Estimation of the Wavevector-Frequency Spectrum of Turbulent Boundary Layer Wall Pressure by Multiple Linear Regression

Abstract

This paper examines the wavevector-frequency spectrum of the turbulent boundary layer wall pressure in the incompressive, inviscid domain in the intermediate and high frequencies range, i.e, wS'/l]^ > > 0.5. It is shown that the wavevectorfrequency spectrum can be normalized by a factor so that it becomes simply a function of nondimensional Strouhal wavenumber U c k,/ij) and U c k 3 /w, where U c is the convective flow velocity, and ki and k 3 are the wavenumbers in the plane of the wall along the streamwise and the crossflow directions, respectively. The normalization factor is the point pressure frequency spectrum times (U c /w) 2 . It follows that the normalized wavevector-frequency spectrum can be scaled with respect to the Strouhal wavenumbers U c k]/w and U c k 3 /o>. The rationale of using a linear regression model for estimating the normalized wavevector-frequency spectrum with a set of measured response data from a wavevector filter is presented. The contention is that the actual spectrum can be obtained by the multiplication of a trial spectrum with a correction spectrum. The correction spectrum is approximated by a polynomial in U c k,/w with a set of coefficients to be determined. The multiple linear regression model relates the response of a measuring system to these coefficients which are determined by least square minimization of a set of measured response data. The advantages of the regression approach are that it relaxes the requirements of the wavevector filter's ability to discriminate against the spectral elements outside the wavenumber bandwidth of the filter, and this approach is capable of better estimating the entire wavevector spectrum as compared to the existing methods which are limited to measurements of the low-wavenumber spectra. Some preliminary numerical results are presented.

Prediction of flow induced sound and vibration of periodically stiffened plates

“…Moreover, as the wavenumbers considered in this figure are well below the convection wavenumber (k c ¼ x=U c % 260 m À1 ), the spectrum for these lowwavenumbers is proportional to the square of the wavenumber. 32 Outside the zero wavenumber region, the pressure spectrum expressed in dB varies relatively slowly compared to the displacement response of the plate [see Fig. 3(b)].…”

TBL-Induced Structural Vibration and Noise

“…A number of parameters in the model and function need further experiments to determine, which is not widely used at present. Hwang and Geib [22] ignore compression factor of the influence of this model to put forward a simplified model. The normalized wavenumber-frequency spectrum iŝ…”

Experimental simulation of turbulent boundary layer induced vibrations by using a synthetic array

“…Under the assumptions of stationarity and homogeneity, TBL excitation is thus represented by its crossspectral density (CSD) function. In the literature, numerous models are available, such as Corcos-like [17,18,19,20] or Chase-like [21,22,23,24] models, for describing TBL wall pressure fluctuations on a rigid plane. These models can be then directly used to determine the statistical properties of the response of a structure, such as a panel, thanks to the random vibration theory [25,26].…”