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High-Order Entropy Stable Formulations for Computational Fluid Dynamics

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

Carpenter, Mark H.↗

Recent Development in the CESE Method for the Solution of the Navier-Stokes Equations Using Unstructured Triangular or Tetrahedral Meshes With High Aspect Ratio

In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.

Chang, Sin-Chung↗

A PANSONIC Navier-Stokes solver

A finite-difference formulation of the full Navier-Stokes equations which demonstrates a capability to economically solve two-dimensional problems has been developed. The basic algorithm was derived from the full, Reynolds-averaged, conservative, Navier-Stokes equations expressed in curvilinear coordinates. Eddy viscosity was determined by the Baldwin and Lomax algebraic turbulence model. This non-iterative, second-order accurate, implicit, numerical algorithm is based on the approximate factorization finite-difference scheme of Beam and Warming. Results indicate a facility for solving subsonic, transonic, and supersonic (hence PANSONIC) flows about arbitrary airfoils for a wide range of Reynolds numbers, Mach numbers, and angles of attack. Current computations demonstrate that vectorized implementations of this algorithm can solve steady-state, two-dimensional problems in five to ten minutes of computer time.

Cooper, G. K.↗

A two-layer diagnostic model of the long-term physical evolution of warm-core ring 82B

The present shipboard data in the 1982 time series on a single Gulf Stream warm core ring are composited on a cylindrical coordinate system following ring motion; 10 C-isotherm depth measurements are used in a two-layer model of the ring's structure to compute gradient current, kinetic energy, available potential energy (APE), and potential vorticity. The ring's evolution can be divided into two periods: April-late June, while the ring is isolated from strong Gulf Stream interaction, during which the ring loses APE at a low rate, and from July onward, following ring interactions with the Gulf Stream and topography with much higher energy loss. Within measurement errors, the potential vorticity at the center of the ring is conserved from April through August, implying nearly inviscid dynamics.

Olson, D. B.↗

Of mice and genes: evolution of vertebrate brain development

In this review the current understanding of genetic and molecular evolution of development, in particular the formation of the major axis of bilateral animals, is critically evaluated, and the early pattern formation in the hindbrain is related as much as possible to these processes. On the genetic level it is proposed that the exuberant multiplication of regulatory genes compared to that of structural genes relates to the increased flexibility of early vertebrate development. In comparisons to fruit flies, many conserved genes are found to be expressed very differently, while many others seem to reflect a comparable pattern and thus suggest a conservation of function. Even genes with a largely conserved pattern of expression may change the level at which they are expressed and the mechanisms by which they are regulated in their expression. Evolution and development of hindbrain motoneurons is reviewed, and it is concluded that both comparative data as well as more recent experimental data suggest a limited importance for the rhombomeres. Clearly, many cell fate-specifying processes work below the level of rhombomeres or in the absence of rhombomeres. It is suggested that more comparative developmental data are needed to establish firmly the relationship between homeobox genes and rhombomere specification in vertebrates other than a few model species.

NASA Discipline Developmental Biology↗

Large Solar-Rejection Filter

NASA utilized Image Intensified Video Cameras for ATV data acquisition from a jet flying at 12.8 km. Afterwards the video was digitized and then analyzed with a modified commercial software package, Image Systems Trackeye. Astrometric results were limited by saturation, plate scale, and imposed linear plate solution based on field reference stars. Time-dependent fragment angular trajectories, velocities, accelerations, and luminosities were derived in each video segment. It was evident that individual fragments behave differently. Photometric accuracy was insufficient to confidently assess correlations between luminosity and fragment spatial behavior (velocity, deceleration). Use of high resolution digital video cameras in future should remedy this shortcoming. A scenically accurate description of matter interpreted as a substance made up of corpuscular constituents was established during the course of the 19th century. In this description, atoms--the building blocks of the matter--form molecules. The properties of the molecules were described by chemistry or thermodynamics depending on what characteristics of the matter were investigated. In both theories, the molecules can dissociate to atoms when the kinetic energies of the atoms exceed the strength of the chemical bonds. The number of atoms is always preserved in a closed system. This is not true, however, when the matter takes up much higher energies at relativistic scales. New particles can be produced at the expense of the kinetic energy. The number of particles is no longer preserved. There are other conserved quantities, however, these quantities, the charge, baryon number, lepton number, are associated with particles that are considered elementary today. The properties and behavior of these elementary particles is the subject of Particle Physics or High Energy Physics. Practice Page: A crewmember touching a positively charged surface was thought to be galvanically isolated from the vehicle ground analogous to a bird on a high voltage power wire. Recent analysis confirms that positive floating potentials, ionospheric currents to the EVA suit, can be hazardous. The analysis is wrong in that the ionospheric plasma itself can close the circuit. Parametric analysis of very low voltage exposures (2 to 15 volts) could cause pain and/or involuntary muscle tetani or spinal cord shock. NASA worked with the Naval Health Research Center Detachment Directed Energy Bioeffects Laboratory to examine the affects electrical hazards could have on extravehicular activity using two models. The results of the two computational models were combined to predict areas of the body in which neurons of different diameters would be excited. They predicted that physiologically active current could be conducted across the crew member causing catastrophic hazards. Future work to analyze additional current paths was proposed. The FUSE spectrum of BB Dor, observed in a high state, is modeled with an accretion disk with a very low inclination (possibly lower than 10 degrees). Assuming an average WD mass of 0.8 solar mass leads to a distance of the order of approximately 650pc, consistent with the extremely low galactic reddening in its direction, and a mass accretion rate of 10 (exp -9) solar mass a year. The spectrum presents some broad and deep silicon and sulfur absorption lines, indicating that these elements are over-abundant: silicon is 3 times solar, and sulfur is 20 times solar. The FUSE spectrum of BB Dor, observed in a high state, is modeled with an accretion disk with a very low inclination (possibly lower than 10 degrees). Assuming an average WD mass of 0.8 solar mass leads to a distance of the order of approximately 650pc, consistent with the extremely low galactic reddening in its direction, and a mass accretion rate of 10 (exp -9) solar mass a year. The spectrum presents some broad and deep silicon and sulfur absorption lines, indicating that these elements are over-abundant: silicon is times solar, and sulfur is 20 times solar. From its previously observed optical emission lines, P831-57 (WD 0334 6400 or Ret 1 in A Catalog and Atlas of Cataclysmic Variables: Living Edition) has been suspected to contain an accretion disk associated with a companion star in orbit around a subdwarf star with a temperature T is greater than 21,000K. P831-57 has therefore been classified as a nova-like. However, our present observations show it to be a DA + dMe binary. The analysis of its Far Ultraviolet Spectroscopic Explorer (FUSE) spectrum (continuum and lines) reveal an average mass white dwarf (Log(g) approximately equals 7.8 plus or minus 0.1)with a temperature T approximately equals 37,000 plus or minus 500K, an extremely low projected rotational velocity, and a distance of about 115 plus or minus 5pc. The photosphere contains C, N, Si, and S (at about 1% of solar abundances). The dMe star is seen as a flux excess in near-infrared photometry and appears to show occasional flaring of about one magnitude as seen in the Harvard plates. There is no evidence of periodic variability in the spectroscopic or photometric data. We find no evidence of a an accretion disk, instead we find evidence of wind accretion as the stellar carbon abundance (N(C)/N(H) = 2.5 x 10 (exp -6) is about ten times larger than predicted by radiative levitation for such a gravity and temperature. The power needs and solutions for the space exploration and lunar mobility program are discussed. Long term missions in space and on the lunar surface require high energy batteries. Rechargeable batteries for mobility systems and portable utility pallet are needed for successful exploration missions. Nanomaterial usage increases the energy density of the cells apart from increasing the power density. The symptoms and threats from acute mountain sickness (AMS) are discussed. The underlying assumptions concerning spacecraft atmosphere mean there is a potential risk to astronauts. The baseline worst case scenario is about 25% based on direct ascent to 8.0 psia with 32% O2. The practical mitigation approach is a staged depressurization scheme. Due to the uncertainty about potential AMS risk the flight surgeon should prepare, focused research should proceed, and current analytical efforts should continue. This slide presentation reviews the threat astronauts face from acute mountain sickness (AMS). The incidence of AMS is highly variable and the risk to astronauts is unclear. However, the potential risk is higher than current EAAs suggest and precautions should be implemented. Due to the uncertain nature of the risk flight surgeons should prepare, and focused research should proceed. Quasiparticle tunneling can be understood at low temperatures using a non-equilibrium kinetic theory. Low-temperature tunneling can be suppressed using existing techniques: island-lead gap engineering, lead cooling with SIN junctions, and quasiparticle traps. The slide presentation reviews the science goals and mission planning for the proposed Jupiter System Observer (JSO). The spacecraft would accommodate 9 instruments making the instrument payload more capable than any previously flown to Jupiter. The would-be mission includes study programs for Jupiter's satellites, interior, magnetosphere and atmosphere. The power needs and solutions for the space exploration and lunar mobility program are discussed. Long term missions in space and on the lunar surface require high energy batteries. Rechargeable batteries for mobility systems and portable utility pallet are needed for successful exploration missions. Nanomaterial usage increases the energy density of the cells apart from increasing the power density. This slide presentation reviews the power requirements for the space exploration and the lunar surface mobility programs. It includes information about the specifications for high energy batteries and the power requirements for lunar rovers,

Roberts, William↗

A direct current rectification scheme for microwave space power conversion using traveling wave electron acceleration

The formation of the Vision-21 conference held three years ago allowed the present author to reflect and speculate on the problem of converting electromagnetic energy to a direct current by essentially reversing the process used in traveling wave tubes that converts energy in the form of a direct current to electromagnetic energy. The idea was to use the electric field of the electromagnetic wave to produce electrons through the field emission process and accelerate these electrons by the same field to produce an electric current across a large potential difference. The acceleration process was that of cyclotron auto-resonance. Since that time, this rather speculative ideas has been developed into a method that shows great promise and for which a patent is pending and a prototype design will be demonstrated in a potential laser power beaming application. From the point of view of the author, a forum such as Vision-21 is becoming an essential component in the rather conservative climate in which our initiatives for space exploration are presently formed. Exchanges such as Vision-21 not only allows us to deviate from the 'by-the-book' approach and rediscover the ability and power in imagination, but provides for the discussion of ideas hitherto considered 'crazy' so that they may be given the change to transcend from the level of eccentricity to applicability.

Manning, Robert M.↗

Stability Analysis of ISS Medications

It is known that medications degrade over time, and that extreme storage conditions will hasten their degradation. The temperature and humidity conditions of the ISS have been shown to be within the ideal ranges for medication storage, but the effects of other environmental factors, like elevated exposure to radiation, have not yet been evaluated. Current operational procedures ensure that ISS medications are re-stocked before expiration, but this may not be possible on long duration exploration missions. For this reason, medications that have experienced long duration storage on the ISS were returned to JSC for analysis to determine any unusual effects of aging in the low- Earth orbit environment. METHODS Medications were obtained by the JSC Pharmacy from commercial distributors and were re-packaged by JSC pharmacists to conserve up mass and volume. All medication doses were part of the ISS crew medical kit and were transported to the International Space Station (ISS) via NASA's Shuttle Transportation System (Space Shuttle). After 568 days of storage, the medications were removed from the supply chain and returned to Earth on a Dragon (SpaceX) capsule. Upon return to Earth, medications were transferred to temperature and humidity controlled environmental chambers until analysis. Nine medications were chosen on the basis of their availability for study. The medications included several of the most heavily used by US crewmembers: 2 sleep aids, 2 antihistamines/decongestants, 3 pain relievers, an antidiarrheal and an alertness medication. Each medication was available at a single time point; analysis of the same medication at multiple time points was not possible. Because the samples examined in this study were obtained opportunistically from medical supplies, there were no control samples available (i.e. samples aged for a similar period of time on the ground); a significant limitation of this study. Medications were analyzed using the HPLC/MS methods described in the United States Pharmacopeia (USP) to measure the amount of intact active ingredient, identify degradation products and measure their amounts. Some analyses were conducted by an independent analytical laboratory, but certain (Schedule) medications could not be shipped to their facility and were analyzed at JSC. RESULTS Nine medications were analyzed with respect to active pharmaceutical ingredient (API) and degradant amounts. Results were compared to the USP requirements for API and degradants/impurities content for every FDA-approved medication. One medication met USP requirements at 5 months after its expiration date. Four of the nine (44% of those tested) medications tested met USP requirements up to 8 months post-expiration. Another 3 medications (33% of those tested) met USP guidelines 2-3 months before expiration. One medication, a compound classed by the FDA as a dietary supplement and sometimes used as a sleep aid, failed to meet USP requirements at 11 months post-expiration. CONCLUSION Analysis of each medication at a single time point provides limited information on the stability of a medication stored in particular conditions; it is not possible to predict how long a medication may be safe and effective from these data. Notwithstanding, five of the nine medications tested (56%) met USP requirements for API and degradants/impurities at least 5 months past expiration dates. The single compound that failed to meet USP requirements is not regulated as strictly as prescription medications are during manufacture; it is unknown if this medication would have met the requirements prior to flight. Notably, it was the furthest beyond its expiration date. Only more comprehensive analysis of flight-aged samples compared to appropriate ground controls will permit determination of spaceflight effects on medication stability.

Wotring, V. E.↗

Bypass transition in compressible boundary layers

Transition to turbulence in aerospace applications usually occurs in a strongly disturbed environment. For instance, the effects of free-stream turbulence, roughness and obstacles in the boundary layer strongly influence transition. Proper understanding of the mechanisms leading to transition is crucial in the design of aircraft wings and gas turbine blades, because lift, drag and heat transfer strongly depend on the state of the boundary layer, laminar or turbulent. Unfortunately, most of the transition research, both theoretical and experimental, has focused on natural transition. Many practical flows, however, defy any theoretical analysis and are extremely difficult to measure. Morkovin introduced in his review paper the concept of bypass transition as those forms of transition which bypass the known mechanisms of linear and non-linear transition theories and are currently not understood by experiments. In an effort to better understand the mechanisms leading to transition in a disturbed environment, experiments are conducted studying simpler cases, viz. the effects of free stream turbulence on transition on a flat plate. It turns out that these experiments are very difficult to conduct, because generation of free stream turbulence with sufficiently high fluctuation levels and reasonable homogeneity is non trivial. For a discussion see Morkovin. Serious problems also appear due to the fact that at high Reynolds numbers the boundary layers are very thin, especially in the nose region of the plate where the transition occurs, which makes the use of very small probes necessary. The effects of free-stream turbulence on transition are the subject of this research and are especially important in a gas turbine environment, where turbulence intensities are measured between 5 and 20 percent, Wang et al. Due to the fact that the Reynolds number for turbine blades is considerably lower than for aircraft wings, generally a larger portion of the blade will be in a laminar transitional state. The effects of large free stream turbulence in compressible boundary layers at Mach numbers are examined both in the subsonic and transonic regime using direct numerical simulations. The flow is computed over a flat plate and curved surface. while many applications operate in the transonic regime. Due the nature of their numerical scheme, a non-conservation formulation of the Navier-Stokes equations, it is a non-trivial extension to compute flow fields in the transonic regime. This project aims at better understanding the effects of large free-stream turbulence in compressible boundary layers at mach number both in the subsonic and transonic regime using direct numerical simulations. The present project aims at computing the flow over a flat plate and curved surface. This research will provide data which can be used to clarify mechanisms leading to transition in an environment with high free stream turbulence. This information is useful for the development of turbulence models, which are of great importance for CFD applications, and are currently unreliable for more complex flows, such as transitional flows.

Vandervegt, J. J.↗

Risks, designs, and research for fire safety in spacecraft

Current fire protection for spacecraft relies mainly on fire prevention through the use of nonflammable materials and strict storage controls of other materials. The Shuttle also has smoke detectors and fire extinguishers, using technology similar to aircraft practices. While experience has shown that the current fire protection is adequate, future improvements in fire safety technology to meet the challenges of long duration space missions, such as the Space Station Freedom, are essential. All spacecraft fire protection systems, however, must deal with the unusual combustion characteristics and operational problems in the low gravity environment. The features of low gravity combustion that affect spacecraft fire safety, and the issues in fire protection for Freedom that must be addressed eventually to provide effective and conservative fire protection systems are discussed.

Friedman, Robert↗

Firex Water Tank, SWMU 069, Confirmatory Sampling Report

The National Aeronautics and Space Administration (NASA) Resource Conservation and Recovery Act (RCRA) permit requires identification and evaluation of known Solid Waste Management Units (SWMU) located at the Kennedy Space Center (KSC). Firex Water Tank (FWT), or the “site,” is designated as SWMU 069 under the NASA RCRA permit. This report summarizes the results of the Confirmatory Sampling (CS) field activities carried out during Fall 2021, at FWT, SWMU 069, KSC, Florida. Three locations of concern (LOCs) were identified by screening historical sample results to current State of Florida soil cleanup target levels (SCTL). A total of 18 soil samples were collected to investigate the historical exceedance locations. Samples at LOC 1 and 2 were analyzed for arsenic and the results for all were below the SCTL. Samples at LOC 3 were analyzed for polynuclear aromatic hydrocarbons and it was determined that certain locations have results that remain above the SCTL. The current land use controls will remain in place at FWT to mitigate potential risks.

Firex↗

Firex Water Tank, SWMU 069, Confirmatory Sampling Report: Revision 2

The National Aeronautics and Space Administration (NASA) Resource Conservation and Recovery Act (RCRA) permit requires identification and evaluation of known Solid Waste Management Units (SWMU) located at the Kennedy Space Center (KSC). Firex Water Tank (FWT), or the “site,” is designated as SWMU 069 under the NASA RCRA permit. This report summarizes the results of the Confirmatory Sampling (CS) field activities carried out during Fall 2021, at FWT, SWMU 069, KSC, Florida. Three locations of concern (LOCs) were identified by screening historical sample results to current State of Florida soil cleanup target levels (SCTL). A total of 18 soil samples were collected to investigate the historical exceedance locations. Samples at LOC 1 and 2 were analyzed for arsenic and the results for all were below the SCTL. Samples at LOC 3 were analyzed for polynuclear aromatic hydrocarbons and it was determined that certain locations have results that remain above the SCTL. The current land use controls will remain in place at FWT to mitigate potential risks.

Firex↗

Violation of Field Line Conservation and Associated Spatial Scales in Particle-In-Cell Simulations and MMS Data

For the first time, space flight technology exists to detect, in situ, violation of magnetic field line conservation. The violation of magnetic line conservation on scales smaller than the system size is a necessary and sufficient condition for finite magnetic field reconnection. We demonstrate that violation of line conservation produces a detectable, structured signature both in particle-in-cell simulations of reconnection and in data from the Magnetospheric Multi-Scale mission. In particle-in-cell simulations of asymmetric reconnection, the quantity-which we call M-that identifies this violation achieves significant values in electron skin depth-scale layers that extend away from the separator, with higher values emerging on the low-density, high-magnetic-field side of the current sheet. At the separator, M owes largely to perpendicular gradients in the parallel electric field, while it attains its highest values away from the separator in dispersed, layered structures associated with gradients in the perpendicular nonideal electric field and electron transport. Sub-ion scale bipolar forms of the quantity also appear further from the separator. In two MMS burst data intervals detecting the electron diffusion region, we find that M exceeds measurement uncertainties both at the separator and near the separatrices. One interval has highly sheared reconnecting fields and the other a stronger guide field. For one event, we determine the location and scale of M and the inner electron diffusion region relative to electron outflows and the magnetic separatrices. The measure can therefore serve as a potent diagnostic for magnetic reconnection in space measurements.

Wendel, Deirdre E.↗

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

Davis, J. E.↗

Magnetopause structure and the question of particle accessibility

A simple plane model of the magnetopause is used to address the question of particle accessibility. Particle motion in the current sheet region is analyzed, showing that the concept of gyromotion is useful even when the electric and magnetic fields vary significantly over the gyroradius, as long as the variation is perpendicular to the drift direction. The first adiabatic invariant for particle motion is defined in such a way that it is preserved in regions of large field gradients, provided that the gradients are in a direction primarily perpendicular to the particle drifts. This generalized invariant provides an adiabatically conserved quantity that can be used to characterize particles as they move from a source region through the drift region and into the magnetopause itself, helping to resolve the accessibility question. Some preliminary results are given for the magnetopause structure based on the location of particle guiding points.

Whipple, E. C.↗

Upper-ocean velocity structure of Gulf Stream warm-core ring 82B

Acoustic-Doppler current profiling of warm-core ring (WCR) 82B revealed changes in the velocity structure over much of the ring's 7-month lifespan. As ring diameter decreased, peak speeds in the high-velocity region decreased from 0.8 m/s in April 1982 to 0.5 m/s in August 1982. Azimuthally averaged velocities revealed the core of WCR 82B to be in near solid-body rotation, with little measurable horizontal divergence at 100 m. In addition, potential vorticity was conserved in the ring core despite interactions with the Gulf Stream and large changes in ring size. Deviations from symmetry in WCR 82B were caused by superposition with the shelf-slope front, small cyclonic eddies, and upper-layer mean flow.

Joyce, T. M.↗

HSR Propulsion System Studies: A Status Report on the Down-Select Process

When the HSR program began there was widespread belief that a simple and familiar turbojet-like engine coupled to an advanced technology mixer-ejector nozzle was the propulsion system of choice for achieving FAR 36-Stage 3 noise requirements. Our ability to quickly demonstrate a practical 20(+) dB suppression nozzle was confidently presumed by many. Our rate of progress towards that objective, however, has been somewhat humbling. At the moment we are reasonably confident of achieving about 15 dB suppression with a mixer-ejector nozzle designed for a high specific thrust turbojet-like cycle. Therefore, if we make no further suppression progress and conservatively assume no new operational procedures such as programmed lapse rate (PLR), then meeting the Stage 3 goal requires a large amount of engine and/or wing oversizing which is economically prohibitive. The scenario is further aggravated by the possibility of eventually needing to comply with even more stringent regulations (Stage 4). While this status may be somewhat disappointing to some, it must be remembered that the HSR program plan involves two generations of mixer-ejector nozzles beyond the current generation I nozzle designs. It is premature to conclude that we cannot design a practical 20(+) dB mixer-ejector nozzle. On the other hand, it is prudent to consider alternative solutions to the noise problem. Thus, we are investigating four other propulsion system concepts.

Strack, W. C.↗

Rheology of Foam Near the Order-Disorder Transition

The first part of our research results are summarized in the recent journal publication: J. Gregory McDaniel and R. Glynn Holt, 'Measurement of aqueous foam rheology by acoustic levitation', Phys. Rev. E 61, 2204 (2000). This aspect of the work was a combination of experiment and analysis. We built a levitation system capable of acoustically levitating small samples of aqueous foam of arbitrary gas and liquid volume fractions. We then modulated the acoustic field to induce normal mode oscillations of the foam samples. The observables from the experiment were frequency and mode number. For dry (roughly > 70% gas by volume) foams and small deformations, we developed an effective medium, normal-modes analysis which took the frequency and mode number from experiment, and gave us the shear elastic modulus of the foam as a function of Poisson's ratio. The second part of our results may be found in a soon-to-be submitted manuscript 'Dynamics of aqueous foam drops', I.Sh. Akhatov, J.G. McDaniel and R.G. Holt, describing our modeling in the wet foam limit by considering the acoustic problem. This aspect of the research is purely theoretical. Beginning from a mass-conserving mixture law, the fully nonlinear equations of motion for a wet (roughly < 10% gas by volume) foam drop of initially spherical shape were derived. The frequencies for normal mode oscillations were derived in the linear inviscid limit. The nonlinear equations were numerically solved to elicit the motion of a foam drop under acoustic excitation. The role of the time-varying void fraction in breathing-mode oscillations is of particular interest. As of the end of the current (NAG#3-2121) grant, this work was not yet concluded. We continue to work on this aspect in order to extend the analysis to cover the transition regime of gas volume fractions, as well as to compare to experiments in the wet regime.

Holt, R. Glynn↗