Search NASA⌕ Search

SEARCH · Search NASA

Results for “Corcos model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

18 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2023

Space Launch System Unsteady Forces Developed from Unsteady-Pressure-Sensitive-Paint–Based Corcos Model Parameters

During atmospheric ascent, launch vehicles (LVs) experience large dynamic loads at transonic conditions where aerodynamic buffet is most critical. To estimate buffet loads, coupled loads analyses typically utilize suitable forcing functions, called buffet forcing functions (BFFs). One of the key buffet environment contributors is the turbulent boundary layer (TBL) on the LV outer skin. The TBL-induced fluctuating pressures can be estimated using the widely-accepted Corcos model. In the context of transonic buffet, the performance of this model is not well established, partly because of lack of data. To fill this gap, NASA recently acquired extremely high-spatial-density data for the Space Launch System (SLS) vehicle, using the unsteady pressure sensitive paint (uPSP) optical measurement technique. A methodology is developed for validation of the Corcos model using these unique data, with a focus on the LV-design application. The model hypotheses are verified and the model parameters are empirically tuned. For selected panels on the vehicle, BFF coherence factors are derived based on the Corcos model and the associated panel BFFs are compared to uPSP data. It is shown that the modeled BFFs are in agreement with direct integration of uPSP data, except for regions where pressure fluctuations are spatially nonuniform. In those regions, the Corcos-based BFFs exhibit inherent limitations of BFF estimation methods that rely on discrete pressure measurements.

buffet↗
NASA NTRSDate not supplied

Validation of the Corcos Model for the Space Launch System using Unsteady Pressure Sensitive Paint

During atmospheric ascent launch vehicles (LVs) experience large dynamic loads at transonic conditions where aerodynamic buffet is most critical. To estimate buffet loads, coupled loads analyses typically utilize suitable forcing functions, called buffet forcing functions (BFFs). One of the key buffet environment contributors is the turbulent boundary layer (TBL) on the LV outer skin. The TBL-induced fluctuating pressures can be estimated using the widely-accepted Corcos model. In the context of transonic buffet, the performance of this model is not well established, partly because of lack of data. To fill this gap, NASA recently acquired extremely high-spatial-density data for the Space Launch System (SLS) vehicle, using the unsteady pressure sensitive paint (uPSP) optical measurement technique. A methodology is developed for validation of the Corcos model using these unique data, with a focus on the LV-design application. The model hypotheses are verified and the model parameters are empirically tuned. For selected panels on the vehicle, BFF coherence factors are derived based on the Corcos model and the associated panel BFFs are compared to uPSP data. It is shown that the modeled BFFs are in agreement with direct integration of uPSP data, except for regions where pressure fluctuations are spatially nonuniform. In those regions, the Corcos-based BFFs exhibit inherent limitations of BFF estimation methods that rely on discrete pressure measurements.

buffet↗
NASA NTRSDate not supplied

Validation of the Corcos Model for the Space Launch System using Unsteady Pressure Sensitive Paint

During atmospheric ascent launch vehicles (LVs) experience large dynamic loads at transonic conditions where aerodynamic buffet is most critical. To estimate buffet loads, coupled loads analyses typically utilize suitable forcing functions, called buffet forcing functions (BFFs). One of the key buffet environment contributors is the turbulent boundary layer (TBL) on the LV outer skin. The TBL-induced fluctuating pressures can be estimated using the widely-accepted Corcos model. In the context of transonic buffet, the performance of this model is not well established, partly because of lack of data. To fill this gap, NASA recently acquired extremely high-spatial-density data for the Space Launch System (SLS) vehicle, using the unsteady pressure sensitive paint (uPSP) optical measurement technique. A methodology is developed for validation of the Corcos model using these unique data, with a focus on the LV-design application. The model hypotheses are verified and the model parameters are empirically tuned. For selected panels on the vehicle, BFF coherence factors are derived based on the Corcos model and the associated panel BFFs are compared to uPSP data. It is shown that the modeled BFFs are in agreement with direct integration of uPSP data, except for regions where pressure fluctuations are spatially nonuniform. In those regions, the Corcos-based BFFs exhibit inherent limitations of BFF estimation methods that rely on discrete pressure measurements.

buffet↗
NASA NTRS2023

Comparison of Corcos-Based and Experimentally-Derived Coherence Factors for Buffet Forcing Function Estimation

In this paper, high-spatial-resolution unsteady Pressure Sensitive Paint (uPSP) data are utilized to compare two methods for panel Buffet Forcing Function (BFF) estimation for the Space Launch System (SLS). Such methods are based on discrete pressure measurements within a panel but employ coherence factors to account for partially-correlated fluctuating pressures across the whole panel. In one method, coherence factors are derived based on the Corcos model, whereas the second method utilizes experimentally-derived coherence factors. To simulate discrete measurements using uPSP data, suitable subsets of the data are extracted. When full uPSP resolution is retained, uPSP data provide a benchmark to assess discrete-measurement-based methods. The analysis focuses on the peak SLS buffet environment located downstream of the Forward Attachment Hardware (FAH) between the core stage and solid rocket boosters. Trends of Corcos-based and experimentally-derived coherence factors are in reasonable agreement with the benchmark. However, at certain frequencies, experimentally-derived coherence factors are sensitive to the separation distance between pressure measurements utilized to compute coherence lengths. Such sensitivity originates from deviation of the experimentally-based coherence function from an exponential decay assumption. On the other hand, the present implementation of the Corcos model fails to capture certain nonturbulent boundary layer related environments, such as a subharmonic of FAH vortex-shedding. For all methods presented in this paper, at near transonic conditions, increased pressure coherence and spatial nonuniformity lead to BFF overestimation and sensitivity to the pressure measurement location within the panel.

transonic buffet↗
NASA NTRSDate not supplied

Comparison of Corcos-based and experimentally-derived coherence factors for BFFs estimation

In this paper, high-spatial-resolution unsteady Pressure Sensitive Paint (uPSP) data are utilized to compare two methods for panel Buffet Forcing Functions (BFF) estimation for the Space Launch System (SLS). Such methods are based on discrete pressure measurements within a panel but employ coherence factors to account for partially-correlated fluctuating pressures across the whole panel. In one method, coherence factors are derived based on the Corcos model, whereas the second method utilizes experimentally-derived coherence factors. To simulate discrete measurements using uPSP data, suitable subsets of the data are extracted. When full uPSP resolution is retained, uPSP data provide a benchmark to assess discrete-measurements-based methods. The analysis focuses on the peak SLS buffet environment located downstream of the Forward Attachment Hardware (FAH) between the core stage and solid rocket boosters. Trends of Corcos-based and experimentally-derived coherence factors are in reasonable agreement with the benchmark. However, at certain frequencies, experimentally-derived coherence factors are sensitive to the separation distance between pressure measurements utilized to compute coherence lengths. Such sensitivity originates from deviation of the experimental-based coherence function from an exponential decay assumption. On the other hand, the present implementation of the Corcos model fails to capture certain non-turbulent boundary layer related environments, such as a subharmonic of FAH vortex-shedding. For all methods presented in this paper, at near transonic conditions, increased pressure coherence and spatial nonuniformity lead to BFF overestimation and sensitivity to the pressure measurement location within the panel.

transonic buffet↗
NASA NTRSDate not supplied

Comparison of Corcos-Based and Experimentally-Derived Coherence Factors for Buffet Forcing Functions Estimation

In this paper, high-spatial-resolution unsteady Pressure Sensitive Paint (uPSP) data are utilized to compare two methods for panel Buffet Forcing Functions (BFF) estimation for the Space Launch System (SLS). Such methods are based on discrete pressure measurements within a panel but employ coherence factors to account for partially-correlated fluctuating pressures across the whole panel. In one method, coherence factors are derived based on the Corcos model, whereas the second method utilizes experimentally-derived coherence factors. To simulate discrete measurements using uPSP data, suitable subsets of the data are extracted. When full uPSP resolution is retained, uPSP data provide a benchmark to assess discrete-measurements-based methods. The analysis focuses on the peak SLS buffet environment located downstream of the Forward Attachment Hardware (FAH) between the core stage and solid rocket boosters. Trends of Corcos-based and experimentally-derived coherence factors are in reasonable agreement with the benchmark. However, at certain frequencies, experimentally-derived coherence factors are sensitive to the separation distance between pressure measurements utilized to compute coherence lengths. Such sensitivity originates from deviation of the experimental-based coherence function from an exponential decay assumption. On the other hand, the present implementation of the Corcos model fails to capture certain nonturbulent boundary layer related environments, such as a subharmonic of FAH vortex-shedding. For all methods presented in this paper, at near transonic conditions, increased pressure coherence and spatial nonuniformity lead to BFF overestimation and sensitivity to the pressure measurement location within the panel.

buffet↗
NASA NTRSDate not supplied

Joint Acceptance Attenuation Factor of Integrated Pressure with Unsteady Pressure-Sensitive Paint Measurements

The Unsteady Pressure-Sensitive Paint (uPSP) is widely used to measure the surface pressure of the scaled model in the wind tunnel tests. Compared to the conventional pressure transducers, uPSP has the advantage of high spatial resolution. With multiple high-speed cameras, the uPSP data collected with the camera pixels are mapped to the surface grid of the scaled model and converted to pressure. The shot noise, which is associated with the quantum processes both in the generation of the photons by the luminescent uPSP and in the conversion of the photons into electrons within the camera, is the dominant component of the noise in the uPSP measurement. The integrated pressure is usually computed as an area-weighted average of the uPSP measured pressures on the grid nodes of a user-defined patch. The effect of the shot noise is reduced in the integrated pressure; however, the measurement of the aerodynamic pressure is also attenuated. This paper discusses the Joint Acceptance Attenuation Factor (JAAF) of the integrated pressure with uPSP measurements. The JAAF is defined as the ratio of the auto or cross Power Spectral Density (PSD) of the integrated aerodynamic pressure on the patch to the average auto PSD of the aerodynamic pressure on the grid nodes of the patch. Under the assumption that the cross spectrum of the aerodynamic pressure can be described with the Corcos model, the closed-form formula of the JAAF is derived for the integrated pressure on rectangular patches via the summation of uPSP measurements on discrete grid nodes. The closed-form formula is verified via the integration of the pressure field of Corcos model over continuous areas. The properties of the JAAF with different parameters are presented and the applications in the comparison of the spectrum of the pressure transducers and uPSP measurements, which were collected in the NASA Space Launch System (SLS) tests with the 11-by-11-foot transonic wind tunnel at NASA Ames Research Center in December 2017 and September 2019 respectively, are also discussed. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding was provided by the NASA Aerosciences Evaluation and Test Capabilities(AETC) Portfolio Office.

Unsteady Pressure-Sensitive Paint↗
NASA NTRSDate not supplied

Joint Acceptance Attenuation Factor of Integrated Pressure with Unsteady Pressure-Sensitive Paint Measurements

The Unsteady Pressure-Sensitive Paint (uPSP) is widely used to measure the surface pressure of scaled models in wind tunnel tests. Compared to the conventional pressure transducers, uPSP has the advantage of high spatial resolution. With multiple high-speed Complementary Metal Oxide Superconductor (CMOS) cameras, the uPSP data collected with the camera pixels are mapped to the surface grid of the scaled model and converted to pressure. The shot noise is the dominant component of the noise in the uPSP measurement. The integrated pressure is usually computed on the grid nodes of a user-defined patch. The effect of shot noise is reduced in the integrated pressure on the patch; however, the measurement of the aerodynamic pressure may also be attenuated by the decorrelation of the flow pressure field being measured. This paper discusses the Joint Acceptance Attenuation Factor (JAAF) of the integrated pressure with uPSP measurements. The JAAF, a function of frequency, is defined as the ratio of the Power Spectral Density (PSD) of the integrated aerodynamic pressure on the patch to the average PSD of the aerodynamic pressure on the grid nodes of the patch. In this paper, the JAAF is investigated for the integrated pressure on rectangular patches, whose edges are defined in the direction along the streamline or across the streamline. Based on the assumption that the surface pressure field can be described by the Corcos model, the closed-form formulas to compute the JAAFs of the integrated pressure on the discrete grid nodes of a rectangular patch and over the continuous area of a rectangular patch are derived respectively. It is shown that the JAAF of the integrated pressure over the continuous area of a rectangular patch is the limit of that on discrete nodes of the rectangular patch when the number of nodes in each row or column goes to infinity. The closed-form formulas of the JAAF derived in this paper, with estimated parameters of the model, are verified with the measurements of the uPSP and the conventional pressure transducer collected in the Space Launch System Ascent Unsteady Aerodynamics Test at NASA Ames Research Center in November 2017. The closed-form formulas of the JAAF of the integrated pressure on the rectangular patches, based on the Corcos model, provide an efficient method to estimate the attenuation of integration by the decorrelation of the flow pressure field and set references for the comparison of the spectrum of the integrated uPSP measurements and the conventional pressure transducer measurements. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding was provided by the NASA Aerosciences Evaluation and Test Capabilities Portfolio Office.

acoustics↗
NASA NTRSDate not supplied

Joint Acceptance Attenuation Factor of Integrated Pressure with Unsteady Pressure-Sensitive Paint Measurements

The Unsteady Pressure-Sensitive Paint (uPSP) is widely used to measure the surface pressure of scaled models in wind tunnel tests. Compared to the conventional pressure transducers, uPSP has the advantage of high spatial resolution. With multiple high-speed Complementary Metal Oxide Superconductor (CMOS) cameras, the uPSP data collected with the camera pixels are mapped to the surface grid of the scaled model and converted to pressure. The shot noise is the dominant component of the noise in the uPSP measurement. The integrated pressure is usually computed on the grid nodes of a user-defined patch. The effect of shot noise is reduced in the integrated pressure on the patch; however, the measurement of the aerodynamic pressure may also be attenuated by the decorrelation of the flow pressure field being measured. This paper discusses the Joint Acceptance Attenuation Factor (JAAF) of the integrated pressure with uPSP measurements. The JAAF, a function of frequency, is defined as the ratio of the Power Spectral Density (PSD) of the integrated aerodynamic pressure on the patch to the average PSD of the aerodynamic pressure on the grid nodes of the patch. In this paper, the JAAF is investigated for the integrated pressure on rectangular patches, whose edges are defined in the direction along the streamline or across the streamline. Based on the assumption that the surface pressure field can be described by the Corcos model, the closed-form formulas to compute the JAAFs of the integrated pressure on the discrete grid nodes of a rectangular patch and over the continuous area of a rectangular patch are derived respectively. It is shown that the JAAF of the integrated pressure over the continuous area of a rectangular patch is the limit of that on discrete nodes of the rectangular patch when the number of nodes in each row or column goes to infinity. The closed-form formulas of the JAAF derived in this paper, with estimated parameters of the model, are verified with the measurements of the uPSP and the conventional pressure transducer collected in the Space Launch System Ascent Unsteady Aerodynamics Test at NASA Ames Research Center in November 2017. The closed-form formulas of the JAAF of the integrated pressure on the rectangular patches, based on the Corcos model, provide an efficient method to estimate the attenuation of integration by the decorrelation of the flow pressure field and set references for the comparison of the spectrum of the integrated uPSP measurements and the conventional pressure transducer measurements. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding was provided by the NASA Aerosciences Evaluation and Test Capabilities Portfolio Office.

acoustics↗
NASA NTRSDate not supplied

Invited: uPSP Launch Vehicle Demonstration Test at NASA Ames Research Center

The Unsteady Pressure-Sensitive Paint (uPSP) Development Team outof NASA Ames Research Center (ARC) has spent the past five yearsimproving the systems and processes to advance the uPSP technology for production-level wind tunnel testing. Already considered turnkey for small-scale and research applications, development in acquisition, calibration, data transfer, and data processing were needed to be useful to customers testing at NASA wind tunnels. This development focused at ARC at the Unitary Plan Wind Tunnel (UPWT) 11-by 11-ft Transonic Wind Tunnel due to the large optical access of the test section and the NASA Advanced Supercomputer(NAS), also located at ARC. A Launch Vehicle Demonstration Test (LVDT) at the UPWT represents a milestone of this initial phase of development where several new improvements were demonstrated in a production wind tunnel environment for the first time. LVDT was conducted in April 2024 and used a 4% forebody Space Launch System (SLS) Block 1B model as the test article. Both a crew and cargo configuration were tested, with varying Mach numbers, pressures, model positions, and camera magnifications. This paper summarizes the details of the test and is part of a collection with four additional papers that provide greater detail on: high-speed lifetime methodology, spectral proper orthogonal decomposition analysis, quality of high-resolution data compared to Corcos model, and data quality, calibration, and uncertainty.

SLS↗
NASA NTRS1973

Acoustic radiation from plates excited by flow noise.

Theoretical formulation of noise radiation from thin, rectangular, flexible plates excited by turbulent wall pressure fluctuations. An extensive parametric study including surface roughness and both plate and flow parameters is presented. From the results, presented graphically, it is possible to predict the spectrum of the total radiated power provided that the power spectral density of the wall-pressure fluctuations, the flow velocity, the plate dimensions and the plate modal damping parameters are known. Along with the parametric study, an estimate of the dependence of the noise radiation on plate boundary conditions based on a consideration of the wavenumber-frequency selectivity of the plate is presented. The parametric study is based on the assumption that the wave number/frequency spectrum of the wall-pressure fluctuations can be described by a Fourier transform of a Corcos model of the cross spectral density. The results indicate that at frequencies above the hydrodynamic-coincidence frequency the radiated power is dependent on the low-wave-number spectrum of the excitation. The dependence on the high-wave-number spectrum, however, is limited to a narrow band of frequencies below the hydrodynamic-coincidence frequency.

Aupperle, F. A.↗
NASA NTRSDate not supplied

Spatiotemporal Analysis of High-Resolution Pressure-Sensitive Paint Measurements on a Launch Vehicle Wind Tunnel Model

An accurate understanding of unsteady aerodynamic loads is critical for launch vehicle structural design and for development of the vibro-acoustic environment for payload components. Analysts commonly use point-wise surface pressure measurements from wind tunnel testing to build statistical models of the in-flight turbulent boundary layer flow structures, often extrapolating over large swaths of the surface due to measurement sparsity. We present novel results from a transonic wind tunnel test using fast-response pressure-sensitive paint (PSP) and show how it can be used to visualize and quantify localized turbulent boundary layer wall pressure statistics with unprecedented spatial resolution. The wind tunnel model is a scaled model of the Space Launch System (SLS) rocket Block 1B Crew configuration and analysis focused on the compression corner between the Service Module fairing and the Universal Stage Adapter.

Corcos Model↗
NASA NTRSDate not supplied

Comparisons of Artemis I and Wind Tunnel Buffet Environments and Induced Structural Responses

This paper presents comparisons of buffet forcing functions (BFFs) and associated structural responses for the Space Launch System from two data sources: 1) Artemis I (AR01) Developmental Flight Instrumentation (DFI) and 2) transonic wind-tunnel (WT) tests. Failures of DFI sensors prevented the development of a complete set of flight-based BFFs, where each BFF is based on azimuthal integration over 360-degrees of unsteady pressures acquired by sensor rings placed at many longitudinal stations along the vehicle. Instead, a set of equivalent flight- and WT-based BFFs was developed based on functional DFI and WT sensors that share the same locations. Root-mean-square (rms) levels of equivalent BFFs from flight and WT data are in-family for most of the cardinal Mach numbers. However, at stations downstream of the booster forward attachment (FA) protuberance, the rms of flight-based BFFs exceed their WT counterparts. Strikingly, vortex-shedding off the FA protuberance occurs at lower frequencies during flight than in WT experiments. This frequency shift propagates onto the spectrum of flight-measured vs. WT-based structural responses. Aside from vortex-shedding frequency mismatch, a generally good agreement between AR01 and WT-based responses is an indirect indication that WT buffet environments are fairly well representative of their AR01 counterpart.

transonic buffet↗
NASA NTRSDate not supplied

Comparisons of Artemis I and Wind Tunnel Buffet Environments and Induced Structural Responses

This paper presents comparisons of buffet forcing functions (BFFs) and associated structural responses for the Space Launch System from two data sources: 1) Artemis I (AR01) Developmental Flight Instrumentation (DFI) and 2) transonic wind-tunnel (WT) tests. Failures of DFI sensors prevented the development of a complete set of flight-based BFFs, where each BFF is based on azimuthal integration over 360-degrees of unsteady pressures acquired by sensor rings placed at many longitudinal stations along the vehicle. Instead, a set of equivalent flight- and WT-based BFFs was developed based on functional DFI and WT sensors that share the same locations. Root-mean-square (rms) levels of equivalent BFFs from flight and WT data are in-family for most of the cardinal Mach numbers. However, at stations downstream of the booster forward attachment (FA) protuberance, the rms of flight-based BFFs exceed their WT counterparts. Strikingly, vortex-shedding off the FA protuberance occurs at lower frequencies during flight than in WT experiments. This frequency shift propagates onto the spectrum of flight-measured vs. WT-based structural responses. Aside from vortex-shedding frequency mismatch, a generally good agreement between AR01 and WT-based responses is an indirect indication that WT buffet environments are fairly well representative of their AR01 counterpart.

transonic buffet↗
NASA NTRS2012

The Influence of Boundary Layer Parameters on Interior Noise

Predictions of the wall pressure in the turbulent boundary of an aerospace vehicle can differ substantially from measurement due to phenomena that are not well understood. Characterizing the phenomena will require additional testing at considerable cost. Before expending scarce resources, it is desired to quantify the effect of the uncertainty in wall pressure predictions and measurements on structural response and acoustic radiation. A sensitivity analysis is performed on four parameters of the Corcos cross spectrum model: power spectrum, streamwise and cross stream coherence lengths and Mach number. It is found that at lower frequencies where high power levels and long coherence lengths exist, the radiated sound power prediction has up to 7 dB of uncertainty in power spectrum levels with streamwise and cross stream coherence lengths contributing equally to the total.

Palumbo, Daniel L.↗
NASA NTRS1996

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.↗
NASA NTRS1996

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.↗
NASA NTRS1956

On the Contribution of Turbulent Boundary Layers to the Noise Inside a Fuselage

The following report deals in preliminary fashion with the transmission through a fuselage of random noise generated on the fuselage skin by a turbulent boundary layer. The concept of attenuation is abandoned and instead the problem is formulated as a sequence of two linear couplings: the turbulent boundary layer fluctuations excite the fuselage skin in lateral vibrations and the skin vibrations induce sound inside the fuselage. The techniques used are those required to determine the response of linear systems to random forcing functions of several variables. A certain degree of idealization has been resorted to. Thus the boundary layer is assumed locally homogeneous, the fuselage skin is assumed flat, unlined and free from axial loads and the 'cabin' air is bounded only by the vibrating plate so that only outgoing waves are considered. Some of the details of the statistical description have been simplified in order to reveal the basic features of the problem. The results, strictly applicable only to the limiting case of thin boundary layers, show that the sound pressure intensity is proportional to the square of the free stream density, the square of cabin air density and inversely proportional to the first power of the damping constant and to the second power of the plate density. The dependence on free stream velocity and boundary layer thickness cannot be given in general without a detailed knowledge of the characteristics of the pressure fluctuations in the boundary layer (in particular the frequency spectrum). For a flat spectrum the noise intensity depends on the fifth power of the velocity and the first power of the boundary layer thickness. This suggests that boundary layer removal is probably not an economical means for decreasing cabin noise. In general, the analysis presented here only reduces the determination of cabin noise intensity to the measurement of the effect of any one of our variables (free stream velocity, boundary layer thickness, plate thickness or the characteristic velocity of propagation in the plate). The plate generates noise by vibrating in resonance over a wide range of frequencies and increasing the damping constant is consequently an effective method of decreasing noise generation. One of the main features of the results is that the relevant quantities upon which noise intensity depends are non-dimensional numbers in which boundary layer and plate properties enter as ratios. This is taken as an indication that in testing models of structures for boundary layer noise it is not sufficient to duplicate in the model the structural characteristics of the fuselage. One must match properly the characteristics of the exicitng pressure fluctuations to that of the structure.

Corcos, G. M.↗