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Steven T. Hocter - One of the best experts on this subject based on the ideXlab platform.
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Sound reflection into a Cylindrical Duct
Proceedings of the Royal Society of London. Series A: Mathematical Physical and Engineering Sciences, 2000Co-Authors: Steven T. HocterAbstract:This paper presents formulae for the sound reflected into a Cylindrical Duct, using the exact solution and Weinstein9s U –function. The U –function has been used previously to give a lucid and practical description of many aspects of Duct acoustics, but it has not yet been used for the acoustic field inside the Duct. Weinstein has presented formulae for the field radiated from a Cylindrical Duct by an incident non–spinning mode, and this is extended in considering the field reflected from the end of the Duct by an incident spinning mode. A simple description of the field expressed in terms of the mode angles used to describe geometrically the propagation of an incident ray through the Duct and out into space can be determined by means of the U –function. The accuracy of the approximation can be measured in parameter spaces dependent upon these mode angles. Further analysis is performed using asymptotic formulae which simplify the U –function, allowing statements to be made about the behaviour of the coupling coefficients for large wavenumbers.
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Sound radiated from a Cylindrical Duct with Keller's geometrical theory
Journal of Sound and Vibration, 2000Co-Authors: Steven T. HocterAbstract:Abstract An exact solution to the problem of radiation from a Cylindrical Duct has been available using the Wiener–Hopf technique for many years, and a number of approximate methods can also be considered. When parameter spaces involving high frequency are required, it is possible to use ray-theory-based techniques to solve the problem. Keller proposed such a method, introducing a geometrical theory of diffraction (GTD) which extended the concept of geometrical optics to account for diffracted rays. When a ray propagates inside the Duct, it will reflect off the Duct rim creating a Keller cone of singly diffracted rays, allowing formulae to be obtained for the singly diffracted field using Keller's GTD. Expressions for the singly diffracted field are presented, and then compared with the exact solution for a range of parameters. The choice of parameters is governed by a set of mode angles which are used in describing geometrically how a ray propagates through the Duct and out into free space.
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exact and approximate directivity patterns of the sound radiated from a Cylindrical Duct
Journal of Sound and Vibration, 1999Co-Authors: Steven T. HocterAbstract:Abstract The exact solution for radiation from a Cylindrical pipe obtained by using the Wiener–Hopf method has been available for over 50 years. Approximate solutions can be used to simplify the problem, and their accuracy compared with the exact solution. Firstly, the exact solution can be simplified by using the method of the steepest descent to cast the problem in the form of Weinstein's U -approximation. A simpler technique involves the use of the Kirchhoff approximation. This vastly simplifies the problem by considering the radiation emanating from a circular aperture in a thin screen. The various formulae are then compared in a parameter space related to the physical structure of a propagating model. If one considers the behaviour of the approximations solely as one of the governing parameters is altered (i.e., as k0a is increased), the physical behaviour of the propagating mode would not linearly change. In considering the parameters in terms of mode angles, one can observe the accuracy of the approximations for various parameters while linearly changing the ray structure.
C. J. Chapman - One of the best experts on this subject based on the ideXlab platform.
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Caustics in Cylindrical Ducts
Proceedings of the Royal Society of London. Series A: Mathematical Physical and Engineering Sciences, 1999Co-Authors: C. J. ChapmanAbstract:This paper determines the caustic structure of the acoustic field reflected from the end face of a circular Cylindrical Duct when the incident field from inside the Duct is a spinning acoustic mode...
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Sound radiation from a Cylindrical Duct. Part 2. Source modelling, nil-shielding directions, and the open-to-Ducted transfer function
Journal of Fluid Mechanics, 1996Co-Authors: C. J. ChapmanAbstract:This paper analyses the sound radiated from the front face of a hard-walled circular Cylindrical Duct in a subsonic mean flow when the Duct contains acoustic sources typical of those in a Ducted-fan aeroengine. Two main results are established for modes of any given frequency and circumferential order. The first result is that in certain easily calculated directions, called here the nil-shielding directions, the sound radiated by Ducted sources is the same as the sound radiated by the corresponding open sources, i.e. by unDucted sources of the same distribution and strength radiating into free space. Thus in these special directions the Duct has no noise-shielding effect. The second result is that, in the Kirchhoff approximation, the sound radiated by the open sources in the nil-shielding directions determines the sound radiated by the Ducted sources in all directions ; i.e. the sound fields radiated by open and Ducted sources are related by an open-to-Ducted transfer function. This function is such that the sound radiated by the Ducted sources is a linear combination of certain diffraction functions, in which the coefficients are given by the sound radiated by the open sources in the nil-shielding directions. The diffraction functions do not depend on the sources and are here calculated explicitly in terms of Bessel functions. The method used in the paper is Kirchhoff's approximation ; within linear theory this gives the nil-shielding directions exactly, i.e. in agreement with the Wiener-Hopf solution, and gives the main beam of the radiated field, including the major side-lobes, to good accuracy. The results are relevant to the sound radiated into the forward arc by a Ducted turbofan aeroengine.
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Sound radiation from a Cylindrical Duct. Part 1. Ray structure of the Duct modes and of the external field
Journal of Fluid Mechanics, 1994Co-Authors: C. J. ChapmanAbstract:This paper determines the ray structure of a spinning acoustic mode propagating inside a semi-infinite circular Cylindrical Duct, and thereby determines the ray structure of the field radiated from the end of the Duct. Inside the Duct, but outside of a caustic Cylindrical surface, the rays are piecewise linear helices; on striking the rim of the end-face of the Duct, these rays produce ‘Keller cones’ of diffracted rays. The cones determine the structure of the radiated field: for example, no rays penetrate two cone-shaped far-field quiet zones centred on the Duct axis; two rays pass through each point in a forward loud zone; and one ray passes through each point in a rearward loud zone. The two rays through each point in the forward loud zone interfere to produce an oscillatory directivity pattern. One quarter of the rays on each cone point back inside the Duct and produce the reflected field. Thus the rim of the end-face of the Duct acts as a ‘ring source’, in which the radiated and reflected fields have their origin. Every propagating Duct mode determines a polar angle and an azimuthal angle; these are taken as parameters specifying the mode and are used to calculate the positions and angles of all the rays. The mathematical method on which the paper is based is Debye's approximation for the Bessel function which appears in the expression for the Duct modes; the approximation shows also that the Duct contains a region of smooth helical rays on which the field consists of inhomogeneous waves: this region is the inner cylinder, lying inside the annulus of piecewise linear helical rays. The results of the paper are very promising for the application of Keller's geometrical theory of diffraction to detailed calculations of the sound radiated from aeroengine Ducts. An alternative description of the field, using Cargill's meridional rays, is summarized.
J. D. Holdeman - One of the best experts on this subject based on the ideXlab platform.
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Mixing and NO(x) Emission Calculations of Confined Reacting Jet Flows in a Cylindrical Duct
2003Co-Authors: J. D. Holdeman, Victor L. OechsleAbstract:Rapid mixing of cold lateral jets with hot cross-stream flows in confined configurations is of practical interest in gas turbine combustors as it strongly affects combustor exit temperature quality, and gaseous emissions in for example rich-lean combustion. It is therefore important to further improve our fundamental understanding of the important processes of dilution jet mixing especially when the injected jet mass flow rate exceeds that of the cross-stream. The results reported in this report describe some of the main flow characteristics which develop in the mixing process in a Cylindrical Duct. A 3-dimensional tool has been used to predict the mixing flow field characteristics and NOx emission in a quench section of an RQL combustor, Eighteen configurations have been analyzed in a circular geometry in a fully reacting environment simulating the operating condition of an actual RQL gas turbine combustion liner. The evaluation matrix was constructed by varying three parameters: 1) jet-to-mainstream momentum-flux ratio (J), 2) orifice shape or orifice aspect ratio, and 3) slot slant angle. The results indicate that the mixing flow field significantly varies with the value of the jet penetration and subsequently, slanting elongated slots generally improve the mixing uniformity at high J conditions. Round orifices produce more uniform mixing and low NO(x) emissions at low J due to the strong and adequate jet penetration. No significant correlation was found between the NO(x) proDuction rates and the mixing deviation parameters, however, strong correlation was found between NO(x) formation and jet penetration. In the computational results, most of the NO(x) formation occurred behind the orifice starting at the orifice wake region. Additional NO(x) is formed upstream of the orifice in certain configurations with high J conditions due to the upstream recirculation.
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optimization of orifice geometry for crossflow mixing in a Cylindrical Duct
Journal of Propulsion and Power, 2000Co-Authors: J. T. Kroll, W. A. Sowa, G. S. Samuelsen, J. D. HoldemanAbstract:Mixing of gaseous jets in a crossflow has significant applications in combustion science and engineering, one example of which is the mixing zone of a rich-burn/quick-mix/lean-burn gas turbine combustor. A major design question is the jet orifice shape and jet orifice number that optimizes the mixing performance. To delineate the optimal orifice features for a given axial distance and momentum-flux ratio, a statistical design of experiments test matrix was established around three variables: the number of orifices, the orifice aspect ratio, and the orifice angle (in circumferential plane). A jet-to-mainstream momentum-flux ratio of 40 and a mass-flow ratio of 2.5 were selected as representative of a practical design. To yield an interpolating equation that predicts the mixing performance of orifice geometry combinations within the range of the test matrix parameters, a regression analysis was conDucted on the data. The results reveal that 1) mixture uniformity is a nonlinear function of the number of orifices, the orifice aspect ratio, and the orifice angle and that 2) optimum mixing occurs when the mean jet trajectories are in the range of 0.30<ζ/R<0.5 (where ζ = R-r) at x/R = 1. At the optimum number of orifices, the difference between shallow-angled slots with large aspect ratios and round holes is minimal and either geometry produces optimal mixing performance.
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Optimization of orifice geometry for crossflow mixing in a Cylindrical Duct
Journal of Propulsion and Power, 2000Co-Authors: J. T. Kroll, W. A. Sowa, G. S. Samuelsen, J. D. HoldemanAbstract:Mixing of gaseous jets in a crossflow has significant applications in combustion science and engineering, one example of which is the mixing zone of a rich-burn/quick-mix/lean-burn gas turbine combustor. A major design question is the jet orifice shape and jet orifice number that optimizes the mixing performance. To delineate the optimal orifice features for a given axial distance and momentum-flux ratio, a statistical design of experiments test matrix was established around three variables: the number of orifices, the orifice aspect ratio, and the orifice angle (in circumferential plane). A jet-to-mainstream momentum-flux ratio of 40 and a mass-flow ratio of 2.5 were selected as representative of a practical design. To yield an interpolating equation that predicts the mixing performance of orifice geometry combinations within the range of the test matrix parameters, a regression analysis was conDucted on the data. The results reveal that 1) mixture uniformity is a nonlinear function of the number of orifices, the orifice aspect ratio, and the orifice angle and that 2) optimum mixing occurs when the mean jet trajectories are in the range of 0.30
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Mixing of Multiple Jets With a Confined Subsonic Crossflow: Part I—Cylindrical Duct
Journal of Engineering for Gas Turbines and Power, 1997Co-Authors: J. D. Holdeman, David S. Liscinsky, V. L. Oechsle, G. S. Samuelsen, C. E. SmithAbstract:This paper summarizes NASA-supported experimental and computational results on the mixing of a row of jets with a confined subsonic crossflow in a Cylindrical Duct. The studies from which these results were excerpted investigated flow and geometric variations typical of the complex three-dimensional flowfield in the combustion chambers in gas turbine engines. The principal observations were that the momentum-flux ratio and the number of orifices were significant variables. Jet penetration was critical, and jet penetration decreased as either the number of orifices increased or the momentum-flux ratio decreased. It also appeared that jet penetration remained similar with variations in orifice size, shape, spacing, and momentum-flux ratio when the number of orifices was proportional to the square root of the momentum-flux ratio. In the Cylindrical geometry, planar variances are very sensitive to events in the near-wall region, so planar averages must be considered in context with the distributions. The mass-flow ratios and orifices investigated were often very large (mass-flow ratio >1 and ratio of orifice area-to-mainstream cross-sectional area up to 0.5), and the axial planes of interest were sometimes near the orifice trailing edge. Three-dimensional flow was a key part of efficient mixing and was observed for all configurations. The results shown also seem to indicate that nonreacting dimensionless scalar profiles can emulate the reacting flow equivalence ratio distribution reasonably well. The results cited suggest that further study may not necessarily lead to a universal “rule of thumb” for mixer design for lowest emissions, because optimization will likely require an assessment for a specific application.
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mixing of multiple jets with a confined subsonic crossflow part i Cylindrical Duct
Journal of Engineering for Gas Turbines and Power-transactions of The Asme, 1997Co-Authors: J. D. Holdeman, David S. Liscinsky, V. L. Oechsle, G. S. Samuelsen, C. E. SmithAbstract:This paper summarizes NASA-supported experimental and computational results on the mixing of a row of jets with a confined subsonic crossflow in a Cylindrical Duct. The studies from which these results were excerpted investigated flow and geometric variations typical of the complex three-dimensional flowfield in the combustion chambers in gas turbine engines. The principal observations were that the momentum-flux ratio and the number of orifices were significant variables. Jet penetration was critical, and jet penetration decreased as either the number of orifices increased or the momentum-flux ratio decreased. It also appeared that jet penetration remained similar with variations in orifice size, shape, spacing, and momentum-flux ratio when the number of orifices was proportional to the square root of the momentum-flux ratio. In the Cylindrical geometry, planar variances are very sensitive to events in the near-wall region, so planar averages must be considered in context with the distributions. The mass-flow ratios and orifices investigated were often very large (mass-flow ratio >1 and ratio of orifice area-to-mainstream cross-sectional area up to 0.5), and the axial planes of interest were sometimes near the orifice trailing edge. Three-dimensional flow was a key part of efficient mixing and was observed for all configurations. The results shown also seem to indicate that nonreacting dimensionless scalar profiles can emulate the reacting flow equivalence ratio distribution reasonably well. The results cited suggest that further study may not necessarily lead to a universal “rule of thumb” for mixer design for lowest emissions, because optimization will likely require an assessment for a specific application.
Tatyana M. Zaboronkova - One of the best experts on this subject based on the ideXlab platform.
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Whistler wave radiation from a pulsed loop antenna located in a Cylindrical Duct with enhanced plasma density
Physics of Plasmas, 2014Co-Authors: Alexander V. Kudrin, Natalya M. Shkokova, Orsolya E. Ferencz, Tatyana M. ZaboronkovaAbstract:Pulsed radiation from a loop antenna located in a Cylindrical Duct with enhanced plasma density is studied. The radiated energy and its distribution over the spatial and frequency spectra of the excited waves are derived and analyzed as functions of the antenna and Duct parameters. Numerical results referring to the case where the frequency spectrum of the antenna current is concentrated in the whistler range are reported. It is shown that under ionospheric conditions, the presence of an artificial Duct with enhanced density can lead to a significant increase in the energy radiated from a pulsed loop antenna compared with the case where the same source is immersed in the surrounding uniform magnetoplasma. The results obtained can be useful in planning active ionospheric experiments with pulsed electromagnetic sources operated in the presence of artificial field-aligned plasma density irregularities that are capable of guiding whistler waves.
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whistler wave radiation from a pulsed loop antenna located in a Cylindrical density Duct
European Conference on Antennas and Propagation, 2013Co-Authors: Alexander V. Kudrin, Natalya M. Shkokova, Vasiliy A Eskin, Tatyana M. ZaboronkovaAbstract:Pulsed radiation from a loop antenna located in a Cylindrical Duct with enhanced plasma density is studied. An expression for the radiated energy is derived and its distribution over the spatial and frequency spectra of the excited waves as a function of the source and Duct parameters is analyzed. Numerical results referring to the case where the frequency spectrum of the antenna current is concentrated in the whistler range are reported. It is shown that under ionospheric conditions, the presence of an artificial Duct with enhanced density can lead to a significant increase in the energy radiated from a pulsed loop antenna compared with the case where the same source is immersed in the surrounding uniform magnetoplasma.
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Excitation and propagation of whistler waves in a magnetoplasma in the presence of a Cylindrical Duct with decreased density
2008Co-Authors: P. V. Bakharev, Alexander V. Kudrin, Tatyana M. ZaboronkovaAbstract:Excitation and propagation of whistler-mode waves in an unbounded magnetoplasma in the presence of a Cylindrical Duct with decreased plasma density are studied. Using a rigorous solution for the total source-excited field comprising both the discrete and continuous parts of the spatial spectrum of waves, the radiation resistance of a source in the form of a loop antenna is determined. Conditions have been revealed under which the power radiated from the loop antenna immersed in a decreased-density Duct is dominated by the contribution of either discrete-or continuous-spectrum modes.
Alexander V. Kudrin - One of the best experts on this subject based on the ideXlab platform.
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Whistler wave radiation from a pulsed loop antenna located in a Cylindrical Duct with enhanced plasma density
Physics of Plasmas, 2014Co-Authors: Alexander V. Kudrin, Natalya M. Shkokova, Orsolya E. Ferencz, Tatyana M. ZaboronkovaAbstract:Pulsed radiation from a loop antenna located in a Cylindrical Duct with enhanced plasma density is studied. The radiated energy and its distribution over the spatial and frequency spectra of the excited waves are derived and analyzed as functions of the antenna and Duct parameters. Numerical results referring to the case where the frequency spectrum of the antenna current is concentrated in the whistler range are reported. It is shown that under ionospheric conditions, the presence of an artificial Duct with enhanced density can lead to a significant increase in the energy radiated from a pulsed loop antenna compared with the case where the same source is immersed in the surrounding uniform magnetoplasma. The results obtained can be useful in planning active ionospheric experiments with pulsed electromagnetic sources operated in the presence of artificial field-aligned plasma density irregularities that are capable of guiding whistler waves.
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whistler wave radiation from a pulsed loop antenna located in a Cylindrical density Duct
European Conference on Antennas and Propagation, 2013Co-Authors: Alexander V. Kudrin, Natalya M. Shkokova, Vasiliy A Eskin, Tatyana M. ZaboronkovaAbstract:Pulsed radiation from a loop antenna located in a Cylindrical Duct with enhanced plasma density is studied. An expression for the radiated energy is derived and its distribution over the spatial and frequency spectra of the excited waves as a function of the source and Duct parameters is analyzed. Numerical results referring to the case where the frequency spectrum of the antenna current is concentrated in the whistler range are reported. It is shown that under ionospheric conditions, the presence of an artificial Duct with enhanced density can lead to a significant increase in the energy radiated from a pulsed loop antenna compared with the case where the same source is immersed in the surrounding uniform magnetoplasma.
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Whistler wave excitation by a pulsed loop antenna located in a Cylindrical Duct with enhanced plasma density
2011 XXXth URSI General Assembly and Scientific Symposium, 2011Co-Authors: N. M. Shmeleva, Alexander V. Kudrin, V. A. Es'kinAbstract:Pulsed radiation from a loop antenna located in a Cylindrical Duct with enhanced plasma density is studied. An expression for the radiated energy is derived and its distribution over the spatial and frequency spectra of the excited waves as a function of the source and Duct parameters is analyzed. Numerical results referring to the case where the frequency spectrum of the current is concentrated in the whistler range are reported. It is shown that under ionospheric conditions, the presence of an artificial Duct with enhanced density can lead to a significant increase in the energy radiated from a pulsed loop antenna compared with the case where the same source is immersed in the surrounding uniform magnetoplasma.
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Excitation of whistler waves in a collisional magnetoplasma in the presence of Ducts with enhanced density
Plasma Physics Reports, 2009Co-Authors: V. A. Es’kin, Alexander V. KudrinAbstract:A study is made of the excitation of waves in the whistler frequency range by a given ring electric current in a collisional magnetoplasma in the presence of a Cylindrical Duct with enhanced density. It is shown that, under certain conditions, dissipative losses due to electron collisions in plasma can lead to a substantial redistribution of the source radiation power over the spatial spectrum of the modes guided by the Duct, as compared to the case of a collisionless plasma. Numerical results are presented that illustrate these changes in the excitation efficiency of whistler modes.
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Excitation and propagation of whistler waves in a magnetoplasma in the presence of a Cylindrical Duct with decreased density
2008Co-Authors: P. V. Bakharev, Alexander V. Kudrin, Tatyana M. ZaboronkovaAbstract:Excitation and propagation of whistler-mode waves in an unbounded magnetoplasma in the presence of a Cylindrical Duct with decreased plasma density are studied. Using a rigorous solution for the total source-excited field comprising both the discrete and continuous parts of the spatial spectrum of waves, the radiation resistance of a source in the form of a loop antenna is determined. Conditions have been revealed under which the power radiated from the loop antenna immersed in a decreased-density Duct is dominated by the contribution of either discrete-or continuous-spectrum modes.
