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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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NASA NTRS2016

Multistatic Aerosol Cloud Lidar in Space: A Theoretical Perspective

Accurate aerosol and cloud retrievals from space remain quite challenging and typically involve solving a severely ill-posed inverse scattering problem. In this Perspective, we formulate in general terms an aerosol and aerosol-cloud interaction space mission concept intended to provide detailed horizontal and vertical profiles of aerosol physical characteristics as well as identify mutually induced changes in the properties of aerosols and clouds. We argue that a natural and feasible way of addressing the ill-posedness of the inverse scattering problem while having an exquisite vertical-profiling capability is to fly a multistatic (including bistatic) lidar system. We analyze theoretically the capabilities of a formation-flying constellation of a primary satellite equipped with a conventional monostatic (backscattering) lidar and one or more additional platforms each hosting a receiver of the scattered laser light. If successfully implemented, this concept would combine the measurement capabilities of a passive multi-angle multi-spectral polarimeter with the vertical profiling capability of a lidar; address the ill-posedness of the inverse problem caused by the highly limited information content of monostatic lidar measurements; address the ill-posedness of the inverse problem caused by vertical integration and surface reflection in passive photopolarimetric measurements; relax polarization accuracy requirements; eliminate the need for exquisite radiative-transfer modeling of the atmosphere-surface system in data analyses; yield the day-and-night observation capability; provide direct characterization of ground-level aerosols as atmospheric pollutants; and yield direct measurements of polarized bidirectional surface reflectance. We demonstrate, in particular, that supplementing the conventional backscattering lidar with just one additional receiver flown in formation at a scattering angle close to 170deg can dramatically increase the information content of the measurements. Although the specific subject of this Perspective is the multistatic lidar concept, all our conclusions equally apply to a multistatic radar system intended to study from space the global distribution of cloud and precipitation characteristics.

aerosols↗

NASA NTRSDate not supplied

Total Variation Majorization Minimization (TV-MM) Approach to Radiometer Brightness Temperature Gridding and Reconstruction

This paper presents the implementation of an algorithm to enhance the image resolution of the Earth's surface brightness temperature (T B ) data measured by radiometers such as the one onboard of the Soil Moisture Active Passive (SMAP) mission. A key step in radiometer T B processing is the conversion of the swath-based calibrated antenna temperature (T A ) measurements to the Level 3 Earth-centered grid. The simplest algorithm to transform this data from swath to gridded format is called drop-in-the-bucket which simply averages surrounding noisy T A samples to form a T B value at the gridded location. This method reduces noise, however produces low resolution products. To obtain a higher resolution product, SMAP uses other techniques such the Backus-Gilbert (BG) algorithm, which is the conventional method used in microwave radiometry. Although this method performs the required interpolation, it is not effective in denoising and removing blurring effects due to antenna filtering of the radiometer image data. Our motivation for this development is to further improve the resolution through post-processing of the radiometer T B image, a highly cost-effective method of image enhancement. The approach adapted in this work is based on the minimization of the Total Variation (TV) regularized objective function that is used extensively in solving general ill-posed linear inverse problems in image processing. Since the TV-based objective function is convex but not everywhere differentiable, there exists many numerical algorithms that can estimate the solution and the one selected for this work is called Majorization- Minimization (MM). By applying this algorithm, simulation experiments were performed based on synthetic data from the Geophysical model as well as real SMAP data to demonstrate the effectiveness of the technique. Results were then compared against the BG method.

Wing Lee↗

NASA NTRS1991

Inverse problems and optimal experiment design in unsteady heat transfer processes identification

Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.

Artyukhin, Eugene A.↗

NASA NTRS1983

PAN AIR modeling studies

PAN AIR is a computer program that predicts subsonic or supersonic linear potential flow about arbitrary configurations. The code's versatility and generality afford numerous possibilities for modeling flow problems. Although this generality provides great flexibility, it also means that studies are required to establish the dos and don'ts of modeling. The purpose of this paper is to describe and evaluate a variety of methods for modeling flows with PAN AIR. The areas discussed are effects of panel density, internal flow modeling, forebody modeling in subsonic flow, propeller slipstream modeling, effect of wake length, wing-tail-wake interaction, effect of trailing-edge paneling on the Kutta condition, well- and ill-posed boundary-value problems, and induced-drag calculations. These nine topics address problems that are of practical interest to the users of PAN AIR.

Towne, M. C.↗

NASA NTRS2017

Decoupled Method for Reconstruction of Surface Conditions From Internal Temperatures On Ablative Materials With Uncertain Recession Model

Obtaining measurements of flight environments on ablative heat shields is both critical for spacecraft development and extremely challenging due to the harsh heating environment and surface recession. Thermocouples installed several millimeters below the surface are commonly used to measure the heat shield temperature response, but an ill-posed inverse heat conduction problem must be solved to reconstruct the surface heating environment from these measurements. Ablation can contribute substantially to the measurement response making solutions to the inverse problem strongly dependent on the recession model, which is often poorly characterized. To enable efficient surface reconstruction for recession model sensitivity analysis, a method for decoupling the surface recession evaluation from the inverse heat conduction problem is presented. The decoupled method is shown to provide reconstructions of equivalent accuracy to the traditional coupled method but with substantially reduced computational effort. These methods are applied to reconstruct the environments on the Mars Science Laboratory heat shield using diffusion limit and kinetically limited recession models.

Oliver, A. Brandon↗

NASA NTRS1979

Calculated global conditions for the unsteady Euler's flow equations

This paper considers the numerical solution of a fluid dynamical system with time-dependent oscillating boundaries. The problem detailed, a compressible and inviscid flow in a one-dimensional pipe with vibrating ends, is examined to develop techniques needed to solve the more complex unsteady flows in turbomachine cascades. The problem is shown to be mathematically ill-posed but by complementing the governing equations with energy conservation, a unique solution is obtained. An artificial damping term is introduced into the governing equations to improve the performance of the time-marching integration.

Kuzo, D. M.↗

NASA NTRS1988

Vortex breakdown in an axisymmetric flow

The breakdown for both an isolated vortex and a vortex flow in a tube is studied by means of a numerical solution of the axisymmetric Navier-Stokes equations for an unsteady, incompressible, and laminar flow. Results are compared to those of other authors and to experiments. Various numerical solution methods and various physical boundary conditions are used in order to explain the existence of different solutions. The computational results reveal that the existence of different solutions is due to slightly different inflow conditions. The numerical problem for the isolated vortex becomes ill-posed at a certain time for the inflow condition of zero axial gradient of the radial velocity component. Different inflow conditions yield breakdown flowfields containing different features of the experimentally observed breakdown structure.

Menne, Stefan↗

NASA NTRS1993

Retrieval of temperature profiles from Martian infrared spectra

In theory, a thermal emission spectrum of Mars (220-1600 cm(exp -1)) contains a wealth of information about the composition and thermal structure of the atmosphere and surface. However, in practice, the ability to retrieve quantitative information from the spectrum is limited by a number of factors including (1) the ill-posed nature of the spectral inversion problem and the resulting nonuniqueness of all solutions; (2) assumptions built into any spectral inversion program; (3) uncertainties in surface pressure, temperature, and emissivity; and (4) uncertainties in the optical properties of atmospheric aerosols. Below, factors (1) and (2) are discussed as fundamental limitations on temperature retrievals from Mariner 9 Infrared Interferometer Spectrometer (IRIS) spectra. In preparation for the Mars Observer mission and the return of tens of thousands of infrared spectra per day from the Thermal Emission Spectrometer (TES), we have developed a fast inversion algorithm to retrieve temperature structure and aerosol opacity from the infrared spectra. The derived atmospheric models will be used to provide the atmospheric contribution to the TES spectra, so that the thermal emission spectra of the underlying surface can be determined for making mineralogical identifications. As a test of our algorithm, we are undertaking a systematic analysis of the entire Mariner 9 Infrared Interferometric Spectrometer (IRIS) dataset of 21,000 plus spectra. While portions of the IRIS dataset have been previously analyzed, the lack of a speedy and robust algorithm to invert the IRIS spectra to retrieve temperature profiles and aerosol opacities has been a major impediment to a truly comprehensive analysis.

Mcmillan, W. Wallace↗

NASA NTRS1991

Single Doppler radar and lidar studies of the dynamics of mixed layers and overlying stable regions

Some examples of profiles of PBL quantities retrieved from Doppler radar and lidar observations are shown, and the extent to which the deduced quantities agree with the traditional eddy viscosity concept is examined. It is found in one case that the concept of 'top down bottom up' diffusion introduced by Wyngaard (1983) is more pertinent than that of the eddy viscosity. In another case it is found that, in stable layers with sufficiently large Richardson number, the momentum fluxes could be counter-gradient. In this latter case the use of a negative turbulence diffusion coefficient would result in an ill-posed differential equation, thus confusing the 'diffusion problem'.

Xu, Mei↗

NASA NTRS2003

Thermocapillary Convection Due to a Stationary Bubble - A Paradox

We analyze the velocity and temperature fields at steady state due to thermocapillary convection around a gas bubble that is stationary in a liquid. A linear temperature field is imposed in the undisturbed liquid. Our interest is in investigating the effect of convective transport of momentum and energy on the velocity and temperature fields. We assume the pertinent physical properties to be constant, and that buoyant convection is negligible. Suitably defined Reynolds and Marangoni numbers are assumed to be small compared with unity. When both the Reynolds and Marangoni numbers are set equal to zero, a solution can be found. In this solution, far from the bubble, the velocity field decays as the inverse of the distance from the bubble, and the disturbance temperature field decays as the inverse of the square of this distance. We now attempt to obtain a solution when the Reynolds number is zero, but the Marangoni number is small, but non-zero, by a perturbation expansion in the Marangoni number. When the temperature field is expanded in a regular perturbation series in the Marangoni number, we show that the problem for the first correction field is ill-posed. The governing equation for this perturbation field contains an inhomogeneity, and the corresponding particular solution neither decays far from the bubble, nor can be canceled by a homogeneous solution. Additional information is included in the original extended abstract.

Balasubramaniam, R.↗

NASA NTRS1984

Neutrino tomography - Tevatron mapping versus the neutrino sky

The feasibility of neutrino tomography of the earth's interior is discussed, taking the 80-GeV W-boson mass determined by Arnison (1983) and Banner (1983) into account. The opacity of earth zones is calculated on the basis of the preliminary reference earth model of Dziewonski and Anderson (1981), and the results are presented in tables and graphs. Proposed tomography schemes are evaluated in terms of the well-posedness of the inverse-Radon-transform problems involved, the neutrino generators and detectors required, and practical and economic factors. The ill-posed schemes are shown to be infeasible; the well-posed schemes (using Tevatrons or the neutrino sky as sources) are considered feasible but impractical.

Wilson, T. L.↗

NASA NTRS1997

The Analysis and Construction of Perfectly Matched Layers for the Linearized Euler Equations

We present a detailed analysis of a recently proposed perfectly matched layer (PML) method for the absorption of acoustic waves. The split set of equations is shown to be only weakly well-posed, and ill-posed under small low order perturbations. This analysis provides the explanation for the stability problems associated with the split field formulation and illustrates why applying a filter has a stabilizing effect. Utilizing recent results obtained within the context of electromagnetics, we develop strongly well-posed absorbing layers for the linearized Euler equations. The schemes are shown to be perfectly absorbing independent of frequency and angle of incidence of the wave in the case of a non-convecting mean flow. In the general case of a convecting mean flow, a number of techniques is combined to obtain a absorbing layers exhibiting PML-like behavior. The efficacy of the proposed absorbing layers is illustrated though computation of benchmark problems in aero-acoustics.

Hesthaven, J. S.↗

NASA NTRS1984

CREKID: A computer code for transient, gas-phase combustion of kinetics

A new algorithm was developed for fast, automatic integration of chemical kinetic rate equations describing homogeneous, gas-phase combustion at constant pressure. Particular attention is paid to the distinguishing physical and computational characteristics of the induction, heat-release and equilibration regimes. The two-part predictor-corrector algorithm, based on an exponentially-fitted trapezoidal rule, includes filtering of ill-posed initial conditions, automatic selection of Newton-Jacobi or Newton iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm was found to compare favorably with LSODE on two representative test problems drawn from combustion kinetics.

Pratt, D. T.↗

NASA NTRS1986

Fast algorithm for calculating chemical kinetics in turbulent reacting flow

This paper addresses the need for a fast batch chemistry solver to perform the kinetics part of a split operator formulation of turbulent reacting flows, with special attention focused on the solution of the ordinary differential equations governing a homogeneous gas-phase chemical reaction. For this purpose, a two-part predictor-corrector algorithm which incorporates an exponentially fitted trapezoidal method was developed. The algorithm performs filtering of ill-posed initial conditions, automatic step-size selection, and automatic selection of Jacobi-Newton or Newton-Raphson iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm, termed CREK1D (combustion reaction kinetics, one-dimensional), compared favorably with the code LSODE when tested on two representative problems drawn from combustion kinetics, and is faster than LSODE.

Radhakrishnan, K.↗

NASA NTRS1996

Analysis of the Hessian for Aerodynamic Optimization: Inviscid Flow

In this paper we analyze inviscid aerodynamic shape optimization problems governed by the full potential and the Euler equations in two and three dimensions. The analysis indicates that minimization of pressure dependent cost functions results in Hessians whose eigenvalue distributions are identical for the full potential and the Euler equations. However the optimization problems in two and three dimensions are inherently different. While the two dimensional optimization problems are well-posed the three dimensional ones are ill-posed. Oscillations in the shape up to the smallest scale allowed by the design space can develop in the direction perpendicular to the flow, implying that a regularization is required. A natural choice of such a regularization is derived. The analysis also gives an estimate of the Hessian's condition number which implies that the problems at hand are ill-conditioned. Infinite dimensional approximations for the Hessians are constructed and preconditioners for gradient based methods are derived from these approximate Hessians.

Arian, Eyal↗

NASA NTRS1992

Departure solutions of the unsteady thin-layer and full Navier-Stokes equations solved using streamline curvature based iteration techniques

The development of a thorough understanding of the mechanisms for vortex eruptions from viscous layers, which are believed to be associated with phenomena such as dynamic stall onset and transition, is crucial if accurate models of such phenomena are to be formulated. The development of such models may, in turn, allow for the possibility that such effects could be accounted for during the design of various aerodynamic devices such as wings, helicopter rotors, and turbomachinery blading and thus lead to designs which are stall free or stall resistant and which have better stall-recovery properties. The present investigation is being conducted as part of an effort to develop analytical and numerical tools which can be used to help improve our understanding of the vortex-eruption mechanism at high Reynolds numbers. The addition of the normal-momentum equation to the classical unsteady boundary-layer equations is crucial according to recent asymptotic analyses of the vortex-eruption problem and is a key feature of the analyses being developed by the present authors. The purpose of this paper is as follows: to describe departure solution behavior observed when using unsteady, streamline-curvature based solution procedures in which nontrivial transverse pressure gradient effects are included; and to show that special treatment of the time-derivative of the normal velocity is needed to eliminate the ill-posed solution behavior, which is observed when small spatial and temporal step sizes are used.

Barnett, M.↗

NASA NTRS1995

A well-posed numerical method to track isolated conformal map singularities in Hele-Shaw flow

We present a new numerical method for calculating an evolving 2D Hele-Shaw interface when surface tension effects are neglected. In the case where the flow is directed from the less viscous fluid into the more viscous fluid, the motion of the interface is ill-posed; small deviations in the initial condition will produce significant changes in the ensuing motion. This situation is disastrous for numerical computation, as small round-off errors can quickly lead to large inaccuracies in the computed solution. Our method of computation is most easily formulated using a conformal map from the fluid domain into a unit disk. The method relies on analytically continuing the initial data and equations of motion into the region exterior to the disk, where the evolution problem becomes well-posed. The equations are then numerically solved in the extended domain. The presence of singularities in the conformal map outside of the disk introduces specific structures along the fluid interface. Our method can explicitly track the location of isolated pole and branch point singularities, allowing us to draw connections between the development of interfacial patterns and the motion of singularities as they approach the unit disk. In particular, we are able to relate physical features such as finger shape, side-branch formation, and competition between fingers to the nature and location of the singularities. The usefulness of this method in studying the formation of topological singularities (self-intersections of the interface) is also pointed out.

Baker, Gregory↗

DOE OSTI2025

Information theory optimization of signals from small-angle scattering measurements

Small-angle X-ray scattering (SAXS) of particles in solution informs on the conformational states and assemblies of biological macromolecules (bioSAXS) outside of cryo- and solid-state conditions. In bioSAXS, the SAXS measurement under dilute conditions is resolution limited, and through an inverse Fourier transform, the measured SAXS intensities directly relate to the physical space occupied by the particles via the P (r)-distribution. Yet, this inverse transform of SAXS data has been historically cast as an ill-posed, ill-conditioned problem requiring an indirect approach. Here, we show that through the applications of matrix and information theories, the inverse transform of SAXS intensity data is a well-conditioned problem. The so-called ill-conditioning of the inverse problem is directly related to the Shannon number. By exploiting the oversampling enabled by modern detectors, a direct inverse Fourier transform of the SAXS data is possible, provided the recovered information does not exceed the Shannon number. The Shannon limit corresponds to the maximum number of significant singular values that can be recovered in a SAXS experiment, suggesting this relationship is a fundamental property of band-limited inverse integral transform problems. This correspondence reduces the complexity of the inverse problem to the Shannon limit and maximum dimension. We propose a hybrid scoring function using an information theory framework that assesses both the quality of the model-data fit as well as the quality of the recovered P (r)-distribution. The hybrid score utilizes the Akaike information criteria and Durbin-Watson statistic that considers parameter-model complexity, i.e., degrees of freedom, and the randomness of the model-data residuals. The described tests and findings extend the boundaries for bioSAXS by completing the information theory formalism initiated by Peter B. Moore to enable a quantitative measure of resolution in SAXS, robustly determine maximum dimension, and more precisely define the best parameter model appropriately representing the observed scattering data.

Rambo, Robert P. [Science and Technology Facilitie↗