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NASA NTRS2000

A gas-kinetic BGK scheme for the compressible Navier-Stokes equations

This paper presents an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the compressible Navier-Stokes equations. The current method extends the previous gas-kinetic Navier-Stokes solver developed by Xu and Prendergast by implementing a general nonequilibrium state to represent the gas distribution function at the beginning of each time step. As a result, the requirement in the previous scheme, such as the particle collision time being less than the time step for the validity of the BGK Navier-Stokes solution, is removed. Therefore, the applicable regime of the current method is much enlarged and the Navier-Stokes solution can be obtained accurately regardless of the ratio between the collision time and the time step. The gas-kinetic Navier-Stokes solver developed by Chou and Baganoff is the limiting case of the current method, and it is valid only under such a limiting condition. Also, in this paper, the appropriate implementation of boundary condition for the kinetic scheme, different kinetic limiting cases, and the Prandtl number fix are presented. The connection among artificial dissipative central schemes, Godunov-type schemes, and the gas-kinetic BGK method is discussed. Many numerical tests are included to validate the current method.

Xu, Kun↗
NASA NTRS2000

A Probabilistic Approach to Aeropropulsion System Assessment

A probabilistic approach is described for aeropropulsion system assessment. To demonstrate this approach, the technical performance of a wave rotor-enhanced gas turbine engine (i.e. engine net thrust, specific fuel consumption, and engine weight) is assessed. The assessment accounts for the uncertainties in component efficiencies/flows and mechanical design variables, using probability distributions. The results are presented in the form of cumulative distribution functions (CDFs) and sensitivity analyses, and are compared with those from the traditional deterministic approach. The comparison shows that the probabilistic approach provides a more realistic and systematic way to assess an aeropropulsion system.

Tong, Michael T.↗
NASA NTRS1999

Modeling of THz Lasers Based on Intersubband Transitions in Semiconductor Quantum Wells

In semiconductor quantum well structures, the intersubband energy separation can be adjusted to the terahertz (THz) frequency range by changing the well width and material combinations. The electronic and optical properties of these nanostructures can also be controlled by an applied dc electric field. These unique features lead to a large frequency tunability of the quantum well devices. In the on-going project of modeling of the THz lasers, we investigate the possibility of using optical pumping to generate THz radiation based on intersubband transitions in semiconductor quantum wells. We choose the optical pumping because in the electric current injection it is difficult to realize population inversion in the THz frequency range due to the small intersubband separation (4-40 meV). We considered both small conduction band offset (GaAs/AlGaAs) and large band offset (InGaAs/AlAsSb) quantum well structures. For GaAs/AlGaAs quantum wells, mid-infrared C02 lasers are used as pumping sources. For InGaAs/AlAsSb quantum wells, the resonant intersubband transitions can be excited by the near-infrared diode lasers. For three- and four-subband quantum wells, we solve the pumpfield-induced nonequilibrium distribution function for each subband of the quantum well system from a set of rate equations that include both intrasubband and intersubband relaxation processes. Taking into account the coherent interactions between pump and THz (signal) waves, we calculate the optical gain for the THz field. The gain arising from population inversion and stimulated Raman processes is calculated in a unified manner. A graph shows the calculated THz gain spectra for three-subband GaAs/AlGaAs quantum wells. We see that the coherent pump and signal wave interactions contribute significantly to the gain. The pump intensity dependence of the THz gain is also studied. The calculated results are shown. Because of the optical Stark effect and pump-induced population redistribution, the maximum THz gain saturates at larger pump intensities.

Liu, Ansheng↗
NASA NTRS2001

A Spectral Algorithm for Solving the Relativistic Vlasov-Maxwell Equations

A spectral method algorithm is developed for the numerical solution of the full six-dimensional Vlasov-Maxwell system of equations. Here, the focus is on the electron distribution function, with positive ions providing a constant background. The algorithm consists of a Jacobi polynomial-spherical harmonic formulation in velocity space and a trigonometric formulation in position space. A transform procedure is used to evaluate nonlinear terms. The algorithm is suitable for performing moderate resolution simulations on currently available supercomputers for both scientific and engineering applications.

Shebalin, John V.↗
NASA NTRS2000

CVS Decomposition of 3D Homogeneous Turbulence Using Orthogonal Wavelets

This paper compares the filtering used in Coherent Vortex Simulation (CVS) decomposition with an orthogonal wavelet basis, with the Proper Orthogonal Decomposition (POD) or Fourier filtering. Both methods are applied to a field of Direct Numerical Simulation (DNS) data of 3D forced homogeneous isotropic turbulence at microscale Reynolds number R(sub lambda) = 168. We show that, with only 3%N retained modes, CVS filtering separates the coherent vortex tubes from the incoherent background flow. The latter is structureless, has an equipartition energy spectrum, and has a Gaussian velocity probability distribution function (PDF) and an exponential vorticity PDF. On the other hand, the Fourier basis does not extract the coherent vortex tubes cleanly and leaves organized structures in the residual high wavenumber modes whose PDFs are stretched exponentials for both the velocity and the vorticity.

Farge, Marie↗
NASA NTRS2000

CVS Filtering of 3D Turbulent Mixing Layers Using Orthogonal Wavelets

Coherent Vortex Simulation (CVS) filtering has been applied to Direct Numerical Simulation (DNS) data of forced and unforced time-developing turbulent mixing layers. CVS filtering splits the turbulent flow into two orthogonal parts, one corresponding to coherent vortices and the other to incoherent background flow. We have shown that the coherent vortices can be represented by few wavelet modes and that these modes are sufficient to reproduce the vorticity probability distribution function (PDF) and the energy spectrum over the entire inertial range. The remaining incoherent background flow is homogeneous, has small amplitude, and is uncorrelated. These results are compared with those obtained for the same compression rate using large eddy simulation (LES) filtering. In contrast to the incoherent background flow of CVS filtering, the LES subgrid scales have a much larger amplitude and are correlated, which makes their statistical modeling more difficult.

Schneider, Kai↗
NASA NTRS2001

A Semianalytical Ion Current Model for Radio Frequency Driven Collisionless Sheaths

We propose a semianalytical ion dynamics model for a collisionless radio frequency biased sheath. The model uses bulk plasma conditions and electrode boundary condition to predict ion impact energy distribution and electrical properties of the sheath. The proposed model accounts for ion inertia and ion current modulation at bias frequencies that are of the same order of magnitude as the ion plasma frequency. A relaxation equation for ion current oscillations is derived which is coupled with a damped potential equation in order to model ion inertia effects. We find that inclusion of ion current modulation in the sheath model shows marked improvements in the predictions of sheath electrical properties and ion energy distribution function.

Bose, Deepak↗
NASA NTRS2001

Rayleigh Scattering Diagnostic for Dynamic Measurement of Velocity Fluctuations in High Speed Jets

A flow diagnostic technique based on the molecular Rayleigh scattering of laser light is used to obtain dynamic density and velocity data in a high speed flow. The technique is based on analyzing the Rayleigh scattered light with a Fabry-Perot interferometer used in the static, imaging mode. An analysis is presented that established a lower bound for measurement uncertainty of about 20 m/sec for individual velocity measurements obtained in a 100 microsecond time interval. Software and hardware interfaces were developed to allow computer control of all aspects of the experiment and data acquisition. The signals from three photomultiplier tubes were simultaneously recorded using photon counting at a 10 kHz sampling rate and 10 second recording periods. Density and velocity data, including distribution functions and power spectra, taken in a Mach 0.8 free jet, are presented.

Seasholtz, Richard G.↗
NASA NTRS2000

Some Thermodynamic Considerations on the Physical and Quantum Nature of Space and Time

It is suggested that the Planck h = m(sub k)c Lambda(sub k) and the Boltzmann k = m(sub k)c nu(sub k)Constants have stochastic foundation. It is further suggested that a body of fluid at equilibrium is composed of a spectrum of molecular clusters (energy levels) the size of which are governed by the Maxwell-Boltzmann distribution function. Brownian motions are attributed to equilibrium between suspensions and molecular clusters. Atomic (molecular) transition between different size atomic- (molecular-) clusters (energy levels) is shown to result in emission/absorption of energy in accordance with Bohr's theory of atomic spectra. Physical space is identified as a tachyonic fluid that is Dirac's stochastic ether or de Broglie's hidden thermostat. Compressibility of physical space, in accordance with Planck's compressible ether, is shown to result in the Lorentz-Fitzgerald contraction, thus providing a causal explanation of relativistic effect in accordance with the perceptions of Poincare and Lorentz. The invariant Schrodinger equation is derived from the invariant Bernoulli equation for incompressible potential flow. Following Heisenberg a temporal uncertainty relation is introduced as Delta(nu(sub Beta)) Delta(Rho(sub Beta)) > = k.

Sohrab, Siavash H.↗
NASA NTRS2000

Langmuir Probe Measurements in an Inductively Coupled Ar/CF4 Plasmas

Technological advancement in the microelectronics industry requires an understanding of the physical and chemical processes occurring in plasmas of fluorocarbon gases, such as carbon tetrafluoride (CF4) which is commonly used as an etchant, and their mixtures to optimize various operating parameters. In this paper we report data on electron number density (ne), electron temperature'(Te), electron energy distribution function (EEDF), mean electron energy, ion number density (ni), and plasma potential (Vp) measured by using Langmuir probe in an inductively coupled 13.56 MHz radio frequency plasmas generated in 50%Ar:50%CF4 mixture in the GEC cell. The probe data were recorded at various radial positions providing radial profiles of these plasma parameters at 10-50 mTorr pressures and 200 W and 300 W of RF power. Present measurements indicate that the electron and ion number densities increase with increase in pressure and power. Whereas the plasma potential and electron temperature decrease with increase in pressure, and they weakly depend on RF power. The radial profiles exhibit that the electron and ion number densities and the plasma potential peak at the center of the plasma with an exponential fall away from it, while the electron temperature has a minimum at the center and it increases steadily towards the electrode edge. The EEDFs have a characteristic drop near the low energy end at all pressures and pressures and their shapes represent non-Maxwellian plasma and exhibit more like Druyvesteyn energy distribution.v

Rao, M. V. V. S.↗
NASA NTRS2001

Infrared Communications for Small Spacecraft: From a Wireless Bus to Cluster Concepts

Nanosatellites operating singly or in clusters are anticipated for future space science missions. To implement this new communications paradigm, we are approaching cluster communications by first developing an infrared (IR) intra-craft wireless bus capability, following initially the MIL-STD-1553B protocol. Benefits of an IR wireless bus are low mass, size, power, and cost, simplicity of implementation, ease of use, minimum EMI, and efficient and reliable data transfer. Our goals are to maximize the reliable link margin in order to afford greater flexibility in receiver placement, which will ease technology insertion. We have developed a concept demonstration using a high-speed visible-band silicon PIN photodiode and a high-efficiency visible LED operating at a data rate up to 4 Mb/sec. In designing an internal IR wireless bus, we have characterized various candidate materials, emitters, and geometries, assuming a single reflection. Thus, we have measured the bidirectional reflectance distribution function (BRDF) for five different materials characteristic of typical spacecraft structures, which range from nearly Lambertian to highly specular. We have fit our data to empirical BRDF functions and modeled the detected irradiance anywhere in the plane of incidence for a divergent (LED) emitter. We have also determined the angular limits on the link geometry to remain within the required bit error rate by determining the received signal-to-noise ratio (SNR) for minimum values of irradiance received at the detector.

Webb, Suzanne C.↗
NASA NTRS2001

Development of an Innovative Algorithm for Aerodynamics-Structure Interaction Using Lattice Boltzmann Method

The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is developed for inviscid compressible flows.

Mei, Ren-Wei↗
NASA NTRS2001

Carbon Nanotubes in Water: MD Simulations of Internal and External Flow, Self Organization

We have developed computational tools, based on particle codes, for molecular dynamics (MD) simulation of carbon nanotubes (CNT) in aqueous environments. The interaction of CNTs with water is envisioned as a prototype for the design of engineering nano-devices, such as artificial sterocillia and molecular biosensors. Large scale simulations involving thousands of water molecules are possible due to our efficient parallel MD code that takes long range electrostatic interactions into account. Since CNTs can be considered as rolled up sheets of graphite, we expect the CNT-water interaction to be similar to the interaction of graphite with water. However, there are fundamental differences between considering graphite and CNTs, since the curvature of CNTs affects their chemical activity and also since capillary effects play an important role for both dynamic and static behaviour of materials inside CNTs. In recent studies Gordillo and Marti described the hydrogen bond structure as well as time dependent properties of water confined in CNTs. We are presenting results from the development of force fields describing the interaction of CNTs and water based on ab-initio quantum mechanical calculations. Furthermore, our results include both water flows external to CNTs and the behaviour of water nanodroplets inside heated CNTs. In the first case (external flows) the hydrophobic behaviour of CNTs is quantified and we analyze structural properties of water in the vicinity of CNTs with diagnostics such as hydrogen bond distribution, water dipole orientation and radial distribution functions. The presence of water leads to attractive forces between CNTs as a result of their hydrophobicity. Through extensive simulations we quantify these attractive forces in terms of the number and separation of the CNT. Results of our simulations involving arrays of CNTs indicate that these exhibit a hydrophobic behaviour that leads to self-organising structures capable of trapping water clusters. In the second case (internal flows) we study the behaviour of water droplets confined inside CNTs. Constant temperature simulations allow us to capture structural properties such as the contact angles and density profiles of the equilibrated drops. By heating and subsequently cooling of the CNT, we are able to measure the evaporation and the condensation rate of the entrapped water.

Jaffe, Richard L.↗
NASA NTRS2001

Stratospheric Age Spectra and Mean Ages from In Situ Observations of Carbon Dioxide

In situ observations of CO2 obtained from 1992 through 2000 using the NASA ER-2 aircraft and high-altitude balloons show that seasonal and interannual variations in CO2 mixing ratios propagate from the troposphere into the lower stratosphere via the tropical tropopause, along with the long-term trend due to fossil fuel combustion. These signals spread laterally and vertically, providing detailed quantitative information about the transport history of sampled air. We have used these data to derive age spectra and mean ages that can be compared with results from models of the stratospheric circulation. For an air parcel at a point in the stratosphere, the age spectrum is defined as the probability distribution function for transit times from the tropical tropopause for each fluid element comprising the parcel. The mean age is the average transit time, corresponding to the first moment of the age spectrum. Age spectra have been derived for altitudes below approximately 20 km for the tropics and for northern midlatitudes where there is sufficient data and where the amplitudes of the seasonal and interannual oscillations in CO2 mixing ratios are large enough to be detected. Tropical age spectra are narrow, with seasonal variation indicating faster ascent during northern winter, consistent with a circulation driven by breaking of extratropical waves. The midlatitude CO2 data are consistent with bimodal age spectra, which could result from a subtropical "barrier" to horizontal exchange over a substantial altitude region. Seasonally resolved mean ages are available with nearly pole-to-pole coverage below 20 km and in the tropics and at middle and high northern latitudes up to the maximum altitude reached by the balloons (approximately 30 km). At ER-2 altitudes, steep meridional gradients in mean age are observed in the subtropics. Between 20 and 30 km, midlatitude air is approximately 2 years older than tropical air at the same altitude. The oldest air sampled was in the Arctic polar vortex with a mean age of .5 plus or minus 0.5 years. This value is much younger than mean ages inferred from simultaneous and previous observations of SF6 in the Arctic vortex, providing evidence for a mesospheric sink for SF6. The mean age in the midlatitude middle stratosphere (approximately 25-32 km) is nearly constant with respect to altitude at 5 plus or minus 0.5 years. Comparison with earlier balloon observations of CO2 dating back to the 1970s shows that the mean age of air in this region has been relatively invariant over the last 25 years.

Andrews, Arlyn E.↗
NASA NTRS2002

Probabilistic Study of Fluid Structure Interaction

A combustor liner was computationally simulated and probabilistically evaluated in view of the several uncertainties in the aerodynamic, structural, material and thermal variables that govern the combustor liner. The interconnection between the computational fluid dynamics code and the finite element structural analysis codes was necessary to couple the thermal profiles with structural design. The stresses and their variations were evaluated at critical points on the liner. Cumulative distribution functions and sensitivity factors were computed for stress responses due to the aerodynamic, mechanical and thermal random variables. It was observed that the inlet and exit temperatures have a lot of influence on the hoop stress. For prescribed values of inlet and exit temperatures, the Reynolds number of the flow, coefficient of thermal expansion, gas emissivity and absorptivity and thermal conductivity of the material have about the same impact on the hoop stress. These results can be used to quickly identify the most critical design variables in order to optimize the design and make it cost effective.

Gorla, Rama S. R.↗
NASA NTRS2002

Theoretical Technology Research for the International Solar Terrestrial Physics (ISTP) Program

During the last four years the UCLA (University of California, Los Angeles) IGPP (Institute of Geophysics and Planetary Physics) Space Plasma Simulation Group has continued its theoretical effort to develop a Mission Oriented Theory (MOT) for the International Solar Terrestrial Physics (ISTP) program. This effort has been based on a combination of approaches: analytical theory, large-scale kinetic (LSK) calculations, global magnetohydrodynamic (MHD) simulations and self-consistent plasma kinetic (SCK) simulations. These models have been used to formulate a global interpretation of local measurements made by the ISTP spacecraft. The regions of applications of the MOT cover most of the magnetosphere: solar wind, low- and high- latitude magnetospheric boundary, near-Earth and distant magnetotail, and auroral region. Most recent investigations include: plasma processes in the electron foreshock, response of the magnetospheric cusp, particle entry in the magnetosphere, sources of observed distribution functions in the magnetotail, transport of oxygen ions, self-consistent evolution of the magnetotail, substorm studies, effects of explosive reconnection, and auroral acceleration simulations. A complete list of the activities completed under the grant follow.

Ashour-Abdalla, Maha↗
NASA NTRS2001

Langmuir Probe Measurements of Inductively Coupled Plasma in CF4/AR/O2 Mixtures

Inductively coupled plasmas of CF4:Ar:O2, which have been of importance to material processing, were studied in the GEC cell at 80:10:10, 60:20:20, and 40:30:30 mixture ratios. Radial distributions of plasma potential (V(sub p)), electron and ion number densities (n(sub e) and n(sub i)), electron temperature (T(sub e)), and electron energy distribution functions (EEDFs) were measured in the mid-plane of plasma across the electrodes in the pressure range of 10-50 mTorr, and RF power of 200 and 300 W. V(sub p), n(sub e) and n(sub i), which peak in the center of the plasma, increase with decrease of pressure. T(sub e) also increases with pressure but peaks toward the electrode edge. Both V(sub p) and T(sub e) remain nearly independent of RF power, whereas n(sub e) and n(sub i) increase with power. In all conditions the EEDFs exhibit non-Maxwellian shape and are more like Druyvesteyn form at higher energies. They exhibit a broad lip in the energy range 0-10 eV suggesting an electron loss mechanism, which could be due to via resonance electron attachment processes producing negative ions in this rich electronegative gas mixture. This behavior is more prominent towards the electrode edge.

Rao, M. V. V. S.↗
NASA NTRS2001

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

Li, Jianzhong↗