Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “delta method”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Tabulation and summary of thermodynamic effects data for developed cavitation on ogive-nosed bodies

Thermodynamic effects data for developed cavitation on zero and quarter caliber ogives in Freon 113 and water are tabulated and summarized. These data include temperature depression (delta T), flow coefficient (C sub Q), and various geometrical characteristics of the cavity. For the delta T tests, the free-stream temperature varied from 35 C to 95 C in Freon 113 and from 60 C to 125 C in water for a velocity range of 19.5 m/sec to 36.6 m/sec. Two correlations of the delta T data by the entrainment method are presented. These correlations involve different combinations of the Nusselt, Reynolds, Froude, Weber, and Peclet numbers and dimensionless cavity length.

Holl, J. W.↗
NASA NTRS1993

Plans to improve the experimental limit in the comparison of the east-west and west-east one-way light propagation times on the rotating earth

The preceding paper describes the results so far (interrupted in the Spring of 1989 because of lack of funds) of an experiment comparing the one-way light propagation times on the surface of the rotating Earth. For the 20 Km path length component in the East-West direction the predicted difference between the opposite sense propagation times would be 160 ps, if the approximately 360 Km/s surface speed of the Earth gives effective light speeds of 3 x 10(exp 8) m/s +/- 360 m/s. This could lead to a prediction of the difference between the clock transport and the light pulse synchronization methods described in the preceding paper: delta(T) = 0.5 (160) = 80 ps. The current upper bound of approximately 100 ps for delta(T) is limited by poorly understood systematic errors. The most important seems to be intensity-dependent time delays in the remote light pulse avalanche photo-diode detector. This will be replaced by a continuously operating circular scan streak camera having single photon sensitivity and a time resolution of approximately 5 ps. (This camera has recently been developed by the Xian Institute of Optics and Precision Mechanics in the P.R.C.). Better isolation from shocks and vibration for the Sigma-Tau hydrogen maser during transport will be provided. It is hoped that delta(T) is less than 20 ps can be achieved.

Alley, C. O.↗
NASA NTRS2001

Thermodynamics of Silicon-Hydroxide Formation in H2O Containing Atmospheres

The formation of volatile silicon-hydroxide species from SiO2 in water containing atmospheres has been identified as a potentially important mode of degradation of Si-based ceramics. Availability of thermodynamic data for these species is a major problem. This study is part of an ongoing effort to obtain reliable, experimentally determined thermodynamic data for these species. The transpiration method was used to measure the pressure of Si-containing vapor in equilibrium with SiO2 (cristobalite) and Ar + H2O(g) with various mole fractions of water vapor, X(sub H2O), at temperatures ranging from 1000 to 1780 K. Enthalpies and entropies for the reaction, SiO2(s) + 2H2O(g) = Si(OH)4(g), were obtained, at X(sub H2O) = 0.15 and 0.37, from the variation of lnK with 1/T according to the 'second law method'. The following data were obtained: delta(H)deg = 52.9 +/- 3.7 kJ/mole and delta(S)deg = -68.6 +/- 2.5 J/mole K at an average temperature of 1550 K, and delta(H)deg = 52.5+/-2.0 kJ/mole and delta(S)deg= -69.7 +/- 1.5 J/moleK at an average temperature of 1384 K, for X(sub H2O)= 0.15 and 0.37, respectively. These data agree with results from the literature obtained at an average temperature of 1600 K, and strongly suggest Si(OH)4(g) is the dominant vapor species. Contradictory results were obtained with the determination of the dependence of Si-containing vapor pressure on the partial pressure of water vapor at 1187 and 1722 K. These results suggested the Si-containing vapor could be a mixture of Si(OH)4 + SiO(OH)2. Further pressure dependent studies are in progress to resolve these issues.

Copland, Evan↗
NASA NTRS1991

On the formulation of a minimal uncertainty model for robust control with structured uncertainty

In the design and analysis of robust control systems for uncertain plants, representing the system transfer matrix in the form of what has come to be termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents a transfer function matrix M(s) of the nominal closed loop system, and the delta represents an uncertainty matrix acting on M(s). The nominal closed loop system M(s) results from closing the feedback control system, K(s), around a nominal plant interconnection structure P(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unsaturated uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, but for real parameter variations delta is a diagonal matrix of real elements. Conceptually, the M-delta structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the currently available literature addresses computational methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty, where the term minimal refers to the dimension of the delta matrix. Since having a minimally dimensioned delta matrix would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta would be useful. Hence, a method of obtaining the interconnection system P(s) is required. A generalized procedure for obtaining a minimal P-delta structure for systems with real parameter variations is presented. Using this model, the minimal M-delta model can then be easily obtained by closing the feedback loop. The procedure involves representing the system in a cascade-form state-space realization, determining the minimal uncertainty matrix, delta, and constructing the state-space representation of P(s). Three examples are presented to illustrate the procedure.

Belcastro, Christine M.↗
NASA NTRS1991

Volumetric measurement of tank volume

A method is disclosed for determining the volume of compressible gas in a system including incompressible substances in a zero-gravity environment consisting of measuring the change in pressure (delta P) for a known volume change rate (delta V/delta t) in the polytrophic region between isothermal and adiabatic conditions. The measurements are utilized in an idealized formula for determining the change in isothermal pressure (delta P sub iso) for the gas. From the isothermal pressure change (delta iso) the gas volume is obtained. The method is also applicable to determination of gas volume by utilizing work (W) in the compression process. In a passive system, the relationship of specific densities can be obtained.

Walter, Richard T.↗
NASA NTRS2018

Assessment and Verification of SLS Block 1-B Exploration Upper Stage and Stage Disposal Performance

Delta-v allocation to correct for insertion errors caused by state uncertainty is one of the key performance requirements imposed on the SLS Navigation System. Additionally, SLS mission requirements include the need for the Exploration Up-per Stage (EUS) to be disposed of successfully. To assess these requirements, the SLS navigation team has developed and implemented a series of analysis methods. Here the authors detail the Delta-Delta-V approach to assessing delta-v allocation as well as the EUS disposal optimization approach.

Patrick, Sean↗
NASA NTRS1981

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

Harten, A.↗
NASA NTRS1999

A Textbook for a First Course in Computational Fluid Dynamics

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

Zingg, D. W.↗
NASA NTRS2018

Improved Detection of Low Stratus and Fog at Dawn from Dual Geostationary (COMS and FY-2D) Satellites

A novel method was proposed to detect low stratus and fog (LSF) at dawn during the summertime using near simultaneous observations from dual geostationary-orbit satellites (GEOs): the Korean Communication, Ocean and Meteorological Satellite (COMS; 128.2 degrees East) and the Chinese Feng-Yun-2D (FY-2D; 86.5 degrees East). The orbital positions of the GEOs provided a large difference (around 46.5 degrees) in the viewing zenith angle (VZA) in the study region (122-132 degrees East, 32.5-42.5 degrees North) and high contrast observations at dawn. Numerical simulations were carried out to derive the optical properties of the LSF and the radiative differences between the GEOs due to both the VZA and spectral response function (SRF). The conventional threshold method, which used the visible reflectance at 0.67 microns (R (sub 0.67)) and the brightness temperature difference between 3.7 microns and 11 microns (BTD (sub 3.7-11), had limitations in detecting LSF at dawn due to weak visible light and fast night-to-day transition. We utilized the observed stereo differences (delta R (sub 0.67), delta BTD (sub 3.7-11) between the two GEOs to improve LSF detection. The dual-satellite observations were verified with ground-based data from 45 stations in South Korea co-located with each GEO pixel. The delta R (sub 0.67) threshold value showed better accuracy (78 percent vs. 67 percent) than the conventional R (sub 0.67) threshold method. In addition, the delta BTD (sub 3.7-11) threshold was better (55 percent vs. 38 percent) than the BTD (sub 3.7-11) threshold. The dual-satellite method allowed more reliable LSF detection using the combination of delta R (sub 0.67) and R (sub 0.67), particularly for LSF without cumuliform or high clouds. Our method is applicable to multiple geostationary satellites for continuous LSF monitoring.

geostationary satellite↗
NASA NTRS1980

A new method for optimizing multiple flyby trajectories

A new procedure has been developed which minimizes total impulsive Delta V for multiple flyby trajectories with constraints on flyby parameters and maneuver times. The method involves solving a bounds-constrained parameter optimization problem with a Newton algorithm utilizing analytic first and second derivatives. Each trajectory segment connecting consecutive maneuver points is found by first targeting from the preceding maneuver point to the parameters of the upcoming flyby and then propagating the resulting trajectory to the next maneuver point. Multi-conic techniques are used for trajectory propagation and for computation of the state transition matrix. This procedure has successfully optimized Galileo satellite tours containing up to 11 flybys.

Damario, L. A.↗
NASA NTRS1993

Computational techniques for high-speed flows with viscous and chemical effects

Algorithms for solving the Euler and the Navier-Stokes equations in conjunction with chemical kinetic equations are presented. The convective flux is estimated from a quasi one dimensional interpolation procedure. Shock, contact, and expansion waves and thermochemical nonequilibrium phenomena are captured by the Lax-Friedrichs technique. Relaxation techniques were developed to enhance their effectiveness in dealing with spatial and temporal stiffness associated with the physical problems. Both explicit and implicit smoothers were implemented into the standard multigrid time stepping method. Unsteady and steady scalar problems are discussed. A perfect gas and equilibrium air shock tube problem is investigated. Numerical schemes and techniques are compared for the problems of shock and boundary layer interaction and three dimensional viscous, nonequilibrium flow encompassing an aerobrake. The results are comparable in accuracy against other high order non-oscillatory techniques. The multigrid methods are assessed using a Mach 8 flow over a complete planar body, a sphere, and a blunt delta wing at 20 deg incidence. Applying an implicit multigrid method on a nested grid of 128 by 64 nodes the reduction factor is 0.25. The central processing unit reduction factor is 2.2 after both the single and multigrid Runge-Kutta solutions converged to machine zero on a grid of 37 by 41 by 73 nodes.

Li, C. P.↗
NASA NTRS1976

An improved method for the prediction of completely three-dimensional aerodynamic load distributions of configurations with leading edge vortex separation

The application of a higher-order subsonic potential flow panel method to the solution of three-dimensional flow about wing and wing-body combinations with leading-edge vortex separation is presented. The governing equations are the linear flow differential equation and nonlinear boundary conditions which require that the flow be parallel to the wing and body surfaces and that the free vortex sheet, springing from the leading and trailing edges, be aligned with the local flow and support no pressure jump. The vortex core is modeled as a simple line vortex which receives vorticity from the free sheet through a connecting sheet. The Kutta condition is imposed on all appropriate edges of the wing. This set of nonlinear equations is solved by an iterative procedure. The Goethert rule accounts for compressibility. The method has been programmed for the CDC 6600. Delta wings, gothic wings, arrow wings, cambered wings, and wing with body have been analyzed. Initial studies involving variations of panel density, vortex sheet sizing, Jacobian update, and initial geometry demonstrate that the present method generally exhibits good convergence characteristics.

Rubbert, p. E.↗
NASA NTRS1989

Performance of FFT methods in local gravity field modelling

Fast Fourier transform (FFT) methods provide a fast and efficient means of processing large amounts of gravity or geoid data in local gravity field modelling. The FFT methods, however, has a number of theoretical and practical limitations, especially the use of flat-earth approximation, and the requirements for gridded data. In spite of this the method often yields excellent results in practice when compared to other more rigorous (and computationally expensive) methods, such as least-squares collocation. The good performance of the FFT methods illustrate that the theoretical approximations are offset by the capability of taking into account more data in larger areas, especially important for geoid predictions. For best results good data gridding algorithms are essential. In practice truncated collocation approaches may be used. For large areas at high latitudes the gridding must be done using suitable map projections such as UTM, to avoid trivial errors caused by the meridian convergence. The FFT methods are compared to ground truth data in New Mexico (xi, eta from delta g), Scandinavia (N from delta g, the geoid fits to 15 cm over 2000 km), and areas of the Atlantic (delta g from satellite altimetry using Wiener filtering). In all cases the FFT methods yields results comparable or superior to other methods.

Forsberg, Rene↗
NASA NTRS1989

A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum

The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies.

Chou, Jack C. K.↗
NASA NTRS1989

A methodology for formulating a minimal uncertainty model for robust control system design and analysis

In the design and analysis of robust control systems for uncertain plants, the technique of formulating what is termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents the transfer function matrix M(s) of the nominal system, and delta represents an uncertainty matrix acting on M(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unstructured uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, and for real parameter variations the diagonal elements are real. As stated in the literature, this structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the literature addresses methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty. Since have a delta matrix of minimum order would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta model would be useful. A generalized method of obtaining a minimal M-delta structure for systems with real parameter variations is given.

Belcastro, Christine M.↗
NASA NTRS1991

Dependence of the critical temperature of laser-ablated YBa2Cu3O(7-delta) thin films on LaAlO3 substrate growth technique

Samples of LaAlO3 made by flame fusion and Czochralski method were subjected to the same temperature conditions that they have to undergo during the laser ablation deposition of YBa2Cu3O(7 - delta) thin films. After oxygen annealing at 750 C, the LaAlO3 substrate made by two methods experienced surface roughening. The degree of roughening on the substrate made by Czochralski method was three times greater than that on the substrate made by flame fusion. This excessive surface roughening may be the origin of the experimentally observed lowering of the critical temperature of a film deposited by laser ablation on a LaAlO3 substrate made by Czochralski method with respect to its counterpart deposited on LaAlO3 substrates made by flame fusion.

Warner, Joseph D.↗