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At least 271 records · Page 15

A theoretical and experimental study of sound attenuation in an annular duct.

The flow duct used in the experiments for this study was described in an earlier paper by Plumblee and Dean (1972). Angular and radial standing modes were excited in isolation, and the modal attenuation and phase speed were measured in an annular duct with locally reacting liners. Contour maps of constant attenuation and phase speed were computed in the wall impedance plane for no-flow and several flow conditions, and experimental data were compared with some of these calculations. The effect of flow on modal attenuation and phase speed was measured and is theoretically verified. The major result of this study is the verification of theoretical predictions which ultimately can lead to a duct liner design optimization without resort to expensive and lengthy test programs.

Plumblee, H. E.↗

A difference theory for noise propagation in an acoustically lined duct with mean flow.

A finite difference formulation is presented for sound propagation in a two-dimensional straight soft-walled duct with uniform flow. The difference analysis is developed in terms of complex notation. The governing acoustic difference equations and the appropriate displacement boundary conditions associated with uniform flow are presented. Example calculations are presented for the sound attenuation in straight hard and soft-walled ducts. At present the finite Mach number case is solved only for the one-dimensional hard walled duct.

Baumeister, K. J.↗

Acoustic radiation patterns for a source in a hard-walled unflanged circular duct

Acoustic radiation patterns are measured over a 320 deg arc for a point source in a finite length, hard walled, unflanged circular duct. The measured results are compared with computed results which are based on the Wiener-Hopf solution for radiation from a semi-infinite unflanged duct. Measurements and computations are presented for frequencies slightly below and slightly above each of the first four higher order radial mode cutoff frequencies. It is found that the computed and measured patterns show better agreement below the mode cut-off frequencies than above and that the agreement is better at lower frequencies that at higher frequencies. The computed radiation patterns do not show fine lobes which are caused by diffraction from the back end of the duct.

Holm, R. G.↗

Radiated sound field measurements from an annular flow duct facility

A series of measured radiated field patterns correlated with defined in-duct conditions is presented, along with a second series of radiation measurements for multiple mode propagation, with individual mode amplitudes and phases at duct termination as well as with angular positions of higher-order stationary duct modes relative to the plane of the radiated field measurement. Though incomplete, these experimental data should prove useful for comparisons with theoretical predictions in testing analytical procedures and prediction techniques.

Plumblee, H. E.↗

Supersonic combustion of hydrogen injected perpendicular to a ducted vitiated airstream

The reaction of hydrogen injected into a supersonic vitiated airstream from perpendicular injectors equally spaced over opposite walls of a two-dimensional duct is experimentally investigated. Information is obtained in the form of pitot pressure and gas sample surveys of the duct exit flow and static pressures along the duct walls for several injector arrangements differing in number, spacing, and size of injectors and operating at two levels of equivalence ratio. The amount of the injected hydrogen reacted is deduced from the static pressure data using a one-dimensional theory and is correlated with relative injection pressure and injector spacing-to-diameter ratio. These results are used with a mixing distribution correlation derived from nonreacting hydrogen-air results to predict static pressure distributions.

Rogers, R. C.↗

Generalized radiation impedances and reflection coefficients of circular and annular ducts

Morse's equation for the radiation impedance of a vibrating rigid piston is extended to give the generalized radiation impedances of all modes in circular and annular ducts which have arbitrary wall admittance and which terminate in an infinite baffle. The extended equation is reduced to a single infinite integral which is a function of the mode radiation directivity factors. An infinite matrix equation is derived which relates the generalized mode reflection coefficients to the radiation impedances. Results are presented which show that the duct-wall admittance is a significant parameter in the effect of duct-determination reflections and that mode-coupling reflection effects may be more important than direct-mode reflection effects.

Zorumski, W. E.↗

Finite-amplitude waves in cylindrical lined ducts

A second-order uniformly valid expansion is obtained for nonlinear waves propagating in a cylindrical duct lined with a point-reacting acoustic material that consists of a porous sheet followed by honey-comb cavities and backed by the impervious walls of the duct. The effect of the liner is taken into account by coupling the waves in the duct with those in the liner. As in the two-dimensional case, the nonlinearity increases the attenuation rate at all frequencies except in narrow bandwidths around the resonant frequencies, irrespective of the geometrical dimensions of the liner or the acoustic properties of the porous sheet.

Nayfeh, A. H.↗

Multiple eigenvalues of sound-absorbing circular and annular ducts

Eigenvalue equations of the form D(lambda) = 0 are studied for acoustic modes in circular and annular ducts without flow. The ducts have locally reacting walls with arbitrary wall admittance. It is shown that circular ducts may have double eigenvalues, or wall admittances where both D(lambda) and D prime (lambda) are zero. These double eigenvalues are formed by the coalescence of the lowest-order eigenfunction with some higher-order eigenfunction. The eigenfunctions, or acoustic modes, associated with the double eigenvalues are found to be orthogonal to themselves so that the standard expansion formula for the acoustic field, which is obtained from a separation-of-variables analysis, is invalid. An alternate expansion formula for the acoustic field is derived. This alternate formula shows that the coalesced acoustic mode is linearly amplified by the transmission distance and exponentially attenuated at the expected rate. The expansion formula also reveals a new eigenfunction, or acoustic mode, which is exponentially attenuated at the same rate as the coalesced eigenfunction.

Zorumski, W. E.↗

Propagation of waves in elliptic ducts. A theoretical study

The cut-off frequencies for high order circumferential modes were calculated for various eccentricities of an elliptic duct section. The problem was studied with a view to the reduction of jet engine compressor noise by elliptic ducts, instead of circular ducts. The cut-off frequencies for even functions decrease with increasing eccentricity. The third order eigen frequencies are oscillatory as the eccentricity increases for odd functions. The eigen frequencies decrease for higher order odd functions inasmuch as, for higher orders, they assume the same values as those for even functions. Deformation of a circular pipe into an elliptic one of sufficiently large eccentricity produces only a small reduction in the cut-off frequency, provided the area of the pipe section is kept invariable.

Baskaran, S.↗

The solution of three-variable duct-flow equations

This paper establishes a numerical method for the solution of three-variable problems and is applied here to rotational flows through ducts of various cross sections. An iterative scheme is developed, the main feature of which is the addition of a duplicate variable to the forward component of velocity. Two forward components of velocity result from integrating two sets of first order ordinary differential equations for the streamline curvatures, in intersecting directions across the duct. Two pseudo-continuity equations are introduced with source/sink terms, whose strengths are dependent on the difference between the forward components of velocity. When convergence is obtained, the two forward components of velocity are identical, the source/sink terms are zero, and the original equations are satisfied. A computer program solves the exact equations and boundary conditions numerically. The method is economical and compares successfully with experiments on bent ducts of circular and rectangular cross section where secondary flows are caused by gradients of total pressure upstream.

Stuart, A. R.↗

Theoretical studies on tone noise from a ducted fan rotor

The method of computing radiated noise from a ducted rotor due to inflow distortion and turbulence are examined. Analytical investigations include an appropriate description of sources, the cut-off conditions imposed on the modal propagation of the pressure waves in the annular duct, and reflections at the upstream end of the duct. Far field sound pressure levels at blade passing frequency due to acoustic radiation from a small scale low speed fan are computed. Theoretical predictions are in reasonable agreement with experimental measurements.

Rao, C. V. R.↗

Comparison of parametric duct-burning turbofan and non-afterburning turbojet engines in a Mach 2.7 transport

A parametric study was made of duct-burning turbofan and suppressed dry turbojet engines installed in a supersonic transport. A range of fan pressure ratios was considered for the separate-flow-fan engines. The turbofan engines were studied both with and without jet noise suppressors. Single- as well as dual-stream suppression was considered. Attention was concentrated on designs yielding sideline noises of FAR 36 (108 EPNdB) and below. Trades were made between thrust and wing area for a constant takeoff field length. The turbofans produced lower airplane gross weights than the turbojets at FAR 36 and below. The advantage for the turbofans increased as the sideline noise limit was reduced. Jet noise suppression, especially for the duct stream, was very beneficial for the turbofan engines as long as duct burning was permitted during takeoff. The maximum dry unsuppressed takeoff mode, however, yielded better results at extremely low noise levels. Noise levels as low as FAR 36-11 EPNdB were obtained with a turbofan in this takeoff mode, but at a considerable gross weight penalty relative to the best FAR 36 results.

Whitlow, J. B., Jr.↗

Propagation of Sound at Moderate and High Intensities in Absorbent and Hard-Walled Cylindrical Ducts

The propagation of plane wave and higher order acoustic modes in both hard-walled and absorbent cylindrical ducts was studied at moderate sound intensities where the linear wave equation is valid, and at high intensities where nonlinear effects can be observed. The experiments were conducted with an anechoically terminated twelve-inch inside-diameter transite pipe. Various types of sound sources were mounted at one end of the duct to generate the desired acoustic fields within the duct. Arrays of conventional loudspeakers were used to generate plane waves and higher order acoustic modes at moderate intensities, and an array of four high intensity electro-pneumatic sound sources was used for the experiments in the nonlinear region. The attenuation of absorbent liners made of several different materials was obtained at moderate intensities for both plane waves and high order modes. It was found that the characteristics of the liners studied did not change appreciably at high intensities.

Mcdaniel, Oliver Herbert↗

A study of reacting free and ducted hydrogen/air jets

The mixing and reaction of a supersonic jet of hydrogen in coaxial free and ducted high temperature test gases were investigated. The importance of chemical kinetics on computed results, and the utilization of free-jet theoretical approaches to compute enclosed flow fields were studied. Measured pitot pressure profiles were correlated by use of a parabolic mixing analysis employing an eddy viscosity model. All computations, including free, ducted, reacting, and nonreacting cases, use the same value of the empirical constant in the viscosity model. Equilibrium and finite rate chemistry models were utilized. The finite rate assumption allowed prediction of observed ignition delay, but the equilibrium model gave the best correlations downstream from the ignition location. Ducted calculations were made with finite rate chemistry; correlations were, in general, as good as the free-jet results until problems with the boundary conditions were encountered.

Beach, H. L., Jr.↗

The effect of initial flow nonuniformity on second-stage fuel injection and combustion in a supersonic duct

The effects of flow nonuniformity on second-stage hydrogen fuel injection and combustion in supersonic flow were evaluated. The first case, second-stage fuel injection into a uniform duct flow, produced data indicating that fuel mixing is considerably slower than estimates based on an empirical mixing correlation. The second-case, two-stage fuel injection (or second-stage fuel injection into a nonuniform duct flow), produced a large interaction between stages with extensive flow separation. For this case the measured wall pressure, heat transfer, and amount of reaction at the duct exit were significantly greater than estimates based on the mixing correlation. Substantially more second-stage fuel burned in the second case than in the first case. Overall effects of unmixedness/chemical kinetics were found not to be significant at the exit for stoichiometric fuel injection.

Russin, W. R.↗

The propagation of plane waves and higher order acoustic modes in multisectioned ducts

A theoretical and experimental study of acoustic propagation in an anechoically terminated multisectioned duct was performed. A unique source array consisting of two concentric rings of sources, providing phase and amplitude control in the radial as well as circumferential direction, was developed to generate plane waves and both spinning and non-spinning higher order modes. Measurement of attenuation and radial mode shapes were taken with various finite length liners inserted between the hard wall sections of a duct with an anechoic termination. A search technique was developed to find the complex eigenvalues for a liner under the assumption of a locally reacting boundary condition. The experimental results were compared with a theoretical analysis which includes the modal transmission and reflection at the interface of each duct section, and this indicated that the local reaction boundary condition is valid for three liner configurations.

Wyerman, B. R.↗

Finite amplitude waves in two-dimensional lined ducts

A second-order uniform expansion is obtained for nonlinear wave propagation in a two-dimensional duct lined with a point-reacting acoustic material consisting of a porous sheet followed by honeycomb cavities and backed by the impervious wall of the duct. The waves in the duct are coupled with those in the porous sheet and the cavities. An analytical expression is obtained for the absorption coefficient in terms of the sound frequency, the physical properties of the porous sheet, and the geometrical parameters of the flow configuration. The results show that the nonlinearity flattens and broadens the absorption vs. frequency curve, irrespective of the geometrical dimensions or the porous material acoustic properties, in agreement with experimental observations.

Nayfeh, A. H.↗