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At least 613 records · Page 34

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NASA NTRS1981

Approximate factorization for incompressible flow

For computational solution of the incompressible Navier-Stokes equations, the approximate factorization (AF) algorithm is used to solve the vectorized momentum equation in delta form based on the pressure calculated in the previous time step. The newly calculated velocities are substituted into the pressure equation (obtained from a linear combination of the continuity and momentum equation), which is then solved by means of line SOR. Computational results are presented for the NACA 66 sub 3 018 airfoil at Reynolds numbers of 1000 and 40,000 and attack angles of 0 and 6 degrees. Comparison with wind tunnel data for Re = 40,000 indicates good qualitative agreement between measured and calculated pressure distributions. Quantitative agreement is only fair, however, with the calculations somewhat displaced from the measurements. Furthermore, the computed velocity profiles are unrealistically thick around the airfoil, due to the excessive amount of artificial viscosity needed for stability. Based on the performance of the algorithm with regard to stability, it is concluded that AF/SOR is suitable for calculations at Reynolds numbers less than 10,000. Speedwise, the method is faster than point SOR by at least a factor of two.

Bernard, R. S.↗

NASA NTRS1981

Some aspects of algorithm performance and modeling in transient analysis of structures

The status of an effort to increase the efficiency of calculating transient temperature fields in complex aerospace vehicle structures is described. The advantages and disadvantages of explicit algorithms with variable time steps, known as the GEAR package, is described. Four test problems, used for evaluating and comparing various algorithms, were selected and finite-element models of the configurations are described. These problems include a space shuttle frame component, an insulated cylinder, a metallic panel for a thermal protection system, and a model of the wing of the space shuttle orbiter. Results generally indicate a preference for implicit over explicit algorithms for solution of transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures).

Adelman, H. M.↗

NASA NTRS1980

A clear-sky spectral solar radiation model for snow-covered mountainous terrain

A clear-sky spectral solar radiation model for direct and diffuse fluxes, combined with topographic calculations from digital terrain data, computes either incident, net, or reflected solar radiation at any point on a snow surface in mountainous terrain. The radiation may be integrated over any wavelength range from 250 to 5000 nm, or over any time step. Atmospheric attenuation parameters are ozone, water vapor, the Angstrom turbidity coefficient and exponent, and the absorptance to reflectance ratio of the atmospheric aerosols. The model derives these, from measurements which may contain both systematic and random errors, by finding the least squares solution to an overdetermined set of nonlinear equations. For calculations over a specified area, it employs table look-up procedures, so that computation speed for the spectral model approaches that for a lumped model. Thus it may be useful as part of a snow surface energy budget calculation over a drainage basin.

Dozier, J.↗

NASA NTRS1980

The application of Seasat-1 radar altimetry to continental shelf circulation modeling

Seasat-1 radar altimetry data have been used to verify a continental shelf circulation model subjected to tidal forcing on the open boundary. The model makes use of the semi-implicit mode of time integration, removing the surface gravity wave time step restriction. Both the altimetry and the model predictions are compared with empirically determined tidal fluctuations and generally good agreement is obtained.

Cornillon, P.↗

NASA NTRS1980

On time discretizations for spectral methods

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

Gottlieb, D.↗

NASA NTRS1981

Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives

A new explicit, time splitting algorithm has been developed for finite difference modelling of the full two and three-dimensional time-dependent, compressible, viscous Navier-Stokes equations of fluid mechanics. The scheme is optimal in the sense that the split operators achieve their maximum allowable time step, i.e., the corresponding Courant number. The algorithm allows a conservation-form formulation. Stability is proven analytically and verified numerically. In proving stability it was shown that all nine matrix coefficients of the Navier-Stokes equations are simultaneously symmetrizable by a similarity transformation. Two such transformations and their resulting symmetric matrix coefficients are presented explicitly.

Abarbanel, S.↗

NASA NTRS1981

Numerical method for gas dynamics combining characteristic and conservation concepts

An efficient implicit numerical method that solves the compressible Navier-Stokes equations in arbitrary curvilinear coordinates by the finite-volume technique is presented. An intrinsically dissipative difference scheme and a fully implicit treatment of boundary conditions, based on characteristic and conservation concepts, are used to improve stability and accuracy. Efficiency is achieved by using a diagonal form of the implicit algorithm and spatially varying time-steps. Comparisons of various schemes and methods are presented for one- and two-dimensional flows, including transonic separated flow past a thick circular-arc airfoil in a channel. The new method is equal to or better than a version of MacCormack's hybrid method in accuracy and it converges to a steady state up to an order of magnitude faster.

Coakley, T. J.↗

NASA NTRS1980

Influence of rotor blade tip shape on tip vortex shedding - An unsteady, inviscid analysis

An unsteady potential flow panel method is described based on a time-stepping procedure and using planar quadrilateral panels to represent the surface of thick blades. Each panel has a constant source and doublet distribution and a central control point where an internal Dirichlet boundary condition is applied. The method includes detail paneling around the tip edge and offers the facility of prescribing a tip-edge separation. Preliminary results are shown for four blade tip shapes which are treated as semi-span wings oscillating in pitch about a mean angle of attack of 6 deg. Further work is planned for the wake model before proceeding to higher angles of attack.

Maskew, B.↗

NASA NTRS1981

Numerical stability of an explicit finite difference scheme for the solution of transient conduction in composite media

A theoretical evaluation of the stability of an explicit finite difference solution of the transient temperature field in a composite medium is presented. The grid points of the field are assumed uniformly spaced, and media interfaces are either vertical or horizontal and pass through grid points. In addition, perfect contact between different media (infinite interfacial conductance) is assumed. A finite difference form of the conduction equation is not valid at media interfaces; therefore, heat balance forms are derived. These equations were subjected to stability analysis, and a computer graphics code was developed that permitted determination of a maximum time step for a given grid spacing.

Campbell, W.↗

NASA NTRS1981

Development of an engineering analysis of progressive damage in composites during low velocity impact

A computerized, analytical methodology was developed to study damage accumulation during low velocity lateral impact of layered composite plates. The impact event was modeled as perfectly plastic with complete momentum transfer to the plate structure. A transient dynamic finite element approach was selected to predict the displacement time response of the plate structure. Composite ply and interlaminar stresses were computed at selected time intervals and subsequently evaluated to predict layer and interlaminar damage. The effects of damage on elemental stiffness were then incorporated back into the analysis for subsequent time steps. Damage predicted included fiber failure, matrix ply failure and interlaminar delamination.

Humphreys, E. A.↗

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 NTRS1982

Some aspects of algorithm performance and modeling in transient thermal analysis of structures

The status of an effort to increase the efficiency of calculating transient temperature fields in complex aerospace vehicle structures is described. The advantages and disadvantages of explicit and implicit algorithms are discussed. A promising set of implicit algorithms with variable time steps, known as the GEAR package is described. Four test problems, used for evaluating and comparing various algorithms, were selected and finite element models of the configurations are described. These problems include a space shuttle frame component, an insulated cylinder, a metallic panel for a thermal protection system, and a model of the space shuttle orbiter wing. Results generally indicate a preference for implicit oer explicit algorithms for solution of transient structural heat transfer problems when the governing equations are stiff.

Adelman, H. M.↗

NASA NTRS1982

Rime ice accretion and its effect on airfoil performance

A methodology was developed to predict the growth of rime ice, and the resulting aerodynamic penalty on unprotected, subcritical, airfoil surfaces. The system of equations governing the trajectory of a water droplet in the airfoil flowfield is developed and a numerical solution is obtained to predict the mass flux of super cooled water droplets freezing on impact. A rime ice shape is predicted. The effect of time on the ice growth is modeled by a time-stepping procedure where the flowfield and droplet mass flux are updated periodically through the ice accretion process. Two similarity parameters, the trajectory similarity parameter and accumulation parameter, are found to govern the accretion of rime ice. In addition, an analytical solution is presented for Langmuir's classical modified inertia parameter. The aerodynamic evaluation of the effect of the ice accretion on airfoil performance is determined using an existing airfoil analysis code with empirical corrections. The change in maximum lift coefficient is found from an analysis of the new iced airfoil shape. The drag correction needed due to the severe surface roughness is formulated from existing iced airfoil and rough airfoil data. A small scale wind tunnel test was conducted to determine the change in airfoil performance due to a simulated rime ice shape.

Bragg, M. B.↗

NASA NTRS1981

Shallow water experiments using an improved Kreiss-Oliger 2-4 scheme

The Abarbanel-Gottleib (AG) modification of the Kreiss-Oliger (KO) scheme is applied to a global 1-level shallow water model and the results compared to results obtained using the standard KO scheme. The standard KO scheme consists of the second order leapfrog scheme for time derivatives and fourth order space differencing for spatial derivatives. The AG scheme modifies the KO scheme in a manner similar to that done by Wilson to the multidimensional leapfrog scheme, obtaining a 35-40% improvement of the maximum time step. Application of the AG scheme expands the domain of influence of the KO scheme by including off-axis grid points.

Takacs, L. L.↗

NASA NTRS1982

Shock-fitted Euler solutions to shock vortex interactions

The interaction of a planar shock wave with one or more vortexes is computed using a pseudospectral method and a finite difference method. The development of the spectral method is emphasized. In both methods the shock wave is fitted as a boundary of the computational domain. The results show good agreement between both computational methods. The spectral method is, however, restricted to smaller time steps and requires use of filtering techniques.

Salas, M. D.↗

NASA NTRS1982

Application of two-point difference schemes to the conservative Euler equations for one-dimensional flows

An implicit finite difference method is presented for obtaining steady state solutions to the time dependent, conservative Euler equations for flows containing shocks. The method used the two-point differencing approach of Keller with dissipation added at supersonic points via the retarded density concept. Application of the method to the one-dimensional nozzle flow equations for various combinations of subsonic and supersonic boundary conditions shows the method to be very efficient. Residuals are typically reduced to machine zero in approximately 35 time steps for 50 mesh points. It is shown that the scheme offers certain advantages over the more widely used three-point schemes, especially in regard to application of boundary conditions.

Wornom, S. F.↗

NASA NTRS1982

A new numerical method for the simulation of three dimensional flow in a pipe

A new numerical technique for simulating three dimensional, unsteady, incompressible pipe flows is presented and its utility and accuracy is shown. Each vector function in the expansion of the velocity field is divergence free and satisfies the boundary conditions for viscous flow. Some of the benefits of the expansion technique are that pressure is eliminated from the dynamics, only two unknowns per mesh point are required, implicit treatment of the viscous terms is provided at no extra computational cost, and no fractional time steps are required. The method uses spectral expansions: Fourier series in the azimuthal and streamwise directions, and Jacobi polynominals in the radial direction.

Leonard, A.↗

NASA NTRS1982

Studies of implicit and explicit solution techniques in transient thermal analysis of structures

Studies aimed at an increase in the efficiency of calculating transient temperature fields in complex aerospace vehicle structures are reported. The advantages and disadvantages of explicit and implicit algorithms are discussed and a promising set of implicit algorithms with variable time steps, known as GEARIB, is described. Test problems, used for evaluating and comparing various algorithms, are discussed and finite element models of the configurations are described. These problems include a coarse model of the Space Shuttle wing, an insulated frame tst article, a metallic panel for a thermal protection system, and detailed models of sections of the Space Shuttle wing. Results generally indicate a preference for implicit over explicit algorithms for transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures). The effects on algorithm performance of different models of an insulated cylinder are demonstrated. The stiffness of the problem is highly sensitive to modeling details and careful modeling can reduce the stiffness of the equations to the extent that explicit methods may become the best choice. Preliminary applications of a mixed implicit-explicit algorithm and operator splitting techniques for speeding up the solution of the algebraic equations are also described.

Adelman, H. M.↗