scholarly journals Homogeneous and Inhomogeneous Mixing in Cumulus Clouds: Dependence on Local Turbulence Structure

2009 ◽  
Vol 66 (12) ◽  
pp. 3641-3659 ◽  
Author(s):  
Katrin Lehmann ◽  
Holger Siebert ◽  
Raymond A. Shaw
Keyword(s):  
Reaction Time ◽  
Time Scale ◽  
Inertial Subrange ◽  
Observation System ◽  
Length Scale ◽  
Damkohler Number ◽  
Mixing Process ◽  
Cumulus Clouds ◽  
Damköhler Number ◽  
Transition Length

Abstract The helicopter-borne instrument payload known as the Airborne Cloud Turbulence Observation System (ACTOS) was used to study the entrainment and mixing processes in shallow warm cumulus clouds. The characteristics of the mixing process are determined by the Damköhler number, defined as the ratio of the mixing and a thermodynamic reaction time scale. The definition of the reaction time scale is refined by investigating the relationship between the droplet evaporation time and the phase relaxation time. Following arguments of classical turbulence theory, it is concluded that the description of the mixing process through a single Damköhler number is not sufficient and instead the concept of a transition length scale is introduced. The transition length scale separates the inertial subrange into a range of length scales for which mixing between ambient dry and cloudy air is inhomogeneous, and a range for which the mixing is homogeneous. The new concept is tested on the ACTOS dataset. The effect of entrained subsaturated air on the droplet number size distribution is analyzed using mixing diagrams correlating droplet number concentration and droplet size. The data suggest that homogeneous mixing is more likely to occur in the vicinity of the cloud core, whereas inhomogeneous mixing dominates in more diluted cloud regions. Paluch diagrams are used to support this hypothesis. The observations suggest that homogeneous mixing is favored when the transition length scale exceeds approximately 10 cm. Evidence was found that suggests that under certain conditions mixing can lead to enhanced droplet growth such that the largest droplets are found in the most diluted cloud regions.

Effects of Damköhler Number on Methane/Oxygen Tubular Combustion Diluted by N2 and CO2

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Baolu Shi ◽  
Qingzhao Chu ◽  
Run Chen
Keyword(s):  
Reaction Time ◽  
Fuel Injection ◽  
Swirling Flow ◽  
Mixing Time ◽  
Velocity Ratio ◽  
Inert Gases ◽  
Injection Velocity ◽  
Damkohler Number ◽  
Helical Structures ◽  
Damköhler Number

To fundamentally elucidate the mixing and its effects on the characteristics of methane/oxygen flame in a rapidly mixed tubular flame burner, experiments were conducted under various oxygen mole fractions and flow rates. Two inert gases of nitrogen and carbon dioxide were used, respectively. The inert gas was added to both the oxidizer and fuel slits to maintain the oxidizer/fuel injection velocity ratio near unity. Based on flow visualization, the mixing process around injection slits and that in the axial downstream were discussed. The Damköhler number (Da1), defined as the ratio of molecular mixing time to reaction time, was selected as a parameter to quantitatively examine the criterion for the establishment of tubular flame from low to ultrahigh oxygen mole fractions (0.21–0.86). The mixing around slit exit determined the tubular flame establishment. Due to a flow time between two neighboring injection slits of fuel and oxidizer, part of the fuel was mixed in the downstream swirling flow, resulting in luminous helical structures. Hence, the Damköhler number (Da2), defined as the flow to the reaction time ratio, was examined. Detailed observations indicated that when Da2 was smaller than unity, the flame was uniform in luminosity, whereas the flame was nonuniform when Da2 ≥ 1. The value of Da2 was about 1.5 times as Da1; however, they correspond to different mixing zones and Da2 can be more easily calculated. The differences in flame stability between N2 and CO2 diluted combustion were also studied.

Evaluation of the One-Well Uranium Leaching Test: Restoration

1982 ◽  
Vol 22 (01) ◽  
pp. 141-150 ◽  
Author(s):  
Muhammad I. Kabir ◽  
Larry W. Lake ◽  
Robert S. Schechter
Keyword(s):  
Acid Leaching ◽  
Leach Solution ◽  
Damkohler Number ◽  
Damköhler Number ◽  
Well Spacing ◽  
Number Of Factors ◽  
Well Pattern ◽  
Mineralized Zone ◽  
Selection Of

Abstract In-situ leach mining for uranium is an emerging technology. Currently, the selection of a well pattern designed to recover mineral values is governed primarily by arguments based on hydrological considerations. The effects of well pattern and well spacing on uranium recovery and oxidant utilization are considered in this paper. As expected, formation permeability heterogeneities and anisotropies are found to be important issues requiring careful consideration, however, it also is shown that chemical factors cannot be ignored. In particular, it is shown that the oxidant efficiency and the produced uranium solution concentrations are sensitive to the presence of other minerals competing with uranium for oxidant. If the Damkohler number for competing minerals, which measures the speed of the reaction, exceeds that for uranium, the competing mineral will have to be oxidized completely to recover a large proportion of the uranium. If the Damkohler number is smaller, it may be possible to achieve considerable selectivity for uranium by adjusting the well spacing. It also is shown that the oxidant efficiency is generally highest for well patterns that give streamlines of roughly equal length and that there is a minimum distance between injection and production wells to utilize oxidant most advantageously. Introduction In-situ solution mining is a process whereby uranium is recovered from permeable sandstone bodies by injecting and producing a leach solution through an array of wells penetrating the mineralized zone. It appears to have broad application and in many situations offers both economic and environmental advantages. The processes may be classified generally as acid or alkaline, but the general features of both are the same. The insoluble uranium in the mineralized zone is in the +4 state of oxidation. To be mobilized, the uranium must be oxidized to the +6 state and complexed either with sulfate in the case of acid leaching or carbonate in the case of alkaline leaching to form highly soluble uranyl sulfates or carbonates. The leach solutions, therefore, contain an oxidant (oxygen, hydrogen peroxide, ferric cations, sodium hyperchlorite, etc.) together with a complexing agent (anion). The choice of leach solution depends on a number of factors including selectivity and injectivity. For example, formations containing more than 1 wt% carbonates are not likely to be candidates for acid leaching because of the large acid requirement and because of permeability loss due to precipitation of calcium sulfate. It is the purpose of this paper to consider the technical factors (as opposed to economic) that govern the choice of well pattern to be used for leaching. The discussion is structured so that the conclusions apply to both alkaline and acid lixiviants and to any oxidant, although an occasional reference to a particular oxidant may appear. Considerable use is made of the computer simulator previously reported. The computational details are available in that paper. A number of factors that pertain to the selection of a well pattern are considered. It is shown that the effectiveness of the oxidant - i.e., the uranium recovered per unit of oxidant injected - is related to the well pattern, to the reaction rates, and to the permeability variations, especially if the formation is anisotropic. Furthermore, the spacing between wells is related to reactions with oxidizable minerals that compete for oxidant. These considerations can be quantified to some extent by studying linear systems. Linear Flow Systems SPEJ P. 132^

An Experimental and Theoretical Study of Heat Conduction and Vulcanization of Rubber Compounds in Molds

1987 ◽  
Vol 60 (1) ◽  
pp. 140-158 ◽  
Author(s):  
Dancheng Kong ◽  
James L. White ◽  
Frederick C. Weissert ◽  
Nobuyuki Nakajima
Keyword(s):  
Heat Conduction ◽  
Curing Kinetics ◽  
Damkohler Number ◽  
Fourier Number ◽  
Fundamental Study ◽  
Damköhler Number ◽  
Rubber Compounds ◽  
Cure Temperature ◽  
Black Other ◽  
Kinetics Of

Abstract A fundamental study on curing of rubber compounds in molds is presented. We have measured the thermal conductivity of a range of rubber compounds determining the influence of carbon black, other fillers, and oil. The heats of reaction associated with the curing kinetics of model compounds were measured. A mathematical model is proposed to predict the temperature profiles for curing a reactive slab. This involves inclusion of an energy generation rate, which depends on time and temperature. This is expressed through a Damkohler number. Solutions of the heat conduction equation are interpreted in terms of the Fourier number and the Damkohler number. Calculations are carried out using experimentally determined thermal conductivities and curing kinetics. Thick parts are shown to heat up more slowly (associated with the Fourier number) and to show greater overshoots of cure temperature (associated with the Damkohler number).

Time scale of dynamic heterogeneity in model ionic liquids and its relation to static length scale and charge distribution

2015 ◽  
Vol 17 (43) ◽  
pp. 29281-29292 ◽  
Author(s):  
Sang-Won Park ◽  
Soree Kim ◽  
YounJoon Jung
Keyword(s):  
Ionic Liquid ◽  
Ionic Liquids ◽  
Charge Distribution ◽  
Power Law ◽  
Structural Relaxation ◽  
Time Scale ◽  
Length Scale ◽  
Dynamic Heterogeneity ◽  
General Power

We find a general power-law behavior: , where ζdh ≈ 1.2 for all the ionic liquid models, regardless of charges and the length scale of structural relaxation.

A General Study of Counterflow Diffusion Flames for Supercritical CO2 Combustion

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
K. R. V. Manikantachari ◽  
Scott Martin ◽  
Ramees K. Rahman ◽  
Carlos Velez ◽  
Subith Vasu
Keyword(s):  
Prandtl Number ◽  
Supercritical Co2 ◽  
Diffusion Flames ◽  
Lewis Number ◽  
Dilution Effect ◽  
Scalar Dissipation ◽  
Damkohler Number ◽  
Nonpremixed Combustion ◽  
Flame Thickness ◽  
Damköhler Number

Abstract A counterflow diffusion flame for supercritical CO2 combustion is investigated at various CO2 dilution levels and pressures by accounting for real gas effects into both thermal and transport properties. The UCF 1.1 24-species mechanism is used to account the chemistry. The nature of important nonpremixed combustion characteristics such as Prandtl number, thermal diffusivity, Lewis number, stoichiometric scalar dissipation rate, flame thickness, and Damköhler number are investigated with respect to CO2 dilution and pressure. The results show that the aforementioned parameters are influenced by both dilution and pressure; the dilution effect is more dominant. Further, the result shows that Prandtl number increases with CO2 dilution and at 90% CO2 dilution, the difference between the Prandtl number of the inlet jets and the flame is minimal. Also, the common assumption of unity Lewis number in the theory and modeling of nonpremixed combustion does not hold reasonable for sCO2 applications due to large difference of Lewis number across the flame and the Lewis number on the flame drop significantly with an increase in the CO2 dilution. An interesting relation between Lewis number and CO2 dilution is observed. The Lewis number of species drops by 15% when increasing the CO2 dilution by 30%. Increasing the CO2 dilution increases both the flow and chemical timescales; however, chemical timescale increases faster than the flow timescales. The magnitudes of the Damköhler number signify the need to consider finite rate chemistry for sCO2 applications. Further, the Damköhler numbers at 90% sCO2 dilution are very small; hence, laminar flamelet assumptions in turbulent combustion simulations are not physically correct for this application. Also, it is observed that the Damköhler number drops nonlinearly with increasing CO2 dilution in the oxidizer stream. This is a very important observation for the operation of sCO2 combustors. Further, the flame thickness is found to increase with CO2 dilution and reduce with pressure.

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