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NASA NTRS1977

Theoretical aspects of sounder antenna operation

The fundamental problem of calculating the radiation from an electric dipole immersed in a magnetoplasma is one of solving Maxwell's equations coupled to the self-consistent field-particle equations describing the plasma. For very small applied antenna voltages, the plasma dynamics may be linearized, and the plasma reaction currents computed self-consistently in terms of the voltage on the antenna. Thus, the short dipole can be idealized as a point dipole of moment P sub o = C sub a, V sub o el, where C sub a is the antenna element-to-plasma capacitance for a sheath of dimensions roughly several plasma Debye lengths and el is the dipole element's length. In actual practice, it is at this point that the first difficulty with the antenna theory arises. Even for small signals, the sheath around such an antenna will exhibit a complex impedance. For larger signals, nonlinear effects appear. Attemps are made to solve this problem.

Fredricks, R. W.↗

NASA NTRS1977

Absolute rate of the reaction of Cl/2P/ with methane from 200-500 K

Rate constants for the reaction Cl + CH4 yields HCl + CH3 were measured in the range 200-500 K by the plot flash photolysis-resonance fluorescence technique. An Arrhenius plot of the mean rate constant observed at 14 equally spaced temperatures is best fit by the expression k = 5.44 times 10 to the minus 19th times T to the exponent 2.50 times exp(-608/T) cu cm per molecule per sec. Appropriate expressions are also given for the rate constant in the two ranges 200-299 K and 299-500 K. These results are compared with a number of other existing determinations of the rate constant by other methods and in different temperature ranges. Most discrepancies are attributed to the nonlinear Arrhenius behavior.

Whytock, D. A.↗

NASA NTRS1984

The photochemistry of a remote marine stratiform cloud

The coupled gas- and aqueous-phase photochemistry of a stratiform cloud in a remote region of the marine atmosphere is investigated with a time-dependent box model. Both scavenging of ambient acidic aerosols and gases as well as aqueous-phase chemical reactions within droplets are found to be important sources of acidity to cloud water and can lead to pH levels in cloud water in the remote marine atmosphere well below 5.6. The major sources of acidity via aqueous-phase chemical reactions are the generation of sulfuric acid from dissolved SO2 and the generation of formic acid from dissolved formaldehyde. In both cases, aqueous-phase free radicals can play a significant role either directly by oxidizing dissolved SO2 and HCHO or indirectly by producing the aqueous-phase oxidant H2O2. The rate of SO2 conversion to sulfuric acid is sensitive to a variety of parameters including the accommodation or sticking coefficient for SO2, H2O2, HO2, and OH, the liquid water content, and the ambient levels of SO2, HNO3, and other acidic or basic gases. Because high levels of SO2 tend to deplete cloud water of H2O3, the possibility exists that the pH of precipitation in polluted regions will respond nonlinearly to reduced SO2 emissions.

Chameides, W. L.↗

NASA NTRS1975

Tracking performance under time sharing conditions with a digit processing task: A feedback control theory analysis

A one dimensional compensatory tracking task and a digit processing reaction time task were combined in a three phase experiment designed to investigate tracking performance in time sharing. Adaptive techniques, elaborate feedback devices, and on line standardization procedures were used to adjust task difficulty to the ability of each individual subject and manipulate time sharing demands. Feedback control analysis techniques were employed in the description of tracking performance. The experimental results show that when the dynamics of a system are constrained, in such a manner that man machine system stability is no longer a major concern of the operator, he tends to adopt a first order control describing function, even with tracking systems of higher order. Attention diversion to a concurrent task leads to an increase in remnant level, or nonlinear power. This decrease in linearity is reflected both in the output magnitude spectra of the subjects, and in the linear fit of the amplitude ratio functions.

Gopher, D.↗

NASA NTRS2005

High-Power Fiber Lasers Using Photonic Band Gap Materials

High-power fiber lasers (HPFLs) would be made from photonic band gap (PBG) materials, according to the proposal. Such lasers would be scalable in the sense that a large number of fiber lasers could be arranged in an array or bundle and then operated in phase-locked condition to generate a superposition and highly directed high-power laser beam. It has been estimated that an average power level as high as 1,000 W per fiber could be achieved in such an array. Examples of potential applications for the proposed single-fiber lasers include welding and laser surgery. Additionally, the bundled fibers have applications in beaming power through free space for autonomous vehicles, laser weapons, free-space communications, and inducing photochemical reactions in large-scale industrial processes. The proposal has been inspired in part by recent improvements in the capabilities of single-mode fiber amplifiers and lasers to produce continuous high-power radiation. In particular, it has been found that the average output power of a single strand of a fiber laser can be increased by suitably changing the doping profile of active ions in its gain medium to optimize the spatial overlap of the electromagnetic field with the distribution of active ions. Such optimization minimizes pump power losses and increases the gain in the fiber laser system. The proposal would expand the basic concept of this type of optimization to incorporate exploitation of the properties (including, in some cases, nonlinearities) of PBG materials to obtain power levels and efficiencies higher than are now possible. Another element of the proposal is to enable pumping by concentrated sunlight. Somewhat more specifically, the proposal calls for exploitation of the properties of PBG materials to overcome a number of stubborn adverse phenomena that have impeded prior efforts to perfect HPFLs. The most relevant of those phenomena is amplified spontaneous emission (ASE), which causes saturation of gain and power at undesirably low levels, and scattering of light from dopants. In designing a given fiber laser for reduced ASE, care must be taken to maintain a correct fiber structure for eventual scaling to an array of many such lasers such that the interactions among all the members of the array would cause them to operate in phase lock. Hence, the problems associated with improving a single-fiber laser are not entirely separate from the bundling problem, and some designs for individual fiber lasers may be better than others if the fibers are to be incorporated into bundles. Extensive calculations, expected to take about a year, must be performed in order to determine design parameters before construction of prototype individual and fiber lasers can begin. The design effort can be expected to include calculations to optimize overlaps between the electromagnetic modes and the gain media and calculations of responses of PBG materials to electromagnetic fields. Design alternatives and physical responses that may be considered include simple PBG fibers with no intensity-dependent responses, PBG fibers with intensity- dependent band-gap shifting (see figure), and broad-band pumping made possible by use of candidate broad-band pumping media in place of the air or vacuum gaps used in prior PBG fibers.

DiDomenico, Leo↗

NASA NTRS2002

Acoustically Enhanced Electroplating Being Developed

In cooperation with the NASA Glenn Research Center, Alchemitron Corp. is developing the Acoustically Enhanced Electroplating Process (AEEP), a new technique of employing nonlinear ultrasonics to enhance electroplating. The applications range from electroplating full-panel electronic circuit boards to electroplating microelectronics and microelectromechanical systems (MEMS) devices. In a conventional plating process, the surface area to be plated is separated from the nonplated areas by a temporary mask. The mask may take many forms, from a cured liquid coating to a simple tape. Generally, the mask is discarded when the plating is complete, creating a solid waste product that is often an environmental hazard. The labor and materials involved with the layout, fabrication, and tooling of masks is a primary source of recurring and nonrecurring production costs. The objective of this joint effort, therefore, is to reduce or eliminate the need for masks. AEEP improves selective plating processes by using directed beams of high-intensity acoustic waves to create nonlinear effects that alter the fluid dynamic and thermodynamic behavior of the plating process. It relies on two effects: acoustic streaming and acoustic heating. Acoustic streaming is observed when a high-intensity acoustic beam creates a liquid current within the beam. The liquid current can be directed as the beam is directed and, thus, users can move liquid around as desired without using pumps and nozzles. The current of the electroplating electrolyte, therefore, can be directed at distinct target areas where electroplating is desired. The current delivers fresh electrolyte to the target area while flushing away the spent electrolyte. This dramatically increases the plating rate in the target area. In addition, acoustic heating of both the liquid in the beam and the target surface increases the chemical reaction rate, which further increases the plating rate. The combined effects of acoustic streaming and heating accelerate the deposition of plating in that area and, thus, provide an effect similar to a mask but without the costs of masking. AEEP further improves the plating process by clearing debris and bubbles from the surface by acoustic radiation pressure and acoustic streaming.

Oeftering, Richard C.↗

NASA NTRS1993

A numerical procedure for analysis of finite rate reacting flows

Combustion processes in rocket propulsion systems are characterized by the existence of multiple, vastly differing time and length scales, as well as flow-speeds at wide variation of Mach numbers. The chemical kinetics processes in the highly active reaction zone are characterized by much smaller scales compared to fluid convective and diffusive time scales. An operator splitting procedure for transient finite rate chemistry problems has been developed using a pressure based method, which can be applied to all speed flows without difficulties. The splitting of chemical kinetics terms formed the fluid-mechanical terms of the species equation ameliorated the difficulties associated with the disparate time scales and stiffness in the set of equations which describes highly exothermic combustion. A combined efficient ordinary differential equations (ODE) solver was used to integrate the effective chemical source terms over the residence time at each grid cell. One and two dimensional reacting flow situations were carried out to demonstrate and verify the current procedure. Different chemical kinetics with different degrees of nonlinearity have also been incorporated to test the robustness and generality of the proposed method.

Shang, H. M.↗

NASA NTRS1986

Sensitivity of an atmospheric photochemistry model to chlorine perturbations including consideration of uncertainty propagation

Models of stratospheric photochemistry are generally tested by comparing their predictions for the composition of the present atmosphere with measurements of species concentrations. These models are then used to make predictions of the atmospheric sensitivity to perturbations. Here the problem of the sensitivity of such a model to chlorine perturbations ranging from the present influx of chlorine-containing compounds to several times that influx is addressed. The effects of uncertainties in input parameters, including reaction rate coefficients, cross sections, solar fluxes, and boundary conditions, are evaluated using a Monte Carlo method in which the values of the input parameters are randomly selected. The results are probability distributions for present atmosheric concentrations and for calculated perturbations due to chlorine from fluorocarbons. For more than 300 Monte Carlo runs the calculated ozone perturbation for continued emission of fluorocarbons at today's rates had a mean value of -6.2 percent, with a 1-sigma width of 5.5 percent. Using the same runs but only allowing the cases in which the calculated present atmosphere values of NO, NO2, and ClO at 25 km altitude fell within the range of measurements yielded a mean ozone depletion of -3 percent, with a 1-sigma deviation of 2.2 percent. The model showed a nonlinear behavior as a function of added fluorocarbons. The mean of the Monte Carlo runs was less nonlinear than the model run using mean value of the input parameters.

Stolarski, R. S.↗

NASA NTRS2013

Spurious Behavior of Shock-Capturing Methods: Problems Containing Stiff Source Terms and Discontinuities

The goal of this paper is to relate numerical dissipations that are inherited in high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities. For pointwise evaluation of the source term, previous studies indicated that the phenomenon of wrong propagation speed of discontinuities is connected with the smearing of the discontinuity caused by the discretization of the advection term. The smearing introduces a nonequilibrium state into the calculation. Thus as soon as a nonequilibrium value is introduced in this manner, the source term turns on and immediately restores equilibrium, while at the same time shifting the discontinuity to a cell boundary. The present study is to show that the degree of wrong propagation speed of discontinuities is highly dependent on the accuracy of the numerical method. The manner in which the smearing of discontinuities is contained by the numerical method and the overall amount of numerical dissipation being employed play major roles. Moreover, employing finite time steps and grid spacings that are below the standard Courant-Friedrich-Levy (CFL) limit on shockcapturing methods for compressible Euler and Navier-Stokes equations containing stiff reacting source terms and discontinuities reveals surprising counter-intuitive results. Unlike non-reacting flows, for stiff reactions with discontinuities, employing a time step and grid spacing that are below the CFL limit (based on the homogeneous part or non-reacting part of the governing equations) does not guarantee a correct solution of the chosen governing equations. Instead, depending on the numerical method, time step and grid spacing, the numerical simulation may lead to (a) the correct solution (within the truncation error of the scheme), (b) a divergent solution, (c) a wrong propagation speed of discontinuities solution or (d) other spurious solutions that are solutions of the discretized counterparts but are not solutions of the governing equations. The present investigation for three very different stiff system cases confirms some of the findings of Lafon & Yee (1996) and LeVeque & Yee (1990) for a model scalar PDE. The findings might shed some light on the reported difficulties in numerical combustion and problems with stiff nonlinear (homogeneous) source terms and discontinuities in general.

Yee, Helen M. C.↗

NASA NTRS2001

Horizontal vestibuloocular reflex evoked by high-acceleration rotations in the squirrel monkey. IV. Responses after spectacle-induced adaptation

The horizontal angular vestibuloocular reflex (VOR) evoked by sinusoidal rotations from 0.5 to 15 Hz and acceleration steps up to 3,000 degrees /s(2) to 150 degrees /s was studied in six squirrel monkeys following adaptation with x2.2 magnifying and x0.45 minimizing spectacles. For sinusoidal rotations with peak velocities of 20 degrees /s, there were significant changes in gain at all frequencies; however, the greatest gain changes occurred at the lower frequencies. The frequency- and velocity-dependent gain enhancement seen in normal monkeys was accentuated following adaptation to magnifying spectacles and diminished with adaptation to minimizing spectacles. A differential increase in gain for the steps of acceleration was noted after adaptation to the magnifying spectacles. The gain during the acceleration portion, G(A), of a step of acceleration (3,000 degrees /s(2) to 150 degrees /s) increased from preadaptation values of 1.05 +/- 0.08 to 1.96 +/- 0.16, while the gain during the velocity plateau, G(V), only increased from 0.93 +/- 0.04 to 1.36 +/- 0.08. Polynomial fits to the trajectory of the response during the acceleration step revealed a greater increase in the cubic than the linear term following adaptation with the magnifying lenses. Following adaptation to the minimizing lenses, the value of G(A) decreased to 0.61 +/- 0.08, and the value of G(V) decreased to 0.59 +/- 0.09 for the 3,000 degrees /s(2) steps of acceleration. Polynomial fits to the trajectory of the response during the acceleration step revealed that there was a significantly greater reduction in the cubic term than in the linear term following adaptation with the minimizing lenses. These findings indicate that there is greater modification of the nonlinear as compared with the linear component of the VOR with spectacle-induced adaptation. In addition, the latency to the onset of the adapted response varied with the dynamics of the stimulus. The findings were modeled with a bilateral model of the VOR containing linear and nonlinear pathways that describe the normal behavior and adaptive processes. Adaptation for the linear pathway is described by a transfer function that shows the dependence of adaptation on the frequency of the head movement. The adaptive process for the nonlinear pathway is a gain enhancement element that provides for the accentuated gain with rising head velocity and the increased cubic component of the responses to steps of acceleration. While this model is substantially different from earlier models of VOR adaptation, it accounts for the data in the present experiments and also predicts the findings observed in the earlier studies.

NASA Discipline Neuroscience↗

NASA NTRS2007

Guaranteeing Pointing Performance of the SDO Sun-Pointing Controllers in Light of Nonlinear Effects

The Solar Dynamics Observatory (SDO) mission is the first Space Weather Research Network mission, part of NASA s Living With a Star program.1 This program seeks to understand the changing Sun and its effects on the Solar System, life, and society. To this end, the SDO spacecraft will carry three Sun-observing instruments to geosynchronous orbit: Helioseismic and Magnetic Imager (HMI), led by Stanford University; Atmospheric Imaging Assembly (AIA), led by Lockheed Martin Space and Astrophysics Laboratory; and Extreme Ultraviolet Variability Experiment (EVE), led by the University of Colorado. Links describing the instruments in detail may be found through the SDO web site.2 The basic mission goals are to observe the Sun for a very high percentage of the 5-year mission (10-year goal) with long stretches of uninterrupted observations and with constant, high-data-rate transmission to a dedicated ground station. These goals guided the design of the spacecraft bus that will carry and service the three-instrument payload. At the time of this publication, the SDO spacecraft bus is well into the integration and testing phase at the NASA Goddard Space Flight Center (GSFC). A three-axis stabilized attitude control system (ACS) is needed both to point at the Sun accurately and to keep the roll about the Sun vector correctly positioned. The ACS has four reaction wheel modes and 2 thruster actuated modes. More details about the ACS in general and the control modes in particular can be found in Refs. [3-6]. All four of SDO s wheel-actuated control modes involve Sun-pointing controllers, as might be expected from such a mission. Science mode, during which most science data is collected, uses specialized guide telescopes to point accurately at the Sun. Inertial mode has two sub-modes, one tracks a Sun-referenced target orientation, and another maintains an absolute (star-referenced) target orientation, that both employ a Kalman filter to process data from a digital Sun sensor and two star trackers. However, this paper is concerned only with the other two modes: Safe Hold (SH) and Sun Acquisition (SA).

Starin, Scott R.↗

NASA NTRS1989

Hypervelocity atmospheric flight: Real gas flow fields

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that have been reduced to a relatively compact set of equations in a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-average behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equations a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. Hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates chemical nonequilibrium is considered, and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

Howe, John T.↗

NASA NTRS1990

Hypervelocity atmospheric flight: Real gas flow fields

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that were reduced to a relatively compact set of equations of a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-averaged behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equation a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. For hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates, chemical nonequilibrium is considered and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

Howe, John T.↗

NASA NTRS1998

High Temperature Mechanical Characterization of Ceramic Matrix Composites

A high temperature mechanical characterization laboratory has been assembled at NASA Lewis Research Center. One contribution of this work is to test ceramic matrix composite specimens in tension in environmental extremes. Two high temperature tensile testing systems were assembled. The systems were assembled based on the performance and experience of other laboratories and meeting projected service conditions for the materials in question. The systems use frames with an electric actuator and a center screw. A PC based data acquisition and analysis system is used to collect and analyze the data. Mechanical extensometers are used to measure specimen strain. Thermocouples, placed near the specimen, are used to measure the specimen gage section temperature. The system for testing in air has a resistance element furnace with molybdenum disilicide elements and pneumatic grips with water cooling attached to hydraulic alignment devices. The system for testing in an inert gas has a graphite resistance element furnace in a chamber with rigidly mounted, water cooled, hydraulically actuated grips. Unidirectional SiC fiber reinforced reaction bonded Si3N4 and triaxially woven, two dimensional, SiC fiber reinforced enhanced SiC composites were tested in unidirectional tension. Theories for predicting the Young's modulus, modulus near the ultimate strength, first matrix cracking stress, and ultimate strength were applied and evaluated for suitability in predicting the mechanical behavior of SiC/RBSN and enhanced SiC/SiC composites. The SiC/RBSN composite exhibited pseudo tough behavior (increased area under the stress/strain curve) from 22 C to 1500 C. The rule of mixtures provides a good estimate of the Young's modulus of the SiC/RBSN composite using the constituent properties from room temperature to 1440 C for short term static tensile tests in air or nitrogen. The rule of mixtures significantly overestimates the secondary modulus near the ultimate strength. The ACK theory provides the best approximation of the first matrix cracking stress when residual stresses are ignored. The theory of Cao and Thouless, based on Weibull statistics, gave the best prediction for the composite ultimate strength. The enhanced SiC/SiC composite exhibited nonlinear stress/strain behavior from 24 C to 1370 C in air with increased ultimate strain when compared to monolithic SiC. The theory of Yang and Chou with the assumption of a frictional fiber/matrix interface provided the best estimate of the Young's modulus. The theory of Cao and Thouless gave the best estimate for the ultimate strength.

Gyekenyesi, John Z.↗

NASA NTRS2006

Assessment of Bulk Absorber Properties for Multi-Layer Perforates in Porous Honeycomb Liners

CONTINUING progress in materials technology provides potential for improved acoustic liners for attenuating broadband fan noise emissions from aircraft engine nacelles. Conventional liners (local-reacting perforate-over-honeycomb structures) provide significant narrow-band attenuation, but limited attenuation over wide bandwidths. Two approaches for increasing attenuation bandwidth are to (1) replace the honeycomb structure with bulk material, or (2) cascade multiple layers of perforate/honeycomb structures. Usage of the first approach is limited because of mechanical and maintenance reasons, while multi-layer liners are limited to about three layers because of their additional mechanical complexity, depth and weight. The current research concerns a novel approach reported by the University of Cincinnati, in which a single-layer conventional liner is converted into an extended-reaction, broadband absorber by making the honeycomb core structure porous. This modified single-layer liner requires no increase in depth and weight, and minimal increase in mechanical complexity. Langley has initiated research to identify potential benefits of liner structures with porous cell walls. This research has two complementary goals: (1) develop and validate experimental techniques for treating multi-layer perforates (representative of the internal cells of a liner with porous cell walls) as 1-D bulk materials, and (2) develop analytical approaches to validate this bulk material assumption. If successful, the resultant model can then be used to design optimized porous honeycomb liners. The feasibility of treating an N-layer perforate system (N porous plates separated by uniform air gaps) as a one-dimensional bulk absorber is assessed using the Two-Thickness Method (TTM), which is commonly used to educe bulk material intrinsic acoustic parameters. Tests are conducted with discrete tone and random noise sources, over an SPL range sufficient to determine the nonlinearity of the test specimens, for test specimens consisting of 5, 10 and 15% porous plates. Measured impedances for two liner thicknesses (e.g., 12 and 24 layers) are used as input to the TTM to determine the characteristic impedance and propagation constant that characterize these liners as bulk absorbers. These parameters are then used to calculate the predicted impedance of liners with different thicknesses (e.g., 36 layers), and a comparison of predicted and measured impedances for these other thicknesses is used to determine the efficacy of this approach. Finally, an independent method is used to educe the propagation constant for a single representative sample, and excellent comparison between the results for this method and those for the TTM provides increased confidence in the results achieved with the TTM. In general, the results demonstrate these multi-layer perforates can be acceptably treated as bulk absorbers.

Jones, Michael G.↗

NASA NTRS1999

Horizontal vestibuloocular reflex evoked by high-acceleration rotations in the squirrel monkey. I. Normal responses

The horizontal angular vestibuloocular reflex (VOR) evoked by high-frequency, high-acceleration rotations was studied in five squirrel monkeys with intact vestibular function. The VOR evoked by steps of acceleration in darkness (3,000 degrees /s(2) reaching a velocity of 150 degrees /s) began after a latency of 7.3 +/- 1.5 ms (mean +/- SD). Gain of the reflex during the acceleration was 14.2 +/- 5.2% greater than that measured once the plateau head velocity had been reached. A polynomial regression was used to analyze the trajectory of the responses to steps of acceleration. A better representation of the data was obtained from a polynomial that included a cubic term in contrast to an exclusively linear fit. For sinusoidal rotations of 0.5-15 Hz with a peak velocity of 20 degrees /s, the VOR gain measured 0.83 +/- 0.06 and did not vary across frequencies or animals. The phase of these responses was close to compensatory except at 15 Hz where a lag of 5.0 +/- 0.9 degrees was noted. The VOR gain did not vary with head velocity at 0.5 Hz but increased with velocity for rotations at frequencies of >/=4 Hz (0. 85 +/- 0.04 at 4 Hz, 20 degrees /s; 1.01 +/- 0.05 at 100 degrees /s, P < 0.0001). No responses to these rotations were noted in two animals that had undergone bilateral labyrinthectomy indicating that inertia of the eye had a negligible effect for these stimuli. We developed a mathematical model of VOR dynamics to account for these findings. The inputs to the reflex come from linear and nonlinear pathways. The linear pathway is responsible for the constant gain across frequencies at peak head velocity of 20 degrees /s and also for the phase lag at higher frequencies being less than that expected based on the reflex delay. The frequency- and velocity-dependent nonlinearity in VOR gain is accounted for by the dynamics of the nonlinear pathway. A transfer function that increases the gain of this pathway with frequency and a term related to the third power of head velocity are used to represent the dynamics of this pathway. This model accounts for the experimental findings and provides a method for interpreting responses to these stimuli after vestibular lesions.

NASA Program Biomedical Research and Countermeasur↗

NASA NTRS1993

Multiple steady states in atmospheric chemistry

The equations describing the distributions and concentrations of trace species are nonlinear and may thus possess more than one solution. This paper develops methods for searching for multiple physical solutions to chemical continuity equations and applies these to subsets of equations describing tropospheric chemistry. The calculations are carried out with a box model and use two basic strategies. The first strategy is a 'search' method. This involves fixing model parameters at specified values, choosing a wide range of initial guesses at a solution, and using a Newton-Raphson technique to determine if different initial points converge to different solutions. The second strategy involves a set of techniques known as homotopy methods. These do not require an initial guess, are globally convergent, and are guaranteed, in principle, to find all solutions of the continuity equations. The first method is efficient but essentially 'hit or miss' in the sense that it cannot guarantee that all solutions which may exist will be found. The second method is computationally burdensome but can, in principle, determine all the solutions of a photochemical system. Multiple solutions have been found for models that contain a basic complement of photochemical reactions involving O(x), HO(x), NO(x), and CH4. In the present calculations, transitions occur between stable branches of a multiple solution set as a control parameter is varied. These transitions are manifestations of hysteresis phenomena in the photochemical system and may be triggered by increasing the NO flux or decreasing the CH4 flux from current mean tropospheric levels.

Stewart, Richard W.↗

NASA NTRS1993

A time-accurate finite volume method valid at all flow velocities

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

Kim, S.-W.↗