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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.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow

The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.

Baysal, Oktay↗
NASA NTRS1986

Recent studies of energy integrals and their applications

In this paper, recent studies concerning path independent integrals, of relevance in the fracture of solids, and the applications of these integrals, are critically summarized. Specific topics dealt with include: (1) unsteady dynamic crack-propagation in (nonlinear) elastic solids and (2) slow stable, as well as fast crack propagation in elastic-plastic materials, which are characterized by an (incremental) flow theory of plasticity, and which are subject to arbitrary loading (and unloading) histories.

Atluri, S. N.↗
NASA NTRS1973

The critical state - A trapped wave model of vortex breakdown.

A model of vortex breakdown is presented, and its predictions are compared with the experiments of Sarpkaya (1971). The model is centered about a theory of long, weakly nonlinear waves propagating on critical flows in tubes of variable cross section. Although the weakly nonlinear theory must be extended beyond its domain of formal validity, many of the experimentally observed features of vortex breakdown are reproduced by the model. The description of the time evolution of the flowfield that is presented requires numerical calculations that are not simple, but some important conclusions may be determined by easy computations. In particular, the axial position of a breakdown may be found from a very simple equation.

Randall, J. D.↗
NASA NTRS1992

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

In the area of solar physics, new calculations of the acoustic wave energy fluxes generated in the solar convective zone was performed. The original theory developed was corrected by including a new frequency factor describing temporal variations of the turbulent energy spectrum. We have modified the original Stein code by including this new frequency factor, and tested the code extensively. Another possible source of the mechanical energy generated in the solar convective zone is the excitation of magnetic flux tube waves which can carry energy along the tubes far away from the region. The problem as to how efficiently those waves are generated in the Sun was recently solved. The propagation of nonlinear magnetic tube waves in the solar atmosphere was calculated, and mode coupling, shock formation, and heating of the local medium was studied. The wave trapping problems and evaluation of critical frequencies for wave reflection in the solar atmosphere was studied. It was shown that the role played by Alfven waves in the wind accelerations and the coronal hole heating is dominant. Presently, we are performing calculations of wave energy fluxes generated in late-type dwarf stars and studying physical processes responsible for the heating of stellar chromospheres and coronae. In the area of physics of waves, a new analytical approach for studying linear Alfven waves in smoothly nonuniform media was recently developed. This approach is presently being extended to study the propagation of linear and nonlinear magnetohydrodynamic (MHD) waves in stratified, nonisothermal and solar atmosphere. The Lighthill theory of sound generation to nonisothermal media (with a special temperature distribution) was extended. Energy cascade by nonlinear MHD waves and possible chaos driven by these waves are presently considered.

Musielak, Z. E.↗
NASA NTRS2019

Efficient Near-Field to Mid-Field Sonic Boom Propagation Using a High-Order Space Marching Method

An efficient strategy for propagating sonic boom signatures from a near-field Computational Fluid Dynamics (CFD) solution to the mid-field is presented. The method is based on a high-order accurate finite-difference discretization of the 3D Euler equations on a specially designed curvilinear grid and a single sweep space marching solution algorithm. The new approach leads to more than a factor of two reduction in overall computational resources compared to the current method used to propagate near-field sonic booms to the ground. Accuracy and efficiency of the near-field to mid-field process is demonstrated using a selection of test cases from the AIAA Sonic Boom Prediction Workshops. Azimuthal dependence of nonlinear wave propagation from the near-field to mid-field is analyzed along with its effects on the ground level noise.

Housman, Jeffrey A.↗
NASA NTRS1992

Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves

The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.

Khabibrakhmanov, I. KH.↗
NASA NTRS1983

A compressible model for the simulation of moist mountain waves

A two-dimensional, nonlinear, nonhydrostatic model is described which allows the calculation of moist airflow in mountainous terrain. The model is compressible, uses a terrain-following coordinate system, and employs lateral and upper boundary conditions which minimize wave reflections. The model's accuracy and sensitivity are examined. These tests suggest that in numerical simulations of vertically propagating, highly nonlinear mountain waves, a wave absorbing layer does not accurately mimic the effects of wave breakdown and dissipation at high levels in the atmosphere. In order to obtain a correct simulation, the region in which the waves are physically absorbed must generally be included in the computational domain (a nonreflective upper boundary condition should be used as well). The utility of the model is demonstrated in two examples (linear waves in a uniform atmosphere and the Jan. 11, 1972 Boulder windstorm) which illustrate how the presence of moisture can influence propagating waves. In both cases, the addition of moisture to the upstream flow greatly reduces the wave response.

Durran, D. R.↗
NASA NTRS1983

Microscopic Lagrangian description of warm plasmas. IV - Macroscopic approximation

The averaged-Lagrangian method is applied to linear wave propagation and nonlinear three-wave interaction in a warm magnetoplasma, in the macroscopic approximation. The microscopic Lagrangian treated by Kim and Crawford (1977) and by Galloway and Crawford (1977) is first expanded to third order in perturbation. Velocity integration is then carried out, before applying Hamilton's principle to obtain a general description of wave propagation and coupling. The results are specialized to the case of interaction between two electron plasma waves and an Alfven wave. The method is shown to be more powerful than the alternative possibility of working from the beginning with a macroscopic Lagrangian density.

Kim, H.↗
NASA NTRS1982

Nonlinear theory of shocked sound propagation in a nearly choked duct flow

The development of shocks in the sound field propagating through a nearly choked duct flow is analyzed by extending a quasi-one dimensional theory. The theory is applied to the case in which sound is introduced into the flow by an acoustic source located in the vicinity of a near-sonic throat. Analytical solutions for the field are obtained which illustrate the essential features of the nonlinear interaction between sound and flow. Numerical results are presented covering ranges of variation of source strength, throat Mach number, and frequency. It is found that the development of shocks leads to appreciable attenuation of acoustic power transmitted upstream through the near-sonic flow. It is possible, for example, that the power loss in the fundamental harmonic can be as much as 90% of that introduced at the source.

Myers, M. K.↗
NASA NTRS1974

Finite-amplitude waves in cylindrical lined ducts

A second-order uniformly valid expansion is obtained for nonlinear waves propagating in a cylindrical duct lined with a point-reacting acoustic material that consists of a porous sheet followed by honey-comb cavities and backed by the impervious walls of the duct. The effect of the liner is taken into account by coupling the waves in the duct with those in the liner. As in the two-dimensional case, the nonlinearity increases the attenuation rate at all frequencies except in narrow bandwidths around the resonant frequencies, irrespective of the geometrical dimensions of the liner or the acoustic properties of the porous sheet.

Nayfeh, A. H.↗
NASA NTRS1974

Finite amplitude waves in two-dimensional lined ducts

A second-order uniform expansion is obtained for nonlinear wave propagation in a two-dimensional duct lined with a point-reacting acoustic material consisting of a porous sheet followed by honeycomb cavities and backed by the impervious wall of the duct. The waves in the duct are coupled with those in the porous sheet and the cavities. An analytical expression is obtained for the absorption coefficient in terms of the sound frequency, the physical properties of the porous sheet, and the geometrical parameters of the flow configuration. The results show that the nonlinearity flattens and broadens the absorption vs. frequency curve, irrespective of the geometrical dimensions or the porous material acoustic properties, in agreement with experimental observations.

Nayfeh, A. H.↗
NASA NTRS1989

A method for exponential propagation of large systems of stiff nonlinear differential equations

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

Friesner, Richard A.↗
NASA NTRS1994

Nonlinear Instability of a Uni-directional Transversely Sheared Mean Flow

It is well known that the presence of a weak cross flow in an otherwise two-dimensional shear flow results in a spanwise variation in the mean streamwise velocity profile that can lead to an amplification of certain three-dimensional disturbances through a kind of resonant-interaction mechanism (Goldstein and Wundrow 1994). The spatial evolution of an initially linear, finite-growth-rate, instability wave in such a spanwise-varying shear flow is considered, The base flow, which is governed by the three-dimensional parabolized Navier-Stokes equations, is initiated by imposing a spanwise- periodic cross-flow velocity on an otherwise two-dimensional shear flow at some fixed streamwise location. The resulting mean-flow distortion initially grows with increasing streamwise distance, reaches a maximum and eventually decays through the action of viscosity. This decay, which coincides with the viscous spread of of the shear layer, means that the local growth rate of the instability wave will eventually decrease as the wave propagates downstream. Nonlinear effects can then become important within a thin spanwise-modulated critical layer once the local instability-wave amplitude and growth rate become sufficiently large and small, respectively. The amplitude equation that describes this stage of evolution is shown to be a generalization of the one obtained by Goldstein and Choi (1989) who considered the related problem of the interaction of two oblique modes in a two-dimensional shear layer.

Wundrow, David W.↗
NASA NTRSDate not supplied

Higher-Order Statistical Moments of Predicted Sonic Boom Waveforms Through Turbulence

Sonic booms generated by supersonic aircraft are affected by turbulence in the atmospheric boundary layer through which they propagate. Turbulence effects lead to random variability of the sonic boom waveforms measured on the ground, complicating the prediction of such waveforms. As an initial effort to predict the waveform variability, the solution of the coherent or mean sonic boom waveform has previously been formulated by the author. The current paper extends the formulation to derive an expression of the second-order statistical moment necessary to calculate the variance of the spectral amplitudes. Since the derivation uses a full wave equation, results using the derived expression will be compared with those obtained using a parabolic approximation. In order to fully quantify the uncertainty of our predictions, the higher order statistical moments are also formulated and are shown to be approximately zero. Consequently, the probability density function (pdf) of the spectral amplitudes is predicted to be Gaussian. The formulation is further extended to determine the pdf of the loudness of sonic booms and quantify the uncertainties associated with the loudness prediction. Results from the formulation are compared with available flight test data.

sonic booms↗