Results for “Power spectral density” — Page 25

NASA NTRS2013

A Review of Spectral Methods for Variable Amplitude Fatigue Prediction and New Results

A comprehensive review of the available methods for estimating fatigue damage from variable amplitude loading is presented. The dependence of fatigue damage accumulation on power spectral density (psd) is investigated for random processes relevant to real structures such as in offshore or aerospace applications. Beginning with the Rayleigh (or narrow band) approximation, attempts at improved approximations or corrections to the Rayleigh approximation are examined by comparison to rainflow analysis of time histories simulated from psd functions representative of simple theoretical and real world applications. Spectral methods investigated include corrections by Wirsching and Light, Ortiz and Chen, the Dirlik formula, and the Single-Moment method, among other more recent proposed methods. Good agreement is obtained between the spectral methods and the time-domain rainflow identification for most cases, with some limitations. Guidelines are given for using the several spectral methods to increase confidence in the damage estimate.

Larsen, Curtis E.↗

NASA NTRS2015

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 900 observation angle, the low-frequency noise could be as much as 10dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite de-correlation region. Numerical predictions, based on three-dimensional RANS solutions for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region increases the low-frequency algebraic decay (the low frequency "rolloff") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspectratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Jet↗

NASA NTRS2015

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 900 observation angle, the low-frequency noise could be as much as 10dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite de-correlation region. Numerical predictions, based on three-dimensional RANS solutions for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region increases the low-frequency algebraic decay (the low frequency "rolloff") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspectratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Aircraft↗

NASA NTRS2016

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 90deg observation angle, the low-frequency noise could be as much as 10 dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite decorrelation region. Numerical predictions of the sound field, based on three-dimensional RANS solutions to determine the mean flow, turbulent kinetic energy and turbulence length and time scales, for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region in the turbulence spectrum increases the low-frequency algebraic decay (the low frequency "roll-off") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspect-ratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Jet↗

NASA NTRS2015

Time Accurate Unsteady Pressure Loads Simulated for the Space Launch System at a Wind Tunnel Condition

Using the Fully Unstructured Three-Dimensional (FUN3D) computational fluid dynamics code, an unsteady, time-accurate flow field about a Space Launch System configuration was simulated at a transonic wind tunnel condition (Mach = 0.9). Delayed detached eddy simulation combined with Reynolds Averaged Naiver-Stokes and a Spallart-Almaras turbulence model were employed for the simulation. Second order accurate time evolution scheme was used to simulate the flow field, with a minimum of 0.2 seconds of simulated time to as much as 1.4 seconds. Data was collected at 480 pressure taps at locations, 139 of which matched a 3% wind tunnel model, tested in the Transonic Dynamic Tunnel (TDT) facility at NASA Langley Research Center. Comparisons between computation and experiment showed agreement within 5% in terms of location for peak RMS levels, and 20% for frequency and magnitude of power spectral densities. Grid resolution and time step sensitivity studies were performed to identify methods for improved accuracy comparisons to wind tunnel data. With limited computational resources, accurate trends for reduced vibratory loads on the vehicle were observed. Exploratory methods such as determining minimized computed errors based on CFL number and sub-iterations, as well as evaluating frequency content of the unsteady pressures and evaluation of oscillatory shock structures were used in this study to enhance computational efficiency and solution accuracy. These techniques enabled development of a set of best practices, for the evaluation of future flight vehicle designs in terms of vibratory loads.

Alter, Stephen J.↗

NASA NTRS2016

Damage Based Analysis (DBA): Theory, Derivation and Practical Application - Using Both an Acceleration and Pseudo-Velocity Approach

The objective of this presentation is to give a brief overview of the theory behind the (DBA) method, an overview of the derivation and a practical application of the theory using the Python computer language. The Theory and Derivation will use both Acceleration and Pseudo Velocity methods to derive a series of equations for processing by Python. We will take the results and compare both Acceleration and Pseudo Velocity methods and discuss implementation of the Python functions. Also, we will discuss the efficiency of the methods and the amount of computer time required for the solution. In conclusion, (DBA) offers a powerful method to evaluate the amount of energy imparted into a system in the form of both Amplitude and Duration during qualification testing and flight environments. Many forms of steady state and transient vibratory motion can be characterized using this technique. (DBA) provides a more robust alternative to traditional methods such Power Spectral Density (PSD) using a Maximax approach.

Pseudo Velocity↗

NASA NTRS2015

A Comparison of PSD Enveloping Methods for Nonstationary Vibration

There is a need to derive a power spectral density (PSD) envelope for nonstationary acceleration time histories, including launch vehicle data, so that components can be designed and tested accordingly. This paper presents the results of the three methods for an actual flight accelerometer record. Guidelines are given for the application of each method to nonstationary data. The method can be extended to other scenarios, including transportation vibration.

Irvine, Tom↗

NASA NTRS2016

Modified Spectral Fatigue Methods for S-N Curves With MIL-HDBK-5J Coefficients

The rainflow method is used for counting fatigue cycles from a stress response time history, where the fatigue cycles are stress-reversals. The rainflow method allows the application of Palmgren-Miner's rule in order to assess the fatigue life of a structure subject to complex loading. The fatigue damage may also be calculated from a stress response power spectral density (PSD) using the semi-empirical Dirlik, Single Moment, Zhao-Baker and other spectral methods. These methods effectively assume that the PSD has a corresponding time history which is stationary with a normal distribution. This paper shows how the probability density function for rainflow stress cycles can be extracted from each of the spectral methods. This extraction allows for the application of the MIL-HDBK-5J fatigue coefficients in the cumulative damage summation. A numerical example is given in this paper for the stress response of a beam undergoing random base excitation, where the excitation is applied separately by a time history and by its corresponding PSD. The fatigue calculation is performed in the time domain, as well as in the frequency domain via the modified spectral methods. The result comparison shows that the modified spectral methods give comparable results to the time domain rainflow counting method.

Irvine, Tom↗

NASA NTRS2016

Performance, Facility Pressure Effects, and Stability Characterization Tests of NASA's Hall Effect Rocket with Magnetic Shielding Thruster

NASA's Hall Effect Rocket with Magnetic Shielding (HERMeS) 12.5 kW Technology Demonstration Unit-1 (TDU-1) has been the subject of extensive technology maturation in preparation for flight system development. Part of the technology maturation effort included experimental evaluation of the TDU-1 thruster with conducting and dielectric front pole cover materials in two different electrical configurations. A graphite front magnetic pole cover thruster configuration with the thruster body electrically tied to cathode, and an alumina front pole cover thruster configuration with the thruster body floating were evaluated. Both configurations were also evaluated at different facility background pressure conditions to evaluate background pressure effects on thruster operation. Performance characterization tests found that higher thruster performance was attained with the graphite front pole cover configuration with the thruster electrically tied to cathode. A total thrust efficiency of 68% and a total specific impulse of 2,820 s was demonstrated at a discharge voltage of 600 V and a discharge power of 12.5 kW. Thruster stability regimes were characterized with respect to the thruster discharge current oscillations and with maps of the discharge current-voltage-magnetic field (IVB). Analysis of TDU-1 discharge current waveforms found that lower normalized discharge current peak-to-peak and root mean square magnitudes were attained when the thruster was electrically floated with alumina front pole covers. Background pressure effects characterization tests indicated that the thruster performance and stability were mostly invariant to changes in the facility background pressure for vacuum chamber pressure below 1×10-5 Torr-Xe (for thruster flow rates of 20.5 mg/s). Power spectral density analysis of the discharge current waveforms showed that increasing the vacuum chamber background pressure resulted in a higher discharge current dominant breathing mode frequency. Finally, IVB maps of the TDU-1 thruster indicated that the discharge current became more oscillatory with higher discharge current peak-to-peak and RMS values with increased facility background pressure at lower thruster mass flow rates; thruster operation at higher flow rates resulted in less change to the thruster's IVB characteristics with elevated background pressure.

Electric Propulsion↗

NASA NTRS2016

Performance, Facility Pressure Effects, and Stability Characterization Tests of NASA's Hall Effect Rocket with Magnetic Shielding Thruster

NASAs Hall Effect Rocket with Magnetic Shielding (HERMeS) 12.5 kW Technology Demonstration Unit-1 (TDU-1) Hall thruster has been the subject of extensive technology maturation in preparation for flight system development. Part of the technology maturation effort included experimental evaluation of the TDU-1 thruster with conducting and dielectric front pole cover materials in two different electrical configurations. A graphite front pole cover thruster configuration with the thruster body electrically tied to cathode and an alumina front pole cover thruster configuration with the thruster body floating were evaluated. Both configurations were also evaluated at different facility background pressure conditions to evaluate background pressure effects on thruster operation. Performance characterization tests found that higher thruster performance was attained with the graphite front pole cover configuration with the thruster electrically tied to cathode. A total thrust efficiency of 68 and a total specific impulse of 2,820 s was demonstrated at a discharge voltage of 600 V and a discharge power of 12.5 kW. Thruster stability regimes were characterized with respect to the thruster discharge current oscillations and with maps of the current-voltage-magnetic field (IVB). Analysis of TDU-1 discharge current waveforms found that lower normalized discharge current peak-to-peak and root mean square magnitudes were attained when the thruster was electrically floated with alumina front pole covers. Background pressure effects characterization tests indicated that the thruster performance and stability was mostly invariant to changes in the facility background pressure for vacuum chamber pressure below 110-5 Torr-Xe (for thruster flow rate above 8 mgs). Power spectral density analysis of the discharge current waveform showed that increasing the vacuum chamber background pressure resulted in a higher discharge current dominant frequency. Finally the IVB maps of the TDU-1 thruster taken at elevated magnetic fields indicated that the discharge current became more oscillatory with increased facility background pressure at lower thruster mass flow rates, where thruster operation at higher flow rates resulted in less change to the thrusters IVB characteristics.

Hall Thrusters↗

NASA NTRS2016

Sub-Femto-g Free Fall for Space-Based Gravitational Wave Observatories: LISA Pathfinder Results

We report the first results of the LISA Pathfinder in-flight experiment. The results demonstrate that two free-falling reference test masses, such as those needed for a space-based gravitational wave observatory like LISA, can be put in free fall with a relative acceleration noise with a square root of the power spectral density of 5.2 +/- 0.1 fm s(exp -2)/square root of Hz, or (0.54 +/- 0.01) x 10(exp -15) g/square root of Hz, with g the standard gravity, for frequencies between 0.7 and 20 mHz. This value is lower than the LISA Pathfinder requirement by more than a factor 5 and within a factor 1.25 of the requirement for the LISA mission, and is compatible with Brownian noise from viscous damping due to the residual gas surrounding the test masses. Above 60 mHz the acceleration noise is dominated by interferometer displacement readout noise at a level of (34.8 +/- 0.3) fm square root of Hz, about 2 orders of magnitude better than requirements. At f less than or equal to 0.5 mHz we observe a low-frequency tail that stays below 12 fm s(exp -2)/square root of Hz down to 0.1 mHz. This performance would allow for a space-based gravitational wave observatory with a sensitivity close to what was originally foreseen for LISA.

space science↗

NASA NTRS2017

A Comparison of Three Random Number Generators for Aircraft Dynamic Modeling Applications

Three random number generators, which produce Gaussian white noise sequences, were compared to assess their suitability in aircraft dynamic modeling applications. The first generator considered was the MATLAB (registered) implementation of the Mersenne-Twister algorithm. The second generator was a website called Random.org, which processes atmospheric noise measured using radios to create the random numbers. The third generator was based on synthesis of the Fourier series, where the random number sequences are constructed from prescribed amplitude and phase spectra. A total of 200 sequences, each having 601 random numbers, for each generator were collected and analyzed in terms of the mean, variance, normality, autocorrelation, and power spectral density. These sequences were then applied to two problems in aircraft dynamic modeling, namely estimating stability and control derivatives from simulated onboard sensor data, and simulating flight in atmospheric turbulence. In general, each random number generator had good performance and is well-suited for aircraft dynamic modeling applications. Specific strengths and weaknesses of each generator are discussed. For Monte Carlo simulation, the Fourier synthesis method is recommended because it most accurately and consistently approximated Gaussian white noise and can be implemented with reasonable computational effort.

Grauer, Jared A.↗

NASA NTRS2016

Modeling SMAP Spacecraft Attitude Control Estimation Error Using Signal Generation Model

Two ground simulation software are used to model the SMAP spacecraft dynamics. The CAST software uses a higher fidelity model than the ADAMS software. The ADAMS software models the spacecraft plant, controller and actuator models, and assumes a perfect sensor and estimator model. In this simulation study, the spacecraft dynamics results from the ADAMS software are used as CAST software is unavailable. The main source of spacecraft dynamics error in the higher fidelity CAST software is due to the estimation error. A signal generation model is developed to capture the effect of this estimation error in the overall spacecraft dynamics. Then, this signal generation model is included in the ADAMS software spacecraft dynamics estimate such that the results are similar to CAST. This signal generation model has similar characteristics mean, variance and power spectral density as the true CAST estimation error. In this way, ADAMS software can still be used while capturing the higher fidelity spacecraft dynamics modeling from CAST software.

Soil Moisture Active Passive↗

NASA NTRS2017

Damage Based Analysis (DBA) - Theory, Derivation and Practical Application Using Both an Acceleration and Pseudo Velocity Approach

The objective of this presentation is to give a brief overview of the theory behind the (DBA) method, an overview of the derivation and a practical application of the theory using the Python computer language. The Theory and Derivation will use both Acceleration and Pseudo Velocity methods to derive a series of equations for processing by Python. We will take the results and compare both Acceleration and Pseudo Velocity methods and discuss implementation of the Python functions. Also, we will discuss the efficiency of the methods and the amount of computer time required for the solution. In conclusion, (DBA) offers a powerful method to evaluate the amount of energy imparted into a system in the form of both Amplitude and Duration during qualification testing and flight environments. Many forms of steady state and transient vibratory motion can be characterized using this technique. (DBA) provides a more robust alternative to traditional methods such Power Spectral Density (PSD) using a maximax approach.

Structural Dynamics↗

NASA NTRS2017

Lower Hybrid Frequency Range Waves Generated by Ion Polarization Drift Due to Electromagnetic Ion Cyclotron Waves: Analysis of an Event Observed by the Van Allen Probe B

We analyze a wave event that occurred near noon between 07:03 and 07:08 UT on 23 February 2014 detected by the Van Allen Probes B spacecraft, where waves in the lower hybrid frequency range (LHFR) and electromagnetic ion cyclotron (EMIC) waves are observed to be highly correlated, with Pearson correlation coefficient of approximately 0.86. We assume that the correlation is the result of LHFR wave generation by the ions polarization drift in the electric field of the EMIC waves. To check this assumption the drift velocities of electrons and H+, He+, and O+ ions in the measured EMIC wave electric field were modeled. Then the LHFR wave linear instantaneous growth rates for plasma with these changing drift velocities and different plasma compositions were calculated. The time distribution of these growth rates, their frequency distribution, and the frequency dependence of the ratio of the LHFR wave power spectral density (PSD)parallel and perpendicular to the ambient magnetic eld to the total PSD were found. These characteristics of the growth rates were compared with the corresponding characteristics of the observed LHFR activity. Reasonable agreement between these features and the strong correlation between EMIC and LHFR energy densities support the assumption that the LHFR wave generation can be caused by the ions polarization drift in the electric field of an EMIC wave.

Van Allen Probes↗

NASA NTRS2017

Performance, Stability, and Plume Characterization of the HERMeS Thruster with Boron Nitride Silica Composite Discharge Channel

NASA's Hall Effect Rocket with Magnetic Shielding (HERMeS) 12.5kW Technology Demonstration Unit-3 (TDU-3) has been the subject of extensive technology maturation in preparation for flight system development. Detailed performance, stability, and plume characterization tests of the thruster were performed at NASA GRC's Vacuum Facility 5 (VF-5). The TDU-3 thruster implements a magnetic topology that is identical to TDU-1. The TDU-3 boron nitride silica composite discharge channel material is different than the TDU-1 heritage boron nitride discharge channel material. Performance and stability characterization of the TDU-3 thruster was performed at discharge voltages between 300V and 600V and at discharge currents between 5A and 21.8A. The thruster performance and stability were assessed for varying magnetic field strength, cathode flow fractions between 5% and 9%, varying harness inductance, and for reverse magnet polarity. Performance characterization test results indicate that the TDU-3 thruster performance is in family with the TDU-1 levels. TDU-3's thrust efficiency of 65% and specific impulse of 2,800sec at 600V and 12.5kW exceed performance levels of SOA Hall thrusters. Thruster stability regimes were characterized with respect to the thruster discharge current oscillations (discharge current peak-to-peak and root mean square magnitudes), discharge current waveform power spectral density analysis, and maps of the current-voltage-magnetic field. Stability characterization test results indicate a stability profile similar to TDU-1. Finally, comparison of the TDU-1 and TDU-3 plume profiles found that there were negligible differences in the plasma plume characteristics between the TDU with heritage boron nitride versus the boron nitride silica composite discharge channel.

ion engines↗

NASA NTRS2018

Subsonic Jet Noise Simulation with JENRE

JENRE, a large eddy simulation code, is used to simulate an unheated, subsonic jet. Results are compared to experiment, with an emphasis on validating the acoustic power spectral density at the farfield. Problems encountered during the development of the simulations are discussed, with solutions to said problems.

Ingraham, Daniel↗

NASA NTRS2019

Sidewall Effects on Exact Reynolds-Stress Budgets in an Impinging Shock Wave/Boundary Layer Interaction

Large-eddy simulations are performed using wall-resolved mesh for a Mach 2.29 impinging shock wave/boundary-layer interaction. Flow conditions are based on an experiment and therefore entire span was simulated, including the two sidewalls. Mean flow comparison with the experimental data showed that the interaction was larger in the simulation. Time-series analysis of a rake of pressure probes immediately downstream of the mean reflected shock position showed a peak in weighted power spectral density occurred about $St_{Lint}=0.01$, owing to a larger interaction length. Budgets of Reynolds-stress transport calculated across the span and along the corner bisector showed high degree of anisotropy. Merging of the secondary flows and separation along the corner gives rise to unstablecounter rotating vortices, which straddle the corner and grow in size. This also leads to a development of new behavior in the viscous sublayer along the corner bisector, where the pressure strain andmolecular diffusion mechanisms become prominent.

Vyas, Manan A.↗