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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 NTRS2003

Model of Fluidized Bed Containing Reacting Solids and Gases

A mathematical model has been developed for describing the thermofluid dynamics of a dense, chemically reacting mixture of solid particles and gases. As used here, "dense" signifies having a large volume fraction of particles, as for example in a bubbling fluidized bed. The model is intended especially for application to fluidized beds that contain mixtures of carrier gases, biomass undergoing pyrolysis, and sand. So far, the design of fluidized beds and other gas/solid industrial processing equipment has been based on empirical correlations derived from laboratory- and pilot-scale units. The present mathematical model is a product of continuing efforts to develop a computational capability for optimizing the designs of fluidized beds and related equipment on the basis of first principles. Such a capability could eliminate the need for expensive, time-consuming predesign testing.

Bellan, Josette↗

NASA NTRS2005

A Theoretical Investigation of Oxidation Efficiency of a Volatile Removal Assembly Reactor Under Microgravity Conditions

Volatile Removal Assembly (VRA) is a subsystem of the Closed Environment Life Support System (CELSS) installed in the International Space Station. It is used for removing contaminants (volatile organics) in the wastewater produced by the space station crews. The major contaminants are formic acid, ethanol, and propylene glycol. The VRA contains a slim packbed reactor (3.5 cm diameter and four 28 cm long tubes in series) to perform catalyst oxidation of wastewater at elevated pressure and temperature under microgravity conditions. In the reactor, the contaminants are burned with oxygen gas (O2) to form water and carbon dioxide (CO2) that dissolves in the water stream. Optimal design of the reactor requires a thorough understanding about how the reactor performs under microgravity conditions. The objective of this study was to develop a mathematical model to interpret experimental data obtained from normal and microgravity conditions, and to predict the performance of VRA reactor under microgravity conditions. Catalyst oxidation kinetics and the total oxygen-water contact area control the efficiency of catalyst oxidation for mass transfer, which depends on oxygen gas holdup and distribution in the reactor. The process involves bubbly flow in porous media with chemical reactions in microgravity environment. This presents a unique problem in fluid dynamics that has not been studied. Guo et al. (2004) developed a mathematical model that predicts oxygen holdup in the VRA reactor. No mathematical model has been found in the literature that can be used to predict the efficiency of catalyst oxidation under microgravity conditions.

Guo, Boyun↗

DOE OSTI2024

Towards verifiable cancer digital twins: tissue level modeling protocol for precision medicine

Cancer exhibits substantial heterogeneity, manifesting as distinct morphological and molecular variations across tumors, which frequently undermines the efficacy of conventional oncological treatments. Developments in multiomics and sequencing technologies have paved the way for unraveling this heterogeneity. Nevertheless, the complexity of the data gathered from these methods cannot be fully interpreted through multimodal data analysis alone. Mathematical modeling plays a crucial role in delineating the underlying mechanisms to explain sources of heterogeneity using patient-specific data. Intra-tumoral diversity necessitates the development of precision oncology therapies utilizing multiphysics, multiscale mathematical models for cancer. This review discusses recent advancements in computational methodologies for precision oncology, highlighting the potential of cancer digital twins to enhance patient-specific decision-making in clinical settings. We review computational efforts in building patient-informed cellular and tissue-level models for cancer and propose a computational framework that utilizes agent-based modeling as an effective conduit to integrate cancer systems models that encode signaling at the cellular scale with digital twin models that predict tissue-level response in a tumor microenvironment customized to patient information. Furthermore, we discuss machine learning approaches to building surrogates for these complex mathematical models. These surrogates can potentially be used to conduct sensitivity analysis, verification, validation, and uncertainty quantification, which is especially important for tumor studies due to their dynamic nature.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1976

A three-dimensional, time-dependent model of Mobile Bay

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.

Pitts, F. H.↗

NASA NTRS1976

Correlation between multispectral photography and near-surface turbidities

Four-band multispectral photography obtained from an aerial platform at an altitude of about 10,000 feet has been utilized to measure near-surface turbidity at numerous sampling sites in the Ross Barnett Reservoir, Mississippi. Correlation of the photographs with turbidity measurements has been accomplished via an empirical mathematical model which depends upon visual color recognition when the composited photographs are examined on either an I squared S model 600 or a Spectral Data model 65 color-additive viewer. The mathematical model was developed utilizing least-squares, iterative, and standard statistical methods and includes a time-dependent term related to sun angle. This model is consistent with information obtained from two overflights of the target area - July 30, 1973 and October 30, 1973 - and now is being evaluated with regard to information obtained from a third overflight on November 8, 1974.

Wertz, D. L.↗

NASA NTRS1976

Compensated control loops for a 30-cm ion thruster

The vaporizer dynamic control characteristics of a 30-cm diameter mercury ion thruster were determined by operating the thruster in an open loop steady state mode and then introducing a small sinusoidal signal on the main, cathode, or neutralizer vaporizer current and observing the response of the beam current, discharge voltage, and neutralizer keeper voltage, respectively. This was done over a range of frequencies and operating conditions. From these data, Bode plots for gain and phase were made and mathematical models were obtained. The Bode plots and mathematical models were analyzed for stability and appropriate compensation networks determined. The compensated control loops were incorporated into a power processor and operated with a thruster. The time responses of the compensated loops to changes in set points and recovery from arc conditions are presented.

Robson, R. R.↗

NASA NTRS1976

Compensated control loops for a 30-cm ion thruster

Robson, R. R.↗

NASA NTRS1979

Compensation for atmospheric effects in LANDSAT data

Preprocessing algorithms were developed to remove or reduce the variations in multispectral data caused by variations in Sun angle and by changes in the atmospheric aerosol and water vapor levels. The two most significant algorithms developed by using mathematical models to define interrelations between the required multiplicative and additive correction factors so that just a few statistical characteristics of a LANDSAT distribution model would be sufficient to drive the mathematical model and to calculate the preprocessing corrections are examined. These are the atmospheric correction (ATCOR) computer program and the XSTAR haze correction algorithm. Neither the ATCOR nor the XSTAR algorithm provides an explicit compensation for the effects of changing LANDSAT view angle. Development efforts are underway to address this aspect of the preprocessing problem.

Lambeck, P. F.↗

NASA NTRS1988

Linear-Quadratic Controller For Aiming A Large Antenna

Independent control and estimator gains selected for optimal performance. Report describes use of techniques of linear-quadratic optimal control to design digital controller aiming large antenna. Based on closed-loop concept including mathematical model of plant and independently-selectable mathematical model estimates state of system.

Nickerson, Jackson A.↗

NASA NTRS1972

Hydrodynamic water impact

The hydrodynamic impact of a falling body upon a viscous incompressible fluid was investigated by numerically solving the equations of motion. Initially the mathematical model simulated the axisymmetric impact of a rigid right circular cylinder upon the initially quiescent free surface of a fluid. A compressible air layer exists between the falling cylinder and the liquid free surface. The mathematical model was developed by applying the Navier-Stokes equations to the incompressible air layer and the incompressible fluid. Assuming the flow to be one dimensional within the air layer, the average velocity, pressure and density distributions were calculated. The liquid free surface was allowed to deform as the air pressure acting on it increases. For the liquid the normalized equations were expressed in two-dimensional cylindrical coordinates. The governing equations for the air layer and the liquid were expressed in finite difference form and solved numerically. For the liquid a modified version of the Marker-and-Cell method was used. The mathematical model has been reexamined and a new approach has recently been initiated. Essentially this consists of examining the impact of an inclined plate onto a quiesent water surface with the equations now formulated in cartesian coordinates.

Kettleborough, C. F.↗

NASA NTRS1971

Application of Monte Carlo techniques to optimization of high-energy beam transport in a stochastic environment

An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.

Parrish, R. V.↗

DOE OSTI2025

Viral Dynamic Models During COVID‐19: Are We Ready for the Next Pandemic?

Mathematical models have been used for about 30 years to improve our understanding of virus-host interaction, in particular during chronic infections. During the COVID-19 pandemic, these models have been used to provide insights into the natural history of acute SARS-CoV-2 infection, optimize antiviral treatment strategies, understand factors associated with transmission, and optimize surveillance systems. The impact of modeling has been accelerated by the availability of unprecedented multidimensional immune data from animal and human systems, which enhanced partnerships between experimentalists and theorists and led to exciting new modeling and statistical developments. In this mini review, we examine the lessons learned from the COVID-19 pandemic and discuss the main insights provided by mathematical models of viral dynamics at the different stages of the outbreak. Although we focus on respiratory infection, we also consider the new areas for development in anticipation of future acute infections from new or reemerging pathogens.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2009

Efficient Model-Based Diagnosis Engine

An efficient diagnosis engine - a combination of mathematical models and algorithms - has been developed for identifying faulty components in a possibly complex engineering system. This model-based diagnosis engine embodies a twofold approach to reducing, relative to prior model-based diagnosis engines, the amount of computation needed to perform a thorough, accurate diagnosis. The first part of the approach involves a reconstruction of the general diagnostic engine to reduce the complexity of the mathematical-model calculations and of the software needed to perform them. The second part of the approach involves algorithms for computing a minimal diagnosis (the term "minimal diagnosis" is defined below). A somewhat lengthy background discussion is prerequisite to a meaningful summary of the innovative aspects of the present efficient model-based diagnosis engine. In model-based diagnosis, the function of each component and the relationships among all the components of the engineering system to be diagnosed are represented as a logical system denoted the system description (SD). Hence, the expected normal behavior of the engineering system is the set of logical consequences of the SD. Faulty components lead to inconsistencies between the observed behaviors of the system and the SD (see figure). Diagnosis - the task of finding faulty components - is reduced to finding those components, the abnormalities of which could explain all the inconsistencies. The solution of the diagnosis problem should be a minimal diagnosis, which is a minimal set of faulty components. A minimal diagnosis stands in contradistinction to the trivial solution, in which all components are deemed to be faulty, and which, therefore, always explains all inconsistencies.

Fijany, Amir↗

NASA NTRS1991

Basic research for the geodynamics program

The mathematical models of space very long base interferometry (VLBI) observables suitable for least squares covariance analysis were derived and estimatability problems inherent in the space VLBI system were explored, including a detailed rank defect analysis and sensitivity analysis. An important aim is to carry out a comparative analysis of the mathematical models of the ground-based VLBI and space VLBI observables in order to describe the background in detail. Computer programs were developed in order to check the relations, assess errors, and analyze sensitivity. In order to investigate the estimatability of different geodetic and geodynamic parameters from the space VLBI observables, the mathematical models for time delay and time delay rate observables of space VLBI were analytically derived along with the partial derivatives with respect to the parameters. Rank defect analysis was carried out both by analytical and numerical testing of linear dependencies between the columns of the normal matrix thus formed. Definite conclusions were formed about the rank defects in the system.

Source record↗

NASA NTRS2003

Quantifying Astronaut Tasks: Robotic Technology and Future Space Suit Design

The primary aim of this research effort was to advance the current understanding of astronauts' capabilities and limitations in space-suited EVA by developing models of the constitutive and compatibility relations of a space suit, based on experimental data gained from human test subjects as well as a 12 degree-of-freedom human-sized robot, and utilizing these fundamental relations to estimate a human factors performance metric for space suited EVA work. The three specific objectives are to: 1) Compile a detailed database of torques required to bend the joints of a space suit, using realistic, multi- joint human motions. 2) Develop a mathematical model of the constitutive relations between space suit joint torques and joint angular positions, based on experimental data and compare other investigators' physics-based models to experimental data. 3) Estimate the work envelope of a space suited astronaut, using the constitutive and compatibility relations of the space suit. The body of work that makes up this report includes experimentation, empirical and physics-based modeling, and model applications. A detailed space suit joint torque-angle database was compiled with a novel experimental approach that used space-suited human test subjects to generate realistic, multi-joint motions and an instrumented robot to measure the torques required to accomplish these motions in a space suit. Based on the experimental data, a mathematical model is developed to predict joint torque from the joint angle history. Two physics-based models of pressurized fabric cylinder bending are compared to experimental data, yielding design insights. The mathematical model is applied to EVA operations in an inverse kinematic analysis coupled to the space suit model to calculate the volume in which space-suited astronauts can work with their hands, demonstrating that operational human factors metrics can be predicted from fundamental space suit information.

Newman, Dava↗

NASA NTRS1986

Flight test planning and parameter extraction for rotorcraft system identification

The present study is concerned with the mathematical modelling of aircraft dynamics on the basis of an investigation conducted with the aid of the Rotor System Research Aircraft (RSRA). The particular characteristics of RSRA make it possible to investigate aircraft properties which cannot be readily studied elsewhere, for example in the wind tunnel. The considered experiment had mainly the objective to develop an improved understanding of the physics of rotor flapping dynamics and rotor loads in maneuvers. The employed approach is based on a utilization of parameter identification methodology (PID) with application to helicopters. A better understanding of the contribution of the main rotor to the overall aircraft forces and moments is also to be obtained. Attention is given to the mathematical model of a rotorcraft system, an integrated identification method, flight data processing, and the identification of RSRA mathematical models.

Wang, J. C.↗

NASA NTRS1988

Identifiability Of Systems With Modeling Errors

Advances in theory of modeling errors reported. Recent paper on errors in mathematical models of deterministic linear or weakly nonlinear systems. Extends theoretical work described in NPO-16661 and NPO-16785. Presents concrete way of accounting for difference in structure between mathematical model and physical process or system that it represents.

Hadaegh, Yadolah "fred"↗

NASA NTRS2021

System Identification for Propellers at High Incidence Angles

Propellers used for electric vertical takeoff and landing (eVTOL) aircraft propulsion systems experience a wide range of aerodynamic conditions, including large incidence angles relative to oncoming airflow. In oblique flow, propellers exhibit deviations in thrust and torque oriented along the propeller axis of rotation, as well as significant off-axis forces and moments. Although important for modeling eVTOL aircraft aerodynamics, sparse experimental data or mathematical models exist for propellers at incidence. This paper describes a propulsion system modeling methodology for the LA-8 tandem tilt-wing, eVTOL aircraft. System identification methods are applied to isolated propeller wind tunnel data gathered across the vehicle's flight envelope to develop a mathematical model of the propulsion system, including a static motor model, dynamic motor model, and propeller aerodynamic model. Modeling results validated against data withheld from the modeling process indicate good predictive capability and agree with theoretical expectations. The results are followed by a discussion of model implementation strategies into high-fidelity eVTOL aircraft simulations.

system identification↗