Impedance of curved ducts
Mathematical solution permits showing that, for circular bends in hardwalled ducts of rectangular cross sections, specific acoustic impedance depends on both frequency and geometry of bend.
Rostafinski, W. A.↗
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Acoustic systems containing curved duct sections
The analysis of waves in bends in acoustical ducting of rectangular cross section was extended to the study of motion near discontinuities. This included determination of the characteristics of the tangential and radial components of the nonpropagating modes. It is established that attenuation of the nonpropagating modes strongly depends on frequency and that, in general, the sharper the bend, the less attenuation may be expected. Evaluation of a bend's impedance and of impedance-generated reflections is also presented in detail.
Rostafinski, W.↗
Nonlinear propagation of a wave packet in a hard-walled circular duct
The method of multiple scales is used to derive a nonlinear Schroedinger equation for the temporal and spatial modulation of the amplitudes and the phases of waves propagating in a hard-walled circular duct. This equation is used to show that monochromatic waves are stable and to determine the amplitude dependance of the cut off frequencies.
Nayfeh, A. H.↗
A comparison of matrix methods for calculating eigenvalues in acoustically lined ducts
Three approximate methods - finite differences, weighted residuals, and finite elements - were used to solve the eigenvalue problem which arises in finding the acoustic modes and propagation constants in an absorptively lined two-dimensional duct without airflow. The matrix equations derived for each of these methods were solved for the eigenvalues corresponding to various values of wall impedance. Two matrix orders, 20 x 20 and 40 x 40, were used. The cases considered included values of wall admittance for which exact eigenvalues were known and for which several nearly equal roots were present. Ten of the lower order eigenvalues obtained from the three approximate methods were compared with solutions calculated from the exact characteristic equation in order to make an assessment of the relative accuracy and reliability of the three methods. The best results were given by the finite element method using a cubic polynomial. Excellent accuracy was consistently obtained, even for nearly equal eigenvalues, by using a 20 x 20 order matrix.
Watson, W.↗
Investigation of two bifurcated-duct inlet systems from Mach 0 to 2.0 over a wide range of angles of attack
A 15.354 percent/scale lightweight fighter type inlet/forebody was tested over a Mach number range of 0 to 2.0. Model configurations consisted of side mounted normal shock and fixed overhead ramp type inlets. Each configuration consisted of two inlets ducted (bifurcated) to supply a single engine face. The normal shock inlet variables included a boundary layer splitter bleed system, alternate boundary layer splitter plates, alternate upper and lower cowl lip shapes, and a blow-in-door (auxiliary inlet) in one lower lip. The only variable of the fixed overhead ramp inlet was the boundary layer bleed flow. Reynolds numbers ranged from 7.6 x 1 million to 19.5 x 1 million/m. Angle of attack ranged from -10 to 35 deg and angle of sideslip from -8 to 8 deg. Test measurements included engine face total pressure recovery, steady state distortion, dynamic distortion, and surface static pressures on the forebody and inlet surfaces.
Latham, E. A.↗
Radiation of cylindrical duct acoustic modes with flow mismatch
Motivated by the problem of Mach number and temperature discontinuity mismatch between the tailpipe and the surrounding medium, and the effect of this flow mismatch on aircraft engine noise, the radiation of spinning turbo-acoustic modes from a round duct is investigated. The model, based on a plug flow exhaust jet, solves the convected wave equations using Fourier transforms, inversion being accomplished via a coupled Wiener-Hopf and Carrier-Koiter technique. It is concluded that the Mach number discontinuity results in a conflict between convection and refraction effects, while the temperature mismatch results in a sharp beaming of sound off to the side.
Savkar, S. D.↗
Jet noise characteristics of unsuppressed duct burning turbofan exhaust system
Recent aero-acoustic tests of model coannular nozzles have shown that less noise is generated if the higher-velocity jet is exhausted from the outer annular passage rather than from the primary nozzle. These findings are of particular significance to a duct-burning turbofan (DBTF) engine being studied for application to an advanced supersonic transport. Unlike conventional turbofan engines that have peak velocities from the primary nozzle, it is possible to design a DBTF engine to have a fan velocity higher than that of the primary flow. Results are presented for a NASA-sponsored model test program that covers a range of fan to primary-area ratios from 0.75 to 1.2, and a range of fan to primary-velocity ratios from 0.4 to 2.8. Correlations are given that relate radiated sound power to fan velocity, fan to primary-velocity ratio, and fan to primary-area ratio. Corresponding exhaust-plume velocity-traverse data are presented which suggest that the observed noise benefits may be due to the more rapid decay of the annular flow because of shear stresses on the inner surface that result from the lower-velocity primary flow.
Packman, A. B.↗
Aero-acoustic performance characteristics of duct burning turbofan exhaust nozzles
A recent experimental investigation has identified the aero/acoustic characteristics of exhaust nozzles for duct heating turbofan engines over a range of simulated flow conditions. Jet noise and performance levels are summarized for a series of coannular nozzles representing both acoustically suppressed and unsuppressed designs operating in a static environment. The basic coannular nozzles were found to provide inherent noise suppression. Multi-element suppressor nozzles provided additional noise suppression, but with appreciable thrust loss. The impact of these results on the advanced supersonic transport studies is also presented, indicating potentially large reductions in take-off gross weight or community noise footprints.
Kozlowski, H.↗
Acoustic systems containing curved duct sections
The analysis of waves in bends in acoustical ducting of rectangular cross section is extended to the study of motion near discontinuities. This includes determination of the characteristics of the tangential and radial components of the non-propagating modes. It is established that attenuation of the non-propagating modes strongly depends on frequency and that, in general, the sharper the bend, the less attenuation may be expected. Evaluation of a bend's impedance and of impedance-generated reflections is also presented in detail.
Rostafinski, W.↗
A study of sound transmission in curved duct bends by the Galerkin method
A computational procedure based on the Galerkin method is developed to study the sound transmission and reflection characteristics of circularly curved bends of rectangular ducts. This procedure is adaptable to routine computer calculation. An important component of the computer program consists of a QR iterative algorithm which solves the matrix eigenvalue problem generated by the Galerkin method. The present procedure produced very satisfactory convergent results when applied even to cases where the incident wave has high frequency and high wave mode numbers. Some properties of the Galerkin solution are investigated. Its relationship to the classical solution by the method of separation of variables is discussed.
Tam, C. K. W.↗
An analysis of the generation of subharmonics in aeroengine ducts and methods of their prevention
When the fans of aero-engine ducts go supersonic they often produce radiation at the subharmonics of blade passage frequency known as Multiple Pure Tones. It has been shown that the conventional explanation that these MPTs are created by the shock waves is inadequate. An alternative mechanism based on the concept of 'strong interaction' between the harmonics during resonance is proposed. Expression for the governing equation for such an interaction is derived. The results show an improved agreement with observed data. The analysis has also led to several practical suggestions for the suppression of noise.
Vaidya, P. G.↗
Practical considerations for the design of two-element duct liner noise suppressors
The results of analytical and experimental design studies for two-segment treatment configurations in rectangular ducts with mean flow are presented. The practical significance of the design optimization method, executed at a single frequency for measured modal input, is considered in the light of sensitivity to variations in wall impedance components and source modal content. The results of analytical parametric studies of the effects of frequency and segment length ratio are presented. The importance of designing for a measured modal content and the importance of the order of the liners in providing the multi-element suppression enhancement effects are demonstrated.
Kraft, R. E.↗
Acoustic pulse propagation in a duct with flow
The effect of a mean flow on acoustic pulse propagation in a wind tunnel of rectangular cross-section is considered both experimentally and theoretically. Pulse shapes in the wind tunnel are recorded by microphones located upstream and downstream of a source. A theoretical model of pulse propagation from a point source located in an infinitely-long rectangular duct carrying a uniform flow is considered. The convective wave equation with boundary conditions appropriate to hard walls is solved by using the Laplace transform. For the input pulse shape used in the experiments, the solution is obtained by numerically evaluating the inverse Laplace transform. The results of experiment and theory are seen to be in good agreement.
Cole, J. E., III↗
A wave-envelope technique for wave propagation in non-uniform ducts
The method of variation of parameters is used to analyze wave propagation in variable area, plane ducts with no mean flow. The method has an explicit representation of the fast axial variation of the acoustic modes, and numerical integration is required only for the slower axial variations of the mode amplitudes and phases. Results are presented which demonstrate the numerical advantages of the method. Comparison of the results with those of a small perturbation theory are given. The relationship between this method and the method of weighted residuals is discussed.
Kaiser, J. E.↗
Modal density function and number of propagating modes in ducts
The question of the number of propagating modes within a small range of mode cut off ratio was raised. The population density of modes were shown to be greatest near cut off and least for the well propagating modes. It was shown that modes of nearly the same cut off ratio behave nearly the same in a sound absorbing duct as well as in the way they propagate to the far. Handling all of the propagating modes individually, they can be grouped into several cut off ratio ranges. It is important to know the modal density function to estimate acoustic power distribution.
Rice, E. J.↗
Optimal one-section and two-section circular sound-absorbing duct liners for plane-wave and monopole sources without flow
A discrete frequency study is made of the influence of source characteristics on the optimal properties of acoustically lined uniform and two section ducts. Two simplified sources, a plane wave and a monopole, are considered in some detail and over a greater frequency range than has been previously studied. Source and termination impedance effects are given limited examination. An example of a turbomachinery source and three associated source variants is also presented. Optimal liner designs based on modal theory approach the Cremer criterion at low frequencies and the geometric acoustics limit at high frequencies. Over an intermediate frequency range, optimal two section liners produced higher transmission losses than did the uniform configurations. Source distribution effects were found to have a significant effect on optimal liner design, but source and termination impedance effects appear to be relatively unimportant.
Lester, H. C.↗
Aerodynamic and acoustic tests of duct-burning turbofan exhaust nozzles
The static aerodynamic and acoustic characteristics of duct-burning turbofan (DBTF) exhaust nozzles are established. Scale models, having a total area equivalent to a 0.127 m diameter convergent nozzle, simulating unsuppressed coannular nozzles and mechanically suppressed nozzles with and without ejectors (hardwall and acoustically treated) were tested in a quiescent environment. The ratio of fan to primary area was varied from 0.75 to 1.2. Far field acoustic data, perceived noise levels, and thrust measurements were obtained for 417 test conditions. Pressure ratios were varied from 1.3 to 4.1 in the fan stream and from 1.53 to 2.5 in the primary stream. Total temperature varied from 395 to 1090 K in both streams. Jet noise reductions relative to synthesized prediction from 8 PNdB (with the unsuppressed coannular nozzle) to 15 PNdB (with a mechanically suppressed configuration) were observed at conditions typical of engines being considered under the Advanced Supersonic Technology program. The inherent suppression characteristic of the unsuppressed coannular nozzle is related to the rapid mixing in the jet wake caused by the velocity profiles associated with the DBTF. Since this can be achieved without a mechanical suppressor, significant reductions in aircraft weight or noise footprint can be realized.
Kozlowski, H.↗
Spectroscopic determination of electrical conductivity in an MHD duct from absolute intensity measurements
Measurements of the electrical conductivity in the NASA Lewis cesium seeded, H2-O2 MHD duct have been previously reported. In order to corroborate the above measurements and to analyze the possibility of nonuniform seed injection as a cause of the deviations, a spectroscopic investigation of the plasma conductivity has been undertaken. Transverse profiles of the absolute integrated intensity were measured from the optically thin lines of CSI-.5664 microns and .5636 microns. Radial profiles of emission coefficient were obtained from the measured transverse profiles of intensity by Abel inversion. Radial profiles of electrical conductivity were then obtained under two different assumptions. In the first, the Cs seed fraction is assumed uniform and equal to the measured flow rate at the time when the temperature and conductivity were obtained. In the second method, the local temperature and pressure are taken to be those given by a one-dimensional channel calculation including heat transfer and friction. In this case profiles of conductivity and seed fractions are obtained. The results of the two methods are compared to the previously measured conductivity.
Wang, S. Y.↗