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At least 307 records · Page 17

Basic Considerations in the Combustion of Hydrocarbon Fuels with Air

Basic combustion research is collected, collated, and interpreted as it applies to flight propulsion. The following fundamental processes are treated in separate chapters: atomization and evaporation of liquid fuels, flow and mixing processes in combustion chambers, ignition and flammability of hydrocarbon fuels, laminar flame propagation, turbulent flames, flame stabilization, diffusion flames, oscillations in combustors, and smoke and coke formation in the combustion of hydrocarbon-air mixtures. Theoretical background, basic experimental data, and practical significance to flight propulsion are presented.

Barnett, Henry C↗

Evaporation and combustion of LOX under supercritical and subcritical conditions

The objective is to study the evaporation and combustion of LOX under supercritical and subcritical conditions both experimentally and theoretically. In the evaporation studies, evaporation rate and surface temperature were measured when LOX vaporizing in helium environments at pressures ranging from 5 to 68 atm. A Varian 3700 gas chromatograph was employed to measure the oxygen concentration above the LOX surface. For the combustion tests, high-magnification video photography was used to record direct images of the flame shape of a LOX/H2/He laminar diffusion flame. The gas composition in the post-flame region is also being measured with the gas sampling and chromatography analysis. These data are being used to validate the theoretical model. A comprehensive theoretical model with the consideration of the solubility of ambient gases as well as variable thermophysical properties was formulated and solved numerically to study the gasification and burning of LOX at elevated pressures. The calculated flame shape agreed reasonably well with the edge of the observed luminous flame surface. The effect of gravity on the flame structure of laminar diffusion flames was found to be significant. In addition, the predicted results using the flame-sheet model were compared with those based upon full equilibrium calculations (which considered the formation of intermediate species) at supercritical pressures. Except at the flame front where temperature exceeded 2,800 K, the flame-sheet and equilibrium solutions in terms of temperature distributions were in very close agreement. The temperature deviation in the neighborhood of the flame front is caused by the effect of high-temperature dissociation.

Yang, A. S.↗

Suppression Characteristics of Cup-Burner Flames in Low Gravity

The structure and suppression of laminar methane-air co-flow diffusion flames formed on a cup burner have been studied experimentally and numerically using physically acting fire-extinguishing agents (CO2, N2, He, and Ar) in normal earth (lg) and zero gravity (0g). The computation uses a direct numerical simulation with detailed chemistry and radiative heat-loss models. An initial observation of the flame without agent was also made at the NASA Glenn 2.2-Second Drop Tower. An agent was introduced into a low-speed coflowing oxidizing stream by gradually replacing the air until extinguishment occurred under a fixed minimal fuel velocity. The suppression of cup-burner flames, which resemble real fires, occurred via a blowoff process (in which the flame base drifted downstream) rather than the global extinction phenomenon typical of counterflow diffusion flames. The computation revealed that the peak reactivity spot (the reaction kernel) formed in the flame base was responsible for attachment and blowoff phenomena of the trailing diffusion flame. The thermal and transport properties of the agents affected the flame extinguishment limits.

Takahashi, Fumiaki↗

A Theory of Oscillating Edge Flames

It has been known for some years that when a near-limit flame spreads over a liquid pool of fuel, the edge of the flame can oscillate relative to a frame moving with the mean speed. Each period of oscillation is characterized by long intervals of modest motion during which the edge gases radiate like those of a diffusion flame, punctuated by bursts of rapid advance during which the edge gases radiate like those in a deflagration. Substantial resources have been brought to bear on this issue within the microgravity program, both experimental and numerical. It is also known that when a near-asphyxiated candle-flame burns at zero gravity, the edge of the (hemispherical) flame can oscillate violently prior to extinction. Thus a web-surfer, turning to the NASA web-site at http://microgravity.msfc.nasa.gov, and following the trail combustion science/experiments/experimental results/candle flame, will find photographs and a description of candle burning experiments carried out on board both the Space-shuttle and the Russian space station Mir. A brief report can also be found in the proceedings of the Fourth Workshop. And recently, in a third microgravity program, the leading edge of the flame supported by injection of ethane through the porous surface of a plate over which air is blown has been found to oscillate when conditions are close to blow-off. A number of important points can be made with respect to these observations: It is the edge itself which oscillates, advancing and retreating, not the diffusion flame that trails behind the edge; oscillations only occur under near limit conditions; in each case the Lewis number of the fuel is significantly larger than 1; and because of the edge curvature, the heat losses from the reacting edge structure are larger than those from the trailing diffusion flame. We propose a general theory for these oscillations, invoking Occam's 'Law of Parsimony' in an expanded form, to wit: The same mechanism is responsible for the oscillations in all three experiments; and no new mechanism is invoked (Occam's original 'Razor'). Such a strategy eliminates Marangoni effects as the source, for these are absent in the second and third experiments. And it eliminates arguments that point to numerically predicted gas eddies as the source, a new mechanism, unelucidated. Indeed, we hypothesize that the essential driving mechanism for the instability is a combination of large Lewis number and heat losses from the reacting structure near the flame edge. Instabilities driven by these mechanisms are commonplace in 1D configurations. Chemical reactor theory, for example, leads to system responses which mimic the response of the candle flame - steady flame, oscillations, extinction. In a combustion context, oscillating instabilities were first reported for diffusion flames in a theoretical study by Kirkby and Schmitz, and here also the instabilities are associated with near-extinction conditions, large Lewis numbers, and heat losses. And deflagrations will oscillate if the Lewis number is large enough, oscillations that are exacerbated when heat losses are present, whether global or to a surface.

Buckmaster, J.↗

Effects of heat loss, preferential diffusion, and flame stretch on flame-front instability and extinction of propane/air mixtures

Flame configurations, flame-front cellular instability, and extinction of propane/air mixtures in the stagnation-point flow are experimentally studied for their dependence on downstream heat loss, preferential diffusion, and flame stretch. Boundaries for lean- and rich-limit extinction, stabilization of corrugated flames, and local extinction caused by sharp curvatures are mapped for varying propane concentrations and freestream velocities. Flame location and temperature at extinction are determined as functions of stagnation surface temperature, extent of preheating, propane concentration, and freestream velocity. Results substantiate the theoretical predictions of the different extinction modes for lean and rich flames in the absence of downstream heat loss, and yield useful insight on the extinction characteristics when finite downstream heat loss does exist. It is further shown that flame-front instability occurs only for rich mixtures in accordance with preferential diffusion considerations, and that flame stretch has a stabilizing effect such that flame-front instability is completely inhibited before the onset of extinction.

Ishizuka, S.↗

Fire Suppression in Low Gravity Using a Cup Burner

Longer duration missions to the moon, to Mars, and on the International Space Station increase the likelihood of accidental fires. The goal of the present investigation is to: (1) understand the physical and chemical processes of fire suppression in various gravity and O2 levels simulating spacecraft, Mars, and moon missions; (2) provide rigorous testing of numerical models, which include detailed combustion-suppression chemistry and radiation sub-models; and (3) provide basic research results useful for advances in space fire safety technology, including new fire-extinguishing agents and approaches.The structure and extinguishment of enclosed, laminar, methane-air co-flow diffusion flames formed on a cup burner have been studied experimentally and numerically using various fire-extinguishing agents (CO2, N2, He, Ar, CF3H, and Fe(CO)5). The experiments involve both 1g laboratory testing and low-g testing (in drop towers and the KC-135 aircraft). The computation uses a direct numerical simulation with detailed chemistry and radiative heat-loss models. An agent was introduced into a low-speed coflowing oxidizing stream until extinguishment occurred under a fixed minimal fuel velocity, and thus, the extinguishing agent concentrations were determined. The extinguishment of cup-burner flames, which resemble real fires, occurred via a blowoff process (in which the flame base drifted downstream) rather than the global extinction phenomenon typical of counterflow diffusion flames. The computation revealed that the peak reactivity spot (the reaction kernel) formed in the flame base was responsible for attachment and blowoff of the trailing diffusion flame. Furthermore, the buoyancy-induced flame flickering in 1g and thermal and transport properties of the agents affected the flame extinguishment limits.

Takahashi, Fumiaki↗

Fire Suppression in Low Gravity Using a Cup Burner

Longer duration missions to the moon, to Mars, and on the International Space Station increase the likelihood of accidental fires. The goal of the present investigation is to: (1) understand the physical and chemical processes of fire suppression in various gravity and O2 levels simulating spacecraft, Mars, and moon missions; (2) provide rigorous testing of numerical models, which include detailed combustion suppression chemistry and radiation sub-models; and (3) provide basic research results useful for advances in space fire safety technology, including new fire-extinguishing agents and approaches. The structure and extinguishment of enclosed, laminar, methane-air co-flow diffusion flames formed on a cup burner have been studied experimentally and numerically using various fire-extinguishing agents (CO2, N2, He, Ar, CF3H, and Fe(CO)5). The experiments involve both 1g laboratory testing and low-g testing (in drop towers and the KC-135 aircraft). The computation uses a direct numerical simulation with detailed chemistry and radiative heat-loss models. An agent was introduced into a low-speed coflowing oxidizing stream until extinguishment occurred under a fixed minimal fuel velocity, and thus, the extinguishing agent concentrations were determined. The extinguishment of cup-burner flames, which resemble real fires, occurred via a blowoff process (in which the flame base drifted downstream) rather than the global extinction phenomenon typical of counterflow diffusion flames. The computation revealed that the peak reactivity spot (the reaction kernel) formed in the flame base was responsible for attachment and blowoff of the trailing diffusion flame. Furthermore, the buoyancy-induced flame flickering in 1g and thermal and transport properties of the agents affected the flame extinguishment limits.

Takahashi, Fumiaki↗

Flame propagation under partially-premixed conditions

This study concentrates on developing a better understanding of triple flames. We relax the assumption of zero heat release, address the issue of stabilization, and, in order to investigate the role that heat release plays in flame propagation in partially premixed combustion, we return to a simple flow field and investigate the behavior of flames in a laminar environment. We solve the compressible Navier-Stokes equations in a two-dimensional domain. At the boundaries, we use an inflow boundary condition on the left and nearly-perfect reflective boundary conditions, required to avoid pressure drift, at the outflow and sides. After the flow and flame are initialized, the mixture fraction is varied at the inlet from its uniform stoichiometric value to a tanh profile varying from zero to one. As the mixture fraction gradient reaches the flame surface only the centerline is exposed to the stoichionetric mixture fraction and locally maintains the planar flame speed and reaction rate. Above this point the mixture is fuel rich, and below fuel lean. As a result, these regions of non-unity equivalence ratio burn less, the reaction rate drops, and the local flame speed is reduced. The excess fuel and oxidizer then combine behind the premixed flame along the stoichiometric surface and burn in a trailing diffusion flame. Thus the 'triple' flame refers to the fuel-rich premixed flame, the fuel-lean premixed flame, and the trailing diffusion flame. Due to heat release, the normal velocity across the flame is increased, whereas the tangential component remains unchanged. Far-field flame speed, local flame speed, and their differences are shown as a function of the local mixing thickness. It was also determined that the lateral position of the flame affects stabilization, and the distribution of the reaction rate along the premixed wings of triple flames affects flame propagation.

Ruetsch, Gregory R.↗

Effects of Gas-Phase Radiation and Detailed Kinetics on the Burning and Extinction of a Solid Fuel

This is the first attempt to analyze both radiation and detailed kinetics on the burning and extinction of a solid fuel in a stagnation-point diffusion flame. We present a detailed and comparatively accurate computational model of a solid fuel flame along with a quantitative study of the kinetics mechanism, radiation interactions, and the extinction limits of the flame. A detailed kinetics model for the burning of solid trioxane (a trimer of formaldehyde) is coupled with a narrowband radiation model, with carbon dioxide, carbon monoxide, and water vapor as the gas-phase participating media. The solution of the solid trioxane diffusion flame over the flammable regime is presented in some detail, as this is the first solution of a heterogeneous trioxane flame. We identify high-temperature and low-temperature reaction paths for the heterogeneous trioxane flame. We then compare the adiabatic solution to solutions that include Surface radiation only and gas-phase and surface radiation using a black surface model. The analysis includes discussion of detailed flame chemistry over the flammable regime and, in particular, at the low stretch extinction limit. We emphasize the low stretch regime of the radiatively participating flame, since this is the region representative of microgravity flames. When only surface radiation is included, two extinction limits exist (the blow-off limit, and the low stretch radiative limit), and the burning rate and maximum flame temperatures are lower, as expected. With the inclusion of surface and gas-phase radiation, results show that, while flame temperatures are lower, the burning rate of the trioxane diffusion flame may actually increase at low stretch rate due to radiative feedback from the flame to the surface.

Rhatigan, Jennifer L.↗

Effects of confinement on partially premixed flames

Partially premixed combustion is an intermediate regime between the limiting cases of premixed and nonpremixed combustion. Although combustion problems are generally approached from one of these two limiting cases, there are many practical situations where flames cannot be considered as purely premixed or nonpremixed, and thus the partially premixed approach must be used. In partially premixed combustion, mechanisms from the premixed and nonpremixed regimes can coexist, and as a result some interesting new phenomena can arise. One such phenomenon is the flame stabilization in laminar mixing layers by triple flames. One of the first observations of triple flames was made by Phillips (1965), who investigated a triple flame propagating in a methane mixing layer. Kioni et al. (1993) also examined triple flames both experimentally and numerically. There have also been numerous analytical studies on the shape and propagation of triple flames under various assumptions by Dold (1989), Dold et al. (1991), and Hartley and Dold (1991). In terms of modeling, Muller et al. (1994) have combined the flamelet formulations for premixed and nonpremixed combustion in order to treat lifted diffusion flames. One common feature in the analytical and numerical studies mentioned above is the assumption of zero heat release, which is necessary to make the problem tractable. The effect of heat release on triple flames was investigated by Ruetsch et al. (1995), where for the unconfined case, flame speeds larger than their premixed counterparts were found. One of the most important practical situations in which these conditions arise is in lifted turbulent jet diffusion flames. At a critical velocity the burning zone of a fuel jet lifts off from the nozzle, moves to increasing distances as the jet velocity increases, and finally blows off. The mechanisms that control these phenomena, i.e. that determine the stability of these flames, are still not understood. In addition to regions where diffusion flame stabilization takes place, partially premixed conditions also exist during the ignition process in nonpremixed systems. Numerical simulations by Reveillon et al. (1994) of the ignition process in a weakly stirred mixture of fuel and oxidizer show that triple flames propagate along lines of stoichiometric mixture fraction throughout the fluid. In addition, Peters (1994) notes that NO(x) emissions are likely to be large in such transient cases, and therefore an understanding of triple flames can provide information concerning pollutant formation. This study extends the work previously done and examines the effects of lateral confinement on partially premixed flames. Once again, we study both the flame structure and propagation.

Ruetsch, G. R.↗

Laminar Soot Processes (Lsp) Experiment: Findings From Ground-Based Measurements

Processes of soot formation and oxidation must be understood in order to achieve reliable computational combustion calculations for nonpremixed (diffusion) flames involving hydrocarbon fuels. Motivated by this observation, the present investigation extended earlier work on soot formation and oxidation in laminar jet ethylene/air and methane/oxygen premixed and acetylene-nitrogen/air diffusion flames at atmospheric pressure in this laboratory, emphasizing soot surface growth and early soot surface oxidation in laminar diffusion flames fueled with a variety of hydrocarbons at pressures in the range 0.1 - 1.0 atm.

Kim, C. H.↗

Combustion Synthesis of Fullerenes and Fullerenic Nanostructures In Microgravity

The objectives of the proposed research were to determine the effects of gravity on fullerenes formation in flames and, based on the observed effects, to develop fundamental understanding of fullerenes formation and to identify engineering principles for fullerenes production. The research method consisted of the operation of laminar diffusion flames under normal- and reduced-gravity conditions, and the collection from the flames and subsequent analysis of condensables including any fullerenes present, using coupled high performance liquid chromatography/mass spectrometry and high resolution transmission electron microscopy. The focus included fullerene molecules C60 and C70 and fullerenic nanostructures including tubes, spherules and other shapes. The normal-gravity experiments were performed at MIT and complementary reduced-gravity experiments were to have been contributed by NASA. The independent variables of interest are gravity, fuel type, fuel/oxygen ratio, pressure, gas velocity at burner, diluent type and concentration. Given the large number of variables and the absence of data on either fullerene formation in diffusion flames or gravitational effects on fullerene formation in diffusion or premixed flames, the first part of the work was exploratory while the later part involved detailed study of the most interesting mechanisms. Samples of condensable material from laminar low pressure benzene/argon/oxygen diffusion flames were collected and analyzed by high-performance liquid chromatography to determine the yields of fullerenes, and by high-resolution transmission electron microscopy (HRTEM) to characterize the fullerenic material, i.e., curved-layer nanostructures, on and within the soot particles. The highest concentration of fullerenes was always detected just above the visible stoichiometric surface of a flame. The percentage of fullerenes in the condensable material increases with decreasing pressure. The overall highest amount of fullerenes was found for a surprisingly high dilution fuel with argon. The maximum flame temperature seems to be of minor importance in fullerene formation. The HRTEM analysis of the soot showed an increase of the curvature of the carbon layers, and hence increased fullerenic character. After this maximum, the curvature decreases. In addition to the soot, the samples included fullerenic nanostructures, such as tubes and spheroids including highly-ordered multilayered or onion-like structures. The soot itself shows highly ordered regions that appear to have been cells of ongoing fullerenic nanostructure formation.

Howard, Jack B.↗

An Experimental Investigation of the Laminar Flamelet Concept for Soot Properties

The soot properties of round, nonbuoyant, laminar jet diffusion flames are described, based on experiments at microgravity carried out on orbit during three flights of the Space Shuttle Columbia, (Flights STS-83, 94 and 107). Experimental conditions included ethylene- and propane-fueled flames burning in still air at an ambient temperature of 300 K and ambient pressures of 35-100 kPa. Measurements included soot volume fraction distributions using deconvoluted laser extinction imaging, and soot temperature distributions using deconvoluted multiline emission imaging. Flowfield modeling based on the work of Spalding is presented. The present work explores whether soot properties of these flames are universal functions of mixture fraction, i.e., whether they satisfy soot state relationships. Measurements are presented, including radiative emissions and distributions of soot temperature and soot volume fraction. It is shown that most of the volume of these flames is bounded by the dividing streamline and thus should follow residence time state relationships. Most streamlines from the fuel supply to the surroundings are found to exhibit nearly the same maximum soot volume fraction and temperature. The radiation intensity along internal streamlines also is found to have relatively uniform values. Finally, soot state relationships were observed, i.e., soot volume fraction was found to correlate with estimated mixture fraction for each fuel/pressure selection. These results support the existence of soot property state relationships for steady nonbuoyant laminar diffusion flames, and thus in a large class of practical turbulent diffusion flames through the application of the laminar flamelet concept.

Diez, F. J.↗

Smoke Point in Co-flow Experiment

The Smoke Point In Co-flow Experiment (SPICE) determines the point at which gas-jet flames (similar to a butane-lighter flame) begin to emit soot (dark carbonaceous particulate formed inside the flame) in microgravity. Studying a soot emitting flame is important in understanding the ability of fires to spread and in control of soot in practical combustion systems space. Previous experiments show that soot dominates the heat emitted from flames in normal gravity and microgravity fires. Control of this heat emission is critical for prevention of the spread of fires on Earth and in space for the design of efficient combustion systems (jet engines and power generation boilers). The onset of soot emission from small gas jet flames (similar to a butane-lighter flame) will be studied to provide a database that can be used to assess the interaction between fuel chemistry and flow conditions on soot formation. These results will be used to support combustion theories and to assess fire behavior in microgravity. The Smoke Point In Co-flow Experiment (SPICE) will lead to a o improved design of practical combustors through improved control of soot formation; o improved understanding of and ability to predict heat release, soot production and emission in microgravity fires; o improved flammability criteria for selection of materials for use in the next generation of spacecraft. The Smoke Point In Co-flow Experiment (SPICE) will continue the study of fundamental phenomena related to understanding the mechanisms controlling the stability and extinction of jet diffusion flames begun with the Laminar Soot Processes (LSP) on STS-94. SPICE will stabilize an enclosed laminar flame in a co-flowing oxidizer, measure the overall flame shape to validate the theoretical and numerical predictions, measure the flame stabilization heights, and measure the temperature field to verify flame structure predictions. SPICE will determine the laminar smoke point properties of non-buoyant jet diffusion flames (i.e., the properties of the largest laminar jet diffusion flames that do not emit soot) for several fuels under different nozzle diameter/co-flow velocity configurations. Luminous flame shape measurements would also be made to verify models of the flame shapes under co-flow conditions. The smoke point is a simple measurement that has been found useful to study the influence of flow and fuel properties on the sooting propensity of flames. This information would help support current understanding of soot processes in laminar flames and by analogy in turbulent flames of practical interest.

Urban, David L.↗

Laser-Induced Incandescence Measurements in Low Gravity

A low-gravity environment offers advantages to investigations concerned with soot growth or flame radiation by eliminating of buoyancy-induced convection. Basic to each type of study is knowledge of spatially resolved soot volume fraction, (f(sub v). Laser-induced incandescence (LII) has emerged as a diagnostic for soot volume fraction determination because it possesses high temporal and spatial resolution, geometric versatility and high sensitivity. Implementation and system characterization of LII in a drop tower that provides 2.2 sec of low-gravity (micro)g) at the NASA Lewis Research Center are described here. Validation of LII for soot volume fraction determination in (micro)g is performed by comparison between soot volume fraction measurements obtained by light extinction [20] and LII in low-gravity for a 50/50 mixture (by volume) of 0 acetylene/nitrogen issuing into quiescent air. Quantitative soot volume fraction measurements within other laminar flames of ethane and propane and a turbulent diffusion flame in (micro)g via LII are also demonstrated. An analysis of LII images of a turbulent acetylene diffusion flame in 1-g and (micro)g is presented.

VanderWal, R. L.↗

PIV Measurements in Weakly Buoyant Gas Jet Flames

Despite numerous experimental investigations, the characterization of microgravity laminar jet diffusion flames remains incomplete. Measurements to date have included shapes, temperatures, soot properties, radiative emissions and compositions, but full-field quantitative measurements of velocity are lacking. Since the differences between normal-gravity and microgravity diffusion flames are fundamentally influenced by changes in velocities, it is imperative that the associated velocity fields be measured in microgravity flames. Velocity measurements in nonbuoyant flames will be helpful both in validating numerical models and in interpreting past microgravity combustion experiments. Pointwise velocity techniques are inadequate for full-field velocity measurements in microgravity facilities. In contrast, Particle Image Velocimetry (PIV) can capture the entire flow field in less than 1% of the time required with Laser Doppler Velocimetry (LDV). Although PIV is a mature diagnostic for normal-gravity flames , restrictions on size, power and data storage complicate these measurements in microgravity. Results from the application of PIV to gas jet flames in normal gravity are presented here. Ethane flames burning at 13, 25 and 50 kPa are considered. These results are presented in more detail in Wernet et al. (2000). The PIV system developed for these measurements recently has been adapted for on-rig use in the NASA Glenn 2.2-second drop tower.

Sunderland, Peter B.↗

Kinetics and Structure of Superagglomerates Produced by Silane and Acetylene

The evolution of smoke in a laminar diffusion flame involves several steps. The first step is particle inception/nucleation in the high-temperature fuel-rich region of the flame followed by surface growth and coagulation/coalescence of the small particles. As the primary spheres grow in size and lose hydrogen, the colliding particles no longer coalesce but retain their identity as a cluster of primary spheres, termed an agglomerate. Finally, in the upper portion of the flame, the particles enter an oxidizing environment which may lead to partial or complete burnout of the agglomerates. Currently there is no quantitative model for describing the growth of smoke agglomerates up to superagglomerates with an overall dimension of 10 microns and greater. Such particles are produced during the burning of acetylene and fuels containing benzene rings such as toluene and polystyrene. In the case of polystyrene, smoke agglomerates in excess of 1 mm have been observed "raining" out from large fires. Evidence of the formation of superagglomerates in a laminar acetylene/air diffusion flame has been recently reported. Acetylene was chosen as the fuel since the particulate loading in acetylene/air diffusion flames is very high. Photographs were obtained by Sorensen using a microsecond xenon lamp of the "stream" of soot just above the flame. For low flow rates of acetylene, only submicrometer soot clusters are produced and they give rise to the homogeneous appearance of the soot stream. When the flow rate is increased to 1.7 cu cm/s, soot clusters up to 10 microns are formed and they are responsible for the graininess and at a flow rate of 3.4 cu cm/s, a web of interconnected clusters as large as the width of the flame is seen. This interconnecting web of superagglomerates is described as a gel state by Sorensen et al (1998). This is the first observation of a gel for a gas phase system. It was observed that this gel state immediately breaks up into agglomerates due to buoyancy induced turbulence and gravitational sedimentation.

Mulholland, G. W.↗