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NASA NTRS1991

Tidal disruption of inviscid protoplanets

Roche showed that equilibrium is impossible for a small fluid body synchronously orbiting a primary within a critical radius now termed the Roche limit. Tidal disruption of orbitally unbound bodies is a potentially important process for planetary formation through collisional accumulation, because the area of the Roche limit is considerably larger then the physical cross section of a protoplanet. Several previous studies were made of dynamical tidal disruption and different models of disruption were proposed. Because of the limitation of these analytical models, we have used a smoothed particle hydrodynamics (SPH) code to model the tidal disruption process. The code is basically the same as the one used to model giant impacts; we simply choose impact parameters large enough to avoid collisions. The primary and secondary both have iron cores and silicate mantles, and are initially isothermal at a molten temperature. The conclusions based on the analytical and numerical models are summarized.

Boss, Alan P.↗

NASA NTRS1988

Chemoviscosity modeling for thermosetting resin systems, part 3

A new analytical model for simulating chemoviscosity resin has been formulated. The model is developed by modifying the well established Williams-Landel-Ferry (WLF) theory in polymer rheology for thermoplastic materials. By introducing a relationship between the glass transition temperature (T sub g (t)) and the degree of cure alpha(t) of the resin system under cure, the WLF theory can be modified to account for the factor of reaction time. Temperature-dependent functions of the modified WLF theory parameters C sub 1 (T) and C sub 2 (T) were determined from the isothermal cure data. Theoretical predictions of the model for the resin under dynamic heating cure cycles were shown to compare favorably with the experimental data. This work represents a progress toward establishing a chemoviscosity model which is capable of not only describing viscosity profiles accurately under various cure cycles, but also correlating viscosity data to the changes of physical properties associated with the structural transformations of the thermosetting resin systems during cure.

Hou, T. H.↗

NASA NTRS1994

X-Ray Emission from a Simulated Cluster of Galaxies

Using the 1993 cluster simulation of Katz & White, we analyze the intracluster medium and investigate the accuracy of the standard hydrostatic method for determining cluster masses. We show that the simulated cluster gas is in hydrostatic equilibrium with a subsonic flow toward the center. Inside a radius of (approx.) 100 kpc, this flow is in a steady state. The cooling time is shorter than a Hubble time within the central 50 kpc. The flow rate is regulated by the gas sink in the middle of the cluster and the PdV work done as the gas flows in, verifying the standard cooling flow scenario. We simulate observations of the cluster using the instrument parameters of the EXOSAT ME detector and the Einstein IPC detector. Even though the intracluster gas is not isothermal, isothermal models of the cluster, excluding regions within 100 kpc of galaxies, fit the EXOSAT X-ray spectra as well as they fit real clusters. The X- ray surface brightness distribution is similar to that of real clusters, again excluding the galaxies. We simulate the procedure used to determine the masses of real clusters. We use the equation of hydrostatic equilibrium together with the temperature derived from an isothermal fit to the simulated EXOSAT spectrum and the density profile derived from a fit to the simulated IPC surface brightness profile to determine the mass. A comparison of the derived mass profile to the actual mass profile shows that errors of a factor of 2 are possible. If the actual temperature profile is used, the cluster mass is found to an accuracy of better than 25% within the virial radius.

Tsai, John C.↗

NASA NTRS1999

Sensitivity of Temperature Profiles Retrieved from Mars Global Surveyor Thermal Emission Spectrometer (MGS/TES) Observations to the GSFC Synthetic Mars Model Atmosphere

Part of the task of interpreting IR spectral features observed by MGS/TES due to surface minerals requires distinguishing those IR signatures from atmospheric signatures of gas and dust. Surface-atmosphere separation for MGS/TES depends on knowledge of the retrieved temperature profile. In turn, the temperature retrieval Erom the observed data depends on molecular parameters including 15 micron CO2 line shape or line intensities which contribute to defining the Mars synthetic radiative transfer model. Using a simple isothermal, homogeneous single layer model of Pinnock and Shine, we find the ratio of (the error in degrees Kelvin of the retrieved temperature profile) to (the percentage error in the absorption coefficient) (deg K/percent) to be 0.4 at 200K. This ratio at 150K and 250K is 0.2 and 0.6, respectively. A more refined model, incorporating observed MGS/TES retrieved temperature profiles, the TES instrumental resolution and the most recent molecular modelling, will yield an improved knowledge of this error sensitivity. We present results of such a sensitivity study to determine the dependence of temperature profiles inverted from MGS/TES on these and other molecular parameters. This work was supported in part by NASA's Mars Data Analysis Program.

Maguire, William C.↗

NASA NTRS2001

Predicting Turbulent Convective Heat Transfer in Fully Developed Duct Flows

The performance of an explicit algebraic stress model (EASM) is assessed in predicting the turbulent flow and forced heat transfer in both straight and wavy ducts, with rectangular, trapezoidal and triangular cross-sections, under fully developed conditions. A comparison of secondary flow patterns. including velocity vectors and velocity and temperature contours, are shown in order to study the effect of waviness on flow dynamics, and comparisons between the hydraulic parameters. Fanning friction factor and Nusselt number, are also presented. In all cases. isothermal conditions are imposed on the duct walls, and the turbulent heat fluxes are modeled using gradient-diffusion type models. The formulation is valid for Reynolds numbers up to 10(exp 5) and this minimizes the need for wall functions that have been used with mixed success in previous studies of complex duct flows. In addition, the present formulation imposes minimal demand on the number of grid points without any convergence or stability problems. Criteria in terms of heat transfer and friction factor needed to choose the optimal wavy duct cross-section for industrial applications among the ones considered are discussed.

Rokni, Masoud↗

NASA NTRS1996

Interplanetary and Interstellar Dust Particles: Reentry Heating and Capture in Aerogel

Studies of interplanetary and interstellar dust can provide significant information on the evolution of the solar system or stars, respectively. However, for reliable analysis it is crucial to know how the particles have been modified during reentry (in the case of interplanetary dust particles, or [DP's) and impact into the capture medium. In the case of stratospheric capture, particles will be heated by atmospheric drag. Subsequent capture of the particles will result in heating, ablation, accretion of the capture medium and possible fragmentation. Modeling of these processes is a useful way of assessing their effects on the interpretation of the compositional data for these particles. Previous work on reentry heating has shown that heat diffusion alone cannot adequately account for temperature gradients observed in IDP's. In fact, for any reasonable thermal parameters, calculations show the particles to be nearly isothermal. Here we extend those studies to include phase transitions. These preliminary results are promising and show a significant temperature gradient for a 100 micron (diameter) particle. The actual capture of the particles in silica aerogel is being modeled using a comprehensive shock hydrodynamic code (called CTH). Various options of this code were investigated to attempt to make the most appropriate choice of methods of impact, equations of state, and processes of energy transfer from capture material to particle. The initial calculations with the code used only 'reasonable' estimates for the physical parameters of silica aerogel. Through the literature searches and personal contacts with the knowledgeable scientists, the best possible mechanical and thermal data have been made available for these computations.

Szydlik, Paul P.↗

NASA NTRS1992

Analysis of stellar occultation data for planetary atmospheres. I - Model fitting, with application to Pluto

Consideration is given to an analytic model for a stellar-occultation light curve developed for a small, spherically symmetric planetary atmosphere that includes thermal and molecular weight gradients in a region that overlies an extinction layer. The model incorporates two equivalent sets of parameters. One set specifies the occultation light curve in terms of signal levels, times, and time intervals. The other set specifies physical parameters of the planetary atmosphere. Equations are given for the transforming between the sets of parameters, including their errors and correlation coefficients. Detailed numerical calculations are presented for a benchmark case. The results obtained are consistent with the isothermal prediction of the 'methane-thermostat' model of Pluto's atmosphere.

Elliot, J. L.↗

NASA NTRS2002

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

Freed, Alan D.↗

NASA NTRS1982

Non-isothermal effects on SO2 absorption by water droplets. I - Model development. II - Results and discussion

An analytic model of SO2 absorption in a falling water droplet is developed and a simulation of SO2 washout is performed. Nonisothermic effects on drop growth, droplet physical parameters, reaction rates, and multicomponent diffusion are treated in the model. The gas-liquid interface is assumed to be at equilibrium, and interfacial resistance is negligible. Raindrops are simulated as falling from a 2 km height through an atmospheric region containing SO2. The droplets decrease in size from evaporation and cooling, and their slightly basic pH aids SO2 absorption. The simulation indicates higher SO2 absorption at higher altitudes, and desorption may occur at ground level. Isothermal effects are concluded to be significant, and quantification of effects will depend on further modelling.

Reda, M.↗

NASA NTRS2000

Sunyaev-Zeldovich Effect-Derived Distances to the High-Redshift Clusters

We determine the distances to the z approximately equals 0.55 galaxy clusters MS 0451.6 - 0305 and Cl 0016 + 16 from a maximum-likelihood joint fit to interferometric Sunyaev-Zeldovich effect (SZE) and X-ray observations. We model the intracluster medium (ICM) using a spherical isothermal beta model. We quantify the statistical and systematic uncertainties inherent to these direct distance measurements, and we determine constraints on the Hubble parameter for three different cosmologies. For an Omega(sub M) = 0.3, Omega(sub lambda) = 0.7 cosmology, these distances imply a Hubble constant of 63(sup +12) (sub -9) (sup + 21) (sub -21) km/s Mp/c, where the uncertainties correspond to statistical followed by systematic at 68% confidence. The best-fit H(sub 0) is 57 km/s Mp/c for an open (Omega(sub M) = 0.3) universe and 52 km/s Mp/c for a flat (Omega(sub M) = 1) universe.

Reese, Erik D.↗

NASA NTRS2002

Determining the Cosmic Distance Scale from Interferometric Measurements of the Sunyaev-Zel'Dovich Effect

The distances to eighteen galaxy clusters are determined, with redshifts ranging from z approx. 0.14 to z approx. 0.78 from a maximum likelihood joint analysis of 30 GHz interferometric Sunyaev-Zel'dovich effect (SZE) and X-ray observations. We model the intracluster medium (ICM) using a spherical isothermal beta model. We quantify the statistical and systematic uncertainties inherent to these direct distance measurements, and we determine constraints on the Hubble parameter for three different cosmologies. These distances imply a Hubble constant of 60((sup +4+13)(sub -4-18)) km s(exp -1) megaparsec(exp -1) for an Omega(sub M) = 0.3, Omega(sub Lambda) = 0.7 cosmology, where the uncertainties correspond to statistical followed by systematic at 68% confidence. With a sample of eighteen clusters, systematic uncertainties clearly dominate. The systematics are observationally approachable and will be addressed in the coming years through the current generation of X-ray satellites (Chandra & XMIM-Newton) and radio observatories (OVRO (Owens Valley Radio Observatory), BIMA (Berkeley Illinois Maryland Association), & VLA (Very Large Array)). Analysis of high redshift clusters detected in future SZE and X-ray surveys will allow a determination of the geometry of the universe from SZE determined distances.

Reese, Erik D.↗

NASA NTRS2002

Determining the Cosmic Distance Scale from Interferometric Measurements of the Sunyaev-Zeldovich Effect

We determine the distances to 18 galaxy clusters with redshifts ranging from z approximately 0.14 to 0.78 from a maximum likelihood joint analysis of 30 GHz interferometric Sunyaev-Zeldovich effect (SZE) and X-ray observations. We model the intracluster medium (ICM) using a spherical isothermal Beta model. We quantify the statistical and systematic uncertainties inherent to these direct distance measurements, and we determine constraints on the Hubble parameter for three different cosmologies. These distances imply a Hubble constant of 60(sup+4+13)(sub-4-18)km s(exp -1)Mpc(exp -1) for an omega(sub Mu)= 0.3,omega(sub Lambda)=0.7 cosmology, where the uncertainties correspond to statistical followed by systematic at 68% confidence. With a sample of 18 clusters, systematic uncertainties clearly dominate. The systematics are observationally approachable and will be addressed in the coming years through the current generation of X-ray satellites (Chandra and XMM-Newton) and radio observatories (Owens Valley Radio Observatory, Berkeley-Illinois-Maryland Association, and Very Large Array). Analysis of high-redshift clusters detected in future SZE and X-ray surveys will allow a determination of the geometry of the universe from SZE-determined distances.

Reese, Erik D.↗

NASA NTRS1991

Effects of elevated temperature on the viscoplastic modeling of graphite/polymeric composites

To support the development of new materials for the design of next generation supersonic transports, a research program is underway at NASA to assess the long term durability of advanced polymer matrix composites (PMC's). One of main objectives of the program was to explore the effects of elevated temperature (23 to 200 C) on the constitutive model's material parameters. To achieve this goal, test data on the observed nonlinear, stress-strain behavior of IM7/5260 and IM7/8320 composites under tension and compression loading were collected and correlated against temperature. These tests, conducted under isothermal conditions using variable strain rates, included such phenomena as stress relaxation and short term creep. The second major goal was the verification of the model by comparison of analytical predictions and test results for off axis and angle ply laminates. Correlation between test and predicted behavior was performed for specimens of both material systems over a range of temperatures. Results indicated that the model provided reasonable predictions of material behavior in load or strain controlled tests. Periods of loading, unloading, stress relaxation, and creep were accounted for.

Gates, Thomas S.↗

NASA NTRS2000

Sunyaev-Zel'dovich Effect Derived Distance to the High Redshift Clusters MS 0451.6-0305 and CL 0016+16

We determine the distances to the z approximately equal to 0.55 galaxy clusters MS 0451.6-0305 and CL 0016+16 from a maximum likelihood joint fit to interferometric Sunyaev-Zel'dovich effect (SZE) and X-ray observations. We model the intracluster medium (ICM) using a spherical isothermal beta-model. We quantify the statistical and systematic uncertainties inherent to these direct distance measurements, and we determine constraints on the Hubble parameter for three different cosmologies. For an OmegaM = 0.3, OmegaL = 0.7 cosmology, these distances imply a Hubble constant of 63(exp 12)(sub -9)(exp +21)(sub -21) km/s/Mpc, where the uncertainties correspond to statistical followed by systematic at 68% confidence. The best fit H(sub o) is 57 km/sec/Mpc for an open OmegaM = 0.3 universe and 52 km/s/Mpc for a flat Omega = 1 universe.

Reese, E. D.↗

NASA NTRS1995

A study of cooling flows in poor clusters of galaxies

We observed three poor clusters with central dominant galaxies (AWM 4, MKW 4, and MKW 3's) using the Position Sensitive Proportional Counter on the ROSAT X-ray satellite. The images reveal smooth, symmetrical X-ray emission filling the cluster with a sharp peak on each central galaxy. The cluster surface brightness profiles can be decomposed using superposed King models for the central galaxy and the intracluster medium. The King model parameters for the cluster portions are consistent with previous observations of these clusters. The newly measured King model parameters for the central galaxies are typical of the X-ray surface brightness distributions of isolated elliptical galaxies. Spatially resolved temperature measurements in annular rings throughout the clusters show a nearly isothermal profile. Temperatures are consistent with previously measured values, but are much better determined. There is no significant drop in temperature noted in the innermost bins where cooling flows are likely to be present, nor is any excess absorption by cold gas required. All cold gas columns are consistent with galactic foreground absorption. We derive mass profiles for the clusters assuming both isothermal temperature profiles and cooling flow models with constant mass flow rates. Our results are consistent with previous Einstein IPC observations by Kriss, Cioffi, & Canizares, but extend the mass profiles out to 1 Mpc in these poor clusters.

Kriss, Gerard A.↗

NASA NTRS1972

Lunar ash flows - Isothermal approximation.

Suggestion of the ash flow mechanism as one of the major processes required to account for some features of lunar soil. First the observational background and the gardening hypothesis are reviewed, and the shortcomings of the gardening hypothesis are shown. Then a general description of the lunar ash flow is given, and a simple mathematical model of the isothermal lunar ash flow is worked out with numerical examples to show the differences between the lunar and the terrestrial ash flow. The important parameters of the ash flow process are isolated and analyzed. It appears that the lunar surface layer in the maria is not a residual mantle rock (regolith) but a series of ash flows due, at least in part, to great meteorite impacts. The possibility of a volcanic contribution is not excluded. Some further analytic research on lunar ash flows is recommended.

Pai, S. I.↗

NASA NTRS2005

On Modeling Air/Space-Borne Radar Returns in the Melting Layer

The bright band is the enhanced radar echo associated with the melting of hydrometeors in stratiform rain where the melting process usually occurs below 0 C isotherm over a distance of about 500m. To simulate this radar signature, a scattering model of melting snow is proposed in which the fractional water content is prescribed as a function of the radius of a spherical mixed- phase particle consisting of air, ice and water. The model is based on the observation that melting starts at the surface of the particle and then gradually develops towards the center. To compute the scattering parameters of a non-uniform melting particle, the particle is modeled as a sphere represented by a collection of 64(exp 3) cubic cells of identical size where the probability of water at any cell is prescribed as a function of the radius. The internal field of the particle, used for deriving the effective dielectric constant, is computed by the Conjugate Gradient and Fast Fourier Transform (CGFFT) numerical methods. To make computations of the scattering parameters more efficient, a multi-layer stratified-sphere scattering model is introduced after demonstrating that the scattering parameters of the non-uniformly melting particle can be accurately reproduced by the stratified sphere. In conjunction with a melting layer model that describes the melting fractions and fall velocities of hydrometeors as a function of the distance from the 0 C isotherm, the stratified-sphere model is used to simulate the radar bright band profiles. These simulated profiles are shown to compare well with measurements from the Precipitation Radar (PR) aboard the Tropical Rainfall Measuring Mission (TRMM) satellite and a dual-wavelength airborne radar. The results suggest that the proposed model of a melting snow particle may be useful in studying the characteristics of the bright-band in particular and mixed- phase hydrometeors in general.

Liao, Liang↗

NASA NTRS1982

Fracture mechanics criteria for turbine engine hot section components

The application of several fracture mechanics data correlation parameters to predicting the crack propagation life of turbine engine hot section components was evaluated. An engine survey was conducted to determine the locations where conventional fracture mechanics approaches may not be adequate to characterize cracking behavior. Both linear and nonlinear fracture mechanics analyses of a cracked annular combustor liner configuration were performed. Isothermal and variable temperature crack propagation tests were performed on Hastelloy X combustor liner material. The crack growth data was reduced using the stress intensity factor, the strain intensity factor, the J integral, crack opening displacement, and Tomkins' model. The parameter which showed the most effectiveness in correlation high temperature and variable temperature Hastelloy X crack growth data was crack opening displacement.

Meyers, G. J.↗