Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximations and Expansions”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Generic hypersonic vehicle performance model

An integrated computational model of a generic hypersonic vehicle was developed for the purpose of determining the vehicle's performance characteristics, which include the lift, drag, thrust, and moment acting on the vehicle at specified altitude, flight condition, and vehicular configuration. The lift, drag, thrust, and moment are developed for the body fixed coordinate system. These forces and moments arise from both aerodynamic and propulsive sources. SCRAMjet engine performance characteristics, such as fuel flow rate, can also be determined. The vehicle is assumed to be a lifting body with a single aerodynamic control surface. The body shape and control surface location are arbitrary and must be defined. The aerodynamics are calculated using either 2-dimensional Newtonian or modified Newtonian theory and approximate high-Mach-number Prandtl-Meyer expansion theory. Skin-friction drag was also accounted for. The skin-friction drag coefficient is a function of the freestream Mach number. The data for the skin-friction drag coefficient values were taken from NASA Technical Memorandum 102610. The modeling of the vehicle's SCRAMjet engine is based on quasi 1-dimensional gas dynamics for the engine diffuser, nozzle, and the combustor with heat addition. The engine has three variable inputs for control: the engine inlet diffuser area ratio, the total temperature rise through the combustor due to combustion of the fuel, and the engine internal expansion nozzle area ratio. The pressure distribution over the vehicle's lower aft body surface, which acts as an external nozzle, is calculated using a combination of quasi 1-dimensional gas dynamic theory and Newtonian or modified Newtonian theory. The exhaust plume shape is determined by matching the pressure inside the plume, calculated from the gas dynamic equations, with the freestream pressure, calculated from Newtonian or Modified Newtonian theory. In this manner, the pressure distribution along the vehicle after body expansion surface is then determined. The aerodynamic modeling, the engine modeling, and the exhaust plume analysis are described in more detail. A description of the computer code used to perform the above calculations is given and an input/output example is then given. The computer code is available on a Macintosh floppy disk.

Chavez, Frank R.↗
NASA NTRS1993

Combining qualitative and quantitative spatial and temporal information in a hierarchical structure: Approximate reasoning for plan execution monitoring

The problem of plan generation (PG) and the problem of plan execution monitoring (PEM), including updating, queries, and resource-bounded replanning, have different reasoning and representation requirements. PEM requires the integration of qualitative and quantitative information. PEM is the receiving of data about the world in which a plan or agent is executing. The problem is to quickly determine the relevance of the data, the consistency of the data with respect to the expected effects, and if execution should continue. Only spatial and temporal aspects of the plan are addressed for relevance in this work. Current temporal reasoning systems are deficient in computational aspects or expressiveness. This work presents a hybrid qualitative and quantitative system that is fully expressive in its assertion language while offering certain computational efficiencies. In order to proceed, methods incorporating approximate reasoning using hierarchies, notions of locality, constraint expansion, and absolute parameters need be used and are shown to be useful for the anytime nature of PEM.

Hoebel, Louis J.↗
NASA NTRS1993

STE thrust chamber technology: Main injector technology program and nozzle Advanced Development Program (ADP)

The purpose of the STME Main Injector Program was to enhance the technology base for the large-scale main injector-combustor system of oxygen-hydrogen booster engines in the areas of combustion efficiency, chamber heating rates, and combustion stability. The initial task of the Main Injector Program, focused on analysis and theoretical predictions using existing models, was complemented by the design, fabrication, and test at MSFC of a subscale calorimetric, 40,000-pound thrust class, axisymmetric thrust chamber operating at approximately 2,250 psi and a 7:1 expansion ratio. Test results were used to further define combustion stability bounds, combustion efficiency, and heating rates using a large injector scale similar to the Pratt & Whitney (P&W) STME main injector design configuration including the tangential entry swirl coaxial injection elements. The subscale combustion data was used to verify and refine analytical modeling simulation and extend the database range to guide the design of the large-scale system main injector. The subscale injector design incorporated fuel and oxidizer flow area control features which could be varied; this allowed testing of several design points so that the STME conditions could be bracketed. The subscale injector design also incorporated high-reliability and low-cost fabrication techniques such as a one-piece electrical discharged machined (EDMed) interpropellant plate. Both subscale and large-scale injectors incorporated outer row injector elements with scarfed tip features to allow evaluation of reduced heating rates to the combustion chamber.

Source record↗
NASA NTRS1959

Pressure Drag of Axisymmetric Cowls Having Large Initial Lip Angles at Mach Numbers from 1.90 to 4.90

The results of experimental and theoretical data on nine cowls are presented to determine the effect of initial lip angle and projected frontal area on the cowl pressure drag coefficient at Mach numbers from 1.90 to 4.90. The experimental drag coefficients were approximated well with two-dimensional shock-expansion theory at the lower cowl-projected areas, but the difference between theory and experiment increased as the cowl area ratio was increased or as shock detachment at the cowl lips was approached. An empirical chart is presented, which can be used to estimate the cowl pressure drag coefficient of cowls approaching an elliptic contour.

Samanich, Nick E.↗
NASA NTRS1970

Intumescent Coatings as Fire Retardants

The development of fire-retardant coatings to protect surfaces which may be exposed to fire or extreme heat is a subject of intense interest to many industries. A fire-retardant paint has been developed which represents a new chemical approach for preparing intumescent coatings, and potentially, is very important to fire-prevention authorities. The requirements for a superior coating include ease of application, suitability to a wide variety of surfaces and finishes, and stability over an extended period of time within a broad range of ambient temperature and humidity conditions. These innovative coatings, when activated by the heat of a fire, react to form a thick, low-density, polymeric coating or char layer. Water vapor and sulphur dioxide are released during the intumescent reaction. Two fire-protection mechanisms thus become available: (1) the char layer retards the flow of heat, due to the extremely low thermal conductivity; and (2) water vapor and sulfur dioxide are released, providing fire quenching properties. Still another mechanism functions in cases where the char, by virtue of its high oxidation resistance and low thermal conductivity, reaches a sufficiently high temperature to re-radiate much of the incident heat load. The coatings consist of dispersions of selective salts of a nitro-amino-arornatic compound. Specifically, para-nitroaniline bisulfate and the ammonium salt of para-nitroaniline-ortho sulphuric acid (2-amino-5-nitrobenzenesulphuric acid) are used. Suitable vehicles are cellulose nitrate of lacquer grade, a nitrite-phenolic modified rubber, or epoxy-polysulfide copolymer. Three separate formulations have been developed. A solvent is usually employed, such as methylethyl ketone, butyl acetate, or toluene, which renders the coatings suitably thin and which evaporates after the coatings are applied. Generally, the intumescent material is treated as insoluble in the vehicle, and is ground and dispersed in the vehicle and solvent like an ordinary coating pigment. The char found on intumescence is better in terms of yield and physical properties than chars obtained from many previously known intumescent materials. Prior to intumescence, the coating has a density of 85 pounds per cubic foot. After intumescence, the density is approximately 0.3 pounds per cubic loot. The linear expansion of the coatings ranges from 70 to 200 times the applied coating thickness.

Parker, J. A.↗
NASA NTRS2016

Empirical Modeling of the Storm Time Innermost Magnetosphere Using Van Allen Probes and THEMIS Data: Eastward and Banana Currents

The structure of storm time currents in the inner magnetosphere, including its innermost region inside 4R(sub E), is studied for the first time using a modification of the empirical geomagnetic field model TS07D and new data from Van Allen Probes and Time History of Events and Macroscale Interactions during Substorms missions. It is shown that the model, which uses basis-function expansions instead of ad hoc current modules to approximate the magnetic field, consistently improves its resolution and magnetic field reconstruction with the increase of the number of basis functions and resolves the spatial structure and evolution of the innermost eastward current. This includes a connection between the westward ring current flowing largely at R > or approx. 3R(sub E) and the eastward ring current concentrated at R < or approx. 3R(sub E) resulting in a vortex current pattern. A similar pattern coined 'banana current' was previously inferred from the pressure distributions based on the energetic neutral atom imaging and first-principles ring current simulations. The morphology of the equatorial currents is dependent on storm phase. During the main phase, it is complex, with several asymmetries forming banana currents. Near SYM-H minimum, the banana current is strongest, is localized in the evening-midnight sector, and is more structured compared to the main phase. It then weakens during the recovery phase resulting in the equatorial currents to become mostly azimuthally symmetric.

Stephens, G. K.↗
NASA NTRS2017

Advanced Mirror Technology Development (AMTD): Year Five Status

The Advanced Mirror Technology Development (AMTD) project is in Phase 2 of a multiyear effort initiated in Fiscal Year (FY) 2012, to mature the Technology Readiness Level (TRL) of critical technologies required to enable 4-m-or-larger monolithic or segmented ultraviolet, optical, and infrared (UVOIR) space telescope primary-mirror assemblies for general astrophysics, ultra-high-contrast observations of exoplanets, and National Interest missions. Key accomplishments of 2016/17 include the completion of the Harris Corp approximately 150 Hz 1.5-meter Ultra-Low Expansion (ULE Registered trademark) mirror substrate using stacked core method to demonstrate lateral stability of the stacked core technology, as well as the characterization and validation by test of the mechanical and thermal performance of the 1.2-meter Zerodur (Registered trademark) mirror using the STOP model prediction and verification of CTE homogeneity.

Space Mirror Technology↗
NASA NTRS1975

Effects of vibrational nonequilibrium on the inviscid design of an axisymmetric nozzle for hypersonic flow

An axisymmetric, hypersonic nozzle for arc-heated air is described. The method of characteristics is used to compute an inviscid nozzle contour in which vibrational nonequilibrium is approximated by the sudden-freeze technique. Chemical reactions are shown to freeze early in the nozzle expansion, and the result of vibrational and chemical freezing on the nozzle contour is demonstrated. The approximate nozzle design is analyzed by an exact calculation based on the method of characteristics for flow with vibrational nonequilibrium. Exit profiles are computed, and the usefulness of the approximate design is discussed. An analysis of the nozzle performance at off-design conditions is presented.

Anders, J. B., Jr.↗
NASA NTRS1973

Note on the modified two-stream approximation of Sagan and Pollack.

The modified two-stream approximation is derived from the radiative transfer equation using a two-point gaussian quadrature and neglecting terms of order l equal to or greater than 3 in the Legendre expansion of the phase function. The results are compared with the Eddington approximation and with exact results for the special cases of perfect absorption, perfect scattering, and a semi-infinite layer with isotropic scattering.

Lyzenga, D. R.↗
NASA NTRS1985

CO 4.6 micron emission lines from the IRC +10216 inner envelope

Results are presented of an investigation of gas in the inner envelope of IRC +10216 at a scale size (approximately 2 arcsec) never observed previously. Observations were made at the 4.6-micrometer fundamental vibration-rotation band of CO, employing an annular observing aperture to isolate radiation resonantly scattered from the extended molecular envelope. In addition to the expected emission up to the expansion velocity of the envelope, both CO and 13CO show evidence of high-velocity features in the blue wing of the line, beyond the 15 km/s expansion velocity. A mass loss rate for the inner envelope of approximately 5-7 x 10 to the -5 solar mass per year is derived (lower than the values derived for the extended envelope from millimeter CO data).

Sahai, R.↗
NASA NTRS1977

A reexamination of two-fluid solar wind models

The two-fluid solar-wind equations have been solved by a method which is approximately 50 times faster than any previously developed, through the use of asymptotic expansions which are self-consistently iterated upon to find a solution that passes through the critical point. The energy assumptions in two-fluid solar-wind models are reexamined, and the conclusions are as follows: (1) proton thermal conduction may not be neglected, (2) the Coulomb logarithm must be calculated as a function of radius, and (3) the electron and proton temperatures at the base need not be equal, even when the time scale for energy exchange between the species is an order of magnitude smaller than the expansion time at the base. It is possible to reproduce reasonable quiet-time solar-wind parameters at 1 AU, but only if the proton temperature is approximately twice the electron temperature at 1 solar radius. This may indicate that extended proton heating is important in the outer solar corona. Winds with velocities at 1 AU of 450 km/s are generated without nonthermal energy deposition but require high proton temperatures as well as very low densities at the base. Higher-velocity solutions are not possible in a spherically symmetric geometry for reasonable particle fluxes at 1 AU, and it is suggested that these higher-velocity states probably require additional heating, acceleration mechanisms, or nonradial flow.

Nerney, S.↗
NASA NTRS1962

A Preliminary Theoretical Study of the Expansion Tube, a New Device for Producing High-Enthalpy Short-Duration Hypersonic Gas Flows

A preliminary theoretical study was conducted of a new technique for producing high-enthalpy gas flows. The device considered utilizes an unsteady expansion process for the purpose of total-enthalpy multiplication. Analyses were conducted for both perfect and real air in equilibrium, assuming idealized diaphragm bursts, centered expansion waves, and continuum flow. Results of the study showed the expansion tube capable of outperforming the conventional shock tunnel by a factor of approximately 2 in velocity for the same test-section ambient density and pressure. The degree of dissociation is low at all phases of the thermodynamic cycle in the expansion tube; thus the test-section air has a good possibility of being in equilibrium. Maximum pressures involved in the cycle for duplicating a typical reentry from, a lunar mission are low enough for existing pressure-vessel techniques. Both the known and anticipated advantages and disadvantages of this new concept are also discussed.

TUBING↗
NASA NTRS1962

A Preliminary Theoretical Study of the Expansion Tube, a New Device for Producing High-Enthalpy Short-Duration Hypersonic Gas Flows

The device considered utilizes an unsteady expansion process for the purpose of total-enthalpy multiplication. Analyses were conducted for both perfect and real air in equilibrium, assuming idealized diaphragm bursts, centered expansion waves, and continuum flow. Results of the study showed the expansion tube capable of outperforming the conventional shock tunnel by a factor of approximately 2 in velocity for the same test-section ambient density and pressure. The degree of dissociation is low at all phases of the thermodynamic cycle in the expansion tube; thus the test-section air has a good possibility of being in equilibrium. Maximum pressures involved in the cycle for duplicating a typical reentry from a lunar mission are low enough for existing pressure-vessel techniques. Both the known and anticipated advantages and disadvantages of this new concept are also discussed.

Trimpi, Robert L.↗
NASA NTRS1975

Thermally generated magnetic fields in laser-driven compressions and explosions

The evolution of thermally generated magnetic fields in a plasma undergoing a nearly spherically symmetric adiabatic compression or expansion is calculated. The analysis is applied to obtain approximate results for the development of magnetic fields in laser-driven compression and explosion of a pellet of nuclear fuel. Localized sources, such as those occurring at composition boundaries in structured pellets or at shock fronts, give stronger fields than those deriving from smoothly distributed asymmetries. Although these fields may approach 10 million G in the late stages of compression, this is not expected to present difficulties for the compression process. Assuming ignition of a nuclear explosion occurs, the sources become much stronger, and values of approximately 10 billion G are obtained at tamper boundaries assuming a 20% departure from spherical symmetry during the explosion.

Tidman, D. A.↗
NASA NTRS1982

Solution of second-order linear system by matched asymptotic expansions

Matched asymptotic expansions (MAE) are used to obtain a first order approximation to the solution of a singularly perturbed second order system. A special case is considered in which the uniform asymptotic solution obtained by MAE is shown to converge to the exact solution. Ways in which the method can be used to sole higher-order linear systems, including those which are not singularly perturbed, are also discussed.

Ardema, M. D.↗
NASA NTRS1986

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x(t)) + the sum to m terms(i=1) u sub i (t)g sub i (x(t)) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗