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NASA NTRS1987

Quantitative characterization of the viscosity of a microemulsion

The viscosity of the three-component microemulsion water/decane/AOT has been measured as a function of temperature and droplet volume fraction. At temperatures well below the phase-separation temperature the viscosity is described by treating the droplets as hard spheres suspended in decane. Upon approaching the two-phase region from low temperature, there is a large (as much as a factor of four) smooth increase of the viscosity which may be related to the percolation-like transition observed in the electrical conductivity. This increase in viscosity is not completely consistent with either a naive electroviscous model or a simple clustering model. The divergence of the viscosity near the critical point (39 C) is superimposed upon the smooth increase. The magnitude and temperature dependence of the critical divergence are similar to that seen near the critical points of binary liquid mixtures.

Berg, Robert F.↗
NASA NTRS1988

Hypersonic shock structure with Burnett terms in the viscous stress and heat flux

The continuum Navier-Stokes and Burnett equations are solved for one-dimensional shock structure in various monatomic gases. A new numerical method is employed which utilizes the complete time-dependent continuum equations and obtains the steady-state shock structure by allowing the system to relax from arbitrary initial conditions. Included is discussion of numerical difficulties encountered when solving the Burnett equations. Continuum solutions are compared to those obtained utilizing the Direct Simulation Monte Carlo method. Shock solutions are obtained for a hard sphere gas and for argon from Mach 1.3 to Mach 50. Solutions for a Maxwellian gas are obtained from Mach 1.3 to Mach 3.8. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Shock density thickness, density asymmetry, and density-temperature separation are all more accurately predicted by the Burnett equations than by the Navier-Stokes equations.

Chapman, Dean R.↗
NASA NTRS1988

The equation of state for stellar envelopes. I - An occupation probability formalism for the truncation of internal partition functions

An equation of state for material in stellar envelopes, subject to the limits of temperature less than about 10 to the 7th K and density less than about .01 g/cu cm is presented. The equation makes it possible to express free energy as the sum of several terms representing effects such as partial degeneracy of the electron, Coulomb interactions among charged particles, finite-volume, hard sphere repulsion, and van der Waals attraction. An occupation probability formalism is used to represent the effects of the plasma in establishing a finite partition function. It is shown that the use of the static screened Coulomb potential to calculate level shifts and to estimate the cutoff of the internal partition function is invalid. For most of the parameter space relevant to stellar envelopes, perturbations arising from the plasma ions are shown to be dominant in establishing the internal partition function.

Hummer, D. G.↗
NASA NTRS1988

The dynamics of particle disks. II - Effects of spin degrees of freedom

The present treatment of the thermal equilibria of differentially-rotating, axisymmetric disks consisting of identical, spin-possessing as well as translational DOF-possessing hard sphere particles characterizes these disks' dynamics by means of two novel parameters: (1) the tangential restitution coefficient, and (2) the dimensionless moment of inertia. It is established that rings composed of spinning particles can generally be thermally balanced within more restricted ranges of the optical depth, as well as at higher values of the normal restitution coefficient, than spinless rings. Mean spin is indefinite in the present framework of neglected finite particle-size effects.

Araki, Suguru↗
NASA NTRS1987

Calculation of the surface tension of liquid metals using a one-component-plasma reference system

The one-component-plasma (OCP) model is used as a reference system instead of the traditional hard-sphere fluid to calculate the liquid-vapor interfacial surface tension of liquid metals within the density functional formalism. The calculated surface tensions of the alkali metals are in excellent agreement with experiment. For the polyvalent metal Al, the result obtained is larger than experimental measurements. It is concluded that the OCP system is not suitable to describe the liquid-vapor phase transition in simple metals which have a nominal plasma parameter larger than the usual freezing value of about 178. The calculated interfacial widths in all cases are narrower than the expected experimental values.

Zeng, X. C.↗
NASA NTRS1989

Validation of MCDS by comparison of predicted with experimental velocity distribution functions in rarefied normal shocks

Velocity distribution functions in normal shock waves in argon and helium are calculated using Monte Carlo direct simulation. These are compared with experimental results for argon at M = 7.18 and for helium at M = 1.59 and 20. For both argon and helium, the variable-hard-sphere (VHS) model is used for the elastic scattering cross section, with the velocity dependence derived from a viscosity-temperature power-law relationship in the way normally used by Bird (1976).

Pham-Van-diep, Gerald C.↗
NASA NTRS1989

Comparison of Burnett, super-Burnett and Monte Carlo solutions for hypersonic shock structure

The continuum Navier-Stokes, Burnett, and super-Burnett equations are solved for one-dimensional shock structures in various monoatomic gases. Solutions for a hard sphere gas, argon, and a Maxwellian gas from Mach 1.3 to Mach 50 are obtained. A numerical method utilizing the complete time-dependent continuum equations and obtaining the steady-state shock structure by allowing the system to relax from arbitrary initial conditions is employed. Shock density, velocity, temperature, and entropy profiles are also obtained using the direct simulation Monte Carlo method, and these results are used as bases for comparison for continuum solution profiles. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Solutions to the super-Burnett equations with coefficients as presently derived, however, are considered to be inferior to those of the Burnett equations.

Fiscko, Kurt A.↗
NASA NTRS1990

The generalized diffusion-convection equation

Starting from the Boltzmann equation, a transport equation is derived for energetic particles in a moving magnetized plasma in which the scattering centers that keep the particles quasi-isotropic are moving with a velocity that is not necessarily the same as that of the plasma. The scattering is characterized by three very loose constraints: (1) there is a rest frame for each scatterer in which the particles scatter elastically; (2) in this frame the scattering will not disturb an isotropic distribution; and (3) the momentum transfer in an average collision may be described by a tensor operating on the particles original momentum. Since the strength of the scattering is not specified, the derivation should be as valid for plasma microturbulence as for hard-sphere scattering. The results show clearly which phenomena are responsible for tying the particles to the plasma in the transport equation.

Jones, Frank C.↗
NASA NTRS1989

Aeroassist flight experiment aerodynamics and aerothermodynamics

The problem is to determine the transitional flow aerodynamics and aerothermodynamics, including the base flow characteristics, of the Aeroassist Flight Experiment (AFE). The justification for the computational fluid dynamic (CFD) Application stems from MSFC's system integration responsibility for the AFE. To insure that the AFE objectives are met, MSFC must understand the limitations and uncertainties of the design data. Perhaps the only method capable of handling the complex physics of the rarefied high energy AFE trajectory is Bird's Direct Simulation Monte Carlo (DSMC) technique. The 3-D code used in this analysis is applicable only to the AFE geometry. It uses the Variable Hard Sphere (VHS) collision model and five specie chemistry model available from Langley Research Center. The code is benchmarked against the AFE flight data and used as an Aeroassisted Space Transfer Vehicle (ASTV) design tool. The code is being used to understand the AFE flow field and verify or modify existing design data. Continued application to lower altitudes is testing the capability of the Numerical Aerodynamic Simulation Facility (NASF) to handle 3-D DSMC and its practicality as an ASTV/AFE design tool.

Brewer, Edwin B.↗
NASA NTRS1989

Monte Carlo simulation of particle acceleration at astrophysical shocks

A Monte Carlo code was developed for the simulation of particle acceleration at astrophysical shocks. The code is implemented in Turbo Pascal on a PC. It is modularized and structured in such a way that modification and maintenance are relatively painless. Monte Carlo simulations of particle acceleration at shocks follow the trajectories of individual particles as they scatter repeatedly across the shock front, gaining energy with each crossing. The particles are assumed to scatter from magnetohydrodynamic (MHD) turbulence on both sides of the shock. A scattering law is used which is related to the assumed form of the turbulence, and the particle and shock parameters. High energy cosmic ray spectra derived from Monte Carlo simulations have observed power law behavior just as the spectra derived from analytic calculations based on a diffusion equation. This high energy behavior is not sensitive to the scattering law used. In contrast with Monte Carlo calculations diffusive calculations rely on the initial injection of supra-thermal particles into the shock environment. Monte Carlo simulations are the only known way to describe the extraction of particles directly from the thermal pool. This was the triumph of the Monte Carlo approach. The question of acceleration efficiency is an important one in the shock acceleration game. The efficiency of shock waves efficient to account for the observed flux of high energy galactic cosmic rays was examined. The efficiency of the acceleration process depends on the thermal particle pick-up and hence the low energy scattering in detail. One of the goals is the self-consistent derivation of the accelerated particle spectra and the MHD turbulence spectra. Presumably the upstream turbulence, which scatters the particles so they can be accelerated, is excited by the streaming accelerated particles and the needed downstream turbulence is convected from the upstream region. The present code is to be modified to include a better description of particle scattering (pitch-angle instead of hard-sphere) and as iterative procedure for treating the self-excitation of the MHD turbulence.

Campbell, Roy K.↗
NASA NTRS1990

DSMC calculations for the delta wing

Results are reported from three-dimensional direct simulation Monte Carlo (DSMC) computations, using a variable-hard-sphere molecular model, of hypersonic flow on a delta wing. The body-fitted grid is made up of deformed hexahedral cells divided into six tetrahedral subcells with well defined triangular faces; the simulation is carried out for 9000 time steps using 150,000 molecules. The uniform freestream conditions include M = 20.2, T = 13.32 K, rho = 0.00001729 kg/cu m, and T(wall) = 620 K, corresponding to lambda = 0.00153 m and Re = 14,000. The results are presented in graphs and briefly discussed. It is found that, as the flow expands supersonically around the leading edge, an attached leeside flow develops around the wing, and the near-surface density distribution has a maximum downstream from the stagnation point. Coefficients calculated include C(H) = 0.067, C(DP) = 0.178, C(DF) = 0.110, C(L) = 0.714, and C(D) = 1.089. The calculations required 56 h of CPU time on the NASA Langley Voyager CRAY-2 supercomputer.

Celenligil, M. Cevdet↗
NASA NTRS1991

Complex angular momentum approximation to hard-core scattering

The complex angular momentum (CAM) approximation for nonrelativistic quantum scattering by a hard sphere - a union of the recently developed CAM uniform approximation with a semiclassical WKB-like approximation valid at large angles - is shown to be remarkably accurate over the complete range of scattering angles and down to size parameters (circumference to de Broglie wavelength ratios) of order unity. The best approximations previously derivable (Fock-type) cannot reach large scattering angles where semiclassical approximations are useful; even at angles where Fock-type approximations are valid, they are typically two or more orders of magnitude less accurate than CAM. The crucial new feature responsible for the high accuracy of the CAM approximation is the treatment of large-angle diffraction associated with (1) tunneling near the edge of the scatterer, and (2) anomalous reflection.

Nussenzveig, H. M.↗
NASA NTRS1991

New approach in direct-simulation of gas mixtures

Results are reported for an investigation of a new direct-simulation Monte Carlo method by which energy transfer and chemical reactions are calculated. The new method, which reduces to the variable cross-section hard sphere model as a special case, allows different viscosity-temperature exponents for each species in a gas mixture when combined with a modified Larsen-Borgnakke phenomenological model. This removes the most serious limitation of the usefulness of the model for engineering simulations. The necessary kinetic theory for the application of the new method to mixtures of monatomic or polyatomic gases is presented, including gas mixtures involving chemical reactions. Calculations are made for the relaxation of a diatomic gas mixture, a plane shock wave in a gas mixture, and a chemically reacting gas flow along the stagnation streamline in front of a hypersonic vehicle. Calculated results show that the introduction of different molecular interactions for each species in a gas mixture produces significant differences in comparison with a common molecular interaction for all species in the mixture. This effect should not be neglected for accurate DSMC simulations in an engineering context.

Chung, Chan-Hong↗
NASA NTRS1991

Testing continuum descriptions of low-Mach-number shock structures

Numerical experiments have been performed on normal shock waves with Monte Carlo Direct Simulations (MCDS's) to investigate the validity of continuum theories at very low Mach numbers. Results from the Navier-Stokes and the Burnett equations are compared to MCDS's for both hard-sphere and Maxwell gases. It is found that the maximum-slope shock thicknesses are described equally well (within the MCDS computational scatter) by either of the continuum formulations for Mach numbers smaller than about 1.2. For Mach numbers greater that 1.2, the Burnett predictions are more accurate than the Navier-Stokes results. Temperature-density profile separations are best described by the Burnett equations for Mach numbers greater than about 1.3. At lower Mach numbers the MCDS scatter is too great to differentiate between the two continuum theories. For all Mach numbers above one, the shock shapes are more accurately described by the Burnett equations.

Pham-Van-diep, Gerald C.↗
NASA NTRS1992

FDDO and DSMC analyses of rarefied gas flow through 2D nozzles

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas expanding through a two-dimensional nozzle and into a surrounding low-density environment. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere model is used as a molecular model and the no time counter method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by factors of 10 to 40 in CPU time, depending on the degree of rarefaction.

Chung, Chan-Hong↗
NASA NTRS1991

Heat transfer in a discrete-velocity gas

Heat transfer of a discrete-velocity gas composed of identical hard sphere molecules between two parallel plates is studied numerically. A finite-difference method recently developed by the authors is used for solving the discrete Boltzmann equations. The temperature distributions between the plates of temperature ratios 2.0 and 4.0, and the heat transfer of temperature ratio 4.0 are presented and are compared with results of other methods.

Inamuro, Takaji↗
NASA NTRS1986

Hot hydrogen atom reactions moderated by H2 and He

Photolysis experiments were performed on the H2-CD4-NH3 and He-CD4-NH3 systems. The photolysis (1849 A) involved only NH3. Mixtures of H2:CD4:NH3 included all combinations of the ratios (200,400,800):(10,20,40):4. Two He:CD4:NH3 mixtures were examined where the ratios equalled the combinations 100:(10,20):4. Abstraction of a D from CD4 by the photolytically produced hot hydrogen from ammonia was monitored by mass spectrometric determination of HD. Both experiment and semiempirical hot-atom theory show that H2 is a very poor thermalizer of hot hydrogens with excess kinetic energy of about 2 eV. Applications of the hard-sphere collision model to the H2-CD4-NH3 system resulted in predicted ratios of net HD production to NH3 decomposition that were two orders of magnitude smaller than the experimental ratios. On the other hand, helium is found to be a very efficient thermalizer; here, the classical model yields reasonable agreement with experiments. Application of a semiempirical hot-atom program gave quantitative agreement with experiment for either system.

Aronowitz, S.↗
NASA NTRS1993

Flow resolution and domain of influence in rarefied hypersonic blunt-body flows

The study assesses the effects of the upstream domain size and grid resolution upon flow properties and body aerodynamics computed for rarefied flows over cold blunt bodies with a direct simulation Monte Carlo (DSMC) particle method. Empirical correlations are suggested for aerodynamic coefficients for two-dimensional flows past a perpendicular flat plate. Free-stream parameters which were varied in the study include the Mach number, Knudsen number, surface temperature, and intermolecular potential. Insufficient grid resolution leads to overprediction of aerodynamic heating and forces in the DSMC method. Solution accuracy correlates well with the Reynolds number defined at the wall temperature and the stagnation mean free path relative to the cell dimension. Insufficient upstream domain size in the DSMC method leads to overprediction of heating and drag. Errors in aerodynamic coefficients correlate well with the distance ahead of the body where flow temperature reaches half of its peak value. Simulation of a hard-sphere gas is more sensitive to grid resolution, while simulation of a Maxwell gas is more sensitive to upstream domain size.

Haas, Brian L.↗