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NASA NTRS1975

Remote sensing techniques for prediction of watershed runoff

Hydrologic parameters of watersheds for use in mathematical models and as design criteria for flood detention structures are sometimes difficult to quantify using conventional measuring systems. The advent of remote sensing devices developed in the past decade offers the possibility that watershed characteristics such as vegetative cover, soils, soil moisture, etc., may be quantified rapidly and economically. Experiments with visible and near infrared data from the LANDSAT-1 multispectral scanner indicate a simple technique for calibration of runoff equation coefficients is feasible. The technique was tested on 10 watersheds in the Chickasha area and test results show more accurate runoff coefficients were obtained than with conventional methods. The technique worked equally as well using a dry fall scene. The runoff equation coefficients were then predicted for 22 subwatersheds with flood detention structures. Predicted values were again more accurate than coefficients produced by conventional methods.

Blanchard, B. J.↗

DOE OSTI2020

Transport of intensity equation: a tutorial

When it comes to “phase measurement” or “quantitative phase imaging”, many people will automatically connect them with “laser” and “interferometry”. Indeed, conventional quantitative phase imaging and phase measurement techniques generally rely on the superposition of two beams with a high degree of coherence: complex interferometric configurations, stringent requirements on the environmental stabilities, and associated laser speckle noise severely limit their applications in optical imaging and microscopy. On a different note, as one of the most well-known phase retrieval approaches, the transport of intensity equation (TIE) provides a new non-interferometric way to access quantitative phase information through intensity only measurement. Despite the insufficiency for interferometry, TIE is applicable under partially coherent illuminations (like the Köhler’s illumination in a conventional microscope), permitting optimum spatial resolution, higher signal-to-noise ratio, and better image quality. In this tutorial, we give an overview of the basic principle, research fields, and representative applications of TIE, focus particularly on optical imaging, metrology, and microscopy. The purpose of this tutorial is twofold. It should serve as a self-contained introduction to TIE for readers with little or no knowledge of TIE. On the other hand, it attempts to give an overview of recent developments in this field. These results highlight a new era in which strict coherence and interferometry are no longer prerequisites for quantitative phase imaging and diffraction tomography, paving the way toward new generation label-free three-dimensional microscopy, with applications in all branches of biomedicine.

42 ENGINEERING↗

DOE OSTI2023

Central speed of sound, the trace anomaly, and observables of neutron stars from a perturbative analysis of scaled Tolman-Oppenheimer-Volkoff equations

The central speed of sound (SS) measures the stiffness of the equation of state (EOS) of superdense neutron star (NS) matter. Its variations with density and radial coordinate in NSs in conventional analyses often suffer from uncertainties of the specific nuclear EOS used. Using the central SS and NS mass/radius scaling obtained from solving perturbatively the scaled Tolman-Oppenheimer-Volkoff (TOV) equations, we study the variations of SS, trace anomaly and several closely related properties of NSs in an EOSmodel- independent manner. We find that the SS increases with the reduced central pressure Pˆ c ≡ P c =ε c (scaled by the central energy density εc), and the conformal bound for SS tends to break down for NSs with masses higher than about 1.9M ⊙ . The ratio P=ε is upper bounded as P=ε ≲ 0.374 around the centers of stable NSs. We demonstrate that it is an intrinsic property of strong field gravity and is more relevant than the perturbative QCD bound on it. While a sharp phase transition at high densities characterized by a sudden vanishing of SS in cores of massive NSs are basically excluded, the probability for a continuous crossover signaled by a peaked radial profile of SS is found to be enhanced as Pˆ c decreases, implying it likely happens near the centers of massive NSs. Moreover, a new and more stringent causality boundary as R max =km ≳ 4.73$M$$^{max}_{NS}$ =M ⊙ þ 1.14 for the NS mass-radius curve is found to be excellently consistent with observational data on NS masses and radii. Here, new constraints on the ultimate energy density and pressure allowed in NSs before collapsing into black holes are obtained and compared with earlier predictions in the literature

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1972

Spin waves in fluids

A working report is presented in order to document early results of research on the stability of laminar boundary layers. The report shows that constitutive equations for a structured continua may be derived by the technique of reinterpreting velocity in the conventional stress to rate-of-strain relationship so as to account for effects of particle rotation. It is demonstrated that accounting for particle structure even at a molecular level makes the fluid viscoelastic with the ability to propagate vector waves. It is shown that particle structure modifies the basic stability equation for the system, which in turn would alter values for critical Reynolds number.

Kistler, E. L.↗

NASA NTRS1985

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Barth, T. J.↗

NASA NTRS1947

Calculation of the Pressure Distribution on Bodies of Revolution in the Subsonic Flow of a Gas: Axially Symmetrical Flow - Part 1

The present report concerns a method of computing the velocity and pressure distributions on bodies of revolution in axially symmetrical flow in the subsonic range. The differential equation for the velocity potential Phi of a compressible fluid motion is linearized tn the conventional manner, and then put in the form Delta(Phi) = 0 by affine transformation. The quantity Phi represents the velocity potential of a fictitious incompressible flow, for which a constant superposition of sources by sections is secured by a method patterned after von Karman which must comply with the boundary condition delta(phi)/delta(n) = 0 at the originally specified contour. This requirement yields for the "pseudo-stream function" psi a differential equation which must be fulfilled for as many points on the contour as source lengths are assumed. In this manner, the problem of defining the still unknown source intensities is reduced to the solution of an inhomogeneous equation system. The pressure distribution is then determined with the aid of Bernoulli's equation and adiabatic equation of state. Lastly, the pressure distributions in compressible and incompressible medium are compared on a model problem.

Bilharz, Herbert↗

NASA NTRS1984

A new aerodynamic integral equation based on an acoustic formula in the time domain

An aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented. Based on a time-dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed (the Ffowcs Williams-Hawking formulation), the loading terms and a conventional thickness source terms are retained. Two surface and three line integrals are employed to solve an equation for the loading noise. The near-field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface. A singular integral equation is thereby derived for the unknown surface pressure, and is amenable to numerical solutions using Galerkin or collocation methods. The technique is useful for studying the nonuniform inflow to the propeller.

Farassat, F.↗

NASA NTRS1990

Equations of motion of slung load systems with results for dual lift

General simulation equations are derived for the rigid body motion of slung load systems. These systems are viewed as consisting of several rigid bodies connected by straight-line cables or links. The suspension can be assumed to be elastic or inelastic, both cases being of interest in simulation and control studies. Equations for the general system are obtained via D'Alembert's principle and the introduction of generalized velocity coordinates. Three forms are obtained. Two of these generalize previous case-specific results for single helicopter systems with elastic or inelastic suspensions. The third is a new formulation for inelastic suspensions. It is derived from the elastic suspension equations by choosing the generalized coordinates so as to separate motion due to cable stretching from motion with invariant cable lengths. The result is computationally more efficient than the conventional formulation, and is readily integrated with the elastic suspension formulation and readily applied to the complex dual lift and multilift systems. Equations are derived for dual lift systems. Three proposed suspension arrangements can be integrated in a single equation set. The equations are given in terms of the natural vectors and matrices of three-dimensional rigid body mechanics and are tractable for both analysis and programming.

Cicolani, Luigi S.↗

NASA NTRS1977

On estimating gravity anomalies - A comparison of least squares collocation with conventional least squares techniques

The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator are described.

Argentiero, P.↗

DOE OSTI2025

Derivation of physical equations for high-speed laser welding using large language models

It is challenging to formulate complex physical phenomena that occur in a manufacturing process, particularly when the available data are limited, rendering conventional data-driven approaches ineffective. This study aims to predict humping onset in high-speed laser welding by introducing a novel framework, namely text-to-equations generative pre-trained transformer (T2EGPT). This method leverages the capabilities of large language models (LLMs), in combination with sparse experimental data and enriched literature data, to derive an interpretable and generalizable equation for predicting humping initiation. By capturing key correlations among physical parameters, T2EGPT generates a compact and dimensionless expression that accurately predicts hump formation. The equation reveals that humping arises from the interplay between inertia-driven backward melt flow and capillary-driven surface stabilization, where inertial forces drive molten metal backward and capillary forces resist surface deformation. Furthermore, compared to traditional data-driven models, T2EGPT demonstrates enhanced predictive accuracy and cross-material transferability. More broadly, this study highlights the potential of LLMs to integrate textual information with data-driven discovery, enabling the extraction of physical laws in data-scarce scientific domains.

36 MATERIALS SCIENCE↗

NASA NTRS1991

On the wall-normal velocity of the compressible boundary-layer equations

Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x,y) plane to a computational (xi,eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability.

Pruett, C. David↗

NASA NTRS1990

Motion and force controlled vibration testing

A technique for controlling both the input acceleration and force in vibration tests is proposed to alleviate the overtesting risks and the problems associated with response limiting in conventional vibration tests of aerospace hardware. Previous research on impedance and force controlled vibration tests is reviewed and a simple equation governing the dual control of acceleration and force is derived. A practical method for implementing the dual control technique in random vibration tests has been demonstrated in JPL's environmental test facility using a conventional digital controller operating in the extremal mode. The dual control technique provides appropriate real-time notching of the input acceleration and a corresponding reduction of the test item response at resonances. Issues concerning the need for force and acceleration phase information, the adequacy of specifying the blocked force, and the derivation of the total force for multipoint supports are discussed.

Scharton, Terry D.↗

NASA NTRS2001

Modeling of two-phase flow in membranes and porous media in microgravity as applied to plant irrigation in space

In traditional applications in soil physics it is convention to scale porous media properties, such as hydraulic conductivity, soil water diffusivity, and capillary head, with the gravitational acceleration. In addition, the Richards equation for water flux in partially saturated porous media also contains a gravity term. With the plans to develop plant habitats in space, such as in the International Space Station, it becomes necessary to evaluate these properties and this equation under conditions of microgravitational acceleration. This article develops models for microgravity steady state two-phase flow, as found in irrigation systems, that addresses critical design issues. Conventional dimensionless groups in two-phase mathematical models are scaled with gravity, which must be assigned a value of zero for microgravity modeling. The use of these conventional solutions in microgravity, therefore, is not possible. This article therefore introduces new dimensionless groups for two-phase models. The microgravity models introduced here determined that in addition to porous media properties, important design factors for microgravity systems include applied water potential and the ratio of inner to outer radii for cylindrical and spherical porous media systems.

Plant Roots/growth & development↗

DOE OSTI2020

Pronghorn Theory Manual

This manual is intended to provide a thorough description of the governing equations; the relations used for material, heat transfer, and fluid flow parameters; and the numerical method utilized in Pronghorn. Detailed derivations of the governing equations are given, beginning from first principles in order to be as explicit as possible about assumptions made along the way and guide any future methods extensions. Additional explanatory or tangential information that is not required for detailed understanding of the governing equations used in Pronghorn is shown in gray boxes in the text. The convention used in this document is to represent all class names (or file names) in typewriter font.

42 ENGINEERING↗

NASA NTRS1975

A numerical method for determining the natural vibration characteristics of rotating nonuniform cantilever blades

A method is presented for determining the free vibration characteristics of a rotating blade having nonuniform spanwise properties and cantilever boundary conditions. The equations which govern the coupled flapwise, chordwise, and torsional motion of such a blade are solved using an integrating matrix method. By expressing the equations of motion and matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the equations are formulated into an eigenvalue problem whose solutions may be determined by conventional methods. Computer results are compared with experimental data.

White, W. F., Jr.↗

NASA NTRS1979

Diffusion approximation for large absorption in radiative transfer

A new diffusion model is developed for radiative transfer in particulate media. It includes the effects of higher Legendre moments while avoiding the mathematical complexities of solving multiple coupled differential moment equations and satisfying higher-order boundary conditions. The method accurately extrapolates the conventional Eddington approximation to problems involving large absorption. Although the simplifying assumptions limit the model to nonbeam incidence and spatial homogeneity of the scattering material, they are nonrestrictive with regard to the size and shape of the medium, the character of background reflections, and the type of phase function.

Meador, W. E.↗

NASA NTRS1989

Indentation fracture toughness of sintered silicon carbide in the Palmqvist crack regime

The fracture toughness of a sintered dense alpha-SiC was estimated by the Vickers indentation microfracture method in the low-load Palmqvist crack regime. It was observed that the use of simultaneously obtained Vickers hardnesses does not yield reliable fracture toughness values, nor does application of the median-crack-derived equations. It is necessary to utilize a load-independent, crack-free hardness value with this toughness estimation method. Although several of the curve-fitting equations yield similar toughnesses, it is concluded for the Palmqvist crack system in this alpha-SiC that the Niihara-Morena-Hasselman (1982) equation is the only one which yields fracture toughness values in agreement with conventional measurement techniques.

Li, Zhuang↗

NASA NTRS1991

A study of hydrogen diffusion flames using PDF turbulence model

The application of probability density function (pdf) turbulence models is addressed in this work. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional CFD flow solver with the Monte Carlo simulation of the pdf evolution equation has been developed. The algorithm has been validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames has been carried out using this algorithm. Numerical results compared favorably with experimental data. The computuations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.

Hsu, Andrew T.↗