Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “characteristic equations”

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.

At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Sequential Bayesian Parameter Estimation of Stochastic Dynamic Load Models

In this paper we focus on the parameter estimation of dynamic load models with stochastic terms-in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty in the aggregated protection characteristics can be formulated as a stochastic differential equation with process noise. We cast the parameter inversion within a Bayesian parameter estimation framework, and we present methods to include process noise. We demonstrate the benefits of considering stochasticity in the parameter estimation and the risks of ignoring it.

Bayesian Statistics↗
DOE OSTI2021

Suggestions on the Vapor Pressure Determination of Molten Salts

The knowledge of the thermophysical properties of coolant and fuel in molten salts nuclear reactors (MSRs), such as thermal stability and vapor pressure, are of remarkable interest, particularly for simulating safe reactor operations. Molten salt reactorsMSRs use molten salt mixtures as the primary coolant and/or fuel and are expected to operate up to 800 °C. With the revival of interest in deploying MSRs, complete thermophysical and thermochemical characterization of these materials is of interest to industry, regulators, and researchers. Vapor pressure data for molten salts are scarce in the literature, both for pure salts but especially for eutectic mixtures. This report describes the effusion method, which consist of measuring the rate of escape of vapor molecules through a small orifice for the determination of the vapor pressure of compounds and may be useful on compounds such as molten salts. Thermogravimetric analysis records the mass loss as a function of time and temperature. There are two equations that can be used to relate the mass loss rate with the vapor pressure: (1) the Knudsen equation and (2) the Langmuir equation. To apply these equations, the system needs to reach a pseudo (or near) equilibrium condition. Therefore, the experimental conditions must be such that allow the condensed and the vapor/gas phases to be in equilibrium. In order to accomplish equilibrium like conditions, the sample must be in an almost-sealed cell except for a small orifice, from where the vapor escapes. In the Knudsen method vacuum is applied to eliminate the effect that the presence of other gas molecules could have on the evaporation rate of the sample. However, Langmuir alleged that in certain conditions, such as at low temperatures and/or when the vapor pressure is low, the rate of evaporation of a substance is independent of the presence of vapor around it. For that reason, some researchers, when measuring the mass loss of a substance with a predictable low vapor pressure, do not apply vacuum when using the Langmuir equation. However, they use a standard substance to parameterize the experimental setup. The use of one equation or the other will depend on the characteristics of the sample and the availability of an appropriate standard. Some important aspects related to the nature of the samples and vapor pressure measurements are described for future consideration.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1986

Dead-time effects in pulse-counting Digicon detectors

The Hubble Space Telescope's High Resolution Spectrograph employs two pulse-counting Digicon detectors to record UV spectra. At higher measured count rates, the intervals between photon arrivals become comparable to the response time of the electronics, so that not every pulse will be counted; this 'paired pulse' effect causes departures from linearity and must be corrected for during raw data reduction. Attention is given to two analytic equations that quantify the dead-time losses. The less attenuated spectra are noted to be severely distorted by these losses; a comparison with the undistorted low count rate data allows a detailed analysis to be made of the pulse-counting characteristics over five decades of input event rates. The present equations and calibration methods should be applicable to all kinds of multichannel pulse-counting detectors.

Ebbets, Dennis C.↗
NASA NTRSDate not supplied

Sparse Linear Algebra Toolkit for Computational Aerodynamics

Finding solutions to sparse linear systems of equations is an essential step in Computational Engineering applications of interest to NASA. Linear systems of equations are composed and solved in almost every computational engineering application. The characteristics of linear systems vary greatly from one application to another. Accordingly, there are a wide variety of methods for the solution of linear systems of equations. The operations and methods prepared by the authors are focused on linear systems of interest to NASA, primarily those associated with Computational Fluid Dynamics (CFD), Aeroelasticity, and Aeroacoustics. The Sparse Linear Algebra Toolkit (SLAT) is a coordinated collection of software featuring operations, methods, and data structures that are useful when solving sparse linear systems of equations on modern computer architectures. The implemented operations and methods are designed and tuned for parallelism in shared memory, in distributed memory, and across the hybrid combination of distributed-shared memory. The toolkit includes novel methods and implementations for modern architectures and facilitates development of new approaches for meeting NASA’s evolving computational engineering challenges using evolving computer architectures that are not available in vendor libraries. In this paper, significant features and interfaces within SLAT are presented and verified for simulations performed with NASA’s CFD solver, FUN3D. The runtime and scaling performance of the Generalized Minimum Residual (GMRES) method implemented in SLAT is analyzed for the linear subproblems within the solution of turbulent Navier-Stokes equations employed in the simulation of high-lift configurations. Prior to this work, the SPARSKIT GMRES implementation was the only Krylov subspace method available within FUN3D. A strong scaling study shows the SLAT GMRES implementation facilitates accurate Reynolds-averaged Navier-Stokes CFD solutions between 15% and 56% faster than the SPARSKIT GMRES implementation.

Stephen L Wood↗
NASA NTRS2010

Deconvolution methods and systems for the mapping of acoustic sources from phased microphone arrays

A method and system for mapping acoustic sources determined from a phased microphone array. A plurality of microphones are arranged in an optimized grid pattern including a plurality of grid locations thereof. A linear configuration of N equations and N unknowns can be formed by accounting for a reciprocal influence of one or more beamforming characteristics thereof at varying grid locations among the plurality of grid locations. A full-rank equation derived from the linear configuration of N equations and N unknowns can then be iteratively determined. A full-rank can be attained by the solution requirement of the positivity constraint equivalent to the physical assumption of statically independent noise sources at each N location. An optimized noise source distribution is then generated over an identified aeroacoustic source region associated with the phased microphone array in order to compile an output presentation thereof, thereby removing the beamforming characteristics from the resulting output presentation.

Brooks, Thomas F.↗
NASA NTRS1989

A nonoscillatory, characteristically convected, finite volume scheme for multidimensional convection problems

A new, nonoscillatory upwind scheme is developed for the multidimensional convection equation. The scheme consists of an upwind, nonoscillatory interpolation of data to the surfaces of an intermediate finite volume; a characteristic convection of surface data to a midpoint time level; and a conservative time integration based on the midpoint rule. This procedure results in a convection scheme capable of resolving discontinuities neither aligned with, nor convected along, grid lines.

Yokota, Jeffrey W.↗
NASA NTRS1990

A nonoscillatory, characteristically convected, finite volume scheme for multidimensional convection problems

A new, nonoscillatory upwind scheme is developed for the multidimensional convection equation. The scheme consists of an upwind, nonoscillatory interpolation of data to the surfaces of an intermediate finite volume; a characteristic convection of surface data to a midpoint time level; and a conservative time integration based on the midpoint rule. This procedure results in a convection scheme capable of resolving discontinuities neither aligned with, nor convected along, grid lines.

Yokota, Jeffrey W.↗
NASA NTRS1989

Development of a Navier-Stokes algorithm for parallel-processing supercomputers

An explicit flow solver, applicable to the hierarchy of model equations ranging from Euler to full Navier-Stokes, is combined with several techniques designed to reduce computational expense. The computational domain consists of local grid refinements embedded in a global coarse mesh, where the locations of these refinements are defined by the physics of the flow. Flow characteristics are also used to determine which set of model equations is appropriate for solution in each region, thereby reducing not only the number of grid points at which the solution must be obtained, but also the computational effort required to get that solution. Acceleration to steady-state is achieved by applying multigrid on each of the subgrids, regardless of the particular model equations being solved. Since each of these components is explicit, advantage can readily be taken of the vector- and parallel-processing capabilities of machines such as the Cray X-MP and Cray-2.

Swisshelm, Julie M.↗
NASA NTRS1988

Development of an aerodynamics algorithm for parallel-processing supercomputers

An explicit flow solver, applicable to the hierarchy of model equations ranging from Euler to full Navier-Stokes, is combined with several techniques designed to reduce computational expense. The computational domain consists of local grid refinements embedded in a global coarse mesh, where the locations of these refinements are defined by the physics of the flow. Flow characteristics are also used to determine which set of model equations is appropriate for solution in each region, thereby reducing not only the number of grid points at which the solution must be obtained, but also the computational effort required to get that solution. Acceleration to steady-state is achieved by applying multigrid on each of the subgrids, regardless of the particular model equations being solved. Since each of these components is explicit, advantage can readily be taken of the vector- and parallel-processing capabilities of machines such as the Cray X-MP and Cray-2.

Swisshelm, Julie M.↗
NASA NTRS1992

Numerical investigations in the backflow region of a vacuum plume

The objective of this research is to numerically simulate the vacuum plume flow field in the backflow region of a low thrust nozzle exit. In space applications, the low thrust nozzles are used as a propulsion device to control the vehicle attitude, or to maneuver the vehicle flight trajectory. When the spacecraft is deployed in the orbit or cruising in a planetary mission, the vacuum plume is created behind the nozzle exit (so called backflow region), by the exhausting gas of the propulsion system or by venting internal gas to the extremely low density ambient. The low density vacuum plume flow regions cover the continuum, transitional and free molecular flow regimes, which were characterized by the Knudsen number K(sub n), K(sub n) = lambda(sub m)/L where lambda(sub m) is the mean free path of the gas molecules and L is the characteristic length of the flow field. The transitional regime is defined by 0.01 is less than or equal to K(sub n) is less than or equal to 10. The conventional Navier-Stokes equations are valid only in the flow region close to the nozzle exit since the validity of the Navier-Stokes equations fails asymptotically as the Knudsen number increases. The vacuum plume characteristics prediction is primarily a problem of transitional aerodynamics.

Liaw, Goang-Shin↗
NASA NTRS2011

Observations of Low-Latitude Plasma Density Enhancements and their Associated Plasma Drifts

Plasma density structures are frequently encountered in the nighttime low-latitude ionosphere by probes on the Communication/Navigation Outage Forecasting System (C/NOFS) satellite. Of particular interest to us here are plasma density enhancements, which are typically observed +/- 15 deg away from the magnetic equator. The low inclination of the C/NOFS satellite offers an unprecedented opportunity to examine these structures and their associated electric fields and plasma velocities, including their field-aligned components, along an east-west trajectory. Among other observations, the data reveal a clear asymmetry in the velocity structure within and around these density enhancements. Previous observations have shown that the peak change in drift velocity associated with a density enhancement occurs simultaneously both perpendicular and parallel to the magnetic field, while the 1results in this paper show that the peak change in parallel fl ow typically occurs 25-100 km to the east of the peak perpendicular ow. We discuss this and other aspects of the observations in relation to the characteristics of the plasma depletions formed near the magnetic equator detected by the same probes on the C/NOFS satellite and to previous observations and theories.

Klenzing, J. H.↗
NASA NTRS1984

Analysis of lateral and torsional vibration characteristics of beams and shafts with end located rotational masses

Partial differential equations are derived for free lateral and torsional vibration of a uniform free-free beam with a rotational mass attached to each extremity. For appropriate boundary conditions, nonlinear algebraic equations are obtained using a symbolic manipulation computer program, the solutions of which enable the computation of the neutral frequencies and mode-shapes. The mode-shapes are linear combinations of trigonometric and hyperbolic sine and cosine functions. A computer program is written for the numerical solution of the algebraic equations mentioned above, which can compute the natural frequencies, mode-shapes, and node points for any given set of parameters, for any given number of modes.

Robertson, D. K.↗
NASA NTRS1973

Perform - A performance optimizing computer program for dynamic systems subject to transient loadings

A description and applications of a computer capability for determining the ultimate optimal behavior of a dynamically loaded structural-mechanical system are presented. This capability provides characteristics of the theoretically best, or limiting, design concept according to response criteria dictated by design requirements. Equations of motion of the system in first or second order form include incompletely specified elements whose characteristics are determined in the optimization of one or more performance indices subject to the response criteria in the form of constraints. The system is subject to deterministic transient inputs, and the computer capability is designed to operate with a large linear programming on-the-shelf software package which performs the desired optimization. The report contains user-oriented program documentation in engineering, problem-oriented form. Applications cover a wide variety of dynamics problems including those associated with such diverse configurations as a missile-silo system, impacting freight cars, and an aircraft ride control system.

Pilkey, W. D.↗
NASA NTRS2012

The Effect of Systematic Error in Forced Oscillation Testing

One of the fundamental problems in flight dynamics is the formulation of aerodynamic forces and moments acting on an aircraft in arbitrary motion. Classically, conventional stability derivatives are used for the representation of aerodynamic loads in the aircraft equations of motion. However, for modern aircraft with highly nonlinear and unsteady aerodynamic characteristics undergoing maneuvers at high angle of attack and/or angular rates the conventional stability derivative model is no longer valid. Attempts to formulate aerodynamic model equations with unsteady terms are based on several different wind tunnel techniques: for example, captive, wind tunnel single degree-of-freedom, and wind tunnel free-flying techniques. One of the most common techniques is forced oscillation testing. However, the forced oscillation testing method does not address the systematic and systematic correlation errors from the test apparatus that cause inconsistencies in the measured oscillatory stability derivatives. The primary objective of this study is to identify the possible sources and magnitude of systematic error in representative dynamic test apparatuses. Sensitivities of the longitudinal stability derivatives to systematic errors are computed, using a high fidelity simulation of a forced oscillation test rig, and assessed using both Design of Experiments and Monte Carlo methods.

Williams, Brianne Y.↗
NASA NTRS1983

Spatial variation of corn canopy temperature as dependent upon soil texture and crop rooting characteristics

A soil plant atmosphere model for corn (Zea mays L.) together with the scaling theory for soil hydraulic heterogeneity are used to study the sensitivity of spatial variation of canopy temperature to field averaged soil texture and crop rooting characteristics. The soil plant atmosphere model explicitly solves a continuity equation for water flux resulting from root water uptake, changes in plant water storage and transpirational flux. Dynamical equations for root zone soil water potential and the plant water storage models the progressive drying of soil, and day time dehydration and night time hydration of the crop. The statistic of scaling parameter which describes the spatial variation of soil hydraulic conductivity and matric potential is assumed to be independent of soil texture class. The field averaged soil hydraulic characteristics are chosen to be representative of loamy sand and clay loam soils. Two rooting characteristics are chosen, one shallow and the other deep rooted. The simulation shows that the range of canopy temperatures in the clayey soil is less than 1K, but for the sandy soil the range is about 2.5 and 5.0 K, respectively, for the shallow and deep rooted crops.

Choudhury, B. J.↗
NASA NTRS1987

Pressure probe study of the water relations of Phycomyces blakesleeanus sporangiophores

The physical characteristics which govern the water relations of the giant-celled sporangiophore of Phycomyces blakesleeanus were measured with the pressure probe technique and with nanoliter osmometry. These properties are important because they govern water uptake associated with cell growth and because they may influence expansion of the sporangiophore wall. Turgor pressure ranged from 1.1 to 6.6 bars (mean = 4.1 bars), and was the same for stage I and stage IV sporangiophores. Sporangiophore osmotic pressure averaged 11.5 bars. From the difference between cell osmotic pressure and turgor pressure, the average water potential of the sporangiophore was calculated to be about -7.4 bars. When sporangiophores were submerged under water, turgor remained nearly constant. We propose that the low cell turgor pressure is due to solutes in the cell wall solution, i.e., between the cuticle and the plasma membrane. Membrane hydraulic conductivity averaged 4.6 x 10(-6) cm s-1 bar-1, and was significantly greater in stage I sporangiophores than in stage IV sporangiophores. Contrary to previous reports, the sporangiophore is separated from the supporting mycelium by septa which prevent bulk volume flow between the two regions. The presence of a wall compartment between the cuticle and the plasma membrane results in anomalous osmosis during pressure clamp measurements. This behavior arises because of changes in solute concentration as water moves into or out of the wall compartment surrounding the sporangiophore. Theoretical analysis shows how the equations governing transient water flow are altered by the characteristics of the cell wall compartment.

NASA Discipline Number 40-30↗
NASA NTRS2004

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

Turpin, Jason B.↗
NASA NTRS1977

Is the common definition of the Mie-Grueneisen equation of state inconsistent

Anharmonic models are used to describe the high temperatures and the electronic effects characteristic of shock wave phenomena and planetary interiors. It is found that a generalized Grueneisen function dependent on temperature and volume is necessary for the self-consistent application of the Mie-Grueneisen equation at the physical conditions encountered in shock wave phenomena or in the interior of planets. It is noted that at temperatures of a few thousand degrees Kelvin, by deriving the function in terms of anharmonic lattice dynamics, the difference between gamma and gamma(th) is of the same order of a magnitude as gamma. This leads to the conclusions that (1) gamma is not a function of temperature and (2) gamma?gamma(th) does not explain either the equation of state of planetary interiors or high-temperature shock wave phenomena.

Mulargia, F.↗