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Finite difference calculation based on eddy diffusivity and mixing length flow theory to characterize supersonic turbulent boundary layer with tangential slot injection
We address the problem of diffusional interactions in a finite sized cluster of spherical particles for volume fractions, V(sub v) in the range 0-0.01. We determined the quasi-static monopole diffusion solution for n particles distributed at random in a continuous matrix. A global mass conservation condition is employed, obviating the need for any external boundary condition. The numerical results provide the instantaneous (snapshot) growth or shrinkage rate of each particle, precluding the need for extensive time-dependent computations. The close connection between these snapshot results and the coarsegrained kinetic constants are discussed. A square-root dependence of the deviations of the rate constants from their zero volume fraction value is found for the higher V(sub v) investigated. This behavior is consistent with predictions from diffusion Debye-Huckel screening theory. By contrast, a cube-root dependence, reported in earlier numerical studies, is found for the lower V(sub v) investigated. The roll-over region of the volume fraction where the two asymptotics merge depends on the number of particles, n, alone. A theoretical estimate for the roll-over point predicts that the corresponding V(sub v) varies as n(sup -2), in good agreement with the numerical results.
Our previous work established the concept of a low-pressure rotating reverse osmosis membrane system. The rotation of the cylindrical RO filter produces shear and Taylor vortices in the annulus of the device that decrease the concentration polarization and fouling commonly seen with conventional RO filtration techniques. A mathematical model based on the film theory and the solution-diffusion model agrees well with the experimental results obtained using this first generation prototype. However, based on the model, the filtrate flux and contaminant rejection depend strongly on the transmembrane pressure. Therefore, the goal of our current work is to improve the flux of the device by increasing the transmembrane pressure by a factor of 3 to 4. In addition, the rejections for a wider variety of inorganic and organic compounds typically found in space mission wastewater are measured.
The simplifed statistical theory developed previously is employed to analyze the equilibrium and near-equilibrium combustion of initially unmixed reactants. It is found that the flame zone in the limit of large Damkohler numbers is very thick and is of the order of the local integral scale of turbulence. This is in contrast to the existing phenomenological theories which predict the infinitesimally thin flame sheet, in the same limit, as it is with the laminar diffusion flame. Qualitative agreements with the available experimental results are shown. It is found that singularities exist at the edges of the flame which are removed as Damkohler number is reduced. Also, it is found that the heat transfer may take place against the local mean temperature gradient in certain regions within the flame.
The objectives of the experiment are fourfold: to provide practical experience implementing the fundamental processes and technology associated with the science and art of integrated circuit (IC) fabrication; to afford the opportunity for the student to apply the theory associated with IC fabrication and semiconductor device operation; to motivate the student to exercise engineering decisions associated with fabricating integrated circuits; and to complement the theory of n-channel MOS and diffused devices that are presented in the classroom by actually fabricating and testing them. Therefore, a balance between theory and practice can be realized in the education of young engineers, whose education is often criticized as lacking sufficient design and practical content.
It has been known for some years that when a near-limit flame spreads over a liquid pool of fuel, the edge of the flame can oscillate relative to a frame moving with the mean speed. Each period of oscillation is characterized by long intervals of modest motion during which the edge gases radiate like those of a diffusion flame, punctuated by bursts of rapid advance during which the edge gases radiate like those in a deflagration. Substantial resources have been brought to bear on this issue within the microgravity program, both experimental and numerical. It is also known that when a near-asphyxiated candle-flame burns at zero gravity, the edge of the (hemispherical) flame can oscillate violently prior to extinction. Thus a web-surfer, turning to the NASA web-site at http://microgravity.msfc.nasa.gov, and following the trail combustion science/experiments/experimental results/candle flame, will find photographs and a description of candle burning experiments carried out on board both the Space-shuttle and the Russian space station Mir. A brief report can also be found in the proceedings of the Fourth Workshop. And recently, in a third microgravity program, the leading edge of the flame supported by injection of ethane through the porous surface of a plate over which air is blown has been found to oscillate when conditions are close to blow-off. A number of important points can be made with respect to these observations: It is the edge itself which oscillates, advancing and retreating, not the diffusion flame that trails behind the edge; oscillations only occur under near limit conditions; in each case the Lewis number of the fuel is significantly larger than 1; and because of the edge curvature, the heat losses from the reacting edge structure are larger than those from the trailing diffusion flame. We propose a general theory for these oscillations, invoking Occam's 'Law of Parsimony' in an expanded form, to wit: The same mechanism is responsible for the oscillations in all three experiments; and no new mechanism is invoked (Occam's original 'Razor'). Such a strategy eliminates Marangoni effects as the source, for these are absent in the second and third experiments. And it eliminates arguments that point to numerically predicted gas eddies as the source, a new mechanism, unelucidated. Indeed, we hypothesize that the essential driving mechanism for the instability is a combination of large Lewis number and heat losses from the reacting structure near the flame edge. Instabilities driven by these mechanisms are commonplace in 1D configurations. Chemical reactor theory, for example, leads to system responses which mimic the response of the candle flame - steady flame, oscillations, extinction. In a combustion context, oscillating instabilities were first reported for diffusion flames in a theoretical study by Kirkby and Schmitz, and here also the instabilities are associated with near-extinction conditions, large Lewis numbers, and heat losses. And deflagrations will oscillate if the Lewis number is large enough, oscillations that are exacerbated when heat losses are present, whether global or to a surface.
A multistage centrifugal compressor, in natural gas re-injection service on an offshore petroleum production platform, experienced subsynchronous vibrations which caused excessive bearing wear. Field performance testing correlated the subsynchronous amplitude with the discharge flow coefficient, demonstrating the excitation to be aerodynamic. Adding two impellers allowed an increase in the diffuser flow angle (with respect to tangential) to meet the diffuser stability criteria based on factory and field tests correlated using the theory of Senoo (for rotating stall in a vaneless diffuser). This modification eliminated all significant subsynchronous vibrations in field service, thus confirming the correctness of the solution. Other possible sources of aerodynamically induced vibrations were considered, but the judgment that those are unlikely has been confirmed by subsequent experience with other similar compressors.
A previous small perturbation analysis of circumferential waves in circumferential compression systems, assuming inviscid flow, is shown to be consistent with observations that narrow diffusers are more stable than wide ones, when boundary layer displacement effect is included. The Moore-Greitzer analysis for finite strength transients containing both surge and rotating stall in axial machines is adapted for a centrifugal compression system. Under certain assumptions, and except for a new second order swirl, the diffuser velocity field, including resonant singularities, can be carried over from the previous inviscid linear analysis. Nonlinear transient equations are derived and applied in a simple example to show that throttling through a resonant value of flow coefficient must occur in a sudden surge-like drop, accompanied by a transient rotating wave. This inner solution is superseded by an outer surge response on a longer time scale. Surge may occur purely as result of circumferential wave resonance. Numerical results are shown for various parametric choices relating to throttle schedule and the characteristic slope. A number of circumferential modes considered simultaneously is briefly discussed.
The nonlinear dissipation of plasma irregularities aligned parallel to an ambient magnetic field is studied numerically using a model which employs both wave-particle and collisional diffusion. A wave-particle diffusion coefficient derived from a local theory of the universal drift instability is used. This coefficient is effective in regions of nonzero plasma gradients and produces triangular-shaped irregularities with spectra which vary as f to the -4th, where f is the spatial frequency. Collisional diffusion acts rapidly on the vertices of the irregularities to reduce their amplitude. The simultaneous action of the two dissipative processes is more efficient than collisions acting alone. In this model, wave-particle diffusion mimics the forward cascade process of wave-wave coupling.
The overcharge condition in secondary lithium batteries employing redox additives for overcharge protection, has been theoretically analyzed in terms of a finite linear diffusion model. The analysis leads to expressions relating the steady-state overcharge current density and cell voltage to the concentration, diffusion coefficient, standard reduction potential of the redox couple, and interelectrode distance. The model permits the estimation of the maximum permissible overcharge rate for any chosen set of system conditions. Digital simulation of the overcharge experiment leads to numerical representation of the potential transients, and estimate of the influence of diffusion coefficient and interelectrode distance on the transient attainment of the steady state during overcharge. The model has been experimentally verified using 1,1-prime-dimethyl ferrocene as a redox additive. The analysis of the experimental results in terms of the theory allows the calculation of the diffusion coefficient and the formal potential of the redox couple. The model and the theoretical results may be exploited in the design and optimization of overcharge protection by the redox additive approach.
The solution of the two nonequilibrium-degree kinetic equation was first determined for the effective length scale and turbulence energy for a spatially homogeneous turbulence field with two characteristic length scales, where the source for one family of eddies exists. This solution was applied to the evaluation of the eddy diffusivity in the combustion chamber of an internal combustion engine. The result was compared with another existing solution. This was carried out to demonstrate the feasibility of obtaining an effective length-scale equation within the context of the kinetic theory. A formulation and partial solution of the compressible plane shear layer are also presented.
The multifluid diffusive model of G. P. Zank et al. (1994), which describes the interaction of the solar wind with a cometary plasma in the outer coma, has been used to model the structure of the Halley bow shock. The theoretical results are compared to in situ observations made by Giotto. We compare the solar wind and cometary ion number densities and pressures upstream and through the quasi-perpendicular and quasi-parallel shocks (observed on the inbound and outbound legs of the encounter, respectively). In general, good agreement is found between theory and observations in terms of shock structure, strength, and location, especially for the quasi-parallel shock. The comparison between tha quasi-perpendicular shock observations and theory is complicated by the apparently nonstationary behavior of the shock, a feature which has been remarked upon by other investigators. The cometary bow shock appears to be an excellent example of an energetic-particle-mediated shock where the energetic particles comprise less than 10% of the total number density.
A diffuse celestial radiation which is isotropic at least on a course scale were measured from the soft X-ray region to about 150 MeV, at which energy the intensity falls below that of the galactic emission for most galactic latitudes. The spectral shape, the intensity, and the established degree of isotropy of this diffuse radiation already place severe constraints on the possible explanations for this radiation. Among the extragalactic theories, the more promising explanations of the isotropic diffuse emission appear to be radiation from exceptional galaxies from matter antimatter annihilation at the boundaries of superclusters of galaxies of matter and antimatter in baryon symmetric big bang models. Other possible sources for extragalactic diffuse gamma radiation are discussed and include normal galaxies, clusters of galaxies, primordial cosmic rays interacting with intergalactic matter, primordial black holes, and cosmic ray leakage from galaxies.
Ambipolar drift in turbulent fluids are considered. Using mean-field electrodynamics, a two-scale theory originally used to study hydromagnetic dynamos, it is shown that magnetic fields can be advected by small-scale magnetosonic (compressional) turbulence or generated by Alfvenic (helical) turbulence. A simple dynamo theory is made and is compared with standard theories in which dissipation is caused by turbulent diffusion. The redistribution of magnetic flux in interstellar clouds is also discussed.
This research deals with reduced-gravity combustion of bi-component droplets initially in the mm size range or larger. The primary objectives of the research are to study the effects of droplet internal flows, thermal and solutal Marangoni stresses, and species volatility differences on liquid species transport and overall combustion phenomena (e.g., gas-phase unsteadiness, burning rates, sooting, radiation, and extinction). The research program utilizes a reduced-gravity environment so that buoyancy effects are rendered negligible. Use of large droplets also facilitates visualization of droplet internal flows, which is important for this research. In the experiments, droplets composed of low- and high-volatility species are burned. The low-volatility components are initially present in small amounts. As combustion of a droplet proceeds, the liquid surface mass fraction of the low-volatility component will increase with time, resulting in a sudden and temporary decrease in droplet burning rates as the droplet rapidly heats to temperatures close to the boiling point of the low-volatility component. This decrease in burning rates causes a sudden and temporary contraction of the flame. The decrease in burning rates and the flame contraction can be observed experimentally. Measurements of burning rates as well as the onset time for flame contraction allow effective liquid-phase species diffusivities to be calculated, e.g., using asymptotic theory. It is planned that droplet internal flows will be visualized in flight and ground-based experiments. In this way, effective liquid species diffusivities can be related to droplet internal flow characteristics. This program is a continuation of extensive ground based experimental and theoretical research on bi-component droplet combustion that has been ongoing for several years. The focal point of this program is a flight experiment (Bi-Component Droplet Combustion Experiment, BCDCE). This flight experiment is under development. However, supporting ground-based studies have been performed. This ground-based research is summarized below.
This research deals with reduced-gravity combustion of bi-component droplets initially in the mm size range or larger. The primary objectives of the research are to study the effects of droplet internal flows, thermal and solutal Marangoni stresses, and species volatility differences on liquid species transport and overall combustion phenomena (e.g., gas-phase unsteadiness, burning rates, sooting, radiation, and extinction). The research program utilizes a reduced gravity environment so that buoyancy effects are rendered negligible. Use of large droplets also facilitates visualization of droplet internal flows, which is important for this research. In the experiments, droplets composed of low- and high-volatility species are burned. The low-volatility components are initially present in small amounts. As combustion of a droplet proceeds, the liquid surface mass fraction of the low-volatility component will increase with time, resulting in a sudden and temporary decrease in droplet burning rates as the droplet rapidly heats to temperatures close to the boiling point of the low-volatility component. This decrease in burning rates causes a sudden and temporary contraction of the flame. The decrease in burning rates and the flame contraction can be observed experimentally. Measurements of burning rates as well as the onset time for flame contraction allow effective liquid-phase species diffusivities to be calculated, e.g., using asymptotic theory. It is planned that droplet internal flows will be visualized in flight and ground-based experiments. In this way, effective liquid species diffusivities can be related to droplet internal flow characteristics. This program is a continuation of extensive ground-based experimental and theoretical research on bi-component droplet combustion that has been ongoing for several years. The focal point of this program is a flight experiment (Bi-Component Droplet Combustion Experiment, BCDCE). This flight experiment is under development. However, supporting ground-based studies have been performed. Some of the most recent ground-based research is summarized.
A typical semiconductor-based optoelectronic device, such as a diode laser, consists of three subsystems: an optical field, an electron-hole plasma (EHP), and a host crystal lattice. The physics of such a device involves the interplay of optical, electrical and thermal processes. A proper description of such a device requires that all three processes are treated on equal footing and in a self-consistent fashion. Furthermore, since a semiconductor laser has intrinsic spatial inhomogeneity, such a self-consistency naturally leads to a set of partial differential equations in space and time. There is a significant lacking of research interest and results on the transport aspects of optical devices in the literature with only a few exceptions. Even the most important carrier diffusion coefficient has not been properly derived and studied so far for optically excited plasma, while most of the work adopted results from electronics community where heavily doped semiconductors with mainly one type of carriers are dealt with. The corresponding transport equation for plasma energy or temperature has received even less attention. In this talk we describe our recent results on such a self-consistent derivation of temperature and carrier-density diffusion equations coupled with the lasing process. 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. The equations derived above are implemented in various limiting cases to a typical diode laser to study the consequences of nonlinear diffusion and the cross diffusion terms on laser behavior, especially the dynamic behavior of a diode laser under modulation. Detailed results will be presented by comparing with the standard rate equation results.
This research deals with reduced-gravity combustion of bi-component droplets initially in the mm size range or larger. The primary objectives of the research are to study the effects of droplet internal flows, thermal and solutal Marangoni stresses, and species volatility differences on liquid species transport and overall combustion phenomena (e.g., gas-phase unsteadiness, burning rates, sooting, radiation, and extinction). The research program utilizes a reduced-gravity environment so that buoyancy effects are rendered negligible. Use of large droplets also facilitates visualization of droplet internal flows, which is important for this research. In the experiments, droplets composed of low- and high-volatility species are burned. The low-volatility components are initially present in small amounts. As combustion of a droplet proceeds, the liquid surface mass fraction of the low-volatility component will increase with time, resulting in a sudden and temporary decrease in droplet burning rates as the droplet rapidly heats to temperatures close to the boiling point of the low-volatility component. This decrease in burning rates causes a sudden and temporary contraction of the flame. The decrease in burning rates and the flame contraction can be observed experimentally. Measurements of burning rates as well as the onset time for flame contraction allow effective liquid-phase species diffusivities to be calculated, e.g., using asymptotic theory. It is planned that droplet internal flows will be visualized in future flight and ground-based experiments. In this way, effective liquid species diffusivities can be related to droplet internal flow characteristics. This program is a continuation of extensive ground based experimental and theoretical research on bi-component droplet combustion that has been ongoing for several years. The focal point of this program is a flight experiment (Bi-Component Droplet Combustion Experiment, BCDCE). This flight experiment is under development. However, supporting studies have been performed. Because of space limitations, only some of the research performed over the last two years (since the 5th Microgravity Combustion Workshop) is summarized here.