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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
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Comparison of numerical techniques for integration of stiff ordinary differential equations arising in combustion chemistry

The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an interactive solution of the algebraic energy conservation equation to compute the temperature does not result in significant errors. In addition, this method is more efficient than evaluating the temperature by integrating its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = at(supra N) N exp(-E/RT) only when the temperature change exceeds an amount delta T that is problem dependent. An approximate expression for the automatic evaluation of delta T is derived and is shown to result in increased efficiency.

Radhakrishnan, K.↗
NASA NTRS1973

The Lyapunov stabilization of satellite equations of motion using integrals

A method is introduced that weakens the Lyapunov or in track instability of satellite equations of motion. The method utilizes a linearized energy integral of satellite motion as a constraint on solutions obtained by numerical integration. The procedure prevents local numerical error from altering the frequency associated with the fast angular variable and thereby reduces the Lyapunov instability and the global numerical error. Applications of the method to satellite motion show accuracy improvements of two to three orders of magnitude in position and velocity after 50 revolutions. A modification of the method is presented that allows the use of slowly varying integrals of motion.

Nacozy, P. E.↗
NASA NTRS1991

Biological production models as elements of coupled, atmosphere-ocean models for climate research

Process models of phytoplankton production are discussed with respect to their suitability for incorporation into global-scale numerical ocean circulation models. Exact solutions are given for integrals over the mixed layer and the day of analytic, wavelength-independent models of primary production. Within this class of model, the bias incurred by using a triangular approximation (rather than a sinusoidal one) to the variation of surface irradiance through the day is computed. Efficient computation algorithms are given for the nonspectral models. More exact calculations require a spectrally sensitive treatment. Such models exist but must be integrated numerically over depth and time. For these integrations, resolution in wavelength, depth, and time are considered and recommendations made for efficient computation. The extrapolation of the one-(spatial)-dimension treatment to large horizontal scale is discussed.

Platt, Trevor↗
DOE OSTI2025

Gaussian FLOWERS: Wind-rose-based analytical integration of Gaussian wake model for extremely fast AEP estimation

A major cost in the study of wind farm layout optimization is the repeated evaluation of the annual energy production (AEP). The current approach to estimating AEP requires a large set of flow simulations to be performed that cover each discrete wind speed and direction combination contained within the wind rose, followed by a probability-weighted sum of the power production resulting from each simulation. Even with inexpensive engineering wake models, this numerical integration scheme can lead to high computational costs. In this paper, we derive an analytical formulation for estimating farm AEP across every wind direction, based on a Gaussian wake velocity model, which reduces the number of wind farm simulations to a single function evaluation. As a result, we find that the Gaussian-FLOWERS approach reduces the time for AEP calculations by more than two orders of magnitude with a small trade-off in accuracy when compared to a conventional approach. This massive reduction in computation cost is useful to reduce overall costs in wind farm layout optimization studies.

17 WIND ENERGY↗
NASA NTRS1984

A numerical transport scheme which avoids negative mixing ratios

A new scheme for numerically integrating the transport equation has been developed. This square root method avoids the problem of negative mixing ratios by using the square root of the concentration instead of the concentration itself as an advective time step. Conservation of total mass at every time step is achieved by extending the concept of quadratic conservation to the numerical time integration method. A few time schemes that fulfill the requirement of step-by-step quadratic conservation are described, the simplest of which is the modified Lax-Wendroff method.

Schneider, H.-R.↗
NASA NTRS1977

Unsteady supersonic aerodynamic theory for interfering surfaces by the method of potential gradient

A generalized solution of the hyperbolic wave equation was further developed to relate the velocity components at a field point to the potential gradient distribution in the dependence domain. Singular integrals were evaluated in closed form, with numerical integration methods for more complex but analytic functions. Idealization of the lifting surfaces by trapezoidal elements with two sides parallel to the streamlines is computationally efficient. Streamwise integrals were performed analytically, and spanwise integrals were neccessary only on element leading and trailing sides. All integrands vanish on the Mach cone. Pressure distribution on a double delta wing and generalized aerodynamic coefficients for three AGARD planforms were calculated and compared with available results.

Jones, W. P.↗
NASA NTRS1991

Effects of anisotropic conduction and heat pipe interaction on minimum mass space radiators

Equations are formulated for the two dimensional, anisotropic conduction of heat in space radiator fins. The transverse temperature field was obtained by the integral method, and the axial field by numerical integration. A shape factor, defined for the axial boundary condition, simplifies the analysis and renders the results applicable to general heat pipe/conduction fin interface designs. The thermal results are summarized in terms of the fin efficiency, a radiation/axial conductance number, and a transverse conductance surface Biot number. These relations, together with those for mass distribution between fins and heat pipes, were used in predicting the minimum radiator mass for fixed thermal properties and fin efficiency. This mass is found to decrease monotonically with increasing fin conductivity. Sensitivities of the minimum mass designs to the problem parameters are determined.

Baker, Karl W.↗
NASA NTRS1994

Algorithms For Integrating Nonlinear Differential Equations

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

Freed, A. D.↗
NASA NTRS1982

A numerical method for integrating the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes

An extension of the method of moments is developed for the numerical integration of the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes. The number density function n sub k (x,t) in each separate droplet packet between droplet mass grid points (x sub k, x sub k+1) is represented by an expansion in orthogonal polynomials with a given weighting function. In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved and the problem of solving the kinetic equations is replaced by one of solving a set of coupled differential equations for the number density function moments. The method is tested against analytic solutions of the corresponding kinetic equations. Numerical results are obtained for different coalescence/breakup and condensation/evaporation kernels and for different initial droplet spectra. Also droplet mass grid intervals, weighting functions, and time steps are varied.

Emukashvily, I. M.↗
NASA NTRS1966

Numerical Studies of the Non-linear Vlasov Equation

The subject of this dissertation is the numerical integration of the initial-value problem for the non-linear Vlasov equation. The Vlasov equation is used to describe the dynamics of a "collisionless", one-dimensional, classical electron gas confined between two perfectly reflecting boundaries. Only the long-range Coulomb interactions of the electrons are considered; effects associated with the discrete structure are neglected. The numerical results obtained for non-linear Landau damping compare well with similar results obtained by Knorr. A general statement of the results on stable initial conditions is: As the degree of non-linearity of the initial conditions is increased, the deviation from linear Landau damping appears sooner and is more severe. In some cases damping was observed to cease. Curves showing the time dependence of the damping decrement are derived and compared with predictions of non-linear theories. New results obtained in this study include the observation that for strongly non-linear cases, the damping of the electric field causes an initially Maxwellian fo (v, O) to develop a peak in the neighborhood of the phase velocity; strong growth of the second harmonic is seen after fo (v, t) develops such a peak. Also new in this study is the interpretation of the development of a certain class of strongly unstable initial conditions as approaching an inhomogeneous equilibrium.

NUMERICAL INTEGRATION↗
DOE OSTI2025

Single-shot femtosecond laser-induced breakdown spectroscopy in low-density gases

Single-shot fs laser-induced breakdown spectroscopy (LIBS) has been used to interrogate low-density gases of H 2 ⁠, CH 4 ⁠, CO 2 ⁠, and H 2 O ranging from 0.5 × 10 15 to 9.1 × 10 15 cm −3 (15–275 mTorr). Strong spectral signatures were observed above the noise baseline for each test gas at all densities considered. Unique molecular signatures were observed for both CH 4 and CO 2 along with atomic features for each gas. The LIBS intensity response with respect to density was determined for each species using Voigt lineshape fitting or numerical integration. Finally, the collection and analysis of LIBS spectra of composite mixtures of CH 4 –CO 2 and CH 4 –H 2 demonstrates that the extraction of individual densities from gas mixtures is feasible at low densities.

Artificial neural networks↗
NASA NTRS1975

Integrated potential formulation of unsteady supersonic aerodynamics for interacting wings

A numerical integrated velocity potential method for the determination of unsteady aerodynamic forces on arbitrary interacting wings and tails in supersonic flow has been developed. Constant Mach number has been assumed throughout the flow field. Normalwash and sidewash integrals have been derived. The upwash integral remains to be derived. Singular integrals in the expressions for the velocity components have been evaluated in closed form. Lifting surfaces are represented by triangular elements defined by arbitrarily spaced characteristic lines and the true surface edges. The wake field is represented by rectangular strip elements. Velocity potential distributions and generalized aerodynamic coefficients have been compared.

Appa, K.↗
NASA NTRS1979

Shuttle program. Onorbit navigation integrator results for typical shuttle orbits

Three types of navigation onorbit numerical integrators were evaluated: (1) power integrators with no delta-V incorporation, just coasting (using Taylor series expansion integrators); (2) coasting integrators using the Cowell method of special perturbations; and (3) coasting integrator using the Pines variation of parameter perturbation method. Results show that the super G integrator is a very simple and effective for 2 and 4 second time steps. Since IMU delta-V data can be easily incorporated in the integration scheme, its use as the standard onorbit navigation propagator for the maintenance of the current state was implemented in the onboard navigation software. The Pines formulation method with a Runge-Kutta-Gill fourth-order integrator method produces excellent results up to 300 second time steps. On orbit prediction with this method was implemented in the onboard onorbit navigation scheme. The Runge-Kutta third order, using Cowell's method, is an excellent general purpose determination integrator for time steps up to a 60 second duration.

Olszewski, O. W.↗