Spheroidal Gas Research Articles

Dynamics of a spheroidal gas bubble near a rigid surface

Non-spherical dynamics of a bubble during its axisymmetric collapse near a planar rigid wall is considered. The liquid surrounding the bubble is ideal incompressible, its flow is potential. The pressure in the bubble is uniform, and varying with respect to adiabatic law. At the beginning of collapse, the bubble is spheroidal, the liquid is motionless. A numerical technique is applied, which is based on a stepwise method in time for calculating the bubble surface movement and on the boundary element method. The initial stage of the bubble collapse till the moment of contact between some parts of the bubble surface (i.e., till losing its one-connectedness) is considered. The effect of the ratio of the semi-axes of the spheroidal bubble and the initial thickness of the liquid layer between the bubble and the wall on the bubble shape, the pressure and velocity fields in liquid are investigated. The region of the problem parameters (the distance from the wall, the bubble non-sphericity) is outlined, in which the bubble collapses with formation of a cumulative liquid jet impacting on the bubble surface part nearest to the wall. The liquid pressures resulting from the impact are estimated.

Grain‐Displacive Gas Migration in Fine‐Grained Sediments

AbstractGas migration mechanisms control the release of gas from seafloor sediments. We study underlying phenomena using transparent sediments subjected to controlled effective stress; this experimental approach allows high‐resolution real‐time monitoring of gas migration through cohesionless granular materials under 3‐D boundary conditions. Observed migration patterns depend on the effective stress at the time of injection and the stress history. Gas migration transitions from pore invasive to grain displacive when the capillary pressure for air entry ΔPAE is greater than the effective stress σ′. This study focuses on grain‐displacive gas migration. The morphology of grain‐displacive gas bodies changes with depth as the sediment stiffness G increases and the effect of surface tension γ vanishes: spheroidal gas bubbles form in the near‐surface, faceted cavities further down, and eventually open‐mode fractures develop at depth. The gas injection pressure is proportional to the effective stress in grain‐displacive migration. Preloading and overconsolidation cause the rotation of principal stresses and gas‐driven openings align with the new minimum principal stress direction. Cyclic loading promotes the upward migration of gas‐filled openings, and there is mechanical memory of previous gas pathways in sediments.

A global stability approach to wake and path instabilities of nearly oblate spheroidal rising bubbles

A global Linear Stability Analysis (LSA) of the three-dimensional flow past a nearly oblate spheroidal gas bubble rising in still liquid is carried out, considering the actual bubble shape and terminal velocity obtained for various sets of Galilei (Ga) and Bond (Bo) numbers in axisymmetric numerical simulations. Hence, this study extends the stability analysis approach of Tchoufag et al. [“Linear stability and sensitivity of the flow past a fixed oblate spheroidal bubble,” Phys. Fluids 25, 054108 (2013) and “Linear instability of the path of a freely rising spheroidal bubble,” J. Fluid Mech. 751, R4 (2014)] (which considered perfectly spheroidal bubbles with an arbitrary aspect ratio) to the case of bubbles with a realistic fore-aft asymmetric shape (i.e., a flatter front and a more rounded rear). The critical curve separating stable and unstable regimes for the straight vertical path is obtained both in the (Ga,Bo) and the (Re,χ) planes, where Re is the bubble Reynolds number and χ its aspect ratio (i.e., the major-to-minor axes length ratio). This provides new insight into the effect of the shape asymmetry on the wake instability of bubbles held fixed in a uniform stream and on the path instability of freely rising bubbles, respectively. For the range of Ga and Bo explored here, we find that the flow past a bubble with a realistic shape is generally more stable than that past a perfectly spheroidal bubble with the same aspect ratio. This study also provides the first critical curve for the onset of path instability that can be compared with experimental observations. The tendencies revealed by this critical curve agree well with those displayed by available data. The quantitative agreement is excellent for O(1) Bond numbers. However, owing to two simplifying assumptions used in the LSA scheme, namely, the steadiness of the base state and the uncoupling between the bubble shape and the flow disturbances, quantitative discrepancies (up to 20%–30%) with experimental threshold values of the Galilei number remain for both small and large Bond numbers.

On the acoustics of gas-bearing marine sediment

Gas forms in marine sediments because of the decay of organisms in anoxic conditions abundant in sediments of inhibited water mobility. Its mechanical and thermodynamic properties, e.g., density and compressibility, which are significantly different from those of the pore water and the grain material will lead to a dramatic decrease in the sediment's sound velocity and effective density, as well as the quality factor, whenever even only a few percent of free gas is present in the sediment. A variety of possible spatial distributions of a gaseous phase has been identified, ranging from free spheroidal gas bubbles in the pore space-filling fluid over various “patchy-saturation” scenarios to the displacement of parts of the total saturated sediment matrix, the respective scheme depending on such factors as grain size, sorting, wettability, among others. These different spatial distribution schemes require individually appropriate conceptions for the calculation of the acoustic properties from sediment physical characteristics. A recently proposed acoustic model [JASA 123, pp. 1941-1951, 2008] has been developed to account for the two cases of free gas bubbles in the pore space and for the local displacement of the saturated sediment.

Mass or heat transfer from spheroidal gas bubbles rising through a stationary liquid

Mass transfer was studied for the case of a spheroidal bubble rising through a stationary liquid. A numerical code that solves the Navier–Stokes equations and the diffusion–advection equation for the concentration was used to characterize the transfer from the bubble to the surrounding liquid phase. Simulations were carried over systematically for Reynolds number ranging from 1 to 1000, Schmidt numbers from 1 to 500 and bubble aspect ratio from 1 to 3. It appears that the use of the equivalent diameter as the characteristic length is the more appropriate to describe the transfer. The effect of bubble aspect ratio on the Sherwood number has been analyzed. At first order the extension of Boussinesq expression using the equivalent diameter can be used for practical purposes. The evolution of the correction factor that compares the Sherwood number to the one of a sphere with same equivalent Peclet number is presented and described using simple correlations. The implementation of these results into Euler–Euler simulations of mass transfer is discussed. It appears that the modification of the interfacial area combined to the modification of the Sherwood number gives a significant contribution to the interfacial source term in the equation of the concentration. Note that the results can also be considered for heat transfer and used for inviscid drops.

DISSECTING GALAXY FORMATION. I. COMPARISON BETWEEN PURE DARK MATTER AND BARYONIC MODELS

We compare assembly of dark matter (DM) halos with and without baryons from identical initial conditions, within the context of cosmological evolution in the {lambda}CDM WMAP3 Universe (baryons+DM, hereafter BDM model, and pure DM, PDM model). In representative PDM and BDM models, we find that baryons contribute decisively to the evolution of the central region, leading to an isothermal DM cusp, and thereafter to a flat DM density core-the result of heating by dynamical friction of the DM+baryon substructure during a quiescent evolution epoch. This process ablates the cold gas from an embedded disk, cutting the star formation rate by a factor of 10, and heats up the spheroidal gas and stellar components, triggering their expansion. The substructure is more resilient to the tidal disruption in the presence of baryons. The disk which formed from inside-out as gas-dominated is transformed into an intermediate Hubble type by z {approx} 2 and to an early type by z {approx} 0.5, based on its gas contents and spheroidal-to-disk stellar mass ratio. We find that only a relatively small {approx}20% fraction of DM particles in PDM and BDM models are bound within the radius of maximal circular velocity in the halo, slightly less somore » within halo characteristic radii-most of the DM particles perform larger radial excursions. The DM particles are unbound to the cusp region. We also find that the fraction of baryons within the halo virial radius somewhat increases during the major mergers and decreases during the minor mergers. The net effect appears to be negligible-an apparent result of our choice of feedback from stellar evolution. Furthermore, we find that the DM halos are only partially relaxed beyond their virialization. While the substructure is being tidally disrupted, mixing of its debris in the halo is not efficient and becomes even less so with z. The phase-space correlations (streamers) formed after z {approx} 1 will survive largely to the present time-an important implication for embedded disk evolution.« less

Black Hole Growth and Activity in a Λ Cold Dark Matter Universe

The observed properties of supermassive black holes suggest a fundamental link between their assembly and the formation of their host spheroids. We model the growth and activity of black holes in galaxies using Λ cold dark matter cosmological hydrodynamic simulations by following the evolution of the baryonic mass component in galaxy potential wells. We find that the observed steep relation between black hole mass and spheroid velocity dispersion, MBH σ4, is reproduced if the gas mass in bulges is linearly proportional to the black hole mass. To a good approximation, this is equivalent to assuming the conversion of a fixed fraction of gas mass into black hole mass. In this model, star formation and supernova feedback in the gas are sufficient for regulating and limiting the growth of the central black hole and of its gas supply. Black hole growth saturates because of the competition with star formation and, in particular, feedback, both of which determine the gas fraction available for accretion. Unless other processes also operate, we predict that the MBH-σ relation is not set in primordial structures but is fully established at low redshifts, z 2, and is shallower at earlier times. Once this relation is established, we find that central black hole masses are related to their dark matter halos simply via MBH ≈ M. We assume that galaxies undergo a quasar phase with a typical lifetime, tQ ~ 2 × 107 yr, the only free parameter of the model, and show that star formation-regulated depletion of gas in spheroids is sufficient to explain, for the most part, the decrease of the quasar population at redshift z < 3 in the optical blue band. However, with the simplest assumption of a redshift-independent quasar lifetime, the model slightly overpredicts optical quasar numbers at high redshifts, although it yields the observed evolution of number density of X-ray-faint quasars over the whole redshift range 1 < z < 6. Finally, we find that the majority of black hole mass is assembled in galaxies by z ~ 3 and that the black hole accretion rate density peaks in rough correspondence to the star formation rate density at z ~ 4-5.

Chemical evolution of two-component galaxies

In this paper, we try to insert into a single evolutionary scheme — in dealing with chemical evolution of galaxies — two different viewpoints that (at least in not too much complicated models) have been treated separately: namely, theS models, allowing mass conservation; andI models, allowing initial zero masses and no mass conservation due to gas inflow. The true evolution of a real proto-galaxy (after reaching the state of maximum expansion) is simulated as follows: A spheroidal gas mass continued to collapse and form stars until a flat configuration is reached after a timeT c has elapsed, while a given amount of gas flows in on a time-scale τ. According to this scheme, the basic equations of chemical evolution are derived and models which simulate the history of solar neighborhood, other regions and Galactic spheroid component are built up, in the whole range between theS-limit (mass conservation) and theI-limit (zero initial mass and subsequent accretion due to inflowing gas). Concerning the solar neighbourhood, we find that neither the occurrence of gas inflow nor inflow on time-scales τ≈2–3 109 yr are necessary in order to reproduce the temporal behaviour and the empirical distribution of metal content, as pointed out by some authors. On the contrary, the constraint on the lower mass limit for stars formed,m mf≳0.01, allows only models with τ≈T c (i.e. inflow time-scale of the order of the contraction time), while the constraint on the disk mass fraction,R D(T a)≲0.75, rules out the cases near theI-limit forT c≈0.55 but permits all cases forT c≈2.75. Concerning other regions, models are built up which roughly simulate elliptical, spiral and irregular galaxies, and all less extended regions resembling such systems. If the stellar birthrate function is assumed to be an universal law, the chemical evolution of the Galactic disk may be understood in terms of different zones (that might be thought as concentric and coaxial rings) the total density of which decreases monotonically, owing to a corresponding decrease in total mass and/or increase in volume, when passing from the center to the border of the disk. The constraintsm mf≳0.01 andR D(T a)≲0.75 for different regions of the Galactic disk would also rule out all models well beyond theS-limit, but further results are required in order to confirm this conclusion. Finally, concerning the Galactic spheroid component, it is found that onlyS models with massive halos (R D(T a)≈0.01) are able to reproduce in an acceptable way the empirical metal abundance distribution. In order to obtain a complete fit, a spheroid component has to be assumed, with a steeper mass spectrum exponent in the stellar birthrate function, and a lower yield of metallicity, in respect to the disk component. According to this last model, a mean value of disk metal content (with respect to spatial distribution) of the order of the solar value also results.

The thermal effects of H2 molecules in rotating and collapsing spheroidal gas clouds

view Abstract Citations (127) References (55) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The thermal effects of H2 molecules in rotating and collapsing spheroidal gas clouds. Hutchins, J. B. Abstract The thermal evolution of a protogalactic density perturbation within the expanding background of various Friedmann universes is studied for the case of a uniform pressure-free spheroid which reaches its maximum extension at some time, undergoes homologous collapse, and rotates as a solid body for times later than the time of maximum extension. Cooling of the cloud by radiation in the rotational lines of H2 molecules formed through various reactions is investigated in order to determine the Jeans mass. Dynamic processes during the precollapse epoch are analyzed, and a theory of heat exchange with the radiation field through rotational transitions of H2 molecules in their electronic and vibrational ground states is developed. Conditions on the matter temperature and electron concentration at the time of maximum extension are presented as explicit functions of the background model parameter and the time of maximum extension. The chemical reaction equations and rates of importance during collapse are discussed, and the collapse dynamics is considered. The thermal effects of H2 molecules are examined as functions of the background model, the time of maximum extension, the initial axial ratio, and rotation for initially spherical, oblate, and prolate clouds. Publication: The Astrophysical Journal Pub Date: April 1976 DOI: 10.1086/154254 Bibcode: 1976ApJ...205..103H Keywords: Hydrogen Clouds; Molecular Gases; Rotating Matter; Stellar Evolution; Temperature Effects; Astronomical Models; Gravitational Collapse; Heat Transfer; Oblate Spheroids; Perturbation Theory; Prolate Spheroids; Stellar Mass; Astrophysics full text sources ADS |

Distorted gas bubbles at large Reynolds number

The distortion of a gas bubble rising steadily in an inviscid incompressible liquid of infinite extent under the action of surface tension forces is investigated theoretically using an appropriate extension of the tensor virial theorem. A convenient parameter for distinguishing the bubble shape is the Weber numberW. The virial method leads to an expression relatingWand the axis ratio χ, of the transverse and longitudinal axes of the bubble. To first order inW, this relation agrees with the linear theory established by Moore (1959). Also, comparison of the results with his (1965) approximate theory reveals similar features and excellent agreement up to χ = 2. In particular, it confirms his prediction of the existence of a maximum Weber number. Although the present work does not consider the stability of these bubbles, it is interesting to note that the maximum value of 3.271 attained byWdiffers only by about 2.8% from the critical Weber number obtained by Hartunian &amp; Sears (1957) for the onset of instability.An approximate method for the study of slightly distorted spheroidal gas bubbles is also formulated and the resulting boundary-value problem solved numerically. The theory is then extended to include gravity. The joint effect of surface tension as well as gravitational forces has not been included in earlier theories. The shapes of the bubbles are traced and compared with the unperturbed spheroids. Comparisons for the velocity of bubble rise are made between the present predictions and some experimental results. In particular the results are compared with recent experimental data for the motion of gas bubbles in liquid metals.

Mass Models of the Galactic System.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Mass Models of the Galactic System. Innanen, Kimmo A. Abstract Models of the galactic mass distribution have been obtained using Schmidt- type nonhomogeneous spheroids. Values of the distance of the sun from the galactic centre of 8.2 and 10.0 kpc with circular velocities near the sun varying from 200 to 250 km/sec were adopted. Each model reproduces a rotation curve which is the smoothed mean of the Leiden and Sydney 21-cm results, together with the Leiden 21-cm observations of the rotation near the galactic center. The total density near the sun was taken to be 0.15 M~pc3. The principal characteristics of the models have been evaluated with an electronic computer. The models show that the mass in a column of unit area at the sun's position, perpendicular to the plane of the model, increases with increasing circular velocity near the sun. The observed mass perpendicular to the plane near the sun is reproduced if the circular velocity near the sun is approximately 200 km/sec. This low value of the circular velocity makes it unnecessary to introduce unknown matter to the model. The total masses of the models vary between 0.6 and 1.2 x 1011M . All of the models may be modified without significantly changing the results if a considerable fraction of the total mass is distributed in Schmidt- type spheroids with little flattening. A comparison of the models with M31 has been made by tilting them to the apparent attitude of M31, and by obtaining "mass profiles" of the resulting long axes of the tilted models. These profiles may be compared with de Vaucouleurs' (Astrophys. J. 128, 465, 1958) photometry along the long axis of M31. The comparison with the models is very good, confirming the existence of additional mass in the central parts of the galactic system. A comparison has also been made between the angular momentum distributions of the models and that of a uniformly rotating, homogeneous spheroidal gas cloud, following the method of Crampin and Hoyle (Astrophys. J. 140, 99, 1964). The comparisons are good and thus tend to confirm the conclusion that the galactic system may have collapsed from such a cloud, without turbulent mixing. Publication: The Astronomical Journal Pub Date: March 1965 DOI: 10.1086/109693 Bibcode: 1965AJ.....70..141I full text sources ADS |

On the gravitational collapse of a cold rotating gas cloud

In the course of researches on the formation of galaxies one meets the following idealized problem. What is the form of the collapse under gravitational forces of a uniformly rotating spheroidal gas cloud? In the special case where initially the gas is absolutely cold and of uniform density within the spheroid, we show that the collapse proceeds through a series of uniform, uniformly rotating spheroids until a disk is formed. This demonstration is followed by some remarks and conjectures as to what will happen in the physical case when the initial temperature is not necessarily zero.