Mathematical modelling of thermal microexplosion in a catalyst granule with point sources of heat release

A mathematical model of heat and mass transfer in a spherical catalyst granule is proposed. Exothermic synthesis reactions are carried out on point active centres located inside a porous ceramic granule. From the surface of the granule the heat of catalytic reactions is removed into liquid synthesis products. The rate of a chemical reaction is modelled by a modified Arrhenius law. In contrast to the homogeneous model of a catalytic granule methods for calculating heat transfer processes in a system of point, active centres do not develop. An iterative procedure is suggested to calculate the unknown temperature and concentration of the reagent at the active centre. It is shown that the temperature of the active centres is significantly higher than in the volume of the granule. The results of modelling a thermal explosion with increasing granule size and reactor temperature are presented.

Study of the kinetics of carboxymethyl cellulose synthesis in a screw reactor

The object of research is the reactor for the synthesis of carboxymethyl cellulose. An important indicator of the quality of sodium carboxymethyl cellulose, which determines the field of its application, is the degree of polymerization. However, obtaining a product with a specific parameter under industrial conditions is associated with a number of difficulties. Therefore, important research tasks are the development of a mathematical model of the kinetics of carboxymethyl cellulose synthesis, experimental studies to determine the rate constants of synthesis reactions, modeling of a screw reactor for the synthesis of carboxymethyl cellulose, and computer studies. When studying the kinetics of reactions of carboxymethyl cellulose, one of the possible approaches was to use a quasi-homogeneous model, which is widely used in modeling processes on a catalyst grain. This approach is used to describe and analyze individual stages; however, a number of difficulties arise in heterogeneous reactions of cellulose. In the course of these reactions, the properties of the solid phase change and the processes, respectively, are unsteady in time. The reaction does not take place on the surface of hard particles, but in the entire volume of the fibers. The concentration and reactivity of cellulose hydroxides, water, and products formed during the reaction remain approximately constant; therefore, the use of a quasi-homogeneous model is quite acceptable and does not cause additional mathematical difficulties. As a result of these experiments, according to the obtained integral curves, the method of least squares was used to find the constants. To determine the values of the kinetic constants, an experiment was carried out in an integral isothermal reactor. During the experiments, the degree of substitution of carboxymethyl cellulose and the concentration of free alkali were measured. As a result of numerous implementations of the search task, the values of the constants and activation energies were obtained. This kinetic modeling approach can be used in the synthesis of other cellulose ethers. The rate constant of the synthesis reaction depends on the process conditions. Using the proposed approach to describing the interaction of cellulose with a reagent, the reaction mixture considered as a quasi-homogeneous system can be described using a single-phase flow model.

Thermodynamic Insight in Design of Methanation Reactor with Water Removal Considering Nexus between CO2 Conversion and Irreversibilities

The inevitable nexus between energy use and CO2 emission necessitates the development of sustainable energy systems. The conversion of CO2 to CH4 using green H2 in power-to-gas applications in such energy systems has attracted much interest. In this context, the present study provides a thermodynamic insight into the effect of water removal on CO2 conversion and irreversibility within a CO2 methanation reactor. A fixed-bed reactor with one intermediate water removal point, representing two reactors in series, was modeled by a one-dimensional pseudo-homogeneous model. Pure CO2 or a mixture of CO2 and methane, representing a typical biogas mixture, were used as feed. For short reactors, both the maximum conversion and the largest irreversibilities were observed when the water removal point was located in the middle of the reactor. However, as the length of the reactor increased, the water removal point with the highest conversion was shifted towards the end of the reactor, accompanied by a smaller thermodynamic penalty. The largest irreversibilities in long reactors were obtained when water removal took place closer to the inlet of the reactor. The study discusses the potential benefit of partial water removal and reactant feeding for energy-efficient reactor design.

Determination of the Deformed Shape of a Masonry Wall Exposed to Fire Loading by a Homogenization Method

The present contribution shows how it is possible to determine the homogenized thermo-elastic characteristics of a natural stone masonry wall, taking into account the material properties of stone and mortar as functions of temperature increase, as well as the geometrical characteristics of their assembly. Joints are incorporated in the analysis through a numerical homogenization procedure. As a result, membrane and bending stiffness coefficients, as well as thermal-induced efforts, of an equivalent plate are obtained. Such homogenized thermomechanical characteristics make it possible to determine the deformed shape of the wall after a certain time of fire exposure. As an example, the calculation procedure is performed on a particular configuration of infinitely wide wall, illustrating the influence of the joints on its thermal deformed shape. To assess the practical validity of this homogenization-based calculation procedure, results of the numerical homogenized model (incorporating joints) are compared to those of a homogeneous model (without joints), and to available experimental results obtained on a 3 m-high, 3 m-wide wall exposed to fire loading.

Investigation of transportation of nanofluid within non-equilibrium porous media

In this investigation, numerical modeling for the behavior of nanomaterial inside a porous zone with imposing Lorentz force has been illustrated. The working fluid is a mixture of H2O and CuO and due to concentration of 0.04, it is reasonable to use the homogeneous model. Two-temperature model for porous zone was employed in which new scalar for calculating temperature of solid region was defined. CVFEM has been applied to model this complex physics. Radiation terms were considered and their influence on Nu has also been considered. Verification with benchmark proves greater accuracy. Dispersing nanopowders helps the fluid to increase velocity and reduce the temperature of inner wall. Rise of Ra results in three strong eddies inside the zone which creates two thermal plumes and it reduces the temperature of square surface about 68%. With rise of Nhs, the power of counter-clockwise vortex reduces about 61.6% and inner wall becomes warmer about 33.3%. Raising the Ha makes thermal plume to vanish and cooling rate decreases about 46.6%. Augment of Nhs makes Nu to reduce about 5.08% while augment of Ra makes it to augment about 35.64%. Also, augmenting Ha makes Nu to decline about 56.45%.

Study of Thermodynamic Effect On the Mechanism of Flashing Flow Under Pressurized Hot Water by a Homogeneous Model

The flashing flow in a Moby_Dick converging-diverging nozzle under pressurized hot water from 460.5 K to 483.5 K is simulated using a homogeneous compressible water-vapor two-phase flow model. The kinematic and thermodynamic mass transfer are accessed using the cavitation model based on the Hertz-Knudsen-Langmuir equation. Our simplified thermodynamic model is coupled with the governing equations to capture the phase-change heat transfer. This numerical method proved its reliability through a comparison with available experimental data of flow parameters inside the nozzle. Consequently, the present numerical method shows good potential for simulating the flashing flow under pressurized hot water conditions. The satisfying prediction of averaged flow parameters with a slight improvement compared to reference numerical data is reproduced. The results confirm a noticeable impact of the thermodynamic effect on the mechanism of flashing flow, resulting in a considerable decrease in the flow temperature and the saturated vapor pressure. The flashing non-equilibrium is significantly decreased, forcing the flashing flow to be classified as the usual cavitation behavior and better suited to homogeneous model. While the temperature drop is highly dependent on evaporation, the thermodynamic suppression is influenced by the condensation. The suppression effect, unobserved in water at a lower temperature in previous studies, is noticeable for the pressurized hot water flow characterized by the cavitation mechanism. The vapor void fraction decreased considerably in the radial and axial directions as the water temperature rose to 483.5 K in this study.

Simulations with a Thermodynamically Consistent Model for Convective Transport in Nanofluids

A non-homogeneous model is used to simulate convective transport in nanofluids. The model is a thermodynamically consistent version of the celebrated Buongiorno model. We study two situations in detail: flow through a pipe that is heated periodically in time at one lateral wall and a~lid driven cavity with a triangular heat source placed within. Both studies reveal the mechanisms of enhanced heat transfer by nanofluids through thermophoresis: the temperature gradient at the wall leads to a reduced concentration of nanoparticles. This reduces the concentration dependent viscosity of the suspension close to the boundary, which in turn leads to a stronger convective transport.

Experimental Study on Void Fractions and Pressure Drops in Three-Phase Flow for Deep Sea Mining

Subsea minerals exist in the deep water within Japan’s exclusive economic zone. There are many technical issues which should be addressed for subsea mining. The air-lift pumping systems are one of promising methods for subsea minerals transport. Flow assurance for three-phase flow is important to design the air-lift pumping system for subsea mining. It is important to establish methods for estimating void fractions and frictional pressure drops. To establish the methods for three-phase flow, we reviewed previous studies for two- or three-phase flow. There are some models to estimate the void fractions such as slip flow model and drift flux model. There are also some models to estimate the frictional pressure drops such as homogeneous model and separated flow model. We calculated void fractions and frictional pressure drops by existing correlation and compared calculated results with experimental data in two- or three-phase flow. In addition, we proposed the methods for estimating the void fractions and frictional pressure drops in three-phase flow. These had fewer number of experimental constants than existing correlations, these could calculate void fractions and frictional pressure drops in more various conditions than existing correlations.