Engineering topics

Kerschen, E. J.

Publications and source records attributed to Kerschen, E. J..

At least 19 records

NASA NTRS1998

Effects of Nose Radius and Aerodynamic Loading on Leading Edge Receptivity

An analysis is presented of the effects of airfoil thickness and mean aerodynamic loading on boundary-layer receptivity in the leading-edge region. The case of acoustic free-stream disturbances, incident on a thin cambered airfoil with a parabolic leading edge in a low Mach number flow, is considered. An asymptotic analysis based on large Reynolds number is developed, supplemented by numerical results. The airfoil thickness distribution enters the theory through a Strouhal number based on the nose radius of the airfoil, S = (omega)tau(sub n)/U, where omega is the frequency of the acoustic wave and U is the mean flow speed. The influence of mean aerodynamic loading enters through an effective angle-of-attack parameter ti, related to flow around the leading edge from the lower surface to the upper. The variation of the receptivity level is analyzed as a function of S, mu, and characteristics of the free-stream acoustic wave. For an unloaded leading edge, a 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. Modest levels of aerodynamic loading are found to further decrease the receptivity level for the upper surface of the airfoil, while an increase in receptivity level occurs for the lower surface. For larger angles of attack close to the critical angle for boundary layer separation, a local rise in the receptivity level occurs for the upper surface, while for the lower surface the receptivity decreases. The effects of aerodynamic loading are more pronounced at larger values of S. Oblique acoustic waves produce much higher receptivity levels than acoustic waves propagating downstream parallel to the airfoil chord.

Hammerton, P. W.↗

NASA NTRS1992

Leading-edge receptivity for blunt-nose bodies

Boundary-layer receptivity in the leading edge region for bodies with blunt leading edges is investigated in this research program. Receptivity theory provides the link between the unsteady disturbance environment in the freestream and the initial amplitudes of instability waves in the boundary layer. This is a critical problem which must be addressed in order to develop more accurate prediction methods for boundary-layer transition.

Hammerton, P. W.↗

NASA NTRS1992

Influence of airfoil thickness on sound generated by high-frequency gust interactions

The sound radiated by interaction of a short wavelength gust with a symmetric thin airfoil is analyzed. The theory is based on a linearization of the Euler equations about the subsonic mean flow past the airfoil. The sound generation mechanism is found to be concentrated in a local region surrounding the parabolic nose of the airfoil; the size of this local region scales on the gust wavelength. At low Mach numbers, moderate values of airfoil thickness decrease the sound power, while at higher Mach numbers the sound power tends to increase with airfoil thickness. Airfoil thickness produces dramatic changes in the far field directivity. Both the sound power and the directivity are strong functions of the gust orientation.

Tsai, C. T.↗

NASA NTRS1990

Influence of airfoil nose radius on sound generated by gust interactions

The sound radiated by interaction of a short wavelength gust (k much greater than 1) with a symmetric thin airfoil is analyzed. The theory is based on a linearization of the Euler equations about the subsonic mean flow past the airfoil. The sound generation mechanism is found to be concentrated in a local region surrounding the parabolic nose of the airfoil; the size of this local region scales on the gust wavelength. Airfoil thickness produces terms of relative order O(sq rt S) in the far field sound, where S is a Strouhal number based on the airfoil nose radius. At low Mach numbers, entropy gusts generate much less sound than vorticity gusts. However, for O(1) Mach numbers and moderate values of S, entropy and vorticity gusts produce similar sound levels.

Tsai, C. T.↗

NASA NTRS1989

Influence of airfoil thickness on convected gust interaction noise

The case of a symmetric airfoil at zero angle of attack is considered in order to determine the influence of airfoil thickness on sound generated by interaction with convected gusts. The analysis is based on a linearization of the Euler equations about the subsonic mean flow past the airfoil. Primary sound generation is found to occur in a local region surrounding the leading edge, with the size of the local region scaling on the gust wavelength. For a parabolic leading edge, moderate leading edge thickness is shown to decrease the noise level in the low Mach number limit.

Kerschen, E. J.↗

NASA NTRS1987

A parametric study of mean loading effects on airfoil gust interaction noise

The influence of airfoil mean loading parameters on the sound generated by interaction with short wavelength vorticity and entropy gusts is examined. It is found that there are two mean flow parameters of importance, the effective leading edge incidence angle and the airfoil lift coefficient. The former controls the total sound power level, while the latter has an important effect on the directivity pattern. For vorticity gusts, positive gust angles result in noise levels which increase with leading edge loading (LEL), while for negative gust angles an increase in LEL may actually reduce the noise level. For low levels of LEL, entropy gusts generate less sound than vorticity gusts, while for larger values of LEL, entropy gusts are at least as important as vorticity gusts.

Kerschen, E. J.↗

NASA NTRS1987

Perfect gas effects in compressible rapid distortion theory

The governing equations presented for small amplitude unsteady disturbances imposed on steady, compressible mean flows that are two-dimensional and nearly uniform have their basis in the perfect gas equations of state, and therefore generalize previous results based on tangent gas theory. While these equations are more complex, this complexity is required for adequate treatment of high frequency disturbances, especially when the base flow Mach number is large; under such circumstances, the simplifying assumptions of tangent gas theory are not applicable.

Kerschen, E. J.↗

NASA NTRS1986

Noise generated by convected gusts interacting with swept airfoil cascades

An analysis is developed for the noise generated by the interaction of a rotor viscous wake with a cascade of swept stator vanes. The stator vanes span a channel formed by infinite parallel walls and containing a subsonic mean flow. High frequency interactions, for which the noise generation is concentrated at the vane leading edge, are considered. The analysis utilizes a superposition of the solution to the isolated stator vane problem, presented in an earlier paper, to develop an approximate solution to the cascade problem. The rotor wake model includes the features of wake circumferential lean and a linear spanwise variation of the magnitude of the wake deficit velocity. Calculations are presented which show that, for rotor wakes with moderate circumferential lean, stator sweep produces substantial reductions in noise level. The vane sweep must be oriented to enhance the phase lags along the vane leading edge produced by wake lean. The noise levels are found to be fairly insensitive to spanwise variations in the wake deficit.

Envia, E.↗

NASA NTRS1986

Influence of airfoil camber on convected gust interaction noise

This paper investigates the effect of airfoil steady loading on the sound generated by the interaction of an airfoil with a convected disturbance. A previous theory, which included only the incidence angle contribution to the mean loading, is extended to include camber. The theory is based on a linearization of the Euler equations about a nonuniform, 0(1) Mach number subsonic mean flow. The discussion concentrates on the case of a slightly cambered airfoil at small incidence angle, interacting with a gust whose wavelength is short compared to the airfoil chord. The small parameter representing the amount of camber and incidence, and the large parameter representing the ratio of airfoil chord to disturbance wavelength, are utilized in a singular perturbation solution to the governing equations. Acoustic power calculations reveal that the amount of sound generated increases significantly with increased loading. More importantly, it is shown that the radiated acoustic power correlates very well with the strength of the mean flow around the leading edge.

Myers, M. R.↗

NASA NTRS1986

Influence of airfoil mean loading on convected gust interaction noise

A theoretical model is developed for the noise generated when a convected vortical or entropic gust encounters an airfoil at nonzero angle of attack. The analysis is based on Rapid Distortion Theory. High frequency gusts, whose wavelengths are short compared to the airfoil chord, are considered. The noise generation is shown to be concentrated near the airfoil leading edge. The level of the generated noise is increased by airfoil mean loading, with the appropriate scaling parameter being the local leading edge incidence angle. The trailing edge simply scatters the leading edge sound field, and here the mean loading effects scale on the airfoil total lift. Calculations are presented which illustrate that, at high frequencies, moderate levels of airfoil steady loading can dramatically increase the noise produced by airfoil convected gust interactions.

Kerschen, E. J.↗

NASA NTRS1984

Effect of airfoil mean loading on convected gust interaction noise

The present theoretical model for noise generation when a convected vortical or entropic gust encounters an airfoil at a nonzero angle-of-attack is based on a linearization of the Euler equations for the steady, subsonic flow past the airfoil. Noise generation is found to be concentrated at local regions which scale on the gust wavelength and are present at airfoil leading and trailing edges. Steady loading of the airfoil affects noise generation at the leading and trailing edges in significantly different ways. Parametric calculations are presented which illustrate that, at high frequencies, moderate levels of airfoil steady loading can drastically increase the noise level produced by airfoil-convected gust interactions.

Myers, M. R.↗

NASA NTRS1984

Noise produced by the interaction of a rotor wake with a swept stator blade

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.

Envia, E.↗

NASA NTRS1983

Constraints on the invariant functions of axisymmetric turbulence

Constraints are derived for the two invariant functions Q1 and Q2 that occur in Chandrasekhar's (1950) development of the axisymmetric turbulence theory. These constraints must be satisfied for the correlation tensor derived from Q1 and Q2 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.↗

NASA NTRS1983

Incidence angle effects on convected gust airfoil noise

An analysis is developed which predicts the influence of airfoil mean loading on noise generation due to convected gusts. The theory is based on a linearization of the exact inviscid equations about a nonuniform compressible mean flow and the solution is developed using singular perturbation techniques. The case of a flat plate airfoil, at incidence angle alpha, interacting with three-dimensional disturbances is analyzed. It is found that in the vicinity of the airfoil leading and trailing edges, local regions are present which scale on the disturbance wavelength, with the noise generation concentrated in these regions. Away from the airfoil edges, the mean flow variation is found to be slow compared to the disturbance wavelength and no significant noise generation occurs. The mean flow variation near the leading edge generates additional noise by distorting the convected gust. The cumulative effect of the airfoil mean loading in the trailing edge region produces a 0(1) phase shift between the disturbances on the upper and lower surfaces of the airfoil. A corresponding 0(1) decrease, compared to the alpha = 0 case, is found in the noise generated at the trailing edge.

Kerschen, E. J.↗

NASA NTRS1983

Noise generation by a finite span swept airfoil

An analysis is developed for the noise generated by a convected gust interacting with a single swept airfoil. The airfoil spans a channel with infinite parallel walls which contains a uniform subsonic mean flow. High frequency gusts, for which the noise generation is concentrated at the airfoil leading edge, are considered. The solution utilizes the Wiener-Hopf technique applied to the equations in nonorthogonal coordinates. Closed form expressions for the farfield acoustic pressure are obtained. The convected gust is assumed to be a plane wave, i.e., the lowest order spanwise mode. Because of the swept leading edge, this convected gust generates acoustic modes of all orders. At high frequencies and low Mach numbers, moderate sweep angles produce substantial noise reductions. The residual acoustic energy is carried mainly by the higher modes. The airfoil sweep also modulates the basic high frequency farfield directivity, producing lobed patterns. The angular modulation of the directivity patterns is most pronounced for the lower order modes.

Kerschen, E. J.↗

NASA NTRS1981

A modal separation measurement technique for broadband noise propagating inside circular ducts

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 outputs 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.↗

NASA NTRS1981

Modal content of noise generated by a coaxial jet in a pipe

Measurements of the hydrodynamic pressure fluctuation levels showed that, for circular obstructions with a flow passage diameter less than one-half of the pipe diameter, hydrodynamic pressure fluctuations were small compared with the acoustic pressure, at locations greater than ten pipe diameters downstream of the restrictions. Thus, in the study currently reported, which was concentrated on measurement of the modal characteristics of the sound field downstream of the restrictions, special techniques to avoid contamination by hydrodynamic 'noise' were not necessary. The major results obtained in the study are scaling laws for the shape of the modal pressure spectrum and for the overall efficiency of noise generation. The characteristics of the modal pressure spectra are discussed. It is shown that the primary parameter controlling the spectrum shape is the frequency ratio (Helmholtz number/Strouhal number). The efficiency levels when plotted as a function of Mach number show a strong dependence on restriction size

Kerschen, E. J.↗

NASA NTRS1980

Fan noise caused by the ingestion of anisotropic turbulence - A model based on axisymmetric turbulence theory

An analytical model of fan noise caused by inflow turbulence, a generalization of earlier work by Mani, 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. For turbulence axial integral length scales much larger than the blade spacing, the spectrum is shown to consist of sharp peaks at the blade passing frequency and its harmonics, with negligible broadband content. The analysis can then be simplified considerably and the total sound power contained within each spectrum peak becomes independent of axial length scale, while the width of the peak is inversely proportional to this parameter. Large axial length scales are characteristic of static fan test facilities, where the transverse contraction of the inlet flow produces highly anisotropic turbulence. In this situation, the rotor/turbulence interaction noise is mainly caused by the transverse component of turbulent velocity.

Kerschen, E. J.↗