Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematical models”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

A mathematical model of the UH-60 helicopter

This report documents the revisions made to a ten-degree-of-freedom, full-flight envelope, generic helicopter mathematical model to represent the UH-60 helicopter accurately. The major modifications to the model include fuselage aerodynamic force and moment equations specific to the UH-60, a canted tail rotor, a horizontal stabilator with variable incidence, and a pitch bias actuator (PBA). In addition, this report presents a full set of parameters and numerical values which describe the helicopter configuration and physical characteristics. Model validation was accomplished by comparison of trim and stability derivative data generated from the UH-60 math model with data generated from a similar total force and moment math model.

Hilbert, K. B.↗
NASA NTRS1984

Mathematical modeling of fluid-electrolyte alterations during weightlessness

Fluid electrolyte metabolism and renal endocrine control as it pertains to adaptation to weightlessness were studied. The mathematical models that have been particularly useful are discussed. However, the focus of the report is on the physiological meaning of the computer studies. A discussion of the major ground based analogs of weightlessness are included; for example, head down tilt, water immersion, and bed rest, and a comparison of findings. Several important zero g phenomena are described, including acute fluid volume regulation, blood volume regulation, circulatory changes, longer term fluid electrolyte adaptations, hormonal regulation, and body composition changes. Hypotheses are offered to explain the major findings in each area and these are integrated into a larger hypothesis of space flight adaptation. A conceptual foundation for fluid electrolyte metabolism, blood volume regulation, and cardiovascular regulation is reported.

Leonard, J. I.↗
DOE OSTI2022

Estimating the population level impact of a gonococcal vaccine candidate: Predictions from a simple mathematical model

Neisseria gonorrhoeae cross-protection was suggested in a New Zealand meningitis B vaccine. We modeled the potential impact of similar vaccines on gonorrhea prevalence in heterosexuals in the United States. Here, our mathematical model incorporated infection, behavior, and vaccination dynamics. Approximate Bayesian Computation calibrated our model to US prevalence. Primary analyses assumed New Zealand vaccine characteristics: 30% efficacy and 2-year duration of protection. We estimated impact under two vaccine coverages (20%, 50%). Reduction in gonorrhea prevalence ranged from 4.8 to 39.4%, depending on vaccine coverage. Vaccine impact was correlated with both size of the highly sexually active subpopulation and sexual mixing between high and low activity subpopulations. A meningitis vaccine providing low efficacy cross-protection against gonorrhea acquisition and short duration of protection could result in a large reduction in gonorrhea prevalence in the United States. Potential dual protective effects can be considered when making vaccine recommendations.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1979

A simplified rotor system mathematical model for piloted flight dynamics simulation

The model was developed for real-time pilot-in-the-loop investigation of helicopter flying qualities. The mathematical model included the tip-path plane dynamics and several primary rotor design parameters, such as flapping hinge restraint, flapping hinge offset, blade Lock number, and pitch-flap coupling. The model was used in several exploratory studies of the flying qualities of helicopters with a variety of rotor systems. The basic assumptions used and the major steps involved in the development of the set of equations listed are described. The equations consisted of the tip-path plane dynamic equation, the equations for the main rotor forces and moments, and the equation for control phasing required to achieve decoupling in pitch and roll due to cyclic inputs.

Chen, R. T. N.↗
NASA NTRS1976

Correlation of AH-1G airframe test data with a NASTRAN mathematical model

Test data was provided for evaluating a mathematical vibration model of the Bell AH-1G helicopter airframe. The math model was developed and analyzed using the NASTRAN structural analysis computer program. Data from static and dynamic tests were used for comparison with the math model. Static tests of the fuselage and tailboom were conducted to verify the stiffness representation of the NASTRAN model. Dynamic test data were obtained from shake tests of the airframe and were used to evaluate the NASTRAN model for representing the low frequency (below 30 Hz) vibration response of the airframe.

Cronkhite, J. D.↗
NASA NTRS1991

Computing Linear Mathematical Models Of Aircraft

Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.

Duke, Eugene L.↗
NASA NTRS1989

Mathematical modeling and analysis of heat pipe start-up from the frozen state

The start-up process of a frozen heat pipe is described and a complete mathematical model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. The two-dimensional transient model for the wall and wick is coupled with the one-dimensional transient model for the vapor flow when vaporization and condensation occur at the interface. A parametric study is performed to examine the effect of the boundary specification at the surface of the outer wall on the successful start-up from the frozen state. For successful start-up, the boundary specification at the outer wall surface must melt the working substance in the condenser before dry-out takes place in the evaporator.

Jang, Jong Hoon↗
NASA NTRS1990

Mathematical modeling and analysis of heat pipe start-up from the frozen state

The start-up process of a frozen heat pipe is described and a complete mathematical model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. The two-dimensional transient model for the wall and wick is coupled with the one-dimensional transient model for the vapor flow when vaporization and condensation occur at the interface. A parametric study is performed to examine the effect of the boundary specification at the surface of the outer wall on the successful start-up from the frozen state. For successful start-up, the boundary specification at the outer wall surface must melt the working substance in the condenser before dry-out takes place in the evaporator.

Jang, J. H.↗
DOE OSTI2020

Mathematical Models for Optimization of Grid-Integrated Energy Storage Systems

Energy storage has been proven to yield positive effects on planning, operation and control of electric grids. It has become a crucial task to properly model the energy storage systems (ESS) under the framework of grid optimization on transmission and distribution networks including microgrids. This paper presents a review on mathematical models and test cases of ESSs used for grid optimization studies, where the network constraints of power systems are included. The existing ESS models are mainly classified into two categories – linear and nonlinear models. The two main categories are further divided into several subcategories respectively; such as mixed-integer linear and convex nonlinear sub-categories. Based on the review and discussions, this paper aims at providing suggestions for choosing proper ESS models for specific grid optimization studies considering the chosen power network model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1973

Mathematical modeling of spinning elastic bodies for modal analysis.

The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.

Likins, P. W.↗
DOE OSTI2016

SU-F-E-20: A Mathematical Model of Linac Jaw Calibration Integrated with Collimator Walkout

Purpose: Accurate jaw calibration is possible, but it does not necessarily achieve good junctions because of collimator rotation walkout. We developed a mathematical model seeking to pick an origin for calibration that minimizes the collimator walkout effect. Methods: We use radioopaque markers aligned with crosshair on the EPID to determine the collimator walkout at collimator angles 0°, 90° and 270°. We can accurately calibrate jaws to any arbitrary origin near the radiation field centre. While the absolute position of an origin moves with the collimator walkout, its relative location to the crosshair is an invariant. We studied two approaches to select an optimal origin. One approach seeks to bring all three origin locations (0°–90°–270°) as close as possible by minimizing the perimeter of the triangle formed by these points. The other approach focuses on the gap for 0°–90° junctions. Results: Our perimeter cost function has two variables and non-linear behaviour. Generally, it does not have zero-perimeter-length solution which leads to perfect jaw matches. The zero solution can only be achieved, if the collimator rotates about a single fixed axis. In the second approach, we can always get perfect 0°–0° and 0°–90° junctions, because we ignore the 0°–270° situation. For our TrueBeams, both techniques for selecting an origin improved junction dose inhomogeneities to less than ±6%. Conclusion: Our model considers the general jaw matching with collimator rotations and proposes two potential solutions. One solution optimizes the junction gaps by considering all three collimator angles while the other only considers 0°–90°. The first solution will not give perfect matching, but can be clinically acceptable with minimized collimator walkout effect, while the second can have perfect junctions at the expense of the 0°–270° junctions. Different clinics might choose between these two methods basing on their clinical practices.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1979

Mathematical model for steady state, simple ampholyte isoelectric focusing: Development, computer simulation and implementation

The elimination of Ampholine from the system by establishing the pH gradient with simple ampholytes is proposed. A mathematical model was exercised at the level of the two-component system by using values for mobilities, diffusion coefficients, and dissociation constants representative of glutamic acid and histidine. The constants assumed in the calculations are reported. The predictions of the model and computer simulation of isoelectric focusing experiments are in direct importance to obtain Ampholine-free, stable pH gradients.

Palusinski, O. A.↗
NASA NTRS2000

Mathematical Model Development and Simulation Support

This report summarizes the work performed in support of the Contact Dynamics 6DOF Facility and the Flight Robotics Lab at NASA/ MSFC in the areas of Mathematical Model Development and Simulation Support.

Francis, Ronald C.↗
NASA NTRS1995

Program Helps Generate Boundary-Element Mathematical Models

Composite Model Generation-Boundary Element Method (COM-GEN-BEM) computer program significantly reduces time and effort needed to construct boundary-element mathematical models of continuous-fiber composite materials at micro-mechanical (constituent) scale. Generates boundary-element models compatible with BEST-CMS boundary-element code for anlaysis of micromechanics of composite material. Written in PATRAN Command Language (PCL).

Goldberg, R. K.↗
DOE OSTI2022

Experimental measurements and mathematical modeling of cold plate for aviation thermal management

Herein, this study, which has been motivated by the recent applications of the cold plate device in aviation thermal management, reports on physics-based mathematical models derived from the conservation laws of mass, momentum, and energy, and empiricism-based models. One of the objectives of the present work is to report on an elaborate and successful experimental work carried out on an additively manufactured device for the purpose of rigorously validating the numerical predictions. The excellent agreement between the numerical predictions and measured performance provides much needed confidence in the implementation, in the software package, of the offset-strip fin passage correlations, as well as in the software implementation of user-defined wavy fin correlations for aerospace heat exchangers and cold plates operating with ram air at Reynolds numbers below 8000. The contributions of this work can also be found in the development of a new and accurate thermal-hydraulic analysis procedure, referred to in this paper as plate-fin analogy. Results from this procedure are compared with those from thermal resistance network. The comparative study in this paper of the bulk and discrete enthalpy flux method is also new, as is the relative assessment of four off-set strip fin thermal-hydraulic models.

42 ENGINEERING↗
DOE OSTI2012

Reduction of Carbon Footprint and Energy Efficiency Improvement in Aluminum Production by Use of Novel Wireless Instrumentation Integrated with Mathematical Modeling

The work addressed the greenhouse gas emission and electrical energy consumption of the aluminum industry. The objective was to provide a means for reducing both through the application of wireless instrumentation, coupled to mathematical modeling. Worldwide the aluminum industry consumes more electrical energy than all activities in many major countries (e.g. the UK) and emits more greenhouse gasses (e.g. than France). Most of these excesses are in the 'primary production' of aluminum; that is the conversion of aluminum oxide to metal in large electrolytic cells operating at hundreds of thousands of amps. An industry-specific GHG emission has been the focus of the work. The electrolytic cells periodically, but at irregular intervals, experience an upset condition known as an 'anode effect'. During such anode effects the cells emit fluorinated hydrocarbons (PFCs, which have a high global warming potential) at a rate far greater than in normal operation. Therefore curbing anode effects will reduce GHG emissions. Prior work had indicated that the distribution of electrical current within the cell experiences significant shifts in the minutes before an anode effect. The thrust of the present work was to develop technology that could detect and report this early warning of an anode effect so that the control computer could minimize GHG emissions. A system was developed to achieve this goal and, in collaboration with Alcoa, was tested on two cells at an Alcoa plant in Malaga, Washington. The project has also pointed to the possibility of additional improvements that could result from the work. Notable among these is an improvement in efficiency that could result in an increase in cell output at little extra operating cost. Prospects for commercialization have emerged in the form of purchase orders for further installations. The work has demonstrated that a system for monitoring the current of individual anodes in an aluminum cell is practical. Furthermore the system has been installed twice on a smelter in the US without exposing workers to hazards usually associated with running signal wires in aluminum plants. The results display the early warning of an anode effect that potentially can be used to minimize such anode effects with their excessive GHG emissions. They also point to a possible, but substantial, economic benefit that could result in improved current efficiency by anode adjustment based on individual anode current measurements.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1998

The Impact of Deviation from Michaelis-Menten Saturation on Mathematical Model Stability Properties

Based on purely abstract ecological theory, it has been argued that a system composed of two or more consumers competing for the same resource cannot persist. By analysis on a Monod format mathematical model, Hubble and others demonstrated that this assertion is true for all but very special cases of such competing organisms which are determined by an index formed by a grouping of. the parameters which characterize the biological processes of the competing organisms. In the laboratory, using a bioreactor, Hansen and Hubble obtained confirmatory results for several cases of two competing species, and they characterized it as "qualitative confirmation" of the assertion. This result is amazing, since the analysis required the exact equality of the hey index, and it seems certain that no pair of organism species could have exactly equal values. It is quite plausible, however, that pairs of organism species could have approximately equal indices, and the question of how different they could be and still have coexistence of the two (or more) presents itself. In this paper, the pursuit of this question and a compatible resolution is presented.

Blackwell, Charles↗