Vladimir Hlavacek

Role of continuation in engineering analysis

Abstract This paper reviews the state of the art of the continuation methods. In particular, a discussion of the tracing of parameter dependent branches of solutions is presented. Basic steps of continuation as predictors, correctors and parametrizations are introduced and their interaction analysed. Such algorithms are emphasized which give rise to reliable general-purpose computer programs and proved to work satisfactorily when applied to nontrivial problems. The review paper includes brief discussion of some topics of most recent interests that are closely related to continuation, as, for instance, stability, branch switching, and tracing of critical boundaries. Several examples illustrate the procedures. Hints on available software complete this paper.

Heat and mass transfer in monolithic honeycomb catalysts—I.

Abstract The body of information presented in this paper is directed to engineers and scientists concerned with control of automobile emissions and exhaust gases from some industrial processes. The differential equations describing heat and mass transfer in a monolithic honeycomb catalyst are developed. Following transport mechanism is considered: convective heat and mass transfer in the holes of the structure, longitudinal thermal conductivity of the honeycomb support and gas-to-solid heat and mass transfer. The magnitudes of governing parameters for monolithic modules in use are discussed. Two methods for the numerical solution of a system of coupled, nonlinear ordinary differential equations with split boundary conditions are proposed. The first method-shooting procedure can be used only for problems with low values of Peclet number. For high values of Peclet number finite-difference approach along with the Newton-Raphson algorithm is suggested. It is shown that two stable steady states exist in certain regions of operation of a particular monolithic structure. The all-metal monolithic supports are more prone to multiplicity of steady states than the ceramic ones. For ceramic supports the two-phase piston-flow model is sufficiently accurate.

Simulation of pressure swing adsorption in fuel ethanol production process

Abstract Fermentation derived ethanol is gaining wide popularity as a car fuel additive. A major challenge in the production of ethanol is the high energy cost associated with the separation of ethanol from the large excess of water. Distillation is usually the method of choice; however, water cannot be completely removed due to the presence of the azeotrope. The pressure swing adsorption (PSA) process is attractive for the final separation since it requires little energy input and is capable of producing a very pure product. The goal of this work was to perform a thorough analysis of the PSA process and find process improvements with the aid of mathematical modeling. A general purpose package for the simulation of a cyclic PSA process was developed. The system of partial differential equations was solved via method of lines using a stiff equation integration package. Parameters for the model are based on the data from an operating plant as well as data from the literature. For the ethanol production technology our model provides a fundamental understanding of the dynamics of the cyclic process and effects of some operating parameters.

Modelling of chemical reactors — X Multiple solutions of enthalpy and mass balances for a catalytic reaction within a porous catalyst particle

As was already shown, equations describing mass and enthalpy balances for an exothermic reaction taking place inside a porous catalyst particle can have more than one stationary solution. In this paper, two conditions for the existence of multiple solutions were stated: (1) the value of parameter γβ has to be greater than a certain critical value, (γβ)*, (2) Thieles modulus has to be simultaneously in the definite range φ1 ⩽ φ ⩽ φ2 on the basis of the model, where the state of the particle is described by means of mean values of concentration and temperature. Values of (γβ)* and the critical limits of Thieles modulus φ1 and φ2 for reactions of power and of adsorption type of kinetics were then calculated. Values thus obtained, are in good agreement with correct values, obtained from numerical integration of conservation equations. In the last part of the paper a general procedure was described, which enables one to determine, whether for a given set of values of physical parameters more than one stationary profile of concentration in the catalyst particle can exist.

Multiplicity and stability in a sequence of two nonadiabatic nonisothermal CSTR

Abstract An analysis of mass and enthalpy balances describing dynamic behavior of two homogeneous CSTR with recirculation is performed. Methods of investigation of regions of existence of multiple steady states and stability are described. Effect of recirculation ratio, Damkohler number, cooling parameter and cooling temperature on the exit temperature is followed. The dependence of the exit temperature on the residence time is analyzed and it is shown that bizarre situations may occur (deformated “mushrooms”, two isolas, etc.). Plots are given to show the influence of system parameters on the reactor behavior.

Packed bed axial thermal conductivity

Abstract Packed bed axial thermal conductivity has been evaluated from steady state packed bed axial temperature profiles. Solid particles of different sizes, shapes and thermal conductivities have been used for measurements, which covered large interval of Reynolds numbers, Re ϵ 3 >. Empirical relation for estimation of Peclet number for axial heat transport, which includes effects of all significant heat transport mechanisms, has been obtained in the form

Interaction between chemical reaction and natural convection in porous media

Abstract Natural convection in porous media has received much attention in the last decades. Most of the work, however, has been devoted to the case of a global driving force resulting from thermal or concentration gradients applied to the boundaries of the system. As changes in the density lead to natural convection, chemical reactions can provide a distributed driving force for secondary flows. The conditions for the onset of natural convection are represented by the critical value of the thermal Rayleigh number. The critical value is found by performing a linear stability analysis of the basic reaction regime. Results are reported for the onset of both oscillatory and monotonic instabilities. The stability of the convective modes is studied by using a variational approach and deriving a set of spectral equations by means of a truncated mode interaction. The initial-value problem is analyzed by continuation routines and bifurcation diagrams are drawn. These diagrams constitute a valuable tool in the design of heterogeneous reacting systems. The numerical solution of the full governing equations serves to corroborate the predictions of the simplified model as well as to illustrate the effects of natural-convection phenomena on systems with chemical reaction.

Particle Size and Reactivity of Aluminum Powders

A comparison of different experimental techniques for metallic particle size evaluation including light diffraction, scanning electron microscope analysis and nitrogen adsorption is presented. Nitrogen adsorption as an appropriate experimental method for particle size evaluation is proposed. Certain aspects of chemical reactivity of micron and submicron aluminum powders in the air, using thermogravimetry and differential thermal analysis (TG/DTA), are discussed. Three metallic Al powders were analyzed: S-400 (Reynolds Co.), ALEX (Argonide Corp.) and WARP-l (Ceramic and Materials Processing, Inc.). TG/DTA analysis revealed that S-400 (specific surface area = 0.3m2 /g) does not react below melting point of Al (2% conversion); ALEX powder (specific surface area = 12.0 m2/g) starts reacting around T = 440°C and 16% reacts before melting point temperature is reached. WARP-1 samples (specific surface area between 16.0 and 26.5 m2/g) react already at T = 200°C and 25 wt% of aluminum is oxidized below melting point temperature. Differential thermal analysis did not discover any “stored” energy in S - 400 or ALEX materials; however, WARP-l samples released thermal energy already at 130 and 230°C, which is assigned to “stored energy”.

Hysteresis and Periodic Activity Behavior in Catalytic Chemical Reaction Systems

Publisher Summary This chapter discusses the experimental aspects of multiplicity of steady states as well as periodic activity of open chemical reacting systems “catalyst-gas.” In the past two decades, a great number of theoretical papers were published on the subject that indicated a number of “pathological” phenomena to be expected in chemically reacting systems. The next step toward a deeper understanding of all these phenomena is possible only through research programs that try to prove these effects on an experimental way. The chapter focuses on experimental aspects of multiplicity and periodic activity. While the trend of the research activity in the area of multiplicity and periodic activity in the 1960s has been focused on theoretical investigation, the recent development has indicated an increase of experimental information. However, the number of experimental papers in comparison with the theoretical studies is still low and the need for additional laboratory studies is obvious.

Combustion of fly-ash carbon. Part I. TG/DTA study of ignition temperature

Combustion experiments in air have been performed using TG/DTA analysis, which served for ignition temperature and kinetics data determination. Fly-ash carbon was treated with carbonates and hydroxides. The ignition temperature dependence on alkali metal salt concentration was investigated. Results showed that the ignition temperature decreased for treated samples. The activation energy of impregnated samples decreased. Qualitative comparison of modified and original samples showed that higher heat of combustion was achieved for impregnated samples.