N - 0 (THRU) ti 0, * (CO'DE) E '(PAGES) $ d (CATEGORY) (NASA CR OR TMX OR AD NUMBER) NASA CR-857 6 ON THE PREDICTION OF-THE NEAR FIELD NOISE OF SUPERSONIC JETS By J. B. Ollerhead Distribution of this report is provided in the interest of information exchange. Responsibility for the contents resides in the author or organization that prepared it. Issued by Originator as Report No. WR 67-6 Prepared under Contract No. NAS 8-21060 by WLE LABORATORIES Huntsville, Ala. for George 6. Marshall Space Flight Center NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTI price $3.00 SUMMARY The phenomenon of noise generation by supersonic jets is reviewed in a comparison of previous theoretical and experimental investigations. It is shown that three fundamental mechanisms exist, which are defined as turbulence-shear noise, Mach wave radiation, and shock-noise. The significance of each type of noise is evaluated, with reference to the nature of the jet- flow structure and particular attention is paid to the acoustic near field. At the present time there is no general method for the prediction of the near field noise of either subsonic or supersonic jets. An appropriate expression is presented, and a series of experiments proposed, by which its empirical coefficients can be determined. These experi- ments would eventually lead to the establishment of scaling laws, enabling the expression to be used to compute the near field sound pressure contours of any supersonic iet of known configuration. i iii TABLE OF CONTENTS Page Number -SUMMARY iii TABLE OF CONTENTS V LIST OF FIGURES vii LIST OF SYMBOLS xi 1.0 1NTRODUCTION 1 2 .o THE STRUCTURE OF AXISYMMETRIC JET EXHAUSTS 6 2.1 Introduction 6 2.2 Jet Mixing 7 2.3 The Development of a Shock Pattern in Supersonic Flow 12 2.4 Definition of Shock Geometry 14 2.5 Mach Number Contours in Exhaust Flow 17 3 .O GENERATION OF SOUND BY TURBULENT JETS 23 3.1 The Noise of Subsonic Jets 23 3.1.1 Lighthill's Theory 23 3.1.2 Extension of Lighthill's Analysis to the Near Field 27 3.1 .3 Correlation of Theory and Experiment for Subsonic 31 Jet Noise 3.2 The Noise of Supersonic Jets 36 3.2.1 Ffowcs Williams' Extension of Lighthill's Theory to 37 Supersonic Flow 3.2.2 The Near Field of Supersonic Jets 43 3.2.3 Correlation of Theory and Experiment for Supersonic 45 Jet Noise Shock Noise 48 TABLE OF CONTENTS (Continued) Page Number 4 .O EXPERIMENTS TO ESTABLISH METHODS FOR THE PREDICTION 50- OF THE NEAR NOISE FIELD OF SUPERSONIC JETS 5 .O CONCLUDING REMARKS 58 REFERENCES 59 APPENDIX A SUPERSONK JET FLOW EQUATIONS 63 APPENDIX B DERIVATION OF THE SOUND FIELD OF CONVECTED 67 LATERAL QUADRUPOLES IN TERMS OF TOTAL SOUND POWER APPENDIX C INITIAL EXPERIMENTS TO MEASURE THE NEAR NOISE 69 FIELD OF A SUPERSONIC JET Vi a LIST OF FIGURES Page Figure 1 Shadowgraph photograph of the Mach Wave Field of a 73 Supersonic Jet, from Unpublished Work at NASA Langley Research Center. Figure 2 Shock Free Supersonic Flow. 74 Figure 3 Calculated Flow Contours for Constant Density 74 Axisymmetric Jet From Reference 17. Figure 4 Variation of Core Length with Exit Mach Number. 75 (After Eldred eta1 . Reference 17). Figure 5 Variation of !/b with Exit Mach Number (From Eldred 75 eta1 . Reference 17). Figure 6 Axial Velocity Decay for Various Exit Mach Numbers 76 Calculated by Method of Reference 17. Figure 7 Jet Spreading Curve Corresponding to Figure 6. 77 Figure 8 Length of Supersonic Core Versus Exit Mach Number. 78 Figure 9 Development of Shock Patterns. 79 Figure 10 Badly Expanded Supersonic Jet Flow. 80 Figure 11 Development of Shock Pattern with Nozzle Exit Pressure, 81 - Design Mach No. = 2.47. From top to bottom; p dpo - 0.497, 0.747, 1.0, 1.53, 1.98. Figure 12 Width of Primary Cell; Empirical Relationships from Love 82 etal. (Reference 31). Figure 13 Effect of Pressure Ratio on Distance to First Mach Disc or 83 Intersection Point for Ideally Expanded Jet, from Love etal. (Reference 31). Figure 14 Variation of Mach Disc Diameter With Pressure Ratio and 84 Design Mach Number for Ideally Expanded Nozzle, from Love etal. (Reference 31). vii LIST OF FIGURES (Continued) Page Figure 15 Similarity of Radial Velocity Profiles in Jet Mixing Region. 85 - Figure 16 Similarity of Radial Velocity and Temperature Profiles in 86 Subsonic Flow of Rocket Exhaust. After Anderson and Johns (Reference 20) Figure 17 Exponent of Downstream Center1ine Pressure Decay. 87 Figure 18 Exponent of Downstream Centerline Temperature Decay. 87 Figure 19 Calculated Centerline Mach Number Decay 88 Figure 20 Axial Variation of b/rE and Mach Number Profiles for 89 ME = 2.0, t = 5fJet. Figure 21a Relationship Between Cartesian and Polar Coordinates. 90 Figure 21b Near Field Amplification due to x, , x3 Lateral 90 Quadrupoles (k r = 0.25). Figure 22 Overall Jet Sound Power Per Unit Nozzle Area Versus 91 Exhaust Velocity, From Reference 37. Figure 23 Jet Noise Directivity. 92 Figure 24 Power Spectral Density of Jet Noise. 93 Figure 25 Location of Maximum Sound Pressure Level in 1/3 Octave 94 Frequency Bands as Function of Modified Strouhal Number, From Reference 17. Figure 26 Modification of Apparent Spectrum by Near Field Effects. 94 Figure 27 Near Field Noise Pattern of a Jet and a Rocket, SPL in 95 Decibels re: 0.0002 dynes/cms*. Figure 28 Effects of Eddy Convection on Emission Volume and 96 Emission Time Differences (Reference 36). viii LlST OF FIGURES (Continued) Page a Figure 29 Typical Cross-Covariance given by Equation 4.5. 97 Figure 30 Coordinate System for Discrete Source Acoustic Model 97 of Jet Stream. Figure 31 Schematic of Proposed Rig for Near Field Correlation 9% Experiments. ix LIST OF SYMBOLS Only those symbols which are widely used are listed below. Other symbols, or different - meanings to those given below, are used only locally and are defined where they first occur. Roman Symbols a speed of sound radius of laminar core mixing width parameter far field pressure autocovariance frequency, Hertz far field directivity function near field directivity function near field directivity function acoustic intensity wave number = 2 ITA cotrelation length; typical eddy dimension M flow Mach number - M Mach number relative to ambient speed of sound A, eddy convection Mach number P mean static pressure P pressure fluctuation (acoustic pressure) total pressure PT P sound power r radius from jet centerline r displacement of field point from sound source = x y N --- r magnitude of 2 r radial coordinate measured from nozzle center (equation 4.10) xi r. component of along x, axis I r. distance from i-th source to observer (equation 4.10) I turbulent stress correlation tensor Rijke t time t ratio of total temperature to ambient temperature T /T To t retarded time (t - r/ao) T temperature T.. turbulent stress tensor -'J T2 mean square of T.. 'I u, u. velocity fluctuation I U mean velocity (in x-direction parallel to iet axis) v, v. veloc ity fluctuation I V mean ve loc i ty V volume V eddy volume e length of primary cell in shock pattern sound power spectral density X axial distance from iet nozzle X Cartesian is 1 ax X position vector of point in acoustic field cv X axial location of sonic point S X axial location of laminar core tip t Y position vector of point in turbulent flow N xii x Greek Symbols far field directionality factor near field directionality factor Y ratio of specific heats 6.. Kronecker delta 'J A incremental factor (e.g., At, Ar) 4 separation vector 'I mixing width parameter (r - a/b ) e angle to iet axis Mach angle eM x wavelength x moving axis separation vector N area vector normal to 0M direction ASN P density U time var jab I e TI 7" time delay, retarded time increment T turbulent shear stress r polar coordinate, phase angle phase angle radian frequency Subscripts perta ining to eddy convect ion nozzle exit plane conditions far field tensor and vector notation m maximum (iet center1ine values) xiii N near field r pertaining to radius r T total conditions 0 ambient conditions 0.5 at radius specified by U, = 0.5 Um 18 28 Cartesian subscripts. xiv a 1 .o INTRODUCTION The rocket engine has the unfortunate side-effect of being a singularly powerful continuous source of poise. Apart from being an obvious physiological problem, this noise is sufficiently intense to constitute a potential hazard to structural components in the close vicinity of the exhaust stream. For this reason, there is a clear need for both understanding and control of the noise generation process. The noise is aerodynamic in origin, and results from the powerful shearing actions which take place as the high velocity exhaust gases mix with the surrounding atmosphere. Although Lighthill (References 1 and 2) established an analytical description of the fundamentals of aerodynamic noise generation as far back as 1952, a theoretical quantitative evaluation of the noise produced by a jet with known nozzle flow conditions still remains beyond reach, in spite of very con- siderable efforts by many investigators. The primary reason for this is the lack of understanding of the turbulence generation mechanisms in a iet flow. However, by judicious use of available experimental tools, much can and has been done to close the gap between theory and experiment. This report reviews previous work, with particular emphasis on the near-noise field, and indicates maior problem areas which are apparent.