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Probability Density Function (PDF) methods provide a means of calculating the properties of turbulent reacting flows. They have been successfully applied to many turbulent flames, including some with finite rate kinetic effects. Here the methods are reviewed with an emphasis on computational issues and their application to turbulent combustion.
The independent and dependent variables associated with drag and heat transfer to a flat plate at zero incidence in high-speed, rarefied flow are analyzed anew to reflect the importance of kinetic effects occurring near the plate surface on energy and momentum transfer, rather than following arguments normally used to describe continuum, higher density flowfields. A new parameter, the wall Knudsen number Knx,w, based on an estimate of the mean free path length of molecules having just interacted with the surface of the plate, is introduced and used to correlate published drag and heat transfer data. The new parameter is shown to provide better correlation than either the viscous interaction parameter X or the widely-used slip parameter Voo for drag and heat transfer data over a wide range of Mach numbers, Reynolds numbers, and plate-to-freestream stagnation temperature ratios.
Nuclear propulsion has been identified as one of the key technologies needed for human exploration of the Moon and Mars. The Nuclear Thermal Rocket (NTR) uses a nuclear reactor to heat hydrogen to a high temperature followed by expansion through a conventional convergent-divergent nozzle. A parametric study of NTR nozzles was performed using the Rocket Engine Design Expert System (REDES) at the NASA Lewis Research Center. The REDES used the JANNAF standard rigorous methodology to determine nozzle performance over a range of chamber temperatures, chamber pressures, thrust levels, and different nozzle configurations. A design condition was set by fixing the propulsion system exit radius at five meters and throat radius was varied to achieve a target thrust level. An adiabatic wall was assumed for the nozzle, and its length was assumed to be 80 percent of a 15 degree cone. The results conclude that although the performance of the NTR, based on infinite reaction rates, looks promising at low chamber pressures, finite rate chemical reactions will cause the actual performance to be considerably lower. Parameters which have a major influence on the delivered specific impulse value include the chamber temperature and the chamber pressures in the high thrust domain. Other parameters, such as 2-D and boundary layer effects, kinetic rates, and number of nozzles, affect the deliverable performance of an NTR nozzle to a lesser degree. For a single nozzle, maximum performance of 930 seconds and 1030 seconds occur at chamber temperatures of 2700 and 3100 K, respectively.
Experimental and theoretical aspects of opposed-flow flame spread over solid fuels are presented with emphasis on the microgravity environments of spacecraft. For high opposing flow velocities, spread rate decreases with increasing velocity eventually leading to flame blowoff due to kinetic effects. At low opposing flow velocities, where diffusional effects are slowed and radiation becomes important, flame spread rate increases with increasing flow velocity. Extinction at low velocities is due to radiative effects. Modeling efforts that include radiation, both solid surface radiation and gas-phase radiation, predict qualitatively the experimental trends observed. Computationally, gas-phase radiation is conveniently included in solution of the conservation equations by employing a Plank mean absorption coefficient, a fraction of radiation that is fed back to the surface, and a shape function that describes the radiative flux distribution along the surface.
A local electrostatic dispersion equation is derived for a shear flow perpendicular to an ambient magnetic field, which includes all kinetic effects and involves only one important parameter. The dispersion equation is cast in the form of Gordeyev integrals and is solved numerically. Numerical solutions indicate that an ion cyclotron instability is excited. The instability occurs roughly at multiples of the ion cyclotron frequency (modified by the shear), with the growth rate or the individual harmonics overlapping in the wavenumber. At large values of the shear parameter, the instability is confined to long wavelengths, but at smaller shear, a second distinct branch at shorter wavelengths also appears. The properties of the instability obtained are compared with those obtained in the nonlocal limit by Ganguli et al. (1985, 1988).
Results are presented of a series of 1D hybrid (kinetic ions and fluid electrons) simulations, using a nondynamic method to form rotational discontinuities (RDs) at an angle of 60 deg between the normal direction and the upstream magnetic field. Ion kinetic effects are found to be important with regard to the stability of the current layer, its thickness and scaling, and its dependence on initial conditions. A detailed examination of the downstream wave train and gradient scale size showed that RDs with alpha1 = +/-180 deg are stable within the framework of the simulation. With proper initialization, electron-sense rotations of -270 deg were found that do not disintegrate immediately but rather appear to consist of a superposition of a solitary wave with -360-deg rotation and a 90-deg ion-sense rotation.
A numerical rate equation model for a continuous wave iodine laser with longitudinally flowing gaseous lasant is validated by approximating two experiments that compare the perfluoroalkyl iodine lasants n-C3F7I and t-C4F9I. The salient feature of the simulations is that the production rate of the dimer (C4F9)2 is reduced by one order of magnitude relative to the dimer (C3F7)2. The model is then used to investigate the kinetic effects of this reduced dimer production, especially how it improves output power. Related parametric and scaling studies are also presented. When dimer production is reduced, more monomer radicals (t-C4F9) are available to combine with iodine ions, thus enhancing depletion of the laser lower level and reducing buildup of the principal quencher, molecular iodine. Fewer iodine molecules result in fewer downward transitions from quenching and more transitions from stimulated emission of lasing photons. Enhanced depletion of the lower level reduces the absorption of lasing photons. The combined result is more lasing photons and proportionally increased output power.
Correlations between plasma properties and magnetic fluctuations in the sub-solar magnetosheath downstream of a quasi-perpendicular shock have been found and indicate that mirror and ion cyclotronlike fluctuations correlate with the magnetosheath proper and plasma depletion layer, respectively (Anderson and Fueselier, 1993). We explore the entire range of magnetic spectral signatures observed from the Active Magnetospheric Particle Tracer Explorers/Charge Composition Explorer (AMPTE/CCE)spacecraft in the magnetosheath downstream of a quasi-perpendicular shock. The magnetic spectral signatures typically progress from predominantly compressional fluctuations,delta B(sub parallel)/delta B perpendicular to approximately 3, with F/F (sub p) less than 0.2 (F and F (sub p) are the wave frequency and proton gyrofrequency, respectively) to predominantly transverse fluctuations, delta B(sub parallel)/delta B perpendicular to approximately 0.3, extending up to F(sub p). The compressional fluctuations are characterized by anticorrelation between the field magnitude and electron density, n(sub e), and by a small compressibility, C(sub e) identically equal to (delta n(sub e)/n(sub e)) (exp 2) (B/delta B(sub parallel)) (exp 2) approximately 0.13, indicative of mirror waves. The spectral characteristics of the transverse fluctuations are in agreement with predictions of linear Vlasov theory for the H(+) and He(2+) cyclotron modes. The power spectra and local plasma parameters are found to vary in concert: mirror waves occur for beta(s ub parallel p) (beta (sub parallel p) identically = 2 mu(sub zero) n(sub p) kT (sub parallel p) / B(exp 2) approximately = 2, A(sub p) indentically = T(sub perpendicular to p)/T(sub parallel p) - 1 approximately = 0.4, whereas cyclotron waves occur for beta (sub parallel p) approximately = 0.2 and A(sub p) approximately = 2. The transition from mirror to cyclotron modes is predicted by linear theory. The spectral characteristics overlap for intermediate plasma parameters. The plasma observations are described by A(sub p) = 0.85 beta(sub parallel P) (exp - 0.48) with a log regression coefficient of -0.74. This inverse A(sub p) - beta(sub parallel p) correlation corresponds closely to the isocontours of maximum ion anisotropy instability growth, gamma (sub m)/omega(sub p) = 0.01, for the mirror and cyclotron modes. The agreement of observed properties and predictions of local theory suggests that the spectral signatures reflect the local plasma environment and that the anisotropy instabilities regulate A(sub p). We suggest that the spectral characteristics may provide a useful basis for ordering observations in the magnetosheath and that the A(sub p) - beta(sub parallel p) inverse correlation may be used as a beta-dependent upper limit on the proton anisotropy to represent kinetic effects.
Numerical simulations of the Farley-Buneman instability in 2-1/2 dimensions using particle ions and fluid electrons show the growth, saturation and nonlinear behavior of two-stream waves. This hybrid technique models the saturated state of the instability for a much longer period of time than the pure particle codes that preceded it. While focusing principally on modeling the topside E region equatorial electrojet, many of these results apply to the auroral two-stream instability as well. The following features are seen in all our hybrid simulations: (1) wave growth at an angle offset from the electron drift direction where the angle depends on the strength of the driving electric field, (2) nonlinear coupling to waves traveling perpendicular to the propagation direction of the principal two-stream waves, (3) a saturated wave phase velocity at or above the sound speed but well below the velocity predicted by linear theory and (4) phase velocities which remain almost constant as a simulated radar sweeps from a horizontal direction to nearly vertical. The nonlinear electron motion dominates the behavior of these waves. Further, these simulations indicate that ion kinetic effects are not essential for the saturation of the instability and that electron temperature effects have a minor impact on the final saturated state.
Coronal heating is at the origin of the X-ray emission and mass loss from the sun and many other stars. While different scenarios have been proposed to explain the heating of magnetically confined and open regions of the corona, they must all rely on the transfer, storage and dissipation of the abundant energy present in photospheric motions. Here we focus on theories which rely on magnetic fields and electric currents both for the energy transfer and storage in the corona. The dissipation of this energy, whether in the form of reconnection in current sheets (nanoflare?) or the dissipation of MHD waves, depends crucially on the development of extremely small scales in the coronal magnetic field, where kinetic effects are likely to be fundamental. The question of whether coronal heating and flares may be viewed respectively as the macroscopic, low-energy average and the high-energy, temporally intermittent aspect of the same underlying driven, dissipative, turbulent system is also addressed, with emphasis placed on the main observational and theoretical stumbling blocks in the way of a confinement or disproof of such a conjecture.
Karma and Rapped recently developed a new sharp interface asymptotic analysis of the phase-field equations that is especially appropriate for modeling dendritic growth at low undercoolings. Their approach relieves a stringent restriction on the interface thickness that applies in the conventional asymptotic analysis, and has the added advantage that interfacial kinetic effects can also be eliminated. However, their analysis focussed on the case of equal thermal conductivities in the solid and liquid phases; when applied to a standard phase-field model with unequal conductivities, anomalous terms arise in the limiting forms of the boundary conditions for the interfacial temperature that are not present in conventional sharp-interface solidification models, as discussed further by Almgren. In this paper we apply their asymptotic methodology to a generalized phase-field model which is derived using a thermodynamically consistent approach that is based on independent entropy and internal energy gradient functionals that include double wells in both the entropy and internal energy densities. The additional degrees of freedom associated with the generalized phased-field equations can be chosen to eliminate the anomalous terms that arise for unequal conductivities.
Atomic force microscopy and high precision optical interferometry allow to analyze the processes that are in the core of our present understanding of faceted crystal growth. Some of these processes will be reviewed. Recent experiments suggest that the Gibbs-Thomson Law (GTL) may not be applicable to the weakly fluctuating strongly polygonized steps, with low kink density. Propagation rate of a straight short step segment changes with the segment length much steeper than predicted by GTL. If the step fluctuations are still well developed, the typical transition length may be determined just by the radius of rounded comers of the polygonized step. If fluctuations do not have enough time to develop, the kinetic effects may be essential. Indeed, 'communications' between comers of a short straight step segment may occur and, thus, the GTL may be implemented only via kink exchange. E.g., dissolutions of this short segment at macroscopic equilibrium occurs as follows: The kinks are split from one comer as a result of fluctuations, and annihilate with kinks of the opposite sign generated by another comer. Similarly, an exchange via chain of kinks on a rough step is the mechanism to implement the GT Law. If there is a supersaturation with respect to a large crystal, the kinks not only diffuse along the step, but move back the generating comers. This 'wind' prevents communication between the comers and places upper limit supersaturation only below which GTL is applicable. Steps replace kinks in the 3D case, though, of course, another dimensionality brings about another physics. Another specific problem to think about is if fluctuations are always fast enough to provide enough kinks for linear dependence of step rate on supersaturation. Increasing azimuthal polygonization of growth hillocks is a sign of insufficient fluctuation rate. Morphological stability of vicinal faces is usually considered on the basis of mutually parallel steps. Azimuthal anisotropy and interlacing of step bunches inducing the well known bunch splitting is another challenge. Among other challenging problems are: existence of surface diffusion on the crystal/so1ution interface, step interaction in solutions, achievement of step flow modes from liquids, impurity effects. New phenomena essential in biomacromolecular crystallization is another interesting area.
A high-energy (28 kJ per pulse) two-stage pulsed plasma thruster (MSFC PPT-1) has been constructed and tested. The motivation of this project is to develop a high power (approximately 500 kW), high specific impulse (approximately 10000 s), highly efficient (greater than 50%) thruster for use as primary propulsion in a high power nuclear electric propulsion system. PPT-1 was designed to overcome four negative characteristics which have detracted from the utility of pulsed plasma thrusters: poor electrical efficiency, poor propellant utilization efficiency, electrode erosion, and reliability issues associated with the use of high speed gas valves and high current switches. Traditional PPTs have been plagued with poor efficiency because they have not been operated in a plasma regime that fully exploits the potential benefits of pulsed plasma acceleration by electromagnetic forces. PPTs have generally been used to accelerate low-density plasmas with long current pulses. Operation of thrusters in this plasma regime allows for the development of certain undesirable particle-kinetic effects, such as Hall effect-induced current sheet canting. PPT-1 was designed to propel a highly collisional, dense plasma that has more fluid-like properties and, hence, is more effectively pushed by a magnetic field. The high-density plasma loading into the second stage of the accelerator is achieved through the use of a dense plasma injector (first stage). The injector produces a thermal plasma, derived from a molten lithium propellant feed system, which is subsequently accelerated by the second stage using mega-amp level currents, which eject the plasma at a speed on the order of 100 kilometers per second. Traditional PPTs also suffer from dynamic efficiency losses associated with snowplow loading of distributed neutral propellant. The twostage scheme used in PPT-I allows the propellant to be loaded in a manner which more closely approximates the optimal slug loading. Lithium propellant was chosen to test whether or not the reduced electrode erosion found in the Lithium Lorentz Force Accelerator (LiLFA) could also be realized in a pulsed plasma thruster. The use of the molten lithium dense plasma injector also eliminates the need for a gas valve and electrical switch; the injector design fulfills both roles, and uses no moving parts to provide, in principle, a highly reliable propellant feed and electrical switching system. Experimental results reported in this paper include: second-stage current traces, high-speed photographic and holographic imaging of the thruster exit plume, and internal mapping of the discharge chamber magnetic field from B-dot probe data. The magnetic field data is used to create a two-dimensional description of the evolution of the current sheet inside the thruster.
We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-interpolated constrained transport scheme is used to maintain a divergence-free magnetic field. We have performed various 1-dimensional test problems in both special and general relativity by using several reconstruction methods and found that the new 3D GRMHD code shows substantial improvements over our previous code. The simulation results show the jet formations from a geometrically thin accretion disk near a nonrotating and a rotating black hole. We will discuss the jet properties depended on the rotation of a black hole and the magnetic field configuration including issues for future research. A General Relativistic Particle-in-Cell Code (GRPIC) has been developed using the Kerr-Schild metric. The code includes kinetic effects, and is in accordance with GRMHD code. Since the gravitational force acting on particles is extreme near black holes, there are some difficulties in numerically describing these processes. The preliminary code consists of an accretion disk and free-falling corona. Results indicate that particles are ejected from the black hole. These results are consistent with other GRMHD simulations. The GRPIC simulation results will be presented, along with some remarks and future improvements. The emission is calculated from relativistic flows in black hole systems using a fully general relativistic radiative transfer formulation, with flow structures obtained by GRMHD simulations considering thermal free-free emission and thermal synchrotron emission. Bright filament-like features protrude (visually) from the accretion disk surface, which are enhancements of synchrotron emission where the magnetic field roughly aligns with the line-of-sight in the co-moving frame. The features move back and forth as the accretion flow evolves, but their visibility and morphology are robust. We would like to extend this research using GRPIC simulations and examine a possible new mechanism for certain X-ray quasi-periodic oscillations (QPOs) observed in blackhole X-ray binaries.
The objectives of this project have been to develop a comprehensive set of fundamental data regarding the combustion behavior of jet fuels and appropriately associated model fuels. Based on the fundamental study results, an auxiliary objective was to identify differentiating characteristics of molecular fuel components that can be used to explain different fuel behavior and that may ultimately be used in the planning and design of optimal fuel-production processes. The fuels studied in this project were Fischer-Tropsch (F-T) fuels and biomass-derived jet fuels that meet certain specifications of currently used jet propulsion applications. Prior to this project, there were no systematic experimental flame data available for such fuels. One of the key goals has been to generate such data, and to use this data in developing and verifying effective kinetic models. The models have then been reduced through automated means to enable multidimensional simulation of the combustion characteristics of such fuels in real combustors. Such reliable kinetic models, validated against fundamental data derived from laminar flames using idealized flow models, are key to the development and design of optimal combustors and fuels. The models provide direct information about the relative contribution of different molecular constituents to the fuel performance and can be used to assess both combustion and emissions characteristics.
Hypersonic air-breathing engines rely on scramjet combustion processes, which involve high speed, compressible, and highly turbulent flows. The combustion environment and the turbulent flames at the heart of these engines are difficult to simulate and study in the laboratory under well controlled conditions. Typically, wind-tunnel testing is performed that more closely approximates engine testing rather than a careful investigation of the underlying physics that drives the combustion process. The experiments described in this paper, along with companion data sets being developed separately, aim to isolate the chemical kinetic effects from the fuel-air mixing process in a dual-mode scramjet combustion environment. A unique fuel injection approach is taken that produces a nearly uniform fuel-air mixture at the entrance to the combustor. This approach relies on the precombustion shock train upstream of the dual-mode scramjet combustor. A stable ethylene flame anchored on a cavity flameholder with a uniformly mixed combustor inflow has been achieved in these experiments allowing numerous companion studies involving coherent anti-Stokes Raman scattering (CARS), particle image velocimetry (PIV), and planar laser induced fluorescence (PLIF) to be performed.
Spacecraft observations and global hybrid (kinetic ions and fluid electrons) simulations have demonstrated that ion dissipation processes at the quasi-parallel bow shock are associated with the formation of structures called spontaneous hot flow anomalies (SHFAs). Previous simulations and recent spacecraft observations have also established that SHFAs result in the formation of magnetosheath filamentary structures(MFS). In this paper we demonstrate that in addition to MFS, SHFAs also result in the formation of magnetos heath cavities that are associated with decreases in density, velocity, and magnetic field and enhancements in temperature. We use the results of a global MHD run to determine the change in the magnetosheath properties associated with cavities due to ion kinetic effects. The results also show the formation of regions of high flow speed called magnetosheath jets whose properties as a function of solar wind Mach number are described in this study. Comparing the properties of the simulated magnetosheath cavities and jets to past spacecraft observations provides good agreement in both cases. We also demonstrate that pressure variations associated with cavities and SHFAs in the sheath result in a continuous sunward and anti sunward magnetopause motion. This result is consistent with previous suggestions that SHFAs may be responsible for the generation of ion cyclotron waves and precipitation of ring current protons in the outer magnetosphere.
We have recently developed a new modeling capability to embed the implicit particle-in-cell (PIC) model iPIC3D into the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme magnetohydrodynamic (MHD) model. The MHD with embedded PIC domains (MHO-EPIC) algorithm Is a two-way coupled kinetic-fluid model. As one of the very first applications of the MHD-EPIC algorithm, we simulate the Interaction between Jupiter's magnetospherlc plasma and Ganymede's magnetosphere. We compare the MHO-EPIC simulations with pure Hall MHD simulations and compare both model results with Galileo observations to assess the Importance of kinetic effects In controlling the configuration and dynamics of Ganymede's magnetosphere. We find that the Hall MHD and MHO-EPIC solutions are qualitatively similar, but there are significant quantitative differences. In particular. the density and pressure inside the magnetosphere show different distributions. For our baseline grid resolution the PIC solution is more dynamic than the Hall MHD simulation and it compares significantly better with the Galileo magnetic measurements than the Hall MHD solution. The power spectra of the observed and simulated magnetic field fluctuations agree extremely well for the MHD-EPIC model. The MHO-EPIC simulation also produced a few flux transfer events (FTEs) that have magnetic signatures very similar to an observed event. The simulation shows that the FTEs often exhibit complex 3-0 structures with their orientations changing substantially between the equatorial plane and the Galileo trajectory, which explains the magnetic signatures observed during the magnetopause crossings. The computational cost of the MHO-EPIC simulation was only about 4 times more than that of the Hall MHD simulation.