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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 127 records · Page 7
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NASA NTRS1998

Manuel Stein's Five Decades of Structural Mechanics Contributions (1944-1988)

Manuel Stein went to work for NACA (National Advisory Committee for Aeronautics) in 1944 and left in 1988. His research contributions spanned five decades of extremely defining times for the aerospace industry. Problems arising from the analysis and design of efficient thin plate and shell aerospace structures have stimulated research over the past half century. The primary structural technology drivers during Dr. Stein's career included 1940's aluminum aircraft, 1950's jet aircraft, 1960's launch vehicles and advanced spacecraft, 1970's reusable launch vehicles and commercial aircraft, and 1980's composite aircraft. Dr. Stein's research was driven by these areas and he made lasting contributions for each. Dr. Stein's research can be characterized by a judicious mixture of physical insight into the problem, understanding of the basic mechanisms, mathematical modeling of the observed phenomena, and extraordinary analytical and numerical solution methodologies of the resulting mathematical models. This paper summarizes Dr. Stein's life and his contributions to the technical community.

Mikulas, Martin M.↗
NASA NTRS1974

The passage of an infinite swept airfoil through an oblique gust

An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

Adamczyk, J. L.↗
NASA NTRS1982

Post-instability in continuous systems. I - Failure of differentiability of solutions in continuum mechanics

It is pointed out that mathematical models of continua are based on certain assumptions regarding functions which must be at least piece-wise differentiable. The assumption about smoothness of the functions makes it possible to use the mathematical technique of differentiable equations. However, this artificial mathematical limitation follows neither from the principles of mechanics nor from the definition of a continuum. The price paid for such a mathematical convenience is instability (in the class of smooth functions) of the solutions to the corresponding governing equations in some regions of the parameters. A new mathematical technique should, therefore, be developed to describe the solutions which are not necessarily differentiable. The present investigation is concerned with the criteria of applicability of the classical models of continua from the view point of stability of the corresponding solutions, postinstability models derived by reformulation of the original models, and postinstability models in enlarged classes of functions.

Zak, M.↗
NASA NTRS1982

A mathematical model of post-instability in fluid mechanics

Postinstability of fluids is eliminated in numerical models by introducing multivalued velocity fields after discarding the principle of impenetrability. Smooth functions are shown to be incapable of keeping the derivatives from going towards infinity when iterating solutions for the governing equations such as those defined by Navier-Stokes. Enlarging the class of functions is shown to be necessary to eliminate the appearance of imaginary characteristic roots in the systems of arbitrary partial differential equations, a condition which leads to physically impossible motions. The enlarging is demonstrated to be achievable by allowing several individual particles with different velocities to appear at the same point of space, and the subsequent multivaluedness of the solutions is purely a mathematical concern, rather than one of actual physical existence. Applications are provided for an inviscid fluid and for turbulence.

Zak, M. A.↗
NASA NTRS1977

A solution to the surface intersection problem

An application-independent geometric model within a data base framework should support the use of Boolean operators which allow the user to construct a complex model by appropriately combining a series of simple models. The use of these operators leads to the concept of implicitly and explicitly defined surfaces. With an explicitly defined model, the surface area may be computed by simply summing the surface areas of the bounding surfaces. For an implicitly defined model, the surface area computation must deal with active and inactive regions. Because the surface intersection problem involves four unknowns and its solution is a space curve, the parametric coordinates of each surface must be determined as a function of the arc length. Various subproblems involved in the general intersection problem are discussed, and the mathematical basis for their solution is presented along with a program written in FORTRAN IV for implementation on the IBM 370 TSO system.

Timer, H. G.↗
NASA NTRS1976

A computerized compensator design algorithm with launch vehicle applications

This short paper presents a computerized algorithm for the design of compensators for large launch vehicles. The algorithm is applicable to the design of compensators for linear, time-invariant, control systems with a plant possessing a single control input and multioutputs. The achievement of frequency response specifications is cast into a strict constraint mathematical programming format. An improved solution algorithm for solving this type of problem is given, along with the mathematical necessities for application to systems of the above type. A computer program, compensator improvement program (CIP), has been developed and applied to a pragmatic space-industry-related example.

Mitchell, J. R.↗
NASA NTRS2019

Regularization and Error Characterization of GRACE Mascons

We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.

B. D. Loomis↗
NASA NTRS2019

Regularization and Error Characterization of GRACE Mascons

We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.

Loomis, B. D.↗
NASA NTRS1981

Precision orbit computations for an operational environment

Taking advantage of the improvements to the Earth's gravitation field and tracking station coordinates, an orbital computational consistency of the order of 5 meters was achieved for total position differences between orbital solutions for the Seasat and GEOS-3. The main source of error in these solutions was in the mathematical models that are required to generate these results, i.e., gravitation, atmospheric drag, etc. Different Earth gravitation fields and tracking coordinates were analyzed and evaluated in obtaining these computational results. Comparisons and evaluations of the Seasat results were obtained in terms of different solution types such as the Doppler only, Laser only, Doppler and Laser, etc. Other investigation using the Seasat data were made in order to determine their effect on the computational results at this particular level of consistency.

Doll, C. E.↗
NASA NTRS1976

Optimum lattice arrangement developed from a rigorous analytical basis

The spanwise vortex-lattice arrangement is mathematically established by lattice solutions of the slender wing which are shown to be analogous to the chordwise vortex-lattice thin wing solution. Solutions for any number N of panels wing theory lift and induced drag and thin wing theory lift and moment are predicted exactly. As N approaches infinity, the slender wing elliptic spanwise loading and thin wing cotangent chordwise loading are predicted, which proves there is mathematical convergence of the vortex-lattice method to the exact answer. Based on this planform spanwise lattice arrangement, an A-vortex-lattice spanwise system is developed for an arbitrary aspect ratio A. This A-lattice has the optimum characteristic of predicting lift accurately for any value of N.

Deyoung, J.↗
NASA NTRS1980

Iterative solutions for one-dimensional diffusion with time varying surface composition and composition-dependent diffusion coefficient

Solutions are given for one-dimensional diffusion problems with a time varying surface composition and also a composition dependent diffusion coefficient. The most general solution does not require special mathematical functions to fit the variation in surface composition or D(C). In another solution, a series expansion may be used to fit the time dependent surface concentration. These solutions make use of iterative calculations that converge rapidly and are highly stable. Computer times are much shorter than that required for finite difference calculations and can efficiently make use of interactive graphics terminals. Existing gas carburization data were used to provide an illustration of an iterative approach with a time varying carbon composition at the free surface.

Chow, M.↗
NASA NTRS2004

Rayleigh-Sommerfield Diffraction vs Fresnel-Kirchhoff, Fourier Propagation and Poisson's Spot

The boundary conditions imposed on the diffraction problem in order to obtain the Fresnel-Kirchhoff (FK) solution are well-known to be mathematically inconsistent and to be violated by the solution when the observation point is close to the diffracting screen 1-3. These problems are absent in the Rayleigh-Sommerfeld (RS) solution. The difference between RS and FK is in the inclination factor and is usually immaterial because the inclination factor is approximated by unity. But when this approximation is not valid, FK can lead to unacceptable answers. Calculating the on-axis intensity of Poisson s spot provides a critical test, a test passed by RS and failed by FK. FK fails because (a) convergence of the integral depends on how it is evaluated and (b) when the convergence problem is xed, the predicted amplitude at points near the obscuring disk is not consistent with the assumed boundary conditions.

RS (RAYLEIGH SOMMERFELD)↗
NASA NTRS1985

On the probability density function of the squared envelope of a sum of random phase vectors

Weber et al. (1980) have found that a generic problem arises in the study of multiuser FHMA/MFSK systems. According to this problem, the presence of the other channel users acts as interference to reception of the desired user's transmission. The present investigation is concerned with a recursive solution in which the recursion parameter is the number of vectors in the sum. A mathematical characterization of such a solution is presented, taking into account the simple two-vector case in which a well-known closed form result is possible. Some numerical results are also discussed. It is pointed out that the considered recursive solution provides a break in the bottleneck associated with the exact computation of the error probability performance of multiuser FHMA/MFSK systems and single access MFSK systems corrupted by multitone jamming.

Simon, M. K.↗
NASA NTRS1999

A Spherical Earth Solution for TOA Lightning Location Retrieval

The problem of retrieving ligntning, ground-strike location on a spherical Earth surface using a network of 4 or more time-of-arrival (TOA) sensors is considered, It is shown that this problem has an analytic solution and therefore does not require the use of nonlinear estimation theory (e.g., minimization). The mathematical robustness of the analytic solution is tested using computer-generated lightning sources and simulated TOA measurement errors. A summary of a quasi-analytic extension of the spherical Earth solution to an oblate spheroid Earth geometry is also provided.

Koshak, W. J.↗
NASA NTRS1989

Optical neural net for classifying imaging spectrometer data

The problem of determining the composition of an unknown input mixture from its measured spectrum, given the spectra of a number of elements, is studied. The Hopfield minimization procedure was used to express the determination of the compositions as a problem suitable for solution by neural nets. A mathematical description of the problem was developed and used as a basis for a neural network solution and an optical implementation.

Barnard, Etienne↗
NASA NTRS2013

Prediction of Ablation Rates from Solid Surfaces Exposed to High Temperature Gas Flow

A mathematical model and a solution algorithm is developed to study the physics of high temperature heat transfer and material ablation and identify the problems associated with the flow of hydrogen gas at very high temperatures and velocities through pipes and various components of Nuclear Thermal Rocket (NTR) motors. Ablation and melting can be experienced when the inner solid surface of the cooling channels and the diverging-converging nozzle of a Nuclear Thermal Rocket (NTR) motor is exposed to hydrogen gas flow at temperatures around 2500 degrees Kelvin and pressures around 3.4 MPa. In the experiments conducted on typical NTR motors developed in 1960s, degradation of the cooling channel material (cracking in the nuclear fuel element cladding) and in some instances melting of the core was observed. This paper presents the results of a preliminary study based on two types of physics based mathematical models that were developed to simulate the thermal-hydrodynamic conditions that lead to ablation of the solid surface of a stainless steel pipe exposed to high temperature hydrogen gas near sonic velocities. One of the proposed models is one-dimensional and assumes the gas flow to be unsteady, compressible and viscous. An in-house computer code was developed to solve the conservations equations of this model using a second-order accurate finite-difference technique. The second model assumes the flow to be three-dimensional, unsteady, compressible and viscous. A commercial CFD code (Fluent) was used to solve the later model equations. Both models assume the thermodynamic and transport properties of the hydrogen gas to be temperature dependent. In the solution algorithm developed for this study, the unsteady temperature of the pipe is determined from the heat equation for the solid. The solid-gas interface temperature is determined from an energy balance at the interface which includes heat transfer from or to the interface by conduction, convection, radiation, and ablation. Two different ablation models are proposed to determine the heat loss from the solid surface due to the ablation of the solid material. Both of them are physics based. Various numerical simulations were carried out using both models to predict the temperature distribution in the solid and in the gas flow, and then predict the ablation rates at a typical NTR motor hydrogen gas temperature and pressure. Solid mass loss rate per foot of a pipe was also calculated from these predictions. The results are presented for fully developed turbulent flow conditions in a sample SS pipe with a 6 inch diameter.

Akyuzlu, Kazim M.↗