Thermal modes of a plug flow reactor with a liquid–liquid heterogeneous system

The thermal modes of a flow plug reactor with an exothermic chemical reaction are numerically simulated. A heterogeneous reaction system consisting of two immiscible liquids is studied: one of the liquids (dispersed phase) in the form of droplets is distributed in the other (dispersion phase). The characteristics of the thermal modes of the reactor at various values of two governing parameters, the Damköhler number and the rate of extraction of the dissolved substance from the dispersed phase into the dispersion phase is examined. Two modes of chemical reaction in the reactor are demonstrated to be possible: low-temperature and high-temperature. Critical criteria of thermal ignition are formulated. The dependence of the structure of the thermal wave on the governing parameters is investigated.     

Autooscillations in a perfectly stirred reactor with a two-step consecutive reaction

A mathematical model of the dynamic behavior of a perfectly stirred reactor in which a two consecutive exothermic reactions occurs is developed. Both stages are exothermic. In the Da-Se parametric space, the region of autooscillations (limiting cycles) is identified. The character of alternation of the stabilities of steady states is investigated. It is shown that, in the region of one steady state, two mechanisms of formation (disappearance) of limiting cycles are realized.     

Regions of multiplicity of steady states of a well-stirred flow reactor with sequential reactions

For a well-stirred reactor in which a consecutive two-step (both exothermic) reaction occurs and heat exchange of which with the environment obeys the Newton law, the region of multiplicity of steady states was examined. It was demonstrated that this a region with five steady states. For a given set of parameters, the dependence of the characteristics of the five-state region on the kinetic parameters of the consecutive reaction was examined. The adiabatic reactor was demonstrated to have no closed trajectories (limiting cycles).     

Steady States of a Plug Flow Reactor Operating on a Heterogeneous Liquid−Liquid System

A plug flow reactor operating on a heterogeneous liquid?liquid system in which an exothermic bimolecular reaction takes place is modeled. The effect of the main governing parameters (Peclet and Damkheler numbers and a dimensionless parameter P characterizing mass transfer between the liquid phases) on the thermal modes of the reactor is examined. Depending on the values of these parameters, one or three steady states can be realized in the reactor. It is established that, with increasing parameter P, the region of multiplicity of steady states expands and shift toward lower values of the Damkohler number. The phenomenon of hysteresis is observed in the region of multiplicity of steady states.     

Self-oscillations in a flow ideal mixing reactor in the region of multiplicity of stationary equilibrium states: a consecutive reaction

A model of a flow ideal mixing reactor for a consecutive two-stage exothermic first-order reaction was considered. The presence of a region of multiplicity of stationary states was established. This multiplicity region can contain regions of three and five stationary states; the region of five states always appears inside the region of three stationary states. Changes in the type of stationary state stability in each of these regions are analyzed. Numerical calculations of phase trajectories in the regions of stationary state stability and instability were performed. A mechanism of the creation of a stable limiting cycle was suggested for the case of three stationary states.     

Thermal regimes of a counterflow reactor: a gas-liquid system

A counterflow reactor model for a system of two phases one of which involves an exothermic bimolecular reaction is considered. At a stationary temperature distribution in the reactor, there are high and low heating regions. For the adiabatic case, maximum heating is only possible at the bottom of the reactor. The maximum stationary temperature in the reactor decreases and shifts toward the top of the reactor as the intensity of heat exchange with the environment increases.     

Thermal explosion in a batch reactor charged with a liquid–solid heterogeneous system

The characteristics of a thermal explosion in an ideal mixing batch reactor charged with a liquid–solid heterogeneous system are studied. The reactor initially contains both phases. The solid reagent dissolves and reacts in the liquid phase. A strong dependence of the critical value of the Semenov parameter on the dimensionless time of complete dissolution of the solid reagent is established. It is shown that, at short times of complete dissolution, the critical value of the Semenov parameter is practically independent on this time, and the thermal explosion occurs as in a homogeneous system, according to Semenov theory. The heterogeneous properties of the reaction system manifest themselves only at long times of complete dissolution.     

Multi-Objective Optimization of Braun-Type Exothermic Reactor for Ammonia Synthesis

The exothermic reactor for ammonia synthesis is a primary device determining the performance of the energy storage system. The Braun-type ammonia synthesis reactor is used as the exothermic reactor to improve the heat release rate. Due to the entirely different usage scenarios and design objectives, its parameters need to be redesigned and optimized. Based on finite-time thermodynamics, a one-dimensional model is established to analyze the effects of inlet gas molar flow rate, hydrogen–nitrogen ratio, reactor length and inlet temperature on the total entropy generation rate and the total exothermic rate of the reactor. It’s found that the total exothermic rate mainly depends on the inlet molar flow rate. Furthermore, considering the minimum total entropy generation rate and maximum total exothermic rate, the NSGA-II algorithm is applied to optimize seven reactor parameters including the inlet molar flow rate, lengths and temperatures of the three reactors. Lastly, the optimized reactor is obtained from the Pareto front using three fuzzy decision methods and deviation index. Compared with the reference reactor, the total exothermic rate of the optimized reactor is improved by 12.6% while the total entropy generation rate is reduced by 3.4%. The results in this paper can provide some guidance for the optimal design and application of exothermic reactors in practical engineering.     

Thermal ignition of a heterogeneous system in a stirring semibatch reactor

The thermal ignition of a heterogeneous two-phase system of two immiscible liquids in a stirring semibatch reactor was modeled. The model took into account the dispersion of one phase in the other, the mass transfer of a reagent from the disperse phase into the dispersion medium, and the bimolecular exothermal reaction that occurred in the latter. The kinetic dependences of reagent concentrations, the dynamics of reactor heating, and the critical conditions of thermal ignition were studied. It was found that the initial temperature of the reactor had a considerable effect on its dynamic behavior.     

Numerical simulation of liquid velocity distribution in a sonochemical reactor

Ultrasonically induced flow is an important phenomenon observed in a sonochemical reactor. It controls the mass transport of sonochemical reaction and enhances the reaction performance. In the present paper, the liquid velocity distribution of ultrasonically induced flow in the sonochemical reactor with a transducer at frequency of 490 kHz has been numerically simulated. From the comparison of simulation results and experimental data, the ultrasonic absorption coefficient in the sonochemical reactor has been evaluated. To simulate the liquid velocity near the liquid surface above the transducer, which is the main sonochemical reaction area, it is necessary to include the acoustic fountain shape into the computational domain. The simulation results indicate that the liquid velocity increases with acoustic power. The variation of liquid height also influences the behavior of liquid velocity distribution and the mean velocity above the transducer centre becomes a maximum when the liquid height is 0.4 m. The liquid velocity decreases with increasing the transducer plate radius at the same ultrasonic power.     

Exothermic effects during sintering of a mixture of nickel and aluminum powders. II

When a mixture of nickel and aluminum powders is sintered there is an exothermic effect which involves a rise of several hundred degrees in the temperature of the compact in a few seconds. The magnitude and nature of the exothermic effect depend on the aluminum content of the mixture, the degree of dispersion of the powders, and the initial porosity of the specimens. The temperature at which the exothermic effect begins moves towards lower temperatures with increase in the degree of dispersion, with increase in the concentration of aluminum in the mixture, and with decrease in the porosity. The magnitude of the heat effect increases with increase in the aluminum content.It is shown that the exothermic effect in the sintering process arises mainly from decomposition of the liquid phase and crystallization of chemical compounds with large heats of formation. A definite role is played by the metallothermic reduction of nickel oxide by aluminum present in the liquid phase and by the formation of intermetallic compounds at the boundaries of dissimilar particles of powder during sintering in the solid phase.     

On a nonstationary theory of thermal explosion in a semi-batch reactor. Homogeneous systems

A thermal explosion in a semi-batch ideal-mixing reactor in which a homogeneous sequential exothermic reaction occurs is numerically simulated. It is shown that the critical condition of a thermal explosion, separating the low- and high-temperature modes of the reaction is realized only after the completion of the stage of introduction of the second reactant into the reactor. With increasing time of this stage, the interval of transition from the low- to the high-temperature mode expands with increasing value of the Semenov criterion, and eventually, the thermal explosion becomes degenerate.     

A comparative study on the gas‐phase and liquid‐phase thermal isomerization reaction of α‐pinene

In this paper, a method of preparation of ocimene is investigated, which is obtained from isomerization reaction of α‐pinene. Two kinds of experimental apparatus are established for the investigation of the thermal isomerization reaction of α‐pinene. The behavior of thermal isomerization reaction of α‐pinene is respectively discussed in the gas phase and in the liquid phase. Under gas phase conditions, the conversion of α‐pinene is 80% and the selectivity of ocimene is 30%–33%. Under liquid phase conditions, the conversion of α‐pinene is 60% and the selectivity of ocimene is 50%–54%. According to the kinetic‐molecular theory of ideal gases, two kinds of reaction models are proposed to visualize the reaction process. In addition, the mechanism and kinetics of thermal isomerization reaction of α‐pinene are respectively discussed. The conclusion is that the gas phase reaction temperature is calculated to be 390–450 °C and the liquid phase reaction temperature is calculated to be 450–550 °C. From a bond dissociation energy point of view, results support the hypothesis that the reaction involves biradical intermediates. Copyright © 2012 John Wiley & Sons, Ltd.     

On the Thermal Explosion Theory of a Heterogeneous Liquid–Liquid System

In this paper, the regularities of a thermal explosion of a heterogeneous system consisting of two immiscible liquids have been studied. Each phase is a solution of A and B reagents. Reagent B is extracted into a solution of reagent A, where the bimolecular exothermic reaction A + B → Products takes place. It has been shown that an exothermic reaction (combustion regime) continues to proceed in the system at high mass-exchange rates between phases after a thermal explosion. As a result, the maximal temperature may significantly exceed the temperature of the thermal explosion. The critical value of the Semenov parameter decreases with an increase in the mass-exchange rate between phases. In the limited range of values of the distribution coefficient of reagent B between phases, the increase of this coefficient is also accompanied by a decrease in the critical value of the Semenov parameter. The concentration of reagent B in the initial phase decreases monotonically due to its extraction into another phase. However, the equilibrium of the extraction of reagent B can shift, due to the temperature dependence of the distribution coefficient during the reaction. Thus, the time dependence of the concentration of reagent B on may be more complex and can pass through a minimum.     

Steady regimes of exothermic autocatalytic reaction in a continued stirred-tank reactor

A continued stirred-tank reactor with an exothermic autocatalytic reaction running in it is modeled. In contrast to the simple kinetic law formulated in terms of a first-order equation, a variety of possible types of thermal isoclines, including isoles, are found for the autocatalytic process in the dimensionless “degree of conversion-temperature” coordinates. A bifurcation curve separating the domains of existence of one and three steady states is constructed in the Se-Da coordinates.     

Stabilization of the front of polymerization of composite materials in a plug-flow reactor

The polymerization of composite materials in a plug-flow reactor is studied based on the theory of combustion. A two-temperature mathematical model of the self-sustained exothermic polymerization front in a monomer-filler mixture is developed with consideration given to the basic macrokinetic characteristics of the process, exothermicity of the chemical reaction, and heat transfer. The structure of the fields of temperature and concentrations of the reactants in the front is studied. The influence of special heat-transfer elements, preheating the feedstock supplied into the reactor, on the dynamics of the polymerization process and on the stabilization of the polymerization front is examined.     

冲击诱发NiTi形状记忆合金相变行为研究

NiTi形状记忆合金的高应变动态响应特性在军事、航空等领域具有重要应用.为研究NiTi合金在动态力学诱导下的相变行为,在不同温区不同冲击速率下,通过轻气炮装置对NiTi合金进行了动态加载实验.利用差示扫描量热仪(DSC),综合物性测量系统分析了冲击波残余效应对NiTi合金相变行为的影响.研究发现:受冲击的样品在第一次DSC热循环中观察到了三个马氏体吸热峰,表现为三步逆马氏体相变,而在第二次热循环中其中两个应力诱发马氏体吸热峰因变形恢复消失.形成两个应力诱发马氏体吸热峰的原因可能是晶粒内部与晶界处的相变过程不同步.受冲击后样品DSC放热峰上出现了一小肩峰,表明可能因中间相(R相)的出现而发生了两步相变,结合电阻测量曲线进一步确认R相的存在,且发现奥氏体相向R相转变以及R相向马氏体相转变这两种相变过程在某一温度范围内可同时进行.同时,文中也具体讨论了不同的冲击加载条件对相变过程的影响.     

The reaction process of the Bi-Sr-Ca-Cu-O system and the forming mechanism of the 2212 superconducting phase

The reaction process and the reaction behavior of each component in the Bi-Sr-Ca-Cu-O system are presented in this paper. It reveals that the reaction is carried out in three different stages: forming of an insulating interphase at 680°C–790°C, forming of the 2212 superconducting phase at 790°C–860°C and forming often semiconducting phases in the presence of the liquid phase at 860°C–970°C. It is also confirmed that the 2212 superconducting phase (T _c=85 K) is formed by the reaction of a trinary interphase together with CuO, SrO and CaO. A new two-step method is presented to prepare the 2212 superconducting phase by a presynthesized interphase.     

Numerical modeling of self-propagating polymerization fronts: The role of kinetics on front stability

Frontal propagation of a highly exothermic polymerization reaction in a liquid is studied with the goal of developing a mathematical model of the process. As a model case we consider monomers such as methacrylic acid and n-butyl acrylate with peroxide initiators, although the model is not limited to these reactants and can be applied to any system with the similar basic polymerization mechanism. A three-step reaction mechanism, including initiation, propagation and termination steps, as well as a more simple one-step mechanism, were considered. For the one-step mechanism the loss of stability of propagating front was observed as a sequence of period doubling bifurcations of the front velocity. It was shown that the one-step model cannot account for less than 100% conversion and product inhomogeneities as a result of front instability, therefore the three-step mechanism was exploited. The phenomenon of superadiabatic combustion temperature was observed beyond the Hopf bifurcation point for both kinetic schemes and supported by the experimental measurements. One- and two-dimensional numerical simulations were performed to observe various planar and nonplanar periodic modes, and the results for different kinetic schemes were compared. It was found that stability of the frontal mode for a one-step reaction mechanism does not differ for 1-D and 2-D cases. For the three-step reaction mechanism 2-D solutions turned out to be more stable with respect to the appearance of nonplanar periodic modes than corresponding 1-D solutions. Higher Zeldovich numbers (i.e., higher effective activation energies or lower initial temperatures) are necessary for the existence of planar and nonplanar periodic modes in the 2-D reactor with walls than in the 1-D case. (c) 1997 American Institute of Physics.     

Quantitative calculation of reaction performance in sonochemical reactor by bubble dynamics

In order to design a sonochemical reactor with high reaction efficiency, it is important to clarify the size and intensity of the sonochemical reaction field. In this study, the reaction field in a sonochemical reactor is estimated from the distribution of pressure above the threshold for cavitation. The quantitation of hydroxide radical in a sonochemical reactor is obtained from the calculation of bubble dynamics and reaction equations. The distribution of the reaction field of the numerical simulation is consistent with that of the sonochemical luminescence. The sound absorption coefficient of liquid in the sonochemical reactor is much larger than that attributed to classical contributions which are heat conduction and shear viscosity. Under the dual irradiation, the reaction field becomes extensive and intensive because the acoustic pressure amplitude is intensified by the interference of two ultrasonic waves.