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Results for “zero-order methods”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

A first-order Lyapunov robustness method for linear systems with uncertain parameters

A method for stability-robustness analysis based on a quadratic Liapunov function that varies linearly with uncertainty parameters is derived. Linear time-invariant systems with structured uncertainties are discussed. The Liapunov function is optimized numerically to maximize the robustness region in parameter space. Numerical results are given for four examples in which the first-order method is compared to previous Liapunov methods. While the zero-order method is slightly better than the first-order method for one example, the first-order method is clearly superior in the other three (more realistic) examples. The first-order method is especially superior for the active control of flexible structures, where robustness with respect to (1) unmodeled coupling between modeled modes and (2) unmodeled modes is important. For such applications, the first-order method is much better at detecting the increased robustness associated with increased separation between frequencies.

Leal, M. A.↗
NASA NTRS1992

A hybrid approach to near-optimal launch vehicle guidance

This paper evaluates a proposed hybrid analytical/numerical approach to launch-vehicle guidance for ascent to orbit injection. The feedback-guidance approach is based on a piecewise nearly analytic zero-order solution evaluated using a collocation method. The zero-order solution is then improved through a regular perturbation analysis, wherein the neglected dynamics are corrected in the first-order term. For real-time implementation, the guidance approach requires solving a set of small dimension nonlinear algebraic equations and performing quadrature. Assessment of performance and reliability are carried out through closed-loop simulation for a vertically launched 2-stage heavy-lift capacity vehicle to a low earth orbit. The solutions are compared with optimal solutions generated from a multiple shooting code. In the example the guidance approach delivers over 99.9 percent of optimal performance and terminal constraint accuracy.

Leung, Martin S. K.↗
NASA NTRS1979

Choice of method for discretization of continuous systems

The paper discusses and compares several common methods of discretizing the transfer function of a continuous control system so that a digital computer can be used. The discretization effect on the frequency response attenuation of the simple transfer function G(s) = 1/(s + 1) is illustrated for the Tusting, Boxer-Thaler, Madwed, linear segment approximation, and stair-step with half period advanced methods. The input frequency must be significantly lower than one-half the sampling error to have negligible discretization error. Phase differences due to discretization are also plotted, and it is seen that the zero-order hold contributes much more phase shift than that due to discretization. In situations where zero-order hold must follow a computer, the method of discretization of a continuous system is not a major factor if phase shift is important.

Mcvey, E. S.↗
NASA NTRS2003

A Reduced-Order Model for Efficient Simulation of Synthetic Jet Actuators

A new reduced-order model of multidimensional synthetic jet actuators that combines the accuracy and conservation properties of full numerical simulation methods with the efficiency of simplified zero-order models is proposed. The multidimensional actuator is simulated by solving the time-dependent compressible quasi-1-D Euler equations, while the diaphragm is modeled as a moving boundary. The governing equations are approximated with a fourth-order finite difference scheme on a moving mesh such that one of the mesh boundaries coincides with the diaphragm. The reduced-order model of the actuator has several advantages. In contrast to the 3-D models, this approach provides conservation of mass, momentum, and energy. Furthermore, the new method is computationally much more efficient than the multidimensional Navier-Stokes simulation of the actuator cavity flow, while providing practically the same accuracy in the exterior flowfield. The most distinctive feature of the present model is its ability to predict the resonance characteristics of synthetic jet actuators; this is not practical when using the 3-D models because of the computational cost involved. Numerical results demonstrating the accuracy of the new reduced-order model and its limitations are presented.

Yamaleev, Nail K.↗
NASA NTRS1995

Supporting technology for the development of Controlled Ecological Life Support Systems (CELSS)

To support the development of Controlled Ecological Life Support Systems (CELSS) in the space program, a metabolic simulator has been selected for use in a closed chamber to test functions of the CELSS. This metabolic simulator is a catalytic reactor which oxidizes the methyl acetate to produce carbon dioxide and water vapor. In this project, kinetic studies of catalytic oxidation of methyl acetate were conducted using monolithic and pellet catalysts with 0.5% (by weight) platinum (Pt) on aluminum oxide (Al2O3). The reaction was studied at a pressure of one atmosphere and at temperatures varying from 160 C to 420 C. By-products were identified at the exit of the preheater and reactor. For the kinetic study with the monolithic catalyst, a linear regression method was used to correlate the kinetic data with zero-order, first-order and Langmuir-Hinshelwood models. Results indicate that the first-order model represents the data adequately at low concentrations of methyl acetate. For higher concentrations of methyl acetate, the Langmuir-Hinshelwood model best represents the kinetic data. Both rate constant and adsorption equilibrium constants were estimated from the regression. A Taguchi orthogonal array (L(sub 9)) was used to investigate the effects of temperature, flow rate, and concentration on the catalytic oxidation of methyl acetate. For the monolithic catalyst, temperature exerts the most significant effect, followed by concentration of methyl acetate. For the pellet catalyst, reaction temperature is the most significant factor, followed by gas flow rate and methyl acetate concentration. Concentrations of either carbon dioxide or oxygen were seen to have insignificant effect on the methyl acetate conversion process. Experimental results indicate that the preheater with glass beads can accomplish thermal cracking and catalytic reaction of methyl acetate to produce acetic acid, methanol, methyl formate, and 1-propanol. The concentration of all by-products was measured in ppmv (parts per million by volume). At higher temperatures, greater amounts of these products are produced, as expected. In all cases, methanol was the predominant concentration detected, followed by methyl formate. At temperatures lower than 320 C for the P-type monolithic catalyst, methanol, acetic acid, and acetone were detected, whereas, for the E-type monolithic catalyst, only methanol was detected at 160 C. Both P and E types of the monolithic catalyst were specified with the same substrates (ceramic), washcoat (Al2O3), and promoter (Pt). However, the manufacturing and treatment procedures were quite different. It was therefore concluded that the performance of the E-type monolithic catalyst is superior to that of the P-type for oxidation of methyl acetate. At higher reaction temperatures, e.g., above 420 C, all reactants and byproducts were completely oxidized using these two types of monolithic catalyst to produce carbon dioxide and water vapor. A complex heterogenous catalytic reaction mechanism was proposed to explain the formation of the byproducts (methanol, acetic acid, and methyl formate) as the methyl acetate traveled through the preheater packed with glass beads. The by-product, 1-propanol, may be formed only through a homogeneous reaction, since it is difficult to develop a reasonable sequence of heterogeneous reaction steps to explain its formation. The homogeneous thermal decomposition of methyl acetate to form free radicals was proposed to explain the formation of 1-propanol, and also methanol, in the preheater. A dual-site catalytic reaction mechanism was proposed for the oxidation of methyl acetate over Pt/Al2O3 monolithic catalyst. The dual-site mechanism describes the chemisorption of oxygen molecules as well as a physical adsorption of methyl acetate on the active sites. On the active sites, methyl acetate is oxidized rapidly to form carbon dioxide and water vapor. A rate equation derived from this mechanism gives the Langmuir-Hinshelwood rate formula which has been observed from the experimental data obtained in this project for high methyl acetate concentration (greater than 1000 ppmv) over a monolithic catalyst. If the oxygen concentration is very high and methyl acetate concentration is very low, the reaction rate equation is then reduced to a first-order with respect to methyl acetate concentration. The first-order model has also been observed from the experimental data obtained in this project for low methyl acetate concentration (less than 1000 ppmv).

Li, Ku-Yen↗
NASA NTRS1985

Picard iterations of boundary-layer equations

A method of solving the boundary-layer equations that arise in singular-perturbation analysis of flightpath optimization problems is presented. The method is based on Picard iterations of the integrated form of the equations and does not require iteration to find unknown boundary conditions. As an example, the method is used to develop a solution algorithm for the zero-order boundary-layer equations of the aircraft minimum-time-to-climb problem.

Ardema, M. D.↗
NASA NTRS1975

Methods for the computation of detailed geoids and their accuracy

Two methods for the computation of geoid undulations using potential coefficients and 1 deg x 1 deg terrestrial anomaly data are examined. It was found that both methods give the same final result but that one method allows a more simplified error analysis. Specific equations were considered for the effect of the mass of the atmosphere and a cap dependent zero-order undulation term was derived. Although a correction to a gravity anomaly for the effect of the atmosphere is only about -0.87 mgal, this correction causes a fairly large undulation correction that was not considered previously. The accuracy of a geoid undulation computed by these techniques was estimated considering anomaly data errors, potential coefficient errors, and truncation (only a finite set of potential coefficients being used) errors. It was found that an optimum cap size of 20 deg should be used. The geoid and its accuracy were computed in the Geos 3 calibration area using the GEM 6 potential coefficients and 1 deg x 1 deg terrestrial anomaly data. The accuracy of the computed geoid is on the order of plus or minus 2 m with respect to an unknown set of best earth parameter constants.

Rapp, R. H.↗
NASA NTRS1991

Modified ICED-ALE method for astrogeophysical plasma flows

The Implicit-Continuous-Eulerian-Difference Mesh-Arbitrary-Lagrangian-Eulerian (ICED-ALE) algorithm of Brackbill and Pracht (1973) is modified for the study of astrophysical plasma flows in which dynamical effects are important. In the present study the general-energy-conservation law is directly applied to the iteration process, with the total (kinetic-, specific-internal-, and magnetic-) energy density being obtained implicitly at the end of the process. An example is computed in which the convergence speed of the latter method is substantially faster than that of the former. The initializing calculation, or explicit phase, in which the electric current density, magnetic diffusion of field, energy augmentation, and zero-order approximation of the flow velocity are given, is described. Consideration is given to the iteration process, or implicit phase, from which the exact Lagrangian solution for energy density, velocity, and a magnetic field is obtained.

Wu, S. T.↗
NASA NTRS1990

Development of a defect stream function, law of the wall/wake method for compressible turbulent boundary layers

The method presented is designed to improve the accuracy and computational efficiency of existing numerical methods for the solution of flows with compressible turbulent boundary layers. A compressible defect stream function formulation of the governing equations assuming an arbitrary turbulence model is derived. This formulation is advantageous because it has a constrained zero-order approximation with respect to the wall shear stress and the tangential momentum equation has a first integral. Previous problems with this type of formulation near the wall are eliminated by using empirically based analytic expressions to define the flow near the wall. The van Driest law of the wall for velocity and the modified Crocco temperature-velocity relationship are used. The associated compressible law of the wake is determined and it extends the valid range of the analytical expressions beyond the logarithmic region of the boundary layer. The need for an inner-region eddy viscosity model is completely avoided. The near-wall analytic expressions are patched to numerically computed outer region solutions at a point determined during the computation. A new boundary condition on the normal derivative of the tangential velocity at the surface is presented; this condition replaces the no-slip condition and enables numerical integration to the surface with a relatively coarse grid using only an outer region turbulence model. The method was evaluated for incompressible and compressible equilibrium flows and was implemented into an existing Navier-Stokes code using the assumption of local equilibrium flow with respect to the patching. The method has proven to be accurate and efficient.

Wahls, Richard A.↗
NASA NTRSDate not supplied

A Zero-order Hold Approach for Fractional-delay Interpolation in Auralization

During the signal processing chain of an auralization simulating the propagation of a sound from a moving source to a stationary receiver, it is often necessary to interpolate between the samples of the source signal in order to arrive at uniformly-spaced samples at the receiver. In some cases, this interpolation is done in the receiver time frame – where the “input” samples of the source have become irregularly spaced due to time dilation effects. Canonical band-limited interpolation methods (i.e., sinc and sinc-derived approaches) cannot be applied in this case as they rely on having a uniformly-spaced input. The use of geometric interpolation methods that can handle irregularly-spaced input may not be grounded in signal processing principles and may produce unwanted artifacts and noise. This presentation outlines the possibility of embedding an irregularly-spaced zero-order hold signal within a highly over-sampled uniformly-spaced signal, and then processing down to the desired sampling rate through successive decimations. Initial distortion and noise characteristics of the approach are shown for some basic propagation geometries. The possible benefits of using such an approach in an auralization scheme with a time-varying Doppler shift are discussed including: the prevention of aliasing, processing time advantages, and the possibility for asynchronous processing.

Auralization↗
NASA NTRS1989

A defect stream function, law of the wall/wake method for compressible turbulent boundary layers

The application of the defect stream function to the solution of the two-dimensional, compressible boundary layer is examined. A law of the wall/law of the wake formulation for the inner part of the boundary layer is presented which greatly simplifies the computational task near the wall and eliminates the need for an eddy viscosity model in this region. The eddy viscosity model in the outer region is arbitrary. The modified Crocco temperature-velocity relationship is used as a simplification of the differential energy equation. Formulations for both equilibrium and nonequilibrium boundary layers are presented including a constrained zero-order form which significantly reduces the computational workload while retaining the significant physics of the flow. A formulation for primitive variables is also presented. Results are given for the constrained zero-order and second-order equilibrium formulations and are compared with experimental data. A compressible wake function valid near the wall has been developed from the present results.

Barnwell, Richard W.↗
NASA NTRS1977

Tube method of sound-absorption measurement extended to frequencies far above cutoff

Equipment had been constructed for measuring sound absorption in the frequency range from 4 to 100 kHz in a large tube 25.4 cm in diameter and 4.8-m long. The technique employs a large moveable solid-dielectric capacitance transducer that completely fills the tube cross section and generates pulses of plane waves. An identical transducer terminates the other end of the tube and serves as a microphone to detect and reflect the sound pulses. Measurements in argon, nitrogen, and air indicate that the attenuation of the sound pulses differs by less than 1% from values calculated for the zero-order mode for frequencies up to 44 times the cutoff frequency for the first 'nonplane' mode. Above that frequency, the measured values are less than those predicted by theory by an amount that is approximately proportional to the wavelength to the -3.1 power. In a smaller tube of similar construction, the high-frequency deviation from theory is absent.

Shields, F. D.↗
DOE OSTI2024

A method for crystallographic mapping of an alpha-beta titanium alloy with nanometre resolution using scanning precession electron diffraction and open-source software libraries

An approach for the crystallographic mapping of two-phase alloys on the nanoscale using a combination of scanned precession electron diffraction and open-source python libraries is introduced in this paper. This method is demonstrated using the example of a two-phase α/β titanium alloy. The data were recorded using a direct electron detector to collect the patterns, and recently developed algorithms to perform automated indexing and analyse the crystallography from the results. Very high-quality mapping is achieved at a 3 nm step size. The results show the expected Burgers orientation relationships between the α laths and β matrix, as well as the expected misorientations between α laths. A minor issue was found that one area was affected by 180° ambiguities in indexing occur due to this area being aligned too close to a zone axis of the α with twofold projection symmetry (not present in 3D) in the zero-order Laue Zone, and this should be avoided in data acquisition in the future. Nevertheless, this study demonstrates a good workflow for the analysis of nanocrystalline two- or multi-phase materials, which will be of widespread use in analysing two-phase titanium and other systems and how they evolve as a function of thermomechanical treatments.

36 MATERIALS SCIENCE↗
NASA NTRS1998

Microcapsules and Methods for Making

Methods of forming multi-lamellar microcapsules having alternating layers of hydrophilic and hydrophobic immiscible liquid phases have been developed using different polymer/solvent systems. The methods use liquid-liquid diffusion and simultaneous lateral phase separation, controlled by proper timed-sequence exposures of immiscible phases and low shear mixing, to form narrow size distributions of spherical, multilamellar microcapsules. The use of special formulations of solubilized drugs, surfactants, and polymeric co-surfactants in aqueous vehicles which are dispersed in hydrocarbon solvents containing small quantities of oil, low molecular weight co-surfactants and glycerides that are aqueous insoluble enables the formation of unique microcapsules which can carry large amounts of pharmaceuticals in both aqueous and non-aqueous solvent compartments. The liquid microcapsules are quickly formed in a single step and can include a polymeric outer 'skin' which protects the microcapsules during physical manipulation or exposure to high shear forces. Water-in-oil and oil-in-water microcapsules have been formed both in 1 x g and in microgravity, which contain several types of drugs co-encapsulated within different fluid compartments inside the same microcapsule. Large, spherical multi-lamellar microcapsules have been formed including a cytotoxic drug co-encapsulated with a radiocontrast medium which has advantages for chemoembolization of vascular tumors. In certain cases, crystals of the drug form inside the microcapsules providing zero-order and first order, sustained drug release kinetics.

Morrison, Dennis R.↗
DOE OSTI2025

Zero-Order Reaction Kinetics v. 3.6

Zero-RK is a software package that simulates chemically reacting systems using sparse, preconditioned, adaptive matrix methods to achieve orders-of-magnitude reduction in simulation time while maintaining accurate results.

McNenly, MatthewJ [Lawrence Livermore National Lab↗
NASA NTRS1982

Validation of zero-order feedback strategies for medium range air-to-air interception in a horizontal plane

A zero order feedback solution of a variable speed interception game between two aircraft in the horizontal plane, obtained by using the method of forced singular perturbation (FSP), is compared with the exact open loop solution. The comparison indicates that for initial distances of separation larger than eight turning radii of the evader, the accuracy of the feedback approximation is better than one percent. The result validates the zero order FSP approximation for medium range air combat analysis.

Shinar, J.↗
NASA NTRS1982

Nonlinear zero-sum differential game analysis by singular perturbation methods

A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane.

Sinar, J.↗