Transient response of structural elements to traveling pressure waves of arbitrary shape.
Dynamic response of simple beam and rectangular plate under traveling shock wave at supersonic speed, using Fourier transforms
SHOCK WAVE↗
SEARCH · Search NASA
Results for “Rectangular Wave”
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.
Nonlinear acoustic propagation in rectangular ducts
The method of multiple scales is used to obtain a second-order uniformly valid expansion for nonlinear acoustic wave propagation in a rectangular duct whose walls are treated with a nonlinear acoustic material. The wave propagation in the duct is characterized by the unsteady nonlinear Euler equations. The results show that nonlinear materials attenuate sound more than linear materials except at high acoustic frequencies. The nonlinear materials produce higher and combination tones which have higher attenuation rates than the fundamentals. Moreover, the attenuation rates of the fundamentals increase with increasing amplitude.
Nayfeh, A. H.↗
Shock diffraction computations over complex structures
This work contains the results of a study aimed at the development of two- and three-dimensional numerical procedures for computing the flowfield generated by the interaction of a blast wave and a rigid body. A number of numerical procedures were applied to two-dimensional problems including both implicit and explicit algorithms. Each was tried on the blast wave-cylinder interaction problem. MacCormack's (1969) method with added fourth-order dissipation yielded the best results and was then applied to the blast wave-truck interaction problems in two dimensions. MacCormack's method was also used in three dimensions to determine the flowfield that results when a blast wave strikes a rectangular parallelepiped at an arbitrary angle. Both the twoand three-dimensional computations were compared with experiments in a number of ways. Two dimensional density contours show qualitative agreement for shock front location and Mach stem formation with spark shadowgraphs taken in a shock tube. Pressure-time histories indicate good quantitative agreement between theory and experiment both in two- and three-dimensions.
Mark, A.↗
Temporal sensitivity
Human visual temporal sensitivity is examined. The stimuli used to measure temporal sensitivity are described and the linear systems theory is reviewed in terms of temporal sensitivity. A working model which represents temporal sensitivity is proposed. The visibility of a number of temporal wave forms, sinusoids, rectangular pulses, and pulse pairs, is analyzed. The relation between spatial and temporal effects is studied. Temporal variations induced by image motion and the effects of light adaptation on temporal sensitivity are considered.
Watson, Andrew B.↗
Multimode Directional Coupler for Utilization of Harmonic Frequencies from TWTAs
A novel waveguide multimode directional coupler (MDC) intended for the measurement and potential utilization of the second and higher order harmonic frequencies from high-power traveling wave tube amplifiers (TWTAs) has been successfully designed, fabricated, and tested. The design is based on the characteristic multiple propagation modes of the electrical and magnetic field components of electromagnetic waves in a rectangular waveguide. The purpose was to create a rugged, easily constructed, more efficient waveguide- based MDC for extraction and exploitation of the second harmonic signal from the RF output of high-power TWTs used for space communications. The application would be a satellitebased beacon source needed for Qband and V/W-band atmospheric propagation studies. The MDC could function as a CW narrow-band source or as a wideband source for study of atmospheric group delay effects on highdata- rate links. The MDC is fabricated from two sections of waveguide - a primary one for the fundamental frequency and a secondary waveguide for the second harmonic - that are joined together such that the second harmonic higher order modes are selectively coupled via precision- machined slots for propagation in the secondary waveguide. In the TWTA output waveguide port, both the fundamental and the second harmonic signals are present. These signals propagate in the output waveguide as the dominant and higher order modes, respectively. By including an appropriate mode selective waveguide directional coupler, such as the MDC presented here at the output of the TWTA, the power at the second harmonic can be sampled and amplified to the power level needed for atmospheric propagation studies. The important conclusions from the preliminary test results for the multimode directional coupler are: (1) the second harmonic (Ka-band) can be measured and effectively separated from the fundamental (Ku-band) with no coupling of the latter, (2) power losses in the fundamental frequency are negligible, and (3) the power level of the extracted second harmonic is sufficient for further amplification to power levels needed for practical applications. It was also demonstrated that third order and potentially higher order harmonics are measurable with this device. The design is frequency agnostic, and with the appropriate choice of waveguides, is easily scaled to higher frequency TWTs. The MDC has the same function but with a number of important advantages over the conventional diplexer.
Simmons, Rainee N.↗
On the properties of warm-plasma-filled rectangular waveguide with strong transverse magnetic field.
Electromagnetic wave propagation in transversely magnetized warm plasma filled rectangular waveguide, analyzing TE and TM modes
Tuan, H.-S.↗
Optimization of suppression for two-element treatment liners for turbomachinery exhaust ducts
Sound wave propagation in a soft-walled rectangular duct with steady uniform flow was investigated at exhaust conditions, incorporating the solution equations for sound wave propagation in a rectangular duct with multiple longitudinal wall treatment segments. Modal analysis was employed to find the solution equations and to study the effectiveness of a uniform and of a two-sectional liner in attenuating sound power in a treated rectangular duct without flow (M = 0) and with uniform flow of Mach 0.3. Two-segment liners were shown to increase the attenuation of sound as compared to a uniform liner. The predicted sound attenuation was compared with measured laboratory results for an optimized two-segment suppressor. Good correlation was obtained between the measured and predicted suppressions when practical variations in the modal content and impedance were taken into account. Two parametric studies were also completed.
Motsinger, R. E.↗
A high frequency analysis of electromagnetic plane wave scattering by perfectly-conducting semi-infinite parallel plate and rectangular waveguides with absorber coated inner walls
An approximate but sufficiently accurate high frequency solution which combines the uniform geometrical theory of diffraction (UTD) and the aperture integration (AI) method is developed for analyzing the problem of electromagnetic (EM) plane wave scattering by an open-ended, perfectly-conducting, semi-infinite hollow rectangular waveguide (or duct) with a thin, uniform layer of lossy or absorbing material on its inner wall, and with a planar termination inside. In addition, a high frequency solution for the EM scattering by a two dimensional (2-D), semi-infinite parallel plate waveguide with a absorber coating on the inner walls is also developed as a first step before analyzing the open-ended semi-infinite three dimensional (3-D) rectangular waveguide geometry. The total field scattered by the semi-infinite waveguide consists firstly of the fields scattered from the edges of the aperture at the open-end, and secondly of the fields which are coupled into the waveguide from the open-end and then reflected back from the interior termination to radiate out of the open-end. The first contribution to the scattered field can be found directly via the UTD ray method. The second contribution is found via the AI method which employs rays to describe the fields in the aperture that arrive there after reflecting from the interior termination. It is assumed that the direction of the incident plane wave and the direction of observation lie well inside the forward half space tht exists outside the half space containing the semi-infinite waveguide geometry. Also, the medium exterior to the waveguide is assumed to be free space.
Noh, H. M.↗
Distribution of wave drag and lift in the vicinity of wing tips at supersonic speeds
The point-source-distribution method of calculating the aerodynamic coefficients of thin wings at supersonic speeds was extended to include the effect of the region between the wing boundary and the foremost Mach wave from the wing leading edge. The effect of this region on the surface velocity potential has been determined by an equivalent function, which is evaluated over a portion of the wing surface. In this manner, the effect of angles of attack and yaw as well as the asymmetry of top and bottom wing surfaces may be calculated. As examples of the method, the pressure distribution on a thin plate wing of rectangular plan form as well as the lift and the drag coefficients as a function of Mach number, angle of attack, and aspect ratio are calculated. The equations for the surface velocity potential of several other plan forms are also included. (author)
AIRFOILS, FLAT-PLATE↗
Input noise approximation in tracker modeling
The validity of approximating random Gaussian distributed inputs used in human response modeling by sums of discrete sine waves is studied. An ideal rectangular power density spectrum is simulated using both filtered Gaussian white noise and sums-of-discrete sine waves with three different input cutoff frequencies in the same compensatory tracking task. Resulting normalized tracking error and quality operator observations are used to investigate apparent discrepancies in human operator characteristics. Results show that discrete and continuous input tracking data compare favorable when the power in the crossover region is taken into account.
Torrey, P. F.↗
Application of finite difference techniques to noise propagation in jet engine ducts
A finite difference formulation is presented for wave propagation in a rectangular two-dimensional duct without steady flow. The difference technique, which should be useful in the study of acoustically treated inlet and exhausts ducts used in turbofan engines, can readily handle acoustical flow field complications such as axial variations in wall impedance and cross section area. In the numerical analysis, the continuous acoustic field is lumped into a series of grid points in which the pressure and velocity at each grid point are separated into real and imaginary terms. An example calculation is also presented for the sound attenuation in a two-dimensional straight soft-walled suppressor.
Baumeister, K. J.↗
Application of finite difference techniques to noise propagation in jet engine ducts
A finite difference formulation is presented for wave propagation in a rectangular two-dimensional duct without steady flow. The difference technique, which should be used in the study of acoustically treated inlet and exhausts ducts used in turbofan engines, can readily handle acoustical flow field complications such as axial variations in wall impedance and cross-section area. In the numerical analysis, the continuous acoustic field is lumped into a series of grid points in which the pressure and velocity at each grid point are separated into real and imaginary terms. An example calculation is also presented for the sound attenuation in a two-dimensional straight soft-walled suppressor.
Baumeister, K. J.↗
Scattering from a microstrip patch
A solution to the problem of plane wave scattering by a rectangular microstrip patch on a grounded dielectric substrate is presented. The model does not include the microstrip feed, and thus doe not include the so-called 'antenna mode' component of the scattering. The solution begins by formulating an electric field integral equation for the surface current density on the microstrip patch. The integral equation is solved using the method of moments. Computed data for the patch radar cross section (RCS) is found to be in close agreement with measurements over a broad frequency range. The microstrip RCS versus frequency consists of a number of large peaks which are identified as impedance or pattern factor resonance peaks.
Newman, Edward H.↗
Application of a Flip-Flop Nozzle on Plume Mixing Enhancement
Mach wave radiation is a major source of noise in high speed jets. It is created by turbulent eddies which travel at supersonic speed within the shear layer of the jet. Downstream of the potential core, the convection speed of the eddies decays and noise production is reduced. Once the convection speeds drops below the speed of sound, eddy Mach wave radiation ceases. Mach wave radiation may be reduced by shortening the core length of the jet. This requires a faster growth of the shear layer, i.e. enhanced mixing in the jet. We investigated the possibility of mixing enhancement by the excitation of the instability waves in a supersonic rectangular jet.
Schreck, Stefan↗
Test Cases for a Rectangular Supercritical Wing Undergoing Pitching Oscillations
Steady and unsteady measured pressures for a Rectangular Supercritical Wing (RSW) undergoing pitching oscillations have been presented. From the several hundred compiled data points, 27 static and 36 pitching oscillation cases have been proposed for computational Test Cases to illustrate the trends with Mach number, reduced frequency, and angle of attack. The wing was designed to be a simple configuration for Computational Fluid Dynamics (CFD) comparisons. The wing had an unswept rectangular planform plus a tip of revolution, a panel aspect ratio of 2.0, a twelve per cent thick supercritical airfoil section, and no twist. The model was tested over a wide range of Mach numbers, from 0.27 to 0.90, corresponding to low subsonic flows up to strong transonic flows. The higher Mach numbers are well beyond the design Mach number such as might be required for flutter verification beyond cruise conditions. The pitching oscillations covered a broad range of reduced frequencies. Some early calculations for this wing are given for lifting pressure as calculated from a linear lifting surface program and from a transonic small perturbation program. The unsteady results were given primarily for a mild transonic condition at M = 0.70. For these cases the agreement with the data was only fair, possibly resulting from the omission of viscous effects. Supercritical airfoil sections are known to be sensitive to viscous effects (for example, one case cited). Calculations using a higher level code with the full potential equations have been presented for one of the same cases, and with the Euler equations. The agreement around the leading edge was improved, but overall the agreement was not completely satisfactory. Typically for low-aspect-ratio rectangular wings, transonic shock waves on the wing tend to sweep forward from root to tip such that there are strong three-dimensional effects. It might also be noted that for most of the test, the model was tested with free transition, but a few points were taken with an added transition strip for comparison. Some unpublished results of a rigid wing of the same airfoil and planform that was tested on the pitch and plunge apparatus mount system (PAPA) showed effects of the lower surface transition Strip on flutter at the lower subsonic Mach numbers. Significant effects of a transition strip were also obtained on a wing with a thicker supercritical section on the PAPA mount system. Both of these flutter tests on the PAPA resulted in very low reduced frequencies that may be a factor in this influence of the transition strip. However, these results indicate that correlation studies for RSW may require some attention to the estimation of transition location to accurately treat viscous effects. In this report several Test Cases are selected to illustrate trends for a variety of different conditions with emphasis on transonic flow effects. An overview of the model and tests is given and the standard formulary for these data is listed. Sample data points are presented in both tabular and graphical form. A complete tabulation and plotting of all the Test Cases is given. Only the static pressures and the real and imaginary parts of the first harmonic of the unsteady pressures are available. All the data for the test are available in electronic file form. The Test Cases are also available as separate electronic files.
Bennett, Robert M.↗
Analysis and Optimization of Plannar Rectangular T-anode Schottky Barrier Diodes for Submillimeter-wave Multipliers
Explore the source record for details and available documents.
semiconductor wafer structure Schottky Barrier Dio↗
Transients in a periodic slab - Coupled waves approach
The reflection and transmission of rectangular and Gaussian pulses impinging on a periodically stratified slab are studied and a number of examples are illustrated and analyzed. The coupled waves approach is used to derive the reflection and transmission coefficient, then the fast Fourier transform is used to illustrate the transient responses.
Elachi, C.↗
Surface Instability of Liquid Propellants in Microgravity During Pulsed Settling Operations
Pulsing reaction control system (RCS) thrusters, vent valves, or other propulsion devices can preserve propellant resources in space, but this operation also effectively introduces a vibration to the vehicle. When the vibration is perpendicular to the liquid propellant surface, Faraday waves may be generated at the liquid-vapor interface. These Faraday instabilities can perturb or break up the liquid surface of cryogenic tanks, leading to inefficiencies in thermal management or even ullage collapse. Drawing from theory and experiments, an engineering model defining the allowable design regions for pulsed settling in microgravity was assembled and verified with computational fluid dynamics (CFD) simulations. A traditional settling metric, the Bond number, was also overlaid in the model to indicate which duty cycles were insufficient to overcome surface tension and aggregate propellant. Mission planners and engineers can consult the tool to rapidly evaluate the stability of a liquid-vapor interface given the pulse frequency and the excitation acceleration. Expressions developed for Faraday waves induced by a sinusoidal forcing input at standard gravity were found to provide excellent predictive capabilities for pulsed, or rectangular, waveforms in the absence of a consistent gravitational acceleration. This study extends the usage of these equations to an alternative forcing function and microgravity environments for the purpose of estimating natural frequencies, surface mode shapes, surface wave amplitudes, and the onset of droplet ejection. CFD simulations with the Loci/STREAM-VoF (Volume of Fluid) solver were initially validated against experimental results in standard gravity. Discrete points on the design map were then investigated with CFD and confirmed that the engineering model reliably indicates surface stability and most Faraday wave characteristics without requiring higher-fidelity tools. The engineering model is highly extensible and can be adapted for various propellant fill fractions, fluid properties, and tank sizes.
Faraday Waves↗