Results for “second harmonic generation” — Page 17

NASA NTRS2001

Plasma Waves Observed in the Cusp Turbulent Boundary Layer: An Analysis of High Time Resolution Wave and Particle Measurements from the Polar Spacecraft

The boundary layer located in the cusp and adjacent to the magnetopause is a region that is quite turbulent and abundant with waves. The Polar spacecraft's orbit and sophisticated instrumentation are ideal for studying this region of space. Our analysis of the waveform data obtained in this turbulent boundary layer shows broadband magnetic noise extending up to a few kilohertz (but less than the electron cyclotron frequency); sinusoidal bursts (a few tenths of a second) of whistler mode waves at around a few tens of hertz, a few hundreds of hertz, and just below the electron cyclotron frequency; and bipolar pulses, interpreted as electron phase-space holes. In addition, bursts of electron cyclotron harmonic waves are occasionally observed with magnetic components. We show evidence of broadband electrostatic bursts covering a range of approx. 3 to approx. 25 kHz (near but less than the plasma frequency) occurring in packets modulated at the frequency of some of the whistler mode waves. On the basis of high time resolution particle data from the Polar HYDRA instrument, we show that these bursts are consistent with generation by the resistive medium instability. The most likely source of the whistler mode waves is the magnetic reconnection site closest to the spacecraft, since the waves are observed propagating both toward and away from the Earth, are bursty, which is often the case with reconnection, and do not fit on the theoretical cold plasma dispersion relation curve.

Pickett, J. S.↗

NASA NTRS1990

Millimeter-wave monolithic diode-grid frequency multiplier

A semiconductor diode structure useful for harmonic generation of millimeter or submillimeter wave radiation from a fundamental input wave is fabricated on a GaAs substrate. A heavily doped layer of n(sup ++) GaAs is produced on the substrate and then a layer of intrinsic GaAs on said heavily doped layer on top of which a sheet of heavy doping (++) is produced. A thin layer of intrinsic GaAs grown over the sheet is capped with two metal contacts separated by a gap to produce two diodes connected back to back through the n(sup ++) layer for multiplication of frequency by an odd multiple. If only one metal contact caps the thin layer of intrinsic GaAs, the second diode contact is produced to connect to the n(sup ++) layer for multiplication of frequency by an even number. The odd or even frequency multiple is selected by a filter. A phased array of diodes in a grid will increase the power of the higher frequency generated.

Maserjian, Joseph↗

NASA NTRS2008

A Numerical Investigation of Turbine Noise Source Hierarchy and Its Acoustic Transmission Characteristics

Understanding the relative importance of the various turbine noise generation mechanisms and the characteristics of the turbine acoustic transmission loss are essential ingredients in developing robust reduced-order models for predicting the turbine noise signature. A computationally based investigation has been undertaken to help guide the development of a turbine noise prediction capability that does not rely on empiricism. The investigation relies on highly detailed numerical simulations of the unsteady flowfield inside a modern high-pressure turbine (HPT). The simulations are developed using TURBO, which is an unsteady Reynolds-averaged Navier-Stokes (URANS) code capable of multi-stage simulations. The purpose of this study is twofold. First, to determine an estimate of the relative importance of the contributions to the coherent part of the acoustic signature of a turbine from the three potential sources of turbine noise generation, namely, blade-row viscous interaction, potential field interaction, and entropic source associated with the interaction of the blade rows with the temperature nonuniformities caused by the incomplete mixing of the hot fluid and the cooling flow. Second, to develop an understanding of the turbine acoustic transmission characteristics and to assess the applicability of existing empirical and analytical transmission loss models to realistic geometries and flow conditions for modern turbine designs. The investigation so far has concentrated on two simulations: (1) a single-stage HPT and (2) a two-stage HPT and the associated inter-turbine duct/strut segment. The simulations are designed to resolve up to the second harmonic of the blade passing frequency tone in accordance with accepted rules for second order solvers like TURBO. The calculations include blade and vane cooling flows and a radial profile of pressure and temperature at the turbine inlet. The calculation can be modified later to include the combustor pattern factor at the turbine inlet to include that contribution to turbine noise. We shall present preliminary analysis of the results obtained so far in order to assess the validity of such an approach and to seek feedback on improving the approach. This work addresses both Area 1 (Turbine Tone Noise) and Area 5 (Influence of the Turbine on Combustor Noise) topics.

VanZante, Dale↗

NASA NTRS2004

BASS Code Development

The BASS computational aeroacoustic code solves the fully nonlinear Euler equations in the time domain in two-dimensions. The acoustic response of the stator is determined simultaneously for the first three harmonics of the convected vortical gust of the rotor. The spatial mode generation, propagation and decay characteristics are predicted by assuming the acoustic field away from the stator can be represented as a uniform flow with small harmonic perturbations superimposed. The computed field is then decomposed using a joint temporal-spatial transform to determine the wave amplitudes as a function of rotor harmonic and spatial mode order. This report details the following technical aspects of the computations and analysis. 1) the BASS computational technique; 2) the application of periodic time shifted boundary conditions; 3) the linear theory aspects unique to rotor-stator interactions; and 4) the joint spatial-temporal transform. The computational results presented herein are twofold. In each case, the acoustic response of the stator is determined simultaneously for the first three harmonics of the convected vortical gust of the rotor. The fan under consideration here like modern fans is cut-off at +, and propagating acoustic waves are only expected at 2BPF and 3BPF. In the first case, the computations showed excellent agreement with linear theory predictions. The frequency and spatial mode order of acoustic field was computed and found consistent with linear theory. Further, the propagation of the generated modes was also correctly predicted. The upstream going waves propagated from the domain without reflection from the in ow boundary. However, reflections from the out ow boundary were noticed. The amplitude of the reflected wave was approximately 5% of the incident wave. The second set of computations were used to determine the influence of steady loading on the generated noise. Toward this end, the acoustic response was determined with three steady loading conditions: design, low-loading, high-loading. The overall trend showed significant (approximately 10 dB) increases in the generated noise for the highly loaded stator.

Sawyer, Scott↗

NASA NTRS2004

Computation of Gust-Cascade Interaction Using the CE/SE Method

The problem 2 in Category 3 of the 4th Computational Aeroacoustic(CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem models rotor-stator interaction in a 2D cascade. It involves complex geometries and flow physics including vortex shedding and acoustic radiation. The parallel version of the 2D nonlinear Euler solver is used with an unstructured triangular mesh to solve this problem. The Giles approach is incorporated with the CE/SE method to handle non-equal pitches of the rotor and stator. Validation on the Giles approach is performed using Problem 3.1 in the 2nd CAA Workshop. The space-time CE/SE method is a finite volume method with second-order accuracy in both space and time. The flux conservation is enforced in both space and time instead of space only. It has low numerical dissipation and dispersion errors. It uses simple non-reflecting boundary conditions and is compatible with unstructured meshes. It is simple, flexible, and generate reasonably accurate solutions. The CE/SE method has been successfully applied to solve numerous practical problems, especially aeroacoustic problems. Some preliminary numerical results of the benchmark problem 3.2 of the 4th CAA Workshop are shown. The steady-state pressure contour is plotted. The mean pressure distribution on the blade surface is compared with Turbo solution showing a good agreement. The sound pressure level versus the rotor harmonic n at the six designated positions on the blade surface, three locations at inlet plane, and three locations at the outlet plane are plotted. It can be seen that the acoustic response exists only at the excitation frequencies (n = 1,2,3). On the blade surface, the acoustic wave at n = 1 is dominant, while at the inlet and outlet planes, the sound pressure level at n = 2 becomes the largest, which is similar to the results presented. The distribution of sound pressure level at different spatial modes along the z- direction is plotted for n = 1,2,3, respectively. It shows that the spatial modes m = -32 and 22 at n = 1 exponentially decay, and the spatial modes m = 10 at n = 2, m = -42 and 12 at n = 3 propagate both upstream and downstream, which agrees with the prediction based on the linearized theory. Some oscillations are observed, which needs to be investigated further. In the final paper, the numerical results will be compared with a frequency-domain solver LINFLUX solution if it is available.

Wang, X.-Y.↗

NASA NTRS2012

Characterization of Deficiencies in the Frequency Domain Forced Response Analysis Technique for Turbine Bladed Disks

Turbine blades in rocket and jet engine turbomachinery experience enormous harmonic loading conditions. These loads result from the integer number of upstream and downstream stator vanes as well as the other turbine stages. The standard technique for forced response analysis to assess structural integrity is to decompose a CFD generated flow field into its harmonic components, and to then perform a frequency response analysis at the problematic natural frequencies. Recent CFD analysis and water-flow testing at NASA/MSFC, though, indicates that this technique may miss substantial harmonic and non-harmonic excitation sources that become present in complex flows. These complications suggest the question of whether frequency domain analysis is capable of capturing the excitation content sufficiently. Two studies comparing frequency response analysis with transient response analysis, therefore, have been performed. The first is of a bladed disk with each blade modeled by simple beam elements. It was hypothesized that the randomness and other variation from the standard harmonic excitation would reduce the blade structural response, but the results showed little reduction. The second study was of a realistic model of a bladed-disk excited by the same CFD used in the J2X engine program. The results showed that the transient analysis results were up to 10% higher for "clean" nodal diameter excitations and six times larger for "messy" excitations, where substantial Fourier content around the main harmonic exists.

Brown, Andrew M.↗

NASA NTRS2021

Boundary Layer Instabilities Over a Cone-Cylinder-Flare Model at Mach 6

Computations are performed to investigate the boundary-layer instabilities over a sharp cone-cylinder-flare model at zero degrees angle of attack. The model geometry and the flow conditions are selected to match the experiments conducted in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. The geometry consists of a nominally sharp 5-degree half-angle cone, followed by a cylindrical segment and then a 10-degree flare. An axisymmetric separation bubble is generated as a result of the laminar shock/boundary-layer interaction in the cylinder-flare region. The comparison of the laminar flow solution and the schlieren images shows a remarkable agreement between the respective locations of both the boundarylayer edge and the reattachment shock. The predicted heat flux distribution is also in agreement with the measured values downstream of the reattachment location. The analysis of convective and global instabilities is performed for flare half angles equal to 8, 10, and 12 degrees and nosetip radii equal to 0.1, 1, and 5 mm. The linear amplification of first and second Mack mode instabilities that begin to amplify in the cone region are computed with a combination of the parabolized stability equations (PSE) and the harmonic linearized Navier-Stokes equations (HLNSE). The predicted frequency spectra of the surface pressure fluctuations associated with both planar and oblique instability waves are compared with the measured spectra at the various locations of the PCB and Kulite sensors. The comparison shows that the computational analysis captures the distinct lobes within the disturbance amplification spectra measured in the experiments, but some differences in amplification characteristics are noted at low frequencies. Overall, the oblique disturbances are found to be more amplified than the planar disturbances. To our knowledge, this represents the first successful comparison between convective instability analysis and measured surface pressure fluctuations for a hypersonic configuration with a separation bubble. Finally, the global instability analysis shows that the laminar flow becomes supercritical for flare half angles larger than 8 degrees. The unstable global mode for the experimental configuration of a 10 degrees flare and a sharp nosetip cone corresponds to a stationary three-dimensional disturbance that is concentrated in the recirculation region and achieves its maximum growth rate for an azimuthal wavenumber of 5.

Boundary layer transition↗

NASA NTRS2022

Boundary Layer Instabilities Over a Cone-Cylinder-Flare Model at Mach 6

Computations are performed to investigate the boundary-layer instabilities over a sharp cone-cylinder-flare model at zero degrees angle of attack. The model geometry and the flow conditions are selected to match the experiments conducted in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. The geometry consists of a nominally sharp 5-degree half-angle cone, followed by a cylindrical segment and then a 10-degree flare. An axisymmetric separation bubble is generated as a result of the laminar shock/boundary-layer interaction in the cylinder-flare region. The comparison of the laminar flow solution and the schlieren images shows a remarkable agreement between the respective locations of both the boundarylayer edge and the reattachment shock. The predicted heat flux distribution is also in agreement with the measured values downstream of the reattachment location. The analysis of convective and global instabilities is performed for flare half angles equal to 8, 10, and 12 degrees and nosetip radii equal to 0.1, 1, and 5 mm. The linear amplification of first and second Mack mode instabilities that begin to amplify in the cone region are computed with a combination of the parabolized stability equations (PSE) and the harmonic linearized Navier-Stokes equations (HLNSE). The predicted frequency spectra of the surface pressure fluctuations associated with both planar and oblique instability waves are compared with the measured spectra at the various locations of the PCB and Kulite sensors. The comparison shows that the computational analysis captures the distinct lobes within the disturbance amplification spectra measured in the experiments, but some differences in amplification characteristics are noted at low frequencies. Overall, the oblique disturbances are found to be more amplified than the planar disturbances. To our knowledge, this represents the first successful comparison between convective instability analysis and measured surface pressure fluctuations for a hypersonic configuration with a separation bubble. Finally, the global instability analysis shows that the laminar flow becomes supercritical for flare half angles larger than 8 degrees. The unstable global mode for the experimental configuration of a 10 degrees flare and a sharp nosetip cone corresponds to a stationary three-dimensional disturbance that is concentrated in the recirculation region and achieves its maximum growth rate for an azimuthal wavenumber of 5.

Hydrodynamic instability↗

NASA NTRS1998

Experimental Simulation of Active Control With On-line System Identification on Sound Transmission Through an Elastic Plate

An adaptive control algorithm with on-line system identification capability has been developed. One of the great advantages of this scheme is that an additional system identification mechanism such as an additional uncorrelated random signal generator as the source of system identification is not required. A time-varying plate-cavity system is used to demonstrate the control performance of this algorithm. The time-varying system consists of a stainless-steel plate which is bolted down on a rigid cavity opening where the cavity depth was changed with respect to time. For a given externally located harmonic sound excitation, the system identification and the control are simultaneously executed to minimize the transmitted sound in the cavity. The control performance of the algorithm is examined for two cases. First, all the water was drained, the external disturbance frequency is swept with 1 Hz/sec. The result shows an excellent frequency tracking capability with cavity internal sound suppression of 40 dB. For the second case, the water level is initially empty and then raised to 3/20 full in 60 seconds while the external sound excitation is fixed with a frequency. Hence, the cavity resonant frequency decreases and passes the external sound excitation frequency. The algorithm shows 40 dB transmitted noise suppression without compromising the system identification tracking capability.

Source record↗

NASA NTRS2015

Coupled CFD/CSD Analysis of an Active-Twist Rotor in a Wind Tunnel with Experimental Validation

An unsteady Reynolds averaged Navier-Stokes analysis loosely coupled with a comprehensive rotorcraft code is presented for a second-generation active-twist rotor. High fidelity Navier-Stokes results for three configurations: an isolated rotor, a rotor with fuselage, and a rotor with fuselage mounted in a wind tunnel, are compared to lifting-line theory based comprehensive rotorcraft code calculations and wind tunnel data. Results indicate that CFD/CSD predictions of flapwise bending moments are in good agreement with wind tunnel measurements for configurations with a fuselage, and that modeling the wind tunnel environment does not significantly enhance computed results. Actuated rotor results for the rotor with fuselage configuration are also validated for predictions of vibratory blade loads and fixed-system vibratory loads. Varying levels of agreement with wind tunnel measurements are observed for blade vibratory loads, depending on the load component (flap, lag, or torsion) and the harmonic being examined. Predicted trends in fixed-system vibratory loads are in good agreement with wind tunnel measurements.

Massey, Steven J.↗

NASA NTRS2019

New Evidence for Third Harmonic Electromagnetic Radiation in Interplanetary Type III Solar Radio Bursts

This article provides new evidence for a third harmonic component in the electromagnetic radiation generated by interplanetary type III solar radio bursts observed locally near 1 AU. This evidence comes mainly from the analysis of the low-frequency radio emissions observed by the Wind spacecraft. The analysis examines, at high-time and high-frequency resolution, the local type III radiation that is occasionally observed at Wind. The associated Langmuir waves and energetic electron beams, as well as simultaneous observations from the Solar Terrestrial Relations Observatory (STEREO) and Ulysses spacecraft where possible, are used to confirm the local nature of the observed radiation and to help identify the solar origin. We find that the detection of a third harmonic component in the local type III radiation near 1 AU is exceedingly rare. However, our analyses indicate that, in addition to the more commonly observed second harmonic component, a third harmonic component is sometimes conspicuously evident in the local type III radiation. We find that the third harmonic component, when observed, is less intense than the second harmonic component, with the intensity ratio varying between 0.3 and 0.7. Sometimes the third harmonic component is expected to be detected, but it is not observed.

Interplanetary↗

DOE OSTI2025

Physics-Driven Construction of Compact Primitive Gaussian Density Fitting Basis Sets

We present a model-assisted density fitting (MADF) basis set generator, an algorithm for generating primitive atomic Gaussian density fitting (DF) basis sets (DFBSs) from a contracted Gaussian orbital basis set (OBS). The MADF algorithm produces DFBSs suitable for accurate robust DF approximation of 2-particle interactions in mean-field and correlated electronic structures. The algorithm is designed to (a) saturate the OBS product space by a large regularized set of primitive solid-harmonic Gaussian shells with nonuniform distribution of exponents, followed by (b) pruning of the shells according to their contributions to the 2- body energy of a correlated atomic ensemble. Building the DFBS generator model almost exclusively on mathematical and physical principles allows one to limit the number of parameters that control the density fitting error to three, with a single set of parameters sufficient for computations with all basis cardinal numbers, with and without correlation of core electrons, with and without scalar and spin-dependent relativistic effects, spanning almost all of the Periodic Table. Performance assessment included basis sets up to quadruple-ζ quality from several major basis set families, using molecules composed of main-group, d-block, and f-block elements. The resulting DF errors in Hartree−Fock and second-order MP2 energies (with relativistic all-electron treatments, when appropriate) were on the order of 20 and 10 μE h per electron, respectively.

Approximation↗

NASA NTRS1976

Method and apparatus for generating coherent radiation in the ultra-violet region and above by use of distributed feedback

Helium in the superfluid state emits copious amounts of radiation in the ultraviolet region when excited by an electron stream. Conventional laser action using mirrors is impossible in superfluid helium because there are no mirrors that will reflect VUV radiation. By utilizing the distributed feedback method, the superfluid helium can be made to lase. By setting up a standing wave in superfluid helium that has a wavelength equal to, or harmonically related to, half the wavelength of the photon radiation chosen to be emitted as laser radiation by the superfluid helium, the need for end mirrors to produce reflection of the laser radiation is eliminated and reflection occurs instead at the wavefronts of the standing wave. The photons leave the superfluid helium at right angles to the standing wave as coherent radiation having a very high intensity. The standing wave established in the superfluid helium may be an acoustical standing wave, a thermal standing wave (second sound), or an electric standing wave.

Saffren, M. M.↗

NASA NTRS1993

On the unique structure of the magnetic fields of Uranus and Neptune

The magnetic fields of Uranus and Neptune, which have comparable dipole, quadrupole, and octupole harmonics, are unique in the present-day solar system, but they resemble the geomagnetic field at the epochs of excursions and reversals known from paleomagnetic data. The precession dynamo model, in which the dominant role in the generation of the planetary magnetic fields is played by external gravitational forces, allows us to propose two scenarios for the formation of the unique topology of the magnetic fields of Uranus and Neptune. In the first case, tidal flows in the 'oceans' of these two planets extend down to the depths where the matter has a noticeable electric conductivity and velocity. A hydromagnetic interaction of the moving conducting fluid with the planetary magnetic field outside the generation region results in the deformation of the field and the deceleration of the motion under the action of the radial magnetic field. In the second case, the deformation of the field facilitates drastic changes in cyclonic cells within the generation region causing instabilities that result in a multi-polar field structure, excursions, and inversions. This paper considers this problem in greater detail by using the Neptune-Triton system as an example.

Dolginov, Sh. SH.↗

NASA NTRSDate not supplied

Nonlinear Nonmodal Analysis of Hypersonic Flow over Blunt Cones

The linear amplification of modal disturbances that lead to boundary-layer transition in two-dimensional/axisymmetric hypersonic configurations is strongly reduced by the presence of a blunt nosetip, and the mechanisms underlying the observed onset of transition over the cone frustum are currently unknown. Linear nonmodal analysis has shown that both planar and oblique traveling disturbances that peak within the entropy layer experience appreciable energy amplification for moderate to large nosetip bluntness. The present study extends the previous linear analysis by including the nonlinear effects. Specifically, the perturbation form of the 2D, harmonic Navier-Stokes equations (HNSE) are solved with a fully implicit formulation and the Newton-Raphson method. The increased number of degrees of freedom for the nonlinear system presents difficulties for solution strategies based on direct solution of the linearized system. Such difficulties are overcome by using the GMRES iterative method with a preconditioner corresponding to a simplified Jacobian without the cross derivative terms. The HNSE solver is verified by comparing with nonlinear parabolized stability equation (NPSE) results for the nonlinear evolution of planar waves in an incompressible Blasius boundary layer and in a Mach 6 flow over a blunt cone. Finally, nonlinear nonmodal results are presented for planar traveling disturbances over the blunt cone. The nonmodal analysis demonstrates that entropy-layer disturbances generated close to the nose tip can seed the amplification of higher frequency Mack’s second-mode instabilities further downstream.

boundary layer transition↗

NASA NTRSDate not supplied

Nonlinear Nonmodal Analysis of Hypersonic Flow over Blunt Cones

The linear amplification of modal disturbances that lead to boundary-layer transition in two-dimensional/axisymmetric hypersonic configurations is strongly reduced by the presence of a blunt nosetip, and the mechanisms underlying the observed onset of transition over the cone frustum are currently unknown. Linear nonmodal analysis has shown that both planar and oblique traveling disturbances that peak within the entropy layer experience appreciable energy amplification for moderate to large nosetip bluntness. The present study extends the previous linear analysis by including the nonlinear effects. Specifically, the perturbation form of the 2D, harmonic Navier-Stokes equations (HNSE) are solved with a fully implicit formulation and the Newton-Raphson method. The increased number of degrees of freedom for the nonlinear system presents difficulties for solution strategies based on direct solution of the linearized system. Such difficulties are overcome by using the GMRES iterative method with a preconditioner corresponding to a simplified Jacobian without the cross derivative terms. The HNSE solver is verified by comparing with nonlinear parabolized stability equation (NPSE) results for the nonlinear evolution of planar waves in an incompressible Blasius boundary layer and in a Mach 6 flow over a blunt cone. Finally, nonlinear nonmodal results are presented for planar traveling disturbances over the blunt cone. The nonmodal analysis demonstrates that entropy-layer disturbances generated close to the nose tip can seed the amplification of higher frequency Mack’s second-mode instabilities further downstream.

boundary layer transition↗

DOE OSTI2024

Efficient laser-driven proton acceleration from a petawatt contrast-enhanced second harmonic mixed-glass laser system

Efficient laser-driven plasma acceleration of ion beams requires precision control of the target–plasma profile, which is crucial to optimize the laser energy transfer. Along the laser propagation direction, this can be achieved by tailoring the temporal structure of the laser pulse. We show for the first time that frequency-doubling of a short pulse (hundreds-femtosecond range) petawatt-class mixed-glass laser system, which results in temporal intensity contrast enhancement, enables surface and volumetric laser–energy coupling, and the acceleration of proton beams from few-nanometer-thick foil targets. Experimentally, maximum ion energies and laser-to-proton energy conversion efficiencies were found to be both maximized at optimum laser and target conditions manifested when the normalized target density nearly equalizes the normalized laser vector potential, which is in agreement with theory and simulations. These signatures are recognized as a unique indication of the interaction between ultra-intense laser pulses with high temporal intensity contrast and ultra-thin nanometer-scale targets. Transverse modulations of accelerated proton beams in the form of bubble- and ring-like structures measured in the thinnest targets provide additional evidence of volumetric laser-driven particle acceleration regimes and transitional features in ultra-thin foil targets specific to laser–plasma interactions characterized by a high temporal intensity contrast. These results open avenues in the generation of high contrast laser pulses from short-pulse-femtosecond petawatt mixed-glass laser systems and demonstrate the feasibility of this technique for applications requiring high laser intensity contrast with high efficiency.

Physics↗

NASA NTRS1975

Study of noise sources in a subsonic fan using measured blade pressures and acoustic theory

Sources of noise in a 1.4 m (4.6 ft) diameter subsonic tip speed propulsive fan running statically outdoors are studied using a combination of techniques. Signals measured with pressure transducers on a rotor blade are plotted in a format showing the space-time history of inlet distortion. Study of these plots visually and with statistical correlation analysis confirms that the inlet flow contains long, thin eddies of turbulence. Turbulence generated in the boundary layer of the shroud upstream of the rotor tips was not found to be an important noise source. Fan noise is diagnosed by computing narrowband spectra of rotor and stator sound power and comparing these with measured sound power spectra. Rotor noise is computed from spectra of the measured blade pressures and stator noise is computed using the author's stator noise theory. It is concluded that the rotor and stator sources contribute about equally at frequencies in the vicinity of the first three harmonics of blade passing frequency. At higher frequencies, the stator contribution diminishes rapidly and the rotor/inlet turbulence mechanism dominates. Two parametric studies are performed by using the rotor noise calculation procedure which was correlated with test. In the first study, the effects on noise spectrum and directivity are calculated for changes in turbulence properties, rotational Mach number, number of blades, and stagger angle. In the second study the influences of design tip speed and blade number on noise are evaluated.

Hanson, D. B.↗