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NASA NTRS1988

Method and models for R-curve instability calculations

This paper presents a simple method for performing elastic R-curve instability calculations. For a single material-structure combination, the calculations can be done on some pocket calculators. On microcomputers and larger, it permits the development of a comprehensive program having libraries of driving force equations for different configurations and R-curve model equations for different materials. The paper also presents several model equations for fitting to experimental R-curve data, both linear elastic and elastoplastic. The models are fit to data from the literature to demonstrate their viability.

Orange, Thomas W.↗

NASA NTRS1987

Numerical calculations of mass transfer flow in semi-detached binary systems

The details of the mass transfer flow near the inner Lagrangian point in a semidetached binary system are numerically calculated. A polytropic equation of state with n = 3/2 is used. The dependence of the mass transfer rate on the degree to which the star overfills its Roche lobe is calculated, and good agreement with previous analytic estimates is found. The variation of mass transfer rate which occurs if the binary system has a small eccentricity is calculated and is used to cast doubt on the model for superhumps in dwarf novae proposed by Papaloizou and Pringle (1979).

Edwards, D. A.↗

NASA NTRS1987

Explicit finite-volume time-marching calculations of total temperature distributions in turbulent flow

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time-marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier-Stokes equations. The entire calculation is performed in the physical domain. This paper investigates the introduction of a new formulation of the energy equation which gives improved transient behavior as the calculation converges. The effect of variable Prandtl number on the temperature distribution through the boundary layer is also investigated. A turbulent boundary layer in an adverse pressure gradient (M = 0.55) is used to demonstrate the improved transient temperature distribution obtained when the new formulation of the energy equation is used. A flat plate turbulent boundary layer with a supersonic free-stream Mach number of 2.8 is used to investigate the effect of Prandtl number on the distribution of properties through the boundary layer. The computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

Nicholson, Stephen↗

NASA NTRS1988

Wing flutter calculations with the CAP-TSD unsteady transonic small disturbance program

The paper describes the application and assessment of the recently developed CAP-TSD transonic small-disturbance code for flutter predicition. The CAP-TSD program has been developed for aeroelastic analysis of complete aircraft configurations and was previously applied to the calculation of steady and unsteady pressures with favorable results. Flutter calculations are presented for two thin swept-and-tapered wing platforms with well-defined modal properties. The calculations are for Mach numbers from low subsonic to low supersonic values, including the transonic range, and are compared with subsonic linear theory and experimental flutter data. The CAP-TSD flutter results are generally in good agreement with the experimental values and are in good agreement with subsonic linear theory when wing thickness is neglected.

Bennett, Robert M.↗

NASA NTRS1988

Recent improvement of spallation cross section calculations, applicable to cosmic ray physics

About half of the cosmic ray nuclei heavier than helium have suffered nuclear transformations while colliding with the interstellar gas. The semiempirical calculations developed for calculating the still unmeasured cross sections had errors of about 25-50 per cent, depending on the target mass interval. Recent precise measurements have permitted significant improvements in the calculation of cross sections. Several such improvements are discussed. A status report on work-in-progress is presented on a general modification of the spallation equation parameters.

Silberberg, R.↗

NASA NTRS1988

Quantum mechanical calculations of vibrational population inversion in chemical reactions - Numerically exact L-squared-amplitude-density study of the H2Br reactive system

Numerically exact, fully three-dimensional quantum mechanicl reactive scattering calculations are reported for the H2Br system. Both the exchange (H + H-prime Br to H-prime + HBr) and abstraction (H + HBR to H2 + Br) reaction channels are included in the calculations. The present results are the first completely converged three-dimensional quantum calculations for a system involving a highly exoergic reaction channel (the abstraction process). It is found that the production of vibrationally hot H2 in the abstraction reaction, and hence the extent of population inversion in the products, is a sensitive function of initial HBr rotational state and collision energy.

Zhang, Y. C.↗

NASA NTRS1988

Calculations of rate constants for the three-body recombination of H2 in the presence of H2

A new global potential energy hypersurface for H2 + H2 is constructed and quasiclassical trajectory calculations performed using the resonance complex theory and energy transfer mechanism to estimate the rate of three body recombination over the temperature range 100 to 5000 K. The new potential is a faithful representation of ab initio electron structure calculations, is unchanged under the operation of exchanging H atoms, and reproduces the accurate H3 potential as one H atom is pulled away. Included in the fitting procedure are geometries expected to be important when one H2 is near or above the dissociation limit. The dynamics calculations explicitly include the motion of all four atoms and are performed efficiently using a vectorized variable-stepsize integrator. The predicted rate constants are approximately a factor of two smaller than experimental estimates over a broad temperature range.

Schwenke, David W.↗

NASA NTRS1988

Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics

The calculation of shape and scale parameters of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by uing the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded. The techniques described were verified with several example problems from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program.

Pai, Shantaram S.↗

NASA NTRS1988

A general formalism for phase space calculations

General formulas for calculating the interactions of galactic cosmic rays with target nuclei are presented. Methods for calculating the appropriate normalization volume elements and phase space factors are presented. Particular emphasis is placed on obtaining correct phase space factors for 2-, and 3-body final states. Calculations for both Lorentz-invariant and noninvariant phase space are presented.

Norbury, John W.↗

NASA NTRS1989

An investigation of using an RQP based method to calculate parameter sensitivity derivatives

Estimation of the sensitivity of problem functions with respect to problem variables forms the basis for many of our modern day algorithms for engineering optimization. The most common application of problem sensitivities has been in the calculation of objective function and constraint partial derivatives for determining search directions and optimality conditions. A second form of sensitivity analysis, parameter sensitivity, has also become an important topic in recent years. By parameter sensitivity, researchers refer to the estimation of changes in the modeling functions and current design point due to small changes in the fixed parameters of the formulation. Methods for calculating these derivatives have been proposed by several authors (Armacost and Fiacco 1974, Sobieski et al 1981, Schmit and Chang 1984, and Vanderplaats and Yoshida 1985). Two drawbacks to estimating parameter sensitivities by current methods have been: (1) the need for second order information about the Lagrangian at the current point, and (2) the estimates assume no change in the active set of constraints. The first of these two problems is addressed here and a new algorithm is proposed that does not require explicit calculation of second order information.

Beltracchi, Todd J.↗

NASA NTRS1989

Calculation of turbulence-driven secondary motion in ducts with arbitrary cross section

Calculation methods for turbulent duct flows are generalized for ducts with arbitrary cross-sections. The irregular physical geometry is transformed into a regular one in computational space, and the flow equations are solved with a finite-volume numerical procedure. The turbulent stresses are calculated with an algebraic stress model derived by simplifying model transport equations for the individual Reynolds stresses. Two variants of such a model are considered. These procedures enable the prediction of both the turbulence-driven secondary flow and the anisotropy of the Reynolds stresses, in contrast to some of the earlier calculation methods. Model predictions are compared to experimental data for developed flow in triangular duct, trapezoidal duct and a rod-bundle geometry. The correct trends are predicted, and the quantitative agreement is mostly fair. The simpler variant of the algebraic stress model procured better agreement with the measured data.

Demuren, A. O.↗

NASA NTRS1987

Calculation of the surface tension of liquid metals using a one-component-plasma reference system

The one-component-plasma (OCP) model is used as a reference system instead of the traditional hard-sphere fluid to calculate the liquid-vapor interfacial surface tension of liquid metals within the density functional formalism. The calculated surface tensions of the alkali metals are in excellent agreement with experiment. For the polyvalent metal Al, the result obtained is larger than experimental measurements. It is concluded that the OCP system is not suitable to describe the liquid-vapor phase transition in simple metals which have a nominal plasma parameter larger than the usual freezing value of about 178. The calculated interfacial widths in all cases are narrower than the expected experimental values.

Zeng, X. C.↗

NASA NTRS1989

Improved calculation of total cross section for pair production by relativistic heavy ions

A calculation of the total cross section for direct electron-positron pair production by heavy ions is described. It combines the use of the Weizsaecker-Williams method for low-energy transfers and existing calculations for high-energy transfers. Higher-order corrections to the total cross section are calculated based on the Weizsaecher-Williams method and existing results for pair production by photons.

Eby, P. B.↗

NASA NTRS1988

An efficient approach for statistical calculations with globally gridded filtered time series

The formulas for performing several statistical calculations based on Fourier coefficients are presented for use in atmospheric observational studies. The calculations discussed include a method for estimating the degree of temporal freedoms of two correlated time series and a method for performing seasonal analyses using a half-year summer/winter projection operator in the frequency domain. A modified lag-correlation calculation is proposed for obtaining lag correlations in the frequency domain. Also, a spectral approach for Empirical Orthogonal Function (EOF) and Extended EOF analysis is given which reduces the size of the matrix to be solved in the eigenproblem.

Gao, X. H.↗

NASA NTRS1989

Equilibrium gas flow computations. I - Accurate and efficient calculation of equilibrium gas properties

This paper treats the accurate and efficient calculation of thermodynamic properties of arbitrary gas mixtures for equilibrium flow computations. New improvements in the Stupochenko-Jaffe model for the calculation of thermodynamic properties of diatomic molecules are presented. A unified formulation of equilibrium calculations for gas mixtures in terms of irreversible entropy is given. Using a highly accurate thermo-chemical data base, a new, efficient and vectorizable search algorithm is used to construct piecewise interpolation procedures with generate accurate thermodynamic variable and their derivatives required by modern computational algorithms. Results are presented for equilibrium air, and compared with those given by the Srinivasan program.

Liu, Yen↗

NASA NTRS1989

Direct calculation of the reactive transition matrix by L-squared quantum mechanical variational methods with complex boundary conditions

A new formalism of the generalized Newton variational principle for the calculation of quantum mechanical state-to-state reaction probabilities is presented. The reformulation involves solving directly for the transition matrix rather than the reactance mtrix so that calculations may be carried out for individual columns of the transition matrix without obtaining solutions for all possible initial channels. The convergence of calculations with real and complex boundary conditions are compared for H + H2 - H2 + H, O + H2 - OH + H, and O + HD - OH + D and OD + H.

Sun, Yan↗

NASA NTRS1990

Calculating Performances Of Fabry-Perot Etalons

Effects of changes in design determined quickly. Etalon Model computer program implements stand-alone mathematical model of an etalon. Designed to perform calculations over many wavelengths. Used to determine sensitivity of filter to changes in temperature, thickness tolerances, or alignment angles of etalon design. Calculates several performance parameters of etalons by use of equations in closed form, and calculates transmission as function of wavelength and uses transmission data to determine additional performance parameters. Developed on IBM PS/2 Model 80-071 computer using Microsoft version 4.01 FORTRAN compiler.

Cross, Patricia L.↗

NASA NTRS1989

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

Greene, William H.↗