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Experimental Observations on a Low Strain Counter-Flow Diffusion Flame: Flow and Bouyancy Effects

Diffusion flames are of great interest in fire safety and many industrial processes. The counter-flow configuration provides a constant strain flow, and therefore is ideal to study the structure of diffusion flames. Most studies have concentrated on the high velocity, high strain limit, since buoyantly induced instabilities will disintegrate the planar flame as the velocity decreases. Only recently, experimental studies in microgravity conditions have begun to explore the low strain regimes. Numerical work has shown the coupling between gas phase reaction rates, soot reaction rates, and radiation. For these programs, size, geometry and experimental conditions have been chosen to keep the flame unaffected by the physical boundaries. When the physical boundaries can not be considered infinitely far from the reaction zone discrepancies arise. A computational study that includes boundary effects and accounts for the deviations occurring when the major potential flow assumptions are relaxed was presented by Borlik et al. This development properly incorporates all heat loss terms and shows the possibility of extinction in the low strain regime. A major constraint of studying the low strain regime is buoyancy. Buoyant instabilities have been shown to have a significant effect on the nature of reactants and heat transport, and can introduce instabilities on the flow that result in phenomena such as flickering or fingering. The counter-flow configuration has been shown to provide a flame with no symmetry disrupting instabilities for inlet velocities greater than 50 mm/s. As the velocity approaches this limit, the characteristic length of the experiment has to be reduced to a few millimetres so as to keep the Rayleigh number (Ra L = (β g 0 L 3 ∆T)/(𝑎v)) below 2000. In this work, a rectangular counter-flow burner was used to study a two-dimensional counter-flow diffusion flame. Flow visualisation and Particle Image Velocimetry served to describe the nature of the stagnation plane for strain rates smaller than 100 (1/s). These experiments were conducted with a non-reacting flow. Video images of a propane air diffusion flame were used to describe the behaviour of a diffusion flame in this regime. Flame geometry and pulsation frequency are described.

J. A. Sutula↗

The Effects of Buoyancy and Dilution on the Structure and Lift-off of Coflow Laminar Diffusion Flames

The ability to predict the coupled effects of complex transport phenomena with detailed chemical kinetics in diffusion flames is critical in the modeling of turbulent reacting flows and in understanding the processes by which soot formation and radiative transfer take place. In addition, an understanding of the factors that affect flame extinction in diffusion flames is critical in the suppression of fires and in improving engine efficiency. The goal of our characterizations of coflow laminar diffusion flames is to bring to microgravity the multidimensional diagnostic tools available in normal gravity, and in so doing provide a broader understanding of the successes and limitations of current combustion models. This will lead to a more detailed understanding of the interaction of convection, diffusion and chemistry in both buoyant and nonbuoyant environments. As a sensitive marker of changes in the flame shape, the number densities of excited-state CH (A(exp 2)delta, denoted CH*), and excited-state OH (A(exp 2)Sigma, denoted OH*) are measured in mu-g and normal gravity. Two-dimensional CH* and OH* number densities are deconvoluted from line-of-sight chemiluminescence measurements made on the NASA KC-135 reduced-gravity aircraft. Measured signal levels are calibrated, post-flight, with Rayleigh scattering. Although CH* and OH* kinetics are not well understood, the CH*, OH*, and ground-state CH distributions are spatially coincident in the flame anchoring region. Therefore, the ground-state CH distribution, which is easily computed, and the readily measured CH*/OH* distributions can be used to provide a consistent and convenient way of measuring lift-off height and flame shape in the diffusion flame under investigation. Given that the fuel composition affects flame chemistry and that buoyancy influences the velocity profile of the flow, we have the opportunity to computationally and experimentally study the roles of fluids and chemistry. In performing this microgravity study, improvements to the computational model have been made and new calculations performed for a range of gravity and flow conditions. Furthermore, modifications to the experimental approach were required as a consequence of the constraints imposed by existing microgravity facilities. Results from the computations and experiments are presented in the following sections.

Walsh, Kevin T.↗

Gravity Effects in Diffusive Coarsening of Bubble Lattices: von Neumann's Law

von Neumann modelled the evolution of two-dimensional soap froths as a purely diffusive phenomenon; the area growth of a given cell was found to depend only on the geometry of the bubble lattice. In the model, hexagons are stable, pentagons shrink and heptagons grow. The simplest equivalent to the area growth law is / approximately t(sub beta). The result depends on assuming (1) an incompressible gas; (2) bubble walls which meet at 120 deg and (3) constant wall thickness and curvature. Each assumption is borne out in experiments except the last one: bubble wall thickness between connecting cells varies in unit gravity because of gravity drainage. The bottom part of the soap membrane is thickened, the top part is thinned, such that gas diffusion across the membrane shows a complex dependence on gravity. As a result, experimental tests of von Neumann's law have been influenced by effects of gravity; fluid behavior along cell borders can give non-uniform wall thicknesses and thus alter the effective area and gas diffusion rates between adjacent bubbles. For area plotted as a function of time, Glazier (J.A. Glazier, S.P. Gross, and I. Stavans, Phys. Rev. A. 36, 306 (1987); J. Stavans, J.A, Glazier, Phys. Rev. Lett. 62, 1318 (1989).) suggest that in some cases their failure to observe von Neumann's predicted growth exponent ((sup beta)theor(sup =1; beta)exp(sup =0.70 + 0.10)) may have been the result of such "fluid drainage onto the lower glass plate". Additional experiments which varied plate spacing gave different beta exponents in a fashion consistent with this suggestion. During preliminary long duration experiments (approximately 100 h) aboard Spacelab-J, a low-gravity test of froth coarsening has examined (1) power law scaling of von Neumann's law (beta values) in the appropriate diffusive limits; (2) new bubble lattice dynamics such as greater fluid wetting behavior on froth membranes in low gravity; and (3) explicit relations for the gravity dependence of the second moment (or disorder parameter) governing the geometric spread in cell-sidedness around the mean of perfect hexagonal filling. By reducing the gravity-induced distortion in lattice wall thickness, the diffusion-limited regime of bubble coarsening becomes available for performing critical tests of network dynamics.

Noever, David A.↗

Laser-Induced Fluorescence Measurements and Modeling of Nitric Oxide in Counterflow Diffusion Flames

The feasibility of making quantitative nonintrusive NO concentration ([NO]) measurements in nonpremixed flames has been assessed by obtaining laser-induced fluorescence (LIF) measurements of [NO] in counterflow diffusion flames at atmospheric and higher pressures. Comparisons at atmospheric pressure between laser-saturated fluorescence (LSF) and linear LIF measurements in four diluted ethane-air counterflow diffusion flames with strain rates from 5 to 48/s yielded excellent agreement from fuel-lean to moderately fuel-rich conditions, thus indicating the utility of a model-based quenching correction technique, which was then extended to higher pressures. Quantitative LIF measurements of [NO] in three diluted methane-air counterflow diffusion flames with strain rates from 5 to 35/s were compared with OPPDIF model predictions using the GRI (version 2.11) chemical kinetic mechanism. The comparisons revealed that the GRI mechanism underpredicts prompt-NO by 30-50% at atmospheric pressure. Based on these measurements, a modified reaction rate coefficient for the prompt-NO initiation reaction was proposed which causes the predictions to match experimental data. Temperature measurements using thin filament pyrometry (TFP) in conjunction with a new calibration method utilizing a near-adiabatic H2-air Hencken burner gave very good comparisons with model predictions in these counterflow diffusion flames. Quantitative LIF measurements of [NO] were also obtained in four methane-air counterflow partially-premixed flames with fuel-side equivalence ratios (phi(sub B)) of 1.45, 1.6, 1.8 and 2.0. The measurements were in excellent agreement with model predictions when accounting for radiative heat loss. Spatial separation between regions dominated by the prompt and thermal NO mechanisms was observed in the phi(sub B) = 1.45 flame. The modified rate coefficient proposed earlier for the prompt-NO initiation reaction improved agreement between code predictions and measurements in the region where prompt-NO dominates. Finally, LIF measurements of NO were obtained in counterflow diffusion flames at 2 to 5 atm. Comparisons between [NO] measurements and predictions show that the GRI mechanism underpredicts prompt-NO by a factor of two to three at all pressures. In general, the results indicate a need for refinement of the CH chemistry, especially the pressure-dependent CH formation and destruction reactions.

Ravikrishna, Rayavarapu V.↗

The Galactic Distribution of Aliphatic Hydrocarbons in the Diffuse Interstellar Medium

The infrared absorption feature near 2950/ cm (3.4 microns), characteristic of dust in the diffuse interstellar medium (ISM), is attributed to C-H stretching vibrations of aliphatic hydrocarbons. We show here that the strength of the band does not scale linearly with visual extinction everywhere, but instead increases more rapidly for objects near the center of the Galaxy, a behavior that parallels that of the Si-O stretching band due to silicate materials in the diffuse ISM. This implies that the grains responsible for the diffuse medium aliphatic C-H and silicate Si-O stretching bands are different from those responsible for much of the observed visual extinction. It also suggests that the distribution of the carbonaceous component of the diffuse ISM is not uniform throughout the Galaxy, but instead may increase in density toward the center of the Galaxy. The similar behavior of the C-H and Si-O stretching bands suggests that these two components may be coupled, perhaps in the form of silicate-core, organic-mantle grains. Several possible models of the distribution of this material are presented and it is demonstrated that the inner parts of the Galaxy has a carrier density that is 5 to 35 times higher than in the local ISM. Depending on the model used, the density of aliphatic material in the local ISM is found to be about 1 to 2 -CH3 groups /cc and about 2 to 5 -CH2- groups/cc. These densities are consistent with the strengths of the 2955 and 2925/ cm (3.38 and 3.42 microns) subfeatures (due to -CH3 and -CH2- groups, respectively) within the overall 2950/ cm (3.4 microns) band being described by the relations A(sub upsilon)/tau(sub 2925/cm) = 270 +/- 40 and A(sub upsilon)/tau(sub 2925/cm) = 250 +/- 40 in the local diffuse ISM.

Sandford, Scott A.↗

Wave Augmented Diffuser for Centrifugal Compressor

A wave augmented diffuser for a centrifugal compressor surrounds the outlet of an impeller that rotates on a drive shaft having an axis of rotation. The impeller brings flow in in an axial direction and imparts kinetic energy to the flow discharging it in radial and tangential directions. The flow is discharged into a plurality of circumferentially disposed wave chambers. The wave chambers are periodically opened and closed by a rotary valve such that the flow through the diffuser is unsteady. The valve includes a plurality of valve openings that are periodically brought into and out of fluid communication with the wave chambers. When the wave chambers are closed, a reflected compression wave moves upstream towards the diffuser bringing the flow into the wave chamber to rest. This action recovers the kinetic energy from the flow and limits any boundary layer growth. The flow is then discharged in an axial direction through an opening in the valve plate when the valve plate is rotated to an open position. The diffuser thus efficiently raises the static pressure of the fluid and discharges an axially directed flow at a radius that is predominantly below the maximum radius of the diffuser.

Skoch, Gary J.↗

Turbulent Flame Processes Via Diffusion Flame-Vortex Ring Interactions

Flame-vortex interactions are canonical configurations that can be used to study the underlying processes occurring in turbulent reacting flows. This configuration contains many of the fundamental aspects of the coupling between fluid dynamics and combustion that could be investigated with more controllable conditions than are possible under direct investigations of turbulent flames. Diffusion flame-vortex ring interaction contains many of the fundamental elements of flow, transport, combustion, and soot processes found in turbulent diffusion flames. Some of these elements include concentrated vorticity, entrainment and mixing, strain and nonequilibrium phenomena, diffusion and differential diffusion, partial premixing and diluent effects, soot formation and oxidation, and heat release effects. Such simplified flowfield allows the complex processes to be examined more closely and yet preserving the physical processes present in turbulent reacting flows. Furthermore, experimental results from the study of flame-vortex interactions are useful for the validation of numerical simulations and more importantly to deepen our understanding of the fundamental processes present in reacting flows. Experimental and numerical results obtained under microgravity conditions of the diffusion flame-vortex ring interaction are summarized in this paper. Results are obtained using techniques that include Flame Luminosity Imaging (FLI), Laser Soot-Mie Scattering (LSMS), Computational Fluid Dynamics and Combustion (CFDC), and Diode Laser Spectroscopy/Iterative Temperature with Assumed Chemistry (DLS/ITAC).

Dahm, Werner J. A.↗

Diffusion Time-Scale of Porous Pressure-Sensitive Paint

Pressure-sensitive paint (PSP) is an optical pressure sensor that utilizes the oxygen quenching of luminescence. PSP measurements in unsteady aerodynamic flows require fast time response of the paint. There are two characteristic time-scales that are related to the time response of PSP. One is the luminescent lifetime representing an intrinsic physical limit for the achievable temporal resolution of PSP. Another is the time-scale of oxygen diffusion across the PSP layer. When the time-scale of oxygen diffusion is much larger than the luminescent lifetime, the time response of PSP is controlled by oxygen diffusion. In a thin homogenous polymer layer where diffusion is Fickian, the oxygen concentration 1021 can be described by the diffusion equation in one-dimension.

Liu, Tianshu↗

Gas Phase Spectroscopy of Cold PAH Ions: Contribution to the Interstellar Extinction and the Diffuse Interstellar Bands

Polycyclic Aromatic Hydrocarbon molecules (PAHs) are ubiquitous in the interstellar medium (ISM) and constitute the building blocks of interstellar dust grains. Despite their inferred important role in mediating the energetic and chemical processes in thc ISM, their exact contribution to the interstellar extinction, and in particular to the diffuse interstellar bands (DIBs) remains unclear. The DIBs are spectral absorption features observed in the line of sight of stars that are obscured by diffuse interstellar clouds. More than 200 bands have been reported to date spanning from the near UV to the near IR with bandwidths ranging from 0.4 to 40 Angstroms (Tielens & Snow 1995). The present consensus is that the DIBs arise from free flying, gas-phase, organic molecules and/or ions that are abundant under the typical conditions reigning in the diffuse ISM. PAHs have been proposed as possible carriers (Allamandola et al. 1985; Leger & DHendecourt 1985). The PAH hypothesis is consistent with the cosmic abundance of Carbon and Hydrogen and with the required photostability of the DIB carriers against the strong VUV radiation field in the diffuse interstellar clouds. A significant fraction of PAHs is expected to be ionized in the diffuse ISM.

Biennier, L.↗

Load Diffusion in Composite and Smart Structures

The research carried out here builds on our previous NASA supported research on the general topic of edge effects and load diffusion in composite structures. Further fundamental solid mechanics studies were carried out to provide a basis for assessing the complicated modeling necessary for the multi-functional large scale structures used by NASA. An understanding of the fundamental mechanisms of load diffusion in composite subcomponents is essential in developing primary composite structures. Some specific problems recently considered were those of end effects in smart materials and structures, study of the stress response of pressurized linear piezoelectric cylinders for both static and steady rotating configurations, an analysis of the effect of pre-stressing and pre-polarization on the decay of end effects in piezoelectric solids and investigation of constitutive models for hardening rubber-like materials. Our goal in the study of load diffusion is the development of readily applicable results for the decay lengths in terms of non-dimensional material and geometric parameters. Analytical models of load diffusion behavior are extremely valuable in building an intuitive base for developing refined modeling strategies and assessing results from finite element analyses. The decay behavior of stresses and other field quantities provides a significant aid towards this process. The analysis is also amenable to parameter study with a large parameter space and should be useful in structural tailoring studies. Special purpose analytical models of load diffusion behavior are extremely valuable in building an intuitive base for developing refined modeling strategies and in assessing results from general purpose finite element analyses. For example, a rational basis is needed in choosing where to use three-dimensional to two-dimensional transition finite elements in analyzing stiffened plates and shells. The decay behavior of stresses and other field quantities furnished by this research provides a significant aid towards this element transition issue. A priori knowledge of the extent of boundary-layers induced by edge effects is also useful in determination of the instrumentation location in structural verification tests or in material characterization tests.

Horgan, C. O.↗

Summer Work Experience: Determining Methane Combustion Mechanisms and Sub-Scale Diffuser Properties for Space Transporation System Engine Testing

To assess engine performance during the testing of Space Shuttle Main Engines (SSMEs), the design of an optimal altitude diffuser is studied for future Space Transportation Systems (STS). For other Space Transportation Systems, rocket propellant using kerosene is also studied. Methane and dodecane have similar reaction schemes as kerosene, and are used to simulate kerosene combustion processes at various temperatures. The equations for the methane combustion mechanism at high temperature are given, and engine combustion is simulated on the General Aerodynamic Simulation Program (GASP). The successful design of an altitude diffuser depends on the study of a sub-scaled diffuser model tested through two-dimensional (2-D) flow-techniques. Subroutines given calculate the static temperature and pressure at each Mach number within the diffuser flow. Implementing these subroutines into program code for the properties of 2-D compressible fluid flow determines all fluid characteristics, and will be used in the development of an optimal diffuser design.

Williams, Powtawche N.↗

Experimental Investigation of Diffuser Hub Injection to Improve Centrifugal Compressor Stability

Results from a series of experiments to investigate whether centrifugal compressor stability could be improved by injecting air through the diffuser hub surface are reported. The research was conducted in a 4:1 pressure ratio centrifugal compressor configured with a vane-island diffuser. Injector nozzles were located just upstream of the leading edge of the diffuser vanes. Nozzle orientations were set to produce injected streams angled at 8, 0 and +8 degrees relative to the vane mean camber line. Several injection flow rates were tested using both an external air supply and recirculation from the diffuser exit. Compressor flow range did not improve at any injection flow rate that was tested. Compressor flow range did improve slightly at zero injection due to the flow resistance created by injector openings on the hub surface. Leading edge loading and semi-vaneless space diffusion showed trends similar to those reported earlier from shroud surface experiments that did improve compressor flow range. Opposite trends are seen for hub injection cases where compressor flow range decreased. The hub injection data further explain the range improvement provided by shroud-side injection and suggest that different hub-side techniques may produce range improvement in centrifugal compressors.

Skoch, Gary J.↗

Diffusivity Measurements Made Instant and Easy

A compact common path interferometer (CPI) system has been developed to measure the diffusivity of liquid pairs. The CPI is an optical technique that can be used to measure changes in the gradient of the refraction index of transparent materials. It uses a shearing interferometer that shares the same optical path from a laser light source to the final imaging plane. The molecular diffusion coefficient of liquids can be determined from the physical relations between changes in the optical path length and liquid phase properties. When the data obtained by using the CPI have been compared with similar results from other techniques, the instrument has been demonstrated to be far superior to other instruments for measuring the diffusivity of miscible liquids while staying very compact and robust (ref. 1). Because of its compactness and ease of use, the CPI has been adopted for use in studies of interface dynamics as well as other diffusion-controlled process applications (ref. 2). This progress will permit experiments in microgravity that can quantitatively answer basic science questions about mass and thermal diffusion and their effect in transport processes. This instrument is a spinoff of a diagnostic development for microgravity fluid physics experiments at the NASA Glenn Research Center that has used optics and electronics existing in the fluid physics laboratory for feasibility studies. Optical diagnostic techniques have become an integral part of many areas of measurement applications in industrial and research laboratories. Many types of interferometers and their phase-shifted versions have been used as instruments for measuring optical wave fronts for lens testing and combustion and fluid flow diagnostics. One of these, the point diffraction interferometer, is considered to be robust (see, for example, ref. 3) because it has a common-path design. The point diffraction interferometer is difficult to align and has a limited measurement range for liquid-phase applications. Interferometry and schlieren techniques have been widely used for many years for gas-flow-visualization. On the other hand, the CPI, which is basically a Wollaston prism Polarizer in combination with an analyser (crystalline quartz retardation plate) is used instead of a point diffraction interferometer unit. The advantage of using the CPI over other optical techniques is that it can make quantitative measurements in liquids with the large index of refraction variations that often occur in interface dynamics studies. This can be simply accomplished by using different prism polarizers for each particular experimental condition.

Rashidnia, Nasser↗

Pattern Formation in Diffusion Flames Embedded in von Karman Swirling Flows

Pattern formation is observed in nature in many so-called excitable systems that can support wave propagation. It is well-known in the field of combustion that premixed flames can exhibit patterns through differential diffusion mechanism between heat and mass. However, in the case of diffusion flames where fuel and oxidizer are separated initially there have been only a few observations of pattern formation. It is generally perceived that since diffusion flames do not possess an inherent propagation speed they are static and do not form patterns. But in diffusion flames close to their extinction local quenching can occur and produce flame edges which can propagate along stoichiometric surfaces. Recently, we reported experimental observations of rotating spiral flame edges during near-limit combustion of a downward-facing polymethylmethacrylate disk spinning in quiescent air. These spiral flames, though short-lived, exhibited many similarities to patterns commonly found in quiescent excitable media including compound tip meandering motion. Flame disks that grow or shrink with time depending on the rotational speed and in-depth heat loss history of the fuel disk have also been reported. One of the limitations of studying flame patterns with solid fuels is that steady-state conditions cannot be achieved in air at normal atmospheric pressure for experimentally reasonable fuel thickness. As a means to reproduce the flame patterns observed earlier with solid fuels, but under steady-state conditions, we have designed and built a rotating, porous-disk burner through which gaseous fuels can be injected and burned as diffusion flames. The rotating porous disk generates a flow of air toward the disk by a viscous pumping action, generating what is called the von K rm n boundary layer which is of constant thickness over the entire burner disk. In this note we present a map of the various dynamic flame patterns observed during the combustion of methane in air as a function of fuel flow rate and the burner rotational speed.

Nayagam, Vedha↗

Fabrication and Characterization of Diffusion Bonds for Silicon Carbide

Diffusion bonds of silicon carbide (SiC) were fabricated using several different types of titanium (Ti) based interlayers between the SiC substrates. The interlayers were an alloyed Ti foil, a pure Ti foil, and a physically vapor deposited (PVD) Ti coating. Microscopy was conducted to evaluate the cross-sections of the resulting bonds. Microprobe analysis identified reaction formed phases in the diffusion bonded region. Uniform and well adhered bonds were formed between the SiC substrates. In the case where the alloyed Ti foil or a thick Ti coating (i.e. 20 micron) was used as the interlayer, microcracks and several phases were present in the diffusion bonds. When a thinner interlayer was used (i.e. 10 micron PVD Ti), no microcracks were observed and only two reaction formed phases were present. The two phases were preferred and fully reacted phases that did not introduce thermal stresses or microcracks during the cool-down stage after processing. Diffusion bonded samples were evaluated with the non-destructive evaluation (NDE) methods of pulsed thermography and immersion ultrasonic testing. Joined SiC substrates that were fully bonded and that had simulated bond flaws in the interlayer were also evaluated using immersion ultrasound. Pull testing was conducted on the bonds to determine the tensile strength. To demonstrate the joining approach for a complex multilayered component for a low NOx injector application, the diffusion bonding approach was used to join three 4" diameter SiC discs that contained complex fuel and air flow channels.

Halbig, Michael↗

Resolving the Origin of the Diffuse Soft X-ray Background

In January 1993, the Diffuse X-ray Spectrometer (DXS) measured the first high-resolution spectrum of the diffuse soft X-ray background between 44-80A. A line-dominated spectrum characteristic of a 10(exp 6)K collisionally ionized plasma' was expected but while the observed spectrum was clearly line-dominated, no model would fit. Then in 2003 the Cosmic Hot Interstellar Plasma Spectrometer (CHIPS) launched and observed the diffuse extreme-ultraviolet (EUV) spectrum between 90- 265A. Although many emission lines were again expected; only Fe IX at 171.1A was detected. The discovery of X-rays from comets led to the realization that heavy ions (Z=6-28) in the solar wind will emit soft X-rays as the ions interact via charge exchange with neutral atoms in the heliosphere and geocorona. Using a new model for solar wind charge exchange (SWCX) emission, we show that the diffuse soft X-ray background can be understood as a combination of emission from charge exchange onto the slow and fast solar wind together with a more distant and diffuse hot (10(exp 6)K) plasma.

Smith, Randall K.↗

Modeling of Particle Acceleration at Multiple Shocks Via Diffusive Shock Acceleration: Preliminary Results

We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models (Protheroe and Stanev, 1998; Moraal and Axford, 1983; Ball and Kirk, 1992; Drury et al., 1999) in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box (Melrose and Pope, 1993; Zank et al., 2000). We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (Emax) appropriate for quasi-parallel and quasi-perpendicular shocks (Zank et al., 2000, 2006; Dosch and Shalchi, 2010) and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).

Parker, Linda Neergaard↗

Modeling of Particle Acceleration at Multiple Shocks via Diffusive Shock Acceleration: Preliminary Results

Successful forecasting of energetic particle events in space weather models require algorithms for correctly predicting the spectrum of ions accelerated from a background population of charged particles. We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box. We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (E(sub max)) appropriate for quasi-parallel and quasi-perpendicular shocks and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).

Parker, L. Neergaard↗