Techniques and errors in measuring cross- correlation and cross-spectral density functions
Instrument errors and data reduction techniques for dynamic pressure cross correlation and cross spectral density function measurements
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Techniques and errors in measuring cross- correlation and cross-spectral density functions
Techniques and errors in measuring cross spectral density and cross correlation functions of stationary dynamic pressure data
DYNAMIC PRESSURE↗
Multiple Point Dynamic Gas Density Measurements Using Molecular Rayleigh Scattering
A nonintrusive technique for measuring dynamic gas density properties is described. Molecular Rayleigh scattering is used to measure the time-history of gas density simultaneously at eight spatial locations at a 50 kHz sampling rate. The data are analyzed using the Welch method of modified periodograms to reduce measurement uncertainty. Cross-correlations, power spectral density functions, cross-spectral density functions, and coherence functions may be obtained from the data. The technique is demonstrated using low speed co-flowing jets with a heated inner jet.
Seasholtz, Richard↗
Simplified model of statistically stationary spacecraft rotation and associated induced gravity environments
A stochastic model of spacecraft motion was developed based on the assumption that the net torque vector due to crew activity and rocket thruster firings is a statistically stationary Gaussian vector process. The process had zero ensemble mean value, and the components of the torque vector were mutually stochastically independent. The linearized rigid-body equations of motion were used to derive the autospectral density functions of the components of the spacecraft rotation vector. The cross-spectral density functions of the components of the rotation vector vanish for all frequencies so that the components of rotation were mutually stochastically independent. The autospectral and cross-spectral density functions of the induced gravity environment imparted to scientific apparatus rigidly attached to the spacecraft were calculated from the rotation rate spectral density functions via linearized inertial frame to body-fixed principal axis frame transformation formulae. The induced gravity process was a Gaussian one with zero mean value. Transformation formulae were used to rotate the principal axis body-fixed frame to which the rotation rate and induced gravity vector were referred to a body-fixed frame in which the components of the induced gravity vector were stochastically independent. Rice's theory of exceedances was used to calculate expected exceedance rates of the components of the rotation and induced gravity vector processes.
Fichtl, G. H.↗
Sound Transmission through Cylindrical Shell Structures Excited by Boundary Layer Pressure Fluctuations
This paper examines sound transmission into two concentric cylindrical sandwich shells subject to turbulent flow on the exterior surface of the outer shell. The interior of the shells is filled with fluid medium and there is an airgap between the shells in the annular space. The description of the pressure field is based on the cross-spectral density formulation of Corcos, Maestrello, and Efimtsov models of the turbulent boundary layer. The classical thin shell theory and the first-order shear deformation theory are applied for the inner and outer shells, respectively. Modal expansion and the Galerkin approach are used to obtain closed-form solutions for the shell displacements and the radiation and transmission pressures in the cavities including both the annular space and the interior. The average spectral density of the structural responses and the transmitted interior pressures are expressed explicitly in terms of the summation of the cross-spectral density of generalized force induced by the boundary layer turbulence. The effects of acoustic and hydrodynamic coincidences on the spectral density are observed. Numerical examples are presented to illustrate the method for both subsonic and supersonic flows.
Tang, Yvette Y.↗
Noise characteristics of combustion augmented high speed jets.
Noise generation by a subsonic flow discharging from a combustion chamber is examined with regard to the relative importance of combustion as a source of noise in such a flow system. Measurements of pressure fluctuations inside the combustor are compared with far-field noise measurements by direct cross-correlations. The cross-correlations and derived cross-spectral densities verify that much of the noise originates inside the combustor. A first-order fluid-mechanical perturbation model is used to predict exit plane velocity fluctuations due to internal pressure fluctuations. Far-field noise levels estimated on this basis are in good agreement with measured values. The overall noise level from the combustor/jet is found to be 10 to 20 dB higher than for an equivalent clean, cold jet at the same exit velocity.
Abdelhamid, A. N.↗
Response of space shuttle insulation panels to acoustic noise pressure
The response of reusable space shuttle insulation panels to random acoustic pressure fields are studied. The basic analytical approach in formulating the governing equations of motion uses a Rayleigh-Ritz technique. The input pressure field is modeled as a stationary Gaussian random process for which the cross-spectral density function is known empirically from experimental measurements. The response calculations are performed in both frequency and time domain.
Vaicaitis, R.↗
On some structure-turbulence interaction problems
The interactions between a turbulent flow structure; responding to its excitation were studied. The turbulence was typical of those associated with a boundary layer, having a cross-spectral density indicative of convection and statistical decay. A number of structural models were considered. Among the one-dimensional models were an unsupported infinite beam and a periodically supported infinite beam. The fuselage construction of an aircraft was then considered. For the two-dimensional case a simple membrane was used to illustrate the type of formulation applicable to most two-dimensional structures. Both the one-dimensional and two-dimensional structures studied were backed by a cavity filled with an initially quiescent fluid to simulate the acoustic environment when the structure forms one side of a cabin of a sea vessel or aircraft.
Maekawa, S.↗
A Fourier approach to cloud motion estimation
A Fourier phase-difference technique for cloud motion estimation from pairs of pictures is described, and results obtained using this technique are compared with the results of a Fourier-domain cross-correlation scheme. The phase-difference technique makes use of the phase of the cross-spectral density and allows motion estimates to be made for individual spatial frequencies, which are related to cloud pattern dimensions. When objects being tracked do not change their shape, size, and orientation to more than a limited degree, both techniques are effective. The phase difference technique is relatively sensitive to the presence of mixtures of motions, changes in cloud shape, and edge effects; in these circumstances, the cross-correlation scheme is preferable. It is suggested that the Fourier transform phase difference estimation methods can be applied in problems such as landmark matching.
Arking, A.↗
Investigation of surface fluctuating pressures on a 1/4 scale YC-14 upper surface blown flap model
Fluctuating pressures were measured at 30 positions on the surface of a 1/4-scale YC-14 wing and fuselage model during an outdoor static testing program. These data were obtained as part of a NASA program to study the fluctuating loads imposed on STOL aircraft configurations and to further the understanding of the scaling laws of unsteady surface pressure fields. Fluctuating pressure data were recorded at several discrete engine thrust settings for each of 16 configurations of the model. These data were reduced using the technique of random data analysis to obtain auto-and cross-spectral density functions and coherence functions for frequencies from 0 to 10 kHz, and cross-correlation functions for time delays from 0 to 10.24 ms. Results of this program provide the following items of particular interest: (1) Good collapse of normalized PSD functions on the USB flap was found using a technique applied by Lilley and Hodgson to data from a laboratory wall-jet apparatus. (2) Results indicate that the fluctuating pressure loading on surfaces washed by the jet exhaust flow was dominated by hydrodynamic pressure variations, loading on surface well outside the flow region dominated by acoustic pressure variations, and loading near the flow boundaries from a mixture of the two.
Pappa, R. S.↗
Maximum likelihood method for estimating airplane stability and control parameters from flight data in frequency domain
A frequency domain maximum likelihood method is developed for the estimation of airplane stability and control parameters from measured data. The model of an airplane is represented by a discrete-type steady state Kalman filter with time variables replaced by their Fourier series expansions. The likelihood function of innovations is formulated, and by its maximization with respect to unknown parameters the estimation algorithm is obtained. This algorithm is then simplified to the output error estimation method with the data in the form of transformed time histories, frequency response curves, or spectral and cross-spectral densities. The development is followed by a discussion on the equivalence of the cost function in the time and frequency domains, and on advantages and disadvantages of the frequency domain approach. The algorithm developed is applied in four examples to the estimation of longitudinal parameters of a general aviation airplane using computer generated and measured data in turbulent and still air. The cost functions in the time and frequency domains are shown to be equivalent; therefore, both approaches are complementary and not contradictory. Despite some computational advantages of parameter estimation in the frequency domain, this approach is limited to linear equations of motion with constant coefficients.
Klein, V.↗
Large-Eddy Simulation of Turbulent Wall-Pressure Fluctuations
Large-eddy simulations of a turbulent boundary layer with Reynolds number based on displacement thickness equal to 3500 were performed with two grid resolutions. The computations were continued for sufficient time to obtain frequency spectra with resolved frequencies that correspond to the most important structural frequencies on an aircraft fuselage. The turbulent stresses were adequately resolved with both resolutions. Detailed quantitative analysis of a variety of statistical quantities associated with the wall-pressure fluctuations revealed similar behavior for both simulations. The primary differences were associated with the lack of resolution of the high-frequency data in the coarse-grid calculation and the increased jitter (due to the lack of multiple realizations for averaging purposes) in the fine-grid calculation. A new curve fit was introduced to represent the spanwise coherence of the cross-spectral density.
Singer, Bart A.↗
A Comparison of Pressure Measurements Between a Full-Scale and a 1/6-Scale F/A-18 Twin Tail During Buffet
In 1993, tail buffet tests were performed on a full-scale, production model F/A-18 in the 80 x 120-foot Wind Tunnel at NASA Ames Research Center. Steady and unsteady pressures were recorded on both sides of the starboard vertical tail for an angle-of-attack range of 20 to 40 degrees and at a sideslip range of -1 6 to 16 degrees at freestream velocities up to 100 knots (Mach 0.15, Reynolds number 1.23 x 10(exp 7). The aircraft was equipped with removable leading edge extension (LEX) fences that are used in flight to reduce tail buffet loads. In 1995, tail buffet tests were performed on a 1/6-scale F-18 A/B model in the Transonic Dynamics Tunnel (TDT) at NASA Langley Research Center. Steady and unsteady pressures were recorded on both sides of both vertical tails for an angle-of-attack range of 7 to 37 degrees at freestream velocities up to 65 knots (Mach 0.10). Comparisons of steady and unsteady pressures and root bending moments are presented for these wind-tunnel models for selected test cases. Representative pressure and root bending moment power spectra are also discussed, as are selected pressure cross-spectral densities.
Moses, Robert W.↗
A Comparison of Pressure Measurements Between a Full-Scale and a 1/16-Scale F/A-18 Twin Tail During Buffet
In 1993, tail buffet tests were performed on a full-scale, production model F/A-18 in the 80-by-120 Foot Wind Tunnel at NASA Ames Research Center. Steady and unsteady pressures were recorded on both sides of the starboard vertical tail for an angle of attack range of 20 to 40 degrees and at a sideslip range of -16 to 16 degrees at freestream velocities up to 100 knots (Mach 0.15, Reynolds number 1.23 x 10(exp 7)). The aircraft was equipped with removable leading edge extension (LEX) fences that are used in flight to reduce tail buffet loads. In 1995, tail buffet tests were performed on a 1/6-scale F-18 A/B model in the Transonic Dynamics Tunnel (TDT) at NASA Langley Research Center. Steady and unsteady pressures were recorded on both sides of both vertical tails for an angle-of-attack range of 7 to 37 degrees at freestream velocities up to 65 knots (Mach 0.10). Comparisons of steady and unsteady pressures and root bending moments are presented for these wind-tunnel models for selected test cases. Representative pressure and root bending moment power spectra are also discussed, as are selected pressure cross-spectral densities.
Moses, Robert W.↗
Modeling of Sound Transmission through Shell Structures with Turbulent Boundary Layer Excitation
The turbulent boundary layer (TBL) pressure field is an important source of cabin noise during cruise of high subsonic and supersonic commercial aircraft. The broadband character of this excitation field results in an interior noise spectrum that dominates the overall sound pressure level (SPL) and speech interference metrics in the forward and midcabins of many aircraft. In the authors' previous study, sound transmission through an aircraft fuselage, modeled by two concentric cylindrical sandwich shells and excited by a TBL statistical model was investigated analytically. An assessment of point and global structural vibration levels and resulting interior noise levels was obtained for different TBL models, flight conditions and fuselage structural designs. However, due to the complication of the shell structure, the important noise transmission mechanisms were difficult to discern. Previous experience has demonstrated that a fundamental understanding of the range of modes (or wavenumbers) generated by the TBL source both in the structure and the acoustic cavity is key to the development of both active and passive control technologies. In an initial effort to provide this insight, the objective of this paper is to develop an analytical model of sound transmission through a simple unstiffened cylindrical aluminum shell excited by a TBL pressure field. The description of the turbulent pressure field is based on the Corcos formulation for the cross-spectral density (CSD) of the pressure fluctuations. The coupled shell and interior and exterior acoustic equations are solved for the structural displacement and the interior acoustic response using a Galerkin approach to obtain analytical solutions. Specifically, this study compares the real part of the normalized CSD of the TBL excitation field, the structural displacement and the interior acoustic field. Further the modal compositions of the structural and cavity response are examined and some inference of the dominant mechanism of noise transmission is made.
Tang, Yvette Y.↗
Case studies of gravity waves associated with isolated tornadic storms on January 13, 1976
Penetrative convection, thunderstorms, squall lines, etc., all generate atmospheric gravity waves which can be observed by a ground-based ionospheric Doppler sounder array. Sources of these waves can be determined from reverse ray tracing computations. Case studies of gravity waves associated with isolated tornadic storms on January 13, 1976 were summarized to establish the minimum data sampling time required for correct spectral analysis and ray tracing computations. It was concluded that the data sampling time can be reduced to two to three times the wave period while still obtaining a reasonably good power spectral density. It was also demonstrated that the data sampling time can be reduced to two to three times the time delay of the wave arrival between two station pairs while still obtaining a justifiably good cross-spectral analysis. Computed source locations of the observed gravity waves are compared with conventional and satellite meteorological data.
Hung, R. J.↗
Field measurement of penetrator seismic coupling in sediments and volcanic rocks
Field experiments were conducted to determine experimentally how well a seismometer installed using a penetrator would be coupled to the ground. A dry lake bed and a lava bed were chosen as test sites to represent geological environments of two widely different material properties. At each site, two half-scale penetrators were fired into the ground, a three-component geophone assembly was mounted to the aft end of each penetrator, and dummy penetrators were fired at various distances to generate seismic signals. The recorded signals were digitized, and cross-spectral analyses were performed to compare the observed signals in terms of power spectral density ratio, coherence and phase difference. The analyses indicate that seismometers deployed by penetrators will be as well coupled to the ground as are seismometers installed by conventional methods for the frequency range of interest in earthquake seismology, although some minor differences were observed at frequencies near the upper limit of the frequency band.
Nakamura, Y.↗
Field Measurements of Penetrator Seismic Coupling in Sediments and Volcanic Rocks
Field experiments were conducted to determine how well a seismometer installed using a penetrator would be coupled to the ground. A dry-lake bed and a lava bed were chosen as test sites to represent geological environments of two widely different material properties. At each site, two half-scale penetrators were fired into the ground, a three-component geophone assembly was mounted to the aft end of each penetrator, and dummy penetrators were at various distances to generate seismic signals. These signals were detected by the penetrator-mounted geophone assembly and by a reference geophone assembly buried or anchored to surface rock and 1-m from the penetrator. The recorded signals were digitized, and cross-spectral analyses were performed to compare the observed signals in terms of power spectral density ratio, coherence, and phase difference. The analyses indicate that seismometers deployed by penetrators will be as well coupled to the ground as are seismometers installed by conventional methods for the frequency range of interest in earthquake seismology.
Nakamura, Y.↗