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Parasitic noise from probes and struts in flows Hoglund, Leif Erik 1975

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PARASITIC NOISE FROM PROBES AND STRUTS IN FLOWS by L e i f E r i k Hoglund B.ApSc, U n i v e r s i t y of B r i t i s h Columbia A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of Mechanical Engineering We accept t h i s thes i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1975 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th i s thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th i s thes i s f o r f i nanc i a l gain sha l l not be allowed without my written permiss ion. Department of r~itEc < r Ci. M c:-The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 D a t e f'XT 7 / 7 i i SUMMARY When a fas t - responding s t a t i c pressure probe is inser ted in to a f low, there are several poss ib le mechanisms f o r the generat ion o f extraneous no i se. If the probe s ignal i s c r o s s - c o r r e l a t e d with the f a r f i e l d sound, then the "probe noise" may contr ibute a dominant f r a c t i o n of the t o t a l c o r r e l a t a b l e noise in the source reg ion. For a standard probe, there is l i k e l y to be contamination from the t i p due to large f l u c t u a t i n g s ide f o r c e s , and from the stem, due to drag f l u c t u a t i o n s . A t heo re t i c a l model is suggested for p red i c t i ng the d i s t o r t i o n of " c a u s a l i t y " c o r r e l a t i o n s ignatures (obtained when i n - f l ow probes are c r o s s - c o r r e l a t e d with the f a r f i e l d sound), due to the probe t i p contamination. The predicted shapes agree well with experiment. In the experimental i n v e s t i g a t i o n s , the contaminated port ion o f the c a u s a l i t y c o r r e l a t i o n s ignature is d i sp laced in time from the " t r u e " j e t pressure c o r r e l a t i o n . The unexpected r e s u l t is the absence o f any s i g n i f i c a n t j e t pressure c o r r e l a t i o n . This leads to the conclus ion that the extent of j e t noise sources may be very sma l l , so that probing devices inser ted into the flow w i l l genera l ly produce a large port ion of the t o t a l c o r r e l a t i o n . TABLE OF CONTENTS 1. INTRODUCTION 1 1.1 Purpose and Scope 1 1.2 Mot ivat ion 2 1.3 Work Done by Others 6 2. AEROACOUSTIC THEORY 8 2.1 Background 8 2.2 Causa l i ty Source Locat ion Technique 11 3. PHYSICAL MODEL OF CONTAMINATION 15 4. ANALYTICAL MODEL 18 5. EXPERIMENTAL APPARATUS 25 5.1 Jet F a c i l i t y 25 5.2 Instrumentation 27 6. EXPERIMENTAL RESULTS 30 6.1 Bruel and Kjaer Microphone Experiments 30 6.2 Normalizing Procedure 33 6.3 Parametric Invest igat ions 35 6.4 Other Sources of Contamination 37 7. CONCLUDING DISCUSSION 39 APPENDIX A 42 APPENDIX B • 47 REFERENCES 49 FIGURES 51 LIST OF FIGURES Figure 1. The E f fec t of Probe Nose Length on the Cross -Corre la t ion Signature 2. A Probe Imbedded in a Turbulent Flow 3. The Proudman Source Mechanism 4. A Hypothetical Causa l i ty Corre la t ion Functipn fo r Pure Jet Noise 5. Geometry Used For the Pred ic t ion of p p ^ {x) 6. Hypothetical Corre la t ion Function For a Standard Probe 7. Jet Plenum and Nozzle 8. Schematic o f Contoured Nozzle 9. Mean Ve l oc i t y P r o f i l e at the Je t Ex i t Plane at M = .99 10. Experimental Set-Up Showing Travers ing Mechanism 11. Signal Paths 12. Construction Deta i l s o f Ku l i te Probe Holder 13. Deta i l s o f A l l In-Flow Probes 14. Probe Tip and Stem Ef fects For a Standard Probe in Steady Flow 15. Experimental and Ana ly t i ca l Causa l i ty Corre lat ions Using a Standard 1/8" B&K Microphone With a Nose Cone 16. Experimental and Ana ly t i ca l Causa l i ty Corre la t ion For a Modi f ied 1/8" B&K Microphone 17. Experimental and Ana ly t i ca l Causa l i ty Corre lat ions M = .35 18. Experimental and Ana ly t i ca l Causa l i ty Corre la t ions M = .51 19. Experimental and Ana ly t i ca l Causa l i ty Corre la t ions M= .68 V Figure 20. Experimental and Ana ly t i ca l Causa l i ty Corre lat ions M = .83 21. Log Cm (T) Versus Log £ n"max • D 22. Log C m ( T ) Versus Log M, 'max J 23. Poss ib le Sources of Probe Noise on the Ku l i te Probes Used v i NOTATION (o ) ' p f l uc tua t i ng s t a t i c pressure measured by the i n - f l ow probing device p ( 0 ^ f l u c tua t i n g s t a t i c j e t pressure p n surface pressure pn the probe p f a r f i e l d pressure x. space coord inate, used to ind ica te the d is tance from a turbu lent source to the f a r f i e l d microphone _x' space coord inate, ind ica tes d i s tance from a po int on the prope to the f a r f i e l d microphone y_ space cord ina te , ind icates a point pos i t ion in the turbulence measured from the pressure taps y'1 indicates a point on the probe surface measured from the pressure taps X space coord inate, ind icates the distance from the pressure taps to the f a r f i e l d microphone v. x 0 : d istance from the j e t ex i t plane in the streamwise d i r e c t i o n y 0 r ad i a l d i s tance from the j e t cen t re l i ne d probe diameter D j e t diameter u,v,w f l uc tua t i ng v e l o c i t y components (primed values denote root-mean^square) U c convection v e l o c i t y Vj v e l o c i t y at the j e t ex i t plane , M j V Mach number at the j e t e x i t plane ( V j / c 0 ) c« speed cof sound p dens i ty 6 angle between a normal to the probe surface and the far f i e l d microphone V l l 6 angle between a s ide force component on the probe surface and and the f a r f i e l d microphone located in the same plane Y angle between a surface normal pn the probe and the plane contain ing both the f a r f i e l d microphone and the probe u n normal surface v e l o c i t y t time t ' some time other than t T a time d i f f e rence given by t - t ' t retarded time = t - — c T T - — C L integra l length sca le T in tegra l time sca le in convert ing frame o f reference Yt, d istance from pressure taps to probe t i p Ypeak distance from the pressure taps to the point on the probe t i p where an incidence-induqed s ide force d i s t r i b u t i o n has maximum value V c c o r re l a t i on volume T j j • L i g h t h i l l ' s s t ress tensor S surface £ space separat ion vector V volume C^ x ) co r re l a t i on c o e f f i c i e n t P p < ° ^ r ^ / f ( f J v j ' , ' ) 1 " H J v % \ • •i . . . I- mi.I l i ^ "*" / C (T ) c o r re l a t i on c o e f f i c i e n t P P C < > > Cx)/(fJ ^ J ~ p ) ACKNOWLEDGEMENTS Sincere thanks must go to Dr. T . E . Siddon. Only h is pat ient guidance and his inva luable exper t i se made th i s work po s s i b l e . Thanks a l so go to Dr. Huw Davies for his i n te re s t and he lpfu l suggest ions, and to Brian Davis f o r acqu i r ing some of the data. A spec ia l thank-you goes to my w i fe , Susan, fo r her cons iderable patience while typ ing th i s t h e s i s . This research was funded under National Research Counci l of Canada Grant A-7106, and Defense Research Board Grant 9611-03. 1. INTRODUCTION 1.1 Purpose and Scope Since the advent of j e t propuls ion there have been substant ia l reduct ions in the noise from j e t s . The most s i g n i f i c a n t improvement has been through the development o f high by-pass r a t i o engines which e f f e c t i v e l y reduce the average j e t e x i t v e l o c i t y . Other reductions r e s u l t from new turbine designs and a c o u s t i c a l l y t reated flow passages ( i . e . , duct l i n i n g s ) . Further reductions w i l l only be poss ib le however, i f more is known about the locat ion o f sources within j e t exhausts. If the ind iv idua l contr ibut ions from each unit o f volume in the source region can be determined, then the l o c a l i z e d e f f e c t s of various suppression techniques and nozzle conf igurat ions can be determined more accura te ly . A source locat ion technique which has shown considerable promise is the so - ca l l ed " c au sa l i t y " c o r re l a t i on technique. In th i s technique, the strength of noise sources is determined by the degree o f co r re l a t i on between a s ignal in the supposed source region (the cause) and the r e s u l t i n g noise detected in the f a r f i e l d . The s implest source s ignal to measure i s the f l u c tua t i n g s t a t i c pressure in the j e t . Unfortunate ly , cer ta in errors w i l l r e s u l t in the co r re l a t i on s ignature when th i s i s done. The most ser ious e r r o r is due to the generation of extraneous noise by the probing device in the flow. This "probe no i se" is sensed by the far f i e l d microphone and w i l l contaminate the co r re l a t i on s ignature. 2 The purpose in th i s work has been to examine the processes which lead to contamination of the c o r r e l a t i o n s ignature. Empirical methods are suggested f o r est imating the extraneous noise f r a c t i o n s , which should lead to ideas fo r minimizing the contamination e f f e c t . Experimental re su l t s are presented and compared to an empir ica l model. Good agreement is ind ica ted. 1.2 Motivation It can be shown'that i f a j e t is made up of N u n c o r r e c t e d sources then the r e l a t i v e cont r ibut ion to the to ta l f a r f i e l d sound p, ... from a s ing le coherent volume source w i l l b e given by a normalized co r re l a t i on c o e f f i c i e n t : < 1 ' 1 ) ^ P C * ) / ^ F ^ ) =C_(.> where p(°) • = measured j e t pressure f l u c t u a t i o n . Furthermore, i f the sources are of r e l a t i v e l y equal s trength, the number o f sources can be estimated Although several researchers have begun using the c a u s a l i t y technique for measuring source strength in reqent year s , the agreement amongst d i f f e r e n t experimenters has npt been good. The tab]e below l i s t s the re su l t s fo r normalized c r o s s - c o r r e l a t i o n c o e f f i c i e n t s for several d i f f e r e n t experimental set-ups, 3 PROBE TYPE & SIZE JET PROBE. DIAMETER MACH POSITION .(INqH.ES) NUMBER COEFFICIENT d / ° Cmax Meecham & Hurdle B&K k" with standard nose cone 6=90° 6.5 .52-.99 .0385 .006 - .O i l Raqkl 12 spec ia l f o i l type d=l/8" fr-3 0=90° 1.5 .083 .08 Lee & g Ribner hot wire g*. =5 to 6 9=40° 7 5 ^0 .02 Schafton 1 4 1/8" B&K & White with nose cone LT =6.4 9=30° .625 .99 ,20 6 = angle measured between the j e t ax is and the far f i e l d microphone x 8= distance from j e t e x i t plape yo f r ad ia l d istance from the j e t centre l i n e d = probe diameter D = j e t diameter Note that the value of C m a x i s quite var iab le and genera l ly increases as the probe s ize becomes a l a r ge r and larger f r a c t i on o f the j e t diameter. Idea l ly we would expect C to have a r e l a t i v e l y invar i an t max i value, independent of the measurement. There are three poss ib le causes f o r the d i f fe rences in the previous t ab le : 1. d i f f e r i n g experimental condit ions 2. er rors in measuring the f l u c t u a t i n g s t a t i c pressure 3. probe noise The f i r s t cause, due to d i f f e r i n g experimental cond i t i ons , i s c e r t a i n l y an important f a c to r in exp la in ing the d i f f e rences . Scharton and White, f o r example, f i l t e r e d the j e t pressure s ignal around the j e t Strouhal frequency (peak noise frequency). If the pressure spectrum at a point in the flow does not peak at the same frequency as the overa l l j e t spectrum, such f i l t e r i n g w i l l lead to an underestimate o f p ^ 0 ^ . According to equation (1.1) t h i s w i l l tend to overestimate the c a u s a l i t y c o r r e l a t i o n c o e f f i c i e n t . Scharton and White 's experiments were a l so taken on -ax i s , while the others were o f f s e t r a d i a l l y to the pos i t ion of maximum shear. Since the root^meari-square j e t pressures are lower qn the get ax i s , th i s w i l l again tend to overestimate the co r re l a t i on c o e f f i c i e n t . The wide range of Mach numbers over which the d i f f e r e n t experiments were conducted could also tend to introduce v a r i a t i o n , s ince the j e t coherence may indeed be expected to increase with Mach number. The problem of the measurement o f s t a t i c pressure in a 15 turbulent flow is well known, and w i l l a l so introduce e r ro r . Siddop has shown however, that i f the flow can be considered l o c a l l y quas i - s teady, and i f the measuring probe is properly a l igned with the average f low, then the error in the measurement of f l u c tua t i on pressure w i l l be 2 2 "~2 ~2 =^ Bp(v +w -v -w ) where B--% to -h, and v and w are the f l u c t u a t i n g cross - f low v e l o c i t y components normal to the probe ax i s . If the pressure in the j e t var ies roughly as puU then the maximum expected e r ro r w i l l be about 20%. Recent work by P lanchon°suppor t s t h i s . It is a premise of t h i s paper, that i t i s the t h i r d poss ib le cause, probe no i se , that contr ibutes much of the va r i a t i on in the re su l t s on the previous page. The work by Meecham anql Hurdle on a large s ized j e t is done with a rather small probing device r e l a t i v e to the j e t diameter and re su l t s in a small normalized c o e f f i c i e n t . The hot wire measurements by Lee and Ribner a l so r e s u l t in a small c o r r e l a t i o n c o e f f i c i e n t , whereas the re su l t s by Scharton & White and Rack! are much higher using la rger probing dev ices. If much of the va r i a t i on is indeed due to the probe s ize and conf igurat ion used, then i t should be poss ib le to show th i s in a systematic way by varying probe s i ze pr geometry. 6 1.3 Work Done by Others 12 Rackl found that i f a probe of the type shown in Figure 1 was shortened or lengthened, the c o r r e l a t i o n s ignature would change. Siddon 1 7 at that time proposed a r a t i o fo r p red i c t i ng extraneous noise due to the probe which he c a l l e d the "probe contamination r a t i o " . If 3 probe such as that shown in Figure 2 is imbedded in a turbulent f low, the t i p w i l l experience ce r t a in l i f t and s ide forces and the stem w i l l undergo f l u c t u a t i n g drag forces . As these forces f l uc tua te with t ime, they w i l l appear as acous t i c d ipo le sources, hence r ad i a t i n g sound. The "probe contamination r a t i o " was meant as a crude estimate o f the r a t i o o f unwanted noise due to l i f t , s ide or drag forces act ing on the probe, to the noise coming from an adjacent co r re l a ted volume element pf turbulence. For contamination; due to drag, he found that the probe contamination r a t i o PCR -K (—i 1 drag Q\DJ M ^ where d=probe diameter D=jet diameter M, = loca l Mach number loc For l i f t or s ide f o r ce s , ? C R n ft " k L ( D ) 4 JZ l oc As expected, smal ler probes w i l l have a lower PCR than la rger probes, and the contamination should reduce with increas ing Mach number. Siddon estimated that has a nominal value o f about 40, and about 80. However these values are only crude estimates ( fo r x/D=4.0, y /D 3 ^ ) . The actual values must c e r t a i n l y depend on the pos i t ion o f the probe within the j e t f low, and on the de ta i l ed probe geometry. Although Siddon has been able to estimate the r e l a t i v e proportion o f probe noise to j e t no i se , and thereby estimate the degree of poss ib le contamination, the re su l t s have not been v e r i f i e d experimental ly. A l so , i f the form of the contaminated c r o s s - c o r r e l a t i o n funct ion can be predicted and i t agrees with experimental f a c t , then th i s w i l l lead to more rigorous ideas about the phys ica l parameters and propert ies o f the flow f i e l d which govern the contamination o f the co r re l a t i on funct ions . 8 2. AEROACOUSTIC THEORY 2.1 Background From the statements o f mass and momentum conservat ion, i t is poss ib le to form a non-homogeneous wave equat ion. m a s s : +- K f u \ _ ) = o momentum: f ^ t i +• c>U\ +- V £ _ ^ j j j = o Combining g ives: ^ (2.D tl - C l V Z f * l M where = / U . U j + f<$'j - Z<j -c D= ambient speed of sound p,p = pressure, dens i ty - inc lud ing both mean and f l u c t u a t i n g parts The dependent var iab les can be wri t ten as the sum of a cqnstant part and a f l uc tua t i ng part at each point in space, so that equation ( 2 . 1 ) can be rewri t ten f o r the f l u c tua t i n g components as: ( 2 . 2 ) - Cj-Vlf' = yTry' ( L i g h t h i l l ' s equation) For acoust ic processes which can be considered ad iaba t i c (as in shock-free flows) the i sen t rop i c equation of s tate can be assumed: - / k £ \ t ' :,-C.y This allows equation (2.2) to be wri t ten in terms of the f l u c tua t i n g pressure. In turbulent flows i t i s usual to assume that viscous s tresses are ^mall compared to Reynold's s tresses ( x . ^ p u . - u . ) , thus equation (2.3) . ' J . J can be fu r ther s i m p l i f i e d . (2.4) - v * P ' ' V'fvM There are two well-known so lut ions to equation (2.4) . The f i r s t , ii due to Proudman, is given below: p(x.,t) i s the acoust ic pressure received in the f a r f i e l d due t,o, in th i s case, momentum f luc tuat ions o f the turbulence in the d i r e c t i o n of the observer (see Figure 3). These momentum f luc tuat ions can be thought of as noise emit ters . The second time de r i va t i ve of these f l uc tua t ions must be integrated over the source regipn to give the cont r ibu t ion to the f a r f i e l d pressure from that reg ion. The square brackets denote eva luat ion at the retarded time t=t-x./c.where x is the distance from the source to the observer, and c; is the speed of sound. JO An equiva lent so lu t ion to equation (2.4) has been suggested 13 by Ribner. , _ f ( 0 In t h i s case, t-he hydrodynamic pressure f l uc tua t i on s p ^ o f the turbulent; flow can be considered as the bas ic source mechanism. Both equation (2.5) and (2.6) are v a l i d only in the geometric f a r f i e l d ( x » y j and the acoust i c f a r f i e l d ( x . » A ) . I f the region o f unsteady flow contains no surfaces th$n e i t h e r equation should accura te ly descr ibe the acoust ic pressure rece ived in the f a r f i e l d . If a surface i s imbedded in the turbulent f low, then an 2 addi t iona l r e s u l t due to Curie must be cons idered. Again the i sent rop ic assumption app l i e s , and the f a r f i e l d approximation has been made; ( 2 . 7 ) P.j = - l j ( p 6 . .-T..) = tota l force per uni t area, exerted on the 1 J 1 J f l u i d by the sur face. u n .=, v e l o c i t y component normal to the surface The two surface in tegra l s descr ibe the add i t iona l radiated : npise r e s u l t i n g from the i n te rac t i on o f the turbulence with the sur face. If the surface is r i g i d (^=0) and i f shear s tresses are small compared to normal s t res ses ( j < < p 6 ^ . j ) » then equation (2.7) can take the reduced form: (2.8) I P n = pressure exerted pn the surface by the f l u i d 9 = angle between a normal to the surface and the observer 2.2 Causa l i ty Source Location Technique T r a d i t i o n a l l y , researchers have obtained estimates of the rad iated acoust ic i n tens i t y from each source region by squaring and time averaging* e i t h e r equation (2.5) or (2.6) , as done below to equation (2.5): The processes are assumed to be s t a t i s t i c a l l y s ta t ionary so that p ( x , t ) p ( x , t ' ) i s only a funct ion of t - t '=x. Two probes, each measuring momentum f l uc tua t i ons in the d i r e c t i o n of the f a r f i e l d microphone, are separated by a l l poss ib le combinations of space separation ( £ ) and time (x). A twprfold integra l over the co r re l a t i on volume and the en t i r e source region is necessary. Because of the enormous number of measurements r equ i red , and because i t i s necessary to take the fourth time de r i va t i ve o f each c ro s s - co r re l a t i on to f i n a l l y get an estimate of p ( x _ , t ) p U , t ' ) , the method has proven to be l a rge ly unsuccessful in obta in ing de ta i l ed information about the spa t i a l d i s t r i b u t i o n o f noise sources with in j e t s . * overbars denote time averages over a time period which i s long compared with c h a r a c t e r i s t i c periods of p ( t ) , More r e c e n t l y , a much s impler but equiva lent method o f 13 determining source strength and d i s t r i b u t i o n has been used by Siddon, 8 12 Meecham and Hurdle, Rackl and others. Both s ides of equation (2.6) ( i f the pressure source model is used) are simply mu l t i p l i ed by the sound pressure received in the f a r f i e l d . Taking a time average and assuming a s t a t i s t i c a l l y s ta t ionary process, (2.11) , r a i pp(x) is the s e l f or "auto" c o r r e l a t i o n of the f a r f i e l d sound with i t s e l f . The contr ibut ion to pp(x) from a s ing le element of source space i s now proport ional to the second time der i va t i ve of a s ing le c o r r e l a t i o n . Thus i t is dependent on only one inf low probe p o s i t i o n , yet i s exact ly equiva lent ~2 to equation (2.9), The f a r f i e l d i n ten s i t y (I=p /pc ) r e s u l t s i f x i s set equal to zero. Correspondingly, the c r o s s - c o r r e l a t i o n funct ion p ^ p must be evaluated at retarded time x = x / c e . The i n ten s i t y I from each noise source volume is a measure of the acoust ic power flow from that source in a given d i r e c t i o n , so that the source strength from a region in the j e t can be wr i t ten as: { 2 A Z ) d i = _L d ? . - J _ \l > V T ) V A hypothetical co r re l a t i on funct ion i s shown in Figure 4. Such 13 a smooth symmetric curve should be, the r e s u l t fo r pure j e t noise with no surfaces i n te rac t i ng with the turbulence. However the c o r r e l a t i o n taken by Rackl (see Figure 1) i s much d i f f e r e n t , i n d i c a t i n g some add i t iona l surface e f f e c t . The acoust ic i n ten s i t y received in the far f i e l d due to both volume and surface e f f e c t s can be found by simply mu l t ip ly ing Curie's^ re su l t (equation (2.8)) b y ' p ( x . t ' ) . (2.13) i p C ^ O p C ^ ) - 1 Again assuming s t a t i o n a r i t y and time averaging, (2.14) f P ^ ^ / j ' I GxsS For researchers using the causa l i t y technique, i t has been common to measure the co r re l a t i on p ^ p and assume that the unwanted port ion pTp w i l l be smal l . It i s c e r t a i n l y true that the t o t a l i n ten s i t y sensed in the far f i e l d w i l l almost exc lu s i ve l y be due to the j e t turbulence. However, the pressure of the surface can s t i l l s e r i ous l y contaminate the c o r r e l a t i o n between l oca l j e t pressure and f a r f i e l d sound i f the probe surface i s comparable in s i ze to the c o r r e l a t i o n volume of the adjacent turbulent "eddies ' 1 . Unfortunate ly, t h i s i s l i k e l y to be true fo r most model j e t experiments (the contaminating e f f e c t i s described t h e o r e t i c a l l y in, sect ion 4 ) . Other than reducing the probe s i z e , only three a l t e rna t i ve s appear ava i l ab le to reduce th^e e f f e c t o f a pressure probe on the j e t pressure- far f i e l d c o r r e l a t i o n . i ) Because the surface term has a d i r e c t i v i t y descr ibed by cos e, i f the f a r f i e l d microphone i s s i tua ted so that cos 8— ^ 0 then the contr ibut ion from the surface w i l l not be inc luded in the c o r r e l a t i o n . i i ) Since the surface term is d ipole in nature, the noise which 6 i t produces w i l l be proport ional to V - e t « ' The j e t noise however, i s 8 known to vary roughly as V j e t , so that the r e l a t i v e cont r ibut ion o f the probe noise should be less at higher speeds. i i i ) In some cases i t may be poss ib le to separate the e f f e c t s of the probe noise from the j e t no i se , as they may occur at d i f f e r e n t delay times on the co r re l a t i on funct ion. • 1 . 3. PHYSICAL MODEL OF CONTAMINATION To understand the process of probe noise contamination, we consider the case of a probe imbedded in a turbulent flow and a l igned with the flow as shown in Figure 2. Although turbulence can r e a l l y only be character ized by s t a t i s t i c a l l y determined s t r u c t u r e s , f o r s i m p l i c i t y we, w i l l consider the flow to be made up of d i s c re te turbulent "edd ies " . If we imagine such an eddy at pos i t i on 2 on the probe, the pressure f luc tua t ions within the eddy w i l l be sensed by the probe, and assuming proper probe des ign, can be assumed to be within 2 0 % of the t rue * pressure f l u c tua t i on s . As a by-product of these v i o l en t i n e r t i a l f l uc tua t ions there w i l l be much smaller acoust i c waves generated, t r a v e l l i n g away from the source reg ion, a r r i v i n g at the f a r f i e l d microphone at a time t l a t e r . The strongest co r re l a t i on between the f a r f i e l d and the probe should resu l t there fo re , i f the probe s ignal is delayed by time t=xVc 0 re l a t i ve to the microphone s i gna l . If the probe is a l igned with the time averaged f low, there w i l l be only n e g l i g i b l e l i f t or s ide forces ac t ing in the v i c i n i t y of the pressure tap. Considerably higher forces w i l l occur however, at the t i p and stem of the probe. These are in the form of : f l u c t u a t i n g l i f t or s ide forces at the t i p , and predominantly drag forces on the stem. A l so , any points on the probe where area changes occur w i l l lead to f l u c t u a t i n g surface forces (and to separat ion i f the area change is sudden). As a r e s u l t , these areas on the probe w i l l a l so be acoust ic emi t ters , rad ia t ing add i t iona l noise which would not have ex i s ted * see Appendix B 16 without the probe being present and which Wi l l be sensed by the f a r f i e l d microphone. This does not mean that the far f i e l d pressure spectrum w i l l be s i g n i f i c a n t l y a l t e r e d , nor that the overa l l f a r f i e l d sound w i l l be increased very s u b s t a n t i a l l y , s ince i t w i l l include noise coming from the e n t i r e j e t and a l l other uncorrelated eddies. Nevertheless , the unwanted probe noise may be appreciable or even greater than the noise produced by the j e t turbulence within one co r re l a t i on volume. Furthermore, the probe noise w i l l often have very s i m i l a r spectra l propert ies to the leg i t imate j e t noise. The noise from the probe t i p and stem w i l l not c o r r e l a t e at exact ly the same time as the j e t noise. To understand t h i s , consider the fo l lowing: i f in f ac t we wanted to get the co r re l a t i on between the probe noise and the f a r f i e l d pressure we can do i t two ways. F i r s t , we could simply move the pressure measuring holes to the t i p , so that the t i p pressures would c o r r e l a t e with the f a r f i e l d microphone at some time t l a t e r , dependent on the sound speed and distance to the f a r f i e l d microphone. Now note that the pressures sensed at the t i p w i l l be the sum of the leg i t imate j e t pressures and the add i t iona l t i p pressure d i s t r i b u t i o n due to l i f t and s ide fo rces ; hence the co r re l a t i on due to probe noise would be exact ly superimposed on the j e t pressure c o r r e l a t i o n . An a l t e r n a t i v e method to get the probe no i se - f a r f i e l d co r re l a t i on would be to leave the holes at point 0 ( in F igure 2), and assume that the turbu lent j e t pressures which occurred at the t i p w i l l be the same as at point 0. Since the distance is shor t , th i s i s reasonably accurate i f the convecting turbu lent f i e l d i s changing s lowly. As the pressure f l uc tua t ions must convect at a v e l o c i t y U over a distance Y from the t i p to the sensing ho les , then an acoust ic s ignal due to the i n te rac t i on of th,e turbulence with the t i p w i l l leave the probe at a time At*Y t /U before the pressure f l uc tua t ions «* c in the turbulence are sensed by the probe at point 0. Consequently, a A strong co r re l a t i on w i l l occur at time t - A t due to the probe t i p no i se , as well as a strong co r re l a t i on at time t . In both cases the f a r f i e l d microphone is c o r r e l a t i n g with the same turbulent "eddy". Now in f ac t we do not want to co r re l a te tfie probe t i p noise with the f a r f i e l d , but th i s happens na tu ra l l y because the v e l o c i t y f i e l d which produces probe noise i s a l so generating l eg i t imate j e t noise of s i m i l a r character . Thus there appears an add i t iona l bump on the co r re l a t i on due to t i p noise before the cor rec t time delay and an add i t iona l bump due to stem noise a f t e r the cor rect time delay. If At i s large enough, then i t may be poss ib le to completely separate the contaminating co r re l a t i on from the j e t pressure c o r r e l a t i o n . Since the real j e t pressure co r re l a t i on is often very much smaller than the probe noise c o r r e l a t i o n , any over lap between the two co r re l a t i on s can obscure the true j e t pressure cor re la t i ons completely. Before quant i ta t i ve source strength ana lys i s can be done i t is necessary to know the magnitude of e r ro r in the c r o s s - c o r r e l a t i o n and i f , indeed, the leg i t imate source- fa r f i e l d co r re l a t i on can ever be detected accurate ly . 4. ANALYTICAL MODEL A primary purpose here is to t h e o r e t i c a l l y pred ic t the s^hape of the c au sa l i t y co r re l a t i on funct ion which w i l l occur, inc lud ing the contamination e f f e c t s of an inser ted probe. The geometry assoc iated with the problem is shown in Figure 5. Deta i l s not given here appear in Appendix A. The c o r r e l a t i o n funct ion p p ^ ( x ) i s the time, averaged product of the j e t (source) pressure p ^ and the corresponding f a r f i e l d acoust ic pressure p. The r e l a t i o n descr ib ing th i s funct ion is obtained in a manner analogous to the der iva t ion of the causa l i t y in tegra l s (equation (2.14)). In the present case however, we mu l t ip l y both s ides of the rad ia t ion equation (equation (2.8)) by the source j e t pressure before time averaging. Again assuming the turbulence to be s t a t i s t i c a l l y s ta t ionary the fo l lowing r e l a t i o n r e s u l t s : p (° ) = pressure measured by the probe. For a well designed probe in quasi-steady f low, th i s w i l l c l o s e l y approximate the true j e t pressure. - the real j e t pressure p = f a r f i e l d pressure . 19 It can be seen that the shape of p p ^ (T) depends on two terms. The f i r s t i s the surface integra l of the c r o s s - c o r r e l a t i o n between the probe detected j e t pressure p^°) and the loca l surface pressures P n measured at a l l other points on the probe surface S. This term represents the unwanted port ion o f the co r re l a t i on due to the probe surface no ise. The second term is a volume integra l of c ro s s - co r re l a t i on s between p^ and the corresponding true j e t pressures p ^ measured at a l l other points in the adjacent regions o f turbulence. This i s the c o r r e l a t i o n r e s u l t i n g from leg i t imate j e t noise. In order to model the contaminated co r re l a t i on between^ the f a r f i e l d pressure and the source j e t pressure, i t i s necessary to estimate in tegra l s I j and L,. It i s known that turbulent eddies e x h i b i t the propert ies o f convection and decay with space and time, so that in t heo re t i c a l predict ions of noise generation by turbulence, i t has been common to assume a convecting Gaussian funct ion f o r p ( ° ) p ( ° ) ' : (4.2) - , _ ^ ' - ( k U s f f - ^ - a i - l l where U c - convection speed of the eddies L j , l^, Lg = in tegra l length scales of the turbulent eddies : being in the d i r e c t i o n of the flow while and Lg are transverse to the flow. T can be considered a t y p i c a l l i f e t i m e of a turbulent eddy. The decay parameter f /T must be non-zero, in order that the flow may generate sound. 20 Subs t i tu t ing (4.2) into 1^ and in tegra t ing with l im i t s at i n f i n i t y y i e l d s the fo l lowing s o l u t i on : A T ( 4 . 3 ) I , - P l . U U . f r I > ~ ^ ( ' - i g O } which pred ic t s a symmetrical curve as shown in Figure 6. The c o r r e l a t i o n should peak at a time delay x=x/c 0 corresponding to the necessary acoust ic t rave l time fo r a pressure disturbance in the source region to reach the f a r f i e l d microphone. Integral 1^  can be wr i t ten in the equiva lent form below (see Appendix A): v r-(4.4) i « ^ hZ ~ where f i s the net s ide force per unit length on the probe in the plane of the f a r f i e l d microphone, and 3 (see Figure 5) is the angle between the force vector and the f a r f i e l d microphone. The in tegra l over y 1 extends from -°° to the probe t i p s ince we imagine the probe to extend i n d e f i n i t e l y downstream a f te r the pressure measuring taps. This simply means that sources of contamination which occur a f t e r the pressure taps (due to drag forces on the stem or to sudden area changes) w i l l not be modelled here. This s i t ua t i on was dup l icated experimental ly by extending the pressure taps a considerable distance in f r on t o f the supporting stem so that contaminations which occur because o f downstream anomalies w i l l appear l a t e r in time on the co r re l a t i on s ignature than the " t rue " pressure c o r r e l a t i o n . For the probe shape being modelled here, the form chosen fo r 21 p f i s : t • . (4.5) p*»/ . . . e ^ c w ^ e - = f c ~ , V - , £ D C B The various terms in th i s empir ica l form are explained as fo l lows: A: As in the j e t pressure c o r r e l a t i o n , th i s term descr ibes the expected decay of turbulence with time. T i s a t yp i ca l time scale f o r decay in the convecting frame of reference. B: This describes the convection of the turbulence in the y ' Dn c length. d i rec t i on and i t s decay with d i s tance. L is the streamwise c o r r e l a t i o n C: This i s a weighting funct ion fo r the c o r r e l a t i o n which approximates the expected s ide force d i s t r i b u t i o n on the probe. It i s sketched approximately in Figure 6. The constant k determines the distance from the probe t i p where the s ide force d i s t r i b u t i o n i s expected to peak. For th i s work we have assumed f m a x to occur at a distance % diameter from the probe t i p , Which requires that k=%. The exact distance depends upon the prec ise probe t i p geometry, but fo r any round-nosed axisymmetric body the peaking distance i s not l i k e l y to be greater than one diameter, or le s s than 1/8 diameter. K is a parameter which governs the magnitude o f the side force d i s t r i b u t i o n , and can be ca l cu la ted i f the to ta l s ide force 22 r e s u l t i n g from cross flow (due to incidence changes) i s known: n • * d C L V 1 T T H 2 TTpv'U, Assuming ^ ^ 2 ; a = jj-s Area =- 29_ and i n t e g r a t i n g , gives K = ^ 'c " 4K* v' i s the root-mean-square value of the cross-stream turbulence v e l o c i t y . D: R i s a parameter which must have units o f pressure. To a f i r s t approximation, R i s assumed to equal the root-mean-square pressure at the point of measurement ( i .e . - .05%pV 2 at x 0=4D, y 0 = J sD ) . C i s a coupl ing 3 c o e f f i c i e n t which attempts to descr ibe the coherence between probe s ide force f and j e t pressure p (° ) when r=0 and y'=0. If the c o r r e l a t i o n were pe r fec t , C would equal 1. Since no information i s a va i l ab l e on the expected co r re l a t i on between f and p ^ , C was l e f t to be f i t t e d to the experimental r e s u l t s . For C to equal 1 would imply an i den t i ca l phase and amplitude va r i a t i on f o r f and p ^ . Although some degree of coherence is to be expected between s ide force (proport ional to v ' / U c ) and the l o ca l j e t pressure, i t i s extremely un l i ke l y that a per fect one-to-one compatab i l i ty e x i s t s . If the funct ion for p v f given in equation (4.5) i s subs t i tu ted into Ij of equation (4.1) the fo l lowing integra l re su l t s (4.6) where • « * - ( f ^ U )*p J- ' These are reasonable values for a s lender axisymmetric body subjected to smal l , auasi -steadv incidence chanaes. 23 Therefore by so lv ing I l s and combining with the so lu t ion f o r I2, we get the contaminated co r re l a t i on func t ion : (4.7) P. P £ - * > - ^ O L' 2 J where Q . - i l l . - ' -L *£ - Y t For.the pos i t i on where turbulence is highest in a round subsonic j e t ( i . e . , x0/D=4 and y 0/D=%), the flow parameters have the fo l lowing nominal values 9: He ~ • 6 Li = .4D Vj ; 6 1 (o) L 2 = L 3 = Lx/3 1 0T 2.2 D V ^ = 2 0 At; other points in the j e t the flow parameters w i l l be d i f f e r e n t , but the form of the funct ion w i l l be s i m i l a r . Ij p red ic t s a r e l a t i v e l y antisymmetric curve as shown in Figure 6 with a maximum slope occurr ing at a time Y p e a k / U c before the cor rect time delay. I2 p red ic t s a symmetric curve a l so shown in Figure 6 which has zero slope at the cor rect time de lay , f = 0. 25 5. EXPERIMENTAL APPARATUS The purpose o f the experimental inves t i ga t ion undertaken was to confirm the general c h a r a c t e r i s t i c s of the co r re l a t i on model. This cons i s t s of two o b j e c t i v e s i f i r s t , to confirm the shape o f the modelled func t ion , and second, to d iscover whether those parameters on which the empirical co r re l a t i on funct ion depends do indeed have the predicted e f f e c t . Probes o f varying s i zes were b u i l t to t e s t the change in contamination re su l t i n g from s ize changes. Each of the probes were tested at Mach numbers ranging from .35 to .83 to determine the change in contamination with v e l o c i t y . 5.1 Jet F a c i l i t y [ A rotary compressor rated at 280 cfpm (.132 m 3/second) of standard a i r was ava i l ab le fqr use. A i r pressure de l i vered was 100 psi (690 KPa). With our 2 cm diameter j e t th i s has a c a p a b i l i t y to run continuously at M=l. For higher v e l o c i t i e s , the r i g must be run in a 3 blow-down mode, fo r which a large 1.9 m rece iver is a va i l ab l e . While the j e t is running at lower v e l o c i t i e s the rece i ve r also serves to e f f e c t i v e l y damp out poss ib le pressure surges caused by the compressor during s tar t -up and shut-down. A F i sher pressure regulator was used to contro l the flow rate at a l l Mach numbers. The flow rate was monitored by both a water manometer f o r low v e l o c i t i e s (M < .35), and a mercury manometer f o r higher v e l o c i t i e s . Both manometers could be read to an accuracy of ± 1 mm. Approximately 5 minutes was required f o r the system to reach e q u i l i b r i u m , a f te r which the flow rate was remarkably s tab le . A s i l e n c e r was placed between the control valve and the j e t plenum in order to e l iminate upstream valve noise. This cons isted simply of loose ly r o l l e d f i b reg l a s s in an enlarged pipe sec t ion . An 8 cm f l e x i b l e hose was used between the control valve and the j e t plenum to fur ther reduce upstream noise due to sharp pipe bends and f i t t i n g s . With the j e t nozzle removed, the upstream valve noise could not be detected with a B&K V microphone when the chamber door was c losed. The chamber was exhausted through a perforated sect ion of the main door, pos i t ioned downstream.of the j e t ax i s . The j e t plenum design is shown in Figure 7 . The plenum cons is ts o f three sec t ions ; i ) a f i b reg la s s l ined sect ion to fur ther reduce noise and to encourage the j e t enter ing the plenum to d i f f u se qu ick ly . i i ) screens and honeycpmb fo r flow s t ra ighten ing i i i ) a short s e t t l i n g sect ion so that those small eddies generated at the screens and honeycomb can be damped out. The maximum v e l o c i t y (at M=.83) in the s e t t l i n g chamber is extremely low (1.8 m/sec) so that the approach flow is e s s e n t i a l l y laminar. The nozzle used (see Figure 8 ) was designed to give a uniform 19 ve loc i t y p r o f i l e at the e x i t plane (Smith and Wang). A p lo t o f the mean ve loc i t y across the e x i t plane is given in Figure 9 . The large contract ion r a t i o (156:1) ensures very thin boundary layers and a low turbulence l e v e l . A spec ia l t raver s ing mechanism was designed to minimize the surface area in c lose proximity to the j e t . This i s shown in Figure 10. The object ive was to e l iminate any undesirable acoust ic r e f l e c t i o n s which might fur ther contaminate thq c o r r e l a t i o n func t ion . The traverse gear is capable of rad ia l and ax ia l movement over the s i g n i f i c a n t regions of j e t turbulence, and is accurate to ±.5 mm. 5.2 Instrumentation The f a r f i e l d microphone was a k" B&K type 4135. This has a f l a t frequency response up to 40 kHz and a maximum phase s h i f t o f 35° at 40 kHz. The output from.this microphone was amp l i f i ed , f i l t e r e d and fed into a Saicor Model43A signal c o r r e l a t o r , channel B. A schematic o f the s ignal path is shown in Figure 11. The in - f low probe consisted o f a .030 i n . (.078 cm) diameter Kul i te semiconductor pressure transducer, imbedded ins ide s t a t i c pressure s leeves o f three d i f f e r e n t seizes. As shown in Figure 12, a sect ion of hypodermic needle was used as a f ixed Ku l i te ho lder , so that d i f f e r e n t probe s izes could t?e tested without constant ly d i s turb ing the Ku l i te transducer. The stem of the probe was a i r f o i l shaped in order to reduce the drag f luc tuat ions and to increase the stem s t i f f n e s s in the ax ia l d i r e c t i o n . The Ku l i te transducer was c a l i b r a ted using a 250 Hz pure tone, and the s e n s i t i v i t y was found to c l o s e l y match the manufacturer's s p e c i f i c a t i o n s . The s ignal from the Ku l i te was amp l i f i ed , f i l t e r e d (20 Hz - 40 kHz) and fed into channel A of the Saicor c o r r e l a t o r . 28 Because the s i ze of the sensing diaphragm on the Ku l i te transducer is very much smaller than the smal lest wavelength to be measured, a l l o f the frequencies o f i n te re s t w i l l appear to the diaphragm as s p a t i a l l y uniform pressure waves. As a r e s u l t , no high frequency r o l l r o f f is expected, so that a frequency response c a l i b r a t i o n f o r the Ku l i te transducer was f e l t to be unnecessary. Since the phase s h i f t is re la ted to t,he frequency response, i t a lso i s expected to change very l i t t l e up to the maximum frequency of i n t e r e s t . When the hypodermic tubing conta in ing the Ku l i te is inser ted in to the s t a t i c pressure s leeves, a small cav i ty is formed d i r e c t l y before the Kul i te diaphragm, which could lead t o a resonant condi t ion at the Helmholtz frequency of the cav i t y . To avoid t h i s , the cav i t y s i ze f o r each probe was kept as small as poss ib le so that resonance was forced to occur above 40 kHz. To concur with the quasi-steady assumption of sect ion 4, the diameter o f the s t a t i c pressure sleeves must be small compared to the expected c o r r e l a t i o n sca les . At x/D=4 and y/D=%, a t yp i ca l streamwise ve loc i t y scale would be about . l x 0 ( . 8 cm) and about .04x o (.32 cm) in the transverse d i r e c t i o n . The largest probe used i s .470 cm in diameter and does show a s l i g h t l y lower overa l l rms pressure than the smal ler probes, i nd i ca t ing some loss of high frequency information due to i t s poorer spa t i a l r e so l u t i on . For accurate pressure measurements in steady flow using a standard probe» i t i s necessary to locate the pressure taps about 6 29 diameters downstream from the nose and about 8 diameters upstream from the stem in order to;cancel the t i p and stem e f f e c t s . For unsteady f low, the pressure taps should be located i n a s i m i l a r pos i t i on in order to be i n sens i t i ve to streamwise v e l o c i t y f l u c tua t i on s . Since a l l three of the s t a t i c pressure sleeves are the same length (see Figure 13) i t was necessary to place the pressure taps for the l a r ges t probe at a d is tance only a 1 i t t l e greater than 4 diameters from the nose. Referr ing to Figure 14, i t can be seen that f o r steady f low, such placement w i l l lead to only a s l i g h t l y la rger e r r o r . , • 1 A 1/8" B&K microphone was used as an in - f l ow probe f o r a port ion of the experimental work in order to demonstrate the e f f e c t on the c ro s s - co r re l a t i on s ignature of changing the probe nose length. To simulate a long probe, a dummy nose piece was glued onto the gr id cap as shown in Figure 13. For a short probe, a standard B&K nose cone was used, a l so shown in Figure 13. A Plotamatic x-y recorder was used to p lot the c o r r e l a t i o n funct ions . Autocorre lat ions were taken in order to non-dimensional ize the c ro s s - co r re l a t i on s with the autocorre la t ion values at x=0. The autocorre la t ion of the in - f low probe was a l so a convenient check fo r c av i t y resonance or probe v i b r a t i o n . .Probe v ib ra t ion can be detected s ince any resonant movement o f the probe would be sensed by the probe as a r e g u l a r i t y in the f low, r e s u l t i n g in a per iod ic au tocor re la t ion func t i on . This became a problem only fo r the largest probe while operat ing at the highest Mach number (M=.83) so that resu l t s f o r t h i s condi t ion are not reported. 6. EXPERIMENTAL RESULTS As discussed in sect ion 4, an ana l y t i c a l model has been developed which is expected to pred ic t the e f f e c t o f probe noise on c au sa l i t y c r o s s - c o r r e l a t i o n s . For a standard probe with a long nose, the port ion of the c r o s s - c o r r e l a t i o n due to probe t i p noise i s predicted to have a maximum slope at a time before the leg i t imate j e t pressure c o r r e l a t i o n , given by the distance Y and the convection v e l o c i t y U peak c (see Figure 6) . The f i r s t experiments, the re fo re , were intended pr imar i l y to confirm the existance of probe t i p . n o i s e , and i t s dependence on probe length f o r i t s time o f occurrance on a c r o s s - c o r r e l a t i o n . If d i f f e r e n t prpbe diameters and a var ie ty of Mach numbers are used as inputs to the ana l y t i c a l model, cer ta in funct iona l re l a t ionsh ips w i l l ex i s t between these var iables and the degree o f contamination. A second set of experiments was ca r r i ed out to te s t the pred icted r e l a t i o n s h i p s . 6.1 Bruel and Kjaer Microphone Experiments Since many experimenters use standard B&K microphones with attached nose cones as probes fo r c r o s s - c o r r e l a t i o n s , i t was decided to dup l i ca te th i s set -up using a 1/8" B&K microphone. A symmetrical a i r f o i l was glued onto the microphone preampl i f ie r (see Figure 13) in order to reduce the drag r e s u l t i n g from the j e t flow. The diaphragm of the microphone was placed at a pos i t i on x0/D=4 and y 0/D=%. The f a r f i e l d microphone was s i tua ted perpendicular to the j e t , so that cos 3 in equation (4.6) w i l l equal unity. In th i s pos i t i on only the side force f luc tuat ions on the probe t i p should contr ibute noise to the f a r f i e l d microphone (drag force f luc tuat ions on the stem w i l l rad iate in the upstream-downstream d i r e c t i o n ) . The experimental r e su l t is p lo t ted in Figure 15, and appears much l i k e leg i t imate j e t no i se , having an almost symmetrical shape at the cor rect time delay. Also p lot ted in F igure 15 i s the ana l y t i c a l r e s u l t . This was evaluated using the expression fo r the j e t noise c o r r e l a t i o n as i t appears in equation (4.3) and adding to i t a numerical in tegrat ion of the probe noise co r re l a t i on term as i t appears in equation (4.6). A best f i t was obtained by ass igning a value .50 to the coupl ing c o e f f i c i e n t C (explained in D fo l lowing equation (4.5) ) . If a constant convection v e l o c i t y i s assumed over the length of the probe, then the time scale on the c r o s s - c o r r e l a t i o n funct ipn can be converted to a length sca le on which a sketch of the in - f low probe can be superimposed with the pressure taps corresponding to x=0. If t h i s i s done, anamolies on the c o r r e l a t i o n funct ion can be projected downward to regions on the probe sketch from which the anomalies occurred. Most o f the peak in the predicted c o r r e l a t i o n curve a t T=0 is, due to the sharp r i s e in pressure near the f ront o f the nose cone. The re su l t i n g probe noise occurs ju s t before the co r rec t time delay but causes a peak a t the cor rec t time delay. The true j e t pressure co r re l a t i on appears as a broader and shorter hump, but is almost completely masked by the probe noise c o r r e l a t i o n . The shape o f the experimental curve agrees well with the ana l y t i c a l r e su l t except f o r a large bump a f te r r=0. The superimposed probe sketch c l e a r l y suggests that t h i s anomaly i s due t o the change in c ros s - sec t iona l area which occurs along the probe. Since only probe t i p noise has been modelled as a source of contamination, no such bump occurs on the ana l y t i c a l curve. If a B&K microphone modif ied as in F igure 13 i s in ser ted in to the flow (again at x/D=4, y/D=^), then the long probe t i p should : ensure that the probe noise from the t i p w i l l be well separated in time from the true j e t pressure c o r r e l a t i o n . Both the experimental and the ana l y t i ca l r e su l t s are p lo t ted in Figure 16. The coupl ing c o e f f i c i e n t C was l e f t unchanged from the previous experiment. As p red i c ted , the probe noise port ion o f the co r re l a t i on does appear to occur at near ly the expected time delay Y n e a k / U c . The predicted j e t noise co r re l a t i on appears as a broad hump in the a n a l y t i c a l curve, and is now c l e a r l y v i s i b l e . There does not appear to be any experimental ly observed counterpart to the predicted j e t noise c o r r e l a t i o n . The bump on the experimental curve which occurs d i r e c t l y a f t e r T=0 is l i k e l y due to the sharp d i s con t i nu i t y on the probe surface where the gr id cap ends. This same noise source was probably a lso ac t i ve in the previous experiment (due to separat ion from the nose cone cap) although i t s presence may have been masked by the very large t i p noise peak which occurred at T=0. A comparison of Figures 15 and 16 c l e a r l y demonstrates the dependence of c au sa l i t y co r re l a t i on s on t i p d i s tance, and confirms the existance o f probe noise as a s i g n i f i c a n t contaminant o f the c o r r e l a t i o n funct ion . Since the use of B&K nose cones f o r pressure co r re l a t i on s in model j e t s i s quite common, our f ind ings suggest the p o s s i b i l i t y that many researchers have been measuring mostly probe noise and very l i t t l e leg i t imate co r re l a t i on from the turbu lent sources. 6.2 Normalizing Procedure It i s perhaps necessary at th i s point to expla in the normal iz ing procedure used in presenting the data. The most common procedure in normal iz ing c ro s s - co r re l a t i on s i s to d i v ide the time-averaged product by the rms values of the two f l u c tua t i ng var iab les being co r re l a ted in equation (1.1): PP^(jPl/p* ) . Such a procedure however, does not c l e a r l y show the e f f e c t o f probe s i ze or Mach number on the c ro s s -c o r r e l a t i o n . Furthermore, i t does not provide a means o f ex t rapo la t ing to other experimental combinations of probe s i z e , j e t diameter, Mach number or f a r f i e l d d i s tance. In the present case, the pressure p received in the f a r f i e l d due to a s ing le turbulent source i s estimated from equation (2.6): -A -t For one noise source the integra l i s only over one co r re l a t i on volume, but 34 for the en t i r e j e t (which is what our far f i e l d microphone measures) the in tegra l must inc lude the e n t i r e j e t volume. The f a r f i e l d pressure from the en t i r e j e t can be considered to vary the re fo re , as fo l lows: \ X C 0 * ^t?" ^ ~ e n t ' ' r e J e t volume If the fo l lowing dimensional approximations are made, V 'v D 3 w D = j e t diameter 6t L L "o D L F turbulent length sca le then P ^ x c ^ C r i ) ^ " T n e P r e s ' s u re p ^ (~p (° ) ) measured by the probe w i l l be some f rac t i on of the ava i l ab le dynamic head, p^ 0^' ^ p-V 2 J J If the expressions for p ( ° ) ' and p are subs t i tu ted in to the c l a s s i c a l l y normalized c r o s s - c o r r e l a t i o n func t i on , the fo l lowing r e s u l t s : This l a s t form r e f l e c t s the normal iz ing procedure used to present a l l o f the data, and enables easy s ca l i ng from one experimental set-up to another, The fp l lowing dimensionless formula should a l so be u se fu l : ( ^ * ) X P 6.3 Parametric Invest igat ions It i s poss ib le to get rough approximations o f the e f f e c t of probe diameter and Mach number on the funct ion pp( Q ) i f ( p . V 2 . ) 2 M 2 D dimensional estimates of p and p ^ are made. If the sound received in the far f i e l d from a s ing le coherent region i s dominated by the probe no i se, then equation (2.8) pred icts that xc St n where A equals the c o r r e l a t i o n area over the probe sur face . Again making dimensional approximations: 6t L L ^ D (at a p a r t i c u l a r x 0 / D , y „ / D ) P n i s the surface pressure on the probe and w i l l be some f r a c t i 2 o f the ava i l ab le dynamic head ^ p-V. J j A ^ d 2 p ( 0 ) ' Subst i tu t ing in to equation (6.1); on ( f j ^ ) H j ^ ( f ^ r n / A " ^ J 1 ^ We expect there fo re , the normalized c ros s^cor re la t ion c o e f f i c i e n t 36 of the probe noise to vary as ^ 2 I . The port ion of the c o r r e l a t i o n due to pure j e t noise however, would not be expected to vary at a l l , unless the degree of coherence in the j e t i s i t s e l f a funct ion of Mach number. As shown in Figure 13, three s t a t i c pressure s leeves were b u i l t for the Ku l i te transducer, a l l about the same length (Y t 1.91 cm) but with d i f f e r e n t d/D r a t i o s ( i . e . , .118, .159 and .236). The three d i f f e r e n t probes were used f o r c ro s s - co r re l a t i on s with the f a r f i e l d microphone at four d i f f e r e n t j e t Mach numbers ( i . e . , .35, .51, .68 and .83). In each case, the pressure taps were placed in the j e t at x 0/D=4, y0/D=h as before. The experimental resu l t s f o r each Mach number are p lotted uppermost in Figures 17 to 20, with predicted curves p lo t ted below in each case. The predicted curves were generated exact ly as in the previous sec t i on , using the c losed form so lu t ion fo r the j e t noise given in equation (4.3) and adding to i t a numerical ly integrated re su l t o f the probe noise as given in equation (4.6). The predicted increase in contamination with diameter appears somewhat stronger than that observed exper imental ly. In Figure 21, the log of the maximum values of the normalized c r o s s - c o r r e l a t i o n funct ion (Cm ( T ) ) i s p lot ted at. a constant Mach number against the log of a l l max three d/D r a t i o s . It i s evident that the predicted va r i a t i on fol lows a / \2 I-) law (this was expected, given by equation (6.2)) whi le experimental ly we observe a I p l law. This discrepancy is possibly because the expression f o r p v u ; f in the a n a l y t i c a l model i m p l i c i t l y assumes quasi-steady condit ions regardless o f probe s i z e . Since the transverse 37 length scale of the turbulent v e l o c i t y f i e l d * is about .3-.4 cm, the r a t i o of eddy s i ze to probe diameter approaches unity f o r the l a rges t probes. Thus a quasi -steady s ide force model (as in Appendix A) w i l l increas ing ly overestimate the actual forces produced as the probe s i z e increases, r e l a t i v e to the eddy s i z e . , For a l l o f the predicted curves, the coupl ing c o e f f i c i e n t C was assigned a value = .36. This gives a good f i t to the experimental re su l t with the smal lest d/D r a t i o at the lowest Mach number, but increas ing ly underestimates the experimental r e su l t s at higher Mach numbers. A p lot o f log C M [ T I A X ( T ) versus log [Mach number] at a constant d/D r a t i o -1 12 (Figure 22) shows that the a n a l y t i c a l re su l t s fo l low a M" " law while the experimental curves show no c l e a r va r i a t i on with Mach number. This could be because jthe coupl ing c o e f f i c i e n t was assumed to be a constant, whereas i t may vary with Mach number i f the t i p forces and measured pressures are bet ter cor re la ted at higher v e l o c i t i e s . It i s a l so a p o s s i b i l i t y that the turbu lent length scales or i n t e n s i t i e s are changing, s ince any increase in these quant i t ies with increas ing Mach number would tend to overestimate the probe noise co r re l a t i on at higher Mach numbers. This problem deserves fur ther i nves t i ga t i on . 6.4 Other Sources of Contamination Although only the contamination due to the s ide forces on the probe t i p has been discussed in th i s work, there are in f a c t , several other poss ib le sources of cor re la ted probe no i se. The mechanisms for these, and * based on v e l o c i t y co r re l a t i on measurements; the pressure sca les could be as much as twice as l a r ge , based pn Planchon's work1.0 t h e i r expected d i r e c t i v i t y patterns are i l l u s t r a t e d approximately in Figure 23. The r e s u l t i n g composite c r o s s - c o r r e l a t i o n funct ion i s shown (hypothet ica l l y ) near the bottom of the f i g u r e . The dominant e f fec t s are due to drag f luc tua t ions on the supporting stem and loca l separat ion points at sharp corners , p a r t i c u l a r l y near the elbow of the probe ho lder. The drag-induced d ipo le was not noted unless the far f i e l d microphone was placed at shallow angles to the j e t centre ! ine ( i . e . , f o r 3—- * -90° ) . A huge 1 i f t - i nduced contaminant was detected from the a i r f o i l stem i f the f a r f i e l d microphone was placed v e r t i c a l l y above the probe in the d i r e c t i o n of the l i f t f l u c tua t i on s . A cons iderably l a rger source of contamination than expected occurred from the change in area as the pressure sleeves meet the a i r f o i l stem. Fa i r i n g or smoothing at t h i s point would only p a r t i a l l y e l iminate th i s source, although the l a rges t probe, which has a diameter c lose to the thickness of the a i r f o i l stem, showed les s contamination. Any c y l i n d r i c a l body in pure cross - f low w i l l experience s ide forces associated with the c i rcumferent ia l pressure d i s t r i b u t i o n , so that even at the pressure taps, small f l u c tua t i n g s ide forces may pose a source o f yet another, although probably weak, contamination. Many of these other contaminant mechanisms are a l so amenable to empir ica l p red i c t i ons , using a turbulence in terac t ion model analogous to the f l u c tua t i ng nose force model used here. A model descr ib ing the drag-induced contaminant on the stem fo r example, w i l l be almost i d e n t i c a l except that an appropriate weighting funct ion which c l o s e l y approximates the expected f l u c t u a t i n g force d i s t r i b u t i o n due to drag w i l l be necessary. 39 7. CONCLUDING DISCUSSION The s i g n i f i c a n t f i nd ing of th i s work is that probe noise has a strong in f luence on pressure c o r r e l a t i o n s with the f a r f i e l d . It i s evident that most conventional in - f low pressure probes w i l l not provide useful co r re l a t i ons with the f a r f i e l d , so that probably probe no i se , and not true turbulence no i se, has been dominant in most of the previous causa l i t y experiments on j e t s . True j e t noise c o r r e l a t i o n s , i f normal ized, should be mainly a funct ion of probe pos i t ion and must not depend on such probe parameters as diameter or geometry. Some Mach number dependence is poss ib le i f the number of j e t noise sources increases or decreases with Mach number. In any event, no c l e a r l y i d e n t i f i a b l e c o r r e l a t i o n with the f a r f i e l d due to j e t noise has been observed in the experiments reported here, This was unexpected, and leads to the idea that the degree o f coherence in the source region may be extremely weak. The resu l t s here ind icate that the maximum co r re l a t i on c o e f f i c i e n t C (equation 1.1) must be smal ler than .015 (based on the smal lest value of d/D), suggesting about 5000 separate and uncorrelated regions o f turbulence (see sect ion 1.2). This i s 6 somewhat cons istant with f ind ings by Lee & Ribner using a hot -wire. Previous co r re l a t i on c o e f f i c i e n t s of order .1 (when using pressure probes) lead to an estimate of about 100 uncorrelated sources. Since no d e f i n i t e ind i ca t ion of " t rue " j e t source strength was noted, i t has not been poss ib le to experimental ly determine a su i t ab le d/D r a t i o where t ip - induced probe noise can be guaranteed to be less than the leg i t imate c o r r e l a t i o n . The curves r e s u l t i n g from the a n a l y t i c a l model ind icate that only at the smal lest d/D r a t i o (.118) was C m "'max ever equal t o , or less than, the predicted j e t no ise. This is only an approximate re su l t s ince the magnitude of the predicted probe noise cor re l a t i ons depends on the choice f o r the coupl ing c o e f f i c i e n t C. For best f i t , C does not vary s u b s t a n t i a l l y with diameter (within the l i m i t s of the quasi-steady model) but var ies by a f ac to r of about 2 over the range of Mach numbers tes ted. Although the ana l y t i c a l model has been tested at only one point in the j e t (x 0/D=4, yo/0=h) and f o r only one prqbe geometry, the method is probably quite general . The p a r t i c u l a r point chosen i s considered to be a region of dominant noise generation in subsonic j e t s , but the model is f l e x i b l e enough so that contaminatipn estimates could be made for other points in the j e t using the appropriate measured values of the turbulence parameters. The shape and parametric dependence of the probe noise co r re l a t i on is reasonably well predicted by the model presented here, although some d i screpanc ies do e x i s t . It is su rp r i s i ng in f a c t , that the experimental trends have been r e f l e c t e d so w e l l , i f we cons ider some o f the imperfections o f the model: turbulence is not Gaussian, yet a Gaussian model has been used fo r both the probe noise co r re l a t i on and the j e t noise c o r r e l a t i o n . Furthermore, the estimates for the length scales in the turbulence are based on an experimental f i t to a space c o r r e l a t i o n func t i on , while the convected time sca le estimate is based on a s i m i l a r f i t to the envelope of space-time c o r r e l a t i o n s . Neither funct ion is a c tua l l y exponent ia l , and in both cases an exponential f i t w i l l be inadequate f o r high f requencies. For the time sca le estimate the f i t is a lso t y p i c a l l y poor at low frequencies. In most cases, these estimates are based on hot wire measurements of the v e l o c i t y f i e l d in very low speed jets (although the value used f o r the convected time sca le here i s based 10 on pressure measurement, but at a very low Mach number), but there i s evidence that length scales based on pressure are somewhat la rger than those based on v e l o c i t y . Measurements in higher speed flows, may a l so ind icate changes in these values. Aside from the crude estimates used fo r the turbulence parameters, the model must a l so be content with only a rough estimate o f the true force d i s t r i b u t i o n on the probe t i p , as well as an a r b i t r a r y se lec t i on of the d is tance from the t i p at which the d i s t r i b u t i o n peaks. In view o f these imperfect ions, i t i s encouraging that the major features of the co r re l a t i on functions are followed so w e l l . Further development w i l l lead hopefu l l y , to a useful research tool which w i l l quant i fy accurate ly the e f f e c t of probe noise in c au sa l i t y co r re l a t i on s as a funct ion of probe diameter, geometry, Mach number, probe p o s i t i o n , e t c . APPENDIX A - PREDICTION OF THE SHAPE OF P ^ ^ ' P ( T ) INCLUDING THE E F F E C T OF SURFACE PROBE NOISE The r e l a t i o n descr ib ing the c o r r e l a t i o n funct ion p p ^ (x) i s obtained by mu l t ip ly ing both s ides of equation (2.8) by p (° ) . (A- l ) (o) ' p i s the surface pressure measured at 0 (see Figure 5) and i s assumed to be = p ^ because of probe design. p (° ) ( 0 , t ' - r / c ) can be taken ins ide the integra l sign because i t is independent of the surface or volume i n teg ra l s . If the processes are s t a t i s t i c a l l y s t a t i onary , the l e f t and r i gh t hand s ides are funct ions of x=t - t ' on ly : coy (A -2 ) C*0 0 7>t Retarded time d i f fe rences due to r^xfa ' .can be neglected i f one assumes that the wavelengths w i l l be genera l ly long compared to the c o r r e l a t i o n s ca le s , so that A-2 can be s i m p l i f i e d to g ive, 4 3 (A-3) 4-TTC: I It = probe noise e f f e c t I2 = leg i t imate j e t noise e f f e c t Estimates for and I must be made in order to evaluate A-3. The procedure f o r est imating 1^  fo l lows. Since cose=cosycos3 (see Figure 5 ), then \PhCosxds = F, the net s ide force on the probe at an instant due to surface pressure imbalances around the probe. I j can now be wri t ten as (A.4) i= -s&i. (p^SW PC Let f = | y r = force per un i t length. The necessary c o r r e l a t i o n t h e r e f o r e , i s between the measured pressure and the force per uni t length along the T o ! 7 " prpbe, p v f . We make two assumptions concerning the form o f t h i s c o r r e l a t i o n : i ) the c o r r e l a t i o n w i l l decay with distance and time i i ) the co r re l a t i on w i l l be weighted by the force d i s t r i b u t i o n over the probe sur face. In t h i s case, we approximate t h i s d i s t r i b u t i o n by the fo l lowing funct ion 44 The c o e f f i c i e n t s K and k determine r e s p e c t i v e l y , the magnitude o f the force and the distance from the t i p at which the funct ion peaks. Both have already been discussed in sect ion 4. The expression f o r p^0^ f is hence given by: 1 I _ J L • • T 1 form of force descr ibes the descr ibes decay These parameters are d i s t r i b u t i o n convection and with t ime; T i s constants, a lready decay with a t yp i ca l decay discussed in sect ion 4 d i s tance; L i s time of turbulence a turbulent length sca le Subst i tu t ing the expression for p f into 1^, we get: (A-5) I - ~C*Atos £ 7 " z dy ° where z=Y^ - y ' . D i f f e r e n t i a t i n g with respect to T, I J becomes: ( A . 6 ) I r r y e V ; x 2 * 2U 2 . £ 2 Y t U c where g = ^ + — 5 - + ^ . The exponent of the exponential in A-6 r L l / 2 1 1 U c " Y t can be put into the form -az -2bz-c where a = ^ b = _ - - _ L - _ ; L 2kd L 2 L 2 Y 2 /U *\2 2Y U * and c = t + / c ' + — . can now be written as two standard 1 2 45 integra l s : 12-( A -8 ) L v = < ^ R * V {j(£JI * " . ^ - M (-£. (M <£^±>* b \ Subst i tut ing the expressions for a, b and c, but de f in ing a new var iab le _ L 2 Q k d " U c T - Y t .» t n e f o 1 lowing can be wr i t t en : ( A-9) I,= o^e^te e ^ 4 ^ ( < ^ u ^ ) To estimate I,,, i t has been common to assume a convecting Gaussian fo r the j e t pressure c o r r e l a t i o n : 46 I^  becomes then, (A-10) The l i m i t s w i l l be at i n f i n i t y f o r each i n teg ra t i on . ( A - l l ) OP •OO 2. S i m i l a r l y , the in tegrat ion in the d i rec t i on s y1 and y 2 w i l l lead to The c o r r e l a t i o n p ^ p(x) i s the sum o f and I (as given in A-3) 2 2-APPENDIX B - STATIC PRESSURE MEASUREMENT IN A TURBULENT FLOW15 If a standard probe is measuring s t a t i c pressure in a turbu lent f i e l d , then the pressure error caused by unsteady cross^-components of v e l o c i t y can be approximated by the pressure d i s t r i b u t i o n on a long cy l i nde r in ideal c ross - f low. The pressure at the surface of the probe, subtracted by the pressure which would have occurred in the absence o f the probe w i l l be given by: where V n is the component of v e l o c i t y normal to the c y l i n d e r . —: If the pressure probe averages the c i r cumferent i a l pressure p e r f e c t l y , then f o r ideal f low the second term w i l l be zero and the f i r s t term w i l l be -%pV n ( t ) . A rea l probe with a f i n i t e number of pressure taps, w i l l not take an exact average over the circumference of the c y l i n d e r , so that the term due to acce le ra t ion w i l l contr ibute to the e r r o r . If mpre than three taps are used, the inaccuracy in averaging over the circumference w i l l be sma l l , so that the error due to the acce lera t ion term w i l l be much less than the e r ro r due to the v e l o c i t y term. For rea l f lows, the 2 er ror due to the v e l o c i t y term can be given by P m ( t ) - P t ( t ) = BpV (t ) m t n where B must be evaluated from quasi-steady f low c a l i b r a t i o n s (B = -h f o r potent ia l f low) . Siddon found values of B between -.31 and - .46 , and Planchon reports - .5 . 48 I f the pressure and v e l o c i t y terms are wr i t ten in terms of mean and f l u c tua t i ng quan t i t i e s , then the unsteady pressure error can be written as: where v n 2 = v ^ w 2 . Squaring and time averaging, The r a t i o v n 4 / ( v n 2 ) 2 ^ 2 f o r a j e t shear l a y e r , therefore 2 . I f the true j e t pressure - .05pV: , then the f r a c t i ona l e r ro r in the rms pressure can be wr i t ten as: (fir ?Q = S ? ( f f i f 2 Considering the worst case, B = -h, v n = .151^, the f r a c t i o n a l e r ro r w i l l be PO - ~.S ( i S j i 1 - i . e . , the expected e r ro r w i l l not •OS $\Jf • ° & exceed 22.5% 49 REFERENCES 1. ' C h u , W . T . , "Turbulence Measurements Relevant to Jet Noise",UTIAS Report No. 119, November (1966). 2. Cur ie , N., "The Influence of So l id Boundaries Upon Aerodynamic Sound", Proc Roy. Soc. A, 231, 505-514, (1955). 3. Dean, R.C., "Aerodynamic Measurements", MIT Press, Cambridge, Mass., (1953). 4. Fuchs, H.V., Michalke, A . , "Four Introductory Lectures on Aerodynamic Noise Theory", Deutsche Luft-und Raumfahrt M i t te i lung 71-20, (1971). 5. Lee, H.K., "Cor re la t ion of Noise, and Flow of a J e t " , UTIAS Rep. 168 . (1971) 6. Lee, H.K., Ribner, H.S., "D i rec t Cor re la t i on of Noise and Flow of a J e t " , J.Acoust.Soc.Am., Vo l . 52. Number 5 part 1,pl280,(1972). 7. Liepmann, H.W., Roshko, A . , "Elements of Gasdynamics", John Wiley & Sons, New York, (1957). 8. Meechan, W.C., Hurdle, P.M., and Hodder, B., " Invest igat ions of the Aero-dynamic Noise Generating Region of a Jet Engine by Means of the Simple Source F lu id D i l a t a t i o n Model", JASA, Vo l . 56, No. 6 (1974). 9. Nayer,B.M.,Siddon, T . E . , and Chu, W.T., "Propert ies of the Turbulence in the T rans i t i on Region of a Round J e t " , Univ. of Toronto Inst, f o r Aerospace Studies T.N.-131 (1974) 10. Planchon, H.P.,"The F luctuat ing S t a t i c Pressure F i e l d in a Round Jet Turbulent Mixing Region", PhD Thes i s , Nuclear Engineering Program, 11. Proudman, I., "The Generation of Noise by I sotropic Turbulence" , Proc. Roy,Soc. A, Vol .214, p.119. 0 9 5 2 ) . 12. Rack l , R., "Two Causa l i ty Cor re la t i on Techniques Appl ied to Je t Noise" , PhD Thes i s , Dept. of Mech. Eng., Un iver s i t y of B r i t i s h Columbia, A p r i l (1973). 13. Ribner, H.S., "The Generation of Sound by Turbulent J e t s " , Advances in Appl ied Mechanics. V o l , 8, Academic Press Inc., New York, 1964. 4. Scharton, T .D . , White, P.H., "Simple Pressure Source Model o f J e t Noise" J.Acoust.Soc.Am., Vo l .52, Part 1, Ju ly (1972). 5. Siddon, T . E . , "On the Response of Pressure Measuring Instrumentation in Unsteady Flow", UTIAS Rep. No. 136, January (1969) 6. Siddon, T . E . , "Surface Dipole Strength by Cros s -Cor re la t ion Method" J.Acoust.Soc.Am., Vo l .53, No.2, p.619-633, Feb. (1973). 7. Siddon, T . E . , "Noise Source Diagnostics Using Causa l i t y Cor re la t i ons ' S p e c i a l i s t s Meeting on Noise Mechanisms, AGARD F lu id Dynamics Panel , Belgium, Sept. (1973). 8. Siddon, T . E . , "Some Observations on Source Detection Methods With App l i ca t i on to Je t Noise" , published in Proceedings of the 2nd Interagency Symposium on Un iver s i t y Research in Transportat ion Noise, North Caro l ina Un iver s i ty -9. Smith, R.H., Wang, C.Y., "Contract ing Cones Giving Uniform Throat Speeds". Jour. Aeor. S c i . , Vo l .11, p.356-360, (1944). Figure 1 - The E f fec t of Probe Nose Length on the Cross -Corre la t ion Signature ACOUSTIC FLUCTUATIONS AS BY-PRODUCTS OF HYDRODYNAMIC FLUCTUATIONS U+u1 HIGH LIFTING AND SIDE FORCES RADIATE ADDITIONAL NOISE PT. 0 - t O P ( 0 ) ' ( t ' ) o SMALL SHEAR AND SIDE FORCES POSITION 2 FLUCTUATING DRAG FORCES A Probe Imbedded in a Turbulent Flow VJl IV 5'3 Figure 3 - The Proudman Source Mechanism x = x/c Figure 4 - A Hypothetical Causa l i ty Corre la t ion Function f o r Pure Jet Noise 55 Figure 6 - Hypothetical Corre la t ion For a Standard Probe Function 1.22 m locat ion of pressure and 4.4 cm th ick 3 mm aluminum steel cross screen honeycomb sect ion 12 cm long members 3 mm hex - f i t s r i ve t ted ins ide ins ide aluminum front o f aluminum cy l i nde r cy l i nder Figure 7 - Jet Plenum and Nozzle VJ1 OS 2 cm d i a . Figure 8 - Schematic of Contoured Nozzle •y 58 o 1.0 .9 .8 CO .7 20 40 60 80 100 120 DISTANCE FROM INSIDE WALL OF NOZZLE (in x .001) Figure 9 - Mean V e l o c i t y P r o f i l e at the Jet Ex i t Plane at M = .99 Figure 11 - Signal Paths |* 38 -*| KULITE TRANSDUCER SEALED WITH SILICONE GREASE C=D3= HYPODERMIC NEEDLE •1.27 DIA TO FIT SHAFT SNUGLY 11 ft SCALE: NONE ALL DIMENSIONS ARE IN MILLIMETRES Figure 12 - Construction Detai l s of Ku l i te Probe Holder 6? DIA = 2.29 K= .118 56 4 ho les , .5 d ia each 20 4 ho les , .7.8 d ia each SCALE: 1.5:1 4 ho les , .78 d ia each B&K SCALES: FULL SIZE MODIFIED B&K 1/8" MICROPHONE (NOSE EXTENDER GLUED TO GRID CAP) 3.2 DIA 3.5 DIA a i r f o i l shaped stem is epoxied to preampl i f ie r 1/8" B&K MICROPHONE WITH STANDARD NOSE CONE 3.8 DIA r=DO| ALL DIMENSIONS ARE IN MILLIMETRES Figure 13 - Deta i l s of A l l In- Flow Probes 3 Figure 14 - Probe Tip and Stem E f fec t s For a Standard Probe in Steady Flow Figure 15 - Experimental and Ana l y t i ca l Causa l i ty Corre la t ions Using a Standard 1/8" B&K Microphone With a Nose Cone 65 Figure 16 - Experimental and Ana ly t i ca l Causa l i ty Cor re l a t i on For a Modif ied 1/8" B&K Microphone 1 -4 - i -- .40 •.32>" .24 .08 T . = - 0 > V 08 .16 : MSEC M = .35 x.= 4 D » 2 o ANALYTICAL RESULTS / (COUPLING COEFFICIENT C = .36) / y 3 = 0 C predicted j e t noise c o r r e l a t i o n 16 MSEC -2 4 - — ; C - 4 - L F 1 9 u r e 1 7 - Experimental and Ana ly t i ca l Causa l i ty Corre la t ions M = .35 Figure 18 - Experimental and Ana ly t i ca l Causa l i ty Corre lat ions M = .51 Figure 19 - Experimental and Ana ly t i ca l Causa l i ty Cor re la t ions £ M = .68 0 0 OS Figure 20 - Experimental and Ana ly t i ca l Causa l i ty Corre la t ions M = .83 72 buf fe t ing forces on the stem cause drag f l uc tua t i on s which rad ia te as shown f l uc tua t ing side forces PP ( 0 )'(x) add i t i ona l s ide force rad ia t ion? u sharp corners or area changes w i l l a l so act as sources ^monopole rad ia t i on due to separat ion from probe end HYPOTHETICAL CORRELATION FUNCTION Figure 23 - Poss ible Sources of Probe Noise on the Ku l i te Probes Used 

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