Aerodynamic Noise 9781487582869

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aerodynamic noise Proceedings of AFOSR-UTIAS Symposium held at Toronto, 20-21 May 1968

aerodynamic noise Proceedings of AFOSR-UTIAS Symposium held at Toronto. 20-21 May 1968

Sponsored by Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force and Institute for Aerospace Studies. University of Toronto

University of Toronto Press

Copyright, Canada, 1969 by University of Toronto Press Printed in Canada Reprinted in 2018 ISBN 978-1-4875-8158-9 (paper)

SBN 8020 1651 0

ORGANIZING COMMITTEE H. S. T. A. J. L. D. P. A. s. J.

w.

Ribner, Chairman Chu Howsmon Reid Sullivan Townsend

PAPERS COMMITTEE Maj. D. L. Calvert, Chairman D. T. Blackstock w. T. Chu G. T. Csanady J. E. Ffowcs Williams M. v. Lowson L. Maestrello D. J. Maglieri c. L. Morfey H. s. Ribner A. R. Seebass T. G. Sofrin SESSION CHAIRMEN

D. L. Calvert

G. T. Csanady K. M. Eldred I. R. Schwartz

U.S. Air Force Office of Scientific Research University of Waterloo, Canada Wyle Laboratories U.S. National Aeronautics and Space Administration

SYMPOSIUM CHAIRMAN H. S. Ribner

University of Toronto, Institute for Aerospace Studies

FOREWORD Noise has evolved as one of the unpleasant by-products of the growth of aviation. In a sociological sense it is regarded as a technological pollutant, while from an engineering point of view it is regarded often as a powerful mill ready to grind to grist the weak or the unwary. As either a pollutant or a pulverizer it may well become the limiting factor in the design and operation of virtually every type of future aircraft, with the possible exception of those used for primary training and private flying. It has been postulated by many that noise is an unavoidable concomitant of the generation of thrust and/or the movement of very large bodies, at substantial speeds, through the atmosphere. It is recognized that as aircraft and power plants have become bigger and more powerful so has tpe noise they generate become more intense and disturbing. In fact,"in some cases, this noise already has exceeded tolerable limits of either people or structure and threatens to reach such proportions in the innnediate future that we cannot hope to control it economically by the simple expedient of operational restrictions alone. However, it is not clear that excessive noise is an inherent ingredient of aeronautical growth and aerodynamic noise must be considered, therefore, to be one of the more important yet difficult and exciting unresolved problems confronting the scientist and engineer. The problem has been with us for many years and its increasingly debilitating effects on aerospace progress, both civilian and military, have been masterrully delineated in such papers as the 16th Wright Brothers lecture given by William Littlewood in 1952 and the recent classic survey "Problems of Aeroplane Noise in the 197O's" by E. J. Richards. Perhaps because the problems confronting the aerospace COilllllUnity are not strictly those of noise, per se, but involve subjective elements of individual and group responses and reactions, as much as because of the complexity of the subject, there has been a depressing degree of pessimism among many scientists and engineers. Activity, and therefore progress, has been agonizingly tenuous and there has been a tendency to sweep this lack of involvement under the twin rugs of futility and activity on other, seemingly more tractable and therefore more attractive, problems. However, the importance of the problem warrants a full re-examination of the basic principles of sound generation, propagation and control. One can never control that which is not understood. Progress in aerodynamic noise abatement can come only from progress in unravelling and understanding the mechanisms of noise generation and propagation (including attenuation). Thus in the hope that ways and means to control this inhibiting and disturbing factor of aerospace growth will be found, the Air Force Office of Scientific Research (AFOSR) and the University of Toronto, Institute for

Aerospace Studies (UTIAS) jointly sponsored a Symposium on Aerodynamic Noise. The Symposium was held in Toronto, Canada,20-21 May 1968 and brought together scientific and engineering specialists in all facets of noise generation, propagation, and attenuation. T~e attendees were welcomed by Major Donatd L. Calvert of AFOSR, who discussed the broad interest of the U.S. Air Force in fundamental research and in Aerodynamic Noise research in par-ticular. Dr. G. N. Patterson, Director of the urIAS, also presented a word of welcome which included a synoptic history of Aerodynamic Noise research at the University of Toronto. The technical program which followed is the subject of these Proceedings. The scope of the Symposium was necessarily limited to correlating the most recent advances and experiences in unveiling the fundamentals of the subject. It is our hope that not only will these Proceedings have a more general and lasting value than had the pros and cons of particular designs been discussed, but that the reader will gain a fuller appreciation of the new horizons in research and engineering revealed by recent activity in Aerodynamic Noise. Perhaps it is not too much to hope also that in studying the papers of this Symposium the reader will himself find insight and inspiration in identifying factors which would require further research for understanding and applicati~n if the full potential of modern aeronautical engineering capability is ever to be reached. Milton Rogers, Chief, Mechanics Branch, Air Force Office of Scientific Research

PREFACE The twenty-two papers published in this Proceedings were selected from twenty-nine papers accepted for presentation at the Symposium. This selection was made by the Papers Committee on the basis of 1000-word abstracts which were studied by Committee members and other referees. At least two referees considered each abstract. The final papers, which were received later, were accepted without further technical editing. The local arrangements were carried out with great competence and conscientiousness by the Organizing Committee with the aid of a number of urIAS personnel. We should like to record here our thanks to everyone involved: in particular to the members of the Organizing Committee, the Papers Committee, and the Session Chairmen, whose names are listed on page v. We are likewise .grateful to Drs. E. A.G. Shaw and T. F. W. Embleton, who were responsible for the program of an overlapping meeting of the Acoustical Society of America, May 20-24, 1968, in Ottawa: they co-operated fully in arranging compatibility of the programs and minimum conflict of their sessions with ours. A final word of appreciation is directed to Dr. G. N. Patterson, Director of urIAS, for his great encouragement and for the readiness with which he put the entire facilities of the Institute at our disposal to insure the success of the Symposium.

H. S. Ribner, Symposium Chairman

CONTENTS

Foreword

vii

Preface

ix

Jets and Noise (1968 Turnbull Lecture(Canada))

3

H.

s.

Ribner

The Development of Engineering Practices in Jet, Compressor, and Boundary Layer Noise(Invited Paper) J.B. Large, J. F. Wilby, E. Grande and A. O. Andersson Scales Pertinent to Noise Generation from a Jet Ian S. F. Jones Estimation of the Intensity of Noise Radiated from a Subsonic Circular Jet G. Krishnappa

89

General Method for Calculating the Sound Pressure Field Emitted by Stationary or Moving Jets M. Kobrynski

111

Jet Noise at Very Low and Very High Speed(Invited Paper) J.E. Ffowcs Williams

131

An Investigation of the Near Noise Fields of a Choked Axi-Synonetric Air Jet R. Westley and J. H. Woolley Noise from Underexpanded Axisynonetric Jet Flows Using Radial Jet Flow Impingement Darshan S. Dosanjh and James C. Yu The Response of a Simple Panel to the Pseudo-Sound Field of a Jet L. Maestrello, M. R. Gedge and A. R. F. Reddaway Atmospheric Absorption of Noise G. M. Coles

209

Attenuation of Sound in Soft-Walled Circular Ducts Edward J. Rice

229

Flow Perturbations Generated by a Shock Wave Interacting with an Entropy Wave Elizabeth Cuadra

251

Trends in Boundary Layer Noise Research(Invited Paper) Patrick Leehey

273

A Review of the Sound-Generating Mechanisms in Aircraft-Engine Fans and Compressors(Invited Paper) C. L. Morfey

299

Discrete Noise Generation and Propagation by a Fan Engine S. Slutsky

331

A Theoretical Study of Helicopter Rotor Noise M. V. Lowson and J.B. Ollerhead

351

A Study of Propeller Noise Research Frederick B. Metzger, Bernard Magliozzi, George B. Towle, and Larry Gray

371

Review of Sonic Boom Theory (Invited Paper) Wallace D. Hayes

387

Recent Results of Sonic Boom Research (Invited Paper) Harvey H. Hubbard

397

Sonic Bang Simulation by Explosives S. J. Hawkins and J. A. Hicks

409

Second-Order Wave Structure: Planar Flows David A. Caughey and Wallace D. Hayes

423

Lifting Aerodynamic Configurations with no Sonic Boom E. L. Resler, Jr.

435

AERODYNAMIC NOISE

JETS AND NOISE* H.S. Ribner Institute for Aerospace Studies University of Toronto, Toronto, Canada SUMMARY Air flow produces a variety of sounds ranging from Aeolian tones to the noise of the Saturn jet. Aircraft noise is discussed with primary emphasis on the jet and secondary emphasis on the fan and compressor . The topics and scope are indicated in the table of contents that follows . TABLE OF CONTENTS 1.

INTRODUCTION W. Rupert Turnbull Noise from Saturn V Noise from the Polar Jet Stream Noise from Commonplace Sources

2.

AIRCRAFT NOISE Some Comparisons Propeller, Fan, and Compressor Noise

3.

COMMUNITY ASPECTS OF JET NOISE AND FAN NOISE Pattern of Jet Noise Effects of Flight Operations Jet Noise Versus Fan Noise PNdB Measure of Noisiness Atmospheric Attenuation Ground Effect Attenuation Atmospheric Refraction

4.

PHYSICAL MECHANISMS OF JET NOISE Introduction Simplified Model of Jet Noise Some Equations Modified Quadrupole Model Self Noise and Shear Noise Convection and Refraction Refraction Experiments at UTIAS

* The W. Rupert Turnbull Lecture 1968, presented at the Annual General Meeting, Canadian Aeronautics and Space Institute, May 6, 1968. A much abbreviated version was given at the Symposium on Aerodynamic Noise under the title, "Physical Mechanisms of Jet Noise in the u8 Law Range" . To be published in the CASI Journal, October, 1968. Reprinted here by special permission .

AFOSR-llrIAS SYMRJSIUM ON AERODYNAMIC NOISE, TORONTO, 20- 2 1 Ma;y , 1968

4 /RIBNER (1968 Turnbull Lecture, Canada)

5.

SUPPRESSION OF JET NOISE Fan Jets Versus Turbojets Corrugated Nozzles and Multiple Jets Suppressor Noise Spectrum Suppressor Noise Directivity Prospects for Improved Suppression

1.

INTRODUCTION

W. Rupert Turnbull. We honour W. Rupert Turnbull as a Canadian pioneer in aeronautics, especially known for his invention of the variable pitch propeller. But he was a man of many parts . It is not so well known that he was trained as an electrical engineer and did graduate work in physics. It was only afterward that he pursued his strong interest in aeronautics. It is as a physicist turned aerodynamicist turned acoustician that I feel a certain kinship to Turnbull. The urgencies of the times shape our interests. It is easy to imagine Turnbull in later times turning his interest to the noise generated by his propellers. And in still later times, with propellers largely supplanted by jets, he might have been involved with the challenge of jet noise. I feel, therefore, that it is quite appropriate that jet noise and related topics should be the subject of a lecture that commemorates his name. Noise from Saturn V. The mightiest sustained man-made noise is produced by the jet of the Saturn V, which radiates some 0.2 billion watts of acoustic power from the launch site. This is roughly the noise generated by a million diesel freight trains travelling 30 to 50 miles per hour. At ten miles- away the Saturn roar reaches 110 dB (Fig. 1), which is comparable with the noise of 4000 freight trains at a distance of 1000 feet.2,3 The Saturn V, 36 stories tall with 7.5 million pounds of thrust, is of course an extreme example. But it does illustrate the awesome power that can be unleashed in jet noise. The efficiency of the noise generation is actually very low - only some 1/2% of the jet kinetic energy is converted into noise - but the jet energy is so fantastically great that the fractional amount converted into noise is still enormous. Noise from the Polar Jet Stream. At least one observer thinks that jet noise may possibly play a minor role in the weather - in the dynamical heating of the upper atmosphere. We refer here not to the mundane noise of aircraft, but to the noise from the atmospheric jet ~tream in the polar regions at night: this may be several hundred kilometers wide, and the speed can exceed 100 meters/sec in winter. The subaudible sound field gene~ated by this enormous jet will have wave lengths measured in hundreds of kilometers and wave periods measured in hundreds of seconds. In a recent study by Maeda4 rough quantitative estimates of this acoustic heating were made employing a form of the theory of jet noise5,6 It was concluded that appreciable acouetic heating is probable with best estimates of .002 to 2°c per at the 75 to 100 km levels. This is insufficient to compensate for the cooling rate of these levels (about

JETS AND NOISE/5 10°c per day) in winter; however, on relaxing certain of the assumptions the figure can be increased to 10°c per day. If the stream velocity exceeds 200 m/sec . for several days the layer around the mesopause can be significantly warmed by the jet noise energy . Maeda based his result~ on the assumption of decaying isotropic turbulence, with estimates for the relevant turbulent velocities and scales . I have tried an alternative noise power estimation based on the empirical formula for noise from a round jet. The result comes out even smaller than Maeda's lowest estimate of 0.002°c per day . Thus it is my belief that Maeda overstates his case, al though the idea of 'jet noise' affecting the weather is intriguing

Noise from Commonplace Sources. More prosaic examples of jet noise abound in our daily experience . I There is the hiss of escaping compressed air or steam. There are the various aerosol products, including the spray deodorants: they discharge nice conical jets on the television screen - accompanied by jet noise . There is even the hiss of air between tongue and teeth in enunciating the sibilant consonants, or in whispering. Again, we might cite the noise that arises on opening a valve in a high pressure air line or a water faucet. Th~s is a different kind of jet noise associated with separated flows, with mechanical vibration playing a role . Valve noise appears to be prominant among the offenders in noisy plumbing. Another very common flow noise is produced by air ventilating and heating systems. Such noise arises from the turbulent flow but it is distinct from jet noise: the main mechanisms are vibration of the duct walls and fluctuating forces on the exit grill work. The dominant cabin noise in modern jet transports - called boundary layer noise - is of similar origin . The fluctuating pressure field in the turbulent boundary layer excites vibration in the aircraft skin, and this in turn radiates noise into the interior. Aeolian tones are produced by a rod or a wire in a wind. The sound has a more or less definite pitch and involves a periodic force on the rod associated with regular vortex shedding. If the rod is irregular and tapered, like a tree limb, a whole spectrum of Aeolian tones is emitted. Thus we have the whistling or sighing of the wind in the trees. 2.

AIRCRAFT NOISE

Some Comparisons. In order to place jet noise in the proper perspective let us catalog the variogs noises associated with aircraft flight . The major headings are : Propellers, Rotors, Fans Jet Noise Boundary Layer Noise Attached boundary layer Separated flow Oscillating shocks Sonic Boom

6 /RIBNER (1968 Turnbull Lecture, Canada) All of these radiate noise from the aircraft. All but the last may serve also as powerful exciters of vibration in the aircraft skin. This - together with ventilating flow - is responsible for the c.a bin noise; it is also of major concern for structural fatigue. Typical maximum fluctuating surface pressures are shown in Fig. 2. Most are in the range where there is possibility of structural fatigue(> 150 dB, roughly), and all exceed the threshold of pain for hearing Tabout 130 dB). The sonic boom process is pictured in Fig. 3 . The conical shock wave - analogous to the v-shaped bow wave of a boat - sweeps over the underlying communities. At ground level the effect mimics the sound field from an explosion. The swept path - or boom carpet - on the ground is limited by refraction to perhaps 60 to 75 miles in width; it is not indefinitely wide as the figure would suggest (the 'cone' is distorted, especially at the bottom). There are numerous other aspects of this fascinating problem that could be discussed9,lO but they are beyond the scope of this paper. The relative noise levels associated with aircraft propulsion are shown in Fig. 411 . The application is to a hovering aircraft. The oversimplified graph states that roughly

~- (!) n

Noise level thrust ' T

A

(1)

at a fixed position; the exponent n varies progressively from. about 1/5 to 3. At the upper extremity turbojets work on the basic principle of moving a small mass of air at high speed; they have high disk loading T/A and produce high noise levels. At the other end of the scale rotors move large masses of air at low speeds, and their low disk loadings result in relatively low noise levels. The analytical basis for eqn . (1) can be sketched only crudely. Aerodynamic noise arises from pulsations of mass (simple sources), of momentum or force ~dipoles), and of momentum flux or Reynolds stress (quadrupoles) 1 • Suppose that a particular noise disturbance consisted of a distribution of one kind of source only with either uniform or random orientations. Suppose also that the characteristic source strengths and frequencies varied in a certain reasonable wayl 2 with the dimensions and the flow vilocity coming through the rotor or propeller or jet (that is,with T/pA ). Then we could show that n = 1

simple sources

2

dipoles

3

quadrupoles

(2)

JETS AND NOISE/7

Propeller, Fan and Compressor Noise. Jet noise (quadrupoles) fits this prescription but the others do not. A well-developed theory 1 3-lT exists for propeller noise (essentially dipoles); by virtue of the blade force (or dipole) distribution being organized in a particular way - a phased circular array 18 - it shows that n f 2. In this case the simplified model of (2) neglects a powerful parameter, the ratio blade tip speed/speed of sound. The importance of this blade-tip Mach number Mtip carries through from propellers to fans to compressors. The noise generation rises sharply as Mtip exceeds unity. Moreover, the effect of a duct housing the fan likewise depends on Mtip: the rotor sound pattern spins with the blades, and this spinning mode propagates down the duct when Mti > 1. When Mtip is somewhat subsonic the pattern decays exponentialjy down the duct. The crossover value of Mtip depends on the mode numberl9 , 20. The choice of subsonically spinning rotors would thus appear to be an attractive feature in design for noise control, except for possible performance penalities. However, the likely presence of strong "interaction" modes, some of them spinning supersonically must also be taken into account: the supersonic modes will not decay in passage through the duct. Such modes will arise from impingement of the guide vane wakes on the rotors, generating fluctuating lift at the blade passage frequency and its harmonics. The rotational aspects of these interaction modes can be visualized in terms of a stroboscopic model: the successive wake impingements on the blades are replaced in this picture by flashes of light. The illuminated pattern may seem to rotate either forward or backward. We can summarize now the various fan or compressor parameters or techniques available for noise alleviation in the design stage: (a) (b) (c) (d) (e)

(f)

Subsonic rotor speeds Relative vane and blade numbers Elimination of inlet guide vanes Increased vane-blade gap Sonic throat Absorptive duct lining

Passing from (a) - already discussed - to (b), theory 19 • 20 indicates how the relative vane and blade numbers may be chosen so that the supersonically spinning interaction modes - the ones which will not decay - will radiate only weakly. Measure (c), of course, by eliminating the first set of vanes, eliminates the major source of interaction noise that propagates forward out of the inlet.Mee.sure (d) depends on the spread and diffusion of the vane wakes with distance downstream of the vanes; the interaction modes are dramatically reduced with vaneblade separation, with a tendency toward a levelling off at about one chord gap 21 . More general procedures are (e) and (f). Measure (e) employs a constriction or sonic throat in the inlet duct: the sound cannot go upstream past the sonic block, except for some leakage through the boundary layer . NASA reports measurements of up to 5 dB overall noise 2 reduction and up to 20 dB in the fundamental blade passage frequencies 2 .

8/RIBNER (1968 Turnbull Lecture, Canada) This procedure is limited of course, to inlet noise . Measure (f), the use of absorptive duct lining, is applicable to both inlet and exhaust ducts. Duct length is naturally a factor and, as with the sonic throat, it may be necessary to elongate the duct to provide an adequate length of absorptive lining . This will entail trade-offs between increased weight and drag on the one hand - and noise reduction on the other hand. 3.

COMMUNITY ASPECTS OF JET NOISE AND FAN NOISE

Pattern of Jet Noise . The pattern of jet noise is shown in Fig.5 2 ~ The contours of equal intensity are more or less heart-shaped; the reasons for this will be explored later . The intercept of this space pattern with the ground defines the ground pattern; there is a 6 dB addition for pressure doubling due to ground reflection. During the takeoff roll the ground pattern sweeps along with the aircraft. We are normally concerned only with the peak of the timevarying intensity experienced by any point during the roll-by or fly-by: this is constant along nearly parallel lines*. Then as the aircraft leaves the ground and climbs, the quasi-parallel contours close in and meet. Thus, the contours of peak int~nsity are very elongated along the direction of flight; for example the 110 PNdB c~utour may extend five miles forward of the start of the takeoff roll Effects of Flight Operations . These peak noise level contours define the encroachment of the noise pattern on the community. For existing aircraft they can be controlled to some extent by operational procedures. The chief variables are power setting, altitude and airspeed. A factor of two decrease in thrust should reduce the noise intensity by 12 dB, a major improvement (12 = 10 log (T 1 /T 2 ) 4 from eqn . (1) with n = 3). And a factor of two increase in altitude should reduce the intensity by 6 dB from the inverse square law alone . Atmospheric attenuation will reduce this still further, a matter we shall enlarge on later . Thirdly, flight speed reduces the relative speed between the jet efflux and the surrounding air : the turbulent mixing is weakened and with it the jet noise. The combined effects of airspeed and thrust are given in Fig . 6 for an example turbojet engine 25 The empirical variations of engine maximum thrust and mass flux with airspeed account for the divergence of the upper two curves . Several operational techniques presently used for takeoff noise alleviation employ (1) Preferential runways (2) Turns during climbout ( 3) Low speed climbout (4) Power cutbacks soon after takeoff * The contours tend to close in a bit as the aircraft gathers speed down the runway, owing to the ·e ffect of the reduced relative velocity inducing the jet noise.

JETS AND NOISE/ 9

The first two are aimed at shifting the noisiest parts of the noise pattern awa;y from residential areas. The last two capitalize on the powerful effect of decreased thrust, with altitude playing a role. The last-mentioned, according to Coles26, and Richards 2 7, makes the best use of both factors: altitude is gained quickly at maximum thrust then the thrust is cut back to a specified minimum (Fig. 7). The high thrust, high noise region is localized to sa;y 3.5 to 4.5 miles from the start of r~~l. (This is only part of the story, and is greatly oversimplified ). But the airline pilots object to all but the first of these (the one over which they have some discretionary power) on the ground that they reduce the margin of safety. In fact, Ruby 28 proposes instead an accelerated climbout at full takeoff power; he argues that this will combine safety and noise alleviation, the latter by virtue of the greater altitudes. Coles' studies show on the contrary that this will make more noise over sensitive regions than with part throttle or cutback operation. Jet Noise Versus Fan ~oise. Our discussion has tacitly assumed that jet noise dominates the aircraft engine noise. This is an oversimplification at best, and a complete falsification at worst. The jet noise does dominate in most phases of turbojet operation. But in the throttled-back landing approach the compressor whine from the inlet dominates in the forward hemisphere (Fig. 8). The fan noise, on the other hand, dominates over the jet noise in most phases of turbofan operati()ll(Fig. 9) . On takeoff the jet noise pre-empts only a certain conical zone to the rear; the fan whine dominates everywhere else. Throttling back from the landing approach reduces the fan noise but little, but completely hushes the jet noise in comparison. Thus a turbofan engine makes almost as much noise on approach as on takeoff. For this reason operational technique is a factor in dealing with approach noise. It has been pointed out 2 5- 2 ·r that -steepening the glide slope beyond the standard 3° will provide substantial noise relief. For example, an increase to 6° is ~redicted to reduce noise levels along the ground track by 11.5 to 14 dB 29 . Of this about 7.5 dB is credited to thrust reduction, the remainder to increased altitude. PNdB Measure of Noisiness. So far we have used the noise level units dB and PNdB rather indiscriminately, hoping they would have a familiar ring. To be more precise the decibel (dB) is defined as Sound pressure level, dB= 20 log 10 (p/p 0 )

(3)

where pis therms sound pressure and p is a reference pressure~ normally.0002 microbars. This is a phy~ical measure of sound intensity. It. follows the ear response roughly in being logarithmic but fails to allow for variation in response with pitch. Within the last decade the perceived noise level PNdB has largely replaced the physical dB ~Ba measure of the subjective 'noisiness' of aircraft and other noises . It has arisen as the outgrowth of a large number of listening tests, especially flyover tests. The

10/RIBNER (1968 Turnbull Lecture, Canada) specification has been defined and redefined as more data has accumulated31. It boils down to a weighted dB average over a frequency spectrum, such that the PNdB rating of the complex sound should approximate the dB rating of a 1000 c.p.s. octave band that sounds equally noisy. A partial definition is perceived noise level, PNdB = 33.3 log10 N + 40 N = 0.3 E n.(dB,f.) + 0.7 n 1

1

max

(4) ( 5)

The units of N and ni are "noys", units of perceived noisiness. The n. are tabulated3 1 as functions of dB for eight octave band center ffequencies fi = 63 to 8000 c.p.s.; these tables are the fruit of the listening tests. The salient feature is that high-pitch noises are relatively "noisier" for the same dB level than low-pitch noises (Fig. 10). Thus in Fig. 11 the turbojet with its strong high frequency content is rated 6 PNdB noisier than the propeller, although both have the same physical noise level in dB. The frequency of takeoffs and landings as well as their individual noisiness in PNdB is a strong factor in public acceptability. In England, as a result of considerable investigation, the subjective effects of the two have been combined in a "Noise and Number Index" NNI = average of peak PNdB levels+ 15 log10 N - 80 Here N is the number of individual occurrences, and the -80 implies that a level PNdB = 80 has negligible annoyance. If we set NNI = 45 as an allowable daily upper limit then the allowable PNdB depends on number of events as follows32 NNI = 45 N 1 2 4 8 16 32 64 128

PNdB 125 120.6 116 111.5 107 102 98 93.5

We must conclude this section by noting that many aeroacousticians remain dubious about the validity of PNdB and NNI, etc., for assessment of community response to complex noises. Major companies (e.g. Boeing) are conducting their own research on subjective response in the effort to come up with better criteria. My own feeling is that the correlation among different schemes for assessing perceived noise level exceeds the differences. One of these ratings is the simple dBA read by an ordin-

JETS AND NOISE/ 11 ary sound level meter with the knob at "A", which switches in a standard frequency weighting network. The great simplicity o~ a.BA commends it, in rrry view, over PNd.B . Atmospheric Attenuat"ion. We have said little about atmospheric attenuation as a factor in the aircraft noise problem. This attenuation has tacitly been taken into account in our considerations, but now we should like to deal with it explicitly, drawing in the main from Reference 33. The noise, of course, diminishes progressively with distance - if we leave out of account for the moment any focusing effects. Colloquial terms for the several attenuation mechanisms are : (i) Inverse square law (ii) Classical attenuation, mc1 "standard" 1, + } (iii) Molecular attenuation ,mmJ "attenuation "\me mm (iv) Ground effect, or "Excess attenuation" The inverse square law (i) merely reflects the spherical spreading of the sound waves; each doubling of the distance reduces the sound intensity (proportional to mean square sound pressure) to one fourth . In acoustic terms this is a 6 dB reduction in sound pressure level. The classical or Stokes-Kirchoff attenuation (ii), reflects the losses due to heat conduction and shear viscosity in the atmosphere (bulk viscosity is not included). More specifically, the ordinary assumption of energy conservation embodied in the isentropic pressuredensity relation is abandoned, and an equation for the rate of energy dissipation owing to viscosity and heat conduction is evaluated. This leads to an exponential decay with slant distance z p2

=

p2 0

(6)

exp (-m z) C

where me

=

w2 \ -4 µ + :-:-3"

pc

3

( Y-1) ..,.

~} p

(7)

and w is the radian frequency, p the density, c the sound speed,µ the coefficient of shear viscosity, k the coefficient of heat conduction and c the specific heat at constant pressure. molecular attenuation (iii) is the dominant part of the standard attenuation (ii) plus (iii); it is normally the larger by a factor of ten to a hundred . The value is very sensitive to the relative humidity and the temperature . In terms of the kinetic theory of gases, the molecular attenuation arises from 'relaxation effects', or lag in the molecular degrees of fz-eedom (vibration and rotation) behind the translational degrees. The ordinary equation of state implies equilibrium and is inapplicable here : it must be replaced (in differential form) by an expression allowing for the lag . Kneser3 4 accomplished thi s by showing in effect that the rate of approach of the internal energy to equilibrium is proportional to its departure from equilibrium. This implies a simple phase lag for harmonic oscillation . The

¥he

12/RIBNER (1968 Turnbull Lecture, Canada)

phase lag is allowed for by writing the speed of sound as a complex constant C

:

-

(.!_ C

LE!m.)-1 2w

(8)

in the wave equation

a2 p azt="

_

1 a2p c~ w

=

This has the solution 33* ( p = p 0 exp [ i wt

_cz )

(9)

0

J

e-½ 111mz

(10)

which represents a damped travelling wave. The damping constant~ represents the molecular attenuation to be added to the constant me representing classical attenuation. For theoretical considerations concerning evaluation of the attenuation coefficient 111m the reader is referred to the survey article Reference 33 or to Refs. 34 to 36. The lag effects are defined in terms Qf a relaxation time 'nor a rel~ation frequency fmax,n = l/2n,n for each of the degrees of freedom n. K:Aeser's theoretical result for the attenuation per wave length A may be written

(11)

for the case of a single important relaxation frequency, as for atmospheric air. The presence of water vapor exerts a catalytic action 37 on the relaxation of the oxygen and dominates the attenuation in air. Thus fmax is a strong function of humidity h; in fact the right hand side is ordinarily converted into a function of h/hmax· Definitive experimental measurements of the combined or "standard" attenuation me+ 111m have been carried out recently by Harris38 These were of a laboratory nature and employed sound decay in a 1.68 meter diameter spherical chamber. The resulting data, smoothed and extrapolated, were used to prepare comprehensive tables of attenuation me + 111m (e.g., in dB per 1000 ft) as a function of temperature, frequency and relative humidity. (The widely used Reference 39 is based on · earlier WQn of Harris). The experimental data for 111m/(111m)max for various frequencies and humidities collapse well at fixed temperature into a single curve vs. h/hmax as predicted; the exact shape, however, ·departs somewhat from Kneser's theoretical curve, eqn. (11).

* In Reference 33 the wave equation and its solution are expressed

in terms of velocity v instead of pressure p; the notion of a complex speed of sound is implicit but not stated.

JETS AND NOISE/13 A working set of attenuation curves from Reference 38 are shown in Fig. 12 for a frequency of 2000 Hz. The caption indicates how attenuation values at 1000 Hz and 4000 Hz may also be estimated; below 1000 Hz the attenuation is small. The powerful role of humidity is very evident. The •standard attenuation~ me+ film, which we have discussed at length, accounts for the attenuation due to viscous and molecular dissipative effects in the atmosphere. We must mention, however, that it does not allow for additiou51 attenuation owing to scattering of sound by atmospheric turbulence Ground Effect Attenuation. Item (iv) in the list of noise attenuation mechanisms is ground effect, also called 'excess attenuation'; it is the excess of the actual attenuation of noise sources near the ground over the predicted 'standard' attenuation plus inverse square law ( (i), (ii), and (iii) jointly). Here the absorption and scattering by houses, trees, and ground cover comes into play. Figure 13 indicates the order of attenuation that may be attained, depending on the ground cover or other barrier. The ground effect comes strongly into play during the takeoff roll of an aircraft. The built-up areas along the sides of the airport receive the benefit of the approximately 20 dB attenuation. However, upon clearing the houses after liftoff this is gone, and there is an abrupt 20 dB (or so) rise that envelops communities under the flight path until power cutback. 26 A quantitative .study of the ground effect attenuation of jet aircraft during the takeoff roll was recently carried out at Los Angeles International and Denver Stapleton Airports. 41 Unfortunately, the nature of the terrain was only crudely characterized as "flat terrain and residentially developed areas" The character, height, and density distribution of the houses were left unspecified. The smoothed measurements were presented as curves of downwind 'excess attenuation' versus distance from the source up to 2000 meters; the curves were for octave bands centered at 31 . 5, 63, 125, 250 and 500 Hz. At 2000 m. the three middle frequency bands all show about 20 dB attenuation. Comparison with Fig. 13 thus suggests that houses and partly wooded terrain provide roughly the same sound attenuation. The authors 41 found a curious enhancement (negative "excess attenuation") of up to 40 dB for frequencies above 1000 Hz. They concluded that this was an artificial effect arising from an excessively large 'standard attenuation' at these frequencies. Thus they propose that the 'standard attenuation' as computed at 2000 Hz and 4000 Hz by the procedure of Reference 39 should be halved in practice for sources at ground level. Atmospheric Refraction. Temperature and wind gradients in the atmosphere can bend the sound rays . Suppose we employ a stratified model of the atmosphere, with horizontal winds W(y) and temperature contours T(y). Then a little geometry will show that the horizontal 'trace' velocity Ci of a given sound ray must remain constant from stratum to stratum. This condition dictates the refraction of. the ray according to

14/RIBNER (1968 Turnbull Lecture, Canada)

W cos/

+ c = Ci cos

f

(12)

Here --~ e

WITH SUPPRESSOR PREDICTED-

/~

EXPERIMENT e

·,~e

.............

~-

so-:-:--.___.___.___,i.__---'_ __.,_ _,__......._--1,,_......__ o• 45° 90° ANGLE FROM JET AXIS

FIG. 26

SUPPRESSOR NOISE DIRECTIONAL PATTERN : EXAMPLE OF EXPERIMENT VS . PREDICTION79

_.__ _. 180°

42/RIBNER (1968 Turnbull Lecture, Canada)

z y

\

\

i '\

\;

\

\

-"~ '-.

FIG. 27

RADIATION PATTERN OF SHIELDINGFLAP SUPPRESSOR67: NOTE LARGE NOISE REDUCTION BELOW AIRCRAFT

\

THE DEVELOPMENT OF ENGINEERING PRACTICES IN JET, COMPRESSOR, AND BOUNDARY LAYER NOISE J.B. Large, J. F. Wilby, E. Grande, and A. 0. Andersson Commercial Airplane Division The Boeing Company, Seattle, Washington SUMMARY

The purpose of this paper is to compare the development of the theoretical aspects of boundary layer, jet, and compressor noise with the evolution of the engineering methods developed for controlling the three noise sources. The usefulness of the theoretical formulations in helping the engineer solve practical problems is also discussed, together with the direction in which the academic community must proceed in order to help the engineer. l.

INTRODUCTION

The increasing public interest in aircraft noise is focusing attention on the work of the engineer in the field of noise reduction. The purpose of this paper is to compare the progress of research into jet, compressor, and boundary-layer-induced noise with the evolution of engineering methods for the control of these three noise sources. The usefulness of existing theoretical formulations in helping the engineer solve the practical problems is discussed, together with the direction in which the academic community must proceed to help the engineer. The study of turbulent-boundary-layer pressure fluctuations and the associated structural responses has been more successful in helping the engineer than has the study of jet or compressor noise. Laboratory measurements of the statistical properties of the wall pressure field for subsonic flow have established nondimensional parameters that are fairly reliable for predicting the pressure field . The experimental research has constructed a good picture of the wall pressure field so that it has not been necessary to rely on theoretical formulations, which have had only limited success. (However, existing flight measurements show a large degree of scatter, which may be associated with the complex flow around the fuselage . Supersonic measurements are limited in number, and the data do not show a good collapse into nondimensional curves for the parameters chosen.) The response of structures to boundary layer excitation has been studied for simple panels under laboratory conditions, and the vibration can be predicted reasonably well by using existing theories. However, it has not been possible to study the more complex panel-stiffener arrays in the laboratory, nor have suitable prediction methods been developed for such multipanel arrays. Further, engineers have not carried out measurements on typical aircraft structures under flight conditions so that the extrapolation from laboratory to full-scale structures can be made with confidence. Structural modifications devised in the laboratory have reduced the vibration and acoustic levels in subsonic flow , but the modifications have not been tested in the laboratory under supersonic flow conditions or in full-scale flight conditions.

AFOSR-UTIAS SYMPOSIUM ON AERODYNAMIC NOISE, TORONTO, 20-21 May , 1968

44/LARGE et al. (Invited Survey Paper) The major sources of all aerodynamic noise for a modem turbojet engine are shown in Fig. l. The study of these sources, which are due to the rotational machinery and the exhaust flow, requires several quite different methods of analysis and solution. · The theoretical study of jet noise has resulted in formulations by Lighthill, Rihner, Ffowcs Williams, and others describing certain mechanisms of jet noise production; in no instance, however, has a method of noise reduction been described except on a speculative basis. The well-known y8 law is an acceptable method of estimating the total acoustic power radiated by medium-speed jet engines, but it is inadequate for the low-speed or high-speed jet engines that will power the next .generation of aircraft. A great mass of engineering data on the design of noise suppressors has been accumulated, but only a few attempts have been made to provide an orderly analysis of the data. So far, the most important parameters in jet noise suppression have not been clearly identified. Until this is achieved, the designs of noise suppressors will show little improvement . .There are two major engineering problems associated with jet noise. The first is the reliable prediction of the acoustic radiation from the jet in terms of the engine parameters. The second is the design of suitable methods to reduce the noise disturbance by either reducing the total acoustic output of the jet or redistributing the acoustic energy. Existing knowledge provides little guidance in solving either problem. This paper discusses possible noise reduction mechanisms-breakup of the jet into small elements, ambient air injection, contraction of the noise-generating region, shielding effects, annular flows, etc.-with supporting theories where these are available. Until recently, the compressor noise problem has been studied mainly from the aspect of the propagation of acoustic waves in ducts (for example, by Sofrin and Morfey); even so, the work has been confined to idealized environments. As yet, the application of the theories to engine design has not produced a dramatic decrease in compressor noise. Only in the last two or three years has progress been made in identifying the sources of compressor noise. The general theory of Lighthill has been applied to rotor noise by Lowson, but is valid for subsonic rotors only. A new approach is required to describe adequately the "multiple-tone" phenomenon associated with supersonic rotors. Current descriptions of multiple-tone noise are qualitative. The effects of the enclosing duct and of rotor-stator interaction have been studied, but the experimental results show a large scatter, and existing theories do not provide reliable estimates of the noise generated. The problem areas requiring immediate attention are discussed herein. Until sufficient progress has been made, the engineer must rely on external means of compressor noise reduction, such as acoustic liners and sonic throats. A comparison of the present understanding of the generating mechanisms of jet and compressor noise with the engineering requirements for the design of suitable noise-reducing systems has shown that there is still a large discrepancy. Critical areas of research are indicated for academic study, and it is essential that progress be made in those areas to give the engineer a reasonable basis for his work in improving the noise _environment of future jet engines. However, the research worker is not solely to blame. In the case of boundary-layer-induced noise in the fuselage, it is the engineer's responsibility to perform well-controlled experiments on aircraft in flight so that full benefit can be derived from the available theoretical and experimental results. In all cases, the errors of the present prediction methods far exceed the tolerances placed on specification of aircraft external or internal noise levels, and improvements in existing knowledge are urgently required.

JET, COMPRESSOR, AND BOUNDARY LAYER NOISE/45

2.

BOUNDARY-LAYER-INDUCED NOISE

General Problem. Much of the interest in jet and compressor noise is directed toward reducing noise at the source. Suppressors are being designed to reduce the jet noise, and compressor or fan studies have indicated ways of reducing discrete-frequency noise at the source. In regard to boundary-layer-induced noise, there has not yet been an attempt to reduce it by controlling the boundary layer so that the structures and associated acoustic insulation can be designed to provide minimum noise levels inside the fuselage . Engineering effort has not been as active on boundary-layer-induced noise as on aerodynamic noise related to community annoyance. However, the airlines' increasing demands for low noise levels in the aircraft interior, the competition between manufacturers, and the approach of supersonic commercial flights have awakened interest in developing the available research results. For many years, the engineering method has assumed that the boundary-layer pressure field had the same correlation characteristics as an acoustic field with the same pressure power spectral density (PSD). The method could have been modified by determining the equivalent acoustic spectrum that would produce the same structural vibration as that induced by the boundary-layer pressure field, but this does not seem to have been attempted. With the aerodynamic pressure field assumed to be identical to an acoustic field, the transmission loss of the fuselage structure was determined from acoustic theory and experiments. The method was modified in some cases to include the effects of panel resonance and coincidence, but these changes did not necessarily improve the predictions. The method should not be dismissed as having no value. When it was first used, there were no correlation data for the boundary-layer pressure field, and it gave at least an order-of-magnitude estimate of the effect of aircraft velocity and altitude. Criticism of the engineer is appropriate, however, because of the lack of effort to apply more recent research results in the development of engineering techniques. When new airplane designs introduce large changes in cruise conditions or in fuselage construction, the "acoustic" extrapolation approach is totally inadequate; yet there is little to replace it. The success of the acoustic method is often difficult to assess because much of the information is hidden behind commercial security. The indications are that it is quite inaccurate in predicting interior noise levels when only the basic flight and structural parameters are given. Discrepancies of 15 to 20 dB between predicted and measured octave-band levels have been reported. It is possible that the method will be suitable for supersonic flight, where the convection velocities in the boundary layer are ~milar to the velocity of sound, but this is fortuitous rather than good design. The design of a fuselage is dictated by structural reliability criteria such as fatigue life, static pressure loading, and crack growth rate, not by acoustic considerations. Thus the relative positions and thicknesses of the longitudinal and circumferential stiffeners, as shown in Fig. 2; result from structural strength considerations. The acoustic engineer has the choice of adding treatment to the inner surface of the fuselage skin or of inserting acoustic insulation between the circumferential stiffeners, but-unless he is extremely fortunate-cannot change the basic structural design. In Fig. 2, damping tape has been applied to the fuselage skin to provide selective noise reduction in local areas. This has the dual effect of increasing the damping coefficient and adding mass to the structure. Figure 3 illustrates the method of introducing sound insulation. Fiberglass blankets are mounted

46/LARGE et al. (Invited Survey Paper) between the skin and the internal decorative trim, the blankets being enclosed in flexible bags or constructed from preformed semirigid panels. Air gaps occur between the skin and insulation or between the insulation and trim. In some designs, the gaps are used as ducts for the air-conditioning system; in other designs, pipes are added to carry the air. In addition to providing acoustic insulation, the blankets act as thermal insulation. The thickness available for insulation, including blankets and air gaps, is dictat.ed not by acoustic considerations, but simply by the depth of the circumferential stiffener-that is, by structural design. If the engineer is to tackle the problem of airplane interior noise successfully, this piecemeal approach must be replaced by an integrated systems approach that includes structural integrity, acoustic and thermal insulation, and overall weight. The problem can be divided into three phases: the pressure field beneath the turbulent boundary layer, the structural vibration field, and the acoustic radiation field inside the fuselage. The structural and acoustic fields can sometimes be considered together, but most research workers consider them separately to better identify the response. To create such a systems approach, the engineer has access to a large literature on boundary-layer pressure fluctuations, but the research results available on structural vibration and acoustic radiation are more limited in scope. Boundary,:!,ayer Pressure Field. Current predictions of the boundary-layer pressure field on a fuselage rely mainly on laboratory measurements under zero-pressure gradients, although it is well established that the flow over a fuselage is an alternating sequence of adverse and favorable pressure gradients. Acceptipg this discrepancy, differences among the results of the various research workers and only partly successful attempts to identify universal nondimensional scaling factors have prevented the complete description of the pressure field. It is possible that the results are adequate for current engineering requirements, but existing flight measurements do not justify this assumption on face value. Reliable pressure correlation measurements have not been made in flight, but pressure PSD functions show a scatter of at least ±5 dB. It is encouraging that the mean spectra for wind-tunnel and flight measurements are similar, but it has to be established whether the scatter in the flight results is experimental error or a true effect. If it is the latter, the cause has to be determined so that the fluctuating pressure field on a fuselage can be reliably predicted. Comparisons of pressure correlation functions for the wind tunnel and the fuselage are not possible at present, but are urgently required. Laboratory measurements should be made to extend the understanding of the pressure gradient influence, and flight measurements should be directed toward the pressure cross PSD. Theoretical analyses have not shown an ability to predict boundary-layer pressure field characteristics. Most investigations have considered the Poisson pressure equation for incompressible flow, but the mean-square pressure· has been studied in extensions to the compressible case. In all cases, broadband and narrowband, longitudinal and lateral directions, the theories have predicted higher correlation coefficients than those m~asured in the wind tunnel. (Typical results are shown in Fig. 4.) A second approach, which replaces the Poisson equation with the Orr-Sommerfield equation, agrees better with experiment, the comparison being made for the longitudinal narrowband correlation coefficient in Fig. 4. However, it does not reproduce the details of the measured characteristics, and the engineer has to resort to empirical representations of the pressure field using nondimensional parameters that permit scaling to conditions on a fuselage.

JJ w

80

~

1¥

~

w

1

70

~

_/2 /p

8 0

1¥

i: ....

12·x1•xo.2s· HONEYCOMB PANEL

60

I

/

I

A\

'o- -0

'\

'\;

-o--"°'- ,

b

c:/

M=0.47

SO'-----'----....._--&-__..__..___ ___.__ _ _ _ __ 100

200

400 600 800 1000 2000 THIRD OCTAVE MID FREQUENCY Hz

4000 6000

FIG. 7B. ACOUSTIC RADIATION FROM BOUNDARY LAYER EXCITED PANELS (MAESTRELLO (4) )

JET, COMPRESSOR, AND BOUNDARY LAYER NOISE/61

COIIUIIA'IID NOZZLE 111A IATI> 4.65

PIG.a. 37-TUBE MIXING NOZZLES

DJ= DIAMETER OF ORIGINAL JET n = NUMBER OF TUBES d=

~ =DIAMETER OF TUBES

[ :MJ~ AREA RATIO J

ENTRAINED AIR

- -- >

- - ----

MIXING REGION OF COALESCED J

FIG. 9. SCHEMATIC OF JET FLOW FROM MULTITUBE

62/ LARGE et al . (Invited Survey Paper)

30

ATTENUATION-dB

20

10

2

FIG.JO

3 4 AREA RATIO

5

6

B

10

VARIATION IN SPL SUPPRESSION OF MULTITUBE NOZZLES

,,,,.--"""" 1

120

110 OCTAVE BAND LEVEL-dB

/

/

/

/

100 90

80 70

8

2

= 45° 3

4 5 6 OCTAVE BANDS

8

9

10

FIG.II. SPL SPECTRA FROM MULTITUBE NOZZLES

JET, COMPRESSOR, AND BOUNDARY LAYER NOISE/63

FIG.12. 259-TUBE MIXING NOZZLE SUPPRESSOR WITH LINED SHROUD

o - STANDARD NOZZLE 6 -259-TUBE NOZZLE 17-259-TUBE WITH 12' LINED SHROUD I> -STD. NOZZLE WITH 12' LINED SHROUD

~

110

z

100

,_

90

0

...""~


Cl.

0u

-

I(/)

z

I.LI I-

z

30 NI A.llSN3.lNI

0

CD

0

ID (!)

LL.

f--' f--'

0

----~

M = 0.63 I I

'

\

l!I =

~/--- \ I

D

\

s

240

0

MEASURED RESULTS

-

COMPUTED INTENSITY

~

·,.,

80

H

Cll

·,.......

........ """'0....._

...............

.......__

--.......

~

.......................

·-e....

70-------+-------+--------+---------t----------o 30°

60°

90°

ANGLE FROM JET AXIS

INTENSITY OF NOISE FIG . 7

120°

150°

~

GENERAL METHOD FOR CALCULATING THE SOUND PRESSURE FIELD EMITTED BY STATIONARY OR MOVING JETS M. Kobrynski o.N.E.R.A., 92 - Chttillon, France 1. INTRODUCTION An analysis of the spectrum associated with the maximum SPL emitted by stationary or moving jets has led to a method of calculation previously published1, which is suitable in both cases £or round jets without silencers, with or without reheat,and £or jet speeds up to 950 metres per second and at £light Mach numbers of up to o.6. But to define the nuisance due to ai-rcraft noise, one expresses now sound pressure levels (SPL) in effective P.N. db 1 s (EPN db) and this poses the problem of calculating the total sound preseUN field emitted b7 jet aircraft. The predetermination of EPN db requires a knowledge of the sound pressure spectrum, not only in the direction of maximum noise, but also at various angles trom the jet axis. 2. SETTING THE PROBLEM Consider a jet aircraft climbing at an angle 0( after taking off, and £lying vertically over the observation point O on the ground (Fig. 1). For each position of the aircraft, provided its flight path is collinear with the jet axis, the sow-1 ray emitted towards O makes an angle 0 with the jet exhaust axis and an angle ff with the horizon, given by:

If = Tl - (B + ct.)

(1)

The speed of the aircraft being known, its position and the time of emission of the noise received at Oare known £unctions of the angles 0 and 'If • The overall SPL and the SPL in various frequency bands will be calculated at O (or at any other point taken on the perpendicular to the projection of the £light path on the ground). For these calculations, JV is increased in steps of fl. 1fl"' 20°, from 20° to 160°. The method 0£ calculation will also be extended to the noise emitted by a fixed jet, at points lying on a straight line which may be parallel or not to the jet axis. 3. PRELIMINARY CALCULATION PROCEDURES The first step is to determine the local OASPL at a point in the £ar field situated on a circle of radius R0 = 30 metres, AP'OSR-UTIAS SYMPOSIUM ON AERODYNAMIC NOISE, TORONTO , 20-21 May, 1968

112/KOBRYNSKI

centered on the nozzle. The result is then used to calculate the SPL associated with the i-th £requency band (the i-th octave, £or instance). For such calculations, it is also necessary to use the characteristic curves 0£ the generalised acoustic spectrum corresponding to the angles considered. The sound levels are then corrected £or geometric and molecular attenuations according to the lengths R 0£ the paths considered. 4. CALCULATING THE OASPL The calculation 0£ the OASPL corresponding to a direction ~ 8 , N 8 , is based upon Lighthill' s theory ot aerodynamic noise extended to moving jets, the laws governing the £low in coaxial jets and finally upon the conclusions drawn £rom Olll' previous experimental work. The theory identities aerodynamic sources in the jet as a volume distribution 0£ quadrupoles radiating in a uniform medium at rest and shows how convection 0£ turbulence in the jets confers a directivity pattern to the sound field. For jet ot low Mach number the 1nt.ensit7 of the sound which would be emitted in the absence of convection is then amplified b7 a factor

(t- Mc

Ct7S

Ne= -

1

8 )_s V.·

-1 2 Ca.

where

Ne is the convection Mach number 0£ the eddies in the jet

~ - is the characteristic. jet speed

Ca is the speed 0£ sound in ambient air., In that expression the -5 th power law was introduced by F£. Williams3 who thus corrected the original -6 th power. For high speed modern jets, this expression is not verified experimentally (Fig. 2) and this has induced us to use, instead 0£ -5, a power - '? which is a £unction 0£ Ne as shown in Fig. 3. Thus, £or a fixed jet, the directivity associated with the overall noise level contains the new term f(J

l.d1,o

where the mean value 0£

(t- #c cos & )- ' o/

(2)

is given by : IG#c

(3)

For a jet in night, the Mach number 0£ the convection rela-

SOUND FIELD OF STATIONARY OR MOVING JETS/113 tive to the atmosphere into which the sound is radiated is

Mc - .!_ Mv 2

where

Mv

Mv =

Ve

,

Ca. is the £light Mach number and

Ve is the aircraft speed. Hence, the convection index £or a mobile jet will be

(4) 1J being given by (3). _, The £actor ( f + Mv cos {J ) in (4) is obtained by Ff. Williams from purely geometric considerations and it shows that £or a given direction, the acoustic radiation is redv:iced to that of those eddies whose emission arrives simultaneously-"'. Stationary Jets. The calCL1lation of the local overall SPL,

Nos, requires : to :

(a) The total acoustic power 0

's = where

~-

f'i S

K

z

,,

fJ S~;

fa

_f

Ps

Ctt

emitted by the jet according

_s

(5) (see appendix)

is the e££ecti ve velocity at the jet exit, in is the density 0£ the £ully expanded jet, is the nozzle-exit area, m2

m/ sec.

Kg/m 3

K is a coefficient found experimentally equal to 1.8x10-4 (b) The space average SPL in the acoustic far £ield which would have been produced by an isotropic distribution of the power ~ , and given by :

(6)

e

(c) The reference SPL, taken along = 90°, £or which the convection index (2) is zero. This reference SPL is given by

(7)

ll4/KOBRYNSKI That SPL equal to v18 mined by value of

is, to within a constant determined experimentally(Fig.61 the SPL given in (b), that is to say, it varies also as • Let us note that the above-mentioned constant is deterthe difference between the mean spatial SPL and the mean the directivity index for the angle considered.

( d) The convection index, corresponding to a direction e and given by (2). (e) The ground effect, included in a constant which is determined experimentally. The resulting formula 1 is

NI$ -- IPLon 7 ttJ

ei2 .SNc8

( f - #c

t"d.l

8) ?

+ c..

&-

(8)

where.C2 is an accumulated constant; and equal to 138 db when R • 30 metres. However, the amplification expected from the convection index agrees with experiments (Fig. 2) only for those values of IJ which are equal to, or greater than, the angle of maximum radiated power 811 (polardiagram). But it is necessary to predict the SPL for all angles (} ~ &/If • The di ~rgence between measured and predicted values for 0 < 8 111 can be avoided by observing that the curves showing the variations of the polar OASPL (Fig. 2) are symmetrical - to a good approximation - with respect to &111 within + 20° of l!J,,,. This angular interval .68 • + 20° is sufficient for the present calculations. Hence it suffices 1or calculations involving D!.~====-::130 ~

...

140 _,

I

.,... f:

22

3

6.36.3

10

FIIEQUEHCY (Kell)

FIG.3

20

SOUND PRESSURE LEVEL SPECTRA (ABSORPTION ON FLANGE) x•ID, y•4D

NOZZLE STATIC

..,

PMSSURE 6p,

140 1-------~130 140

14()~

p : -.............-"""'=''30 140

:!!

140

>-.........___....1,30

;

140

f Cl

130 ~ 140 u,

3 FREQUENCY

FIG.4

6.3 6.3

Kl

(Kc/1)

SOUND PRESSURE LEVEL SPECTRA ( ABSORPTION ON X•6D

, ■ 7D

FLANGE)

20

NOISE FIELDS OF CHOKED JEr/157

7,000

6,000

5,000

\ B,

4,000 M 0.

u

.,; w

u z

~

3,000

w

~l

::, 0

...a: t,J

:,:

u

2,000

A, 2 1 - iooo 00 oo_

w w a:

u

o---o _ _ o - 0 -0 - -0

Q>o O

U)

Ooooooo o

1,00_0

ooo

Do 0

0

0

PRESSURE RATIO, R

u..._ ___.3....._.....,_4_~.....,___,.......6____,,1__.....,e__,_.....,9_--.-_.,o

w

~

~

~

~

~

w

NOZZLE STATIC - AMBIENT PRESSURE, bPr, psi

SCREECH FREQUENCIES vs. NOZZLE PRESSURE

FIG. 5

X•ID

Y• 4D

160

A,2

0

0

PRESSURE RATIO, R

7 4 6 8 10 5 9 110...__ _......,_ _....___,._....___-r...__ _...,___ __._~_..,____.---, 0

10

20

30

40

50

NOZZLE STATIC - AMBIENT PRESSURE, .t.p, psi

FIG. 6

SCREECH SOUND PRESSURE LEVEL vs NOZZLE PRESSURE, X • ID, y • 4 D

60

158/WESTLEY AND WOOLLEY 7,000

0 0

o,

0

0

(D

0

0

6,000

5,000

. a.

u

f3

4,000

i3

z

"'::,a "'0:

3,000

LL

:c '-'

"'"''-'0: u,

2 ,000

1,000 PRESSURE RATIO, R 3 _ _............. 2 _ _.....,. 4 5 6 _ _7.,__ _8.._,--_..__,,~ 9 10 0 ..._ _...__..,....._

w

~

~

~

~

~

NOZZLE STATIC -AMBIENT PRESSURE, 6pT, pal

FIG. 7

SCREECH FREQUENCIES vs. NOZZLE PRESSURE (ABSORPTION

ON FLANGE) Y•4D

X •10

160

5

1 ~

100

N

.,

0 0 0

~6

.

140

_; i

"'0 > z "' m ~

130

"'>

~ 0

::.s

120

oo Do

,j:fX> 110

FIG. 8

0

0

Ooa:,OOCff'

4

PRESSURE

o&

RATIO, R

8

6

10 20 30 40 NOZZLE STATIC -AMBIENT PRESSURE, (:,.p ,

pol

SCREECH SOUND PRESSURE LEVEL vs NOZZLE PRESSURE , X =ID y=4D (ABSORPTION ON

FLANGE}

10·

9 00

60

NOISE FIELDS OF CHOKED JET/159

. ~~',-

,0010 : ; ; - - - --;;: :;:-----;:,-;;---.- - - - - :.. - --~••- - - ~ - - - - - : ; : - , . - - ~.. AXIAL DISTANCE X ,

FIG. 9 t-EAR SOUND FIELD OF JET SCREECH ~P=6psi. SPL,\i oct. O

I

t

S

4

EXCESS NOZZLE STATIC PRESSI.R

t

I

7a.

t.P•l5ptl.

SCREECH FREQI.ENCY (MODE A,) f• 2125 ell.

-'--- - ~---~--~---• ~'-----'------'---e o --«> -2 01

20

40

e0

1DO

AXIAL DISTANCE X

FIG. 10

NEAR S()l.N) FELD OF f l SCREECH AP~ 15psl S.P.L -A, 0ct.

16O/WESTLEY AND WOOLLEY

. ,.

/

- -- -,,..-- ,_' - -

w ~40

~

~ ...J

s 0

0

"'

150 140

·ID FLANGE

ID NOZZLE

20

30

60 50 40 AXIAL DISTANCE, X

70

80

90

~0

FIG.16 AXIAL TRAVERSE OF TOTAL SOUND PRES~ FIELD y = 1.50

NOISE FIELDS OF CHOKED JET/163

60 50 X ..; 40 0

z ~

/ COMPRESSION OISTURBANCE

"' 30

0

...J

-'--,;;.- region downstream of the re-====::-5-.--. ~~fleeted shock end. (See _ _rt~--Ll.·-··~,;{_', .J...:_y>;, -+·,,. , Fig. 4.) Some of the direc, \ _o/. y,11,Az-,.tf 1-'///// tional waves typified by their ', ' -~~?II ., · . , " ,n the shadowraph. Lowson ~--_-/i;,_ r:, --- --------an~ Olle~head 8 explained --1/ th 1 s s pl 1 t end phenomenon on the basis of the Mach reflec5KE1CH OF TVPCAL ACOU5TIC EM15SICH:,. tion caused by the interaction of two intense spherical waves. Similar observations have also been reported by others (references 7, 16 and 18) and can be considered as characteristic of the radiated sound field of a supersonic jet flow. The intense directional waves which appeared to originate from the shear layer near the nozzle exit in many respects resemble the eddy Mach wave radiation. In an attempt to associate these directional waves with eddy Mach wave emission, the acoustic Mach number ME (defined as mean exit speed of the jet/ambient sound speed) was found to be 1.5. The mean inclination angle e of the directional wavefront was measured to be 37°. If these directional acoustic waves are assumed to be eddy Mach waves, the mean eddy convection Mach number Mc, defined as mean eddy convection speed/ambient sound speed and given by Mc= cos- 1 e, is 1.25. Therefore, the mean eddy convection speed is 0.83 times the mean jet exit speed. This value is lower than that reported by Ollerhead 7 , and is a more reasonable value if the directional waves are in effect generated by the eddies convected supersonically relative to the ambient speed of sound .

-•- r:-~~'\

--K--- _

/0 , - , .:-\- t:y:'~.,,;-::,"-\ - '..,..,._.,~·-;--....._""~ - -

':>-~.~~:;,-

-- 1/Po/ · ---:,~ ---- / 1/

IV.

INTERACTING JET FLOWS

Acoustical Investigation. The total acoustic power variation with percent impingement is presented in Figure 5. For all x/d values used, the PWL values at zero percent impingement (with impinging jet nozzle assembly in place) agreed closely with that of the main jet alone (i.e., without nozzle assembly) operated at the same total pressure. This excluded the possibility of any definitive effect on the noise emission by the impinging jet nozzle assembly for these x/d conditions. For

UNDEREXPANDED JET FLOWS USING RADIAL IMPINGEMENT/177

FIG. 4. SPARK SHADOWGRAPH OF MAIN JET ALONE. A. SOURCE OF DI RE CTI ONAL ACOUSTIC EMISSION. B. SOURCES OF SPHERICAL ACOUSTIC EMISSION.

p™ = 150 psig

I~ 149

.,>-->--

!TQ

148 ..... 0 .

1◄7

,..,...

J

w

>

~

llll

IU,1

145

0

150

. .. • '2

·-

149 148

0---o- -

•4w.

,..,

1.-...(1)

00 •1•M1N,IIIOlflllt

0"

"6 ~

lll(l

IUD

147 I

~ ~~ .0--

1450

.d

••

)()d-0. 4

12

16

20

PERCENT

2'4

28

~

•

;. i!t

... O 0

►

I:

•4,..,_

11.M-4.0

'

/'\

6

I

,',!°\,•,

'/

II laN.flOll[III

NOZZL.£ AAAANGCMENT I

IMPINGEMENT.

FIG. 6

DIRECTIVITY

. ,,.1.Ut)

1u., IU:,1

1l0

~,\

.

32

IMPIN;EMENT

TOTAL POW ER LEVEL VS. PERCENT

ll!

••

P,,.-lfo()PSI;

FIG. 5

.

••

N

0

146

ll:S.,

,,. I "-

32

8

SPl,.(ft)

llJ.3

lll.l

a:

~

•/.IW,

ll)D

~ 146

"'.,,

JCAl-0.6

S"Ltlll)

O 0

·•

Pn,•l!IO~

INO[X VS. AZIMUTH

ANGLE .

178/DOSANJH AND YU

....,.,.

percent impingement greater than :: 4%, significantly, for almost all the operating conditions investigated, PWL decreased with increasing percent impingement ·• Ill • value. At x/d = 0.4 and 0.6, '"'~~~~. with 16% impingement for nozzle arrangement I, and at x/d = 0.6, ... ,... ... 111 with 20% impingement for nozzle : ,! •--• :~ arrangement II, the tota 1 power level was 2 dB lower than that at zero percent impingement. Furthermore, with percent im' pingement as high as 32%, the • total acoustic power levels were • still mostly lower than qr comNOZnE AIIIANGEIENT I parable to the 0% impingement values. The peaks in the total FIG. 7 OIAECTMTY INDEX VS. AZIMUTH AN61.E. acoustic power curve at x/d = 0.4 and 0.6 of nozzle arrangement II, where the corresponding total acoustic power was higher than the zero percent impingement values, are discussed later under Shadowgraphic Investigation • Typical directivity indices are plotted in Figure 6 and 7 for nozzle arrangement I and II respectively. For nozzle arrangement I, the directivity index values are 150 presented for 0% impingement, I I XA:l•O.• Iminimum acoustic power emission, I and 32% impingement. For nozzle ,,.,i 140 arrangement II, these are given 38 : a ah 'Q 8 for 0% impingement, peak acoustic 41 & ~ ~ 130 - power emission, and minimum aCD o MAIN JET ALONE I\,; 150 "0 ., coustic power emission. For all o 16 % IMP. MIN. POWER · •32%1 IMP. I ~ x/d values at zero percent imw I > 120 50 IOOkH, pingement, the directivity index 2 10 20 5 ~ I FREQUENCY variations with azimuth angle are a: in close agreement. This 150 strengthens the validity of the I 0 XAl•0.6 earlier conclusion that the imI z i ~pinging jet nozzle housing did ~ 1•0 . fr not interfere with the sound w ., 8 g • field of the main jet flow. In ~ t ' . l5 130 nozzle arrangement I the characIo• MAIN JET ALONE P,c 150 If,% IMP. MIN. POWER teristic directional peak at 30° ., 8 32o/o IMP. i azimuth angle was conmon for the ' I 120 2 5 I 10 20 50 100 kHz bulk of data gathered. Addi ti onFREQUENCY al peaks of lesser magnitude also NOZZLE ARRANGEMENT I Pnr' 50 PSIG occurred at 60° and 90° azimuth angles at minimum ~coustic power FIG. 8 1/3 OCTAVE POWER SPECTRA. and 32% impingement depending on x/d value. Comparing the directivity index curves for the zero percent, minimum acoustic power, and 32% impingement at a fixed x/d value, it is seen that the effect of impingement flow is to make the acoustic emission progressively less •4•

~

••••

::

Ill.•

•IO 111-. llllllf:JI 01,

1N.l

IU4

0

.. • - -

,...

M•l,0

0

.

""

"

.

0

0

'

0

•

0

I

...J

i

0

0

f-

1•

0

0

.. . 0

0

0

• 0

0.

'

UNDEREXPANDED JET FLOWS USING RADIAL IMPINGEMENT/179

directional. In addition to a reduction in total acoustic power, a redistribution of directionality is often helpful from a noise abatement viewpoint. In nozzle arrangement II, the directivity index curves (corresponding to the conditions where the peaks in the total acoustic power were higher than the zero percent impingement value (at x/d = 0.4 and 0.6 in Fig. 7} showed a shift of the directional peak from its usual 30° azimuth angle to 45°. This new azimuth position of the directional peak coincides with the direction of propagation of the intense discrete directional waves which were observed with x/d = 0.4, and is discussed under Shadowgraphic Investigation • The 1/3 octave band power spectra for nozzle arrangement I at x/d = 0.4 and 0.6 are given in Figure 8. The spectra are rather flat and continuous; no discrete peak is observed. At 16% impingement the reduction in the total acoustic power obviously results from an overall reduction in acoustic power at each individual component frequency. However, the most significant reI~ ductions occur within the higher Ifrequency range from 10 kHz to 8 )(M-0.4 ~ 63 kHz. At 32% impingement, a 3 140 shift in spectrum towards the !?Q i g ., a1 • 'le 8 higher frequencies was noted; the • ii • ii 130 acoustic power in the lower fre• ~ ~;: ~ ~:E~i\:° quencies slightly decreases, • 16% IMP• .., ~ whereas that in the higher freI > 120 ii ~ I 50 100~ quencies slightly increases. 2 10 20 FREQUENCY er In Figure 9, the 1/3 octave .., 3' . band power spectra for nozzle Er 150 arrangement II are given for 0 x/d = 0.4 and 0.6. Discrete sound XAl•0.6 I z emissions at 25 kHz are seen at CD 140 peak and/or minimum acoustic power ee 8 ; : ! e • for both x/d values. This discrete i e~ emission corresponds to a Strouhal - ••12~ MAIN JET Al.ONE P..,-150 llof'. number of 0.58 based on main jet •20¾ IMP. MIN. POWER g' exit diameter and velocity. The 120 2 5 I 10 20 50 100kHl maximum jump in 1/3 octave band FREQUENCY power level is nearly 8 dB. The NOZZLE ARRANGEMENT I Fln,rf50PSIG occurrence of this discrete sound emission is also accompanied by a FIG. 9 1/3 OCTAVE POI/ER SPECTRA. slight increase in acoustic power level at higher frequencies than 25 kHz. Since the conditions at which the discrete emission occurred corre~ponded exactly to the operating conditions where the trend of variation in the total acoustic power deviated from the usual pattern (see Fig. 5}, therefore, it seems plausible that this discrete emission is responsible for the high level of the acoustic power radiation by the interacting jet flows. However, if this discrete emission was in reality confined only to a small solid angle, its integrated contribution to the total acoustic power may not be dominant. By cross-examining the spectral data, it was found that this discrete peak appeared at all eight measuring stations in sound pressure spectra. The maximum jump in sound pressure spectra occurred at 45° azimuth angle was 8 dB and even at 120° azimuth angle,i.e., upstream of the jet exit,it was

. ..

•

.

Q

...J

. ..

c(

0

. 0

•

D

I

0

n

180/DOSANJH AND YU

still 4 dB. It could therefore be concluded that this discrete sound emission may be chiefly responsible for the abnormally high level of the noise emitted by the interacting jet flows at x/d = 0.4 and 0.6 with nozzle arrangement II. Shadowgraphic Investigation. A sequence of typical shadowgraphs, showing the development of shock structure and radiated sound field for nozzle arrangement I operated at x/d = 0.4, is reproduced in Figure 10. The typical development and progression of the shock fronts with percent impingement is sketched and discussed below. (1) At zero percent impingement, there exists only one welldefined shock cell labelled I; two additional shock cells appearing downstream are quite weak and not well formed. (2) As the impingement ratio increased to 4%, the length of the reflected shocks and diameter of the Mach disc changedand new shock system, labelled II, emerged downstream of the original shock system. In most cases the emergence of the new shock structure II corresponded to the percent impingement conditions where the total acoustic power emitted by the interacting jets peaked slightly. (3) As percent impingement increased, the new shock I ) - ~ - ~ - ~-- < structure II moved downstream relative to the original shock structure I which receded upstream. (4) Even2 ) ~ - - ~-- ( - - ~ ~ tually, an approximately equal spac~ ing was established between the new ~ shock structure II and the original ~ shock structure I. This condition generally corresponds to the minimum total acoustic power emission. Similar observations were also reported by Dosanjh and Montegani 16 where a converging main jet was used. (5) FU:711 DIRECTION Further increase in percent impingement caused the emerged shocks II to move continuously downstream towards the next original shock structure I, until finally 1 at 32% impingement as shown in (6), the shock systems I and II almost coincide again. The radiated sound field revelaed two interesting features: (1) from 0% impingement to the condition of minimum total acoustic power the apparent strength of both directional and spherical waves became progressively weaker;(2} for greater percent impingement, the apparent strength of spherical waves increased. If the intensity of the projected wave image is assumed to be a reasonable guide to acoustic intensity, the initial decrease in the total acoustic power of the interacting jet flows would be due to the weakening of the strength of sources of both the directional and spherical waves . Furthermore the subsequent increase in the total acoustic power (for percent impingement condition higher than that for minimum total acoustic power} would be attributable to the shock-end sources of spherical waves. Since the spherical waves appeared to be non-directional, the corresponding sound field would also be non-directional,which agrees with the observed change from the directional to less directional distribution at higher percent impingement reported earlier (Fig. 6).

3)-- 1 .3. For D/2y < 1.25 the interacting jet flows appeared stable as the shocks were well defined and spreading of the jet flow was normal and a noise reduction in the main jet flow was achieved by using a radially impinging jet flow. This observation qualitatively suggests the importance of radial impingement 15,~~-----------~ location of the noise emission from interacting jet flows. However, a more thorough investigation by using a number of impinging jet nozzles with different annular exit diameters and width or a single impingei 1.2 ment jet nozzle with variable : annular nozzle exit diameter NOZZLE AR~taMENT I "'~ I.I and width is needed in order to establish a more concrete basis for the evaluations of I.OQO~-Q~2~~Cl4-~0.6 -~0.8---'-1Jl---'-1.2---'1~ the effect of radial impingement location on the resulting sound FIG. 12 VARIATION OF D/2Y WITH X/d. field of the interacting jet flows. Effect of Main Jet flow Mach Number: Attempts were made to correlate the acoustical results obtained in this investigation with those reported by Dosanjh and Montegani 16 in a similar investigation using underexpanded axisymmetric converging main jet flows. In nozzle arrangement I of this investigation, the total acoustic power emitted by the interacting jet flows showed an· almost immediate decrease, with the addition of impinging jet flow, for ·all x/d > 0.4. In reference 16, the same trend in total acoustic power was observed. However, the decrease occurred only at axial impingement locations x/d > 1;2. The corresponding centerline flow Mach number at x/d = 1.2 for the main jet flow from a converging choked nozzle used in reference 16 was calculated to be 2.9, and the centerline Mach number at x/d = 0.4 of the main jet flow from a conical convergent-divergent nozzle used in the present investigation was estimated to be approximately 2.8. It may therefore be interesting to note that the noise emitted by both supersonic jet flows was reduced with the addition of impinging jet flow if the axial impingement location was such that the local main jet centerline Mach number was equal to or greater than 2.8 or so. Whether or not this experimental observation points towards any basic acoustic phenomenon can be established only by additional investigations.

UNDEREXPANDED JET FLOWS USING RADIAL IMPINGEMENT/187

IV.

CONCLUSIONS For Main Jet Alone it is concluded that:

(1) The rate of increase of the total acoustic power emitted by a supersonic jet flow issuing from a conical convergent-divergent nozzle with the operating total pressure was minimum near the nozzle design total pressure. (2) With main jet operating total pressure PrM > 140 psig, the total acoustic power PWL emitted by the main jet flow increased linearly. This seems to be related to the reappearance of the Mach disc in the underexpanded jet flows. The transition in the slope of PWL with PTM appears to be similar to the transition from U8 law to U3 law. It 1s speculated that this transition is related to some flow characteristics other than the jet exit velocity.

For Interacting Jet Flows it is concluded that: (1) The noise emitted by a supersonic jet flow can be reduced by using radial annular jet flow impingement. (2) The addition and increase of impinging jet flow caused an almost ill1llediate decrease in noi'se emitted by the combined interacting jet flows for almost all the operating conditions investigated. The minimum total acoustic power level was 2 dB lower than that of the main jet operated at the same condition. (3) In arrangement II, under certain operating conditions the emission of intense, acoustic wavefronts of a single discrete frequency resulted in a high level of noise radiated by the interacting jet flows. It is speculated that the resonance of the cavity between the jet flow boundaries and housing of the nozzles is responsible for inducing such discrete emission. (4) Correlation between the acoustical results of the present investigation and those observed with underexpanded axisynmetric jet flow issuing from a converging nozzle 16 indicated that the noise from high speed jet flow could possibly be reduced with the addition of radially impinging jet flow if the centerline Mach number of the main jet at the location of axial impingement is equal to or greater than approximately 2.8.

REFERENCES Lighthill, M. J. On Sound Generated Aerodynamically. I- General Theory. Proc. Roy. Soc. A, Vol. 211, 1952 . 2. Lighthill, M. J. On Sound Generated Aerodynamically. II- Turbulence as a Source of Sound. Proc. Roy. Soc. A, Vol. 222, 1954. 3. Ribner, H. S. The Generation of Sound by Turbulent Jets. Advances in Applied Mechanics, Vol. 8, Academic Press, New York, 1964. 4. Ffowcs-Williams, J . E. The Noise From Turbulence Convected at High Speed. Proc. Roy. Soc. A, Vol. 255, 1963. 5. Ffowcs-Williams, J. E. and Maidanik, G., The Mach Wave Field Radiated by Supersonic Turbulent Shear Flows. J. Fluid Mech., Vol. 21, Part 4, 1965. 1.

188/DOSANJH AND YU

6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Phillips, 0. M. On the Generation of Sound by Supersonic Turbulent Shear Layers. J. Fluid Mech., Vol. 9, Part 1, 1960. Ollerhead, J. 8., Some Shadowgraph Experiments With a Cold Supersonic Jet. Wyle Research Report WR66-44, October, 1966. Ollerhead, J. 8. On the Prediction of the Near Field Noise of Supersonic Jets. NASA CR-857, 1967. Franklin, R. E. Noise Measurements on Cold Jets Using ConvergentDivergent Nozzles. Aeronautical Quarterly, Vol. 8, 1957. Ribner, H. S. Acoustic Energy Flux From Shock-Turbulence Interaction. UTIAS Rep. No. 108, July, 1967. Lighthill, M. J. On the Energy Scattered From the Interaction of Turbulence With Sound or Shock Waves. Proc. Camb. Phil. Soc. Vol. 49, 1953. Hollingsworth, M.A., Richards, E. J. On the Sound Generated by the Interaction of a Vortex and a Shock Wave. ARC 18257 FM2371, 1956. Dosanjh, D. S. and Weeks, T. M. Interaction of a Starting Vortex as Well as a Vortex Street With a Traveling Shock Wave. AIAA Journal, Vol. 3, No. 2, 1965. Powell, A. On the Mechanism of Choked Jet Noise. Proc. Phys. Soc. 8, Vol. 66, 1953. Dosanjh, D. S. and Sheeran, W. J. Experiments on Two-Dimensional Transversely Impinging Jets. AIAA Journal, February, 1963. Dosanjh, D. S. and Montegani, F. J. Reduction of Noise From Underexpanded Axisymmetric Jet Flows Using Radial Jet Flow Impingement. AIAA Paper No. 68-81. Yu, J.C. Experimental Investigation of Noise From Interacting Axisyrrmetric Supersonic Jet Flows. Master's Thesis, Syracuse University, June, 1968. Lowson, M. V., and Ollerhead, J . 8. Shadowgraph Visuijlization of Jet Noise. Wyle Laboratories Research Staff, Huntsville, Alabama. Abstract listed in JASA, Vol. 41, No. 6, p. 1610, June, 1967.

THE RESPONSE OF A SIMPLE PANEL TO THE PSEUDO-SOUND FIELD OF A JET L. Maestrello, M. R. Gedge and A. R. F. Reddaway The Boeing Company Seattle, Washington SUMMARY Prediction techniques are applied to a typical aircraft panel of size 7 x 12 x 0.080 in. mounted along, and just outside of the wake of a model jet. From measurements made, a functional representation of the pseudo-sound wall pressure correlation is obtained and is used to predict the response characteristics of the panel. The predicted mean square response is in fair agreement with the measured values, but the predicted displacement spectra are somewhat erroneous. The upper frequency limit of the finite element technique is restricted by the number of elements in the grid system, above which response predictions incur ever increasing error in both frequency and amplitude. However, at these higher mode numbers the continuum technique becomes increasingly more accurate due to the decreasing dependence of modal frequency and shape on the panel edge conditions. NOTATION a

omn wmn plate model damping

a, b

length of panel sides

D

jet nozzle diameter

E

Young's modulus

f

frequency f = w/2n

g

acceleration due to gravity

m,n

mode number

mn

0

mean square pressure

P(w)

power spectrum of the pressure fluctuation

P(~,n;iw)

cross power spectral density of the pressure field

q

dynamic pressure

R(~,n;t)

normalized space time correlation of the pressure fluctuations mean convection velocity of the pressure fluctuations

AFOSR-UTIAS SYMFOSIUM ON AERODYNAMIC NOISE, TORONTO, 20-21 May, 1968

19O/MAESTRELLO et al.

u

jet exit velocity

X

distance along the plate from jet exit plane

x,y ;x' ,y'

coordinates of points on the panel

0

mean square displacement Y(w)

power spectrum of panel displacement

z

coordinate perpendicular to x,y plane

M

surface density

0.

decay parameter

0 mn

modal damping ratio= tf/2f mn

n

spatial separation across the panel normal to the flow spatial separation along the panel in the flow direction

\/

Poisson's ratio

T

time delay

w

modal frequency of panel

w

jet characteristic frequency

w

radial frequency

[H*(iw)]

complex conjugate of admittance matrix

[-A-]

diagonal matrix of elemental areas

[H(iw)]T

transpose of admittance matrix

[P(iw)]

matrix of the cross-power spectral density of the pressure field.

mn 0

1.

INTRODUCTION

The study of structure excited by the pseudo-sound pressure field of a jet is of importance in aircraft design since fatigue can be induced when the power plant is mounted adjacent to structural members; in addition, the vibration of the structure contributes to the sound level in the interior. It is the purpose of this paper to present a method for predicting the response of a simple panel to this excitation . Two approaches are used, namely, a continuum method and a finite element

RESPONSE OF SIMPLE PANEL TO JET/191

method. The emphasis is on the physical explanation and on comparison between predicted values from the two approaches and experimental measurements. Past work has shown that the finite element technique is at the moment, only practical for the lowest modes of vibration of complex structures, while the continuum method is practical for all modes of a simple structure. The finite element method used in this paper was developed by Fuller and Newson (Ref. 1) who computed the response of a complex beam to random excitation. Jacobs and Lagerquist (Ref. 2) extended the method to two dimensions and determined the displacement spectral density of a panel subject to a turbulent boundary layer. The continuum method has been used by several investigators, including Wilby (Ref. 3), Maestrello (Ref. 4 and 5), Strawderman (Ref. 6), el Baroudi (Ref. 7), White (Ref. 8), Lambert and Tack (Ref. 9) and Lyon (Ref. 10). Both methods have shown some degree of correlation with measurements, for turbulent boundary layer excited structures. Up to the present time, most of the interest in the study of the random excitation of structures has been centered on the response of panels to turbulent boundary layer and acoustic pressure fields; however, Trubert (Ref. 11) has investigated the excitation of a cantilevered beam by pseudo-sound. Also, Clarkson and Ford (Ref. 12) have measured the response of a multiple panel structure to jet noise. Extensive near field measurements have been made by MolloChristensen, whose latest observations are reported in Ref. 13 where he proposes a model of the source distribution along the jet. Hibner in Ref. 14 and in earlier papers, suggested an alternative formalism of the Lighthill integrand, which he expresses in terms of the pseudo-sound pressure fluctuations. Ffowcs-Williams (Ref. 15) attempts to evaluate the pseudo-sound pressure and suggests an approximate relationship between the near and far pressure fields. 2.

MEASUREMENTS

The wall pressure fluctuations were measured on a rigid wall using flush-mounted pressure transducers. It is assumed that there is no interaction between the panel and the fluid; therefore, the pressure measured at the rigid wall is assumed to be the same as that over the flexible panel . The pressure measurements were taken with two Bruel and Kjaer type 4136, 0,25" diameter transducers, for flow velocities of 824 and 550 fps, upstream and downstream of X/D 0 = 2 and 4. A simple aluminum panel (12" x 7" x .080") was mounted in a rigid steel frame at an angle 8 degrees to the jet axis just outside of the wake (Figure 1). The panel displacements were measured using two Photocon capacitance probes mounted behind the panel on a traversing mechanism attached to the rigid frame. Both cross correlations and power spectra of the wall pressure and displacent fluctuations were measured. 3.

PROPERTIES OF THE PRESSURE FIELD

The pseudo-sound field, which dominates within and near to the wake of the jet, consists of turbulent pressure fluctuations which do not radiate sound (the acoustic field present in this region is of a

192/MAESTRELLO et al.

negligible intensity) . It exhibits the characteristics of convected turbulence in the flow direction and cross-correlation decay in space and time. However, no convective features are apparent in the lateral direction. The pressure field is not homogeneous, but it is assumed to be stationary and ergodic in that the panel loading is determined from the measured cross-power spectral densities and cross-correlations which are both time-averaged functions. Measurement indicates that the pressure field changes with the increase of X/D 0 , and for the present case where the panel length is much greater than jet nozzle diameter there is a noticeable variation in the mean square pressure along the panel.

4.

MODEL OF WALL PRESSURE FLUCTUATIONS

The characteristics of the pressure power spectrum and the crosscorrelation are given in Figures 2 and 3. A function which approximates the properties measured is of the form: -a1 It I -a 2 Is I . -a 3 In I ( s ) ( l) R(s,n;t) = e e e cosw 0 t - U C

This model of the cross-correlation fits the measurements made upstream and downstream of the point X/D 0 = 4. The model exhibits spatial and temporal decay and convection in the flow direction. The convection velocity is estimated from the correlogram by taking an average value of s/t at the peaks. The power spectrum is obtained by taking the Fourier transform of the autocorrelation,

+ (w 0

-

2 2 2 w) ][a 1 + (w + w) ] 0

(2)

The comparison between model and measurements is shown in Figures 2 and 3 . The power spectra measured at various points along the jet stream indicate that its shape and magnitude varies with the distance downstream, Fig . 2. This can be explained by the fact that the panel experiences the pressure field immediately adjacent to it, which changes as the jet stream develops . The peak frequency decreases from the jet exit with increasing distance downstream. This effect is also reflected in a variation in Uc, a, and p2' In the region where the model is constructed, these parameters vary slowly over the correlation area, and so they have been assumed constant; however, much more rapid changes in these parameters are encountered at smaller X/D 0 • Table l shows the magnitude of the variation in the model parameters with U0 = 550 and 824 ft/sec and X/D0 = 2 and 4. The constants listed in the table are approximate. The above measured convection velocity ratios of the pressure field are of similar magnitude to the values obtained from velocity me_a surement made by previous investigators in the region of the jet with hotwire anemometers (see Fisher and Davies, Ref. 16, Chu, Ref. 17 and Wills, Ref . 18. This would seem to indicate that the properties of the

RESPONSE OF SIMPLE PANEL TO JET/193 turbulence within the wake are still apparent at the boundary. T ~ ratio of root mean square pressure to jet exit dynamic pressure 11/p'Z/q is lower than that for a turbulent boundary layer; this is to be expected, since the jet flow is not constrained to act upon the panel. The power spectrum, Fig. 2, downstream of X/D 0 > 2.5 collapses onto a non-dimensionalized curve using the local Strouhal number of D0 f/U 0 ~ (X/Xo + 1)3 obtained from continuity considerations along the jet axis. The model fits the power spectrum accurately at the higher frequencies above the peak, but at the peak and at lower frequencies the model deviates from the measured. At distance X/D 0 < 2.5 the power spectrum is influenced to a greater extent by the induced flow between panel and jet stream. Due to the nature of pseudo-sound in the region, the higher frequencies are predominant and this, combined with the lower frequency contribution from the induced flow, results in a broader spectrum than at stations downstream. From Fig. 2 the peak amplitude of the power spectra corresponds to Strouhal number of about 1 . 4 which gives 2,rU WO=

D

1.4

0

0

(x./x0 +

1) 3

( 3)

The cross power spectral density P(~,n;iw) of the pseudo-sound pressure field is obtained from the cross correlation function, Eq. 1, P ( ~;n;iw ) = 2 1,r

J"" R(~;n;, )e -iw1: d1: _o:,

= CP ( ~,n;w ) -iQ ( ~,n;w) p (4)

where the co-spectral density is : CP(~,n;w) = P(w) e

-a2l~I

and the quadrature spectral density is: Q(~,n;w) p

5,

STRUCTURAL RESPONSE

The assessment of ·the vibration response of simple panels to a pseudo-sound pressure field in terms of modal shape, mean square displacement, power spectrum, and correlation is considered by using two approaches : a) continuum method, and b) finite element method. The continuum method used in this paper is the same approach as that used by Maestrello (Refs. 4 and 5) for the response of a simple panel excited by a turbulent boundary layer. This method has been used for a large number of modes; however, it has been restricted to simple panels. The finite element approach has been used for the vibration analysis of a panel response to turbulent boundary layer, by Jacobs and Lagerquist (Ref. 2) and has had considerable success in simple panel prediction with the advantage of being easily applicable

194/MAESTRELL0 et al.

to complex structures; however, it has limitations in resolving the higher order modes. The finite element technique is used in the lower frequency response analysis due to its superior definition of modal frequency and shape while the continuum method, which in this part of the paper assumes simply supported boundary conditions, will inherently be more accurate for the higher modes. Continuum Theory. Since the wall pressure correlation in the present case is of a relatively simple form, a closed form of the solution for the response was obtained. It was assumed that the panel damping was small, boundaries were simply supported, cross modal effects were negligible, and also that the modes are orthogonal. Lyon (Ref. 10) and Dyer (Ref. 19) derived the following expression for the cross correlation of the panel displacement.

LL t

(Y(x,y, t)Y*(x' ,y', t')) •

t'

dt 0

dt~ [

a

a

b

dx 0 [

dy 0 [

b

dx~[ dy~

(5)

g(x,y,tlx 0 ,y 0 ,t 0 )g*(x:y:t'lx',y',t')(f(x ,y 0 ,t 0 )f*(x',y',t')) 0 0 0 0 0 0 0 where the forcing function for the jet pseudo-sound field is given by Eq . 1: p2 e-a1lto-t~1-a2lxo-x~1-a3IY0-y~I

------------ = f(x y t )f*(x' y' t')

o'o'o

o'o'o

For lightly-damped systems, the impulse response functions have the form:

(

Io

g x,y,t x ,y ,t

o

) ~ o

cj,mn(x,y)cj,mn(xo,yo)

a:

---------

m,n

where U(t-t ) = l when t 0

and U(t-t ) = 0 when t 0

wmnM

0

0

>


1). The sound pressure level at the liner and thus the liner resistance (fig. 7) decreases down the duct. This effect could be handled by a new determination for the Bj of equation (10) at several locations along the duct. After the sound pressure level at the liner has dropped say 2 dB the characteristic solutions could be refitted to the remaining pressure wave (not necessarily a plane wave). This new solution could be used for a distance and then the refitting be repeated until the end of the duct is reached. Approximate solutions could also be devised. The extremes of the sound power levei at the liner, for instance, could be used in an attempt to bracket the exact solution. The initial (duct entrance) sound pressure level was used in obtaining the theoretical curve (solid curve) of figure 8(b). 5. CONCWSIONS A theory that describes the propagation and attenuation of an

24O/RICE initially plane traveling pressure wave in a circular duct with an acoustically soft wall has been presented. The first ten characteristic function solutions were used in a Fourier-Bessel series to fit the plane traveling wave at the lined duct entrance. The results of the analysis may be summarized as follows. l. For a duct diameter to wavelength ratio greater than one the initial plane wave '\ffiS found to beam toward the duct axis. This results in a redistribution of the sound power within the duct. The sound pressure level at the wall liner, where acoustic energy must be absorbed, can be greatly reduced, while the sound power level is affected only slightly. 2. The theoretical sound power attenuation was found to agree well with experimental data. The data was taken with a cylindrical duct, lined with a perforated plate material, mounted on the inlet of a J-65 engine. The experimental suppressor was designed on the basis of an approximate theory valid for hard walls. The results of the present analysis show the reason that the suppressor design failed to provide high noise reduction. 3. For a given duct length to diameter ratio and duct diameter to wave length ratio an absolute maximum sound power attenuation was found in the liner impedance plane. This maximum was always found to be at negative wall reactance. With increasing duct diameter to wavelength ratio the maximum attenuation point was found to move to larger liner resistance arid more negative liner reactance. The maximum sound power attenuation was found to be nearly proportional to L/D and to have a strong frequency dependence through the ratio of duct diameter to wavelength. 4. The region in the wall impedance plane over which a given sound power attenuation can be obtained increases approximately in proportion to L/D. 6. APPENDIX

Calculation of the Bessel Function with Complex ArguI11ent. The calculation of the Bessel function with complex argument was done in a computer program subroutine. The following calculation methods were used. · If R::; 10 or if R ~ (l + (20/~))n the infinite series definition (ref. 5) of the Bessel :function was used as:

_'\' (-l)k(~)2k+n

L

or

k!(k + n)!

k=O

(26).

~os{2k + n)0 + i sin(2k + n)~

ATTENUATION OF SOUND IN SOFT-WALLED CIRCULAR DUCTS/241 If R > 10 and R > (1 + (20/~))n, the following asymptotic expansion {ref. 5) was used:

where (28)

E 00

= 1 +

k=l

(-l)kSiik-1 {2k)!(8Rei8 )

00

~

=

LJ -(

(-1)

2k

k-1

s4k_ 3 2-k---1-)-~-(8_R_e_i_ f 8 ..,)z""k__...

(29)

k=l

and

SJ= (4n2 - 12)(4n2 - 32)(4n2 - 52) • . • (4n2 - j2) The series of equation (29) were terminated in two ways: when the modulus of the kth _term of Un{Rei0) exceeded the modulus of the kth term of Vn(Rei 8 )i or when the modulus of the kth term cf either was less than 10- o. Rapid convergence occurs in equation (26) for R > n. Both equations (26) and (27) were tested over wide ranges of R, e, and n. For large n the dividing line between the two methods is R = (1 + (20/~))n. If R < 10, equation (26) converges more rapidly for any n. Double precision arithmetic was used in all cases. Calculation of Complex Eigenvalues. The complex eigenvalues must be determined from the solution of equation (8) {derived in the text and repeated here):

_f_ - l - i~Jo(aj) p 0 C~ - ~ - ajJ1(aj)

(8)

where again: ( 6)

The method of reference 4 was used in the solution of equation (8) for large wall impedance.

242/RICE

Let

and

Using equation (6), substituting equation (30) into equation (8), and then differentiating equation (8) with respect to e, there results: (31) Equation (31) is a first-order nonlinear differential equation which can be solved for F in an infinite series solution in e.

at

,"';e0b:~: con;::o•:)vhich must be a}pplied are:

( 32) is the j-th root of J 1 (Rj) = 0

and

Rj

or Rj

= o, 3.8317, 7.0156, etc. for For small wall impedance let

j

= 1,

2, 3, etc.

e = !E

(33)

Substitution of equation (33) into equation (31) yields : (1 + f2F) dF + F = 0

(34)

df

The boundary conditions are:

at

f = 0

0,1 = 0

(all

is the j-th root of

( 35)

= 2.4048, 5.5201, 8.6437, etc. for j = 1, 2, 3, etc. For every mode there is a region in the impedance plane where the series solutions of both equation (31) and equation (34) diverge (at least on the computer using double precision arithmetic). This region is around the branch line. The branch line is defined here as the curve in the liner impedance plane (t/~, x/~) on which two solutions to equation (8) have the same R but different 0(Rj = Hit but ej # 0k). The critical values of Rj on the branch line are 3.1962, 6.3064, • • • or: or

Rj

(36) In this critical impedance region the method of reference e for solving nonlinear equations was applied directly to equation (8).

ATTENUATION OF SOUND IN SOFT-WALLED CIRCULAR DUCTS/243

REFERENCES

l. Morse, P. M. Vibration and Sound. McGraw-Hill Book Co., Inc. 1948 ( 2nd ed. ) • 2. Morse, P. M. The Transmission of Sound Inside Pipes. J. Acoust. Soc. Am. 11, 205 (1939). 3. Molloy, C. T7" and Honigman, E. Attenuation of Sound in Lined Circular Ducts. J . Acoust. Soc. Am. 1§.., 267 (1945). 4. Fisher, E. Attenuation of Sound in Circular Ducts. J. Acoust. Soc. Am • .!1., 121 ( 1945). 5. Hildebrand, F. B. Advanced Calculus for Engineers. PrenticeHall, Inc, 1949. 6. Morfey, C. L. Rotating Pressure Patterns in Ducts - Their Generation and Transmission. J. Sound Vibration l, 60 (1964). 7. :Ehillips, B. Effects of High-Wave Amplitude and Mean Flow on a Helmholtz Resonator. NASA TM X-1582, 1968 •. 8. Marquardt, D. W. An Algorithm for least-Squares Estimation of Nonlinear Parameters. Soc. Ind. Appl. Math • .!!, 431 (1963). 9. Smith, L. J., Acker L. W. and Feiler, C. E. Sound Measurements on a Full-Scale Jet-Engine Inlet-Noise-Suppressor Cowling. Proposed NASA TN.

244/RICE

- - Present solution - - - - Ref: 1 -30dB

1.8 1.6

1.4 1.2 ,e, .; V

C

1.0

-S!

·;;;

f ;;;

.8

3::

.6

-1.2

-1. 0

-. 8

Wall reactance, x

Figure 1. Sound power attenuation contours for Tl • 1, UD • 3.

ATTENUATION OF SOUND IN SOFT-WALLED CIRCULAR DUCTS/245

JOO 8)

60

T

'1)

~e -'

a:,

~

3

20

·2

::,

8. C

~::, .,C

10

8

::

.,"'

6

,::, C

4

~

i

::,

LIO I 2 3

5:

E ::, E

·;;

5

2

i

I .I

.2

Figure 2.

.4

. 6 .8 I 2 'Frequency parameter .. 'IJ

4

6

8

Maximum possible sound power attenuation-frequency dependence.

10

8 6

1) .

5

4

2 ,e,

.; V C

~

·;;;

e

.; .8 ;;:: .6 .4

Constant LID 'IJ

.2

.l

Figure 3.

.4

.6

.8 l

Wall reactance. -x

4

6

8 10

Locus of maximum sound po,ver attenuation in the wall impedance plane.

246/RICE 6

dB

2 -------...-10

,,,

,,•"2000 Hz .;

< -2 u

C

j

1

Frequency parameter, 11 Figure Slbl. Sound power attenuation contours at resistance of maximum attenuation tfig. 31 and LID • 5.

Sound power attenuations (-dB) 11 QI 1 ILM ~l to 3L~ a1 B9 5LN ~2 ~8

I\)

.;:-

w

LID

4

'11

---10

Or

--- 1 ----0.1

x•O

-I

>< .,. u

C:

.!!!

~

-2

C:

-3

.,e

e

a

-c,

.,·

""

----- - ---------

I I I I

.7

1

I

1. 5

I

I

2

I

4 111

3

LID• 3 . 15

I

•2

I

.3

I

.4

I

.5

I

5

I I I I I .7

1

I I I I I

6 7 8 9 10

I

1.5

I

2

I

15

I

3

I

20

I

4

115

. 02

. 01....__ _. _ _ _ _ ~ - - ~ - - ~ - - ~ .8 1.0 .6 .4 •2 0 Radial position, r/r w

Figure 6. Radial pressure profiles at several duct lengths.

o:>

--~

H

~

1. 6

C:

., :::;

~

,,,,.

,e,

~

.g

--~

/ ,,,,. ,,

,,

1.8

All curves at 4>• 1.6,

~-------->,-~-------LID• 0

---- X 4>

2. 0

,,

/.

Figure 7. Resistance and reactance of a perforated plate liner as a function of frequency. Calculations by method of reference 7. Steady flow-by velocity 350 fps, air 40° F. Liner open area ratio 0. 08, thickness 0. 02 inch, hole diameter 0. 05 inch, back cavity depth 1 inch. 11 1 and 11 5 scales give 11 for L • 30 inches and LID• 1 and 5.

- .... I

4 140,' I I

''

/

'

~ '

I

,;--

'

/ / /

2

1 a,

'i"

c-

0

~ ::,

~_ -::::;

, m/'120 I / -- ...._'-. .......... I . -. . , -- ...._,

/ //

':[

........

---.:

60

Theoretical attenuations at several sound pressure levels

~'/

dB level - - - 150 - - 140 - - - 130

I'

► 8

I

I

8

\

0 (a)

~

~ 20

., [

=:;:,

'!ii

c-

I

0

~

0

'O C

, -Experimental

::,

0 V'I

4

c{'

0

~

'!ii ~

I

'O

3 I-

21-

/ 0

I

0 11-~ ,, ,,, ,,

ol--1 600

800

/

/

/

I

1000

/

I

I

I

I

\

:,

I

,- 1 'o

Note: e = 500 ~=JOO

//

:E GI lQ

...

1E

~

E :::>

z

Region Me< 1

~

5

..c

IJ

GI

o,40 C

~

~ 30 8

GI

'o ~ 'o~

RegionM > 1 e

2

Upstream Moch Number, M1

2

> ·.;:

-I


6

..c

3

~

2 1.6

z

IJ

~~1.1 1.4 2 3 6

20

0 · 20 20 40 60 80 100 Inclination of Upstream Entropy Wove, 6 -degrees FIGURE 3b. VARIATION OF EFFECTIVE MACH NUMBER, NORMAL SHOCK CASE

I

() -----

50----------,

0 · 20 20 40 60 80 100 Entropy Wove Inclination, 6 -degrees

FIGURE 3c . EFFECTIVE MACH NUMBER, OBLIQUE SHOCK CASE, WEDGE HALF-ANGLE (e - /3) = 12°

5.0

...-::---..1,

~1 +1.0 1:4

'-!./

-

-

70

1:4

E

.

Entropy Wave Inclination, 6 - degrees

~-----1

70

£.

...:>.,,

60

-

1:4

...

-

,~8

80 89

5-30

.,, QI

C

w E

::>-

-IU

ta9

QI

0

Cl

FIGURE 4o . GENERA TED PRESSURE DISTURBANCE, NORMAL SHOCK CASE

-

0

15 20 z Upstream Moch Number, M1 ~

0

0 1.0 G,

.

~

-----15-30 E 00 e

0

QI

-1.0

•

:>

]... .2...

~

.,,

0 - -,2 ' deg.~

"'O

I

2 +O 5

.2

6

.

+ QI1 . 2 , ~

O0!:-----:!:5,------,1~0:::::=:==;::115======20 Upstream Moch Number, M1

FIGURE 4b . DOWNSTREAM ENTROPY WAVE AMPLITUDE, NORMAL SHOCK CASE

0.5

~ 0.2 >u

-

Entropy Wave Inclination, 6 - degrees I

~

~

1~~

I~

'---------,89

·.: o. 1' . ~ 0.05

~

0

()

::,; H

:.a: ~

~

()

>-3

H

:.a:

0 .02.____~_ __.__ _.___..__-...J 0 4 8 12, 16 20 Upstream Mach Number, M1

FIGURE 4c. GENERATED VORTICITY, NORMAL SHOCK CASE

0

~

>-3 ::,:

~ ~ ~

t-
O or the streamtube always increases in area through the turbine pod. The turbine work must equal the propeller work Wpin equation (6), making this substitution, equation (6) becomes

AA A~-

__g_

(lt )-

AA' M2 AR. e

\I\ _!_

1-1 ·l

I (10)

This equation relates the area reduction AA due to the flow through the ducted fan to the area increase due to the exhaust gas from the turbine supplying the power to run the fan. If we require that /J.A::,, bA' then it is easily shown that the cycle efficiency vt must be for ( 11 ) The efficiency for the cycle we are using is of course \I\= I - e;Tc. or (11) imposes a condition on the pressure rise through the canpressor. Equation (11) indicates the parameters governing the sonic boan reduction for the scheme described here. High Mach number flight requires an efficient power plant to supply the power to the fan and the higher the allowable turbine blade temperature, the less stringent the

44O/RESLER efficiency requirement. Of course there are other possible schemes, sane of which are better than the one described here to demonstrate the parameters involved. SUMMARY

It has been demonstrated here that there are a class of supersonic configurations that have lift but no sonic boan. Using these principles, the sonic boan due to lift can be alleviated by integrating the engine design with the design of the rest of the aircraft. ACKNOWLEDGMENTS This work has been partially supported by the United : States Air Force Office of Scientific Research wxier contract AF49(638)-1346, and by the National Aeronautics and Space Administration under NGR33-O1O-O57. REFERENCES 1.

Lomax, H. The Wave Drag of Arbitrary Configurations in Linearized Flow as Determined by Areas and Forces in Oblique Planes. NACA RM-A-55A-18, Jan. 1955.

M>I ~

FIGURE 1.

~VES

LINEARIZED BUSEMANN BIPLANE.

+ FIGURE 2.

EQUIVALENT CYLilIDERS ACCORDING TO AREA RULE FOR BUSEMANN BIPLANE.

CONFIGURATIONS WITH NO SONIC BOOM/441

+ FIGURE 3.

BODY WITH THICKNESS, NO SONIC BOOM BUT WAVE DRAG AND EQUIVALENT CYLINDERS FROM GROUND (- Tr/z) •

M>I

-----FIGURE 4.

TWO DIMENSIONAL LIFTING CONFIGURATION WITH NO SONIC BOOM.

0:222znzzzza Asov£ (+ TT/2) FIGURE 5.

EQUIVALENT CYLINDERS ACCORDIOO TO AREA RULE FOR CONFIGURATION IN FIGURE 4.

442/RESLER

FIGURE 6.

CONSTRUCTION OF THREE DIMENSIONAL CONFIGURATION WITH LIFT AND NO SONIC BOOM FROM EQUIVALENT BODY OF REVOLUTION ACCORDING TO AREA RULE.

T

5 FIGURE 7 •

NO THRUST TURBINE CYCLE ON TEMPERATURE ENTROPY DIAGRAM.