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NASA NTRS1986

A numerical method for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

In the present paper, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BEC) systems has been developed and evaluated. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme and a central differencing plus artificial dissipation scheme are used to approximate the convection terms in the governing equations. Effects of these two schemes on the accuracy of numerical predictions are studied. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm, SIMPLE-C. Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present numerical method.

Chen, Y. S.↗
NASA NTRS1989

Optical interferometers for tests of relativistic gravity in space

A space-based astrometric interferometer with a large optical bandwidth is considered. POINTS (Precision Optical INTerferometry in Space) would measure the angular separation of two stars separated by about 90 deg on the sky with a nominal measurement error of 5 microarcseconds (mas). For a pair of mag 10 stars, the observation would require about 10 minutes. It is estimated that the instrument would measure daily the separation of two stars for each of about 60 pairs of stars; a random sequence of such measurements, if suitably redundant, contains the closure information necessary to detect and correct time dependent measurement biases to well below the nominal measurement accuracy. The 90 deg target separation permits absolute parallax measurements in all directions. A redundant observing schedule for 300 stars and 5 quasars would provide extra redundancy to compensate for the quasars' higher magnitude. If a nominal 30-day observation sequence were repeated 4 times per year for 10 years, stellar parameter uncertainties would be obtained of: 0.6 mas, position; 0.4 mas/y, proper motion; and 0.4 mas, parallax. This set of well-observed stars and quasars would form a rigid frame and the stars would serve as reference objects for measurements of all additional targets, as well as being targets of direct scientific interest. The instrument global data analysis since objectives are considered including a relativity test and technology.

Reasenberg, R. D.↗
NASA NTRS2019

Orbital Path and Spacecraft Attitude Correction for the MODIS Lunar Spatial Characterization

For the Moderate Resolution Imaging Spectroradiometer(MODIS) on the Terra and Aqua platforms, regularlyscheduled lunar observations using spacecraft roll maneuvershave been used extensively for sensor characterization. Whilethe primary purpose of these observations is for radiometriccalibration of the reflective solar bands, they have also beenleveraged for a number of other sensor performance assessments,such as the band-to-band (BBR) and detector-to-detector (DDR)spatial registration. The spatial registration calculations arecomplicated by the fact that the Moon does not move in astraight path across the sensor field-of-view (FOV). This path isdetermined by the relative orbital motion between the spacecraftand the Moon and the instrument attitude error that resultsfrom the roll maneuver. In this work, we develop a correctionfor the MODIS lunar spatial characterization measurements bycalculating the predicted path of the Moon across the sensor FOVusing spacecraft and lunar ephemeris data to model the relativeorbital motion between the spacecraft and the Moon along withspacecraft attitude error data acquired during the roll maneuver.The difference between measured and predicted positions of theMoon in the MODIS FOV can be used to calculate the BBRand DDR results. Since the predicted path across the FOV willbe the same for each band, the BBR results will be minimallyaffected. However, we will show that the along-scan spread inthe DDR can be significantly reduced, which results in a muchgreater consistency throughout the full mission for both Aquaand Terra MODIS.

Truman Wilson↗
NASA NTRS1999

Work on Planetary Atmospheres and Planetary Atmosphere Probes

A summary final report of work accomplished is presented. Work was performed in the following areas: (1) Galileo Probe science analysis, (2) Galileo probe Atmosphere Structure Instrument, (3) Mars Pathfinder Atmosphere Structure/Meteorology instrument, (4) Mars Pathfinder data analysis, (5) Science Definition for future Mars missions, (6) Viking Lander data analysis, (7) winds in Mars atmosphere Venus atmospheric dynamics, (8) Pioneer Venus Probe data analysis, (9) Pioneer Venus anomaly analysis, (10) Discovery Venus Probe Titan probe instrument design, and (11) laboratory studies of Titan probe impact phenomena. The work has resulted in more than 10 articles published in archive journals, 2 encyclopedia articles, and many working papers. This final report is organized around the four planets on which there was activity, Jupiter, Mars, Venus, and Titan, with a closing section on Miscellaneous Activities. A major objective was to complete the fabrication, test, and evaluation of the atmosphere structure experiment on the Galileo probe, and to receive, analyze and interpret data received from the spacecraft. The instrument was launched on April 14, 1989. Calibration data were taken for all experiment sensors. The data were analyzed, fitted with algorithms, and summarized in a calibration report for use in analyzing and interpreting data returned from Jupiter's atmosphere. The sensors included were the primary science pressure, temperature and acceleration sensors, and the supporting engineering temperature sensors. Computer programs were written to decode the Experiment Data Record and convert the digital numbers to physical quantities, i.e., temperatures, pressures, and accelerations. The project office agreed to obtain telemetry of checkout data from the probe. Work to extend programs written for use on the Pioneer Venus project included: (1) massive heat shield ablation leading to important mass loss during entry; and (2) rapid planet rotation, which introduced terms of motion not needed on Venus. When the Galileo Probe encountered Jupiter, analysis and interpretation of data commenced. The early contributions of the experiment were to define (1) the basic structure of the deep atmosphere, (2) the stability of the atmosphere, (3) the upper atmospheric profiles of density, pressure, and temperature. The next major task in the Galileo Probe project was to refine, verify and extend the analysis of the data. It was the verified, and corrected data, which indicated a dry abiabatic atmosphere within measurement accuracy. Temperature in the thermosphere was measured at 900 K. Participation in the Mars atmospheric research included: (1) work as a team member of the Mars Atmosphere Working Group, (2) contribution to the Mars Exobiology Instrument workshop, (3) asssistance in planning the Mars global network and (4) assitance in planning the Soviet-French Mars mission in 1994. This included a return to the Viking Lander parachute data to refine and improve the definition of winds between 1.5 and 4 kilometer altitude at the two entry sites. The variability of the structure of Mars atmosphere was addressed, which is known to vary with season, latitude, hemisphere and dust loading of the atmosphere. This led to work on the Pathfinder project. The probe had a deployable meteorology mast that had three temperature sensors, and a wind sensor at the tip of the mast. Work on the Titan atmospheric probe was also accomplished. This included developing an experiment proposal to the European Space Agency (ESA), which was not selected. However, as an advisor in the design and preparation of the selected experiment the researcher interacted with scientist on the Huygens Probe Atmosphere Structure Experiment. The researcher also participated in the planning for the Venus Chemical Probe. The science objectives of the probe were to resolve unanswered questions concerning the minor species chemistry of Venus' atmosphere that control cloud formation, greenhouse effectiveness, and the thermal structure. The researcher also reviewed problems with the Pioneer Venus Probe, that caused anomalies which occurred on the Probes at and below 12.5 km level of the Venus' atmosphere. He convened and participated in a workshop that concluded the most likely hardware cause was insulation failure in the electrical harness outside the Probes' pressure vessels. It was discovered that the shrink tubing material failed at 600K. This failure could explain the anomalies experienced by the probes. The descent data of the Pioneer probes, and the Soviet Vega Lander was analyzed to evaluate the presence of small scale gravity waves in and below the Venus cloud layer.

Lester, Peter↗
NASA NTRS2012

Accurate ab initio Quartic Force Fields of Cyclic and Bent HC2N Isomers

Highly correlated ab initio quartic force field (QFFs) are used to calculate the equilibrium structures and predict the spectroscopic parameters of three HC2N isomers. Specifically, the ground state quasilinear triplet and the lowest cyclic and bent singlet isomers are included in the present study. Extensive treatment of correlation effects were included using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, denoted CCSD(T). Dunning s correlation-consistent basis sets cc-pVXZ, X=3,4,5, were used, and a three-point formula for extrapolation to the one-particle basis set limit was used. Core-correlation and scalar relativistic corrections were also included to yield highly accurate QFFs. The QFFs were used together with second-order perturbation theory (with proper treatment of Fermi resonances) and variational methods to solve the nuclear Schr dinger equation. The quasilinear nature of the triplet isomer is problematic, and it is concluded that a QFF is not adequate to describe properly all of the fundamental vibrational frequencies and spectroscopic constants (though some constants not dependent on the bending motion are well reproduced by perturbation theory). On the other hand, this procedure (a QFF together with either perturbation theory or variational methods) leads to highly accurate fundamental vibrational frequencies and spectroscopic constants for the cyclic and bent singlet isomers of HC2N. All three isomers possess significant dipole moments, 3.05D, 3.06D, and 1.71D, for the quasilinear triplet, the cyclic singlet, and the bent singlet isomers, respectively. It is concluded that the spectroscopic constants determined for the cyclic and bent singlet isomers are the most accurate available, and it is hoped that these will be useful in the interpretation of high-resolution astronomical observations or laboratory experiments.

Inostroza, Natalia↗
NASA NTRS1992

Mobility power flow analysis of coupled plate structure subjected to mechanical and acoustic excitation

The mobility power flow approach that was previously applied in the derivation of expressions for the vibrational power flow between coupled plate substructures forming an L configuration and subjected to mechanical loading is generalized. Using the generalized expressions, both point and distributed mechanical loads on one or both of the plates can be considered. The generalized approach is extended to deal with acoustic excitation of one of the plate substructures. In this case, the forces (acoustic pressures) acting on the structure are dependent on the response of the structure because of the scattered pressure component. The interaction between the plate structure and the acoustic fluid leads to the derivation of a corrected mode shape for the plates' normal surface velocity and also for the structure mobility functions. The determination of the scattered pressure components in the expressions for the power flow represents an additional component in the power flow balance for the source plate and the receiver plate. This component represents the radiated acoustical power from the plate structure. For a number of coupled plate substrates, the acoustic pressure generated by one substructure will interact with the motion of another substructure. That is, in the case of the L-shaped plate, acoustic interaction exists between the two plate substructures due to the generation of the acoustic waves by each of the substructures. An approach to deal with this phenomena is described.

Cuschieri, J. M.↗
NASA NTRS2003

First Year Wilkinson Microwave Anisotropy Probe(WMAP) Observations: Data Processing Methods and Systematic Errors Limits

We describe the calibration and data processing methods used to generate full-sky maps of the cosmic microwave background (CMB) from the first year of Wilkinson Microwave Anisotropy Probe (WMAP) observations. Detailed limits on residual systematic errors are assigned based largely on analyses of the flight data supplemented, where necessary, with results from ground tests. The data are calibrated in flight using the dipole modulation of the CMB due to the observatory's motion around the Sun. This constitutes a full-beam calibration source. An iterative algorithm simultaneously fits the time-ordered data to obtain calibration parameters and pixelized sky map temperatures. The noise properties are determined by analyzing the time-ordered data with this sky signal estimate subtracted. Based on this, we apply a pre-whitening filter to the time-ordered data to remove a low level of l/f noise. We infer and correct for a small (approx. 1 %) transmission imbalance between the two sky inputs to each differential radiometer, and we subtract a small sidelobe correction from the 23 GHz (K band) map prior to further analysis. No other systematic error corrections are applied to the data. Calibration and baseline artifacts, including the response to environmental perturbations, are negligible. Systematic uncertainties are comparable to statistical uncertainties in the characterization of the beam response. Both are accounted for in the covariance matrix of the window function and are propagated to uncertainties in the final power spectrum. We characterize the combined upper limits to residual systematic uncertainties through the pixel covariance matrix.

Hinshaw, G.↗
NASA NTRS2015

A Sampling Based Approach to Spacecraft Autonomous Maneuvering with Safety Specifications

This paper presents a methods for safe spacecraft autonomous maneuvering that leverages robotic motion-planning techniques to spacecraft control. Specifically the scenario we consider is an in-plan rendezvous of a chaser spacecraft in proximity to a target spacecraft at the origin of the Clohessy Wiltshire Hill frame. The trajectory for the chaser spacecraft is generated in a receding horizon fashion by executing a sampling based robotic motion planning algorithm name Fast Marching Trees (FMT) which efficiently grows a tree of trajectories over a set of probabillistically drawn samples in the state space. To enforce safety the tree is only grown over actively safe samples for which there exists a one-burn collision avoidance maneuver that circularizes the spacecraft orbit along a collision-free coasting arc and that can be executed under potential thrusters failures. The overall approach establishes a provably correct framework for the systematic encoding of safety specifications into the spacecraft trajectory generations process and appears amenable to real time implementation on orbit. Simulation results are presented for a two-fault tolerant spacecraft during autonomous approach to a single client in Low Earth Orbit.

Spacecraft↗
NASA NTRS1989

Simulation of spacecraft attitude dynamics using TREETOPS and model-specific computer Codes

The simulation of spacecraft attitude dynamics and control using the generic, multi-body code called TREETOPS and other codes written especially to simulate particular systems is discussed. Differences in the methods used to derive equations of motion--Kane's method for TREETOPS and the Lagrangian and Newton-Euler methods, respectively, for the other two codes--are considered. Simulation results from the TREETOPS code are compared with those from the other two codes for two example systems. One system is a chain of rigid bodies; the other consists of two rigid bodies attached to a flexible base body. Since the computer codes were developed independently, consistent results serve as a verification of the correctness of all the programs. Differences in the results are discussed. Results for the two-rigid-body, one-flexible-body system are useful also as information on multi-body, flexible, pointing payload dynamics.

Cochran, John E.↗
NASA NTRS1995

Alfven waves, alpha particles, and pickup ions in the solar wind

Past studies of the properties of Alfven waves in the solar wind have indicated that (1) the amplitude of the velocity fluctuations is almost always smaller than expected on the basis of the amplitude of the field fluctuations, even when the anisotropy of the plasma is taken into account, and (2) the alpha particles do not participate in the wave motions because they 'surf' on the waves carried by the proton fluid. Ulysses data are used to demonstrate that (1) the discrepancy between the velocity and field fluctuations is greater at high heliographic latitudes than in the ecliptic plane, and (2) the alphas do participate in the waves, being either in phase or out of phase with the proton motions depending on whether the differential flow speed between the alphas and protons is greater than or less than the 'observed' wave speed, B(sub o)(delta v squared / delta B squared)exp 1/2, as determined from the ratio of the amplitudes of the velocity and magnetic fluctuations. It is proposed that the modification of Alfven wave propagation speed is due to pressure anisotropies resulting from asymmetric distributions of interstellar pickup ions. If the proposed explanation is correct, it indicates that scattering of pickup ions onto a (bi)spherical shell may not be as complete as generally supposed.

Goldstein, B. E.↗
NASA NTRS2004

Resolving the Issues with Flywheel Position Sensors

For the past few years, the Advanced Electrical Systems Branch here at NASA Glenn has been pursuing research in the area of flywheels. The purpose of these pursuits has been t o explore the potential for flywheels to replace current battery-powered systems in space. So far it has been learned that flywheels offer large momentum storage capacity, comparatively small volume, high durability, and near- complete discharge capabilities, all of which are advancements over the existing nickel hydrogen and nickel cadmium batteries. Another significant advantage of flywheels is the potential they offer for combining the function of attitude control with energy storage. During the summer of 2004, I worked with Dr. Barbara Kenny in the Advanced Electrical Systems Branch, supporting the work she is doing by analyzing and testing some new components for the new Generation-2 flywheel. To monitor the speed and angular position of the flywheel rotor, a once-around (OAR) signal along with a sensorless algorithm is used. The OAR signal is used for the magnetic bearings that keep the flywheel suspended for frictionless operation. The sensorless algorithm is used for the flywheel motor/generator control. The OAR is generated from position sensors that monitor a circular plate. The plate has a cut down the middle such that one half of the circle is on a slightly lower level than the other. Every half-turn, or 180, the sensors detect the "cut" on the plate, and trigger the OAR, telling the computer that the rotor has made half a revolution. This, however, doesn't provide needed detailed information about the angular position of the rotor, since it only provides a signal alert every half- revolution. This is enough information for the magnetic bearing control but is insufficient for the motor/generator control. A new resolver was designed such that it would give continuous angle information rather than the 180 degree information of the OAR. The new resolver has two separate observable pieces: a flat middle section to monitor vertical motion, and an angled section around the circumference, which, when observed from above, produces a sine-wave displacement through the entire 360" revolution. My first job when I arrived this summer was to calibrate the sensors that would be mounted on the inside of the flywheel casing to monitor the position (angular and vertical) of the shaft. After calibration, I used the sensors to evaluate voltage outputs created by position differences between two pairs of sensors on the angled portion of the resolver for eight different angular positions, moving the resolver vertically and laterally through its entire potential range of motion. The results of these tests will be used to determine the rotor angular (and axial) position from the sensor readings once the new flywheel unit is assembled. The sensorless algorighm mentioned above consists of two operations: the signal injection method and the back electro-motive force (EMF). The signal injection is meant to work at low speeds, while the back EMF algorithm is meant to work at higher speeds. Both work together to determine the correct estimate of rotor position and speed based on the measured motor/generator current. It was determined that we wanted to know exactly how accurate our estimation methods were, and so a resolver (a commercially available mechanical sensor mounted to the motor/generator shaft to measure rotor position and speed) and a "Resolver to Digital" (R2D) circuit board was purchased to make the comparison to the existing estimation. My work related to the R2D board has included the following: creating two connector cables (one to power the circuit and one to get readable output off the board), writing Simulink code to process the board's output, and building a dSpace panel to control and monitor the circuit. The next step in the process will be to perform tests to compare the estimated rotor position and speed from the sensorless algorithm to the actual rotor and speed from the resolver signal.

Fehrmann, Elizabeth A.↗
NASA NTRS1973

Quadrature solution for the general relativistic motion of a satellite or a planet.

The general relativistic motion of a particle in a bounded orbit around a central mass M is derived with the aid of the Schwarzschild field of M. A quadrature gives the central angle as a quasi-periodic function of an effective true anomaly. The mean rate of advance of the pericenter is investigated. Classical and general relativistic orbiters with the same initial conditions are compared, taking into account the treatment of the general relativistic effect by means of a differential correction. General relativistic variations are discussed, giving attention to the variation of the eccentric anomaly and the variation of the central angle.

Vinti, J. P.↗
NASA NTRS1997

Vertical Transport Processes for Inert and Scavenged Species: TRACE-A Measurements

The TRACE-A mission of the NASA DC-8 aircraft made a large-scale survey of the tropical and subtropical atmosphere in September and October of 1992. Both In-situ measurements of CO (G. Sachsen NASA Langley) and aerosol size (J. Browell group, NASA Langley) provide excellent data sets with which to constrain vertical transport by planetary boundary layer mixing and deep-cloud cumulus convection. Lidar profiles of aerosol-induced scattering and ozone (also by Bremen) are somewhat require more subtle interpretation as tracers, but the vertical information on layering largely compensates for these complexities. The reason this DC-8 dataset is so useful is that very large areas of biomass burning over Africa and South America provide surface sources of appropriate sizes with which to characterize vertical and horizontal motions; the major limitation of our source description is that biomass burning patterns move considerably every few days, and daily burning inventories are a matter of concurrent, intensive research. We use the Penn State / NCAR MM5 model in an assimilation mode on the synoptic and intercontinental scale, and assess the success it shows in vertical transport descriptions. We find that the general level of emissions suggested by the climatological approach (Will. Has, U. of Montana) appears to be approximately correct, possibly a bit low, for this October, 1992, time period. Vertical transport in planetary boundary layer mixing to 5.5 kin was observed and reproduced in our simulations. Furthermore we find evidence that Blackader "transilient" or matrix-transport scheme is needed, but may require some adaptation in our tracer model: CO seems to exhibit very high values at the top of the planetary boundary layer, a process that stretches the eddy-diffusion parameterization. We will report on progress in improving the deep convective transport of carbon monoxide: the Grail scheme as we used it at 100 kin resolution did not transport enough material to the upper troposphere. We expect to be able to attribute this to either parameterization reasons (inadequacy of this parameterization at the large 100km scale) or other reasons. Nevertheless, the qualitative nature of deep transport by clouds shows up well in the simulations. As for scavengable species, the simulations predict tens of micrograms per standard cubic meter of smoke aerosol in the boundary layer. In a straightforward illustration of our simple bulk-mass scavenging parameterization, to one or two micrograms per standard cubic meter of smoke aerosol in the free troposphere just above the source regions: very high concentrations for the free troposphere. We expect to report on comparisons of these predictions to a variety of observations.

Chatfield, Robert B.↗
NASA NTRS2011

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Roberts, Craig E.↗
NASA NTRS1995

Blending Velocities In Task Space In Computing Robot Motions

Blending of linear and angular velocities between sequential specified points in task space constitutes theoretical basis of improved method of computing trajectories followed by robotic manipulators. In method, generalized velocity-vector-blending technique provides relatively simple, common conceptual framework for blending linear, angular, and other parametric velocities. Velocity vectors originate from straight-line segments connecting specified task-space points, called "via frames" and represent specified robot poses. Linear-velocity-blending functions chosen from among first-order, third-order-polynomial, and cycloidal options. Angular velocities blended by use of first-order approximation of previous orientation-matrix-blending formulation. Angular-velocity approximation yields small residual error, quantified and corrected. Method offers both relative simplicity and speed needed for generation of robot-manipulator trajectories in real time.

Volpe, Richard A.↗
NASA NTRS1976

A theoretical study of the acoustic impedance of orifices in the presence of a steady grazing flow

An analysis of the oscillatory fluid flow in the vicinity of a circular orifice with a steady grazing flow is presented. The study is similar to that of Hersh and Rogers but with the addition of the grazing flow. Starting from the momentum and continuity equations, a considerably simplified system of partial differential equations is developed with the assumption that the flow can be described by an oscillatory motion superimposed upon the known steady flow. The equations are seen to be linear in the region where the grazing flow effects are dominant, and a solution and the resulting orifice impedance are presented for this region. The nonlinearity appears to be unimportant for the usual conditions found in aircraft noise suppressors. Some preliminary conclusions of the study are that orifice resistance is directly proportional to grazing flow velocity (known previously from experimental data) and that the orifice inductive (mass reactance) end correction is not a function of grazing flow. This latter conclusion is contrary to the widely held notion that grazing flow removes the effect of the orifice inductive end correction. This conclusion also implies that the experimentally observed total inductance reduction with grazing flow might be in the flow within the orifice rather than in the end correction.

Rice, E. J.↗
NASA NTRS1998

New AFM Techniques for Investigating Molecular Growth Mechanisms of Protein Crystals

Atomic Force Microscopy (AFM) has emerged as a powerful technique for investigating protein crystal growth. Earlier AFM studies were among the first to demonstrate that these crystals grew by dislocation and 2D nucleation growth mechanisms [1]. These investigations were restricted to the micron range where only surface features, such as dislocation hillocks and 2D islands are visible. Most AFM instruments can scan at higher resolutions and have the potential to resolve individual protein molecules at nanometer ranges. Such scans are essential for determining the molecular packing arrangements on crystal faces and for probing the growth process at the molecular level. However, at this resolution the AFM tip influences the image produced, with the resulting image being a convolution of the tip shape and the surface morphology [2]. In most studies this problem is resolved by deconvoluting the image to obtain the true surface morphology. Although deconvolution routines work reasonably well for simple one- dimensional shapes, for complex surfaces this approach does not produce accurate results. In this study we devised a new approach which takes advantage of the precise molecular order of crystal surfaces, combined with the knowledge of individual molecular shapes from the crystallographic data of the protein and the AFM tip shape. This information is used to construct expected theoretical AFM images by convoluting the tip shape with the constructed crystal surface shape for a given surface packing arrangement. By comparing the images from actual AFM scans with the constructed ones for different possible surface packing arrangements, the correct packing arrangement can be conclusively determined. This approach was used in this study to determine the correct one from two possible packing arrangements on (I 10) faces of tetragonal lysozyme crystals. Another novel AFM technique was also devised to measure the dimension of individual growth units of the crystal faces. Measuring these units was not attempted before and most studies have assumed that the growth unit consisted of individual protein molecules. The linescan mode of AFM instruments allows the crystal surface to be scanned along a single line. By scanning across a growth step an image showing the motion of the step is obtained. Normally such an image shows a straight line for continuous and constant step velocity. In this study by increasing the scan rate and by decreasing the step velocity (by decreasing the supersaturation), we were able to capture images of individual growth events, shown by jump discontinuities in the step line. By suitable integration of the image the growth unit dimension in the scanned direction can be obtained. Since multiple units can be involved in the growth process it is necessary to collect a statistically relevant sample before drawing conclusions about the growth mechanism. This technique was successfully employed to obtain the dimensions of growth units for the (110) face, showing that they consisted of various aggregates corresponding to the 43 helices in the crystal structure.

Li, Huayu↗
NASA NTRS2000

Inertial Effects in Suspension Dynamics

The present work analyses the dynamics of a suspension of heavy particles in shear flow. The magnitude of the particle inertia is given by the Stokes number St = m(gamma/6(pi)a, which is the ratio of the viscous relaxation time of a particle tau(sub p) = m=6pi(eta)a to the flow time gamma(sup -1). Here, m is the mass of the particle, a is its size, eta is the viscosity of the suspending fluid and gamma is the shear rate. The ratio of the Stokes number to the Reynolds number, Re = (rho)f(gamma)a(exp 2)/eta, is the density ratio rho(sub p)/rho(sub f). Of interest is to understand the separate roles of particle (St) and fluid (Re) inertia in the dynamics of suspensions. In this study we focus on heavy particles, rho(sub p)/rho(sub f) much greater than 1, for which the Stokes number is finite, but the Reynolds number is sufficiently small for inertial forces in the fluid to be neglected; thus, the fluid motion is governed by the Stokes equations. On the other hand, the probability density governing the statistics of the suspended particles satisfies a Fokker-Planck equation that accounts for both configuration and momentum coordinates, the latter being essential for finite St. The solution of the Fokker-Planck equation is obtained to O(St) via a Chapman-Enskog type-procedure, and the conditional velocity distribution so obtained is used to derive a configuration-space Smoluchowski equation with inertial corrections. The inertial effects are responsible for asymmetry in the relative trajectories of two spheres in shear flow, in contrast to the well known symmetric structure in the absence of inertia. Finite St open trajectories in the plane of shear suffer a downward lateral displacement resulting from the inability of a particle of finite mass to follow the curvature of the zero-Stokes-number pathlines. In addition to the induced asymmetry, the O(St) inertial perturbation dramatically alters the nature of the near-field trajectories. The stable closed orbits (for St = 0) in the plane of shear now spiral in, approaching particle-particle contact in the limit. All trajectories starting from an initial offset of O(St(sup 1/2) or less (which remain open for St = 0) also spiral in. The asymmetry of the trajectories leads to a non-Newtonian rheology and diffusive behavior. The latter because a given particle (moving along a finite St open trajectory) suffers a net displacement in the transverse direction after a single interaction. A sequence of such uncorrelated displacements leads to the particle executing a random walk. The inertial diffusivity tensor is anisotropic on account of differing strengths of interaction in the gradient and vorticity directions. Since the entire region (constituting an in finite area) of closed orbits in the plane of shear spirals onto contact for #finite St, the latter represents a singular surface for the pair-distribution function. The exact form of the pair-distribution function at contact is still, however, indeterminate in the absence of non-hydrodynamic effects. It should also be noted that finite St non-rectilinear flows do not support a spatially uniform number density owing to the cross-streamline inertial migration of particles.

J. F. Brady↗