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    Publication Date: 2016-06-07
    Description: The plane wave propagation, the stability and the rectangular duct mode problems of a compressible inviscid linearly sheared parallel, but otherwise homogeneous flow, are shown to be governed by Whittaker's equation. The exact solutions for the perturbation quantities are essentially Whittaker M-functions. A number of known results are obtained as limiting cases of exact solutions. For the compressible finite thickness shear layer it is shown that no resonances and no critical angles exist for all Mach numbers, frequencies and shear layer velocity profile slopes except in the singular case of the vortex sheet.
    Keywords: ACOUSTICS
    Type: NASA. Langley Res. Center Advan. in Eng. Sci., Vol 3; p 851-860
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  • 4
    Publication Date: 2019-06-28
    Description: The reflection and transmission characteristics of plane waves scattered by a finite-thickness shear layer having a linear velocity profile and bounded by two otherwise uniform parallel flows is examined using the pressure perturbation equation solutions in the shear layer shown previously to be in terms of Whittaker M functions. In addition to the angle of plane wave incidence and the relative Mach number of the flows bounding the shear layer, it is found that the scattering properties of the shear layer depend crucially upon a parameter tau in such a manner that the case tau approaching zero characterizes the long wavelength properties of the layer and the case tau approaching infinity characterizes the short wavelength properties of the layer. In contrast to the region of ordinary reflection in the cases where the corresponding vortex sheet does not have a Brewster angle, the values of the reflection coefficient up to tau of 2 follow those of the vortex sheet; for the case for which the corresponding vortex sheet has a Brewster angle, the magnitude of the reflection coefficient may be sensitive to even small changes in tau in certain cases.
    Keywords: ACOUSTICS
    Type: AIAA PAPER 79-0627
    Format: text
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  • 5
    Publication Date: 2019-06-27
    Description: The plane wave propagation, the stability, and the rectangular duct mode problems of a compressible, inviscid, linearly sheared, parallel, homogeneous flow are shown to be governed by Whittaker's equation. The exact solutions for the perturbation quantities are essentially the Whittaker M-functions where the nondimensional quantities have precise physical meanings. A number of known results are obtained as limiting cases of the exact solutions. For the compressible finite thickness shear layer it is shown that no resonances and no critical angles exist for all Mach numbers, frequencies, and shear layer velocity profile slopes except in the singular case of the vortex sheet.
    Keywords: ACOUSTICS
    Type: NASA-CR-162465 , SU-JIAA-TR-5 , Ann. Meeting of the Soc. of Eng. Sci.; Hampton, VA; United States
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  • 6
    Publication Date: 2019-06-27
    Description: The equation describing the plane wave propagation, the stability, or the rectangular duct mode characteristics in a compressible inviscid linearly sheared parallel, but otherwise homogeneous flow, is shown to be reducible to Whittaker's equation. The resulting solutions, which are real, viewed as functions of two variables, depend on a parameter and an argument, the values of which have precise physical meanings depending on the problem. The exact solutions in terms of Whittaker functions are used to obtain a number of known results of plane wave propagation and stability in linearly sheared flows as limiting cases in which the speed of sound goes to infinity (incompressible limit) or the shear layer thickness, or wave number, goes to zero (vortex sheet limit). The usefulness of the exact solutions is then discussed in connection with the problems of plane wave propagation and the stability of a finite thickness layer with a linear velocity profile.
    Keywords: ACOUSTICS
    Type: NASA-CR-162577 , SU-JIAA-TR-12
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  • 7
    Publication Date: 2019-06-27
    Description: The energy reflection coefficient is evaluated numerically for plane waves incident on a plane shear layer having a linear velocity profile. The shear layer is found to exhibit no resonances and no Brewster angles. The behavior of the reflection coefficient depends crucially on the parameter tau, a nondimensional measure of the disturbance Strouhal number with respect to the disturbance Mach number in the mean flow direction. For moderate values of tau, the amplified reflection regime degenerates into the total reflection one, whereas in the ordinary reflection regime the variation of the reflection coefficient with tau depends on whether or not the corresponding vortex sheet has a Brewster angle. The results indicate that caution should be exercised in uncritically modeling a finite thickness shear layer by a corresponding vortex sheet.
    Keywords: ACOUSTICS
    Type: NASA-CR-166181 , SU-JIAA-TR-20
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  • 8
    Publication Date: 2019-06-27
    Description: Inviscid fluctuations in a compressible linearly sheared, but otherwise homogeneous, parallel two-dimensional flow are considered. The equation describing the plane wave propagation (PWP), the stability, or the rectangular duct mode characteristics in such a flow is shown to be reducible to Whittaker's equation. The exact solutions are applied to problems of PWP and stability in linearly sheared flows as limiting cases in which the speed of sound goes to infinity (incompressible limit) or the shear layer thickness, or wave number, goes to zero (vortex sheet limit). With respect to the PWP it is shown that the shear layer possesses no resonances and no Brewster angles, while with regard to the problem of the stability of a finite thickness shear layer with a linear velocity profile, it is shown that the thin layer is unstable to long wavelength disturbances for all Mach numbers.
    Keywords: ACOUSTICS
    Type: Journal of Sound and Vibration; 68; Jan. 22
    Format: text
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  • 9
    Publication Date: 2019-06-28
    Description: Experiments with a truncated and untruncated airfoils of profiles NACA 640A10, were carried out in subsonic wind tunnels in a velocity range of 19m/s to 54m/s corresponding to Reynolds numbers of 200,000 to 468,000 based on the chord. Airfoil spanned the test section to achieve two dimensionality of the model. Velocity measurements, pressure measurements, and vortex shedding in the wake were measured using a hotwire and pressure transducers. The measured chordwise static pressure distribution on the smooth trailing edge airfoil along the midspan plane, agreed with the theoretical results calculated on the basis of the potential flow for that airfoil. Boundary layer profiles measured in the midspan plane, behind the maximum thickness of the airfoil show no separation of the flow. Spanwise distribution of the measured static pressure on the upper surface of the airfoil shows uniformity for both configurations with and without the boundary layer trip. This uniformity of pressure distribution and separation indicates that the flow on the airfoil was uniform and two dimensional in character.
    Keywords: AERODYNAMICS
    Type: NASA-CR-168563 , SU-JIAA-TR-39
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  • 10
    Publication Date: 2019-07-13
    Description: A calibration was made of the acoustic and aerodynamic characteristics of a small, open-jet wind tunnel in an anechoic room. The jet nozzle was 102 mm diameter and was operated subsonically. The anechoic-room dimensions were 7.6 m by 5.5 m by 3.4 m high (wedge tip to wedge tip). Noise contours in the chamber were determined by various jet speeds and exhaust collector positions. The optimum nozzle/collector separation from an acoustic standpoint was 2.1 m. Jet velocity profiles and turbulence levels were measured using pressure probes and hot wires. The jet was found to be symmetric, with no unusual characteristics. The turbulence measurements were hampered by oil mist contamination of the airflow.
    Keywords: RESEARCH AND SUPPORT FACILITIES (AIR)
    Type: NASA-TM-84081
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