Bio: H.K.Daniel Hsuen is an academic researcher from University of Rochester. The author has contributed to research in topics: Char & Saddle-node bifurcation. The author has an hindex of 3, co-authored 4 publications receiving 29 citations.
TL;DR: In this article, the bifurcation behavior of a mathematical model that describes mass and heat transport and chemical reaction in a one-dimensional diffusion flame is investigated, where a numerical scheme based on B-spline interpolation is used to spatially discretize the system, and a Gear-type integrator is employed to study the oscillatory behavior of the solutions.
Abstract: The bifurcation behavior of a mathematical model that describes mass and heat transport and chemical reaction in a one-dimensional diffusion flame is investigated. A numerical scheme based on B-spline interpolation is used to spatially discretize the system, and a Gear-type integrator is employed to study the oscillatory behavior of the solutions. Results are reported on the multiplicity characteristics of the steady-state solutions. Loci of limit points and Hopf bifurcation points are constructed on planes defined by two of the parameters of the problem in order to divide the planes into regions with different multiplicity and stability characteristics. A complete classification of solution loci in terms of the above characteristics—multiplicity, stability, and bifurcation direction at Hopf bifurcation points—is presented for the parameter region investigated. Direct integration in time is used to study the oscillatory behavior of the system for certain parameter values.
TL;DR: In this paper, a detailed investigation of the steady-state multiplicity structure of the combustion of porous char particles in an environment of oxygen and nitrogen was presented, with particular emphasis on the effects of thermal radiation on the steady state features of the problem, and a shooting method and a method based on B-spline collocation were employed for the solution of the model equations and the direct location of singular points of the solution loci.
Abstract: This study presents a detailed investigation of the steady-state multiplicity structure of the combustion of porous char particles in an environment of oxygen and nitrogen. Particular emphasis was placed on the effects of thermal radiation on the steady-state features of the problem. A shooting method and a method based on B-spline collocation were employed for the solution of the model equations and the direct location of singular points of the solution loci. Our extensive numerical computations showed that the key parameters for the appearance of multiplicity of solutions higher than three, up to five steady states, are the effective diffusivity and effective thermal conductivity in the porous medium. however, multiplicity of five steady states is found only in a rather small region of the parametric space which lies outside the domain of “feasible” parameter values for low and intermediate porosity values.
TL;DR: In this paper, the steady-state bifurcation behavior of a char combustion system with three chemical reactions is investigated and the effects of several model parameters on the behavior of steady state solutions are investigated in detail.
Abstract: The steady-state bifurcation behavior of a char combustion system which involves the reactions C + 1 2 O2 → CO, CO + built1 2 O2 → Co2 and CO 2 + C → 2CO is investigated. The loci of limit points, double limit points, and hysteresis points are constructed and used to divide the investigated parametric space into regions of different number solutions or different type of solution loci. The effects of several model parameters on the behavior of steady-state solutions are investigated in detail. Our computational results show that the existence of thermal radiation reduces the region of multiple steady-state solutions, but the presence of CO and CO2 in the environment favors the appearance of solution loci with four limit points. The multiplicity characteristics of the problem depend strongly on the interplay of the three chemical reactions, but the occurrence of the heterogeneous reaction of CO2 with carbon is not necessary for solution loci with five steady states to occur.
TL;DR: In this paper, diffusion and reaction models of varying complexity are used to study the stability of the combustion of single char particles, and the feasibility of occurrence of oscillatory combustion is investigated.
Abstract: Diffusion and reaction models of varying complexity are used to study the stability of the combustion of single char particles. In contrast to past studies which have considered only the reaction of carbon with oxygen, both the heterogeneous reactions of carbon with oxygen and carbon dioxide and the homogeneous oxidation of carbon monoxide are taken into account in the formulation of the mathematical models. Emphasis is placed on the investigation of the feasibility of occurrence of oscillatory combustion. Our results show that high rates of the C-O2 reaction and high concentration of O2 in the ambient favor the occurrence of multiple steady states and oscillatory solutions, but the appearance of oscillatory instability is suppressed by the homogeneous reaction in the gas phase and the presence of CO and CO2 in the ambient. The parametric investigation of the problem reveals, in agreement with the results of past studies, that the heat capacity of the porous solid, the Lewis number, and the thickness of t...
TL;DR: This paper concentrates on its chemical/biological engineering relevance, especially for reaction/diffusion and hydrodynamic processes, and restricts its attention to systems that do not change their structure during the process, so that self-organizational criticality is explained, but not utilized.
Abstract: Complexity is a very diversified and branched subject and, ironically, is itself quite complex. In this paper, although we present the different aspects and definitions of complexity, we concentrate on its chemical/biological engineering relevance, especially for reaction/diffusion and hydrodynamic processes. System theory is used as the common language to unify concepts, and emphasis is given to bifurcation, chaos as the basis of behavioral complexity and the configuration of processes as the basis for structural complexity. Natural processes are grouped under biocomplexity, while man-made processes are treated as complexity alone. We restrict our attention in this paper to systems that do not change their structure during the process, so that self-organizational criticality is explained, but not utilized. Computational complexity is intrinsically inherent in all the processes we consider, but it is not given much attention in this paper. Despite these severe limitations on the scope of our paper, the subject is still quite complex and branched, and this paper tries to bring it to the attention and interest of a wider spectrum of chemical/biological engineers in both academia and industry.
TL;DR: In this paper, the authors studied the transient behavior of a chemically active, fluid-saturated fault zone under shear and provided regimes of stable creep, nonperiodic and periodic seismic slip events due to chemical pressurization, depending on the physical properties of the fault material.
Abstract: This work studies the transient behavior of a chemically active, fluid-saturated fault zone under shear. These fault zones are displaying a plethora of responses spanning from ultrafast instabilities, like thermal pressurization, to extremely slow creep localization events on geological timescales. These instabilities can be described by a single model of a rate-dependent and thermally dependent fault, prone to fluid release reactions at critical temperatures which was introduced in our companion work. In this study we integrate it in time to provide regimes of stable creep, nonperiodic and periodic seismic slip events due to chemical pressurization, depending on the physical properties of the fault material. It is shown that this chemically induced seismic slip takes place in an extremely localized band, several orders of magnitude narrower than the initial shear zone, which is indeed the signature field observation. Furthermore, in the field and in laboratory experiments the ultralocalized deformation is embedded in a chemical process zone that forms part of the shear zone. The width of this zone is shown here to depend on the net activation energy of the chemical reaction. The larger the difference in forward and backward activation energies, the narrower is the chemical process zone. We apply the novel findings to invert the physical parameters from a 16year GPS observation of the Cascadia episodic tremor and slip events and show that this sequence is the fundamental mode of a serpentinite oscillator defined by slow strain localization accompanying shear heating and chemical dehydration reaction at the critical point, followed by diffusion and backward reaction leading the system back to slow slip.
TL;DR: In this article, the behavior of a fluid-saturated fault under shear is studied, based on the assumption that the material inside exhibits rate and temperature-dependent frictional behavior.
Abstract: In this paper, we study the behavior of a fluid-saturated fault under shear, based on the assumption that the material inside exhibits rate- and temperature-dependent frictional behavior. A creeping fault of this type can produce excess heat due to shear heating, reaching temperatures which are high enough to trigger endothermic chemical reactions. We focus on fluid-release reactions and incorporate excess pore pressure generation and porosity variations due to the chemical effects (a process called chemical pressurization). We provide the mathematical formulation for coupled thermo-hydro-chemo-mechanical processes and study the influence of the frictional, hydraulic, and chemical properties of the material, along with the boundary conditions of the problem on the behavior of the fault. Regimes of stable-frictional sliding and pressurization emerge, and the conditions for the appearance of periodic creep-to-pressurization instabilities are then derived. The model thus extends the classical mechanical stick-slip instabilities by identifying chemical pressurization as the process governing the slip phase. The different stability regimes identified match the geological observations about subduction zones. The model presented was specifically tested in the Episodic Tremor and Slip sequence of the Cascadia megathrust, reproducing the displacement data available from the GPS network installed. Through this process, we identify that the slow slip events in Cascadia could be due to the in situ dehydration of serpentinite minerals. During this process, the fluid pressures increase to sublithostatic values and lead to the weakening of the creeping slab.
TL;DR: In this article, a first-person approach based on physics, continuum mechanics, and chemistry of serpentinite in the megathrust interface was used to reconcile the periodic nature of slow seismic events, their localization at intermediate depths, and the origin of the nonvolcanic fluids that are responsible for the tremor activity.
Abstract: During the last decade, knowledge over episodic tremor and slip (ETS) events has increased dramatically owing to the widespread installation of GPS and seismic networks. The most puzzling observations are (i) the periodic nature of slow seismic events, (ii) their localization at intermediate depths (estimated 15–40 km), and (iii) the origin of the nonvolcanic fluids that are responsible for the tremor activity. We reconcile these observations using a first principles approach relying on physics, continuum mechanics, and chemistry of serpentinite in the megathrust interface. The approach reproduces the GPS sequences of 17 years of recording in Cascadia, North America, as well as over 10 years in the Hikurangi Trench of New Zealand. We show that strongly endothermic reactions, such as serpentinite dehydration, are required for ETS events. We report that in this tectonic setting, it is its chemical reaction kinetics, not the low friction, that marks serpentinite as a key mineral for stable, self-sustained oscillations. We find that the subduction zone instabilities are driven from the ductile realm rather than the brittle cover. Even when earthquakes in the cover perturb the oscillator, it relaxes to its fundamental mode. Such a transition from stable oscillations to chaos is witnessed in the ETS signal of NZ following the M6.8, 2007 seismic event, which triggered a secondary mode of oscillations lasting for a few years. We consequently suggest that the rich dynamics of ductile modes of failure may be used to decipher the chaotic time sequences underpinning seismic events.
TL;DR: In this paper, a coal char particle in hot bubbling fluidized bed (FB) was analyzed by a model of combustion, which includes phenomena of heat and mass transfer through a porous char particle, as well as heterogeneous reaction at the interior char surface and homogeneous reaction in the pores.
Abstract: The temperatures of a coal char particle in hot bubbling fluidized bed (FB) were analyzed by a model of combustion. The unsteady model includes phenomena of heat and mass transfer through a porous char particle, as well as heterogeneous reaction at the interior char surface and homogeneous reaction in the pores. The parametric analysis of the model has shown that above 550 °C combustion occurs under the regime limited by diffusion. The experimental results of temperature measurements by thermocouple in the particle center during FB combustion at temperatures in the range 590–710 °C were compared with the model predictions. Two coals of different rank were used: lignite and brown coal, with particle size in the range 5–10 mm. The comparisons have shown that the model can adequately predict the histories of temperatures in char particles during combustion in FB. In the first order, the model predicts the influence of the particle size, coal rank (via porosity), and oxygen concentration in its surroundings.