Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Mathematics”

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 1,333 records · Page 74

Symposium on Combustion /International/, 16th, Massachusetts Institute of Technology, Cambridge, Mass., August 15-20, 1976, Proceedings

Aspects of combustion technology in power systems are considered, taking into account a combustion in large boilers, the control of over-all thermal efficiency of combustion heating systems, a comparison of mathematical models of the radiative behavior of a large-scale experimental furnace, a concentric multiannular swirl burner, and the effects of water introduction on diesel engine combustion and emissions. Attention is also given to combustion and related processes in energy production from coal, spray and droplet combustion, soot formation and growth, the kinetics of elementary reactions, flame structure and chemistry, propellant ignition and combustion, fire and explosion research, mathematical modeling, high output combustion systems, turbulent flames and combustion, and ignition, optical, and electrical properties.

Source record↗

A fixed tilt solar collector employing reversible vee-trough reflectors and vacuum tube receivers for solar heating and cooling systems

The usefulness of vee-trough concentrators in improving the efficiency and reducing the cost of collectors assembled from evacuated tube receivers was studied in the vee-trough/vacuum tube collector (VTVTC) project. The VTVTC was analyzed rigorously and various mathematical models were developed to calculate the optical performance of the vee-trough concentrator and the thermal performance of the evacuated tube receiver. A test bed was constructed to verify the mathematical analyses and compare reflectors made out of glass, Alzak and aluminized FEP Teflon. Tests were run at temperatures ranging from 95 to 180 C. Vee-trough collector efficiencies of 35 to 40% were observed at an operating temperature of about 175 C. Test results compared well with the calculated values. Predicted daily useful heat collection and efficiency values are presented for a year's duration of operation temperatures ranging from 65 to 230 C. Estimated collector costs and resulting thermal energy costs are presented. Analytical and experimental results are discussed along with a complete economic evaluation.

Selcuk, M. K.↗

Satellite orbit computation methods

Mathematical and algorithmical techniques for solution of problems in satellite dynamics were developed, along with solutions to satellite orbit motion. Dynamical analysis of shuttle on-orbit operations were conducted. Computer software routines for use in shuttle mission planning were developed and analyzed, while mathematical models of atmospheric density were formulated.

Source record↗

UTSI atmospheric science program

Two areas of research were carried out concerned with meteorological and environmental inputs to aviation systems. One effort dealt with the investigation of wind fields about bluff geometries typical of buildings or other man made obstructions to the surface wind and the behavior of craft flying through these disturbed wind fields. The second effort was the definition and mathematical models of atmospheric wind shear associated with thunderstorms, stable boundary layers, and synoptic fronts. These mathematical models can be utilized in flight simulators to train pilots and flight crews and to develop instrumentation for landing in adverse wind shear conditions.

Frost, W.↗

Fluid mechanics of continuous flow electrophoresis

The following aspects of continuous flow electrophoresis were studied: (1) flow and temperature fields; (2) hydrodynamic stability; (3) separation efficiency, and (4) characteristics of wide gap chambers (the SPAR apparatus). Simplified mathematical models were developed so as to furnish a basis for understanding the phenomena and comparison of different chambers and operating conditions. Studies of the hydrodynamic stability disclosed that a wide gap chamber may be particularly sensitive to axial temperature variations which could be due to uneven heating or cooling. The mathematical model of the separation process includes effects due to the axial velocity, electro-osmotic cross flow and electrophoretic migration, all including the effects of temperature dependent properties.

Saville, D. A.↗

Space ecosynthesis: An approach to the design of closed ecosystems for use in space

The use of closed ecological systems for the regeneration of wastes, air, and water is discussed. It is concluded that such systems, if they are to be used for the support of humans in space, will require extensive mechanical and physico-chemical support. The reason for this is that the buffering capacity available in small systems is inadequate, and that natural biological and physical regulatory mechanisms rapidly become inoperative. It is proposed that mathematical models of the dynamics of a closed ecological system may provide the best means of studying the initial problems of ecosystem closure. A conceptual and mathematical model of a closed ecosystem is described which treats the biological components as a farm, calculates the rates of flow of elements through the system by mass-balance techniques and control theory postulates, and can evaluate the requirements for mechanical buffering activities. It is suggested that study of the closure of ecosystems can significantly aid in the establishment of general principles of ecological systems.

Macelroy, R. D.↗

Wind shear modeling for aircraft hazard definition

Mathematical models of wind profiles were developed for use in fast time and manned flight simulation studies aimed at defining and eliminating these wind shear hazards. A set of wind profiles and associated wind shear characteristics for stable and neutral boundary layers, thunderstorms, and frontal winds potentially encounterable by aircraft in the terminal area are given. Engineering models of wind shear for direct hazard analysis are presented in mathematical formulae, graphs, tables, and computer lookup routines. The wind profile data utilized to establish the models are described as to location, how obtained, time of observation and number of data points up to 500 m. Recommendations, engineering interpretations and guidelines for use of the data are given and the range of applicability of the wind shear models is described.

Frost, W.↗

Development of a nonlinear switching function and its application to static lift characteristics of straight wings

A mathematical modeling technique was developed for the lift characteristics of straight wings throughout a very wide angle of attack range. The technique employs a mathematical switching function that facilitates the representation of the nonlinear aerodynamic characteristics in the partially and fully stalled regions and permits matching empirical data within + or - 4 percent of maximum values. Although specifically developed for use in modeling the lift characteristics, the technique appears to have other applications in both aerodynamic and nonaerodynamic fields.

Hewes, D. E.↗

Similarity laws of lunar and terrestrial volcanic flows

A mathematical model for the terrestrial and lunar volcanic flows is proposed. This mathematical model, which is one-dimensional, steady duct flow of a mixture of a gas and small solid particles (rock), has been analyzed in detail. The similarities and the differences of the essential features of lunar and terrestrial volcanic flows are determined. Numerical results for the equilibrium two-phase flows of lunar and terrestrial volcanics under similar conditions are presented. The main results of the theoretical model are: the lunar crater is much larger than the corresponding terrestrial crater; the exit velocity from the lunar volcanic flow may be higher than the lunar escape velocity but the exit velocity of terrestrial volcanic flow is much less than that of the linear case (this result confirms the hypothesis that Australian tektites came from the moon, as a stream of rock and gas of extremely high speed), and the thermal effects on the lunar volcanic flow are much larger than those in the terrestrial case.

Pai, S. I.↗

Effects of solid-propellant temperature gradients on the internal ballistics of the Space Shuttle

The internal ballistic effects of combined radial and circumferential grain temperature gradients are evaluated theoretically for the Space Shuttle solid rocket motors (SRMs). A simplified approach is devised for representing with closed-form mathematical expressions the temperature distribution resulting from the anticipated thermal history prior to launch. The internal ballistic effects of the gradients are established by use of a mathematical model which permits the propellant burning rate to vary circumferentially. Comparative results are presented for uniform and axisymmetric temperature distributions and the anticipated gradients based on an earlier two-dimensional analysis of the center SRM segment. The thrust imbalance potential of the booster stage is also assessed based on the difference in the thermal loading of the individual SRMs of the motor pair which may be encountered in both summer and winter environments at the launch site. Results indicate that grain temperature gradients could cause the thrust imbalance to be approximately 10% higher in the Space Shuttle than the imbalance caused by SRM manufacturing and propellant physical property variability alone.

Sforzini, R. H.↗

Load and dynamic assessment of B-52B-008 carrier aircraft for finned configuration 1 space shuttle solid rocket booster decelerator subsystem drop test vehicle. Volume 2: Airplane flutter and load analysis results

The airplane flutter and maneuver-gust load analysis results obtained during B-52B drop test vehicle configuration (with fins) evaluation are presented. These data are presented as supplementary data to that given in Volume 1 of this document. A brief mathematical description of airspeed notation and gust load factor criteria are provided as a help to the user. References are defined which provide mathematical description of the airplane flutter and load analysis techniques. Air-speed-load factor diagrams are provided for the airplane weight configurations reanalyzed for finned drop test vehicle configuration.

Quade, D. A.↗

A static acoustic signature system for the analysis of dynamic flight information

The Army family of helicopters was analyzed to measure the polar octave band acoustic signature in various modes of flight. A static array of calibrated microphones was used to simultaneously acquire the signature and differential times required to mathematically position the aircraft in space. The signature was then reconstructed, mathematically normalized to a fixed radius around the aircraft.

Ramer, D. J.↗

A fixed tilt solar collector employing reversible vee-through reflectors and evaluated tube receivers for solar heating and cooling systems

The Vee-Trough/Evacuated Tube Collector (VTETC) was analyzed rigorously and various mathematical models were developed to calculate the optical performance of the vee-trough concentrators, and the quasi-steady state thermal performance of the evacuated tube receivers. Tests were run to verify the mathematical analyses. Back-silvered glass mirror, Alzak, Aluminized Teflon, and Kinglux (electropolished aluminum reflectors) were tested. Additional tests were run at temperatures ranging from 80 to 190 C (176-374 F). For the glass mirror reflectors, peak efficiencies, based on aperture area and operating temperatures of 125 C (257 F), were over 40%. Efficiencies of about 40% were observed at temperatures of 150 C (302 F) and 30% at 175 C (347 F). Test data for several days, predicted daily useful heats, and efficiency values are presented for a full year. These theoretical values were then compared with actual data points for the same temperature range.

Selcuk, M. K.↗

Computer formulations of aircraft models for simulation studies

Recent developments in formula manipulation compilers and the design of several symbol manipulation languages, enable computers to be used for symbolic mathematical computation. A computer system and language that can be used to perform symbolic manipulations in an interactive mode are used to formulate a mathematical model of an aeronautical system. The example demonstrates that once the procedure is established, the formulation and modification of models for simulation studies can be reduced to a series of routine computer operations.

Howard, J. C.↗

Investigation of the free flow electrophoretic process. Volume 1: Executive summary

The effect of gravity on the free flow electrophoretic process was investigated. The demonstrated effects were then compared with predictions made by mathematical models. Results show that the carrier buffer flow was affected by gravity induced thermal convection and that the movement of the separating particle streams was affected by gravity induced buoyant forces. It was determined that if gravity induced buoyant forces were included in the mathematical models, then effective predictions of electrophoresis chamber separation performance were possible.

Weiss, R. A.↗

Investigation of the free flow electrophoretic process. Volume 2: Technical analysis

The effect of gravity on the free flow electrophoretic process was investigated. The demonstrated effects were then compared with predictions made by mathematical models. Results show that the carrier buffer flow was affected by gravity induced thermal convection and that the movement of the separating particle streams was affected by gravity induced buoyant forces. It was determined that if gravity induced buoyant forces were included in the mathematical models, then effective predictions of electrophoresis chamber separation performance were possible. The results of tests performed using various methods of electrophoresis using supportive media show that the mobility and the ability to separate were essentially independent of concentration, providing promise of being able to perform electrophoresis with higher inlet concentrations in space.

Weiss, R. A.↗

OPS MCC level B/C formulation requirements: Area targets and space volumes processor

The level B/C mathematical specifications for the area targets and space volumes processor (ATSVP) are described. The processor is designed to compute the acquisition-of-signal (AOS) and loss-of-signal (LOS) times for area targets and space volumes. The characteristics of the area targets and space volumes are given. The mathematical equations necessary to determine whether the spacecraft lies within the area target or space volume are given. These equations provide a detailed model of the target geometry. A semianalytical technique for predicting the AOS and LOS time periods is disucssed. This technique was designed to bound the actual visibility period using a simplified target geometry model and unperturbed orbital motion. Functional overview of the ATSVP is presented and it's detailed logic flow is described.

Bishop, M. J., Jr.↗

Research on an augmented Lagrangian penalty function algorithm for nonlinear programming

The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.

Frair, L.↗