Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Numerical differentiation”

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 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Two-demensional analysis of heat and mass transfer in porous media using the strongly implicit procedure

Numerical results of the heat and mass transfer in a porous matrix are presented. The coupled, nonlinear partial differential equations describing this physical phenomenon are solved in finite difference form for two dimensions, using a new iterative technique (the strongly implicit procedure). The influence of the external environment conditions (heating and pressure) is shown to produce two-dimensional flow in the porous matrix. Typical fluid and solid temperature distributions in the porous matrix and internal pressure distributions are presented.

Curry, D. M.↗
NASA NTRS1977

Variants and extensions of a fast direct numerical cauchy-riemann solver, with illustrative applications

Revised and extended versions of a fast, direct (noniterative) numerical Cauchy-Riemann solver are presented for solving finite difference approximations of first order systems of partial differential equations. Although the difference operators treated are linear and elliptic, one significant application of these extended direct Cauchy-Riemann solvers is in the fast, semidirect (iterative) solution of fluid dynamic problems governed by the nonlinear mixed elliptic-hyperbolic equations of transonic flow. Different versions of the algorithms are derived and the corresponding FORTRAN computer programs for a simple example problem are described and listed. The algorithms are demonstrated to be efficient and accurate.

Martin, E. D.↗
NASA NTRS1986

Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.

Pratt, D. T.↗
NASA NTRS1988

Evolution of inclined galactic gas disks. I - A cloud-fluid approach

In this paper, numerical models are developed to follow the time-dependent behavior of inclined gas disks in nonspherical galaxies. Differential equations are developed which describe the time rate of change of the orbits of mass elements composing a thin, smoothly warping and twisting gas disk. These equations include multiple moments due to the nonsphericity of the galactic mass distribution, Coriolis effects arising from determination of orbits in a reference frame which tumbles with the surface figure of the galaxy, and viscous forces arising from cloud-cloud collisions. A cloud-fluid approach is used in determining the viscous forces. Physical arguments are used to determine the maximum permissible local value of the coefficient of kinematic viscosity. For small initial inclinations, analytic expressions are obtained for the inclination as a function of time and for the settling time, and the features of the solution are discussed.

Steiman-Cameron, Thomas Y.↗
NASA NTRS1993

Conservative high-order-accurate finite-difference methods for curvilinear grids

Two fourth-order-accurate finite-difference methods for numerically solving hyperbolic systems of conservation equations on smooth curvilinear grids are presented. The first method uses the differential form of the conservation equations; the second method uses the integral form of the conservation equations. Modifications to these schemes, which are required near boundaries to maintain overall high-order accuracy, are discussed. An analysis that demonstrates the stability of the modified schemes is also provided. Modifications to one of the schemes to make it total variation diminishing (TVD) are also discussed. Results that demonstrate the high-order accuracy of both schemes are included in the paper. In particular, a Ringleb-flow computation demonstrates the high-order accuracy and the stability of the boundary and near-boundary procedures. A second computation of supersonic flow over a cylinder demonstrates the shock-capturing capability of the TVD methodology. An important contribution of this paper is the dear demonstration that higher order accuracy leads to increased computational efficiency.

Rai, Man M.↗
NASA NTRS1995

Transport phenomena in the micropores of plug-type phase separators

This study numerically investigates the transport phenomena within and across a porous-plug phase separator. The effect of temperature differential across a single pore and of the sidewall boundary conditions, i.e., isothermal or linear thermal gradient, are presented and discussed. The effects are quantified in terms of the evaporation mass flux across the boundary and the mean surface temperature. A two-dimensional finite element model is used to solve the continuity, momentum, and energy equations for the liquid. Temperature differentials across the pore interface of 1.0, and 1.5 K are examined and their effect on evaporation flux and mean surface temperature is shown. For isothermal side boundary conditions, the evaporation flux across the pore is directly proportional and linear with Delta T. For the case of an imposed linear thermal gradient on the side boundaries, Biot numbers of 0.0, 0.15, and 0.5 are examined. The most significant effect of Biot number is to lower the overall surface temperature and evaporation flux.

Fazah, M. M.↗
NASA NTRS1996

Time-Dependent Thermally-Driven Interfacial Flows in Multilayered Fluid Structures

A computational study of thermally-driven convection in multilayered fluid structures will be performed to examine the effect of interactions among deformable fluid-fluid interfaces on the structure of time-dependent flow in these systems. Multilayered fluid structures in two models configurations will be considered: the differentially heated rectangular cavity with a free surface, and the encapsulated cylindrical liquid bridge. An extension of a numerical method developed as part of our recent NASA Fluid Physics grant will be used to account for finite deformations of fluid-fluid interfaces.

Haj-Hariri, Hossein↗
NASA NTRS1997

Chemical and Thermal Analysis

Work during the past three years has included significant research in several areas aimed at further clarification of the aging and chemical failure mechanism of thermoplastics (PVDF or Tefzel) for pipes. Among the areas investigated were the crystallinity changes associated with both the Coflon and Tefzel after various simulated environmental exposures using X-Ray diffraction analysis. We have found that significant changes in polymer crystallinity levels occur as a function of the exposures. These crystallinity changes may have important consequences on the fracture, fatigue, tensile, and chemical resistance of the materials. We have also noted changes in the molecular weight distribution and the increased crosslinking of the Coflon material using Gel Permeation Chromatographic Analysis. Again these changes may result in variations in the mechanical and chemical properties in the material. We conducted numerous analytical studies with methods including X-ray Diffraction, Gel Permeation Chromatography, Fourier Transform Infrared Spectroscopy, and Differential Scanning Calorimetry. We investigated a plethora of aged samples of both Tefzel and Coflon that were forwarded from MERL. Pressurized tests were performed on powdered PVDF in a modified Fluid A, which we will call A-2. In this case the ethylene diamine concentration was increased to 3 percent in methanol. Coflon pipe sections and powdered Coflon were exposed in pressure cells at 1700 psi at three separate test temperatures.

Bulluck, J. W.↗
NASA NTRS1998

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Resonant-Triad Interaction

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented using the generalized scaling of Lee. It is shown that resonant-triads can interact nonlinearly within the common critical layer when their (fundamental) Strouhal numbers are different by a factor whose magnitude is of the order of the growth rate multiplied by the wavenumber of the instability wave. Since the growth rates of the instability modes become larger and the critical layers become thicker as the instability waves propagate downstream, the frequency-detuned resonant-triads that grow independently of each other in the upstream region can interact nonlinearly in the later downstream stage. In the final stage of the non-equilibrium critical-layer evolution, a wide range of instability waves with the scaled frequencies differing by almost an Order of (l) can nonlinearly interact. Low-frequency modes are also generated by the nonlinear interaction between oblique waves in the critical layer. The system of partial differential critical-layer equations along with the jump equations are presented here. The amplitude equations with their numerical solutions are given in Part 2. The nonlinearly generated low-frequency components are also investigated in Part 2.

Lee, Sang Soo↗
NASA NTRS2006

Heat Transfer of Thermocapillary Convection in a Two-Layered Fluid System Under the Influence of Magnetic Field

Heat transfer of a two-layer fluid system has been of great importance in a variety of industrial applications. For example, the phenomena of immiscible fluids can be found in materials processing and heat exchangers. Typically in solidification from a melt, the convective motion is the dominant factor that affects the uniformity of material properties. In the layered flow, thermocapillary forces can come into an important play, which was first emphasized by a previous investigator in 1958. Under extraterrestrial environments without gravity, thermocapillary effects can be a more dominant factor, which alters material properties in processing. Control and optimization of heat transfer in an immiscible fluid system need complete understanding of the flow phenomena that can be induced by surface tension at a fluid interface. The present work is focused on understanding of the magnetic field effects on thermocapillary convection, in order to optimize material processing. That is, it involves the study of the complicated phenomena to alter the flow motion in crystal growth. In this effort, the Marangoni convection in a cavity with differentially heated sidewalls is investigated with and without the influence of a magnetic field. As a first step, numerical analyses are performed, by thoroughly investigating influences of all pertinent physical parameters. Experiments are then conducted, with preliminary results, for comparison with the numerical analyses.

Ramachandran, N.↗
NASA NTRS2010

Station Keeping of Small Outboard-Powered Boats

Three station keeping controllers have been developed which work to minimize displacement of a small outboard-powered vessel from a desired location. Each of these three controllers has a common initial layer that uses fixed-gain feedback control to calculate the desired heading of the vessel. A second control layer uses a common fixed-gain feedback controller to calculate the net forward thrust, one of two algorithms for controlling engine angle (Fixed-Gain Proportional-integral-derivative (PID) or PID with Adaptively Augmented Gains), and one of two algorithms for differential throttle control (Fixed-Gain PID and PID with Adaptive Differential Throttle gains), which work together to eliminate heading error. The three selected controllers are evaluated using a numerical simulation of a 33-foot center console vessel with twin outboards that is subject to wave, wind, and current disturbances. Each controller is tested for its ability to maintain position in the presence of three sets of environmental disturbances. These algorithms were tested with current velocity of 1.5 m/s, significant wave height of 0.5 m, and wind speeds of 2, 5, and 10 m/s. These values were chosen to model conditions a small vessel may experience in the Gulf Stream off of Fort Lauderdale. The Fixed-gain PID controller progressively got worse as wind speeds increased, while the controllers using adaptive methodologies showed consistent performance over all weather conditions and decreased heading error by as much as 20%. Thus, enhanced robustness to environmental changes has been gained by using an adaptive algorithm.

Fisher, A. D.↗
NASA NTRS2016

NASAs VESGEN: Systems Analysis of Vascular Phenotypes from Stress and Other Signaling Pathways Using GeneLab.

One fundamental requirement shared by humans with all higher terrestrial life forms, including insect wings, higher land plants and other vertebrates, is a complex, fractally branching vascular system. NASA's VESsel GENeration Analysis (VESGEN) software maps and quantifies vascular trees, networks, and tree-network composites according to weighted physiological rules such as vessel connectivity, tapering and bifurcational branching. According to fluid dynamics, successful vascular transport requires a complex distributed system of highly regulated laminar flow. Microvascular branching rules within vertebrates, dicot leaves and the other organisms therefore display many similarities. One unifying perspective is that vascular patterning offers a useful readout that necessarily integrates complex molecular signaling pathways. VESGEN has elucidated changes in vascular pattern resulting from inflammatory, stress response, developmental and other signaling within numerous tissues and major model organisms studied for Space Biology. For a new VESGEN systems approach, we analyzed differential gene expression in leaves of Arabidopsis thaliana reported by GeneLab (GLDS-7) for spaceflight. Vascular-related changes in leaf gene expression were identified that can potentially be phenocopied by mutants in ground-based experiments. To link transcriptional, protein and other molecular change with phenotype, alterations in the Euclidean and dynamic dimensions (x,y,t) of vascular patterns for Arabidopsis leaves and other model species are being co-localized with signaling patterns of single molecular expression analyzed as information dimensions (i,j,k,...). Previously, Drosophila microarray data returned from space suggested significant changes in genes related to wing venation development that include EGF, Notch, Hedghog, Wingless and Dpp signaling. Phenotypes of increasingly abnormal ectopic wing venation in the (non-spaceflight) Drosophila wing generated by overexpression of a Notch antagonist were analyzed by VESGEN. Other VESGEN research applications include the mouse retina, GI and coronary vessels, avian placental analogs and translational studies in the astronaut retina related to health challenges for long-duration missions.

Venation↗
NASA NTRS2016

Using NASA's GeneLab for VESGEN Systems Analysis of Vascular Phenotypes from Stress and Other Signaling Pathways

One fundamental requirement shared by humans with all higher terrestrial life forms, including other vertebrates, insects, and higher land plants, is a complex, fractally branching vascular system. NASA's VESsel GENeration Analysis (VESGEN) software maps and quantifies vascular trees, networks, and tree-network composites according to weighted physiological rules such as vessel connectivity, tapering and bifurcational branching. According to fluid dynamics, successful vascular transport requires a complex distributed system of highly regulated laminar flow. Microvascular branching rules within vertebrates, dicot leaves and the other organisms therefore display many similarities. A unifying perspective is that vascular patterning offers a useful readout of molecular signaling that necessarily integrates these complex pathways. VESGEN has elucidated changes in vascular pattern resulting from inflammatory, developmental and other signaling within numerous tissues and major model organisms studied for Space Biology. For a new VESGEN systems approach, we analyzed differential gene expression in leaves of Arabidopsis thaliana reported by GeneLab (GLDS-7) for spaceflight. Vascularrelated changes in leaf gene expression were identified that can potentially be phenocopied by mutants in ground-based experiments. To link transcriptional, protein and other molecular change with phenotype, alterations in the spatial and dynamic dimensions of vascular patterns for Arabidopsis leaves and other model species are being co-localized with signaling patterns of single molecular expression analyzed as information dimensions. Previously, Drosophila microarray data returned from space suggested significant changes in genes related to wing venation development that include EGF, Notch, Hedghog, Wingless and Dpp signaling. Phenotypes of increasingly abnormal ectopic wing venation in the (non-spaceflight) Drosophila wing generated by overexpression of a Notch antagonist were analyzed by VESGEN. Other VESGEN research applications include the mouse retina, GI and coronary vessels, avian placental analogs and translational studies in the astronaut retina related to health challenges for long-duration missions.

Venation↗
NASA NTRS1996

Further Development of a New, Flux-Conserving Newton Scheme for the Navier-Stokes Equations

This paper is one of a series of papers describing the development of a new numerical approach for solving the steady Navier-Stokes equations. The key features in the current development are (1) the discrete representation of the dependent variables by way of high order polynomial expansions, (2) the retention of all derivatives in the expansions as unknowns to be explicitly solved for, (3) the automatic balancing of fluxes at cell interfaces, and (4) the discrete simulation of both the integral and differential forms of the governing equations. The main purpose of this paper is, first, to provide a systematic and rigorous derivation of the conditions that are used to simulate the differential form of the Navier-Stokes equations, and second, to extend our previously-presented internal flow scheme to external flows and nonuniform grids. Numerical results are presented for high Reynolds number flow (Re = 100,000) around a finite flat plate, and detailed comparisons are made with the Blasius flat plate solution and Goldstein wake solution. It is shown that the error in the streamwise velocity decreases like r(sup alpha)(Delta)y(exp 2), where alpha approx. 0.25 and r = delta(y)/delta(x) is the grid aspect ratio.

Scott, James R.↗
NASA NTRS2018

Increasing the Statistical Rigor of Cross-Species Differential Expression Analysis

Microgravity inflicts substantial, but undercharacterized, pressure on organisms that induces metabolic responses such as increased microbial virulence and antibiotic resistance, altered organ weights in developing rats, and loss of bone tissue in astronauts. Numerous studies have analyzed the effects of microgravity on specific organisms, tissues, or test conditions, but these projects are necessarily limited by the small sample size of space research. Increasing the sample size of spaceflight studies is non-trivial; however, pooling data from numerous studies can greatly increase the statistical rigor of comparative analyses. The GeneLab houses datasets from 73 spaceflight studies that performed transcription profiling assays. These data encompass a diverse array of organisms ranging from Escherichia coli to Mus musculus to Homo sapiens and comprise studies analyzing ionizing radiation, mammalian pregnancy, etc. Collectively, the GeneLab database contains a large quantity of transcription assays and RNA sequence data analyzing Differential Gene Expression (DGE) between microand normogravity. Xspecies, a cross-species analysis method for DGE developed by Kristiansson, et al. in 2012, identifies homologous genes between species that are universally up- or downregulated in response to test conditions. Previous work by an intern at GeneLab applied Xspecies to 19 datasets containing seven different species and identified 14 homologous groups differentially expressed under spaceflight conditions including several heat shock proteins and cytoskeletal components. Unfortunately, these results may be biased by the disproportionate number of studies on Arabidopsis thaliana (5) and Mus musculus (6) and the results are not normalized by evolutionary distances. Here, we present modifications to the Xspecies algorithm that permits incorporation of multi-omic data and normalizes data for effect size, directionality, and evolutionary distances. We then apply this algorithm to all currently available GeneLab studies

Xspecies↗
NASA NTRS1991

The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices

Toeplitz matrices occur in many mathematical, as well as, scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations to partial differential equations. Quasi-Toeplitz matrices are the result of non-Dirichlet boundary conditions for the difference approximations. The eigenvalue problem for a banded Toeplitz or quasi-Toeplitz matrix of large order is, in general, analytically intractable and (for non-normal matrices) numerically unreliable. An asymptotic (matrix order approaches infinity) approach partitions the eigenvalue analysis of a quasi-Toeplitz matrix into two parts, namely the analysis for the boundary condition independent spectrum and the analysis for the boundary condition dependent spectrum. The boundary condition independent spectrum is the same as the pure Toeplitz matrix spectrum. Algorithms for computing both parts of the spectrum are presented. Examples are used to demonstrate the utility of the algorithms, to present some interesting spectra, and to point out some of the numerical difficulties encountered when conventional matrix eigenvalue routines are employed for non-normal matrices of large order. The analysis for the Toeplitz spectrum also leads to a diagonal similarity transformation that improves conventional numerical eigenvalue computations. Finally, the algorithm for the asymptotic spectrum is extended to the Toeplitz generalized eigenvalue problem which occurs, for example, in the stability of Pade type difference approximations to differential equations.

Beam, Richard M.↗
NASA NTRS1986

Optimization methods and silicon solar cell numerical models

An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.

Girardini, K.↗