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NASA NTRS1993

Incompressible spectral-element method: Derivation of equations

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

Deanna, Russell G.↗

NASA NTRS2001

A Highly Accurate Technique for the Treatment of Flow Equations at the Polar Axis in Cylindrical Coordinates using Series Expansions

Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius (1). Extension of the method described here for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical or spherical coordinates with finite-differences schemes of various level of accuracy is immediate.

Constantinescu, George S.↗

NASA NTRS1995

Wear Measurement System

Lewis Research Center developed a tribometer for in-house wear tests. Implant Sciences Corporation (ISC), working on a NASA contract to develop coatings to enhance the wear capabilities of materials, adapted the tribometer for its own use and developed a commercial line of user-friendly systems. The ISC-200 is a pin-on-disk type of tribometer, functioning like a record player and creating a wear groove on the disk, with variables of speed and load. The system can measure the coefficient of friction, the wear behavior between materials, and the integrity of thin films or coatings. Applications include measuring wear on contact lenses and engine parts and testing disk drives.

Source record↗

NASA NTRS2005

Friction Properties of Surface-Fluorinated Carbon Nanotubes

Surface modification of the tubular or sphere-shaped carbon nanoparticles through chemical treatment, e.g., fluorination, is expected to significantly affect their friction properties. In this study, a direct fluorination of the graphene-built tubular (single-walled carbon nanotubes) structures has been carried out to obtain a series of fluorinated nanotubes (fluoronanotubes) with variable C(n)F (n =2-20) stoichiometries. The friction coefficients for fluoronanotubes, as well as pristine and chemically cut nanotubes, were found to reach values as low as 0.002-0.07, according to evaluation tests run in contact with sapphire in air of about 40% relative humidity on a ball-on-disk tribometer which provided an unidirectional sliding friction motion. These preliminary results demonstrate ultra-low friction properties and show a promise in applications of surface modified nanocarbons as a solid lubricant.

Wal, R. L. Vander↗

NASA NTRS2021

Experimental Flight Validation of the Prandtl 1933 Bell Spanload

This report describes the validation of the 1933 Prandtl bell spanload. This spanload is the minimum induced drag of a wing for a given structural weight with properties that eliminate adverse yaw. Aircraft using the Prandtl bell spanload were flown and investigated. The results of this research show that many previously held assumptions should be rethought, and the creation of aircraft using the Prandtl bell spanload will require considerable new techniques. Part of this work centered on the use of inverse methods. The usual first-step approach to a computational fluids problem is to create a geometry of the aircraft. Once this geometry exists, the computational fluids solution has been solved; however, the problem of creating the geometry still exists. A very small segment of the computational fluids world has concentrated on inverse solutions. This design approach begins with an end result - the computational fluids solution; from this end result, the geometry is sought. A more generic inverse tool was desired that would allow for the design of wings - specifically Prandtl bell spanload wings. Such a tool has been developed and allows for variable taper, aspect ratio, sweep, airfoils, and design-lift coefficients; output from the tool results in twist distribution of wings.

Albion H. Bowers↗

NASA NTRS1988

Linear Least Squares for Correlated Data

Throughout the literature authors have consistently discussed the suspicion that regression results were less than satisfactory when the independent variables were correlated. Camm, Gulledge, and Womer, and Womer and Marcotte provide excellent applied examples of these concerns. Many authors have obtained partial solutions for this problem as discussed by Womer and Marcotte and Wonnacott and Wonnacott, which result in generalized least squares algorithms to solve restrictive cases. This paper presents a simple but relatively general multivariate method for obtaining linear least squares coefficients which are free of the statistical distortion created by correlated independent variables.

Dean, Edwin B.↗

NASA NTRS2020

Temporal and spatial variability in surface roughness and accumulation rate around 88° S from repeat airborne geophysical surveys

We use repeat high-resolution airborne geophysical data consisting of laser altimetry, snow, and Ku-band radar and optical imagery acquired in 2014, 2016, and 2017 to analyze the spatial and temporal variability in surface roughness, slope, wind deposition, and snow accumulation at 88° S, an elevation bias validation site for ICESat-2 and potential validation site for CryoSat-2. We find significant small-scale variability (<10 km) in snow accumulation based on the snow radar subsurface stratigraphy, indicating areas of strong wind redistribution are prevalent at 88° S. In general, highs in snow accumulation rate correspond with topographic lows, resulting in a negative correlation coefficient of r(exp 2)=−0.32 between accumulation rate and MSWD (mean slope in the mean wind direction). This relationship is strongest in areas where the dominant wind direction is parallel to the survey profile, which is expected as the geophysical surveys only capture a two-dimensional cross section of snow redistribution. Variability in snow accumulation appears to correlate with variability in MSWD. The correlation coefficient between the standard deviations of accumulation rate and MSWD is r(exp 2)=0.48, indicating a stronger link between the standard deviations than the actual parameters. Our analysis shows that there is no simple relationship between surface slope, wind direction, and snow accumulation rates for the overall survey area. We find high variability in surface roughness derived from laser altimetry measurements on length scales smaller than 10 km, sometimes with very distinct and sharp transitions. Some areas also show significant temporal variability over the course of the 3 survey years. Ultimately, there is no statistically significant slope-independent relationship between surface roughness and accumulation rates within our survey area. The observed correspondence between the small-scale temporal and spatial variability in surface roughness and backscatter, as evidenced by Ku-band radar signal strength retrievals, will make it difficult to develop elevation bias corrections for radar altimeter retrieval algorithms.

Michael Studinger↗

NASA NTRSDate not supplied

Design Exploration of a Transonic Cruise Slotted Airfoil

A knowledge-based aerodynamic design method, CDISC, has been leveraged for the computational design exploration of the cruise slotted airfoil as a drag-saving technology for single aisle, transonic transport aircraft. Aerodynamic predictions were generated using the NASA USM3D Reynolds-averaged Navier-Stokes flow solver, and laminar flow assessments were conducted using the NASA BLSTA3D boundary layer profile solver paired with the LASTRAC stability analysis and transition prediction software. The CDISC design method was used to parametrically vary several slotted-airfoil design variables to understand their impact on aerodynamic performance. In addition to establishing best practices for slotted airfoil design, it was observed that the historically noted skin-friction penalty for cruise slotted airfoils was attributed to the low-Reynolds-number boundary layer of the flap. At cruise, this skin-friction penalty negated any potential decrease in pressure drag enabled by the cruise slotted airfoil architecture. This observation led to the development of an Aft-Laminar Multi-element Airfoil concept that uses airfoil shaping to promote natural laminar flow on the flap. At cruise conditions, the concept is predicted to offer a 2.7% reduction in sectional drag relative to a fully turbulent supercritical airfoil. Off-design analyses showed that laminar flow could be maintained with near-cruise variations in angle of attack and Mach number, resulting in sustained aerodynamic efficiency improvements and a delay in the drag rise Mach number. A low-speed, high-lift analysis at takeoff conditions predicted a maximum lift coefficient of 2.4 could be achieved by use of a variable-camber leading edge on the main element and simple deflection of the flap. These computationally-predicted benefits have motivated future research toward an aft-laminar cruise slotted wing design as an incremental step toward the application of natural laminar flow technology on transonic commercial transports.

Brett R Hiller↗

NASA NTRS2014

A Generic Nonlinear Aerodynamic Model for Aircraft

A generic model of the aerodynamic coefficients was developed using wind tunnel databases for eight different aircraft and multivariate orthogonal functions. For each database and each coefficient, models were determined using polynomials expanded about the state and control variables, and an othgonalization procedure. A predicted squared-error criterion was used to automatically select the model terms. Modeling terms picked in at least half of the analyses, which totalled 45 terms, were retained to form the generic nonlinear aerodynamic (GNA) model. Least squares was then used to estimate the model parameters and associated uncertainty that best fit the GNA model to each database. Nonlinear flight simulations were used to demonstrate that the GNA model produces accurate trim solutions, local behavior (modal frequencies and damping ratios), and global dynamic behavior (91% accurate state histories and 80% accurate aerodynamic coefficient histories) under large-amplitude excitation. This compact aerodynamics model can be used to decrease on-board memory storage requirements, quickly change conceptual aircraft models, provide smooth analytical functions for control and optimization applications, and facilitate real-time parametric system identification.

Grauer, Jared A.↗

NASA NTRS1993

Space transportation vehicle design evaluation using saturated designs

An important objective in the preliminary design and evaluation of space transportation vehicles is to find the best values of design variables that optimize the performance characteristic (e.g. dry weight). For a given configuration, the vehicle performance can be determined by the use of complex sizing and performance evaluation computer programs. These complex computer programs utilize iterative algorithms and they are generally too expensive and/or difficult to use directly in multidisciplinary design optimization. An alternative is to use response surface methodology (RSM) and obtain quadratic polynomial approximations to the functional relationships between performance characteristics and design variables. In RSM, these approximation models are then used to determine optimum design parameter values and for rapid sensitivity studies. Constructing a second-order model requires that 'n' design parameters be studied at least at 3 levels (values) so that the coefficients in the model can be estimated. There, 3(n) factorial experiments (point designs or observations) may be necessary. For small values of 'n' such as two or three, this design works well. However, when a large number of design parameters are under study, the number of design points required for a full-factorial design may become excessive. Fortunately, these quadratic polynomial approximations can be obtained by selecting an efficient design matrix using central composite designs (CCD) from design of experiments theory. Each unique point design from the CCD matrix is then conducted using computerized analysis tools (e.g. POST, CONSIZ, etc.). In the next step, least squares regression analysis is used to calculate the quadratic polynomial coefficients from the data. However, in some multidisciplinary applications involving a large number of design variables and several disciplines, the computerized performance synthesis programs may get too time consuming and expensive to run even with the use of efficient central composite designs. In such cases, it may be preferable to keep the number of design points to an absolute minimum and trade some model accuracy with cost. For this purpose, another class of experimental designs, called saturated D-optimal designs may be utilized for generating a matrix of vehicle designs. A design is called saturated when the number of design points is exactly equal to the number of terms in the model to be fitted. As a result, saturated designs require the absolute minimum number of design points ((n+1)(n+2)/s) to estimate the quadratic polynomial model coefficients. Saturated designs can be generated using the D-optimality criterion. A good saturated design should give rise to least squares estimates with minimum generalized variance.

Unal, Resit↗

NASA NTRS2023

Impacts of SLR Ground Station Geographic Distribution on Time-Variable Gravity Recovery

Satellite laser ranging (SLR) continues to be an essential technique for estimating Earth's low-degree gravity field. The Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) do not accurately recover certain coefficients, which are needed for quantifying large-scale mass redistribution as part of Earth's time-variable gravity (TVG) field. In case of an inter-mission gap, as with GRACE and GRACE-FO, SLR can continue to provide mass-change measurements. The current SLR ground network consists of around 40 stations. However, these are not uniformly distributed and the quantity and quality of data varies widely between sites. We anticipate that future stations will improve SLR-derived gravity estimates and we investigate their potential impact on the solution in this simulation study. A single new station that enhances network geometry, particularly in the Southern hemisphere, increases the sensitivity of the network by up to 12% for certain coefficients. The addition of 5 new future stations improves certain coefficients up to 18%. We find new stations are limited in their ability to decorrelate certain coefficients regardless of their location, but that adding more data and increasing network uniformity still benefits the overall solution.

E S Tucker↗

NASA NTRS2010

High Resolution ECG for Evaluation of Heart Function During Exposure to Subacute Hypobaric Hypoxia

High altitude climbing presents a wide spectrum of health risks, including exposure to hypobaric hypoxia. Risks are also typically exacerbated by the difficulty in appropriately monitoring for early signs of organ dysfunction in remote areas. We investigated whether high resolution advanced ECG analysis might be helpful as a non-invasive and easy-to-use tool (e.g., instead of Doppler echocardiography) for evaluating early signs of heart overload in hypobaric hypoxia. Nine non-acclimatized healthy trained alpine rescuers (age 43.7 plus or minus 7.3 years) climbed in four days to the altitude of 4,200 m on Mount Ararat. Five-minute high-resolution 12-lead electrocardiograms (ECGs) were recorded (Cardiosoft) in each subject at rest in the supine position on different days but at the same time of day at four different altitudes: 400 m (reference altitude), 1,700 m, 3,200 m and 4,200 m. Changes in conventional and advanced resting ECG parameters, including in beat-to-beat QT and RR variability, waveform complexity, signal-averaged, high-frequency and spatial/spatiotemporal ECG was estimated by calculation of the regression coefficients in independent linear regression models. A p-value of less than 0.05 was adopted as statistically significant. As expected, the RR interval and its variability both decreased with increasing altitude, with trends k = -96 ms/1000 m with p = 0.000 and k = -9 ms/1000 m with p = 0.001, respectively. Significant changes were found in P-wave amplitude, which nearly doubled from the lowest to the highest altitude (k = 41.6 microvolt/1000 m with p = 0.000), and nearly significant changes in P-wave duration (k = 2.9 ms/1000 m with p = 0.059). Changes were less significant or non-significant in other studied parameters including those of waveform complexity, signal-averaged, high-frequency and spatial/spatiotemporal ECG. High resolution ECG analysis, particularly of the P wave, shows promise as a tool for monitoring early changes in heart function due to exposure to high altitude.

Zupet, Petra↗

NASA NTRSDate not supplied

Impact of Magnetohydrodynamic (MHD) Induced Drag on High Ballistic Coefficient Aerocapture at Neptune

This paper presents analyses illustrating the benefits of magnetohydrodynamic (MHD) drag force control for a capsule performing aerocapture at Neptune relative to the same capsule utilizing conventional aerodynamic-only control across a range of design and flight conditions. MHD technology utilizes an onboard mag-net to create a magnetic field that interacts with the ionized plasma surrounding the capsule at hypersonic velocities, thus creating an electron current and inducing a Lorentz force used to increase capsule drag. The study assumes a 4.57-meterMars Science Laboratory (MSL) 70-degree sphere-cone capsule aerodynamic shape arrives hyperbolically at Neptune and aerocaptures into a synchronous Tri-ton orbit (3986 km x 430,000 km orbit inclined 157 degrees) that offers repeated flyby opportunities. Hyperbolic arrival velocity and the capsule entry mass (i.e., ballistic coefficient) are varied over a wide range of values to study the impact of these variables on key flight performance and sizing parameters. Results show reduced heat rates, heat loads, and thermal protection system mass for MHD cases at all conditions, with the benefit of MHD relative to conventional aerodynamic-only options increasing as ballistic coefficient increases, suggesting the payoff for MHD is significantly better for high-mass entry system design concepts with high ballistic coefficients.

Entry Descent and Landing↗

NASA NTRS1971

Fatigue failure of materials under narrow band random vibrations. I.

A novel approach for the study of fatigue failure of materials under the multifactor influence of narrow band random vibrations is developed. The approach involves the conduction of an experiment in conjunction with various statistical techniques. Three factors including two statistical properties of the excitation or response are considered and varied simultaneously. A minimum of 6 tests for 3 variables is possible for a fractional f actorial design. The four coefficients of the predicting equation can be independently estimated. A look at 3 predicting equations shows the predominant effect of the root mean square stress of the first order equation.

Huang, T. C.↗

NASA NTRS1974

The diffusive idealization of charged particle transport in random magnetic fields

The transport of charged particles diffusing in a random magnetic field parallel to a relatively large guiding field is presented. The same coefficient of diffusion is obtained by three methods. Two corrections must be added to the expression in which the diffusive flux is proportional to the gradient of the density. Explicit expressions are given for a characteristic time and a characteristic length which describe the corrections. The well known divergence of the coefficient of diffusion, which is implied by the quasilinear analysis of pitch angle scattering, does not occur if the scattering rate is finite at 90 deg pitch angle. This effect is illustrated by formulas which give the coefficient of diffusion when the quasilinear expression is perturbed by a variable amount of isotropic scattering.

Earl, J. A.↗

NASA NTRS1978

Shear strength of fillet welds in aluminum alloy 2219

Fillet size is discussed in terms of theoretical or design dimensions versus as-welded dimensions, drawing attention to the inherent conservatism in the design load sustaining capabilities of fillet welds. Emphasis is placed on components for the solid rocket motor, external tank, and other aerospace applications. Problems associated with inspection of fillet welds are addresses and a comparison is drawn between defect counts obtained by radiographic inspection and by visual examination of the fracture plane. Fillet weld quality is related linearly to ultimate shear strength. Correlation coefficients are obtained by simple straight line regression analysis between the variables of ultimate shear strength and accumulative discontinuity summation. Shear strength allowables are found to be equivalent to 57 percent of butt weld A allowables (F sub tu.)

Lovoy, C. V.↗

NASA NTRS1982

Sensitivity analysis results of the effects of various parameters on composite design

Sensitivity analysis results are presented to assess the effects of a multitude of important parameters on fiber composite design and structural response. These results were obtained by using optimum design procedures in conjunction with sensitivity analyses. Sensitivity analyses were performed to assess the effects on composite optimum design and structural response of parameters such fiber transverse and shear properties, in situ matrix elastic and strength properties, correlation coefficients used in composite micromechanics and in combined strength predictions, processing variables, and perturbations of loading conditions. The results show that matrix properties, fiber volume ratio and small perturbations of the loading conditions have significant effects on certain composite structural responses. The remaining parameters have negligible effect.

Chamis, C. C.↗

NASA NTRS1982

Computation of consistent boundary quantities in finite element thermal-fluid solutions

The consistent boundary quantity method for computing derived quantities from finite element nodal variable solutions is investigated. The method calculates consistent, continuous boundary surface quantities such as heat fluxes, flow velocities, and surface tractions from nodal variables such as temperatures, velocity potentials, and displacements. Consistent and lumped coefficient matrix solutions for such problems are compared. The consistent approach may produce more accurate boundary quantities, but spurious oscillations may be produced in the vicinity of discontinuities. The uncoupled computations of the lumped approach provide greater flexibility in dealing with discontinuities and provide increased computational efficiency. The consistent boundary quantity approach can be applied to solution boundaries other than those with Dirichlet boundary conditions, and provides more accurate results than the customary method of differentiation of interpolation polynomials.

Thornton, E. A.↗