Oxygen Transport Equations Research Articles

Modelling oxygen-limited and self-sustained smoldering propagation: Thermochemical treatment of food waste in an inert porous medium

Smoldering treatment is emerging as a valuable engineering tool for many processes, including food waste treatment. However, smoldering systems are currently not well-understood nor optimized. Therefore, numerical models provide invaluable insight into the process dynamics, which improves our understanding and supports the development of novel systems. These smoldering models couple heat, mass, and momentum transfer with pyrolysis and oxidation chemical reactions within porous media. While recent models have untangled many aspects of these systems, local oxygen transport rates from bulk flow to the fuel surface are still not well-resolved. In this work, local oxygen-transport equation was approximated by an analytic derivation based on the gas–solid oxygen non-equilibrium hypothesis. With the improved oxygen-transport equation, a 2D model with five-step reaction scheme for smoldering propagation of food waste in sand was developed. Kinetic parameters obtained from TG experiments were incorporated into the bed-scale smoldering propagation model. The developed model was validated with experimental data that stretched from robust to weak smoldering propagation. It was demonstrated that the developed model matches well with experiments. Furthermore, this model revealed: (i) the emergence of non-uniform gas flow in the reactor, (ii) the evolution of the kinetic- and oxygen-transport-limiting regimes, and (iii) valuable insight into the fundamental changes with smoldering robustness.

Oxygen transfer characteristics of bubbly jet in regular waves

The dissolved oxygen level is an important index of the water environment, and in this paper, the oxygen transfer of the bubbly jet in regular waves is investigated numerically and experimentally. The Reynolds-averaged Navier-Stokes equations, the re-normalisation group k-e equations, and the volume of fluid (VOF) technique are used along with a 2-D CFD model to simulate the wave and bubble motions as well as the turbulence, and a dissolved oxygen transport equation is used to model the oxygen transfer behavior both through the bubbly interface and the wave surface. A series of experiments are conducted to validate the mathematical model, with good agreement. In addition, a group of dimensionless parameters are defined from the wave parameter and the aeration parameter, and their relationships with the total oxygen transfer coefficient are explored. Furthermore, the dimensional analysis and the least squares methods are used to derive simple prediction formulas for the total oxygen transfer coefficient, and they are validated with the related experimental data.

Experimental Validation of Surface Coverage Model for Li-Air Battery

The Lithium-air battery has captured so much interest and been considered as a promising candidate for the future renewable energy sources because of its high specific energy density comparable to gasoline. But unfortunately, the maximum amount of the lithium metal utilized is limited because of the tunnel blockage and surface coverage inside cathode, which are caused by insoluble lithium composite generated at cathode. In other words, the total energy capacity is restricted by the cathode under adequate lithium. So if we can fully understand how the deposits work on the cathode, we are supposed to develop a better cathode, which can hold more products per unit volume, with immensely higher energy capacity per unit cathode volume. This paper describes a surface coverage model and two relative dominating effects, electrode passivation and transport resistance. By using the electron conservation combined with experimental formula from previous works, we could investigate how much the insoluble there is and the coverage coefficient used to evaluate what degree deposits damage the effectivity of cathode to. We could use the coverage coefficient to describe the effective surface area under different stage of precipitation. We may go further to obtain the oxygen profile by taking the oxygen transport equation into account. Then we have a chance to use the above model to formulate the loss of effective voltage and total energy capacity. We could eventually split the voltage loss into 2 pieces, one caused by electrode passivation and another caused by oxygen transport resistance. We can compare them to find out which one is the prime force to kill the battery, or that they cooperate together. We can also know how much deposits the cathode can be filled with before exhausted. Then the total energy capacity is ready to come out by integrating the voltage along the time under constant current. By looking into the integral, there are actually three parts, which are the capacity without considering voltage loss effect, and two capacity losses solely considering the voltage loss from the electrode passivation or oxygen transport resistance respectively. If we compare these different part, we could have a knowledge of whether the capacity loss is immense enough to be cared about, or which kind of loss costs more. To validate our model, we will also perform the experiments by using our sandwich cell to get the discharging curve, which will be used to validate our model by comparing the voltage loss and energy capacity loss. The sandwich cell structure from bottom to top is: bottom frame, aluminum foil, lithium metal, separator, rubble sealing ring, top frame with air window and electrolyte pool on top, and cathode. The whole cell is assembled by using screws. We could get open circuit voltage and discharging curves under different current. The data will be used to validate and improve our model mentioned above.

Quantifying the importance of daily stream water temperature fluctuations on the hyporheic thermal regime: Implication for dissolved oxygen dynamics

• We model the heat transport in the hyporheic zone by using a Lagrangian approach. • We examine the role of the stream water temperature on hyporheic thermal regime . • We examine the role of hyporheic thermal regime on dissolved oxygen (DO) kinetics. • Via a thermal Damköhler number we relate stream morphology and temperature signal. • We show the impact of temperature variation on the evolution of DO concentration. Water temperature is a primary driver of aquatic organism migration, drift, growth and metabolism in both stream and hyporheic zone. Here, we focus on the role of the naturally occurring daily stream water temperature oscillations on the hyporheic thermal regime and on dissolved oxygen (DO) dynamics within the hyporheic zone. We choose DO as target dissolved element because of its importance for aquatic habitat quality and its role in controlling biogeochemical reactions and pool-riffle morphology as bed form because of its ubiquity and ecological relevance. To address the first objective, we introduce a new thermal Damköhler number, Da T , which is the ratio between the median residence time of stream water and the time scale of daily amplitude attenuation of water temperature within the hyporheic zone. Application of the model to a wide range of pool-riffle dimensions shows the dependence of hyporheic water temperature distribution on hyporheic residence time. The latter is a function of the interaction between stream flow and bed form morphology. Our results show that Da T increases with stream size indicating that large streams have more thermally stable hyporheic zones than small streams. To address the second objective, we analytically solve the heat and dissolved oxygen transport equations through the streambed sediment with isotropic and homogeneous hydraulic properties by means of a Lagrangian approach, under the hypothesis that transverse dispersion can be neglected and the DO reaction rate is temperature dependant. We apply these coupled transport models to characterize the distribution of DO concentrations within the hyporheic zone. This analysis shows a relation between the patterns of water temperature and of DO concentrations with important feedbacks on the life and metabolism of aquatic organisms; as well as on the reaction rates, which control the biogeochemical processes within the streambed sediment. We analyze the effects of temperature variations on the kinetics of DO assuming constant and periodic fluctuations of DO concentrations in the stream water. Our results show that for streams with pool and riffle morphology, the latter effect is more important than that of temperature dependent reaction rates.

C224 肺内のガス交換に関する工学的研究(OS-13: 生体熱工学)

Numerical calculations were carried out to reveal both velocity and oxygen concentration fields around a red blood cell. It is well-known that the cell changes its shape and orientation, as it flows in a capillary. The mass and momentum conservation equations for the blood plasma were solved along with the oxygen transport equation. The effects of the shape of the red blood cell on the velocity and oxygen concentration fields are numerically investigated using a numerical model consisting of the blood plasma, red cell and capillary wall.

Ion transport membrane reactors for oxy-combustion – Part I: intermediate-fidelity modeling

Oxy-fuel combustion, particularly using an integrated oxygen ion transport membrane (ITM), is a thermodynamically attractive concept that seeks to mitigate the penalties associated with CO 2 capture from power plants. Oxygen separation in an ITM system consists of many distinct physical processes, ranging from complex electrochemical and thermo-chemical reactions, to conventional heat and mass transfer. The dependence of ITM performance on power cycle operating conditions and system integration schemes must be captured in order to conduct meaningful process flow and optimization studies where multiple degrees of freedom are considered. An axially spatially-distributed, quasi two-dimensional model is developed based on fundamental conservation equations, semi-empirical oxygen transport equations obtained from the literature, and simplified fuel oxidation kinetic mechanisms. Aspects of reactor engineering such as geometric structure, flow configuration and the relationship between oxygen transport, fuel conversion and pressure drop are explored. Emphasis is placed on model robustness, modularity, and low computational expense in order to evaluate the myriad of ITM possibilities within a power cycle simulation quickly and accurately. Overall, the model seeks to bridge the gap between detailed CFD studies and overly-simplified black-box models found in ITM-power cycle analyses, and provides a tool for the analysis and design of ITM systems.

Erratum: "A comprehensive mathematical model of microscopic dose deposition in photodynamic therapy" [Med. Phys. 34, 282-293 (2007)

Erratum: "A comprehensive mathematical model of microscopic dose deposition in photodynamic therapy" [Med. Phys. 34, 282-293 (2007)

Oxygen transport and consumption by suspended cells in microgravity: A multiphase analysis

A rotating bioreactor for the cell/tissue culture should be operated to obtain sufficient nutrient transfer and avoid damage to the culture materials. Thus, the objective of the present study is to determine the appropriate suspension conditions for the bead/cell distribution and evaluate oxygen transport in the rotating wall vessel (RWV) bioreactor. A numerical analysis of the RWV bioreactor is conducted by incorporating the Eulerian-Eulerian multiphase and oxygen transport equations. The bead size and rotating speed are the control variables in the calculations. The present results show that the rotating speed for appropriate suspensions needs to be increased as the size of the bead/cell increases: 10 rpm for 200 microm; 12 rpm for 300 microm; 14 rpm for 400 microm; 18 rpm for 600 microm. As the rotating speed and the bead size increase from 10 rpm/200 microm to 18 rpm/600 microm, the mean oxygen concentration in the 80% midzone of the vessel is increased by approximately 85% after 1-h rotation due to the high convective flow for 18 rpm/600 microm case as compared to 10 rpm/200 microm case. The present results may serve as criteria to set the operating parameters for a RWV bioreactor, such as the size of beads and the rotating speed, according to the growth of cell aggregates. In addition, it might provide a design parameter for an advanced suspension bioreactor for 3-D engineered cell and tissue cultures.

An analytical study of the PEM fuel cell with axial convection in the gas channel

A quasi two-dimensional mathematical model for a polymer electrolyte membrane (PEM) fuel cell is developed with consideration of axial convection in the gas channel and analytical solutions are obtained. A half-cell model which contains the cathode gas channel, gas diffuser, catalyst layer, and the membrane is investigated. To account for the effect of gas velocity in the gas channel, axial convection is included in the oxygen transport equation of the gas channel. Expressions for the oxygen mass fraction distribution in the gas channel, gas diffuser, and catalyst layer, and the current density and the membrane phase potential in the catalyst layer and membrane are derived. The solutions are presented in the form of infinite series. The polarization curve is also expressed as a function of the surface overpotential. Due to the advantage of the closed-form solutions this model can be easily employed as a diagnostic tool for PEM fuel cell simulations.

An Analytical Solution of a Half‐Cell Model for PEM Fuel Cells

A mathematical model for polymer electrolyte membrane (PEM) fuel cells is developed and rigorous analytical solutions of the model are obtained. The modeling domain consists of the cathode gas channel, gas diffuser, catalyst layer, and the membrane. To account for the composite structure of the gas diffuser and for its gradient in liquid water content, the gas diffuser is modeled as a series of parallel layers with different porosity and tortuosity. Starting from the oxygen transport equations and Ohm's law for proton migration, expressions for the oxygen mass fraction distribution in the gas channel, gas diffuser, and catalyst layer, and current density and membrane phase potential in the catalyst layer and membrane are derived. The solutions are presented in terms of the physical and thermodynamic parameters of the fuel cell. The polarization curve is expressed parametrically as a function of the surface overpotential. Expressions for cathode internal and overall effectiveness factors, active fraction of the catalyst layer, catalyst layer resistance, limiting current density, and the slope of the polarization curve are also presented. Due to the advantage of the closed‐form solutions this model can be easily used as a diagnostic tool for a PEM fuel cell operating on and air. © 2000 The Electrochemical Society. All rights reserved.

Interaction between Oxygen Transfer Mechanisms in Lake Models

Dissolved oxygen (DO) distributions in stratified lakes can be simulated by a one-dimensional (vertical), deterministic, unsteady (time-variant) diffusion equation with surface gas transfer as a boundary condition and photosynthetic oxygen production as an internal source. Both surface gas transfer and vertical diffusion depend on turbulence near the water surface. The interaction between these two mechanisms, and photosynthetic productivity of dissolved oxygen in lake models is therefore studied analytically and numerically. The analytical solution of the DO transport equation in a semiinfinite medium is developed. Predicted DO concentrations at depth z are shown to depend on three dimensionless parameters, and the strength of net photosynthetic oxygen production is an important parameter in this analysis. The increases of DO concentrations due to photosynthesis are modulated by surface aeration and vertical diffusion in the lake. A numerical solution of the dissolved oxygen transport equation is also obtained and used to illustrate simulated DO profiles over an entire open water season in two Minnesota lakes. The analytical solution is used to explain certain features of the numerical results.

Dissolved oxygen model for regional lake analysis

A deterministic, one-dimensional, unsteady dissolved oxygen (D.O.) model has been formulated to simulate summer D.O. conditions (stratification) in a wide raange of lakes of the north central United States and to study potential impacts of global climate change. The simulation includes contributions by photosynthesis, plant respiration, reaeration, biochemical oxygen demand (BOD) and sedimentary oxygen demand (SOD) as source and sink terms. The one-dimensional vertical oxygen transport equation is solved in conjunction with the heat transport equation in daily time steps beginning 1 March and ending 31 October. Lake morphometry, trophic status and daily weather parameters have to be specified as input, and daily profiles of water temperature and dissolved oxygen are obtained as output. The model finds the onset of summer-stratification from initially isothermal and constant D.O. conditions. Trophic status is related to Secchi depth, phytoplankton ( chlorophyll-a) concentrations, BOD and SOD. Field data from seven lakes (11 years) have been used to calibrate and validate the D.O. model. The simulations for dimictic lakes with strong stratification are better than for weakly stratified polymictic lakes, i.e. the model works better for deep lakes than for shallow lakes. The average standard errors for calibration and validation are 1.4 and 1.9 mg D.O.1−1, respectively. The temperature simulations, especially the mixed-layer depth, affect the D.O. simulation results. A sensitivity analysis to model coefficients was also conducted. The model is most sensitive to sedimentary oxygen demand (SOD). Twenty seven classes of lakes (3 depths × 3 areas × 3 trophic states) in the north central U.S. were analyzed with the model. Simulated mean daily dissolved oxygen concentrations in the epilimnion are near saturation, those in the hypolimnion vary considerably depending particularly on length of time since the onset of stratification and the sedimentary oxygen demand.

Analysis of oxygen transport from pulsatile, viscous blood flow to diseased coronary arteries of man

Oxygen transport to multiple “non-obstructive” plaque regions in main coronary arteries of man was examined by numerically solving the oxygen transport equation for convective and diffusive processes in the lumen for actual variations of blood flow rate and the velocity field during the cardiac cycle. Oxygen transport to the wall varied significantly along the arterial section, was strongly dependent upon the various flow regions that occurred, and varied considerably during the cardiac cycle. A drastic reduction in oxygen transport to the arterial wall occurred at the incipient separation location on the back side of a plaque where it is believed that the lumen side resistance to oxygen transport is at least an order of magnitude greater than the inner avascular wall resistance, and therefore the availability of oxygen for cellular respiration is essentially boundary layer controlled. In vivo measurements with oxygen microelectrodes in animals are needed to learn more about variations of oxygen transport in plaque regions, in particular on the back side of plaques where hypoxia may occur.