Coupling of twin rectangular supersonic jets

Transcription

1 J. Fluid Mec. (1998), vol. 54, pp Printed in te United Kingdom c 1998 Cambridge University Press 12 Coupling of twin rectangular supersonic jets By GANESH RAMAN 1 AND RAY TAGHAVI 2 1 NYMA, Inc., Experimental Fluid Dynamics Section, NASA Lewis Researc Center Group, Brook Park, OH 44142, USA 2 Department of Aerospace Engineering, University of Kansas, Lawrence, KS 6645, USA (Received 21 Marc 199 and in revised form 18 August 199) Twin jet plumes on aircraft can couple, producing dynamic pressures significant enoug to cause structural fatigue. For closely spaced jets wit a moderate aspect ratio (e.g. 5), previous work as establised tat two coupling modes (antisymmetric and symmetric) are kinematically permissible. However, te dynamics of twin-jet coupling ave remained unexplored. In tis paper a more fundamental assessment of te steady and unsteady aspects of twin-jet coupling is attempted. Wile we document and discuss te nole spacings and Mac numbers over wic pase-locked coupling occurs, our concentration is muc more on answering te following questions: Wat mecanism causes te jets to couple in one mode or te oter? Wy do te jets switc from one mode to anoter? Are te two modes mutually exclusive or do tey overlap at te transition point? Our results reveal, among many tings, te following. (i) For very closely spaced twin jets in te side-by-side configuration pased feedback based on source to nole exit distance of adjacent jets does not fully explain te coupling modes. However, te null pase regions surrounding te jets were te pase of an acoustic wavefront (arriving from downstream) does not vary appears to correlate well wit te existence of te symmetric mode. Wen te null regions of adjacent jets do not overlap antisymmetric coupling occurs and wen tey do overlap te jets couple symmetrically. We provide a simple correlation using a parameter (α) tat can be used as a simple test to determine te mode of coupling. (ii) Te switc from te antisymmetric to te symmetric mode of coupling appears to occur because of an abrupt sift in te effective screec source from te tird to te fourt sock, wic in turn causes te null pase region surrounding te jets to grow abruptly and overlap. (iii) Te two modes are mutually exclusive. Our results provide considerable insigt into te twin-jet coupling problem and offer ope for designing twin-jet configurations tat minimie damage to aircraft components. 1. Introduction 1.1. Background and motivation Twin jet plumes on aircraft can couple, producing iger dynamic pressures in te inter-nole region, wic in turn can cause sonic fatigue of external nole flaps. Hay & Rose (19) and Berndt (1984) ave evidence tat ig dynamic pressures can cause nole or tail plane damage. Suc damage is believed to be caused by te components of sock noise radiating upstream. Sock noise is made up of broadband (see Harper-Bourne & Fiser 19) and discrete tone (see Powell 195) components tat are produced by weak and strong interactions of te coerent structures wit

2 124 G. Raman and R. Tagavi te socks, respectively (Tam 1991). Te discrete tone (screec) is produced by a feedback loop tat involves a growing ydrodynamic disturbance tat interacts wit te socks to produce a tone. Te tone ten propagates upstream to te jet exit and couples wit te ydrodynamic disturbances. Altoug it was not establised tat screec was present in te fligt tests of Berndt (1984), it was noted tat te pattern of ig dynamic pressures measured in te laboratory experiments matced te pattern of ardware damage tat occurred during te fligt test program. Tus, tere is significant value in performing laboratory studies on twin supersonic jets tat screec at a discrete frequency. Te present fundamental researc program on twin-jet coupling was undertaken to resolve numerous issues underlined by Tam & Seiner (198), and Morris (199). Tam & Seiner (198) pointed to te need for documenting details of te antisymmetric mode of coupling and conditions under wic tis occurred. Morris (199) empasied te need for detailed experimental data on te twin-jet resonance problem. Considerable work as been done on twin jet models to alleviate problems wit te US Air Force B1-B and F-E, at te NASA Langley Researc Center (Seiner, Manning & Ponton 1988; Seiner et al. 1992; Norum & Searin 1986); by te US Air Force (Saw 199; Walker 199); and by McDonnell Douglas Aerospace (Wleien 198; Zil & Wleien 199). However, wit te exception of te work by Zil & Wleien (199), very little as been done on twin rectangular jets. In addition, te above papers did not address details of te near acoustic field and te mecanism of coupling. Rectangular jets are currently of interest because of teir use in military aircraft, and especially in situations requiring vectored trust, stealt, or tail-less fligt. Te present results are also intended to provide input to te screec simulation efforts of Cain et al. (1995), Cain & Bower (1996), and Tam & Sen (1998). It is oped tat te insigt provided ere will stimulate te development of twin-jet screec prediction metodology Objectives Our experiments are directed towards elping answer some of te following specific questions about te interaction of twin jets: Wat mecanism causes te jets to couple in one mode or te oter or not at all? (i.e. does te coupling occur troug te acoustic field surrounding te jet or te ydrodynamic fields of te two jets?) Wat causes te jets to switc from one mode to anoter? How does te mode transition occur? (i.e. are te two dominant modes mutually exclusive, or do tey overlap at te transition point?). In addition to te above issues te paper documents te effect of varying te Mac number and nole spacing on te coupling and provides a detailed documentation of te near acoustic field. We also take into consideration tat te problem is one of dynamic pressure loads in te inter-nole region. Most previous studies conducted time-averaged sound pressure level measurements. In te present work we used an ensemble-averaged time sequence over an entire screec cycle to assess te periodic loading. Te rectangular noles in te present study were originally used in a stacked configuration for mixing enancement and noise reduction studies (Rice 1995; Raman & Tagavi 1996). In te present work te noles were used in te twin-jet exaust configuration (see figure 1) to study details of te coupling effect. Te paper begins wit a description of te twin-jet apparatus and te measurement and data analysis tecniques ( 2). Conditions for twin-jet coupling are discussed in.1 followed by a caracteriation of te dominant modes of coupling (.2). A

3 Coupling of twin rectangular supersonic jets 125 (X, Z)-plane Z (Y, Z ) plane Fixed nole Air from valve 1 Valve 2 X s Jet 1 Jet 2 y Moveable nole Micropone Nole exit dimensions (mm) Figure 1. Sketc of twin supersonic rectangular nole set-up. detailed depiction of te near acoustic field of coupled jets is provided in.. An explanation for wy te twin jets select one coupling mode over te oter and a parameter tat can be used to determine te mode of coupling are given in.4. Finally, observations on mode transition are included in Experimental details Experiments were conducted in te continuous-flow supersonic jet facility at te NASA Lewis Researc Center. Te facility consisted of a plenum tank tat included inflow conditioning and acoustic treatment. Two convergent noles were placed side by side wit teir narrow dimensions parallel and teir long dimensions in te same plane (see figure 1). A positioning apparatus kept one of te noles fixed and te second nole was moved to acieve various inter-nole spacings. Micropones mounted on te noles monitored te acoustic pase relationsip between te two jets. A detailed description of te facility, spark-sclieren system and micropone accuracy is given in Raman & Tagavi (1996), and Raman (199a) and will not be reiterated ere. A pase-locked time sequence over one screec cycle elps assess periodic canges in acoustic loading. Pase-averaged measurements (see Panda 1996) of near-field pressures were made using a reference micropone at te nole exit and a measurement micropone tat traversed te entire (Y, Z)-plane (or (x, )- in some cases, see te sketc in figure 1). Te signal from te reference micropone was band-pass filtered about te screec frequency to eliminate pase jitter. Data were ensemble-averaged over 1 oscillation cycles. Te data acquisition rate (2 kh) was cosen so tat pase-averaged distributions could be computed for time steps per cycle (depending on te screec frequency). Pase averaged measurements on te (Y,Z)-plane included 5 data points, and te Y and Z values were bot.65 cm adequate to resolve te acoustic wavelengt (.9 and.5 cm for coupling mode I and II, respectively). For measurements on te (X,Z)- and (X,Y )-planes, we used 22 and 91 data points, respectively, and X, Y, and Z values of.65 cm, wic was also adequate to resolve te wavelengt of te acoustic wave.

4 126 G. Raman and R. Tagavi Weak complex interaction Antisymmetric coupling, mode I Symmetric coupling, mode II Nole spacing, s/ Mac number, M j Figure 2. Coupling types for various twin-jet spacings and Mac numbers.. Results and discussion.1. Conditions for twin-jet coupling Te effect of varying nole spacing on te coupling of te twin rectangular jets was investigated. Figure 2 is a diagram sowing te effect of varying te nole spacing (centre to centre) and te jet s fully expanded Mac number on te coupling. Coupling is defined as te pase locking of te screec instability of two adjacent jets. We observe only two out of te four possible modes determined by Zil & Wleien (199), Morris (199), and Tam & Ties (199). Tey determined tat wen te jets flap (i.e. eac jet oscillates antisymmetrically) in te normal direction (X,Zplane), tere are two preferred modes of coupling: one mode in wic te jets are antisymmetric or out of pase (18 ) wit respect to eac oter and anoter were tey are symmetric or in pase wit respect to eac oter. In addition to te above modes two more modes are possible if te jets flap in te lateral direction (X,Y - plane). However, suc lateral oscillations are observed only in low-aspect-ratio jets. Our jets ave an aspect ratio of 5 and do not exibit dominant lateral (X,Y -plane) oscillations. Tus, te only possible oscillations for te two jets are in te normal (X,Z) plane. In te present paper we refer to te two dominant coupling modes as mode I (antisymmetric) and mode II (symmetric). From figure 2 it can be seen tat a weak complex interaction (multiple tones present and pase-locked jet coupling absent) existed even wen te jets were spaced s/ = apart. Note tat s represents te inter-nole spacing (centre to centre) and te smaller nole dimension. At bot s/ = 1 and, weak complex interaction was observed. At s/ =.9 and 8.9, weak complex interaction was observed between M j =1. and 1.5, but pase-locked coupling (mode I) coupling existed (antisymmetric) between M j =1.5 and At s/ =6. tere was mode I pase-locked coupling between M j =1. and 1.62.

5 Coupling of twin rectangular supersonic jets 12 Finally, at s/ =5.5 tere was weak complex interaction between M j =1. and 1., mode I pase-locked coupling between M j =1. and 1.5, and mode II pase-locked coupling between M j =1.5 and We will consider tis last case in detail. Tus, at te closest spacing studied (s/ = 5.5) two strong modes of coupling existed: (i) antisymmetric (mode I), and (ii) symmetric (mode II). At s/ =5.5 te jets stay coupled in te antisymmetric (mode I) from M j =1.to 1.5 even toug te frequency canged from 14 to 488 and produced a cange in te acoustic wavelengt from λ/ =4.8 to If te two jets were operated at fully expanded Mac numbers suc tat te screec frequency produced by one of te jets is witin about % of tat of te oter ten pase-locked coupling occurred at small inter-nole spacings. In contrast a weak complex interaction occurred if one jet ad a screec frequency tat was 1% iger tan tat of te oter (weak complex interaction was also acieved by operating te jets at different Mac numbers). Figure sows examples of pase-locked coupling and weak complex interaction as we define tem in tis paper. Figures and are spectra from antisymmetric and symmetric pase-locked coupling cases (te micropones for jets 1 and 2 were located at y/ = 2.5 and +2.5, respectively (x/ =,/ = 1 for bot cases)). To obtain te weak complex interaction cases we operated te two jets at different Mac numbers M j =1.525 and 1.54 for te data in figure and 1.59 and 1.5 for te data in figure ). In figure note tat jet 1 ad a dominant screec frequency of 24 H (2 db), wereas jet 2 ad a dominant screec frequency of 98 H (6 db). Note also tat besides tese two frequencies tere are some sidebands and oter tones tat could be produced by sum and difference frequencies. Te discussion of tese is not witin te scope of te present work (see Walker, Gordeyev & Tomas 1995 tat deals wit a screecing jet wit multiple tones). Furter evidence of weak complex interaction is presented in figure. Te reasoning is te same as tat offered wit figure. Figure 4 sows spectra and coerence between micropones on adjacent noles for various inter-nole spacings. Spectra sown in figure 4(a d) are from a micropone placed on nole 1 (see figure 1). Spectra from te micropone on nole 2 are virtually identical and tus omitted. Te coerence between te two micropone signals is sown in figure 4(e ). At very large nole spacings (s/ = ) te measurements (figure 4e) indicate tat te signals from jets 1 and 2 ave low coerence. In addition, at suc large nole spacings te two jets produce screec tones at sligtly different frequencies, and tis is seen as two closely spaced peaks in te coerence. As te internole spacing is decreased only a single peak is visible in te coerence measurement and te value of te coerence function approaces 1 (figure 4f ). Anoter obvious cange tat is observed as te inter-nole spacing is decreased is te relatively ig coerence at frequencies lower tan te screec frequency. It is clear tat tere are coerent pressure fluctuations in a band of frequencies tat are in te range of te ydrodynamic instability modes growing in te jet..2. Dominant modes of coupling Te two modes will now be described using te flow visualiation potograps of figure 5 and te data of figure 6. Sclieren flow visualiation of te two modes of coupling is sown in figure 5(a f). Te tree views sown include te edge view (figure 5a, d),a rotation from te edge view (figure 5b, e) anda9 rotation from te edge view tat provides te plan view (figure 5c, f). For bot modes of coupling te jets flap in te plane (X,Z) seen in figure 5(a, d). For mode I coupling te two jets flapped 18 out of pase wit respect to eac oter. Since one jet ides te

6 128 G. Raman and R. Tagavi Jet 2 Jet Jet 2 Jet Jet 2 Jet Jet 2 Jet Frequency (H) 1 2 Frequency (H) Figure. Spectra depicting pase-locked coupling and weak complex interaction of twin jets. s/ =5.5, dased curves are vertically offset by 4 db. Pase-locked coupling mode I, M j =1.48, pase-locked coupling mode II, M j =1.55, weak complex interaction obtained by operating jets at M j of and 1.54, weak complex interaction obtained by operating jets at M j of 1.59 and 1.5. oter in te edge view (figure 5a), te picture provides an integrated image of te two out of pase sinuous oscillations. In te case of mode II, te jets were coupled in pase and te edge view sows a single unified oscillation (figure 5d). In te view sinuous oscillations are seen between te fourt and fift sock cells. Tese oscillations are out of pase in figure 5 (mode I) and in pase in figure 5(e) (mode II). Te plan view (figure 5(c, f)) does not reveal details of te oscillations but is included to document te spanwise sock-cell structure during coupling. Figure 6 compares te frequency and amplitude of single and coupled jets over te entire Mac number range. Te figure also depicts te relative pase variation between te two coupled jets. Figure 6 sows tat wen two jets are operated individually te screec frequency versus Mac number curve could be sligtly different if tere are manufacturing imperfections. Wen bot jets were operated simultaneously te twin jets picked a screec frequency tat was different from te frequency of eiter jet operated individually. However, te frequency of te coupled jets was closer to te frequency of jet 1 tan tat of jet 2 for mode I coupling (peraps because jet 1 ad a iger screec amplitude tan jet 2, see figure 6b). In oter words te coupling produces a new feedback loop at a new frequency tat overrides te original feedback loops of te two jets. Note also tat a small sift in frequency occurred (figure 6a) wen te coupled twin jets switced to mode II (at a fully expanded Mac number of 1.5). Te screec amplitude data sown in figure 6 were obtained using micropone 2 located midway between te two noles (x/ =,y/ =,/ = 1) for te

7 Coupling of twin rectangular supersonic jets (e) 15 Coerence ( f ) 15 Coerence (g) 15 Coerence () 15 Coerence Frequency (H) 1 2 Frequency (H) Figure 4. Spectra and coerence between micropone signals from adjacent noles for various inter-nole spacings. M j =1.55. (a, e) s/ =, (b, f) 9,(c, g) 8,(d, ) 5.5. twin coupled jets and for te case were only one jet was operated. It is clear tat te sound pressure levels for mode I coupling were about db lower tan te single jet cases. Note tat tese levels are lower tan wat could be obtained by a mere difference of te sound pressure levels of te two individual jets. Tus screec cancellation produced by mode I coupling in te inter-nole region is very strong. Altoug a switc from mode I to II increased te sound pressure levels by 2 db, mode II did not exibit significant screec amplification (i.e. te levels were not muc iger tan te sum of te sound pressure levels of te individual jets).

8 1 G. Raman and R. Tagavi (e) ( f ) Figure 5. Sclieren flow visualiation of te two modes of coupling. (a c) mode I, (d f) mode II. (a, d) edge view (smaller dimension) of te jets, (b, e) view after rotating noles by from edge view, (c, f) plan view (larger dimension) of te jets. Te pase difference sown in figure 6 was between micropones 1 and, and tis measurement indicated weter te jets were coupled antisymmetrically or symmetrically. A pase difference of 18 between symmetrically located micropones on noles 1 and indicated tat tey were coupled out of pase up to an M j of 1.5, beyond wic a mode switc occurred and te jet coupling became symmetric. Details of te difference between te two modes of coupling will be described in later subsections. A brief discussion of te differences between circular and rectangular screecing

9 Coupling of twin rectangular supersonic jets Micropones 1 2 Nole 1 Nole 2 y Frequency (H) 9 Jet 1, Mic. 1 Jet 2, Mic. Twin jets coupled, Mic M j Jet 1, Mic. 2 Jet 2, Mic. 2 Twin jets coupled, Mic M j Pase difference between micropones 1 and (deg.) M j Figure 6. Caracteristics of single and twin coupled jets versus Mac number. s/ = 5.5. Screec frequency versus Mac number, screec tone amplitude versus Mac number, pase difference between jets 1 and 2 versus Mac number. jets is in order before concluding tis subsection. A single circular jet exibits several modes of screec (Powell 195) often referred to as stages A E. In contrast, te single rectangular jet (aspect ratio 5) as one dominant mode. Wen twin circular jets are operated simultaneously, te jet modes can couple in more tan one way, depending on nole spacing and te Mac number. However, te sound pressure level in te inter-nole region rises dramatically wen te B (elical) modes of te two jets couple (Norum & Searin 1986). In comparison, te present twin-rectangular-jet experiments

10 12 G. Raman and R. Tagavi exibit coupling in two modes (I and II as described earlier). Mode I reduces te sound pressure in te inter-nole region and mode II augments it... Te near acoustic field of coupled jets Focus now sifts to te near acoustic field produced by te two types of coupling. Detailed measurements were made on te two planes (Y,Z and X,Z) described in figure 1. Te (Y,Z)-plane was located at x/ =, and te (X,Z)-plane was located at y/ =. Figure (a d) sows te magnitude and relative pase on te (Y,Z)-plane. Te magnitude (expressed as SPL in db) was obtained by moving a micropone over te entire (Y,Z)-plane. Te relative pase was obtained from te cross-spectral pase between te traversing micropone and a reference micropone. For mode I coupling (figure a), te two jets displayed an amplitude minimum between te two noles. Te relative pase plot (figure b) sowed a 18 pase difference between symmetric locations on eiter side of y/ =. In contrast, for mode II coupling (figure c) te acoustic signature on te (Y,Z)-plane indicated tat te two jets ad combined into one wit te maximum sound pressure level occurring in te inter-nole region. Te pase plot (figure d) sows a ero degree pase difference between symmetric locations on eiter side of y/ =. Altoug te problem at and is one of dynamic pressure loads, most previous studies ave focused on average sound pressure levels. Pase-averaged measurements on te (Y,Z)-plane for mode I and II coupling are sown in figures 8 and 9, respectively. Te solid and dased lines represent positive and negative pases of te screec cycle, respectively. Note tat te pressure waves were propagating upstream (normal to te (Y,Z)-plane sown in figures 8 and 9) and wat one sees in figures 8 and 9 is a projection on te (Y,Z)-plane at various pases of te screec cycle. From figures 8 and 9 it is clear tat te pressure waves were antisymmetric and symmetric, respectively (as evidenced by te dual regions of alternating positive and negative pressures, and by single regions of alternating positive and negative pressures, respectively). We now sift our attention to te (X,Z)-symmetry plane. Detailed features of pressure waves during feedback can be seen from te pase-averaged data of figures 1 and for coupled jets in modes I and II. Similar data on te instantaneous pressure field of a round jet were given in Westley & Woolley (1969, 19), and studied in more detail recently by Panda (1996). For mode I coupling (figure 1) were te pressure is minimied on te (X,Z)-plane, tere are weak axially (x) propagating and vertically () propagating waves (seen as islands of alternating solid and dased lines). However, for mode II coupling, were te pressure is maximied on te (X,Z)-plane, te axially propagating waves dominate (figure ). From te contour values of figures 1 and (not sown) and te corresponding single jet cases (also not sown in te interest of conciseness) te maximum and minimum pressures on te symmetry plane (X,Z) for te various cases are sown in figure 12. Tese maxima and minima could ave occurred at different locations on te plane for te various cases. However, tis aspect is not considered ere. It is clear tat mode I coupling decreased te spread between te maximum and minimum (figure 12a) and mode II coupling increased it (figure 12b). More interestingly, note tat te single jet cases at M j values tat produce mode I coupling (figure 12a) and mode II coupling (figure 12b) were quite different. Figure 1 compares te pase-averaged near acoustic field (at one pase of te reference signal) in te (X,Y )-plane (see figure 1 for coordinates), for single and coupled twin jets. Te (X,Y )-plane was located at / =. Te data sown in

11 Coupling of twin rectangular supersonic jets y/ y/ Figure. Time-averaged near acoustic field in te (Y,Z)-plane for twin coupled jets. s/ = 5.5. (a, c) Amplitude, (b, d) relative pase, (a, b) mode I coupling, M j =1.48, (c, d) mode II coupling, M j =1.55. figure 1a, b were obtained by operating a single jet at fully expanded Mac numbers tat produced te two modes of coupling wen bot jets were operated simultaneously. Te instantaneous pressure patterns for te two single jet cases (figure 1a, b) do not sow notable differences between tem. For te coupled jet cases, mode I coupling (figure 1c) clearly displays tat te sources of adjacent jets are anti-pase in y over te entire axial extent of te jets. In contrast, for mode II coupling (figure 1d) te sources of bot jets were in-pase and te combined picture resembled tat of a single jet. Finally, we ope tat te detailed documentation of te near acoustic field provided in tis subsection will serve as bencmark data for comparison wit numerical simulations..4. Coupling mecanism Tam & Ties (199) studied te wave-modes in a rectangular jet tat were given by te eigensolutions of te linearied governing equations. Tey found tat tere were four linearly independent families of eigensolutions tat were invariant to

12 14 G. Raman and R. Tagavi (e) ( f ) (g) y/ y/ Figure 8. Pase-averaged near acoustic field in te (Y,Z)-plane for twin jets coupling in mode I. M j =1.48, s/ =5.5. Pase difference from frame to frame is. Parts (a g) represent alf a cycle. Solid and dased lines represent positive and negative pases of te screec cycle, respectively. certain transformations. Te four families tat tey identified as being kinematically permissible were te same as te four possible coupling modes identified by Morris (199) and Zil & Wleien (199) (i.e. modes tat were antisymmetric or symmetric in te normal () and lateral (y) directions). In our experiment eac rectangular screecing jet (aspect ratio = 5) exibited wat Tam & Ties (199) termed a family 2 instability (i.e. flapping in te (X,Z)- plane). Te coupled twin jets in our experiments (also aving an aspect ratio of 5) exibited eiter a family 4 (mode I of tis paper, were eac jet was antisymmetric

13 Coupling of twin rectangular supersonic jets (e) ( f ) (g) () y/ y/ Figure 9. Pase-averaged near acoustic field in te (Y,Z)-plane for twin jets coupling in mode II. M j =1.55, s/ =5.5. Pase difference from frame to frame is 25. Parts () represent alf a cycle. Solid and dased lines represent positive and negative pases of te screec cycle, respectively.

14 16 G. Raman and R. Tagavi (e) ( f ) (g) x/ x/ 18 Figure 1. Pase-averaged near acoustic field in te (X,Z)-plane for twin jets coupling in mode I. M j =1.48, s/ =5.5. Pase difference from frame to frame is. Parts (a g) represent alf a cycle. Solid and dased lines represent positive and negative pases of te screec cycle, respectively.

15 Coupling of twin rectangular supersonic jets 1 (e) ( f ) (g) () x/ x/ 18 Figure. Pase-averaged near acoustic field in te (X,Z)-plane for twin-jets coupling in mode II. M j =1.55, s/ =5.5. Pase difference from frame to frame is 25. Parts (a ) represent alf a cycle. Solid and dased lines represent positive and negative pases of te screec cycle, respectively.

16 18 G. Raman and R. Tagavi Sound pressure ( Pa) Max, single jet Min, single jet Max, coupled in mode I Min, coupled in mode I Sound pressure ( Pa) Max, single jet Min, single jet Max, coupled in mode II Min, coupled in mode II Pase of screec cycle (deg.) Figure 12. Maximum and minimum pase-averaged pressure loads on te (X,Z)-plane for single and twin coupled jets during one screec cycle. M j =1.48. Mode I coupling, M j =1.55, Mode II coupling. wit respect to te oter) or a family 2 (mode II of tis paper, were eac jet was symmetric wit respect to te oter) instability. Tus, te two modes tat were known to be kinematically permissible for te aspect ratio used were observed. Te issue now is wat mecanism caused te twin jets to coose one coupling mode over te oter? To answer te above question we recall tat wen two jets are in close proximity, eac becomes a sound source for te feedback loop of te oter jet. Te pase relationsip between te source of eac jet and te nole exit of te oter ten determines te mode of coupling (Wleien 198). Tis idea was confirmed in earlier work (Rice 1995; Raman & Tagavi 1996) on multiple rectangular jets in a stacked configuration. Te present work differs from te Raman & Tagavi (1996) work in two important ways. In te present work te jets are in a side-by-side configuration (see figure 1) and te inter-nole spacing is very small. For te present configuration pased feedback from adjacent jets does not explain te coupling modes or te sudden switc from mode I to mode II. Tis is clear from te fact tat te jets remained coupled in mode I from M j =1. to 1.5 even toug te screec frequency canged from 14 to 488 and produced a corresponding cange in te acoustic wavelengt from λ/ =4.8 to Furter, after te mode switc (from I to II) occurred at M j =1.5, te jets remained coupled in mode II even as te Mac number was increased furter. Te data of figures 14 and will be used to examine ow te jets coose te

17 Coupling of twin rectangular supersonic jets y y x/ x/ Figure 1. Comparison of te pase-averaged near acoustic field in te (X,Y )-plane for single and coupled twin jets. Single jet, M j =1.48, single jet, M j =1.55, twin jets coupled in mode I, M j =1.48, twin jets coupled in mode II, M j =1.55. coupling mode. Figure 14(a, b) sows data similar to tat of figure (a, c) but for a single nole tat was operated at fully expanded jet Mac numbers (M j ) tat produced te two types of coupling. Altoug only one nole (located at y/ = 2.5) was operated te time-averaged amplitude was measured over te entire twin-jet coupling region on te (Y,Z)-plane. Figure 14 sows tat at te fully expanded jet Mac number (M j ) tat produced mode I coupling te peak amplitude was closer to te outer edge of te nole lip (/ = ). In contrast, it can be seen from figure 14 tat at te M j tat produced mode II coupling, te peak amplitude (island) was located farter away from te outer edge of te nole lip (/ = ). Figure sows te relative pase corresponding to te amplitude data of figure 14(a, b) along te y/ = 2.5 line in te near nole region. Particularly important ere is te null pase region surrounding te jets (n1 and n2 in figure ) were te pase of an acoustic wavefront (arriving from downstream) does not vary over a small distance. Note tat te null region is defined as te extent in over wic te pase cange is 1 (our measurement accuracy is ± 5 ). Te existence of tis null region and its growt wit M j appears to occur (at least to some extent) because of te movement of te equivalent source of screec furter downstream tat causes te wavefronts arriving at te nole exit plane to be flatter in te near nole region.

18 14 G. Raman and R. Tagavi y/ y/ Figure 14. Time-averaged near acoustic field in te (Y,Z)-plane for single jets. M j =1.48, M j = M j = 1.48 M j = 1.55 DU π / n1 n2 (null region) Figure. Relative pase variation in te near-nole region of single jets. x/ =, y/ = 2.5. Tis null region must be accounted for in determining te coupling modes of closely spaced jets. Tabulated experimental results for te sock spacings, acoustic wavelengts, screec source locations, and te growt of te null region of a single jet wit M j are given in tables 1 and 2. Te sock spacings (average of first five sock cells) given in table 1 agree wit te predictions of Tam (1988) and Morris, Bat & Cen (1989). An explicit comparison is not sown since te objective ere was not to ceck sock spacing teories but to explain te mecanism for twin-jet coupling. In table 1 te equivalent screec source was at te end of te tird sock cell for M j < 1.5 and at te end of te fourt sock-cell for M j > 1.5. Te source sift was derived based on te relative pase measured along a single line in te transverse direction () at te nole exit plane (see Raman 199b). Sclieren flow visualiation also substantiated tis finding (see Raman & Tagavi 1996). Table 2 sows tat te null region n/ for single jets can grow from 1. at M j =1.5 to 4.81 at M j =1.5. Based on te null region a simple explanation can now be provided for te two modes of coupling.

19 Coupling of twin rectangular supersonic jets 141 Axial distance of Mac Acoustic Sock spacing, screec source number, Frequency, wavelengt L s / from nole exit, Twin-jet coupling M j f (H) λ/ (average) q s / mode I (antisymmetric) I II (symmetric) II II Table 1. Sock spacings and screec source location for various jet operating conditions. Mac number M j Nole spacing s/ Null region n/ α = s 2n Test for determining coupling mode TABLE 2. A simple test for determining te coupling mode. n n α s n n Positive α (2n < s) produces mode I Negative α (2n > s) produces mode II s Unsaded and saded area are 18 out of pase From Table 2 it can be seen (if one were to imagine two jets placed side by side) tat wen te null regions of bot jets did not overlap, mode I coupling occurred, and wen tey did overlap te jets coupled in mode II. Furter, table 2 also sows tat te sign of α((s 2n)/) determined te mode of coupling. In oter words, if te nole spacing (s/, were was te small dimension of te nole) was larger tan twice te null region, we saw mode I coupling. If te inequality is reversed (2n >s), ten mode II coupling was observed. Tus, altoug bot modes of coupling are kinematically permissible, te coice of coupling mode depends on te sie of te null region relative to te nole spacing (see sketc in table 2)..5. Mode switc mecanism and transition In.4 we documented te abrupt switc from mode I to II. A question tat naturally arises is wat causes te abrupt mode switc? Our explanation is tat at M j =1.5 tere was an abrupt sift in te equivalent source of screec from te tird to te fourt sock cell tat caused an abrupt growt of te null region. Proof of te source sift and a model for te growt of te null region for single jets was provided by Raman & Tagavi (1996) and Raman (199b) and will not be reiterated ere. However, we wis to point out tat altoug tere were numerous sources, te effective source centre (for rectangular jets) depended on only one or two sock cells (tird or fourt) depending on te jet Mac number (Raman 199b). Te abrupt growt of te null region at M j =1.5 in turn caused te null regions of bot jets to overlap (negative α) and produced an abrupt switc from mode I to II.

20 142 G. Raman and R. Tagavi Relative magnitude 1 Time Relative magnitude Time Frequency (H) Frequency (H) 1 Figure 16. Steadiness of twin jets coupled in mode I. s/ =5.5, M j =1.48. Time-averaged spectrum from micropone mounted on nole 1 (x/ =, y/ = 2.5, / = 1), time-averaged spectrum from micropone mounted in between noles 1 and 2 (x/ =,y/ =,/ = 1), (c, d) instantaneous spectra for te frequency range from 1 H, micropone locations te same as tat for cases (a, b), respectively. For jets tat were coupled it was also important to address te issue of steadiness and transition from one mode to anoter. Figure 16(a, b) represents time-averaged spectra for mode I coupling from a micropone located on nole 1 (x/ =, y/ = 2.5, / = 1) and anoter located mid-way between te two noles (x/ =,y/ =,/ = 1). Te amplitude of te dominant coupled mode was iger at y/ = 2.5 tan at y/ = as sown earlier in figure. Te instantaneous spectra sown in figure 16(c, d) address te steadiness issue. Te instantaneous spectra were obtained by taking a long time sequence and performing an FFT on smaller segments. Te resulting plot sows te variation of spectra wit time. One limitation of te instantaneous spectra was tat 124 samples were required for eac line in te plot. Te sampling of 124 points even at 2 kh required s; wit a 4% overlap between consecutive lines in te instantaneous spectra tis time reduced to.2 1 s. For a typical screec signal of H frequency te time scale was seconds wic was an order of magnitude lower tan te resolution scale of te instantaneous spectra. Tus, eac line in te instantaneous spectrum included numerous screec cycles. Neverteless tis tecnique was still of limited use in resolving issues pertaining to steadiness. Going back to figure 16(c, d) wic ooms in on te region from to 1 kh one can see tat te dominant coupling frequency was steady in time. In comparison, a frequency tat was sligtly lower tan te dominant frequency was unsteady in figure 16(c, d). Similar observations can be made from figure 1(a d) for mode II coupling. However, a difference between figures 16 and 1 is tat mode II coupling (figure 1) produced levels tat were

21 Coupling of twin rectangular supersonic jets Relative magnitude Time Relative magnitude Time Frequency (H) Frequency (H) 1 Figure 1. Steadiness of twin jets coupled in mode II. s/ =5.5, M j =1.55. Parts (a d) as described in te caption for figure 16. iger at y/ = (figure 1b) tan at y/ = 2.5 (figure 1a). Te reverse was true for figure 16. Note tat ad te coupling not been steady for modes I and II (figures 16 and 1) we would not ave been able to make te detailed pase-averaged measurements described in.. Finally, we approac te issue of mode transition. It is of interest to know if modes I and II are mutually exclusive or can bot coexist at te transition point. A furter point of interest is weter te modes switc back and fort before te jets make a final selection. Te data of figure 18 were taken wile increasing te Mac number from 1.49 (Mode I) to 1.51 (Mode II). Te time-averaged spectrum (figure 18a) from te micropone on nole 1 indicated te presence of bot modes. In contrast, te instantaneous spectra indicated tat a switc occurred from mode I to II, and tat bot modes did not coexist. (Even wen te jet was operated at te mode switc point, te two coupling modes never coexisted.) Tis tecnique was used earlier (Raman 199a) to spot mutually exclusive switcing or te co-existence of two modes in jets from bevelled noles. Note tat te mode switc is also accompanied by a frequency jump to a lower frequency (also seen previously in figure 6a). Te micropone located in between te two noles (figure 18b, d) sowed some interesting features. Te time-averaged spectrum (figure 18b) sowed a ig-amplitude mode II and a low-amplitude mode I, agreeing wit te data of figure (i.e. mode I always exibited a minimum in te inter-nole region). Te instantaneous spectrum of figure 18 indicated te transition from low pressure levels (mode I) to iger levels (mode II). It is of interest to see if te reverse appened wen te Mac number was reduced from 1.51 (mode II) to 1.49 (mode I). Figure 19(a d) sows tat tis was indeed te case. Hysteresis, if any, was not pronounced.

22 144 G. Raman and R. Tagavi Relative magnitude 1 Time Relative magnitude Time Frequency (H) Frequency (H) 1 Figure 18. Transition from mode I to II, s/ =5.5, M j increased from 1.48 to Parts (a d) as described in te caption for figure Relative magnitude 1 Time 15 Relative magnitude Time Frequency (H) Frequency (H) 1 Figure 19. Transition from mode II to I, s/ =5.5, M j decreased from 1.55 to Parts (a d) as described in te caption for figure 16.

23 Coupling of twin rectangular supersonic jets Summary and conclusions Te twin-rectangular-jet problem is important in closely spaced twin-engine aircraft. We explored details of te near acoustic field and coupling mecanisms. It was found tat if te jets ad sligtly different frequencies, te one wit te iger screec amplitude dominated and influenced te frequency of te coupled jets. Antisymmetric coupling produced minimum pressure in te inter-nole region, wereas symmetric coupling produced maximum pressure in te same region. Pase-locked motions were observed and were found to persist over te entire screec cycle. We determined te ensemble-averaged periodic pressure loadings and finally documented te transition from te antisymmetric to te symmetric mode. We focused on answering te tree questions raised in 1.2. Our results indicate te following. For very closely spaced twin jets in te side-by-side configuration pased feedback based on source to nole exit distance of adjacent jets does not fully explain te coupling modes. Te null region surrounding te jets were te acoustic wavefronts arriving from downstream are flat over a small radial distance appears to influence te mode of coupling. We provide a parameter (α) tat can be used as a simple test to determine te mode of coupling. Te switc from te antisymmetric to te symmetric mode of coupling appears to occur because of an abrupt sift in te effective screec source from te tird to te fourt sock, wic in turn causes te null pase region surrounding te jets to grow abruptly and overlap. Te two observed modes were mutually exclusive. Te data presented provide considerable insigt into te twin jet coupling problem even toug we ave not been able to answer all questions regarding tis complicated problem. A version of tis paper was presented at te rd AIAA/CEAS Aeroacoustics conference. Te autors are grateful to Professor C. K. W. Tam of Florida State University for providing insigtful comments. Dr Steven Walker of te US Air Force (Wrigt Laboratory) and Dr Alan Cain of McDonnell Douglas Aerospace encouraged and motivated tis work. Te autors tank Dr J. Panda for providing a computer routine for pase-averaged data acquisition and Mr Ken Weiland and Dr Carolyn Mercer for teir sclieren expertise. REFERENCES Berndt, D. E Dynamic pressure fluctuations in te internole region of a twin-jet nacelle. SAE Paper SAE Aerospace Cong. & Expo., Long Beac, CA. Cain, A. B.& Bower, W. W Modeling supersonic jet screec: differential entrainment and amplitude effects. AIAA Paper Cain, A. B., Bower, W. W., Walker, S. H. & Lockwood, M. K Modeling supersonic jet screec. Part 1: vortical instability wave modeling. AIAA Paper Harper-Bourne, M. & Fiser, M. J. 19 Te noise from sock waves in supersonic jets. Noise mecanisms. AGARD CP, pp Hay, J. A. & Rose,E.G.19 In-fligt sock cell noise. J. Sound Vib., Morris, P. J. 199 Instability waves in twin supersonic jets. J. Fluid Mec. 22, 29. Morris, P. J., Bat, T. R. S. & Cen, G A linear sock cell model for jets of arbitrary exit geometry. J. Sound Vib. 12, Norum, T. D. & Searin, J. G Dynamic loads on twin jet exaust noles due to sock noise. J. Aircraft 2, Panda, J An experimental investigation of screec noise generation. AIAA Paper Powell, A. 195 On te mecanism of coked jet noise. Proc. Pys. Soc. Lond. 66, Raman, G. 199a Screec tones from rectangular jets wit spanwise oblique sock cell structures. J. Fluid Mec.,

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