Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Residual distribution”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Mazaheri, Alireza↗
NASA NTRS2016

High-Order Residual-Distribution Schemes for Discontinuous Problems on Irregular Triangular Grids

In this paper, we develop second- and third-order non-oscillatory shock-capturing hyperbolic residual distribution schemes for irregular triangular grids, extending our second- and third-order schemes to discontinuous problems. We present extended first-order N- and Rusanov-scheme formulations for hyperbolic advection-diffusion system, and demonstrate that the hyperbolic diffusion term does not affect the solution of inviscid problems for vanishingly small viscous coefficient. We then propose second- and third-order blended hyperbolic residual-distribution schemes with the extended first-order Rusanov-scheme. We show that these proposed schemes are extremely accurate in predicting non-oscillatory solutions for discontinuous problems. We also propose a characteristics-based nonlinear wave sensor for accurately detecting shocks, compression, and expansion regions. Using this proposed sensor, we demonstrate that the developed hyperbolic blended schemes do not produce entropy-violating solutions (unphysical stocks). We then verify the design order of accuracy of these blended schemes on irregular triangular grids.

Mazaheri, Alireza↗
NASA NTRS2014

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

Mazaheri, Alireza R.↗
NASA NTRS2000

Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

Barth, Timothy↗
NASA NTRS1991

Distributed Minimal Residual (DMR) method for acceleration of iterative algorithms

A new method for enhancing the convergence rate of iterative algorithms for the numerical integration of systems of partial differential equations was developed. It is termed the Distributed Minimal Residual (DMR) method and it is based on general Krylov subspace methods. The DMR method differs from the Krylov subspace methods by the fact that the iterative acceleration factors are different from equation to equation in the system. At the same time, the DMR method can be viewed as an incomplete Newton iteration method. The DMR method was applied to Euler equations of gas dynamics and incompressible Navier-Stokes equations. All numerical test cases were obtained using either explicit four stage Runge-Kutta or Euler implicit time integration. The formulation for the DMR method is general in nature and can be applied to explicit and implicit iterative algorithms for arbitrary systems of partial differential equations.

Lee, Seungsoo↗
NASA NTRS1990

Numerical experiments in geomagnetic modeling

Numerical tests were made, using least squares fitting of a spherical harmonic model, to a selection of Magsat data to determine the practical limits of this technique with modern computers. The resulting (M102189) model, whose coefficients were adjusted up to n = 50, was compared with M07AV6, a previous model which used least squares (on vector data) for coefficients up to n = 29, and Gauss-Legendre quadrature (on Z residuals) to adjust the coefficients up to n = 63. For the new least squares adjustment to n = 50 a condition number of 115 was obtained for the solution matrix, with a resulting precision of 11 significant figures. The M102189 model shows a lower and more Gaussian residual distribution than did M07AV6, though the Gaussian envelope fits to the residual distributions, even for the scalar field, gives "standard deviations' never lower than 6 nT, a factor of three higher than the estimated Magsat observational errors. Ionospheric currents are noted to have a significant effect on the coefficients of the internal potential functions.

Cain, Joseph C.↗
NASA NTRS1993

Hypervelocity impact study: The effect of impact angle on crater morphology

The Space Power Institute (SPI) of Auburn University has conducted preliminary tests on the effects of impact angle on crater morphology for hypervelocity impacts. Copper target plates were set at angles of 30 deg and 60 deg from the particle flight path. For the 30 deg impact, the craters looked almost identical to earlier normal incidence impacts. The only difference found was in the apparent distribution of particle residue within the crater, and further research is needed to verify this. The 60 deg impacts showed marked differences in crater symmetry, crater lip shape, and particle residue distribution. Further research on angle effects is planned, because the particle velocities for these shots were relatively slow (7 km/s or less).

Crawford, Gary↗
NASA NTRS1990

Charge exchange of low-energy ions in thin carbon foils

In order to calibrate a time-of-flight mass spectrometer which is to be flown in the solar wind, the charge exchange properties of low-energy ions in thin carbon foils have been investigated. Incident ions of He, C, N, O, Ne, and Ar with energies in the range 0.5-2 keV/nucleon have been used to measure charge-state distribution, residual energy, and angular distribution after transmission through thin (1-6 microgram/sq cm) carbon foils. Within such foils, an equilibrium between ionization and recombination of the projectile is rapidly established, and, consequently, the charge state of the emerging particle depends essentially on its residual velocity. A comparison of the charge exchange properties of Ne-22 with Ne-20 demonstrates that indeed the velocity (and not the energy) of the emerging particle determines its final charge. A comparison of properties of different elements provides an indication of an electron shell effect. Predictions for the energy loss of ions within the carbon foils made with the TRIM code are in good agreement with the experimental results presented in this paper.

Buergi, Alfred↗
NASA NTRS2014

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

Mazaheri, Alireza↗
NASA NTRS2015

Multiscale and Multiphysics Modeling of Additive Manufacturing of Advanced Materials

The objective of this proposed project is to research and develop a prediction tool for advanced additive manufacturing (AAM) processes for advanced materials and develop experimental methods to provide fundamental properties and establish validation data. Aircraft structures and engines demand materials that are stronger, useable at much higher temperatures, provide less acoustic transmission, and enable more aeroelastic tailoring than those currently used. Significant improvements in properties can only be achieved by processing the materials under nonequilibrium conditions, such as AAM processes. AAM processes encompass a class of processes that use a focused heat source to create a melt pool on a substrate. Examples include Electron Beam Freeform Fabrication and Direct Metal Deposition. These types of additive processes enable fabrication of parts directly from CAD drawings. To achieve the desired material properties and geometries of the final structure, assessing the impact of process parameters and predicting optimized conditions with numerical modeling as an effective prediction tool is necessary. The targets for the processing are multiple and at different spatial scales, and the physical phenomena associated occur in multiphysics and multiscale. In this project, the research work has been developed to model AAM processes in a multiscale and multiphysics approach. A macroscale model was developed to investigate the residual stresses and distortion in AAM processes. A sequentially coupled, thermomechanical, finite element model was developed and validated experimentally. The results showed the temperature distribution, residual stress, and deformation within the formed deposits and substrates. A mesoscale model was developed to include heat transfer, phase change with mushy zone, incompressible free surface flow, solute redistribution, and surface tension. Because of excessive computing time needed, a parallel computing approach was also tested. In addition, after investigating various methods, a Smoothed Particle Hydrodynamics Model (SPH Model) was developed to model wire feeding process. Its computational efficiency and simple architecture makes it more robust and flexible than other models. More research on material properties may be needed to realistically model the AAM processes. A microscale model was developed to investigate heterogeneous nucleation, dendritic grain growth, epitaxial growth of columnar grains, columnar-to-equiaxed transition, grain transport in melt, and other properties. The orientations of the columnar grains were almost perpendicular to the laser motion's direction. Compared to the similar studies in the literature, the multiple grain morphology modeling result is in the same order of magnitude as optical morphologies in the experiment. Experimental work was conducted to validate different models. An infrared camera was incorporated as a process monitoring and validating tool to identify the solidus and mushy zones during deposition. The images were successfully processed to identify these regions. This research project has investigated multiscale and multiphysics of the complex AAM processes thus leading to advanced understanding of these processes. The project has also developed several modeling tools and experimental validation tools that will be very critical in the future of AAM process qualification and certification.

Liou, Frank↗
NASA NTRS1982

Residual stress in high modulus carbon fibers

The modulus and residual strain in carbon fibers are measured by successively electrochemically milling away the fiber surface. Electrochemical etching is found to remove the carbon fiber surface very uniformly, in contrast to air and wet oxidation. The precision of fiber diameter measurements is improved by using a laser diffraction technique instead of optical methods. More precise diameter measurements reveal that past correlations of diameter and fiber modulus are largely measurement artifact. The moduli of most carbon fibers decrease after the outer layers of the fibers are removed. Owing to experimental difficulties, the moduli and strengths of the fibers at their centers are not determined, and moduli are estimated on the basis of microstructure. The calculated residual stresses are found to be insensitive to these moduli estimates as well as the exact form of regression equation used to describe the moduli and residual strain distributions. Axial compressive residual stresses are found to be very high for some higher modulus carbon fibers. It is pointed out that the compressive stress makes the fibers insensitive to surface flaws when loaded in tension but it may initiate failure by buckling when loaded in compression.

Chen, K. J.↗
NASA NTRS2015

Characterization of Residual Stress Effects on Fatigue Crack Growth of a Friction Stir Welded Aluminum Alloy

An on-line compliance-based method to account for residual stress effects in stress-intensity factor and fatigue crack growth property determinations has been evaluated. Residual stress intensity factor results determined from specimens containing friction stir weld induced residual stresses are presented, and the on-line method results were found to be in excellent agreement with residual stress-intensity factor data obtained using the cut compliance method. Variable stress-intensity factor tests were designed to demonstrate that a simple superposition model, summing the applied stress-intensity factor with the residual stress-intensity factor, can be used to determine the total crack-tip stress-intensity factor. Finite element, VCCT (virtual crack closure technique), and J-integral analysis methods have been used to characterize weld-induced residual stress using thermal expansion/contraction in the form of an equivalent delta T (change in local temperature during welding) to simulate the welding process. This equivalent delta T was established and applied to analyze different specimen configurations to predict residual stress distributions and associated residual stress-intensity factor values. The predictions were found to agree well with experimental results obtained using the crack- and cut-compliance methods.

Newman, John A.↗
NASA NTRS1990

Residual circulations calculated from satellite data: Their relations to observed temperature and ozone distributions

Monthly mean residual circulations were calculated from eight years of satellite data. The diabatic circulation is usually found to give a good approximation to the residual circulation, but this is not always the case. In particular, an example is shown at 60 deg S and 30 mbar where the diabatic and residual circulations show very different annual variations. Correlations between the vertical component of the residual circulation and temperature and ozone were computed. The computations indicate that yearly variations of temperatures in the tropics are under radiative control, except during stratospheric warmings. Interannual variations in seasonal mean temperatures are shown to be under dynamical control everywhere. Correlations between seasonal means of the vertical component of the residual circulation and ozone mixing ratios are consistent with what would be expected from the ozone variations being due to differences in the ozone transport, although transport effects cannot easily be distinguished from photochemical effects above the altitude of the ozone mixing ratio peak. Finally, variations in total ozone are examined in comparison with residual circulation variations. A one to two month phase lag is seen in the annual variation in the total ozone at 60 deg N with respect to the maximum downward residual motions. This phase lag is greater at 60 deg N than at 60 deg S. There is evidence at 60 deg S of a greater downward trend in the mean zonal ozone maxima than there is in the minima. A decreasing trend in the maximum descending motion is seen to accompany the ozone trend at 60 deg S.

Geller, Marvin A.↗
NASA NTRS1992

Residual circulations calculated from satellite data - Their relations to observed temperature and ozone distributions

Monthly mean residual circulations were calculated from eight years of satellite data. The diabatic circulation is usually found to give a good approximation to the residual circulation, but this is not always the case. In particular, an example is shown at 60 deg S and 30 mbar where the diabatic and residual circulations show very different annual variations. Correlations between the vertical component of the residual circulation and temperature and ozone were computed. The computations indicate that yearly variations of temperatures in the tropics are under radiative control, except during stratospheric warmings. Interannual variations in seasonal mean temperatures are shown to be under dynamical control everywhere. Correlations between seasonal means of the vertical component of the residual circulation and ozone mixing ratios are consistent with what would be expected from the ozone variations being due to differences in the ozone transport, although transport effects cannot easily be distinguished from photochemical effects above the altitude of the ozone mixing ratio peak. Finally, variations in total ozone are examined in comparison with residual circulation variations. A one to two month phase lag is seen in the annual variation in the total ozone at 60 deg N with respect to the maximum downward residual motions. This phase lag is greater at 60 deg N than at 60 deg S. There is evidence at 60 deg S of a greater downward trend in the mean zonal ozone maxima than there is in the minima. A decreasing trend in the maximum descending motion is seen to accompany the ozone trend at 60 deg S.

Geller, Marvin A.↗
NASA NTRS1977

Residual stresses in boron/tungsten and boron/carbon fibers

Longitudinal residual stress distribution is determined for 102-micron diam B/W and B/C fibers. The 102-micron diam B/W fibers are deposited on a 12.7-micron diam tungsten wire resistively heated in a BCl3-H2 reactor. The 102-micron diam B/C fibers are made by deposition of boron on a pyrolytic graphite-coated carbon fiber. The longitudinal residual stress distribution is calculated from measurements of the change in length of the fiber produced by removal of the surface through electropolishing. It is found that for both types of fibers, the residual stress vary from a compressive stress at the surface to a tensile stress in the boron near the core. Closer to the core and in the core, significant differences in the residual stresses are observed for the B/W and B/C fibers.

Behrendt, D. R.↗
NASA NTRS1976

Longitudinal residual stresses in boron fibers

A technique is proposed for measuring the longitudinal residual stress distribution in commercial CVD (Chemical Vapor Deposition) boron on tungsten fibers of 102, 142, and 203 microns in diameter. The experimental apparatus is so designed that continuous measurements are made of the length changes of a boron fiber specimen as the surface of the fiber is removed by electropolishing. The effects of surface removal on core residual stress and core-initiated fracture are discussed. The three sizes of boron fibers investigated show similar residual stress distributions, i.e., compressive at the surface, tensile near the core, and for the 102-micron fiber compressive again in the core. It is shown that an increase in UTS is due to the increase in the compressive stress at the core produced by fiber contraction during surface removal. An expression is derived for calculating the longitudinal residual stress at a given radius for an as-received fiber of a certain radius from measurements of the axial strain produced by removal of the surface by electropolishing.

Behrendt, D. R.↗