SEARCH · Engineering Papers

Results for “mathematical physics”

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.

SourceResearch connectionFrom yearThrough year

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

At least 919 records · Page 51

All sources NASA NTRS DOE OSTI

NASA NTRS1987

Space Station/Shuttle Orbiter dynamics during docking

Mathematical models of a reference space station configuration (Power Tower) and a Space Shuttle Orbiter are developed and used to study the dynamic behavior of the Space Station/Orbiter system just prior to and subsequent to an impulsive docking of the two spacecraft. The physical model of the space station is a collection of rigid and flexible bodies. The orbiter is modeled as a rigid body. An algorithm developed for use in digitally simulating the dynamics of the system is described and results of its application are presented.

Fitz-Coy, N. G.↗

NASA NTRS2017

Development of a Three-Dimensional, Unstructured Material Response Design Tool

A preliminary verification and validation of a new material response model is presented. This model, Icarus, is intended to serve as a design tool for the thermal protection systems of re-entry vehicles. Currently, the capability of the model is limited to simulating the pyrolysis of a material as a result of the radiative and convective surface heating imposed on the material from the surrounding high enthalpy gas. Since the major focus behind the development of Icarus has been model extensibility, the hope is that additional physics can be quickly added. This extensibility is critical since thermal protection systems are becoming increasing complex, e.g. woven carbon polymers. Additionally, as a three-dimensional, unstructured, finite-volume model, Icarus is capable of modeling complex geometries. In this paper, the mathematical and numerical formulation is presented followed by a discussion of the software architecture and some preliminary verification and validation studies.

Thermal Protection System↗

NASA NTRS2014

Elastic Model Transitions: A Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes a hybrid approach for determining physical displacements by augmenting the original quadratically constrained least squares (LSQI) algorithm with Direct Shape Mapping (DSM) and modifying the energy constraints. The approach presented is applicable to simulation of the elastic behavior of launch vehicles and other structures that utilize discrete LTI finite element model (FEM) derived mode sets (eigenvalues and eigenvectors) that are propagated throughout time. The time invariant nature of the elastic data presents a problem of how to properly transition elastic states from the prior to the new model while preserving motion across the transition and ensuring there is no truncation or excitation of the system. A previous approach utilizes a LSQI algorithm with an energy constraint to effect smooth transitions between eigenvector sets with no requirement that the models be of similar dimension or have any correlation. This approach assumes energy is conserved across the transition, which results in significant non-physical transients due to changing quasi-steady state energy between mode sets, a phenomenon seen when utilizing a truncated mode set. The computational burden of simulating a full mode set is significant so a subset of modes is often selected to reduce run time. As a result of this truncation, energy between mode sets may not be constant and solutions across transitions could produce non-physical transients. In an effort to abate these transients an improved methodology was developed based on the aforementioned approach, but this new approach can handle significant changes in energy across mode set transitions. It is proposed that physical velocities due to elastic behavior be solved for using the LSQI algorithm, but solve for displacements using a two-step process that independently addresses the quasi-steady-state and non-steady-state contributions to the elastic displacement. For structures subject to large external forces, such as thrust or atmospheric drag, it is imperative to capture these forces when solving for elastic displacement. To simplify the mathematical formulation, assumptions are made regarding mass matrix normalization, constant external forcing, and constant viscous damping. These simplifications allow for direct solutions to the quasi-steady-state displacements through a process titled Direct Shape Mapping. DSM solves for the displacements using the eigenvalues of the elastic modes and the external forcing and returns a set of elastic displacements dictated by the eigenvectors of the post-transition mode set. For the non-steady-state contributions to displacement we formulate a LSQI problem that is constrained by energy of the non-steady state terms. The contributions from the quasi-steady-state and non-steady state solutions are then combined to obtain the physical displacements associated with the new set of eigenvectors. Results for the LSQI-DSM approach show significant reduction/complete removal of transients across mode set transitions while maintaining elastic motion from the prior state. For time propagation applications employing discrete elastic models that need to be transitioned in time and where running with full a full mode set is not feasible, the method developed offers a practical solution to simulating vehicle elasticity.

Hannan, Mike R.↗

NASA NTRS1993

Three-dimensional solidification and melting using magnetic field control

A new two-fluid mathematical model for fully three dimensional steady solidification under the influence of an arbitrary acceleration vector and with or without an arbitrary externally applied steady magnetic field have been formulated and integrated numerically. The model includes Joule heating and allows for separate temperature dependent physical properties within the melt and the solid. Latent heat of phase change during melting/solidification was incorporated using an enthalpy method. Mushy region was automatically captured by varying viscosity orders of magnitude between liquidus and solidus temperature. Computational results were obtained for silicon melt solidification in a parallelepiped container cooled from above and from a side. The results confirm that the magnetic field has a profound influence on the solidifying melt flow field thus changing convective heat transfer through the boundaries and the amount and shape of the solid accrued. This suggests that development of a quick-response algorithm for active control of three dimensional solidification is feasible since it would require low strength magnetic fields.

Dulikravich, George S.↗

NASA NTRS2002

Reentry Vehicle Flight Controls Design Guidelines: Dynamic Inversion

This report addresses issues in developing a flight control design for vehicles operating across a broad flight regime and with highly nonlinear physical descriptions of motion. Specifically it addresses the need for reentry vehicles that could operate through reentry from space to controlled touchdown on Earth. The latter part of controlled descent is achieved by parachute or paraglider - or by all automatic or a human-controlled landing similar to that of the Orbiter. Since this report addresses the specific needs of human-carrying (not necessarily piloted) reentry vehicles, it deals with highly nonlinear equations of motion, and then-generated control systems must be robust across a very wide range of physics. Thus, this report deals almost exclusively with some form of dynamic inversion (DI). Two vital aspects of control theory - noninteracting control laws and the transformation of nonlinear systems into equivalent linear systems - are embodied in DI. Though there is no doubt that the mathematical tools and underlying theory are widely available, there are open issues as to the practicality of using DI as the only or primary design approach for reentry articles. This report provides a set of guidelines that can be used to determine the practical usefulness of the technique.

Ito, Daigoro↗

NASA NTRS2002

Overall Traveling-Wave-Tube Efficiency Improved By Optimized Multistage Depressed Collector Design

Depressed Collector Design The microwave traveling wave tube (TWT) is used widely for space communications and high-power airborne transmitting sources. One of the most important features in designing a TWT is overall efficiency. Yet, overall TWT efficiency is strongly dependent on the efficiency of the electron beam collector, particularly for high values of collector efficiency. For these reasons, the NASA Glenn Research Center developed an optimization algorithm based on simulated annealing to quickly design highly efficient multistage depressed collectors (MDC's). Simulated annealing is a strategy for solving highly nonlinear combinatorial optimization problems. Its major advantage over other methods is its ability to avoid becoming trapped in local minima. Simulated annealing is based on an analogy to statistical thermodynamics, specifically the physical process of annealing: heating a material to a temperature that permits many atomic rearrangements and then cooling it carefully and slowly, until it freezes into a strong, minimum-energy crystalline structure. This minimum energy crystal corresponds to the optimal solution of a mathematical optimization problem. The TWT used as a baseline for optimization was the 32-GHz, 10-W, helical TWT developed for the Cassini mission to Saturn. The method of collector analysis and design used was a 2-1/2-dimensional computational procedure that employs two types of codes, a large signal analysis code and an electron trajectory code. The large signal analysis code produces the spatial, energetic, and temporal distributions of the spent beam entering the MDC. An electron trajectory code uses the resultant data to perform the actual collector analysis. The MDC was optimized for maximum MDC efficiency and minimum final kinetic energy of all collected electrons (to reduce heat transfer). The preceding figure shows the geometric and electrical configuration of an optimized collector with an efficiency of 93.8 percent. The results show the improvement in collector efficiency from 89.7 to 93.8 percent, resulting in an increase of three overall efficiency points. In addition, the time to design a highly efficient MDC was reduced from a month to a few days. All work was done in-house at Glenn for the High Rate Data Delivery Program. Future plans include optimizing the MDC and TWT interaction circuit in tandem to further improve overall TWT efficiency.

Vaden, Karl R.↗

NASA NTRS2012

The International Space Station: A National Laboratory

After more than a decade of assembly missions and the end of the space shuttle program, the International Space Station (ISS) has reached assembly completion. With other visiting spacecraft now docking with the ISS on a regular basis, the orbiting outpost now serves as a National Laboratory to scientists back on Earth. The ISS has the ability to strengthen relationships between NASA, other Federal entities, higher educational institutions, and the private sector in the pursuit of national priorities for the advancement of science, technology, engineering, and mathematics. The ISS National Laboratory also opens new paths for the exploration and economic development of space. In this presentation we will explore the operation of the ISS and the realm of scientific research onboard that includes: (1) Human Research, (2) Biology & Biotechnology, (3) Physical & Material Sciences, (4) Technology, and (5) Earth & Space Science.

Giblin, Timothy W.↗

NASA NTRS1994

An Earth Albedo Model: A Mathematical Model for the Radiant Energy Input to an Orbiting Spacecraft Due to the Diffuse Reflectance of Solar Radiation from the Earth Below

Past missions have shown that the earth's albedo can have a significant effect on the sun sensors used for spacecraft attitude control information. In response to this concern, an algorithm was developed to simulate this phenomenon, consisting of two parts, the physical model of albedo and its effect on the sun sensors. This paper contains the theoretical development of this model, practical operational notes, and its implementation in a FORTRAN subroutine.

Flatley, Thomas W.↗

NASA NTRS1981

An efficient code for the simulation of nonhydrostatic stratified flow over obstacles

The physical model and computational procedure of the code is described in detail. The code is validated in tests against a variety of known analytical solutions from the literature and is also compared against actual mountain wave observations. The code will receive as initial input either mathematically idealized or discrete observational data. The form of the obstacle or mountain is arbitrary.

Pihos, G. G.↗

NASA NTRS1985

NASA/JSC orbital debris study: Debris model

The possibility of the creation of a debris belt around the Earth is discussed. A computer model which describes the near-Earth space environment created by the existing spacecraft and fragments from the associated spent launching vehicle attachments and explosions was developed. The present debris model adopts the mathematical formulations published in a paper by Kessler. Thus, the model uses more rigorous mathematical formulation in calculating the collision rate between two orbiting objects than the one published by Kessler and Cour-Palais (1978). The present model contains many general but detailed analyses on the debris environment such as manipulating and/or sorting the existing debris objects, the physical dimensions of the objects and extrapolating the number density describing to include the unobservable small objects.

Roberts, J. B.↗

NASA NTRS1989

Contamination concerns in the modular containerless processing facility

This paper describes the problems of the control and management of contamination in the Modular Containerless Processing Facility (MCPF), that is being currently developed at the JPL for the Space Station, and in the MCPF's precursor version, called the Drop Physics Module (DPM), which will be carried aboard one or more Space Shuttle missions. Attention is given to the identification of contamination sources, their mode of transport to the sample positioned within the chamber, and the protection of the sample, as well as to the mathematical simulatiom of the contaminant transport. It is emphasized that, in order to choose and implement the most appropriate contamination control strategy for each investigator, a number of simplified mathematical simulations will have to be developed, and ground-based contamination experiments will have to be carried out with identical materials.

Seshan, P. K.↗

NASA NTRS1993

Boundary layer receptivity and control

Receptivity processes initiate natural instabilities in a boundary layer. The instabilities grow and eventually break down to turbulence. Consequently, receptivity questions are a critical element of the analysis of the transition process. Success in modeling the physics of receptivity processes thus has a direct bearing on technological issues of drag reduction. The means by which transitional flows can be controlled is also a major concern: questions of control are tied inevitably to those of receptivity. Adjoint systems provide a highly effective mathematical method for approaching many of the questions associated with both receptivity and control. The long term objective is to develop adjoint methods to handle increasingly complex receptivity questions, and to find systematic procedures for deducing effective control strategies. The most elementary receptivity problem is that in which a parallel boundary layer is forced by time-harmonic sources of various types. The characteristics of the response to such forcing form the building blocks for more complex receptivity mechanisms. The first objective of this year's research effort was to investigate how a parallel Blasius boundary layer responds to general direct forcing. Acoustic disturbances in the freestream can be scattered by flow non-uniformities to produce Tollmien-Schlichting waves. For example, scattering by surface roughness is known to provide an efficient receptivity path. The present effort is directed towards finding a solution by a simple adjoint analysis, because adjoint methods can be extended to more complex problems. In practice, flows are non-parallel and often three-dimensional. Compressibility may also be significant in some cases. Recent developments in the use of Parabolized Stability Equations (PSE) offer a promising possibility. By formulating and solving a set of adjoint parabolized equations, a method for mapping the efficiency with which external forcing excites the three-dimensional motions of a non-parallel boundary layer was developed. The method makes use of the same computationally efficient formulation that makes the PSE currently so appealing. In the area of flow control, adjoint systems offer a powerful insight into the effect of control forces. One of the simplest control strategies for boundary layers involves the application of localized mean wall suction.

Hill, D. C.↗

NASA NTRS1996

Buoyancy-Driven Heat Transfer During Application of a Thermal Gradient for the Study of Vapor Deposition at Low Pressure Using and Ideal Gas

A mathematical model has been developed to determine heat transfer during vapor deposition of source materials under a variety of orientations relative to gravitational accelerations. The model demonstrates that convection can occur at total pressures as low as 10-2 mm Hg. Through numerical computation, using physical material parameters of air, a series of time steps demonstrates the development of flow and temperature profiles during the course of vapor deposition. These computations show that in unit gravity vapor deposition occurs by transport through a fairly complicated circulating flow pattern when applying heat to the bottom of the vessel with parallel orientation with respect to the gravity vector. The model material parameters for air predict the effect of kinematic viscosity to be of the same order as thermal diffusivity, which is the case for Prandtl number approx. 1 fluids. Qualitative agreement between experiment and the model indicates that 6-(2-methyl-4-nitroanilino)-2,4-hexadiyn-l-ol (DAMNA) at these pressures indeed approximates an ideal gas at the experiment temperatures, and may validate the use of air physical constants. It is apparent that complicated nonuniform temperature distribution in the vapor could dramatically affect the homogeneity, orientation, and quality of deposited films. The experimental test i's a qualitative comparison of film thickness using ultraviolet-visible spectroscopy on films generated in appropriately oriented vapor deposition cells. In the case where heating of the reaction vessel occurs from the top, deposition of vapor does not normally occur by convection due to a stable stratified medium. When vapor deposition occurs in vessels heated at the bottom, but oriented relative to the gravity vector between these two extremes, horizontal thermal gradients induce a complex flow pattern. In the plane parallel to the tilt axis, the flow pattern is symmetrical and opposite in direction from that where the vessel is positioned vertically. The ground-based experiments are sufficient preliminary tests of theory and should be of significant interest regarding vapor deposited films in microgravity.

Frazier, D. O.↗

NASA NTRS1998

Analyzing Space-Based Interferometric Measurements of Stars and Network Measurements of Gamma-Ray Bursts

Since the announcement of the discovery of sources of bursts of gamma-ray radiation in 1973, hundreds more reports of such bursts have now been published. Numerous artificial satellites have been equipped with gamma-ray detectors including the very successful Compton Gamma Ray Observatory BATSE instrument. Unfortunately, we have made no progress in identifying the source(s) of this high energy radiation. We suspected that this was a consequence of the method used to define gamma-ray burst source "error boxes." An alternative procedure to compute gamma-ray burst source positions, with a purely physical underpinning, was proposed in 1988 by Taff. Since then we have also made significant progress in understanding the analytical nature of the triangulation problem and in computing actual gamma-ray burst positions and their corresponding error boxes. For the former, we can now mathematically illustrate the crucial role of the area occupied by the detectors, while for the latter, the Atteia et al. (1987) catalog has been completely re-reduced. There are very few discrepancies in locations between our results and those of the customary "time difference of arrival" procedure. Thus, we have numerically demonstrated that the end result, for the positions, of these two very different-looking procedures is the same. Finally, for the first time, we provide a sample of realistic "error boxes" whose non-simple shapes vividly portray the difficulty of burst source localization.

Taff, L. G.↗

NASA NTRS1986

Boundary perturbation method for free boundary problem in convectively cooled continuous casting

Novel mathematical techniques are here used to treat general boundary conditions in convectively cooled continuous ingot casting problems, applying a constant convective heat transfer coefficient at the ingot sides (so that the temperature distribution along the sides is unknown). The problem is first inverted to treat the physical coordinates as dependent variables of temperature and heat flow, mapping the ingot into a region that is nearly rectangular. A boundary perturbation method is then used to obtain an analytical solution in this near-rectangular region. Solidification interface shapes depend on two dimensionless parameters: one is a function of the casting velocity, while the other is dependent on the convective heat transfer coefficient at the cooled wall.

Siegel, R.↗

NASA NTRS1986

Quasistatic evolution of magnetostatic coronal structures

Four separate but related studies of coronal magnetostatic equilibria under a variety of boundary conditions and distributions of coronal current are reviewed. Physically, all four studies assume an axisymmetric corona whose radial magnetic field at the coronal base is dipolar. Electric currents in the model coronas are assumed to flow in the azimuthal direction, giving rise to Lorentz forces that must be balanced by pressure gradients and gravity. Mathematically, such coronas are described by the equation of magnetostatic force balance and Ampere's law. Although highly idealized, the axisymmetric magnetostatic models described provide insights into the behavior of a variety of coronal structures. The models show how more realistic current sheet boundary conditions and coronal density variations may be modeled.

Wolfson, Richard↗

NASA NTRS1994

Preparation of course materials: Elementary mathematics of powered flight

Non-science students at William and Mary will soon be required to take a mathematics course in order to earn a bachelor's degree. A standard menu of technique courses is the usual way in which universities provide for this requirement: Trigonometry, probability, geometry for teachers, and the like. In this work, we attempt to break away from these largely unsuccessful choices. Our intent is to prepare material that sets a variety of simple mathematical procedures in the context of a commonly experienced part of students' lives: riding in commercial airplanes. The work, begun last summer at Langley, is now close to completion and trial in upcoming fall term at William and Mary. As of this writing, the narrative is complete for 12 to 14 projected sections. We have prepared material on wind triangles, wind roses, navigation maps, drag induced loss of velocity for unpowered missiles (tennis balls), luggage and its effect on center of gravity, localized magnetic declination and VOR orientation, geometry of great circles, terminal velocity for falling bodies, pressure vessels: tires and balloons and blimps, global structure of declination lines, map projections (mercator, azimuthal equidistant, Lambert), ears and their reaction to altitude change. The next section will treat lift, drag and thrust. The last will treat control surfaces. The entire approach avoids any effort to investigate mathematical topics that arise in the solution of problems. And by the same token, we avoid any organized attempt to explain aeronautical engineering, even on an elementary level. We look only at enough mathematics to do a problem and we select only engineering topics that permit some kind of (elementary) mathematical analysis. In the end, we will think of the material as successful if two things happen: Students must come away with some confidence that even lay people can quantify parts of their surroundings. Other potential instructors must be willing to gain enough familiarity with the physical content of the material so that it can be used at other universities.

Rublein, George T.↗

NASA NTRS1996

Consumption, supply and transport: self-organization without direct communication

Swimming bacteria of the species Bacillus subtilis require and consume oxygen. In static liquid cultures the cells' swimming behaviour leads them to accumulate up oxygen concentration gradients generated by consumption and supply. Since the density of bacterial cells exceeds that of the fluid in which they live, fluid regions where cells have accumulated are denser than depleted regions. These density variations cause convection. The fluid motion is dynamically maintained by the swimming of the cells toward regions of attraction: the air-fluid interface and the fluctuating advecting attractors, gradients of oxygen concentration that are embedded in the convecting fluid. Because of the fluid dynamical conservation laws, these complex physical and biological factors generate patterns ordered over distances > 10000 bacterial cell diameters. The convection enhances long-range transport and mixing of oxygen, cells and extracellular products by orders of magnitude. Thus, through the interplay of physical and biological factors, a population of undifferentiated selfish cells creates functional dynamic patterns. Populations of bacteria that have organised themselves into regularly patterned regions of vigorous convection and varying cell concentration interact with their environment as if they were one purposeful, coherent multicellular individual. The mathematical and experimental ingredients of these remarkable phenomena are presented here.

Non-NASA Center↗