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Results for “equations of state”

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 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Switched electrical networks and bilinear equations

An investigation is conducted concerning the state equations which arise in the description of power processing systems. Attention is given to the role played by Lie groups and Lie algebras in the characterization of the dynamical features of the systems. The bilinear equations used for the representation of the network characteristics are discussed along with the nature of the solutions for the equations. The application of the described approaches is illustrated with the aid of a number of network examples.

Wood, J. R.↗
DOE OSTI2024

Assessing equation of state-independent relations for neutron stars with nonparametric models

Relations between neutron star properties that do not depend on the nuclear equation of state offer insights on neutron star physics and have practical applications in data analysis. Such relations are obtained by fitting to a range of phenomenological or nuclear physics equation of state models, each of which may have varying degrees of accuracy. In this study we revisit commonly used relations and reassess them with a very flexible set of phenomenological nonparametric equation of state models that are based on Gaussian processes. Our models correspond to two sets: equations of state which mimic hadronic models, and equations of state with rapidly changing behavior that resemble phase transitions. Here we quantify the accuracy of relations under both sets and discuss their applicability with respect to expected upcoming statistical uncertainties of astrophysical observations. We further propose a goodness-of-fit metric which provides an estimate for the systematic error introduced by using the relation to model a certain equation-of-state set. Overall, the nonparametric distribution is more poorly fit with existing relations, with the I–Love–Q relations retaining the highest degree of universality. Fits degrade for relations involving the tidal deformability, such as the binary-Love and compactness-Love relations, and when introducing phase transition phenomenology. For most relations, systematic errors are comparable to current statistical uncertainties under the nonparametric equation of state distributions.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1992

Computer aided design of digital controller for radial active magnetic bearings

A five degree of freedom Active Magnetic Bearing (AMB) system is developed which is controlled by digital controllers. The model of the radial AMB system is linearized and the state equation is derived. Based on the state variables feedback theory, digital controllers are designed. The performance of the controllers are evaluated according to experimental results. The Computer Aided Design (CAD) method is used to design controllers for magnetic bearings. The controllers are implemented with a digital signal processing (DSP) system. The control algorithms are realized with real-time programs. It is very easy to change the controller by changing or modifying the programs. In order to identify the dynamic parameters of the controlled magnetic system, a special experiment was carried out. Also, the online Recursive Least Squares (RLS) parameter identification method is studied. It can be realized with the digital controllers. Online parameter identification is essential for the realization of an adaptive controller.

Cai, Zhong↗
NASA NTRS1984

Temporal evolution of the solar wind and the formation of a standing shock

The temporal evolution of the solar wind from one steady state to another is explored when momentum deposition produces multiple critical points in the flow. It is shown that the wind always evolves in time to a new steady state compatible with the solution of the steady state equation of motion. However, for the same initial state and identical asymptotic momentum deposition rate, the temporal evolution pattern of the wind depends on the detailed time history of momentum addition and is therefore not unique. This feature plays an important role in the particular case when multiple (three in this study) steady states exist for identical boundary conditions; each one of these solutions is thus shown to be physically accessible. The details of the temporal evolution pattern of the wind reveal the formation of a shock discontinuity whenever the flow becomes supersonic at a critical point upstream from the initial critical point. If the flow remains supersonic at that inner critical point, the shock can become a standing one, depending on the strength and the temporal history of momentum addition. The results of this study indicate that the time scale required for the solar wind to evolve between steady states is of the order of 30-60 hours. Furthermore, the results also reveal the interesting and novel phenomenon that a standing shock is likely to develop in the inner solar wind flow within this time frame, in particular, in coronal hole regions with rapidly diverging geometries.

Habbal, S. R.↗
NASA NTRS1990

Multigrid for hypersonic inviscid flows

The use of multigrid methods to solve the Euler equations for hypersonic flow is discussed. The steady state equations are considered with a Runge-Kutta smoother based on the time accurate equations together with local time stepping and residual smoothing. The effect of the Runge-Kutta coefficients on the convergence rate was examined considering both damping characteristics and convection properties. The importance of boundary conditions on the convergence rate for hypersonic flow is discussed. Also of importance are the switch between the second and fourth difference viscosity. Solutions are given for flow around the bump in a channel and flow around a biconic section.

Decker, Naomi H.↗
NASA NTRS1983

Separation of time scales in aircraft trajectory optimization

Two methods for analyzing the time-scale properties of aircraft trajectory optimization problems are presented. Time-scale properties must be identified before solutions can be obtained by using singular perturbation methods. Both methods only require a knowledge of the state equations, the aircraft characteristics, and the bounds on the state and control variables. Although these methods give only rough estimates of time-scale separation, they do not require that an 'exact' optimal trajectory be known, as do the more rigorous methods, and they are an improvement on the ad hoc methods currently in use. The two methods are applied to an example problem for a high performance aircraft.

Ardema, M. D.↗
NASA NTRS1993

State-constrained booster trajectory solutions via finite elements and shooting

This paper presents an extension of a FEM formulation based on variational principles. A general formulation for handling internal boundary conditions and discontinuities in the state equations is presented, and the general formulation is modified for optimal control problems subject to state-variable inequality constraints. Solutions which only touch the state constraint and solutions which have a boundary arc of finite length are considered. Suitable shape and test functions are chosen for a FEM discretization. All element quadrature (equivalent to one-point Gaussian quadrature over each element) may be done in closed form. The final form of the algebraic equations is then derived. A simple state-constrained problem is solved. Then, for a practical application of the use of the FEM formulation, a launch vehicle subject to a dynamic pressure constraint (a first-order state inequality constraint) is solved. The results presented for the launch-vehicle trajectory have some interesting features, including a touch-point solution.

Bless, Robert R.↗
NASA NTRS1976

Control methods for aiding a pilot during STOL engine failure transients

Candidate autopilot control laws that control the engine failure transient sink rates by demonstrating the engineering application of modern state variable control theory were defined. The results of approximate modal analysis were compared to those derived from full state analyses provided from computer design solutions. The aircraft was described, and a state variable model of its longitudinal dynamic motion due to engine and control variations was defined. The classical fast and slow modes were assumed to be sufficiently different to define reduced order approximations of the aircraft motion amendable to hand analysis control definition methods. The original state equations of motion were also applied to a large scale state variable control design program, in particular OPTSYS. The resulting control laws were compared with respect to their relative responses, ease of application, and meeting the desired performance objectives.

Nelson, E. R.↗
NASA NTRS1991

Parameterization of planetary wave breaking in the middle atmosphere

A parameterization of planetary wave breaking in the middle atmosphere has been developed and tested in a numerical model which includes governing equations for a single wave and the zonal-mean state. The parameterization is based on the assumption that wave breaking represents a steady-state equilibrium between the flux of wave activity and its dissipation by nonlinear processes, and that the latter can be represented as linear damping of the primary wave. With this and the additional assumption that the effect of breaking is to prevent further amplitude growth, the required dissipation rate is readily obtained from the steady-state equation for wave activity; diffusivity coefficients then follow from the dissipation rate. The assumptions made in the derivation are equivalent to those commonly used in parameterizations for gravity wave breaking, but the formulation in terms of wave activity helps highlight the central role of the wave group velocity in determining the dissipation rate. Comparison of model results with nonlinear calculations of wave breaking and with diagnostic determinations of stratospheric diffusion coefficients reveals remarkably good agreement, and suggests that the parameterization could be useful for simulating inexpensively, but realistically, the effects of planetary wave transport.

Garcia, Rolando R.↗
NASA NTRS2000

Isentropic Compression of Multicomponent Mixtures of Fuels and Inert Gases

In selected aerospace applications of the fuels hydrazine and monomethythydrazine, there occur conditions which can result in the isentropic compression of a multicomponent mixture of fuel and inert gas. One such example is when a driver gas such as helium comes out of solution and mixes with the fuel vapor, which is being compressed. A second example is when product gas from an energetic device mixes with the fuel vapor which is being compressed. Thermodynamic analysis has shown that under isentropic compression, the fuels hydrazine and monomethylhydrazine must be treated as real fluids using appropriate equations of state. The appropriate equations of state are the Peng-Robinson equation of state for hydrazine and the Redlich-Kwong-Soave equation of state for monomethylhydrazine. The addition of an inert gas of variable quantity and input temperature and pressure to the fuel compounds the problem for safety design or analysis. This work provides the appropriate thermodynamic analysis of isentropic compression of the two examples cited. In addition to an entropy balance describing the change of state, an enthalpy balance is required. The presence of multicomponents in the system requires that appropriate mixing rules are identified and applied to the analysis. This analysis is not currently available.

Barragan, Michelle↗
NASA NTRS1992

Effects of retardation in relativistic equations with confining interaction

A method has been developed for solving two body relativistic bound state equations in momentum space with a confining interaction. A total of six different three dimensional reductions of the Bethe-Salpeter equations are studied with particular emphasis placed on the competing roles of relativistic kinematics and retardation. The results indicate that these two effects counteract each other and this sheds some light on why nonrelativistic models of meson spectroscopy have been quite successful.

Maung, Khin Maung↗
NASA NTRS1991

On two-dimensional relativistic stellar winds

Stellar wind is of great interest, because many of the astrophysical systems possess wind like structures. For a long time only nonrelativistic winds have been studied. However, recently it was proposed by Kennel et al. that the relativistic pulsar wind with the plasma, consisting of electrons and positrons, can be responsible for the observed features of the Crab nebula. The study of Kennel et al. revealed the inconsistency of the assumption of the wind zero temperature with the observational data. It has been shown that only for high relativistic temperatures can high Mach numbers be reached, which allows the possibility of a shock formation. The analysis of Kennel et al. was extended into the 2-D case by using conventional magnetohydrodynamic equations for a relativistic plasma with an isotropic relativistic temperature. The state equation is assumed polytropic.

Gedalin, M. E.↗
NASA NTRS1985

Generating Tables of Thermodynamic Properties

Thermodynamic Property Generation program produces tables for any fluid for which state equation, vapor pressure equation, specific heat equation, and critical constants are known. Program calculates thermodynamic properties at any state providing way of obtaining properties at extreme environmental conditions.

Nguyen, S. N.↗
NASA NTRS1984

Approximation methods for inverse problems involving the vibration of beams with tip bodies

Two cubic spline based approximation schemes for the estimation of structural parameters associated with the transverse vibration of flexible beams with tip appendages are outlined. The identification problem is formulated as a least squares fit to data subject to the system dynamics which are given by a hybrid system of coupled ordinary and partial differential equations. The first approximation scheme is based upon an abstract semigroup formulation of the state equation while a weak/variational form is the basis for the second. Cubic spline based subspaces together with a Rayleigh-Ritz-Galerkin approach were used to construct sequences of easily solved finite dimensional approximating identification problems. Convergence results are briefly discussed and a numerical example demonstrating the feasibility of the schemes and exhibiting their relative performance for purposes of comparison is provided.

Rosen, I. G.↗
NASA NTRS1996

Thermohydrodynamic Analysis of Cryogenic Liquid Turbulent Flow Fluid Film Bearings

Computational programs developed for the thermal analysis of tilting and flexure-pad hybrid bearings, and the unsteady flow and transient response of a point mass rotor supported on fluid film bearings are described. The motion of a cryogenic liquid on the thin film annular region of a fluid film bearing is described by a set of mass and momentum conservation, and energy transport equations for the turbulent bulk-flow velocities and pressure, and accompanied by thermophysical state equations for evaluation of the fluid material properties. Zeroth-order equations describe the fluid flow field for a journal static equilibrium position, while first-order (linear) equations govern the fluid flow for small amplitude-journal center translational motions. Solution to the zeroth-order flow field equations provides the bearing flow rate, load capacity, drag torque and temperature rise. Solution to the first-order equations determines the rotordynamic force coefficients due to journal radial motions.

Luis San Andres↗