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Open-source MFIX-DEM software for gas-solids flows: Part II — Validation studies

With rapid advancements in computer hardware and numerical algorithms, computational fluid dynamics (CFD) has been increasingly employed as a useful tool for investigating the complex hydrodynamics inherent in multiphase flows. An important step during the development of a CFD model and prior to its application is conducting careful and comprehensive verification and validation studies. Accordingly, efforts to verify and validate the open-source MFIX-DEM software, which can be used for simulating the gas–solids flow using an Eulerian reference frame for the continuum fluid and a Lagrangian discrete framework (Discrete Element Method) for the particles, have been made at the National Energy Technology Laboratory (NETL). In part I of this paper, extensive verification studies were presented and in this part, detailed validation studies of MFIX-DEM are presented. A series of test cases covering a range of gas–solids flow applications were conducted. In particular the numerical results for the random packing of a binary particle mixture, the repose angle of a sandpile formed during a side charge process, velocity, granular temperature, and voidage profiles from a bounded granular shear flow, lateral voidage and velocity profiles from a monodisperse bubbling fluidized bed, lateral velocity profiles from a spouted bed, and the dynamics of segregation of a binary mixture in a bubbling bed were compared with available experimental data, and in some instances with empirical correlations. In addition, sensitivity studies were conducted for various parameters to quantify the error in the numerical simulation.

42 ENGINEERING↗

Challenges in Implementing a Multi-Partnership Geothermal Power Plant

The UND-CLR binary geothermal power plant project is a piggyback operation on a secondary-recovery water-flood project in the Cedar Hills oil field in the Williston Basin. Two open-hole horizontal wells at 2,300 m and 2,400 m depths with lateral lengths of 1,290 m and 860 m produce water at a combined flow of 51 l s -1 from the Lodgepole formation (Miss.) for injection into the Red River formation (Ordovician). The hydrostatic head for the Lodgepole is at ground surface and the pumps, which are set at 650 m depth, have run continuously since 2009. Water temperature at the wellhead is 103 °C and CLR passes the water through two large air-cooled heat exchangers prior to injection. In all aspects, the CLR water flood project is ideal for demonstration of electrical power production from a low-temperature geothermal resource. However, implementation of the project from concept to power production was analogous to breaking trail in deep snow in an old growth forest. There were many hidden bumps, detours, and in some instances immoveable barriers. Problems with investors, cost share, contracts with CLR, resistance from local industry, cost of installation, delays by the ORC supplier, and the North Dakota climate all caused delays and setbacks. Determination and problem solving by the UND team eventually overcame most setbacks, and in April 2016, the site began generating power. Figure 1: Schematic of the water supply well at the UND CLR binary geothermal power plant REFERENCES Williams, Snyder, and Gosnold, 2016, Low Temperature Projects Evaluation and Lesson Learned, GRC Transactions, Vol. 40, 203-210 Gosnold, LeFever, Klenner, Mann, Salehfar, and Johnson, 2010, Geothermal Power from Coproduced Fluids in the Williston Basin, GRC Transactions, Vol. 34, 557-560

Coproduced, geothermal, binary power↗

PARTICLE TRANSPORT IN EVOLVING PROTOPLANETARY DISKS: IMPLICATIONS FOR RESULTS FROM STARDUST

Samples returned from comet 81P/Wild 2 by the Stardust mission confirm that substantial quantities of crystalline silicates were incorporated into the comet at the time of its formation. We investigate the constraints that this observation places upon protoplanetary disk physics, under the assumption that outward transport of particles processed at high temperatures occurs via a combination of advection and turbulent diffusion in an evolving disk. We also look for possible constraints on the formation locations of such particles. Our results are based upon one-dimensional disk models that evolve with time under the action of viscosity and photoevaporative mass loss, and track solid transport using an ensemble of individual particle trajectories. We find that two broad classes of the disk model are consistent with the Stardust findings. One class of models features a high particle diffusivity (a Schmidt number, Sc < 1), which suffices to diffuse particles up to 20 {mu}m in size outward against the mean gas flow. For Sc {>=} 1 such models are unlikely to be viable and significant outward transport appears to require that the particles of interest settle into a midplane layer that experiences an outward gas flow. In either class of models, the mass of inner disk material that reaches the outer disk is a strong function of the initial compactness of the disk. Hence, models of grain transport within steady-state disks underestimate the efficiency of outward transport. Neither model results in sustained outward transport of very large particles exceeding a millimeter in size. We show that in most circumstances, the transport efficiency falls off rapidly with time. Hence, high-temperature material must be rapidly incorporated into icy bodies to avoid fallback to small radii. We suggest that significant radial transport may only occur during the initial phase of rapid disk evolution. It may also vary substantially between disks depending upon their initial mass distributions. We discuss how our model may inform recent Spitzer observations of crystalline silicates in T Tauri star-disk systems.

79 ASTRONOMY AND ASTROPHYSICS↗

ASYMPTOTIC SELF-SIMILAR SOLUTIONS WITH A CHARACTERISTIC TIMESCALE

For a wide variety of initial and boundary conditions, adiabatic one-dimensional flows of an ideal gas approach self-similar behavior when the characteristic length scale over which the flow takes place, R, diverges or tends to zero. It is commonly assumed that self-similarity is approached since in the R {yields} {infinity}(0) limit the flow becomes independent of any characteristic length or timescales. In this case, the flow fields f(r, t) must be of the form f(r,t)=t{sup {alpha}}{sub f}F(r/R) with R {proportional_to} ({+-}t){sup {alpha}}. We show that requiring the asymptotic flow to be independent only of characteristic length scales implies a more general form of self-similar solutions, f(r,t)=R{sup {delta}}{sub f}F(r/R) with R-dot {proportional_to}R{sup {delta}}, which includes the exponential ({delta} = 1) solutions, R {proportional_to} e {sup t/{tau}}. We demonstrate that the latter, less restrictive, requirement is the physically relevant one by showing that the asymptotic behavior of accelerating blast waves, driven by the release of energy at the center of a cold gas sphere of initial density {rho} {proportional_to} r {sup -{omega}}, changes its character at large {omega}: the flow is described by 0 {<=} {delta} < 1, R {proportional_to} t {sup 1/(1-{delta})}, solutions for {omega} < {omega}{sub c}, by {delta}>1 solutions with R {proportional_to} (-t){sup 1/({delta}-1)} diverging at finite time (t = 0) for {omega}>{omega}{sub c}, and by exponential solutions for {omega} = {omega}{sub c} ({omega}{sub c} depends on the adiabatic index of the gas, {omega}{sub c} {approx} 8 for 4/3 < {gamma} < 5/3). The properties of the new solutions obtained here for {omega} {>=} {omega}{sub c} are analyzed, and self-similar solutions describing the t>0 behavior for {omega}>{omega}{sub c} are also derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SUB-CHANDRASEKHAR MASS MODELS FOR SUPERNOVAE

For carbon-oxygen white dwarfs accreting hydrogen or helium at rates in the range {approx}(1-10) x 10{sup -8} M{sub sun} yr{sup -1}, a variety of explosive outcomes is possible well before the star reaches the Chandrasekhar mass. These outcomes are surveyed for a range of white dwarf masses (0.7-1.1 M{sub sun}), accretion rates ((1-7) x 10{sup -8} M{sub sun} yr{sup -1}), and initial white dwarf temperatures (0.01 and 1 L{sub sun}). The results are particularly sensitive to the convection that goes on during the last few minutes before the explosion. Unless this convection maintains a shallow temperature gradient and unless the density is sufficiently high, the accreted helium does not detonate. Below a critical helium ignition density, which we estimate to be (5-10) x 10{sup 5} g cm{sup -3}, either helium novae or helium deflagrations result. The hydrodynamics, nucleosynthesis, light curves, and spectra of a representative sample of detonating and deflagrating models are explored. Some can be quite faint indeed, powered at peak for a few days by the decay of {sup 48}Cr and {sup 48}V. Only the hottest, most massive white dwarfs considered with the smallest helium layers, show reasonable agreement with the light curves and spectra of common Type Ia supernovae (SNe Ia). For the other models, especially those involving lighter white dwarfs, the helium shell mass exceeds 0.05 M{sub sun} and the mass of the {sup 56}Ni that is synthesized exceeds 0.01 M{sub sun}. These explosions do not look like ordinary SNe Ia or any other frequently observed transient.

79 ASTRONOMY AND ASTROPHYSICS↗

THE TRANSITIONAL STRIPPED-ENVELOPE SN 2008ax: SPECTRAL EVOLUTION AND EVIDENCE FOR LARGE ASPHERICITY

Supernova (SN) 2008ax in NGC 4490 was discovered within hours after shock breakout, presenting the rare opportunity to study a core-collapse SN beginning with the initial envelope-cooling phase immediately following shock breakout. We present an extensive sequence of optical and near-infrared spectra, as well as three epochs of optical spectropolarimetry. Our initial spectra, taken two days after shock breakout, are dominated by hydrogen Balmer lines at high velocity. However, by maximum light, He I lines dominated the optical and near-infrared spectra, which closely resembled those of normal Type Ib supernovae (SNe Ib) such as SN 1999ex. This spectroscopic transition defines Type IIb SNe, but the strong similarity of SN 2008ax to normal SNe Ib beginning near maximum light, including an absorption feature near 6270 A due to H{alpha} at high velocities, suggests that many objects classified as SNe Ib in the literature may have ejected similar amounts of hydrogen as SN 2008ax, roughly a few x 0.01 M{sub sun}. Only the unusually early discovery of SN 2008ax allowed us to observe the spectroscopic signatures of the hydrogen-rich outer ejecta. Early-time spectropolarimetry (six and nine days after shock breakout) revealed strong line polarization modulations of 3.4% across H{alpha}, indicating the presence of large asphericities in the outer ejecta and possibly that the spectrum of SN 2008ax could be dependent on the viewing angle. After removal of interstellar polarization, the continuum shares a common polarization angle with the hydrogen, helium, and oxygen lines, while the calcium and iron absorptions are oriented at different angles. This is clear evidence of deviations from axisymmetry even in the outer ejecta. Intrinsic continuum polarization of 0.64% only nine days after shock breakout shows that the outer layers of the ejecta were quite aspherical. A single epoch of late-time spectropolarimetry as well as the shapes of the nebular line profiles demonstrate that asphericities extended from the outermost layers all the way down to the center of this core-collapse SN. SN 2008ax may in some ways be an extragalactic analog of the explosion giving rise to Cassiopeia A, which has recently been determined to be a remnant of an SN IIb.

79 ASTRONOMY AND ASTROPHYSICS↗

X-Ray Spectra from General Relativistic Radiation Magnetohydrodynamic Simulations of Thin Disks

We compare X-ray emission from several general relativistic, multifrequency, radiation magnetohydrodynamic simulations of thin black hole accretion disks with different accretion rates and spins. The simulations were performed using the M1 closure scheme, resolved with 12 frequency (energy) bins logarithmically spaced from 5 × 10 −3 to 5 × 10 3 ​​​ keV. We apply a general relativistic Monte Carlo transport code to postprocess the simulation data with greater fidelity in frequency resolution and Compton scattering treatment. Despite the relatively few energy bins and Kompaneets approximation to Compton scattering utilized in the M1 method, we find generally good agreement between the methods. Both produce prominent thermal profiles with peaks around 2–2.5 keV, where agreement is particularly strong and representative of the soft state. Both also find weaker (lower-luminosity) thermally sourced emission extending out to 100 keV due to the hotter innermost regions of the disks. Inverse Compton scattering becomes increasingly effective at hardening spectral outputs with increasing black hole spin, and becomes the dominant mechanism for photons that escape with energies between 10 to several hundred keV. At very high rates of spin, the radiation flux in this upscattered component becomes comparable to the thermal flux, a phenomenon typically associated with intermediate states. Beyond 10 4 keV, we observe faint, free–free emission from hot, optically thin coronal regions developing near the horizon, common to both spinning and nonspinning black holes.

79 ASTRONOMY AND ASTROPHYSICS↗

Electric Power Generation from Low to Intermediate Temperature Resourcces

The UND-CLR Binary Geothermal Power Plant was a collaborative effort of the U.S. Department of Energy (DOE), Continental Resources, Inc. (CRL), Slope Electric Cooperative (SEC), Access Energy, LLC (AE), Basin Electric Cooperative (BEC), Olson Construction, the North Dakota Industrial Commission Renewable Energy Council (NDIC-REC), the North Dakota Department of Commerce Centers of Excellence Program (NDDC-COE), and the University of North Dakota (UND). The primary objective of project was to demonstrate/test the technical and economic feasibility of generating electricity from non-conventional, low-temperature (90 ºC to 150 °C) geothermal resources using binary technology. CLR provided the access to 98 ºC water flowing at 51 l s-1 at the Davis Water Injection Plan in Bowman County, ND. Funding for the project was from DOE –GTO, NDIC-REC, NDD-COE, and BEC. Logistics, on-site construction, and power grid access were facilitated by Slope Electric Cooperative and Olson Construction. Access Energy supplied prototype organic Rankine Cycle engines for the project. The potential power output from this project is 250 kW at a cost of $3,400 per kW. A key factor in the economics of this project is a significant advance in binary power technology by Access Energy, LLC. Other commercially available ORC engines have efficiencies 8 to 10 percent and produce 50 to 250 kW per unit. The AE ORC units are designed to generate 125 kW with efficiencies up to 14 percent and they can be installed in arrays of tens of units to produce several MW of power where geothermal waters are available. This demonstration project is small but the potential for large-scale development in deeper, hotter formations is promising. The UND team’s analysis of the entire Williston Basin using data on porosity, formation thicknesses, and fluid temperatures reveals that 4.0 x 1019 Joules of energy is available and that 1.36 x 109 MWh of power could be produced using ORC binary power plants. Much of the infrastructure necessary to develop extensive geothermal power in the Williston Basin exists as abandoned oil and gas wells. Re-completing wells for water production could provide local power throughout the basin thus reducing power loss through transmission over long distances. Water production in normal oil and gas operations is relatively low by design, but it could be one to two orders of magnitude greater in wells completed and pumped for water production. A promising method for geothermal power production recognized in this project is drilling horizontal open-hole wells in the permeable carbonate aquifers. Horizontal drilling in the aquifers increases borehole exposure to the resource and consequently increases the capacity for fluid production by up to an order of magnitude.

15 GEOTHERMAL ENERGY↗

Investigation of species-mass diffusion in binary-species boundary layers at high pressure using direct numerical simulations

Here, direct numerical simulations of single-species and binary-species temporal boundary layers at high pressure are performed with special attention to species-mass diffusion. The working fluids are nitrogen or a mixture of nitrogen and methane. Mean profiles and turbulent fluctuations of mass fraction show that their qualitative characteristics are different from those of streamwise velocity and temperature, due to the different boundary conditions. In a wall-parallel plane near the wall, the streamwise velocity and temperature have streaky patterns and the fields are similar. However, the mass fraction field at the same location is different from the streamwise velocity and temperature fields indicating that species-mass diffusion is not similar to the momentum and thermal diffusion. In contrast, at the centre and near the edge of the boundary layer, the mass fraction and temperature fields have almost the same pattern, indicating that the similarity between thermal and species-mass diffusion holds away from the wall. The lack of similarity near the wall is traced to the Soret effect that induces a temperature-gradient-dependent species-mass flux. As a result, a new phenomenon has been identified for a non-isothermal binary-species system – uphill diffusion, which in its classical isothermal definition can only occur for three or more species. A quadrant analysis for the turbulent mass flux reveals that near the wall the Soret effect enhances the negative contributions of the quadrants. Due to the enhancement of the negative contributions, small species-concentration fluid tends to be trapped near the wall.

42 ENGINEERING↗

Halted-pendulum Relaxation: Application to White Dwarf Binary Initial Data

Studying compact-star binaries and their mergers is integral to determining progenitors for observable transients. Today, compact-star mergers are typically studied via state-of-the-art computational fluid dynamics codes. One such numerical technique, smoothed particle hydrodynamics (SPH), is frequently chosen for its excellent mass, energy, and momentum conservation. The natural treatment of vacuum and the ability to represent highly irregular morphologies make SPH an excellent tool for the study of compact-star binaries and mergers. For many scenarios, including binary systems, the outcome of simulations is only as accurate as the initial conditions. For SPH, it is essential to ensure that the particles are distributed regularly, representing the initial density profile but without long-range correlations. Particle noise in the form of high-frequency local motion and low-frequency global dynamics must be damped out. Damping the latter can be as computationally intensive as the actual simulation. We discuss a new and straightforward relaxation method, halted-pendulum relaxation (HPR), to remove global oscillation modes of SPH particle configurations. In combination with effective external potentials representing gravitational and orbital forces, we show that HPR has an excellent performance in efficiently relaxing SPH particles to the desired density distribution and removing global oscillation modes. We compare the method to frequently used relaxation approaches and test it on a white dwarf binary model at its Roche-lobe overflow limit. We highlight the importance of our method in achieving accurate initial conditions and its effect on achieving circular orbits and realistic accretion rates when compared with other general relaxation methods.

79 ASTRONOMY AND ASTROPHYSICS↗

Beowawe Bottoming Binary Unit

This binary plant is the first high-output refrigeration based waste heat recovery cycle in the industry. Its working fluid is environmentally friendly and as such, the permits that would be required with a butane based cycle are not necessary. The unit is modularized, meaning that the unit’s individual skids were assembled in another location and were shipped via truck to the plant site. This project proves the technical feasibility of using low temperature brine. The development of the unit led to the realization of low temperature, high output, and environmentally friendly heat recovery systems through domestic research and engineering. The project generates additional renewable energy for Nevada, resulting in cleaner air and reduced carbon dioxide emissions. Royalty and tax payments to governmental agencies will increase, resulting in reduced financial pressure on local entities. The major components of the unit were sourced from American companies, resulting in increased economic activity throughout the country.

15 GEOTHERMAL ENERGY↗

Sensitivity measurements for a 250 MHz quartz shear-horizontal surface acoustic wave biosensor under liquid viscous loading

Surface acoustic wave (SAW) devices have been used in biochemical assays due to their high sensitivity. The device sensitivity is a function of changes in the density and viscosity of the liquid. Here, we studied the effect of fluid viscosity using a 250 MHz quartz shear-horizontal (SH)-SAW biosensor by monitoring different concentrations of binary aqueous/glycerol solutions. In this study, the sensitivity of the biosensor was determined by fitting the data to models derived from perturbation theory. Measurements in water were used as the reference. For a 0% to 50% glycerol solution, an 87°–204° separation in the phase shift was observed. The slope of the plot of the phase shift vs (ηρ)0.5 was used to indicate the sensor’s sensitivity. The sensitivity for our 250 MHz quartz SH-SAW sensors was calculated to be 3.7×10−3m2sKg. The corresponding mass sensitivity was determined to be 9.25 × 105m2Kg. The limit of detection was calculated to be 36 picograms (pg), while the limit of quantification or LOQ was calculated to be 109 pg. Traditionally, liquid phase measurements have been challenging for SAW devices because liquids dampen the vibrating sensors severely. This problem has been largely solved using a transverse (shear) wave instead of the more popular longitudinal or Rayleigh waves. Liquid measurements are now possible using transverse waves, also known as shear waves, because transverse waves are only minimally attenuated by liquids. Shear-horizontal SAW sensors (SH-SAW) show great promise as label-free biosensors because of their ability to handle liquid samples. However, the viscosity of the liquid still induces loading effects and can be measured when the liquid is loaded onto the SH-SAW propagating surface (delay line). When the liquid above the delay line is perturbed by physical or chemical changes, such as binding to a receptor, it alters the propagating acoustic wave. The SH-SAW device can measure these changes in liquid properties as a change in the wave’s phase compared to the original wave. The device’s phase shift was recorded as a function of the changes in the density and viscosity of the binary glycerol solution and used to determine the sensitivity in the linear dynamic range of responses.

Materials Science↗

THREE-DIMENSIONAL SIMULATIONS OF RAYLEIGH-TAYLOR MIXING IN CORE-COLLAPSE SUPERNOVAE

We present multidimensional simulations of the post-explosion hydrodynamics in three different 15 M{sub sun} supernova models with zero, 10{sup -4} Z{sub sun}, and Z{sub sun} metallicities. We follow the growth of the Rayleigh-Taylor (RT) instability that mixes together the stellar layers in the wake of the explosion. Models are initialized with spherically symmetric explosions and perturbations are seeded by the grid. Calculations are performed in two-dimensional (2D) axisymmetric and three-dimensional (3D) Cartesian coordinates using the new Eulerian hydrodynamics code, CASTRO. We find as in previous work that RT perturbations initially grow faster in 3D than in 2D. As the RT fingers interact with one another, mixing proceeds to a greater degree in 3D than in 2D, reducing the local Atwood number and slowing the growth rate of the instability in 3D relative to 2D. By the time mixing has stopped, the width of the mixed region is similar in the 2D and 3D simulations provided the RT fingers show significant interaction. Our results imply that 2D simulations of light curves and nucleosynthesis in supernovae that die as red giants may capture the features of an initially spherically symmetric explosion in far less computational time than required by a full 3D simulation. However, capturing large departures from spherical symmetry requires a significantly perturbed explosion. Large-scale asymmetries cannot develop through an inverse cascade of merging RT structures; they must arise from asymmetries in the initial explosion.

79 ASTRONOMY AND ASTROPHYSICS↗

THE ORIGIN OF COSMIC RAYS: EXPLOSIONS OF MASSIVE STARS WITH MAGNETIC WINDS AND THEIR SUPERNOVA MECHANISM

One prediction of particle acceleration in the supernova (SN) remnants in the magnetic wind of exploding Wolf-Rayet and red supergiant stars is that the final spectrum is a composition of a spectrum E {sup -7/3} and a polar cap component of E {sup -2} at the source. This polar cap component contributes to the total energy content with only a few percent, but dominates the spectrum at higher energy. The sum of both components gives spectra which curve upward. The upturn was predicted to occur always at the same rigidity. An additional component of cosmic rays from acceleration by SNe exploding into the interstellar medium adds another component for hydrogen and for helium. After transport, the predicted spectra J(E) for the wind-SN cosmic rays are E {sup -8/3} and E {sup -7/3}; the sum leads to an upturn from the steeper spectrum. An upturn has now been seen by the CREAM mission. Here, we test the observations against the predictions and show that the observed properties are consistent with the predictions. Hydrogen can be shown to also have a noticeable wind-SN component. The observation of the upturn in the heavy element spectra being compatible with the same rigidity for all heavy elements supports the magneto-rotational mechanism for these SNe. This interpretation predicts the observed upturn to continue to curve upward and approach the E {sup -7/3} spectrum. If confirmed, this would strengthen the case that SNe of very massive stars with magnetic winds are important sources of Galactic cosmic rays.

79 ASTRONOMY AND ASTROPHYSICS↗

TOWARD REALISTIC PROGENITORS OF CORE-COLLAPSE SUPERNOVAE

Two-dimensional (2D) hydrodynamical simulations of progenitor evolution of a 23 M{sub sun} star, close to core collapse (in {approx}1 hr in one dimension (1D)), with simultaneously active C, Ne, O, and Si burning shells, are presented and contrasted to existing 1D models (which are forced to be quasi-static). Pronounced asymmetries and strong dynamical interactions between shells are seen in 2D. Although instigated by turbulence, the dynamic behavior proceeds to sufficiently large amplitudes that it couples to the nuclear burning. Dramatic growth of low-order modes is seen as well as large deviations from spherical symmetry in the burning shells. The vigorous dynamics is more violent than that seen in earlier burning stages in the three-dimensional (3D) simulations of a single cell in the oxygen burning shell, or in 2D simulations not including an active Si shell. Linear perturbative analysis does not capture the chaotic behavior of turbulence (e.g., strange attractors such as that discovered by Lorenz), and therefore badly underestimates the vigor of the instability. The limitations of 1D and 2D models are discussed in detail. The 2D models, although flawed geometrically, represent a more realistic treatment of the relevant dynamics than existing 1D models, and present a dramatically different view of the stages of evolution prior to collapse. Implications for interpretation of SN1987A, abundances in young supernova remnants, pre-collapse outbursts, progenitor structure, neutron star kicks, and fallback are outlined. While 2D simulations provide new qualitative insight, fully 3D simulations are needed for a quantitative understanding of this stage of stellar evolution. The necessary properties of such simulations are delineated.

79 ASTRONOMY AND ASTROPHYSICS↗

RADIATION PRESSURE FROM MASSIVE STAR CLUSTERS AS A LAUNCHING MECHANISM FOR SUPER-GALACTIC WINDS

Galactic outflows of cool ({approx}10{sup 4} K) gas are ubiquitous in local starburst galaxies and in most high-redshift galaxies. Hot gas from supernovae has long been suspected as the primary driver, but this mechanism suffers from its tendency to destroy the cool gas. We propose a modification of the supernova scenario that overcomes this difficulty. Star formation is observed to take place in clusters. We show that, for L* galaxies, the radiation pressure from clusters with M{sub cl} {approx}> 10{sup 6} M{sub sun} is able to expel the surrounding gas at velocities in excess of the circular velocity v{sub c} of the disk galaxy. This cool gas travels above the galactic disk before supernovae erupt in the driving cluster. Once above the disk, the cool outflowing gas is exposed to radiation and hot gas outflows from the galactic disk, which in combination drive it to distances of {approx}50 kpc. Because the radiatively driven clouds grow in size as they travel, and because the hot gas is more dilute at large distance, the clouds are less subject to destruction. Therefore, unlike wind-driven clouds, radiatively driven clouds can give rise to the metal absorbers seen in quasar spectra. We identify these cluster-driven winds with large-scale galactic outflows. The maximum cluster mass in a galaxy is an increasing function of the galaxy's gas surface density, so only starburst galaxies are able to drive cold outflows. We find the critical star formation rate for launching large-scale cool outflows to be {Sigma}-dot{sub *}{sup crit} approx. 0.05 M{sub sun} yr{sup -1} kpc{sup -2}, in good agreement with observations.

79 ASTRONOMY AND ASTROPHYSICS↗

FEEDBACK FROM CENTRAL BLACK HOLES IN ELLIPTICAL GALAXIES: TWO-DIMENSIONAL MODELS COMPARED TO ONE-DIMENSIONAL MODELS

We extend the black hole (BH) feedback models of Ciotti, Ostriker, and Proga to two dimensions. In this paper, we focus on identifying the differences between the one-dimensional and two-dimensional hydrodynamical simulations. We examine a normal, isolated L{sub *} galaxy subject to the cooling flow instability of gas in the inner regions. Allowance is made for subsequent star formation, Type Ia and Type II supernovae, radiation pressure, and inflow to the central BH from mildly rotating galactic gas which is being replenished as a normal consequence of stellar evolution. The central BH accretes some of the infalling gas and expels a conical wind with mass, momentum, and energy flux derived from both observational and theoretical studies. The galaxy is assumed to have low specific angular momentum in analogy with the existing one-dimensional case in order to isolate the effect of dimensionality. The code then tracks the interaction of the outflowing radiation and winds with the galactic gas and their effects on regulating the accretion. After matching physical modeling to the extent possible between the one-dimensional and two-dimensional treatments, we find essentially similar results in terms of BH growth and duty cycle (fraction of the time above a given fraction of the Eddington luminosity). In the two-dimensional calculations, the cool shells forming at 0.1-1 kpc from the center are Rayleigh-Taylor unstable to fragmentation, leading to a somewhat higher accretion rate, less effective feedback, and a more irregular pattern of bursting compared with the one-dimensional case.

79 ASTRONOMY AND ASTROPHYSICS↗