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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 NTRS1972

Numerical analysis of the transient response of an axisymmetric ablative char layer considering internal flow effects

The differential equations governing the transient response of the char layer of an ablating axisymmetric body, internal pyrolysis gas flow effects being considered, have been derived. These equations have been expanded into finite difference form and programed for numerical solution on a digital computer. Numerical results compare favorably with simplified exact solutions. The complete numerical analysis was used to obtain solutions for two representative body shapes subjected to a typical entry heating environment. Pronounced effects of the lateral flow of pyrolysis gases on the mass flow field within the char layer and the associated surface and pyrolysis interface recession rates are shown.

Pittman, C. M.↗
NASA NTRS1980

A new approach in cascade flow analysis using the finite element method

A new approach in analyzing the potential flow past cascades and single airfoils using the finite element method is developed. In this analysis the circulation around the airfoil is not externally imposed but is directly computed in the numerical solution. Different finite element discretization patterns, orders of piecewise approximation, and grid sizes are used in the solution. The results obtained are compared with existing experimental measurements and exact solutions in cascades and single airfoils.

Baskharone, E.↗
NASA NTRS1988

Hierarchic plate and shell models based on p-extension

This paper is concerned with formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on (1) estimation of the relative error in energy norm; (2) equilibrium tests; and (3) observation of the convergence of quantities of interest.

Szabo, Barna A.↗
NASA NTRS1988

Hierarchic plate and shell models based on p-extension

Formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work was studied. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on: (1) estimation of the relative error in energy norm; (2) equilibrium tests, and (3) observation of the convergence of quantities of interest.

Szabo, Barna A.↗
NASA NTRS1989

Thrust law effects on the long-period modes of aerospace craft

An analytical study is presented of the longitudinal long-period dynamics of an aerospace craft in a nearly circular orbit, with a thrust law depending arbitrarily on the speed and altitude. A plane of engine possibilities is first defined, with points corresponding to propulsion systems having prescribed thrust slopes with respect to speed and altitude. Approximate expressions for the characteristic roots and times are obtained by first identifying a small quantity in the coefficients of the characteristic equation, and then expanding in a perturbation series about the origin of the plane of engine possibilities, for which the solution is always known. These expressions agree very well with the exact solutions over a wide range of altitudes and thrust laws. The period of the oscillatory translational mode (phugoid) is found to be independent to first order of the thrust law, generalizing results found by previous investigators for specific thrust laws. The results apply to the speed range from hypersonic to orbital.

Markopoulos, Nikos↗
NASA NTRS1992

Grid generation and flow solution method for Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS1994

Enhanced simulation software for rocket turbopump, turbulent, annular liquid seals

One of the main objectives of this work is to develop a new dynamic analysis for liquid annular seals with arbitrary profile and to analyze a general distorted interstage seal of the space shuttle main engine high pressure oxygen turbopump (SSME-ATD-HPOTP). The dynamic analysis developed is based on a method originally proposed by Nelson and Nguyen. A simpler scheme based on cubic splines is found to be computationally more efficient and has better convergence properties at higher eccentricities. The first order solution of the original analysis is modified by including a more exact solution that takes into account the variation of perturbed variables along the circumference. A new set of equations for dynamic analysis are derived based on this more general model. A unified solution procedure that is valid for both Moody's and Hirs' friction models is presented. Dynamic analysis is developed for three different models: constant properties, variable properties, and thermal effects with variable properties. Arbitrarily varying seal profiles in both axial and circumferential directions are considered. An example case of an elliptical seal with varying degrees of axial curvature is analyzed in detail. A case study based on predicted clearances of an interstage seal of the SSME-ATD-HPOTP is presented. Dynamic coefficients based on external specified load are introduced to analyze seals that support a preload. The other objective of this work is to study the effect of large rotor displacements of SSME-ATD-HPOTP on the dynamics of the annular seal and the resulting transient motion. One task is to identify the magnitude of motion of the rotor about the centered position and establish limits of effectiveness of using current linear models. This task is accomplished by solving the bulk flow model seal governing equations directly for transient seal forces for any given type of motion, including motion with large eccentricities. Based on the above study, an equivalence is established between linearized coefficients based transient motion and the same motion as predicted by the original governing equations. An innovative method is developed to model nonlinearities in an annular seal based on dynamic coefficients computed at various static eccentricities. This method is thoroughly tested for various types of transient motion using bulk flow model results as a benchmark.

Padavala, Satya↗
NASA NTRS1994

Robust inverse kinematics using damped least squares with dynamic weighting

This paper presents a general method for calculating the inverse kinematics with singularity and joint limit robustness for both redundant and non-redundant serial-link manipulators. Damped least squares inverse of the Jacobian is used with dynamic weighting matrices in approximating the solution. This reduces specific joint differential vectors. The algorithm gives an exact solution away from the singularities and joint limits, and an approximate solution at or near the singularities and/or joint limits. The procedure is here implemented for a six d.o.f. teleoperator and a well behaved slave manipulator resulted under teleoperational control.

Schinstock, D. E.↗
NASA NTRS1995

Application of the space-time conservation element and solution element method to two-dimensional advection-diffusion problems

The existing 2-D alpha-mu scheme and alpha-epsilon scheme based on the method of space-time conservation element and solution element, which were constructed for solving the linear 2-D unsteady advection-diffusion equation and unsteady advection equation, respectively, are tested. Also, the alpha-epsilon scheme is modified to become the V-E scheme for solving the nonlinear 2-D inviscid Burgers equation. Numerical solutions of six test problems are presented in comparison with their exact solutions or numerical solutions obtained by traditional finite-difference or finite-element methods. It is demonstrated that the 2-D alpha-mu, alpha-epsilon, and nu-epsilon schemes can be used to obtain numerical results which are more accurate than those based on some of the traditional methods but without using any artificial tuning in the computation. Similar to the previous 1-D test problems, the high accuracy and simplicity features of the space-time conservation element and solution element method have been revealed again in the present 2-D test results.

Wang, Xiao-Yen↗
NASA NTRS1982

Exact triple integrals of beam functions

Definite triple integrals encountered in applying the Galerkin method to the problem of heat and mass transfer across rectangular enclosures are discussed. Rather than evaluating them numerically, the technique described by Reid and Harris (1958) was extended to obtain the exact solution of the integrals. In the process, four linear simultaneous equations with triple integrals as unknowns were obtained. These equations were then solved exactly to obtain the closed form solution. Since closed form representations of this type have been shown to be useful in solving nonlinear hydrodynamic problems by series expansion, the integrals are presented here in general form.

Jhaveri, B. S.↗
NASA NTRS1975

Steady-state solution of the semi-empirical diffusion equation for area sources

The problem investigated can be solved exactly in a simple manner if the equations are written in terms of a similarity variable. The exact solution is used to explore two questions of interest in the modelling of urban air pollution, taking into account the distribution of surface concentration downwind of an area source and the distribution of concentration with height.

Lebedeff, S. A.↗
NASA NTRS1983

An investigation of the accuracy of finite difference methods in the solution of linear elasticity problems

The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.

Bauld, N. R., Jr.↗
NASA NTRS1987

Decoupled direct method for sensitivity analysis in combustion kinetics

An efficient, decoupled direct method for calculating the first order sensitivity coefficients of homogeneous, batch combustion kinetic rate equations is presented. In this method the ordinary differential equations for the sensitivity coefficients are solved separately from , but sequentially with, those describing the combustion chemistry. The ordinary differential equations for the thermochemical variables are solved using an efficient, implicit method (LSODE) that automatically selects the steplength and order for each solution step. The solution procedure for the sensitivity coefficients maintains accuracy and stability by using exactly the same steplengths and numerical approximations. The method computes sensitivity coefficients with respect to any combination of the initial values of the thermochemical variables and the three rate constant parameters for the chemical reactions. The method is illustrated by application to several simple problems and, where possible, comparisons are made with exact solutions and those obtained by other techniques.

Radhakrishnan, Krishnan↗
NASA NTRS1994

Coagulation algorithms with size binning

The Smoluchowski equation describes the time evolution of an aerosol particle size distribution due to aggregation or coagulation. Any algorithm for computerized solution of this equation requires a scheme for describing the continuum of aerosol particle sizes as a discrete set. One standard form of the Smoluchowski equation accomplishes this by restricting the particle sizes to integer multiples of a basic unit particle size (the monomer size). This can be inefficient when particle concentrations over a large range of particle sizes must be calculated. Two algorithms employing a geometric size binning convention are examined: the first assumes that the aerosol particle concentration as a function of size can be considered constant within each size bin; the second approximates the concentration as a linear function of particle size within each size bin. The output of each algorithm is compared to an analytical solution in a special case of the Smoluchowski equation for which an exact solution is known . The range of parameters more appropriate for each algorithm is examined.

Statton, David M.↗
NASA NTRS1994

A grid generation and flow solution method for the Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS1959

Evaluation of Several Approximate Methods for Calculating the Symmetrical Bending-Moment Response of Flexible Airplanes to Isotropic Atmospheric Turbulence

Several approximate procedures for calculating the bending-moment response of flexible airplanes to continuous isotropic turbulence are presented and evaluated. The modal methods (the mode-displacement and force-summation methods) and a matrix method (segmented-wing method) are considered. These approximate procedures are applied to a simplified airplane for which an exact solution to the equation of motion can be obtained. The simplified airplane consists of a uniform beam with a concentrated fuselage mass at the center. Airplane motions are limited to vertical rigid-body translation and symmetrical wing bending deflections. Output power spectra of wing bending moments based on the exact transfer-function solutions are used as a basis for the evaluation of the approximate methods. It is shown that the force-summation and the matrix methods give satisfactory accuracy and that the mode-displacement method gives unsatisfactory accuracy.

Bennett, Floyd V.↗
NASA NTRS1993

An accuracy assessment of Cartesian-mesh approaches for the Euler equations

A critical assessment of the accuracy of Cartesian-mesh approaches for solving the Euler equations is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of error of the Cartesian mesh approaches, but also to compare the magnitude of the error directly to that obtained with a structured mesh approach. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies. Adaptive and uniform mesh refinement is evaluated for Ringleb's flow and the supersonic flow through an axisymmetric inlet.

Coirier, William J.↗
NASA NTRS1967

Theoretical Study of Natural Convection Flows in Closed-End Cylindrical Vessels Final Report

This study is concerned with the analytical solutions of natural convection flows in closed-end cylindrical vessels to obtain exact solutions of temperature and velocity distribution in the laminar flow region under steady state condition. The temperature and velocity distributions, in general power series of displacements, are substituted into the three basic equations of continuity, momentum and energy. The relationships between coefficients of all powers are obtained through initial and boundary conditions and recurrence formulae. For constant wall temperature conditions the general solution of temperature and velocity may be expressed as a function of displacement, geometry ratio and Rayleigh number. Prandtl number does not enter as an independent parameter.

Convective flow↗