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NASA NTRS1996

The Parent Magmas of the Cumulate Eucrites: A Mass Balance Approach

The cumulate eucrite meteorites are gabbros that are related to the eucrite basalt meteorites. The eucrite basalts are relatively primitive (nearly flat REE patterns with La approx. 8-30 x CI), but the parent magmas of the cumulate eucrites have been inferred as extremely evolved (La to greater than 100 x CI). This inference has been based on mineral/magma partitioning, and on mass balance considering the cumulate eucrites as adcumulates of plagioclase + pigeonite only; both approaches have been criticized as inappropriate. Here, mass balance including magma + equilibrium pigeonite + equilibrium plagiociase is used to test a simple model for the cumulate eucrites: that they formed from known eucritic magma types, that they consisted only of magma + crystals in chemical equilibrium with the magma, and that they were closed to chemical exchange after the accumulation of crystals. This model is tested for major and Rare Earth Elements (REE). The cumulate eucrites Serra de Mage and Moore County are consistent, in both REE and major elements, with formation by this simple model from a eucrite magma with a composition similar to the Nuevo Laredo meteorite: Serra de Mage as 14% magma, 47.5% pigeonite, and 38.5% plagioclase; Moore County as 35% magma, 37.5% pigeonite, and 27.5% plagioclase. These results are insensitive to the choice of mineral/magma partition coefficients. Results for the Moama cumulate eucrite are strongly dependent on choice of partition coefficients; for one reasonable choice, Moama's composition can be modeled as 4% Nuevo Laredo magma, 60% pigeonite, and 36% plagioclase. Selection of parent magma composition relies heavily on major elements; the REE cannot uniquely indicate a parent magma among the eucrite basalts. The major element composition of Y-791195 can be fit adequately as a simple cumulate from any basaltic eucrite composition. However, Y-791195 has LREE abundances and La/Lu too low to be accommodated within the model using any basaltic eucrite composition and any reasonable partition coefficients. Postcumulus loss of incompatible elements seems possible. It is intriguing that Serra de Mage, Moore County, and Moama are consistent with the same parental magma; could they be from the same igneous body on the eucrite parent asteroid (4 Vesta)?

Treiman, Allan H.↗

NASA NTRS2000

GRACE Mission Design: Impact of Uncertainties in Disturbance Environment and Satellite Force Models

The Gravity Recovery and Climate Experiment (GRACE) primary mission will be performed by making measurements of the inter-satellite range change between two co-planar, low altitude, near-polar orbiting satellites. Understanding the uncertainties in the disturbance environment, particularly the aerodynamic drag and torques, is critical in several mission areas. These include an accurate estimate of the spacecraft orbital lifetime, evaluation of spacecraft attitude control requirements, and estimation of the orbital maintenance maneuver frequency necessitated by differences in the drag forces acting on both satellites. The FREEMOL simulation software has been developed and utilized to analyze and suggest design modifications to the GRACE spacecraft. Aerodynamic accommodation bounding analyses were performed and worst-case envelopes were obtained for the aerodynamic torques and the differential ballistic coefficients between the leading and trailing GRACE spacecraft. These analyses demonstrate how spacecraft aerodynamic design and analysis can benefit from a better understanding of spacecraft surface accommodation properties, and the implications for mission design constraints such as formation spacing control.

Mazanek, Daniel D.↗

NASA NTRS2000

Aerothermal Analysis and Design of the Gravity Recovery and Climate Experiment (GRACE) Spacecraft

The Gravity Recovery and Climate Experiment (GRACE) primary mission will be performed by making measurements of the inter-satellite range change between two co-planar, low altitude near-polar orbiting satellites. Understanding the uncertainties in the disturbance environment, particularly the aerodynamic drag and torques, is critical in several mission areas. These include an accurate estimate of the spacecraft orbital lifetime, evaluation of spacecraft attitude control requirements, and estimation of the orbital maintenance maneuver frequency necessitated by differences in the drag forces acting on both satellites. The FREEMOL simulation software has been developed and utilized to analyze and suggest design modifications to the GRACE spacecraft. Aerodynamic accommodation bounding analyses were performed and worst-case envelopes were obtained for the aerodynamic torques and the differential ballistic coefficients between the leading and trailing GRACE spacecraft. These analyses demonstrate how spacecraft aerodynamic design and analysis can benefit from a better understanding of spacecraft surface accommodation properties, and the implications for mission design constraints such as formation spacing control.

Mazanek, Daniel D.↗

NASA NTRS1973

Effects of physical librations of the moon on the orbital elements of a lunar satellite.

Physical librations of the moon are small cyclic perturbations with periods of one month and longer, and amplitudes of 100 arc seconds or less. This paper gives data on the magnitude of the physical librations, the geometrical effects on the orbital elements, and the equivalent changes in the coefficients in the gravitational potential. It is shown that geometrical effects can be accommodated either by using an inertial axes system or by compensating for the lunar librations and precession when the selenographic axes are used. Further, it is shown that physical effects are small and negligible for all but the most exacting endeavors.

Ferrari, A. J.↗

NASA NTRS1993

Techniques for estimating Space Station aerodynamic characteristics

A method was devised and calculations were performed to determine the effects of reflected molecules on the aerodynamic force and moment coefficients for a body in free molecule flow. A procedure was developed for determining the velocity and temperature distributions of molecules reflected from a surface of arbitrary momentum and energy accommodation. A system of equations, based on momentum and energy balances for the surface, incident, and reflected molecules, was solved by a numerical optimization technique. The minimization of a 'cost' function, developed from the set of equations, resulted in the determination of the defining properties of the flow reflected from the arbitrary surface. The properties used to define both the incident and reflected flows were: average temperature of the molecules in the flow, angle of the flow with respect to a vector normal to the surface, and the molecular speed ratio. The properties of the reflected flow were used to calculate the contribution of multiply reflected molecules to the force and moments on a test body in the flow. The test configuration consisted of two flat plates joined along one edge at a right angle to each other. When force and moment coefficients of this 90 deg concave wedge were compared to results that did not include multiple reflections, it was found that multiple reflections could nearly double lift and drag coefficients, with nearly a 50 percent increase in pitching moment for cases with specular or nearly specular accommodation. The cases of diffuse or nearly diffuse accommodation often had minor reductions in axial and normal forces when multiple reflections were included. There were several cases of intermediate accommodation where the addition of multiple reflection effects more than tripled the lift coefficient over the convex technique.

Thomas, Richard E.↗

NASA NTRS1991

Joining of materials with engineered interlayers

A reliable method to join a variety of different materials is developed which uses engineered coatings to produce strong bonds by solid-state techniques at low temperatures (300-400 C). The strong bonds are capable of accommodating the strains created between Si and most substrates due to differences in thermal expansion coefficients. The approach encompasses two phases: noble metal compliant interlayers and functionally gradient interlayer bonding. Preliminary results are presented and the Ag interlayer bonds are microstructurally characterized confirming that the planar magnetron sputtered coatings/bonds are fully dense and metallurgically sound.

Challenger, Kenneth D.↗

NASA NTRS1995

Theoretical overview and modeling of the sodium and potassium atmospheres of mercury

A general theoretical overview for the sources, sinks, gas-surface interactions, and transport dynamics of sodium and potassium in the exospheric atmsophere of Mercury is given. Information for these four factors, which control the spatial distribution of these two alkali-group gases about the planet, is incorporated in numerical models. The spatial nature and relative importance of the initial source atom atmosphere and the ambient (ballistic hopping) atom atmosphere are then examined and are shown to be controlled and coupled to a great extent by the extremely large and variable solar radiation acceleration experienced by sodium and potassium as they resonantly scatter solar photons. The lateral (antisunward) transport rate of thermally accommodated sodium and potassium ambient atoms is shown to be driven by the solar radiation acceleration and, over a significant portion of Mercury's orbit about the Sun, is sufficiently rapid to be competitive with the short photoionization lifetimes for these atoms when they are located on the summit surface near or within about 30 deg of the terminator. The lateral transport rate is characterized by a migration time determined by model calculations for an ensemble of atoms initially starting at a point source on the surface (i.e., a numerical spacetime dependent Green's function). Four animations for the spacetime evolution of the sodium (or potassium) atmosphere produced by a point source on the surface are presented on a videotape format. For extended surface sources for sodium and potassium, the local column density is determined by competition between the photoionization lifetimes and the lateral transport times of atoms originating from different surface source locations. Sodium surface source fluxes (referenced to Mercury at perihelion) that are required on the sunlit hemisphere to reproduce the typically observed several megarayleighs of D2 emission-line brightness and the inferred column densities of 1-2 x 10(exp 11) atoms per sq cm range from approximately 2-5 x 10(exp 7) atoms/sq cm/sec. The sodium model is applied to study observational data that document an anticorrelation in the average sodium column density and solar radiation acceleration. Lateral transport driven by the solar radiation acceleration is shown to produce this behavior for combinations of different sources and surface accomodation coefficients. The best fit model fits to the observational data require a significant degree of thermal accommodation of the ambient sodium atoms to the surface and a source rate that decreases as an inverse power of 1.5 to 2 in heliocentric distance.

Smyth, William H.↗

NASA NTRS1986

Symbolic generation of elastic rotor blade equations using a FORTRAN processor and numerical study on dynamic inflow effects on the stability of helicopter rotors

The process of performing an automated stability analysis for an elastic-bladed helicopter rotor is discussed. A symbolic manipulation program, written in FORTRAN, is used to aid in the derivation of the governing equations of motion for the rotor. The blades undergo coupled bending and torsional deformations. Two-dimensional quasi-steady aerodynamics below stall are used. Although reversed flow effects are neglected, unsteady effects, modeled as dynamic inflow are included. Using a Lagrangian approach, the governing equations are derived in generalized coordinates using the symbolic program. The program generates the steady and perturbed equations and writes into subroutines to be called by numerical routines. The symbolic program can operate on both expressions and matrices. For the case of hovering flight, the blade and dynamic inflow equations are converted to equations in a multiblade coordinate system by rearranging the coefficients of the equations. For the case of forward flight, the multiblade equations are obtained through the symbolic program. The final multiblade equations are capable of accommodating any number of elastic blade modes. The computer implementation of this procedure consists of three stages: (1) the symbolic derivation of equations; (2) the coding of the equations into subroutines; and (3) the numerical study after identifying mass, damping, and stiffness coefficients. Damping results are presented in hover and in forward flight with and without dynamic inflow effects for various rotor blade models, including rigid blade lag-flap, elastic flap-lag, flap-lag-torsion, and quasi-static torsion. Results from dynamic inflow effects which are obtained from a lift deficiency function for a quasi-static inflow model in hover are also presented.

Reddy, T. S. R.↗

NASA NTRS1971

Dynamic upper atmospheric force model on stabilized vehicles for a high-precision trajectory computer program

The upper atmosphere model draws heavily on the behavior of the earth's upper atmosphere which exhibits cyclic as well as irregular variations in density profile, temperature, pressure, and composition in unison with solar activities as deduced from the more recent land-based and satellite observations. The lift and drag model is designed specifically for inertially stabilized vehicles of the Mariner class, with possible extension to gravity gradient stabilized vehicles of the GEOS class. The model considers operation in the free molecular flow regimes with large Knudsen numbers. The vehicle is considered a composite structure with basic components having well-defined shapes, each with its own surface characteristics in terms of temperature, reflectivity, and accommodation of free stream molecules. The model takes into account both the calculation of precise aerodynamic force coefficients in terms of expansion of modified Bessel functions in speed ratios and angle of attack, and approximate force coefficients when the speed ratios approach infinity. Other considerations include specular and diffused reflectivity, shielding, and shadow effects.

Khatib, A. R.↗

NASA NTRS1971

Heat transfer and forces on concave surfaces in free molecule flow.

A Monte Carlo modeling technique is described for mathematically simulating free molecular flows over a concave spherical surface and a concave cylindrical surface of finite length. The half-angle of the surfaces may vary from 0 to 90 degrees, and the incident flow may have an arbitrary speed ratio and an arbitrary angle of attack. Partial diffuse reflection and imperfect energy accommodation for molecules colliding with the surfaces are also considered. Results of heat transfer, drag and lift coefficients are presented for a variety of flow conditions. The present Monte Carlo results are shown to be in very good agreement with certain available theoretical solutions.

Fan, C.↗

NASA NTRS1981

Some applications of aerodynamic formulations to problems in aircraft dynamics

Two applications of mathematical modeling to aerodynamic problems are cussed. The first application is an investigation of the capacity of a nonlinear aerodynamic mathematical model to describe the aerodynamic reactions on an airfoil with a deflecting flap in transonic flow. Flow field computational methods are used to evaluate the nonlinear, unsteady aerodynamic data in terms of characteristic motions called for by the model. Histories of unconstrained motions of the flap are generated from the flap equations of motion, with the aerodynamic reactions specified by the mathematical model. In the second application wing rock is investigated. The most recent model accommodates experimental results wing rock by admitting the existence of aerodynamic hysteresis in the variation of the steady state rolling moment coefficient with roll angle is described.

Schiff, L. B.↗

NASA NTRS1978

Aircraft model prototypes which have specified handling-quality time histories

Several techniques for obtaining linear constant-coefficient airplane models from specified handling-quality time histories are discussed. The pseudodata method solves the basic problem, yields specified eigenvalues, and accommodates state-variable transfer-function zero suppression. The algebraic equations to be solved are bilinear, at worst. The disadvantages are reduced generality and no assurance that the resulting model will be airplane like in detail. The method is fully illustrated for a fourth-order stability-axis small motion model with three lateral handling quality time histories specified. The FORTRAN program which obtains and verifies the model is included and fully documented.

Johnson, S. H.↗

NASA NTRS1989

Free-molecule-flow force and moment coefficients of the aeroassist flight experiment vehicle

Calculated results for the aerodynamic coefficients over the range of + or - 90 deg in both pitch and yaw attitude angles for the Aeroassist Flight Experiment (AFE) vehicle in free molecule flow are presented. The AFE body is described by a large number of small flat plate surface elements whose orientations are established in a wind axes coordinate system through the pitch and yaw attitude angles. Lift force, drag force, and three components of aerodynamic moment about a specified point are computed for each element. The elemental forces and moments are integrated over the entire body, and total force and moment coefficients are computed. The coefficients are calculated for the two limiting gas-surface molecular collision conditions, namely, specular and diffuse, which assume zero and full thermal accommodation of the incoming gas molecules with the surface, respectively. The individual contribution of the shear stress and pressure terms are calculated and also presented.

Blanchard, Robert C.↗

NASA NTRS1984

Flap-lag damping of an elastic rotor blade with torsion and dynamic inflow in hover from symbolically generated equations

A program written in FORTRAN IV and coded into subroutines for subsequent numerical study is used to derive symbolically the governing equations of motion of the elastic rotor blade and the dynamic inflow equations. By rearranging the coefficients of the equations, the blade and dynamic inflow equations are converted into equations in a multiblade coordinated system. The final multiblade equations can accommodate any number of elastic blade modes. It is noted that with a given data set, the entire process, from the derivation of the equations to the numerical calculations, is computerized and requires only limited user interface. To demonstrate the usefulness of the approach, damping data in hover with and without dynamic inflow effects are presented for various rotor blade models, including flap-lag, flap-lag-torsion, quasi-static torsion, and rigid blade lag-flap.

Reddy, T. S. R.↗

NASA NTRS1976

Aircraft model prototypes which have specified handling-quality time histories

Several techniques for obtaining linear constant-coefficient airplane models from specified handling-quality time histories are discussed. One technique, the pseudodata method, solves the basic problem, yields specified eigenvalues, and accommodates state-variable transfer-function zero suppression. The method is fully illustrated for a fourth-order stability-axis small-motion model with three lateral handling-quality time histories specified. The FORTRAN program which obtains and verifies the model is included and fully documented.

Johnson, S. H.↗

NASA NTRS1983

Accommodation of practical constraints by a linear programming jet select

An experimental spacecraft control system will be incorporated into the Space Shuttle flight software and exercised during a forthcoming mission to evaluate its performance and handling qualities. The control system incorporates a 'phase space' control law to generate rate change requests and a linear programming jet select to compute jet firings. Posed as a linear programming problem, jet selection must represent the rate change request as a linear combination of jet acceleration vectors where the coefficients are the jet firing times, while minimizing the fuel expended in satisfying that request. This problem is solved in real time using a revised Simplex algorithm. In order to implement the jet selection algorithm in the Shuttle flight control computer, it was modified to accommodate certain practical features of the Shuttle such as limited computer throughput, lengthy firing times, and a large number of control jets. To the authors' knowledge, this is the first such application of linear programming. It was made possible by careful consideration of the jet selection problem in terms of the properties of linear programming and the Simplex algorithm. These modifications to the jet select algorithm may by useful for the design of reaction controlled spacecraft.

Bergmann, E.↗

NASA NTRS1990

Flow boiling with enhancement devices for cold plate coolant channel design

The use of flow boiling for thermal energy transport is intended to provide an alternative for accommodating higher heat fluxes in commercial space systems. The objectives are to: (1) examine the variations in both the mean and local (axial and circumferential) heat transfer coefficients for a circular coolant channel with either smooth walls, spiral fins, or both spiral fins and a twisted tape; (2) examine the effects of channel diameter and subcooling; and (3) develop an improved reduction analysis and/or suggest possible heat transfer correlation of the present data. Freon-11 is the working fluid. Two-dimensional (circumferential and axial) wall temperature distributions were measured for coolant channels with the above noted internal geometries. The flow regimes which are being studied are: (1) single phase; (2) subcooled flow boiling; and (3) stratified flow boiling. The inside diameter of all test sections is near 1.0 cm. Cicumferentially averaged heat transfer coefficients at several axial locations were obtained for selected coolant channels for a mass velocity of 210 kg/sq m s, an exit pressure of 0.19 MPa (absolute), and an inlet subcooling of 20.8 C. Overall (averaged over the entire channel) heat transfer coefficients were compared for the above channel geometries. This comparison showed that the channel with large pitch spiral fins had higher heat transfer coefficients at all power levels.

Boyd, Ronald D., Sr.↗

NASA NTRS2014

Supersonic Retropropulsion Test 1853 in NASA LaRC Unitary Plan Wind Tunnel Test Section 2

A supersonic retropropulsion experiment was conducted in the Langley Research Center Unitary Plan Wind Tunnel Test Section 2 at Mach numbers of 2.4, 3.5, and 4.6. Intended as a code validation effort, this study used pretest computations to size and refine the model such that tunnel blockage and internal flow separations were minimized. A 5-in diameter 70 degree sphere-cone forebody, which can accommodate up to four 4:1 area ratio nozzles, followed by a 9.55 inches long cylindrical aft body was selected for this test after computational maturation. The primary measurements for this experiment were high spatial-density surface pressures. In addition, high speed schlieren video and internal pressures and temperatures were acquired. The test included parametric variations in the number of nozzles utilized, thrust coefficients (roughly 0 to 4), and angles of attack (-8 to 20 degrees). The run matrix was developed to also allow quantification of various sources of experimental uncertainty, such as random errors due to run-to-run variations and systematic errors due to flowfield or model misalignments. To accommodate the uncertainty assessment, many runs and replicates were conducted with the model at various locations within the tunnel and with model roll angles of 0, 60, 120, and 180 degrees. This test report provides operational details of the experiment, contains a review of trends, and provides all schlieren and pressure results within appendices.

Berry, Scott A.↗