Edward J Kerschen

Interests

No activities entered.

Courses

Scholarly Contributions

Journals/Publications

• Wittich, D. J., Duffin, D. A., Jumper, E. J., Cain, A. B., & Kerschen, E. J. (2009). Passive shear layer regularization experiments in wind tunnels and feed-forward adaptive-optic correction. 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition.
  More info

  Abstract: Shear layer regularization is a fundamental requirement in a Feed-Forward, Adaptive-Optic (FFAO) wavefront correction scheme applied to a beam passing through the shear layer. 'Passive regularization' exploits the self-sustained oscillations of a shear layer over a resonant cavity, thereby eliminating the need for active flow control actuation. In wind tunnel tests, a strong acoustic resonance coupled with the cavity shear layer feedback mechanism produced a robust, predictable shear layer motion. The unsteady pressure at the upstream wall of the cavity was periodic enough to be used as a reliable phase reference. This phase reference was used to drive a phase-locked wavefront acquisition system and, ultimately, a deformable mirror which applied a feed-forward wavefront correction. The source of the strong acoustic resonance resulted from trapped duct modes, a result of the particular cavity and wind tunnel geometry combination. Unsteady pressure data indicated that this otherwise undesirable source of resonance can be mitigated by lining the wind tunnel wall opposite the cavity with an acoustically absorbent material. Copyright © 2009 by Wittich, Duffin, Jumper, Cain and Kerschen.
• Cain, A. B., Ng, T. T., Jumper, E. J., Wittich, D. J., Cavalieri, D., & Kerschen, E. J. (2008). An optical propagation improvement system and the importance of aeroacoustics. 39th AIAA Plasmadynamics and Lasers Conference.
  More info

  Abstract: Use of an airborne platform for a directed energy system is currently severely limited by aero-optic aberrations arising from density variations in air flowing over the aircraft; the primary limitation is for aft pointing applications. Innovative Technology Applications Company (ITAC), in collaboration with the University of Notre Dame (ND), is working to develop, design, construct and test a turret/adaptive fairing that provides a large field of regard for propagation of a lethal beam from an airborne platform at up to transonic speed. The conceptual design incorporates a fairing that includes a tuned cavity between the aperture and the aft-fairing that excites a resonance mode that robustly regularizes optical aberrations imposed by the shear layer over the entire Mach number range. The cavity will be exposed to the flow only when using the beam in an aft pointing direction. Optical-aberration regularization is the exact requirement for robust feed-forward adaptive-optic correction of a laser propagated through the controlled shear layer. This paper will describe the importance of understanding aeroacoustic behavior to effectively develop aero-optic capability that is based on cavity resonances. Copyright © 2008 by Cain, Ng, Jumper, Wittich, Cavalieri, Kerschen.
• Kerschen, E. J., & Cain, A. B. (2008). Aeroacoustic mode trapping for a wind tunnel with a cavity in the wall. 39th AIAA Plasmadynamics and Lasers Conference.
  More info

  Abstract: The cavity resonance phenomenon has recently been suggested as an approach for regularizing the shear layer downstream of an aero-optic turret. Experiments on this geometry have been carried out in wind tunnels, with the cavity recessed in one wall. In this paper, we present a theoretical analysis which shows that this geometry can lead to an aeroacoustic mode-trapping phenomenon. The mode trapping arises when the cut-on frequencies fTcr for the tunnel cross-stream eigenmodes are higher than the cut-on frequencies fCT cr for the corresponding cavity-tunnel modes (in the region of the tunnel containing the cavity). Between these two critical frequencies, fCT cr < f < fTcr, there are frequency windows where mode trapping can occur. Because the acoustic radiation away from the cavity region is inhibited in these frequency windows, a cavity resonance field that involves a trapped mode can reach very high amplitudes, far in excess of the amplitude that would be found for the cavity geometry in an external flow environment. The theory predicts the characteristics of the cavity-tunnel and tunnel modes, and the frequency windows for aeroacoustic mode trapping, as a function of geometry and Mach number. Results of the theory are compared with experiments, confirming the importance of the mode-trapping phenomenon. Copyright © 2008 by the authors.
• Nelson, C. C., Cain, A. B., Kerschen, E. J., & Raman, G. (2006). Simulations of helmholtz resonator powered resonance tubes at moderate pressure ratios. Collection of Technical Papers - 44th AIAA Aerospace Sciences Meeting, 13, 9633-9650.
  More info

  Abstract: The present paper reports on recent work to further understand the properties of Heimholt? resonator Powered Resonance Tubes (PRT). Three different PRT geometries with Heimholt? resonators were examined. For comparison, a single straight tube resonator was also simulated. Simulation results are compared to both theoretical and experimental findings. The simulations were found to be in excellent qualitative agreement with both theory and experiment. The use of Heimholt? resonators as part of a PRT is found to be an effective means of obtaining lower frequency output without requiring as long a resonator chamber as with a straight tube.
• Alvarez, J. O., & Kerschen, E. J. (2005). Influence of wind tunnel walls on cavity acoustic resonances. Collection of Technical Papers - 11th AIAA/CEAS Aeroacoustics Conference, 1, 57-69.
  More info

  Abstract: Flow-acoustic resonances leading to high unsteady pressure levels may occur in flow past cavities. The long-standing semi-empirical model of Rossiter, and a more complete theoretical model recently developed by the authors, both predict the existence of several resonance frequencies. The unsteady pressure spectra measured in experiments typically also contain several resonance peaks, consistent in nature with the theory. However, in wind-tunnel experiments where the cavity is embedded In one of the wind-tunnel walls, the pressure spectrum may shift to the case of a single dominant frequency, sometimes quite abruptly and only for a narrow range of flow speeds. In the present paper, we develop a modified theoretical prediction method that explicitly accounts for the presence of wind-tunnel walls. The cross-stream eigenmodes play a central role in the theory. We show that, in the frequency (or Mach number) band where a higher-order eigenmode is cut-on in the tunnel-cavity section, but cut-off in the upstream and downstream tunnel sections, the nearly-trapped nature of the acoustic field causes a dramatic increase in the growth rate for the global flow-acoustic resonance mode. This provides an explanation for the dominant mode behavior that has been observed in experiments.
• Hammerton, P. W., & Kerschen, E. J. (2005). Leading-edge receptivity for bodies with mean aerodynamic loading. Journal of Fluid Mechanics, 535, 1-32.
  More info

  Abstract: Boundary-layer receptivity in the leading-edge region of a cambered thin airfoil is analysed for the case of a low-Mach-number flow. Acoustic free-stream disturbances are considered. Asymptotic results based on large Reynolds number (U2/ων ≫ 1) are presented, supplemented by numerical solutions. The influence of mean aerodynamic loading enters the theory through a parameter μ, which provides a measure of the flow speed variations in the leading-edge region, due to flow around the leading edge from the lower surface to the upper. A Strouhal number based on airfoil nose radius, S = ωrn/U, also enters the theory. The variation of the receptivity level as a function of μ and S is analysed. Modest levels of aerodynamic loading are found to decrease the receptivity level for the upper surface of the airfoil, while the receptivity is increased for the lower surface. For larger angles of attack close to the critical angle for boundary layer separation, a local rise in the receptivity occurs for the upper surface, while on the lower surface the receptivity decreases. These effects are more pronounced at larger values of S. While the Tollmien-Schlichting wave does not emerge until a downstream distance of O((U2/ων)1/3U/ω), the amplitude of the Tollmien-Schlichting wave is influenced by the acoustic free-stream disturbances only in a relatively small region near the leading edge, of length approximately 4U/ω). The numerical receptivity coefficients calculated, together with the asymptotic eigenfunctions presented, provide all the necessary information for transition analysis from the interaction of acoustic disturbances with leading-edge geometry. © 2005 Cambridge University Press.
• Cain, A. B., Kerschen, E. J., Tassy, J. M., & Raman, G. (2004). Simulation of powered resonance tubes: Helmholtz resonator geometries. 2nd AIAA Flow Control Conference.
  More info

  Abstract: PRT actuators, which consist of a high pressure air supply jet, a resonance tube, and an integration slot, are capable of producing high amplitude pressure oscillations. The traditional approach requires a very long resonance tube when low frequencies are desired. A Helmholtz based PRT offers a method of substantially reducing the resonance tube length requirement. This paper is focused on present simulation results for such a design with comparisons to theory and experiment. At low NPR values a Helmholtz response in simulations and experiments shows good correspondence with theory. At higher values of NPR the computational and experimental comparisons to theory suggest that non-linear effects must be considered and that screech in particular can suppress or shift the Helmholtz response. The effort to integrate simulations, theory, and experiment has been fruitful. There is general agreement between these three methods in terms of the frequency, amplitude, and directivity of the actuator output field, to the extent that they have been examined. © 2004 by Alan Cain, Edward Kerschen, Julianna Tassy, and Ganesh Raman.
• Kerschen, E. J., Cain, A. B., & Raman, G. (2004). Analytical modeling of helmholtz resonator based powered resonance tubes. 2nd AIAA Flow Control Conference.
  More info

  Abstract: The Powered Resonance Tube (PRT) actuator, in which a high-speed jet impinges on the open end of a quarter-wavelength resonance tube, is an effective device for producing high-amplitude pressure oscillations. For low frequency applications, however, the size of the PRT actuator can be quite large, due to the length of the quarter-wavelength tube. In order to reduce the actuator size, we propose an alternative design in which the quarter-wavelength tube is replaced by a Helmholtz resonator. The Helmholtz resonator has a narrow neck coupled to a backing cavity of much larger diameter. The resonant frequency is determined by the ratio of fluid stiffness in the backing cavity to fluid mass in the neck; proper choice of geometry leads to a resonator length that is small compared to the length of a quarter-wavelength tube. We present an analysis of Helmholtz resonator behavior which predicts the influence of geometry on the resonant frequency and the capacity of the resonator to absorb an unsteady volume flux. Comparisons are made with companion numerical simulations for a Helmholtz PRT actuator. © 2004 by the authors.
• Peake, N., & Kerschen, E. J. (2004). Influence of mean loading on noise generated by the interaction of gusts with a cascade: Downstream radiation. Journal of Fluid Mechanics, 515, 99-133.
  More info

  Abstract: We consider the effects of blade mean loading on the noise generated by the interaction between convected vorticity and a blade row. The blades are treated as flat plates aligned at a non-zero incidence angle, δ, to the oncoming stream, and we take harmonic components of the incident vorticity field with reduced frequency k, and use asymptotic analysis in the realistic limit k ≫ 1, δ ≪ 1 with kδ = 0 (1). In a previous paper (Peake & Kerschen, J. Fluid Mech., vol. 347 (1997), pp. 315-346) we have analysed the sound radiated back upstream, but the field in the blade passages and the sound radiated downstream are also of considerable practical interest, and are considered in this paper. The flow is seen to consist of inner regions around each leading edge, in which sound is generated by the local gust-airfoil and gust-flow interactions, and an outer region in which the incident gust and the acoustic radiation interact with the non-uniform mean flow and the other blades. It is shown that the complicated multiple interactions between the blades can be represented by images in potential-streamfunction space, yielding closed-form expressions for the phase distortion experienced by sound waves propagating down the blade passages. The acoustic radiation downstream of the cascade at O(1) distances is dominated by the duct-mode beams that emanate from the passages, while the far downstream field is generated by the diffraction of the duct modes by the trailing edges. The modal amplitudes of the radiation field far downstream tend to be largest when the mode direction is close to the propagation direction of the duct mode which generated it, corresponding to the way (in uniform flow) in which the radiation from a single blade passage tends to be beamed in the duct-mode directions. Although the diffraction coefficient for the scattering from a single trailing edge is singular in these directions, we show how uniformly valid expressions can be derived by combining the trailing-edge fields in an appropriate way, thereby describing the larger amplitude in the beam directions. The steady non-uniform flow downstream has the effect of tilting the directions of the beams by O(δ) angles away from the duct-mode directions, which are explicitly determined. Throughout this analysis it will be seen that the interaction with the non-uniform mean flow introduces phase corrections of size O(kδ), which, given the way in which interference effects between the multiple blades dominate unsteady cascade flow, proves to be highly significant. © 2004 Cambridge University Press.
• Raman, G., Khanafseh, S., Cain, A. B., & Kerschen, E. (2004). Development of high bandwidth powered resonance tube actuators with feedback control. Journal of Sound and Vibration, 269(3-5), 1031-1062.
  More info

  Abstract: A high bandwidth powered resonance tube (PRT) actuator potentially useful for noise and flow control applications was developed. High bandwidth allows use of the same actuator at various locations on an aircraft and over a range of flight speeds. The actuator selected for bandwidth enhancement was the PRT actuator, which is an adaptation of the Hartmann whistle. The device is capable of producing high-frequency and high-amplitude pressure and velocity perturbations for active flow control applications. Our detailed experiments aimed at understanding the PRT phenomenon are complemented by an improved analytical model and direct numerical simulations. We provide a detailed characterization of the unsteady pressures in the nearfield of the actuator using phase averaged pressure measurements. The measurements revealed that propagating fluctuations at 9 kHz were biased towards the upstream direction (relative to the supply jet). A complementary computational study validated by our experiments was useful in simulating the details in the region between the supply jet and the resonance tube where it was difficult to gather experimental data. High bandwidth was obtained by varying the depth of the resonance tube that determines the frequency produced by the device. Our actuator could produce frequencies ranging from 1600 to 15,000 Hz at amplitudes as high as 160 dB near the source. The frequency variation with depth is predicted well by the quarter wavelength formula for deep tubes but the formula becomes increasingly inaccurate as the tube depth is decreased. An improved analytical model was developed, in which the compliance and mass of the fluid in the integration slot is incorporated into the prediction of resonance frequencies of the system. Finally a feedback controller that varied both the resonance tube depth and spacing to converge on a desired frequency was developed and demonstrated. We are optimistic that numerous potential applications exist for such high bandwidth high dynamic range actuators. © 2003 Published by Elsevier Science Ltd.
• Raman, G., Sarpotdar, S., Tassy, J., Cain, A. B., & Kerschen, E. (2004). An overview of the development of high bandwidth powered resonance tube actuators: Experiments and simulations. Collection of Technical Papers - 10th AIAA/CEAS Aeroacoustics Conference, 1, 658-672.
  More info

  Abstract: The development of high bandwidth powered resonance tube (PRT) actuators is discussed. High bandwidth allows use of the same actuator at various locations on an aircraft and over a range of flight speeds. The actuator selected for bandwidth enhancement was the PRT actuator, which is an adaption of the Hartmann whistle. The detailed nearfield data provided information of the actuation signal directivity and its variation with actuation frequency. The computational work that was conducted at Reynolds number required to simulate details observed in experiments.
• Cain, A. B., Kerschen, E. J., Raman, G., & Sarpotdar, S. (2003). Simulation of powered resonance tubes: Understanding parameter space. 9th AIAA/CEAS Aeroacoustics Conference and Exhibit.
  More info

  Abstract: New simulations of powered resonance tubes (PRT) have been performed at two Reynolds numbers that differ by a factor of 10. The lower Reynolds results show strong regularity with some disorder showing up in the higher Reynolds number cases. Remarkably the simulations show that the dominant frequencies, amplitude and directivity of the PRT actuator output field are largely unaffected by the factor of 10 increase in Reynolds number considered here. However, the increase in Reynolds number is shown to substantially affect the width of the resonance peaks, and the vorticity distributions and flow details more generally. The effort to integrate simulations, theory, and experiment has been fruitful. There is general agreement between these three methods in terms of the frequency, amplitude, and directivity of the actuator output field, to the extent that they have been examined. © 2003 by the authors.
• Cain, A. B., Kerschen, E. J., & Raman, G. (2002). Simulation of acoustic characteristics and mechanisms of powered resonance tubeso. 8th AIAA/CEAS Aeroacoustics Conference and Exhibit.
  More info

  Abstract: Flow simulations have been performed as part of our effort to better understand powered resonance tube behavior. Scaled simulations of the powered resonance tube have produced reasonable correspondence to laboratory experiments, in terms of the frequency (simulated at 7.6 kHz, laboratory value 7.2 kHz) and amplitude (a simulation value of 160dB, laboratory value 157dB) of the resonant response. The laboratory experiments were performed at Illinois Institute of Technology and are described in Raman et al. (2002). The simulations suggest new insights into the complexity and details of the flowfield. The simulations show that the flow in the integration slot is primarily on the resonance tube side, with almost no flow on the supply tube side of the integration slot. The numerical results suggest that the acoustic waves from the resonance in the resonance tube drive an unsteady separation at the supply tube. The unsteady separation at the supply tube in turn drives the observed large oscillations in the shock structure. The unsteady separation seems to be a key aspect of the resonance phenomena. © 2002 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc.
• Cain, A. B., Kerschen, E. J., Raman, G., & Khanafseh, S. (2002). Simulation of powered resonance tubes: Effects of pressure ratio and freestream flow©. 1st Flow Control Conference.
  More info

  Abstract: Flow simulations have been performed as part of our effort to better understand powered resonance tube behavior. Scaled simulations of the powered resonance tube have produced reasonable correspondence to laboratory experiments, in terms of the frequency and amplitude of the resonant response. The simulations suggest new insights into the complexity and details of the flowfield. The simulations show that the flow in the integration slot is primarily on the resonance tube side, with almost no flow on the supply tube side of the integration slot. The numerical results suggest that the acoustic waves from the resonance in the resonance tube drive an unsteady separation at the supply tube. The unsteady separation at the supply tube in turn drives the observed large oscillations in the shock structure. The unsteady separation seems to be a key aspect of the resonance phenomena. Very recently it has been discovered that for shallow resonance tubes, the pressure ratio affects the response frequency. Also, the resonance tube is found to impose strong pressure disturbances in a Mach 0.5 boundary layer flow. The presence of the Mach 0.5 external stream and boundary layer reduces the resonance frequency by about 12%, relative to the case without an external stream. © 2002 by the author(s).
• Saric, W. S., Reed, H. L., & Kerschen, E. J. (2002). Boundary-layer receptivity to freestream disturbances. Annual Review of Fluid Mechanics, 34, 291-319.
  More info

  Abstract: The current understanding of boundary-layer receptivity to external acoustic and vortical disturbances is reviewed. Recent advances in theoretical modeling, numerical simulations, and experiments are discussed. It is shown that aspects of the theory have been validated and that the mechanisms by which freestream disturbances provide the initial conditions for unstable waves are better understood. Challenges remain, however, particularly with respect to freestream turbulence.
• Peake, N., & Kerschen, E. J. (2001). The noise downstream of a cascade of loaded airfoils. 7th AIAA/CEAS Aeroacoustics Conference and Exhibit.
  More info

  Abstract: In this paper we consider the interaction between vortical gusts of reduced frequency k and a cascade of flat-plate blades at an angle of inclination δ to the oncoming subsonic mean flow. In the asymptotic limit A: » 1 with kδ = 0(1) it turns out that the unsteady flow can be described using matched asymptotic expansions, and in earlier papers we have described how to use this method to determine the radiation field upstream of the cascade and in the blade passages. In this paper we turn our attention to the field downstream of the cascade, and describe the theoretical framework and principal analytical expressions. A particular feature will be potential strong acoustic beaming in directions matching with the modal directions in the blade passages. © 2001 by N. Peake and EJ. Kerschen.
• Reba, R. A., & Kerschen, E. J. (2001). Boundary-layer effects on performance of surface-mounted actuators for active noise control. 7th AIAA/CEAS Aeroacoustics Conference and Exhibit.
  More info

  Abstract: A theoretical analysis is developed for the effects of the viscous boundary-layer on the acoustic field produced by surface-mounted actuators. The analysis is based on linearization about a two-dimensional compressible subsonic mean flow. Asymptotic solutions are developed for the unsteady boundary-layer flow over an acoustically-compact actuator that is long compared to the triple-deck scale. The analysis shows that boundary-layer effects play a significant role in determining the acoustic field, and that traditional approaches used to account for acousticallythin boundary layers are not always adequate. In addition to the acoustic monopole field associated with the actuator volume flux, acoustic monopole and dipole fields are produced at leading order by deflection of the boundary layer into the oncoming free-stream. The boundary-layer analysis is applied to a model problem for active control of gust-airfoil interaction noise using actuators mounted near the leading-edge of the airfoil. © 2001 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc.
• Hammerton, P. W., & Kerschen, E. J. (1997). Boundary-layer receptivity for a parabolic leading edge. Part 2. The small-Strouhal-number limit. Journal of Fluid Mechanics, 353, 205-220.
  More info

  Abstract: In Hammerton & Kerschen (1996), the effect of the nose radius of a body on boundary-layer receptivity was analysed for the case of a symmetric mean flow past a two-dimensional body with a parabolic leading edge. A low-Mach-number two-dimensional flow was considered. The radius of curvature of the leading edge, rn, enters the theory through a Strouhal number, S ωrn/U, where ω is the frequency of the unsteady free-stream disturbance and U is the mean flow speed. Numerical results revealed that the variation of receptivity for small S was very different for free-stream acoustic waves propagating parallel to the mean flow and those free-stream waves propagating at an angle to the mean flow. In this paper the small-S asymptotic theory is presented. For free-stream acoustic waves propagating parallel to the symmetric mean flow, the receptivity is found to vary linearly with S, giving a small increase in the amplitude of the receptivity coefficient for small S compared to the flat-plate value. In contrast, for oblique free-stream acoustic waves, the receptivity varies with S1/2, leading to a sharp decrease in the amplitude of the receptivity coefficient relative to the flat-plate value. Comparison of the asymptotic theory with numerical results obtained in the earlier paper confirms the asymptotic results but reveals that the numerical results diverge from the asymptotic result for unexpectedly small values of S.
• Myers, M. R., & Kerschen, E. J. (1997). Influence of camber on sound generation by airfoils interacting with high-frequency gusts. Journal of Fluid Mechanics, 353, 221-259.
  More info

  Abstract: A theoretical model is developed for the sound generated when a convected disturbance encounters a cambered airfoil at non-zero angle of attack. The model is a generalization of a previous theory for a flat-plate airfoil, and is based on a linearization of the Euler equations about the steady, subsonic flow past the airfoil. High-frequency gusts, whose wavelengths are short compared to the airfoil chord, are considered. The airfoil camber and incidence angle are restricted so that the mean flow past the airfoil is a small perturbation to a uniform flow. The singular perturbation analysis retains the asymptotic regions present in the case of a flat-plate airfoil: local regions, which scale on the gust wavelength, at the airfoil leading and trailing edges; a 'transition' region behind the airfoil which is similar to the transition zone between illuminated and shadow regions in optical problems; and an outer region, far away from the airfoil edges and wake, in which the solution has a geometric-acoustics form. For the cambered airfoil, an additional asymptotic region in the form of an acoustic boundary layer adjacent to the airfoil surface is required in order to account for surface curvature effects. Parametric calculations are presented which illustrate that, like incidence angle, moderate amounts of airfoil camber can significantly affect the sound field produced by airfoil-gust interactions. Most importantly, the amount of radiated sound power is found to correlate very well with a single aerodynamic loading parameter, αeff, which is an effective mean-flow incidence angle for the airfoil leading edge.
• Peake, N., & Kerschen, E. J. (1997). Influence of mean loading on noise generated by the interaction of gusts with a flat-plate cascade: Upstream radiation. Journal of Fluid Mechanics, 347, 315-346.
  More info

  Abstract: The sound generated by the interaction between convected vortical and entropic disturbances and a blade row is a significant component of the total noise emitted by a modern aeroengine, and the blade geometry has an important effect on this process. As a first step in the development of a general prediction scheme, we model in this paper just the action of the blade mean loading by treating the blades as flat plates aligned at a non-zero incidence angle, δ, to the oncoming stream, and consider harmonic components of the incident field with reduced frequency k. We then use asymptotic analysis in the realistic limit k ≫ 1, δ 1 with kδ = O(1) to make a consistent asymptotic expansion of the compressible Euler equations. The flow is seen to consist of inner regions around each leading edge, in which sound is generated by the local gust-airfoil and gust-flow interactions, and an outer region in which both the incident gust is distorted according to rapid distortion theory and the out-going sound is refracted by the non-uniform mean flow. The complicated multiple interactions between the sound and the cascade are included to the appropriate asymptotic order, and analytical expressions for the forward radiation are derived. It is seen that even a relatively small value of δ can have a significant effect, thanks to both the O(δk1/2) change in the amplitudes and the O(kδ) change in the phases of the various radiation components, corresponding to the additional source mechanisms associated with the flow distortion around each leading edge and the effects of propagation through the non-uniform flow, respectively. Further work will extend this analysis to include the effects of camber and thickness.
• Hammerton, P. W., & Kerschen, E. J. (1996). Boundary-layer receptivity for a parabolic leading edge. Journal of Fluid Mechanics, 310, 243-267.
  More info

  Abstract: The effect of the nose radius of a body on boundary-layer receptivity is analysed for the case of a symmetric mean flow past a body with a parabolic leading edge. Asymptotic methods based on large Reynolds number are used, supplemented by numerical results. The Mach number is assumed small, and acoustic free-stream disturbances are considered. The case of free-stream acoustic waves, propagating obliquely to the symmetric mean flow is considered. The body nose radius, rn, enters the theory through a Strouhal number, S = ωrn/U, where ω is the frequency of the acoustic wave and U is the mean flow speed. The finite nose radius dramatically reduces the receptivity level compared to that for a flat plate, the amplitude of the instability waves in the boundary layer being decreased by an order of magnitude when S = 0.3. Oblique acoustic waves produce much higher receptivity levels than acoustic waves propagating parallel to the body chord.
• Myers, M. R., & Kerschen, E. J. (1995). Influence of incidence angle on sound generation by airfoils interacting with high-frequency gusts. Journal of Fluid Mechanics, 292, 271-304.
  More info

  Abstract: A theoretical model is developed for the sound generated when a convected vortical or entropic gust encounters an airfoil at non-zero angle of attack. The theory is based on a linearization of the Euler equations about the steady subsonic flow past the airfoil. High-frequency gusts, whose wavelengths are short compared to the airfoil chord, but long compared to the displacement of the mean-flow stagnation point from the leading edge, are considered. The analysis utilizes singular-perturbation techniques and involves four asymptotic regions. Local regions, which scale on the gust wavelength, are present at the airfoil leading and trailing edges. Behind the airfoil a 'transition' region, which is similar to the transition zone between illuminated and shadow zones in optical problems, is present. In the outer region, far away from the airfoil edges and wake, the solution has a geometric-acoustics form. The primary sound generation is found to be concentrated in the local leading-edge region. The trailing edge plays a secondary role as a scatterer of the sound generated in the leading-edge region. Parametric calculations are presented which illustrate that moderate levels of airfoil steady loading can significantly affect the sound field produced by airfoil-gust interactions.
• Peake, N., & Kerschen, E. J. (1995). A uniform asymptotic approximation for high-frequency unsteady cascade flow. Proceedings - Royal Society of London, A, 449(1935), 177-186.
  More info

  Abstract: The scattering of harmonic gusts by a two-dimensional, infinite cascade of flat plates is a model problem which is relevant to the prediction of noise generation by rotating turbomachinery. The problem can be solved analytically using the Wiener-Hopf technique, and the key step involves the exact factorization of a certain generic kernel function, K, using infinite products. An approximation factorization, based on the realistic asymptotic limit of large reduced frequency, has been derived. An important limitation of Peake's approximation, however, is that it becomes invalid when any of the acoustic modes in the system are close to cut-off. We therefore present new asymptotic factors which overcome this non-uniformity. The accuracy of this new approximation, across a whole range of operating parameters, is demonstrated by comparison with the exact results. (from Authors)
• Myers, M. R., & Kerschen, E. J. (1992). The acoustic field of a near-surface source at intermediate distances: A simple result using matched asymptotic expansions. Journal of the Acoustical Society of America, 92(3), 1743-1753.
  More info

  Abstract: The method of matched asymptotic expansions is used to determine simple expressions for the acoustic field due to a source near a rigid boundary in an inhomogeneous medium. The observation distance is assumed to be large compared to the wavelength but short compared to the length scale over which the medium varies. Three asymptotic regions are identified: a local or source region, an outer or geometric-acoustics region, and a boundary layer containing an outer scattered field. The approach is illustrated in detail for the case of a simple source above a rigid surface in an environment for which the square of the index of refraction varies linearly with distance from the surface. Numerical comparisons show that, over a wide parameter range, the asymptotic results agrees well with the Hankel-transform solution for the linearly varying medium. The theory is then extended to account for more general media variations and sources with complex directivities.
• Kerschen, E. J., & Myers, M. R. (1987). PERFECT GAS EFFECTS IN COMPRESSIBLE RAPID DISTORTION THEORY.. AIAA journal, 25(3), 504-507.
  More info

  Abstract: The interaction of unsteady disturbances with aerodynamic flows is a problem of fundamental interest, with applications to sound generation, structural vibration, and aeroelastic flutter. In the classical treatment of such problems, the mean flow is generally assumed to be uniform. However, in actual applications the mean flow gradients are often substantial. A more realistic approach is to allow the mean flow to be nonuniform, but to linearize the unsteady disturbances about this nontrivial mean flow. Goldstein's inhomogeneous wave equation is linear but has variable coefficients and a complicated source term. The main purpose of this paper is to present an alternative simplified form of Goldstein's inhomogeneous wave equation that incorporates the perfect gas thermodynamic relations.
• Envia, E., & Kerschen, E. J. (1984). NOISE PRODUCED BY THE INTERACTION OF A ROTOR WAKE WITH A SWEPT STATOR BLADE.. AIAA Paper.
  More info

  Abstract: An analysis is developed for the noise generated by the interaction of rotor viscous wakes and a single swept stator vane. The stator vane spans a channel with infinite parallel walls which contains a uniform subsonic mean flow. High frequency wakes, for which the noise generation is concentrated at the vane leading edge, are considered. The general wake pattern is expanded in spanwise modes and solutions for each mode are derived using the Wiener-Hopf technique applied to the equations in the nonorthogonal coordinates. Closed form expressions for the acoustic farfield are obtained. The results of the analysis are used in parametric calculations of rotor viscous wake-stator vane interactions in order to study the effectiveness of sweep as a noise reduction mechanism. For the cases studied, moderate stator sweep angles produce sizeable reductions in the level of the farfield noise. The presence of rotor wake circumferential lean actually increases the noise reduction produced by moderate stator sweep angles.
• Myers, M. R., & Kerschen, E. J. (1984). EFFECT OF AIRFOIL MEAN LOADING ON CONVECTED GUST INTERACTION NOISE.. AIAA Paper.
  More info

  Abstract: Behind the airfoil a wake region, which is similar to the transition zone between illuminated and shadow zones in optical problems, is present. In the outer region, far away from the airfoil edges and wake, the solution has a geometric acoustics behavior. The airfoil steady loading affects the noise generation at the leading and trailing edges in significantly different ways. The increase in leading edge noise scales on the local leading edge steady loading, rather than on the airfoil total lift. The trailing edge is essentially a scatterer of the leading edge noise, and here it is the airfoil total loading that affects the amplitude of the scattered field. Parametric calculations are presented which illustrate that, at high frequencies, moderate levels of airfoil steady loading can dramatically increase the noise level produced by airfoil convected gust interactions.
• Kerschen, E. J. (1983). CONSTRAINTS ON THE INVARIANT FUNCTIONS OF AXISYMMETRIC TURBULENCE.. AIAA journal, 21(7), 978-985.
  More info

  Abstract: Constraints are derived for the two invariant functions Q//1 and Q//2 that occur in Chandrasekhar's development of the axisymmetric turbulence theory. These constraints must be satisfied for the correlation tensor derived from Q//1 and Q//2 to be that of a stationary random process, i. e. , for the turbulence to be realizable. The equivalent results in spectrum space are also developed. Applications of the constraints in aerodynamic noise modeling are discussed. It is shown that significant errors in prediction can be introduced by the use of turbulence models which violate the constraints.
• Kerschen, E. J., & Balsa, T. F. (1981). TRANSFORMATION OF THE EQUATION GOVERNING DISTURBANCES OF A TWO-DIMENSIONAL COMPRESSIBLE FLOW.. AIAA journal, 19(10), 1367-1370.
  More info

  Abstract: The article concerns the propagation of small-amplitude inviscid and unsteady disturbances on steady nonuniform mean flows. It is shown that, when the behavior of the two-dimensional and compressible mean flow is approximated by the tangent gas relations, the inhomogeneous wave equation can be transformed into a much simpler form involving only one variable coefficient. Further simplifications are possible when the mean flow is a small perturbation of a uniform stream.
• Kerschen, E. J., & Johnston, J. P. (1981). A modal separation measurement technique for broadband noise propagating inside circular ducts. Journal of Sound and Vibration, 76(4), 499-515.
  More info

  Abstract: A measurement technique which separates broadband noise propagating inside circular ducts into the acoustic duct modes is developed. The technique is also applicable to discrete frequency noise. The acoustic modes are produced by weighted combinations of the instantaneous output of microphones spaced around the duct circumference. The technique is compared with the cross spectral density approach presently available and found to have certain advantages, and disadvantages. Considerable simplification of both the new technique and the cross spectral density approach occurs when no correlation exists between different circumferential mode orders. The properties leading to uncorrelated modes and experimental tests which verify this condition are discussed. The modal measurement technique is applied to the case of broadband noise generated by flow through a coaxial obstruction (nozzle or orifice) in a pipe. Different circumferential mode orders are shown to be uncorrelated for this type of noise source.
• Kerschen, E. J., & Johnston, J. P. (1981). Modal content of noise generated by a coaxial jet in a pipe. Journal of Sound and Vibration, 76(1), 95-115.
  More info

  Abstract: The problem investigated was that of noise generated by air flow through a coaxial obstruction in a long, straight pipe of inside diameter, D = 97 mm. Downstream modal pressure spectra in the 200-6000 Hz frequency range were measured by a new technique [1] for orifices and nozzles of diameter d where 0·03 ≤ ( d D) ≤ 0·52. The Mach numbers of the flow through the restrictions ranged from 0·15 to choked conditions. The shape of the modal frequency spectrum was found to be determined by the frequency ratio fr = He St = UiD a0d, where Ui is the jet velocity and a0 is the speed of sound in the gas downstream of the restriction. This parameter is the ratio of two non-dimensional frequencies: namely, He, which controls acoustic propagation inside circular ducts, and St, which scales the jet noise spectrum shape. At low fr(
• Kerschen, E. J., & Gliebe, P. R. (1980). FAN NOISE CAUSED BY THE INGESTION OF ANISOTROPIC TURBULENCE - A MODEL BASED ON AXISYMMETRIC TURBULENCE THEORY.. AIAA Paper.
  More info

  Abstract: An analytical model of fan noise caused by in-flow turbulence is presented. Axisymmetric turbulence theory is used to develop a statistical representation of the inflow turbulence valid for a wide range of turbulence properties. Both the dipole source due to rotor blade unsteady forces and the quadrupole source resulting from the interaction of the turbulence with the rotor potential field are considered. The effects of variations in turbulence properties and fan operating conditions are evaluated.
• Kerschen, E. J., & Johnston, J. P. (1980). MODE SELECTIVE TRANSFER OF ENERGY FROM SOUND PROPAGATING INSIDE CIRCULAR PIPES TO PIPE WALL VIBRATION.. Journal of the Acoustical Society of America, 67(6), 1931-1934.
  More info

  Abstract: Experimental results are presented which exhibit a mode selective transfer of energy from sound propagating inside a circular pipe to pipe wall vibration. The experiments use broadband noise generated by flow through a restriction in the plastic (PVC) pipe. For each higher acoustic duct mode, the energy transfer occurs in a narrow frequency band located slightly above the higher-mode cut-on frequency. A match in axial phase velocity between the higher acoustic duct mode and a compatible pipe wall vibrational mode is proposed as the mechanism for the energy transfer. Theoretical predictions for the frequency at which the axial phase velocity match occurs show good agreement with the experimental results.