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Results for “Mathematical Modeling”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

A mathematical model for simulating noise suppression of lined ejectors

A mathematical model containing the essential features embodied in the noise suppression of lined ejectors is presented. Although some simplification of the physics is necessary to render the model mathematically tractable, the current model is the most versatile and technologically advanced at the current time. A system of linearized equations and the boundary conditions governing the sound field are derived starting from the equations of fluid dynamics. A nonreflecting boundary condition is developed. In view of the complex nature of the equations, a parametric study requires the use of numerical techniques and modern computers. A finite element algorithm that solves the differential equations coupled with the boundary condition is then introduced. The numerical method results in a matrix equation with several hundred thousand degrees of freedom that is solved efficiently on a supercomputer. The model is validated by comparing results either with exact solutions or with approximate solutions from other works. In each case, excellent correlations are obtained. The usefulness of the model as an optimization tool and the importance of variable impedance liners as a mechanism for achieving broadband suppression within a lined ejector are demonstrated.

Watson, Willie R.↗
NASA NTRS1987

Automatic mathematical modeling for space application

A methodology for automatic mathematical modeling is described. The major objective is to create a very friendly environment for engineers to design, maintain and verify their model and also automatically convert the mathematical model into FORTRAN code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine simulation mathematical model called Propulsion System Automatic Modeling (PSAM). PSAM provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. PSAM contains an initial set of component process elements for the Space Shuttle Main Engine simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. PSAM is then able to automatically generate the model and the FORTRAN code. A future goal is to download the FORTRAN code to the VAX/VMS system for conventional computation.

Wang, Caroline K.↗
NASA NTRS1973

V/STOL tilt rotor aircraft study mathematical model for a real time simulation of a tilt rotor aircraft (Boeing Vertol Model 222), volume 8

This report documents the development of a real time mathematical model of a tilt rotor aircraft. This mathematical model is to be used in conjunction with the NASA Flight Simulator for Advanced Aircraft (FSAA) at Ames Research Center for evaluation of aircraft performance and handling qualities. In addition to developing the mathematical model, a parallel programming effort was conducted utilizing Boeing-Vertol's Hybrid Simulation Laboratory for the purpose of developing and evaluating model simplification. The mathematical model is an eleven degree of freedom total force model. This model includes the basic six degree of freedom rigid body .outer loop equations written about the instantaneous center of gravity with the inertial and aerodynamic terms included. The rotor is treated as a point source of forces and moments with appropriate response time lags and actuator dynamics. The wing has one vertical bending and one wing torsion degree of freedom. These structural degrees of freedom are treated on a "quasistatic" basis; i.e., the natural frequencies of vibration of the structure are much higher than the· frequencies of the rigid body motion, and the coupling is in the aerodynamic terms. Each nacelle has an independent pitch degree of freedom about the wing pivot. The aerodynamics of the wing, tail, rotors, landing gear and fuselage are included. Wing and tail mutual interference effects and turbine engine performance and dynamic responses' are represented.

H Rosenstein↗
NASA NTRS1971

Redundancy management of electrohydraulic servoactuators by mathematical model referencing

A description of a mathematical model reference system is presented which provides redundancy management for an electrohydraulic servoactuator. The mathematical model includes a compensation network that calculates reference parameter perturbations induced by external disturbance forces. This is accomplished by using the measured pressure differential data taken from the physical system. This technique was experimentally verified by tests performed using the H-1 engine thrust vector control system for Saturn IB. The results of these tests are included in this report. It was concluded that this technique improves the tracking accuracy of the model reference system to the extent that redundancy management of electrohydraulic servosystems may be performed using this method.

Campbell, R. A.↗
NASA NTRS1988

Automatic mathematical modeling for real time simulation system

A methodology for automatic mathematical modeling and generating simulation models is described. The models will be verified by running in a test environment using standard profiles with the results compared against known results. The major objective is to create a user friendly environment for engineers to design, maintain, and verify their model and also automatically convert the mathematical model into conventional code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine Simulation. It is written in LISP and MACSYMA and runs on a Symbolic 3670 Lisp Machine. The program provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. It contains an initial set of component process elements for the Space Shuttle Main Engine Simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. The system is then able to automatically generate the model and FORTRAN code. The future goal which is under construction is to download the FORTRAN code to VAX/VMS system for conventional computation. The SSME mathematical model will be verified in a test environment and the solution compared with the real data profile. The use of artificial intelligence techniques has shown that the process of the simulation modeling can be simplified.

Wang, Caroline↗
DOE OSTI2019

Within-host mathematical models of hepatitis B virus infection: Past, present, and future

Mathematical modeling has been instrumental in enhancing our understanding of the viral dynamics of hepatitis B virus (HBV) infection. We give a primer on HBV infection in humans and a brief overview of the development of within-host mathematical models of HBV infection. In the last decade, models have advanced from considering chronic HBV infections under therapy to the pathogenesis of infection. We also summarize estimates of key viral dynamic parameters that have varied greatly among studies, and show that they impact model predictions. Here, future directions for mathematical modeling of HBV infection are proposed to better understand emerging therapies, the HBV life cycle, predicting cure, and the mechanisms involved in the immune response to HBV.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1996

Comprehensive Mathematical Model Of Real Fluids

Mathematical model of thermodynamic properties of water, steam, and liquid and gaseous hydrogen and oxygen developed for use in computational simulations of flows of mass and heat in main engine of space shuttle. Similar models developed for other fluids and applications. Based on HBMS equation of state.

Anderson, Peter G.↗
NASA NTRS1983

Review and verification of CARE 3 mathematical model and code

The CARE-III mathematical model and code verification performed by Boeing Computer Services were documented. The mathematical model was verified for permanent and intermittent faults. The transient fault model was not addressed. The code verification was performed on CARE-III, Version 3. A CARE III Version 4, which corrects deficiencies identified in Version 3, is being developed.

Rose, D. M.↗
NASA NTRS1980

Mathematical modeling of the aerodynamics of high-angle-of-attack maneuvers

This paper is a review of the current state of aerodynamic mathematical modeling for aircraft motions at high angles of attack. The mathematical model serves to define a set of characteristic motions from whose known aerodynamic responses the aerodynamic response to an arbitrary high angle-of-attack flight maneuver can be predicted. Means are explored of obtaining stability parameter information in terms of the characteristic motions, whether by wind-tunnel experiments, computational methods, or by parameter-identification methods applied to flight-test data. A rationale is presented for selecting and verifying the aerodynamic mathematical model at the lowest necessary level of complexity. Experimental results describing the wing-rock phenomenon are shown to be accommodated within the most recent mathematical model by admitting the existence of aerodynamic hysteresis in the steady-state variation of the rolling moment with roll angle. Interpretation of the experimental results in terms of bifurcation theory reveals the general conditions under which aerodynamic hysteresis must exist.

Schiff, L. B.↗
DOE OSTI2020

Effect of hydrophobic ionic liquids aqueous solubility on metal extraction from hydrochloric acid media: Mathematical modelling and trivalent thallium behavior

A mathematical model to explain cations’ solubility of both protic and aprotic ionic liquids in a wide range of hydrochloric acid solutions has been developed. The concept of this model is based on an assumption of the mineral acid extraction into the organic phase, formation of a salt there between an ionic liquid cation and chloride-anion due to ions recombination and partial salt back-extraction. The proposed approach allows estimating corresponding extraction constants. Comparison of calculated and experimentally measured solubility product constants shows that they are in good agreement. It has been determined also that the more the hydrophilicity of the ionic liquids’ cation the more hydrochloric acid is extracted. Furthermore, this model has been utilized to facilitate analysis of thallium transfer into hydrophobic ionic liquids providing insights into the mechanism of metal extraction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2003

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Martin, Michael A.↗
NASA NTRS2005

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Seymour, David C.↗