Boundary Layer Pressure Field Research Articles

A formulation for turbulent-flow-induced vibration of elastic plates with general boundary conditions

A formulation for studying the vibration characteristics of the rectangular plate with general boundary conditions excited by the turbulent boundary layer is developed in this paper. The Rayleigh-Ritz method, modified Fourier spectral approach, and the classical theory of elastic plates are employed to establish the vibration model of the rectangular plate. Besides, the sound pressures are calculated by the Rayleigh integral and the turbulent boundary layer pressure field is described by the cross-spectral density expression of the Corcos model. The power spectral density of vibration characteristics can be obtained according to the stochastic theory. The results indicated that the power spectral density of responses calculated in this paper are consistent with those in the references, which validate the accuracy of the developed formulation. The innovation of this formulation lies in the application of modified Fourier spectral approach to the turbulent-flow-induced vibration for the first time. The velocity power spectral density of the plate with classical and elastic boundary conditions are studied, and the influences of the boundary conditions are discussed. The boundary conditions affect the vibration response by controlling the system stiffness of the plate. Moreover, the influences of turbulent flow speed and direction under different boundary conditions are studied. It is found that the increasing turbulent flow speed leads to the increase of the vibration level, and the growth rate is similar under different boundary conditions. The velocity power spectral densities are slightly different when a turbulent flow along the short side and long side of the plate.

Tip vortex sound

The aerodynamic sound generated by the convection of a tip vortex past a trailing edge is examined. For angles of attack greater than ± 5 deg, a vortex is generated that produces a high-frequency fluctuating pressure field several hundred hertz in bandwidth, and as much as 5 dB above the boundary layer wall pressure field, centered at roughly twice the frequency of vortex shedding due to Helmholtz wake instabilities. Sound is generated as the vortex-induced pressure field is scattered by the trailing edge. The increase in the acoustic source level, quantified by fluctuating boundary layer surface pressure statistics both near the trailing edge of the foil and under the tip vortex, corresponds in level and frequency to the increase in measured radiated noise. The wall pressure field due to tip vortex flow is superimposed on the boundary layer pressure field and apparently does not alter the wall pressure field at other frequencies. The directivity of the radiated tip vortex sound shows a reduction in the sound in the plane of the foil around the tip. This suggests that a quarter plane Green's function is required to describe the radiated noise. [Work supported by O.N.R.]

Vibrational response of water‐loaded flat plate to a turbulent boundary layer pressure field

The vibrational response of a 1.2‐ × 40‐ × 200‐mm flush‐mounted flat plate, with heavy accelerometers attached to the backside, to a turbulent boundary layer (TBL) pressure field was measured at several flow velocities in a 190‐ × 190‐mm low noise water tunnel. The measured response spectra of the water‐loaded stainless steel flat plate was compared with the calculated response in the 400‐ to 1500‐Hz frequency range using the plate modal properties and the pressure spectra. The phase indicated convection velocity varied with separation and frequency and was accounted for in the plate response calculations. The plate modal properties were obtained experimentally by in situ modal analysis and the plate was found to have a large number of heavily damped modes in the same frequency range. The turbulent boundary layer pressure field driving the plate was measured upstream and downstream from the plate and was found to be unaffected by the vibrating plate. The two‐point pressure cross spectra at the wall for the TBL were found to vary with the axial and transverse separations in a way similar to that of the Corcos similarity model and followed the multiplication hypothesis but had a different form of explicit dependence upon the separation.

Features of the turbulent boundary layer pressure field on an elastic surface

In any approach to calculation of the wall pressure spectrum of a TBL based on an inhomogeneous (Lighthill) wave equation, singularities of the spectral density arise along various lines or surfaces in (k,ω) space. These lines of surfaces correspond to the acoustic or structural dispersion relations, and the singularities may be controlled by such mechanisms as surface finiteness, dissipation in the structure or fluid, and surface compliance. This paper will examine the way in which these various mechanisms control the singularities in different regimes of the spatial and dynamical parameters involved, and will give scaling laws for the pressure spectral densities at the critical conditions in (k,ω) space. [Work supported by ONR, Code 425.]

Nonlinear Panel Response from a Turbulent Boundary Layer

The vibration of a flexible elastic plate is investigated by a Monte Carlo technique. The response analysis is performed in time domain by numerically simulating the resulting generalized forces. The nonlinear plate deflection and mutual interaction between the plate motion and external and/or internal airflow is included. The fluid perturbations due to the structural motion are described by linear aerodynamic theory. The boundary-layer pressure field is idealized as a homogeneous multidimensional Gaussian random process with mean zero. The plate differential equations of motion and boundary conditions are satisfied in a Galerkin sense by developing a modal solution. Illustrative examples are presented for subsonic and supersonic flow regions using shallow cavity and two plate mode approximations.

Interior noise radiated by an airplane fuselage subjected to turbulent boundary layer excitation and evaluation of noise reduction treatments

The acoustic power radiated by an airplane fuselage structure exposed to a turbulent boundary layer pressure field has been measured at two flight Mach numbers. For a single fuselage panel the radiated power is approximately 90 and 70 dB relative to 10 −13 W at Mach 0·85 and 0·55 respectively. Damping tape and rubber wedge treatments, applied to the structure, reduce the acoustic radiation but they are more effective at Mach 0·85 than at Mach 0·55 The flight test data are in poor agreement with available wind tunnel measurements, indicating the need for improvements in scaling laws.

Response of a Conical Shell to a Turbulent Boundary Layer Pressure Field

A thin truncated conical shell can be looked upon as a series of cylinders of varying diameters. This point of view, in conjunction with some well-known vibration properties of rectangular flat plates, circular flat plates, and cylinders, yields an approximate description of the vibration properties of conical shells. Comparison with available experimental results is encouraging. The same approximate approach is used in a slightly different form for estimating the vibration response of a conical shell to a turbulent boundary-layer pressure field. Response is found to increase gradually from the smaller end of the conical shell to the larger end.

Sound Radiated by an Elastic Plate Excited by Boundary Layer Turbulence

The problem of sound radiation by an elastic plate excited by turbulent boundary-layer pressures is investigated. In determining the velocity response, the area of the plate is assumed to be effectively infinite. To provide a more accurate description of the plate motion in the high-frequency range, the Timoshenko-Mindlin thick plate equation of motion is used. Describing the boundary layer pressure field by a narrow-band cross-correlation function proposed by White [J. Acoust. Soc. Am. 40, 1354–1362 (1966)], an expression for the spectral density of the mean-square farfield pressure is obtained. For frequencies above coincidence, the directivity pattern of the mean-square farfield pressure displays two relative maxima. The angles at which the pattern displays its maxima are distinctly different from those that are predicted using classical plate theory. [Work supported by Naval Ship Systems Command, General Hydromechanics Research Program, administered by the Naval Ship Research and Development Center.]

Response of a Transducer System to Turbulent Boundary Layer Pressure Field

A system of flush-mounted pressure transducers can be considered as a spatial and a spectral filter. The filtering properties of systems consisting of a single transducer, two transducers, and three transducers were previously treated by the authors. [73rd Meeting of the Acoustical Society of America, 21 April 1967, New York, Abstract N/EF8]. This treatment was conducted in {x,ω} space. In this paper, the same problem is analyzed; however, the analysis here is conducted and illustrated in {k,ω} space, the Fourier conjugate of the real physical {x,t} space. It is argued that defining the filtering properties of the transducer systems in {k,ω} space offers certain conceptual advantages. This is particularly relevant when one considers the response of the transducer systems to pressure fields that are stationary, both spatially and temporally. The variations in the filtering properties of these systems as functions of the sizes and the sensitivities of the individual transducers and the separations between the centers of the transducers are discussed. It is shown that by properly adjusting the sizes, the sensitivities and the separations, substantial variations in the normalized response of the systems to the pressure field in a turbulent boundary layer can be achieved.

Boundary Layer Excitation of Plates

In a previous theory of boundary layer excitation of plates [I. Dyer, J. Acoust. Soc. Am. 31, 922–928 (1959)] it was assumed that the boundary layer pressure field could be represented by a vanishingly small spatial correlation convected along the plate surface. A result of the theory was that the plate modes were statistically independent for small enough values of the convection speed. A re-evaluation of the theory shows that under some conditions mode coupling may be of importance when the convection speed is unrestricted and when the size of the correlated pressure field is not allowed to shrink to zero. The convection effect is shown to be far more important in producing mode coupling than the finite size of the field. It is likely, therefore, that the delta-function approximation used in the previous theory adequately describes the boundary layer pressure field and that the extension to the theory with unrestricted convection speeds makes the calculations more precise. (Supported by the Office of Naval Research.)

Prediction of Aircraft Interior Noise Levels

The current techniques available for predicting interior noise levels are outlined, and the limitations of these techniques, particularly in their application to future high-speed aircraft, are discussed. The relative importance of each external noise source is discussed, with special emphasis on the boundary layer, the engines, and the wake. Interaction of the noise sources and the effect of this interaction on interior noise predictions are mentioned—for example, the interaction of the engine noise on the boundary layer pressure field. Also, the anticipated exterior noise levels for future aircraft are estimated. Presented curves, obtained from flight test data, laboratory measurements, and analysis, compare transmission loss through the fuselage side wall (skin plus soundproofing) of a modern transport airplane. In the commentary on these results, an attempt is made to explain the discrepancies between the predictions. The relative merit of each prediction method is discussed, together with that of another method, namely, a boundary layer test facility. In conclusion, the paper contains a brief discussion explaining the influence that aircraft interior noise requirements have on the design of fuselage side walls, including skin gage, damping properties, and stringer and frame spacings.

Boundary Layer Induced Flow Noise

A discussion is given on the magnitude of flow noise in underwater devices associated with turbulent boundary layers. Measurements by Willmarth and Harrison of boundary layers in air are used to determine a phenomenological form for the boundary layer pressure field. In calculating the resulting noise, attention is restricted to geometries and conditions of interest in underwater devices. In essence the work is an extension and improvement of that presented previously (Dyer, Second Symposium on Naval Hydrodynamics). [Supported by the Office of Naval Research under Contract Nonr-2321(00), Task NR 062-205.]