p a r t s  of the experimentally 
determined admittances for  the M = 0.l6 nozzle. A11 of these points 
are "singular value" points because only 3 transducers were used to  
monitor the dynamic pressures. 
A considerable mount of e f fo r t  vas expended on the determina- 
t ion  of admittances using data o b t ~ i n e d  from t ~ r o  pressure aqplitude 
measurements and the phase difference between these two pressures. 
This is an a l te rna te  method of obtaining admittance data t ha t  could 
be used i n  addit ion t o  the technique of using three pressure measwe- 
ments . After a r e l i a b l e  phase meter tras found, i t  vas discovered 
that the measurement of the phase difference was subject t o  much 
uncertainty, vhich i s  re la ted  t o  the f a c t  t h a t  the f'xequency is  not 
held constant during the t e s t  but i s  continually changing a t  a slotr 
r a t e .  Because of t h i s  uncertainty, the acquisit ion of admittance 
data by the phase difference technique has been discontinued. This 
technique v . r i l l  be reconsidered a t  a l a t e r  date.  
me M = 0.16 nozzle x r i l l  be tested using 5 presswe transducers. 
Previous tesks ?dl1 be repeated t o  ver i& data reparc@ducib11,i9;yI W e e  
new nozzles % r i l l  be designed and "ckzeir fabricat ion phase IA%L have 
begwe Dm of these nozzles t&U be designed for bri = 64.32 k&P- 
a l  15 and 45 dewees. The tatfsea nozag! ~ I I  be c%es%gned for 
M = O .O8 and a hdf-angle of br degrees. The nonlinear regression 
technique ~ d l l  be pro&rammsd and verified. All other mayticall 
investigations  rill be continued. 
References 
1. Zinn, B. T., Smith, A. J., Jr., and Daniel, B. R., "~ehavior of 
Nozzles and Acoustic Liners in Three-Bimensional Acoustic Fields, " 
Quarterly Report for Period 1 June 69 to 31 Am. 69, Georgia 
Institute of Technolow, School of Aerospace mineering, September, 
1969 
2. Pfahl, R. C., Jr . and Mitchel, B. J., 't~onlinear Regression 
Mekhods for Simultaneous Property Measurement, " AIAA Jowrnal, 
Vol. 8, 80. 6, June 3-970, pp. LO&-a053.  
3. Crocco, L. , Sirignano, W. A. , "~ehavior of Supercritical Nozzles 
Under Three Dhensi snal Oscillatory Condi lions, " MARmgraph 117, 
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Behavior of nozzles and acoustic liners in three-dimensional acoustic fields Quarterly report, 1 Sep. - 31 Nov. 1970

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