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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 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

A finite element computational method for high Reynolds number laminar flows

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.

Kim, Sang-Wook↗
NASA NTRS1984

Spectral methods for exterior elliptic problems

Spectral approximations for exterior elliptic problems in two dimensions are discussed. As in the conventional finite difference or finite element methods, the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions. A spectral boundary treatment is introduced at infinity which is compatible with the infinite order interior spectral scheme. Computational results are presented to demonstrate the spectral accuracy attainable. Although a simple Laplace problem is examined, the analysis covers more complex and general cases.

Canuto, C.↗
NASA NTRS1988

The calculation of flow over iced airfoils

Progress toward the development of a method for predicting the flowfield of an iced airfoil is described and shown to offer the prospect of a priori calculations of the effects of ice accretion and roughness on airfoil performance. The approach is based on interaction of inviscid flow solutions obtained by a panel method and improved upon by a finite-difference boundary-layer method which, operating in an inverse mode, incorporates viscous effects including those associated with separated flows. Results are presented for smooth, rough and iced airfoils as a function of angle of attack. Those for smooth and rough airfoils confirm the accuracy of the method and its applicability to surfaces with roughness similar to that associated with insect deposition and some forms of ice. Two procedures have been developed to deal with large ice accretion and their performance is examined and shown to be appropriate to the engineering requirements.

Cebeci, Tuncer↗
NASA NTRS1999

Comparison of AGE and Spectral Methods for the Simulation of Far-Wakes

Turbulent flow simulation methods based on finite differences are attractive for their simplicity, flexibility and efficiency, but not always for accuracy or stability. This report demonstrates that a good compromise is possible with the Advected Grid Explicit (AGE) method. AGE has proven to be both efficient and accurate for simulating turbulent free-shear flows, including planar mixing layers and planar jets. Its efficiency results from its localized fully explicit finite difference formulation (Bisset 1998a,b) that is very straightforward to compute, outweighing the need for a fairly small timestep. Also, most of the successful simulations were slightly under-resolved, and therefore they were, in effect, large-eddy simulations (LES) without a sub-grid-scale (SGS) model, rather than direct numerical simulations (DNS). The principle is that the role of the smallest scales of turbulent motion (when the Reynolds number is not too low) is to dissipate turbulent energy, and therefore they do not have to be simulated when the numerical method is inherently dissipative at its resolution limits. Such simulations are termed 'auto-LES' (LES with automatic SGS modeling) in this report.

Bisset, D. K.↗
NASA NTRS1972

Analysis of the transient response of shell structures by numerical methods.

This paper examines some basic considerations underlying dynamic shell response analysis and the impact of these considerations upon the practical aspects of solution by numerical methods. Emphasis is placed on the solution of linear problems. The present states of development of the finite difference and finite element methods are reviewed, and techniques for the treatment of temporal variation are discussed. An examination is made of the frequency parameters characteristic of thin shell theory, applied excitations, and spatial mesh geometries, and the significance of these parameters with respect to computational convergence is illustrated.

Geers, T. L.↗
NASA NTRS1982

Finite analytic numerical solution of axisymmetric Navier-Stokes and energy equations

Convective heat transfer for steady state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature and heat transfer coefficients for flow with Reynolds number of 5.0, 100.0, 1000.0, and 2000.0, and Prandtl number of 0.1, 1.0, and 10.0 with uniform grid sizes are reported for axisymmetric pipe with sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic solution is stable, converges rapidly, and simulates the convection of fluid flow accurately since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values thereby minimizing the false numerical diffusion.

Chen, C.-J.↗
NASA NTRS1973

Numerical marching techniques for fluid flows with heat transfer

The finite difference formulation and method of solution is presented for a wide variety of fluid flow problems with associated heat transfer. Only a few direct results from these formulations are given as examples, since the book is intended primarily to serve a discussion of the techniques and as a starting point for further investigations; however, the formulations are sufficiently complete that a workable computer program may be written from them. In the appendixes a number of topics are discussed which are of interest with respect to the finite difference equations presented. These include a very rapid method for solving certain sets of linear algebraic equations, a discussion of numerical stability, the inherent error in flow rate for confined flow problems, and a method for obtaining high accuracy with a relatively small number of mesh points.

Hornbeck, R. W.↗
NASA NTRS1981

Calculation of sensitivity derivatives in thermal problems by finite differences

The optimum design of a structure subject to temperature constraints is considered. When mathematical optimization techniques are used, derivatives of the temperature constraints with respect to the design variables are usually required. In the case of large aerospace structures, such as the Space Shuttle, the computation of these derivatives can become prohibitively expensive. Analytical methods and a finite difference approach have been considered in studies conducted to improve the efficiency of the calculation of the derivatives. The present investigation explores two possibilities for enhancing the effectiveness of the finite difference approach. One procedure involves the simultaneous solution of temperatures and derivatives. The second procedure makes use of the optimum selection of the magnitude of the perturbations of the design variables to achieve maximum accuracy.

Haftka, R. T.↗
NASA NTRS1986

Preconditioned conjugate residual methods for the solution of spectral equations

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Wong, Y. S.↗
DOE OSTI2025

A transient near to far field transformation method and verification benchmarking procedure

The numerical calculation of electromagnetic far fields in the time-domain requires a near to far field transformation (NTFF) method. While time-domain NTFF methods for popular finite-difference time-domain (FDTD) approaches are well established, there is little discourse on NTFF methods for finite-element time-domain (FETD) codes. Here, this work is concerned with the development of an NTFF method for the Empire FETD code, which utilizes curl and divergence conforming elements. This discretization presents a difficulty in obtaining the equivalent electric current for the NTFF. Straightforward finite element interpolation of the fields is shown to give poor accuracy. Alternative interpolation methods are recommended. An expanding magnetic quadrupole pulse benchmark problem, which is fully developed in the appendices, provides the basis for quantitative comparison.

FETD↗
NASA NTRS1976

Numerical solution of nonlinear partial differential equations of mixed type

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Jameson, A.↗
NASA NTRS1996

Numerical Study of Multigrid Methods with Various Smoothers for the Elliptical Grid Generation Equations

A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with finite differences, and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and efficiency. Different smoothers are tried to improve the convergence of iterations. The methods are applied to four 2D grid generation problems over a wide range of grid distortions. The results of the study help to select smoothing schemes and the overall multigrid procedures for elliptic grid generation.

Golik, W. L.↗
NASA NTRS1989

Understanding transition and turbulence through direct simulations

Direct simulations consist in solving the full Navier-Stokes equations, without any turbulence model, and describing all the detailed features of the flow. Usually the flows are three-dimensional and time-dependent and contain both coarse and fine structures, which makes the numerical task very challenging in terms of both the algorithm and the computational effort. Most of the work until now has involved spectral methods, which are highly accurate but not very flexible in terms of geometry or complex equations. For that reason, future work will also rely on high-order finite-difference or other methods. Direct simulations complement experimental work, and both contribute to the theory and the empirical knowledge of turbulence. Once such a simulation has been shown to be accurate, the flow field is completely known in three dimensions and time, including the pressure, the vorticity and any other quantity. On the other hand, most simulations to date solved the incompressible equations in rather simple geometries, and direct simulations will always be limited to moderate Reynolds numbers. Extensive simulations have been conducted in homogeneous turbulence, channel flows, boundary layers, and mixing layers. Much effort is devoted to addressing flows with compressibility and chemical reactions, and to new geometries such as a backward-facing step.

Spalart, P. R.↗
NASA NTRS2000

Onset of Convection Due to Surface Tension Variations in Multicomponent and Binary Fluid Layers

Under certain conditions, such as in thin liquid films or microgravity, surface tension variations along a free surface can induce convection. Convection onset due to surface tension variation is important to many terrestrial technological processes in addition to microgravity materials processing applications. Examples include coating, drying crystallization, solidification, liquid surface contamination, and containerless processing. In double-diffusive and multicomponent systems, the spatial variations of surface tension are associated with two or more stratifying agencies, respectively. For example, both temperature and species (concentration) gradients are associated with convection in the solidification of binary alloys or salt ponds. The direction of the two (or more) gradients has a profound effect on the nature of the flow at or slightly beyond the onset of convection. Our recent work at the NASA Lewis Research Center focused on characterizing surface-tension-induced onset of convection, often referred to as Marangoni-Benard convection. Exact solutions for the stationary neutral stability of multicomponent fluid layers with interfacial deformation were derived. These solutions also permit the computation of a boundary curve that separates the long and finite wavelength instabilities. Computing points along this boundary using the exact solution (when possible) is more efficient than the typical numerical approaches, such as finite difference or spectral methods. Above the curve, a long wavelength instability was predicted, suggesting that convection would occur principally through one large flow cell in the layer, whereas below the curve, finite wavelength instabilities occur which suggest multiple finite-sized circulation cells. For many common liquids with layer depths greater than 100 mm, finite wave instability is predicted under terrestrial conditions; however, with little exception, long wavelength instability is predicted in microgravity for the identical fluid systems.

Skarda, J. Raymond Lee↗
NASA NTRS1994

The least-squares finite element method for low-mach-number compressible viscous flows

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

Yu, Sheng-Tao↗
NASA NTRSDate not supplied

Realistic Thermographic Simulation of Impact Damage with Quadrupole Method

Flash thermography has been shown to be an effective method for detection of delaminations in carbon fiber reinforced polymer (CFRP) composite structures. Improved understanding of the limitations of the technique can be obtained by simulating the inspection process. Time domain finite difference and finite element methods are well suited for such simulations but can be computationally intensive. An alternate method is to solve the Laplace transform of the heat equation, then invert the Laplace transform to produce a time domain response. Often this is referred to as the thermal quadrupole method and is well suited for simulating flash thermography. The quadrupole method has been used extensively for simulating one-dimensional heat flow in multilayer systems with contact resistances at the interfaces. It is also applicable for three dimensional configurations, in particular for simulation of changes in thermographic response due to delaminations in composites. This presentation discusses three-dimensional simulations with realistic shapes and contact resistances at the interfaces between layers. The results of these simulations are compared to thermography measurements on composites specimens with impact induced delaminations.

thermography↗
NASA NTRSDate not supplied

Realistic Thermographic Simulation of Impact Damage with Quadrupole Method

Flash thermography has been shown to be an effective method for detection of delaminations in carbon fiber reinforced polymer (CFRP) composite structures. Improved understanding of thelimitations of the technique can be obtained by simulating the inspection process. Time domainfinite difference and finite element methods are well suited for such simulations but can be computationally intensive. An alternate method is to solve the Laplace transform of the heat equation, then invert the Laplace transform to produce a time domain response. Often this is referred to as the thermal quadrupole method and is well suited for simulating flash thermography. The quadrupole method has been used extensively for simulating one-dimensional heat flow in multilayer systems with contact resistances at the interfaces. It is also applicable for three dimensional configurations, in particular for simulation of changes in thermographic response due to delaminations in composites. This presentation discusses three-dimensional simulations with realistic shapes and contact resistances at the interfaces between layers. The results of these simulations are compared to thermography measurements on composites specimens with impact induced delaminations.

Thermography↗