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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 217 records · Page 12

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NASA NTRS1984

A strongly implicit procedure for the compressible Navier-Stokes equations

The strongly implicit procedure of Stone is used to obtain numerical solutions of the compressible Navier-Stokes equations in conservative form. In contrast to the spatially split Douglas-Gunn type methods, the method is shown to be numerically stable for the three-dimensional wave equation. The method is applied to a variety of external and internal two-dimensional flow problems involving shock wave boundary-layer interaction for both laminar and turbulent flows. The results are in good agreement with other methods and/or experiments. The storage penalty associated with the method is discussed and a simple, yet effective, means of minimizing the problem is presented.

Walters, R. W.↗

NASA NTRS2003

Subsonic and Supersonic Effects in Bose-Einstein Condensate

A paper presents a theoretical investigation of subsonic and supersonic effects in a Bose-Einstein condensate (BEC). The BEC is represented by a time-dependent, nonlinear Schroedinger equation that includes terms for an external confining potential term and a weak interatomic repulsive potential proportional to the number density of atoms. From this model are derived Madelung equations, which relate the quantum phase with the number density, and which are used to represent excitations propagating through the BEC. These equations are shown to be analogous to the classical equations of flow of an inviscid, compressible fluid characterized by a speed of sound (g/Po)1/2, where g is the coefficient of the repulsive potential and Po is the unperturbed mass density of the BEC. The equations are used to study the effects of a region of perturbation moving through the BEC. The excitations created by a perturbation moving at subsonic speed are found to be described by a Laplace equation and to propagate at infinite speed. For a supersonically moving perturbation, the excitations are found to be described by a wave equation and to propagate at finite speed inside a Mach cone.

Zak, Michail↗

NASA NTRS1992

A study of shock-associated magnetohydrodynamic waves in the solar wind

Three major topics were addressed, one theoretical and two observational. The topics were: (1) an attempt to understand the evolution of the large-amplitude magnetohydrodynamic (MHD) waves in the foreshock, using a nonlinear wave equation called the Derivative Nonlinear Schrodinger equation (henceforth DNLS) as a model, (2) using the extensive set of ISE data to test for the presence of various nonlinear wave processes which might be present, and (3) a study of plasma turbulence in the interstellar medium which might be physically similar to that in the solar wind. For these investigations we used radioastronomical techniques. Good progress was made in each of these areas and a separate discussion of each is given.

Spangler, Steven R.↗

NASA NTRS1987

Active stability augmentation of large space structures: A stochastic control problem

A problem in SCOLE is that of slewing an offset antenna on a long flexible beam-like truss attached to the space shuttle, with rather stringent pointing accuracy requirements. The relevant methodology aspects in robust feedback-control design for stability augmentation of the beam using on-board sensors is examined. It is framed as a stochastic control problem, boundary control of a distributed parameter system described by partial differential equations. While the framework is mathematical, the emphasis is still on an engineering solution. An abstract mathematical formulation is developed as a nonlinear wave equation in a Hilbert space. That the system is controllable is shown and a feedback control law that is robust in the sense that it does not require quantitative knowledge of system parameters is developed. The stochastic control problem that arises in instrumenting this law using appropriate sensors is treated. Using an engineering first approximation which is valid for small damping, formulas for optimal choice of the control gain are developed.

Balakrishnan, A. V.↗

NASA NTRS1988

A Mathematical Formulation of the SCOLE Control Problem. Part 2: Optimal Compensator Design

The study initiated in Part 1 of this report is concluded and optimal feedback control (compensator) design for stability augmentation is considered, following the mathematical formulation developed in Part 1. Co-located (rate) sensors and (force and moment) actuators are assumed, and allowing for both sensor and actuator noise, stabilization is formulated as a stochastic regulator problem. Specializing the general theory developed by the author, a complete, closed form solution (believed to be new with this report) is obtained, taking advantage of the fact that the inherent structural damping is light. In particular, it is possible to solve in closed form the associated infinite-dimensional steady-state Riccati equations. The SCOLE model involves associated partial differential equations in a single space variable, but the compensator design theory developed is far more general since it is given in the abstract wave equation formulation. The results thus hold for any multibody system so long as the basic model is linear.

Balakrishnan, A. V.↗

NASA NTRS1992

Long time behavior of unsteady flow computations

This paper addresses a specific issue of time accuracy in the calculation of external aerodynamic problems. The class of problems discussed consists of inviscid compressible subsonic flows. These problems are governed by a convective equation. A key issue that is not understood is the long time behavior of the solution. This is important if one desires transient calculations of problems governed by the Euler equations or its derivatives such as the small disturbance equations or the potential formulations for the gust problem. Difficulties arise for two dimensional problems where the time rate decay solutions of the wave equation is slow. In concert with the above mentioned problem, exterior flows require proper modeling of the boundary conditions. In particular, this requires the truncation of infinite regions into finite regions with the aid of artificial boundaries. These boundary conditions must be consistent with the physics of the unbounded problem as well as consistent in time and space. Our treatment of the problem is discussed in detail and examples are given to verify the results.

Hariharan, S. I.↗

NASA NTRS1995

Radial energy transport by magnetospheric ULF waves: Effects of magnetic curvature and plasma pressure

The 'radial' transport of energy by internal ULF waves, stimulated by dayside magnetospheric boundary oscillations, is analyzed in the framework of one-fluid magnetohydrodynamics. (the term radial is used here to denote the direction orthogonal to geomagnetic flux surfaces.) The model for the inhomogeneous magnetospheric plasma and background magnetic field is axisymmetric and includes radial and parallel variations in the magnetic field, magnetic curvature, plasma density, and low but finite plasma pressure. The radial mode structure of the coupled fast and intermediate MHD waves is determined by numerical solution of the inhomogeneous wave equation; the parallel mode structure is characterized by a Wentzel-Kramer-Brillouin (WKB) approximation. Ionospheric dissipation is modeled by allowing the parallel wave number to be complex. For boudnary oscillations with frequencies in the range from 10 to 48 mHz, and using a dipole model for the background magnetic field, the combined effects of magnetic curvature and finite plasma pressure are shown to (1) enhance the amplitude of field line resonances by as much as a factor of 2 relative to values obtained in a cold plasma or box-model approximation for the dayside magnetosphere; (2) increase the energy flux delivered to a given resonance by a factor of 2-4; and (3) broaden the spectral width of the resonance by a factor of 2-3. The effects are attributed to the existence of an 'Alfven buoyancy oscillation,' which approaches the usual shear mode Alfven wave at resonance, but unlike the shear Alfven mode, it is dispersive at short perpendicular wavelengths. The form of dispersion is analogous to that of an internal atmospheric gravity wave, with the magnetic tension of the curved background field providing the restoring force and allowing radial propagation of the mode. For nominal dayside parameters, the propagation band of the Alfven buoyancy wave occurs between the location of its (field line) resonance and that of the fast mode cutoff that exists at larger radial distances.

Kouznetsov, Igor↗

NASA NTRS1976

On the equations governing the gravitational perturbations of the Kerr black hole

Teukolsky's radial equation governing the general, non-axisymmetric, gravitational perturbations of the Kerr black hole is reduced to the form of a one-dimensional wave equation by making use of the transformation which enables the treatment of the non-axisymmetric modes in exactly the same way as the axisymmetric modes.

Chandrasekhar, S.↗

NASA NTRS1980

Rigorous solutions for sound radiation from circular ducts with hyperbolic horns or infinite plane baffle

A rigorous treatment is presented of sound radiation from circular ducts with either a hyperbolic horn or an infinite plane baffle. In the analysis hyperboloidal wave functions are used, which are defined here, for the first time, as a class of eigensolutions of the wave equation for oblate spheroidal co-ordinates. The numerical results include the complex conversion (or reflection) coefficients and the radiation directivity for various incident wave modes, spinning modes as well as axisymmetric modes. The solutions are valid for the whole frequency range including frequencies above and below the cut-off frequencies of the duct modes involved.

Cho, Y. C.↗

NASA NTRS1977

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

Karney, C. F. F.↗

NASA NTRS1986

Three-Dimensional Radiative-Transfer Equation

Progress made toward interpretation of radiometric observations. Paper discusses equation of radiative transfer in three-dimensional, inhomogeneous, scattering medium illuminated from above and bounded below by laterallyinhomogeneous, reflective plane. Representation of radiation field with full three-dimensional variability derived by use of spatial Fourier transform and matrix-operator techniques developed previously for one-dimensional version of problem. Equations useful for radiometric measurements from aircraft and spacecraft. Although derivations and resulting equations complicated, use of Fourier-transform, matrix-operator approach to solve practical problems simpler than direct solution of complete three-dimensional, linear wave equations.

Martonchik, J. V.↗

NASA NTRS1979

Supersonic propeller noise in a uniform flow

The reported investigation is concerned with an extension of a theory presented by Hawkings and Lowson (1974). The extension considers also forward flight. Attention is given to the retarded potential solution of the convected wave equation, the Fourier components of acoustic pressure, the zones of relative silence and Doppler amplification, and the asymptotic evaluation of a noise field for a large wave number. The discussed analysis provides the Fourier coefficients of the acoustic signature of a supersonic rotor in a uniform flow. The results are represented by an integral over the blade planform which must be evaluated numerically. The fast Fourier transform can be employed for the Fourier inversion.

Jou, W.-H.↗

NASA NTRS1981

Two-dimensional analytical model of twin jet shielding

Estimation of the impact of jet noise requires analytical modeling not only of the noise source mechanism, but also of the propagation of noise from the source to receiver. One factor which influences the jet noise path is shielding of one jet by another in a twin jet configuration. An analytical model is developed to investigate the shielding phenomenon. The two-dimensional wave equation is solved for a stationary line source impinging upon a cylinder of heated flow. The solution estimates the diffraction and scattering of the incident sound wave by the shielding jet in a plane normal to the jet axis. The frequency dependence of the normalized sound pressure estimated by the model is found to agree in form with empirical data. The azimuthal redistribution of the incident sound shows that, as the frequency of maximum shielding is approached, the scattered sound becomes more highly concentrated into lobes adjacent to the shielding zone.

Gerhold, C. H.↗

NASA NTRS1987

Heating of the solar corona by the resonant absorption of Alfven waves

An improved method for calculating the resonance absorption heating rate is discussed and the results are compared with observations in the solar corona. To accomplish this, the wave equation for a dissipative, compressible plasma is derived from the linearized magnetohydrodynamic equations for a plasma with transverse Alfven speed gradients. For parameters representative of the solar corona, it is found that a two-scale description of the wave motion is appropriate. The large-scale motion, which can be approximated as nearly ideal, has a scale which is on the order of the width of the loop. The small-scale wave, however, has a transverse scale much smaller than the width of the loop, with a width of about 0.3-250 km, and is highly dissipative. These two wave motions are coupled in a narrow resonance region in the loop where the global wave frequency equals the local Alfven wave frequency. Formally, this coupling comes about from using the method of matched asymptotic expansions to match the inner and outer (small and large scale) solutions. The resultant heating rate can be calculated from either of these solutions. A formula derived using the outer (ideal) solution is presented, and shown to be consistent with observations of heating and line broadening in the solar corona.

Davila, Joseph M.↗

NASA NTRS1989

Assessment of numerical techniques for unsteady flow calculations

The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, numerical approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several numerical schemes for unsteady flow calculations. In the present study, Fourier error analysis is performed for various numerical schemes based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between numerical and exact solutions, although second-order upwind scheme captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference scheme. Among various numerical approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.

Hsieh, Kwang-Chung↗

NASA NTRS1976

Acoustic radiation from sources convected at transonic speeds

Each supersonic jet contains a long segment of transonic flow, and it is known through acoustic experiments that the strongest noise production region is embedded in this segment. The linearized convected wave equation breaks down in the transonic regime and a nonlinear equation must be used. Amplitude, directivity, and the transonic similarity rule for noise radiation can be established through proper matching of the displacement amplitude between the source and the wave field. This paper is a first step towards establishing a general theory of transonic aeroacoustics.

Pao, S. P.↗

NASA NTRS2015

Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics

Combustion instability modeling of Solid Rocket Motors (SRM) remains a topic of active research. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process, acoustics, and steady-state gas dynamics. Recent advances in defining the energy transport of disturbances within steady flow-fields have been applied by combustion stability modelers to improve the analysis framework [1, 2, 3]. Employing this more accurate global energy balance requires a higher fidelity model of the SRM flow-field and acoustic mode shapes. The current industry standard analysis tool utilizes a one dimensional analysis of the time dependent fluid dynamics along with a quasi-three dimensional propellant grain regression model to determine the SRM ballistics. The code then couples with another application that calculates the eigenvalues of the one dimensional homogenous wave equation. The mean flow parameters and acoustic normal modes are coupled to evaluate the stability theory developed and popularized by Culick [4, 5]. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The current study employs the COMSOL multiphysics finite element framework to model the steady flow-field parameters and acoustic normal modes of a generic SRM. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluates the gas flow inside of a SRM using St. Robert's law to model the solid propellant burn rate, no slip boundary conditions, and the hybrid outflow condition. Results from the HMNF model are verified by comparing the pertinent ballistics parameters with the industry standard code outputs (i.e. pressure drop, thrust, ect.). These results are then used by the coefficient form of the mathematics module to determine the complex eigenvalues of the Acoustic Velocity Potential Equation (AVPE). The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. The results of the steady-state CFD and AVPE analyses are used to calculate the linear acoustic growth rate as is defined by Flandro and Jacob [2, 3]. In order to verify the process implemented within COMSOL we first employ the Culick theory and compare the results with the industry standard. After the process is verified, the Flandro/Jacob energy balance theory is employed and results displayed.

Fischbach, Sean R.↗

NASA NTRS1980

Experimental determination of the admittances of aluminized propellants by the impedance tube method

The adaptation of the impedance tube concept for the determination of the pressure coupled admittances and response functions of burning solid propellants is discussed. The results obtained in experiments with UTP-3001 and UTP-19360 aluminized propellants are presented. It is shown that the admittance Y remains constant during the quasi-steady burn period of a test, indicating constant driving of the gas phase disturbance by the burning solid propellant. The measured real part of the admittance is positive, indicating that the burning aluminized propellant is driving the gas phase oscillations. In addition, the measured high gas phase damping, provided by the aluminum oxide particles in the gas phase, suggests that the latter can significantly increase the damping in unstable solid rockets over the investigated frequency range. Finally, it is shown that the wave structure obtained by numerically solving the impedance tube wave equations which utilize the determined propellant admittance as an initial condition and the determined value of G to describe the gas phase losses is in excellent agreement with the measured wave structure.

Baum, J. D.↗