Engineering topics
Publications and source records attributed to Rice, E. J..
Computer Program (written in FORTRAN IV) for design annular acoustic liners for turbofan engines first estimates noise generated by turbofan engine, then permits methodical examination of alternative choices of noise reduction.
The angles of propagation of the wave fronts associated with duct modes are derived for a cylindrical duct with soft walls (acoustic suppressors) and a uniform steady flow. The angle of propagation with respect to the radial coordinate (angle of incidence on the wall) is shown to be a better correlating parameter for the optimum wall impedance of spinning modes than the previously used mode cutoff ratio. Both the angle of incidence upon the duct wall and the propagation angle with respect to the duct axis are required to describe the attenuation of a propagating mode. Using the modal propagation angles, a geometric acoustics approach to suppressor acoustic performance was developed. Results from this approximate method were compared to exact modal propagation calculations to check the accuracy of the approximate method. The results are favorable except in the immediate vicinity of the modal optimum impedance where the approximate method yields about one-half of the exact maximum attenuation.
The main emphasis is upon the propagation angle with respect to the duct axis and its relation to the far-field acoustic radiation pattern. When the steady flow Mach number is accounted for in the duct, the propagation angle in the duct is shown to be coincident with the angle of the principal lobe of far-field radiation obtained using the Wiener-Hopf technique. Different Mach numbers are allowed within the duct and in the external field. For static tests with a steady flow in an inlet but with no external Mach number the far-field radiation pattern is shifted considerably toward the inlet axis when compared to zero Mach number radiation theory. As the external Mach number is increased the noise radiation pattern is shifted away from the inlet axis. The theory is developed using approximations for sound propagation in circular ducts. An exact analysis using Hankel function solutions for the zero Mach number case is given to provide a check of the simpler approximate theory.
The angles of propagation of the wave fronts associated with duct modes are derived for a cylindrical duct with soft walls (acoustic suppressors) and a uniform steady flow. The angle of propagation with respect to the radial coordinate (angle of incidence on the wall) is shown to be a better correlating parameter for the optimum wall impedance of spinning modes than the previously used mode cutoff ratio. Both the angle of incidence upon the duct wall and the propagation angle with respect to the duct axis are required to describe the attenuation of a propagating mode. Using the modal propagation angles, a geometric acoustics approach to suppressor acoustic performance was developed. Results from this approximate method were compared to exact modal propagation calculations to check the accuracy of the approximate method. The results are favorable except in the immediate vicinity of the modal optimum impedance where the approximate method yields about one-half of the exact maximum attenuation.
The angles of propagation for the wave front making up a duct mode are presented with the Mach number in the duct. Approximate equations are derived to provide simple utilitarian expressions. These expressions are valid only near the outer wall which is the most important region since the bulk of the acoustic intensity is located there. Exact solutions using Hankel functions are given in an appendix. These data corroborate the approximate solution accuracy near the outer wall. The axial propagation angle is used to infer information about the far-field radiation pattern. The resultant axial angle of propagation in the duct is shown to agree exactly with the peak of the principal lobe to far-field radiation obtained from formal radiation calculations when the Mach number is uniform everywhere. The obtained solution is extended to cover the case of different Mach numbers inside and outside the duct for which exact calculations have not been available for engine inlet configurations.
The turbofan engine's noise-producing components are discussed in terms of efficient and economical noise reduction techniques that do not penalize the engine performance or weight significantly. Specific topics covered include fan noise, acoustic suppression, jet noise technology, combustor noise, and aircraft noise prediction.
Inlet suppressor far-field directivity suppression was quantitatively compared with that predicted using an approximate linear design and evaluation method based upon mode cutoff ratio. The experimental data was obtained using a series of cylindrical point-reacting inlet liners on a YF102 engine. The theoretical prediction program is based upon simplified sound propagation concepts derived from exact calculations. These indicate that all of the controlling phenomenon can be approximately correlated with mode cutoff ratio which itself is intimately related to the angles of propagation within the duct. The theory-data comparisons are intended to point out possible deficiencies in the approximate theory which may be corrected. After all theoretical refinements are made, then empirical corrections can be applied.
A correlating equation relating the optimum acoustic impedance for the wall lining of a circular duct to the acoustic mode cut-off ratio, is presented. The optimum impedance was correlated with cut-off ratio because the cut-off ratio appears to be the fundamental parameter governing the propagation of sound in the duct. Modes with similar cut-off ratios respond in a similar way to the acoustic liner. The correlation is a semi-empirical expression developed from an empirical modification of an equation originally derived from sound propagation theory in a thin boundary layer. This correlating equation represents a part of a simplified liner design method, based upon modal cut-off ratio, for multimodal noise propagation.
A correlating equation relating the optimum acoustic impedance for the wall lining of a circular duct to the acoustic mode cut-off ratio is presented and compared to exact calculations. The optimum impedance was correlated with cut-off ratio because the cut-off ratio appears to be the fundamental parameter governing the propagation of sound in the duct. Modes with similar cut-off ratios respond in a similar way to the acoustic liner. The correlating equation is useful for the design of suppressors for aircraft engine inlets having a steady mean flow with a boundary layer and spinning mode noise source excitation. The correlation is a semi-empirical expression developed from an empirical modification of an equation originally derived from sound propagation theory in a thin boundary layer. Exact calculations of the optimum wall impedance were made over a wide range of frequency parameters, boundary layer thicknesses and flow Mach numbers to develop and verify the correlation. This correlating equation represents a part of a simplified liner design method, based upon modal cut-off ratio, for multimodal noise propagation.
A comparison is made between approximate equations for far-field acoustic radiation patterns and exact equations for single and multimodal excitations in order to determine the validity range for the approximate approach. It is found that for single-mode cases: (1) the gross behavior of the primary lobes is adequately described by the approximate equations, (2) some error is found for lower and zero radial order modes, and (3) some agreement is yielded between exact and approximate sidelobes, although the approximate equation was not intended to simulate sidelobes. Multimodal approximate equations are compared to exact equations for various distributions of modal power; for all cases excellent agreement is found. For multimodal patterns it is noted that many modes influence the final level and shape of the directivity curve, although the major contributions are from the higher radial order modes.
The length of multiple-pure-tone (MPT) treatment required to reasonably suppress the MPT's produced by a supersonic tip speed fan was defined. Other suppression, broadband, and blade passing frequency, which might be accomplished were also determined. The experimental results are presented in terms of both far-field and duct acoustic data.
The far-field sound radiation theory for a circular duct was studied for both single mode and multimodal inputs. The investigation was intended to develop a method to determine the acoustic power produced by turbofans as a function of mode cut-off ratio. With reasonable simplifying assumptions the single mode radiation pattern was shown to be reducible to a function of mode cut-off ratio only. With modal cut-off ratio as the dominant variable, multimodal radiation patterns can be reduced to a simple explicit expression. This approximate expression provides excellent agreement with an exact calculation of the sound radiation pattern using equal acoustic power per mode.
The far-field sound radiation theory for a circular duct was studied for both single mode and multimodal inputs. The investigation was intended to develop a method to determine the acoustic power produced by turbofans as a function of mode cut-off ratio. This information is essential for the design of acoustic suppressors in engine ducts. With reasonable simplifying assumptions the single mode radiation pattern was shown to be reducible to a function of mode cut-off ratio only (modal indices removed). With modal cut-off ratio as the dominant variable, multimodal radiation patterns can be reduced to a simple explicit expression. This approximate expression provides excellent agreement with an exact calculation of the sound radiation pattern using equal acoustic power per mode. Radiation patterns for cases other than equal modal power are presented using the approximate radiation equation. An approximate expression for the duct termination losses as a function of cut-off ratio is also included.
The purpose of the experimental program reported herein was to define the length of multiple pure tone (MPT) treatment required to reasonably suppress the MPT's produced by a supersonic tip speed fan and also determine what other suppression, broadband, and blade passing frequency (BPF), might be accomplished. The experimental results are presented in terms of both far-field and duct acoustic data. Front quadrant sound power level reduction in the far field is shown to agree with duct measurements over the range of treatment lengths. Detailed one-third octave and narrow band spectra at the maximum forward noise angle are presented. Some detailed analyses of one-third-octave band amplitudes are shown as a function of far-field angle. An approximate spinning mode duct propagation analysis is then introduced which predicts the acoustic suppression by the treatment on the multiple pure tones.
Approximate equations for the far field acoustic radiation patterns in the forward quadrant from a flanged circular duct were compared with exact equations for both single and multimodal excitations. The single mode comparison showed good agreement between the exact and approximate equations for the principal lobes of higher radial order modes. For lower and especially for zero radial order modes, there was some error in the angular location and decibel level of principal lobe peak pressure obtained from the approximate equation. Some agreement of sidelobes was also observed although the approximate equation was not intended to simulate the sidelobes. The multimodal approximate summation equations consisting only of a simple function of directivity angle and an acoustic power biasing function were checked against the exact equations for several distributions of modal power and showed excellent agreement with exact equations for all cases. Although many modes contribute to the final level and shape of the directivity curve, the major contributions appear to come from the higher radial order modes.
Often raised questions in duct sound propagation studies involve the total number of propagating modes, the number of propagating radial modes for a particular spinning lobe number, and the number of modes possible between two given values of cutoff ratio or eigenvalue. These questions can be answered approximately by using the modal distribution function which is the integral of the modal density function for ducts in a manner similar to that previously published for architectural acoustics. The modal density functions are derived for rectangular and circular ducts with a uniform steady flow. Results from this continuous theory are compared to the actual (discrete) modal distributions.
A design package is presented for the specification of acoustic liners for turbofans. An estimate of the noise generation was made based on modifications of existing noise correlations, for which the inputs are basic fan aerodynamic design variables. The method does not predict multiple pure tones. A target attenuation spectrum was calculated which was the difference between the estimated generation spectrum and a flat annoyance-weighted goal attenuated spectrum. The target spectrum was combined with a knowledge of acoustic liner performance as a function of the liner design variables to specify the acoustic design. The liner design method at present is limited to annular duct configurations. The detailed structure of the liner was specified by combining the required impedance (which is a result of the previous step) with a mathematical model relating impedance to the detailed structure. The design procedure was developed for a liner constructed of perforated sheet placed over honeycomb backing cavities. A sample calculation was carried through in order to demonstrate the design procedure, and experimental results presented show good agreement with the calculated results of the method.
Generalized approximate equation for duct-lining sound attenuation can be used for initial acoustic-liner design and analysis.