Perfect Mixing Research Articles

The dependence between the structural-morphological features mixes 0.8SiO2/0.2Al2O3 from the time of mechanicall treatment

This paper highlights the relationship between changes in structural and morphological features, electronic structure and exanging of time mechanical treatment at microbraker (MBT). Scaning electron microscopy revealed a change in the morphological features of nanoscale powders. From the comparison of SEM images of 0.8SiO2/0.2Al2О3 mixture before and after MBT, it is established that due to MBT, the agglomerates of the initial components are simultaneously crushed with perfect mixing particles of oxides between each other and the formation of new agglomerates with a denser structure. The increase in processing time leads to an increase in the density of the nanocomposite. The effect of time of mechanical treatment on the structural parameters and phase composition of mixtures of silicon dioxide and titanium were studied using the method of X-ray structural analysis. The established agglomeration is accompanied by a change in the lattice parameter c with a change in the regions of coherent scattering of crystalline Al2О3. Ultra-soft X-ray emission spectroscopy was used to study the distribution of Op-, Sisd- and Alsd- valence electrons in 0.8SiO2/0.2Al2О3 powder mixtures after the different time of mechanicall treatment. An increase in atomic charges has been measured and can be explained by the transfer of electrons from Si and Al to O atoms in split Opπ-binding states.

Experimental analysis of late direct injection combustion mode in a compression-ignition engine fuelled with biodiesel/diesel blends

A compression ignition reciprocating internal combustion engine has been modified to allow operation with late direct injection of rapeseed biodiesel fuel blends. The purpose of these modifications is to reduce both the engine's carbon footprint and emission of nitrogen oxides and soot, without decreasing performance or using expensive emission post-treatment systems. The experimental part of this work is based on the measurement of the main pollutants being emitted and the analysis of the combustion process, which is accomplished by the study of the heat release rate curve. This curve is derived from the experimental chamber pressure data, in combination with a zero-dimensional thermodynamic model assuming a perfect mixing reactor with temporal variation in volume and chemical composition, temperature-dependent properties and heat losses. The analysis of the experimental results allows deepening the knowledge of the combustion process in a compression ignition engine with late direct injection using different biodiesel blends. There is a significant reduction (>50%) of emissions of nitrogen oxides in comparison with the original configuration. This allows considering the modified configuration as an advanced combustion mode, intermediate between conventional compression ignition engines and homogeneous charge compression ignition combustion mode.

A simulation study of nonideal mixing effect on the dynamic response of an exothermic CSTR with Cholette’s model

Abstract The study of nonideal mixing effect on the dynamic behaviors of CSTRs has very rarely been published in the literature. In this work, Cholette’s model is employed to explore the nonideal mixing effect on the dynamic response of a nonisothermal CSTR. The analysis shows that the mixing parameter n (the fraction of the feed entering the zone of perfect mixing) and m (the fraction of the total volume of the reactor), indeed affect the characteristic roots of transfer function of a real CSTR, which determine the system stability. On the other hand, the inverse response and overshoot response are also affected by the nonideal mixing in a nonisothemal CSTR. These results are of much help for the design and control of a real CSTR.

Simulation study of the nonideal mixing effect on the stability of continuous and discrete proportional control of a nonadiabatic CSTR based on Cholette’s model

ABSTRACT Studies on discrete control continuous stirred tank reactor (CSTR) with Cholette’s model have not been published in the literature because the mathematical model is far too complicated. This work uses Cholette’s model with discrete proportional control with the mixing parameter n (the fraction of the feed entering the perfect mixing zone) and m (the fraction of the total volume of the reactor) to study exothermic CSTR behavior. Meanwhile, exothermic CSTR continuous proportional control is used to compare the discrete proportional control results. It is found that the nonideal mixing parameters m and n indeed affect the control stability of both the continuous and discrete proportional control. The contribution of this paper is that this analysis can determine the stability region in the control system phase plane. Furthermore, if the nonideal mixing effect is ignored, the stable control system may become unstable and unsafe. Our results are of significant help for CSTR control in industry because the ideal mixing is hardly attainable in reality.

Influence of Flue Gas Pattern Flow in Boiler Radiant Section on Heat Transfer

Abstract During the sizing of the radiant zone in boilers and furnaces, the most often used method is the Lobo-Evans model. This method is based on the perfect mixing model for flue gas flow inside the fire box, which represents a conservative or pessimistic flow pattern. This paper presents a different, optimistic model which is based on the plug flow for flue gas flow which results in the largest possible heat duty. The proposed model is given in two distinct forms—integral and numerical. As shown in the paper, the integral model results in small deviations with respect to the numerical model and, as such, is well suited for the engineering practice. Paper also presents an engineering approach to the calculation of the conductive heat transfer through the membrane wall, which is shown to be sufficiently accurate and simple for engineering calculations.

On Finding the Right Sampling Line Height through a Parametric Study of Gas Dispersion in a NVB

The tracer gas method is one of the common ways to evaluate the air exchange rate in a naturally ventilated barn. One crucial condition for the accuracy of the method is that both considered gases (pollutant and tracer) are perfectly mixed at the points where the measurements are done. In the present study, by means of computational fluids dynamics (CFD), the mixing ratio NH3/CO2 is evaluated inside a barn in order to assess under which flow conditions the common height recommendation guidelines for sampling points (sampling line and sampling net) of the tracer gas method are most valuable. Our CFD model considered a barn with a rectangular layout and four animal-occupied zones modeled as a porous medium representing pressure drop and heat entry from lying and standing cows. We studied three inflow angles and six combinations of air inlet wind speed and temperatures gradients covering the three types of convection, i.e., natural, mixed, and forced. Our results showed that few cases corresponded to a nearly perfect gas mixing ratio at the currently common recommendation of at least a 3 m measurement height, while the best height in fact lied between 1.5 m and 2.5 m for most cases.

Hybrid System Level and Coarse Grid CFD Tool for Three-Dimensional Natural Circulation, Mixing, and Stratification Modeling

Natural circulation, mixing, and stratification are important phenomena for the design and safety analysis of many advanced reactor designs with passive safety features as well as large open regions, such as pool reactor designs, spent fuel pools, and containments. Various modeling methods ranging from zero-dimensional (0-D) lumped volumes (or perfect mixing) to full three-dimensional (3-D) computational fluid dynamics (CFD) have been used. Historically, 0-D lumped volume approaches, combined with other modeling methods and assumptions, have been applied to perform so-called conservative analyses, but with the advancement of computational resources and best-estimate-plus-uncertainty methods, it is very desirable to have advanced, multidimensional modeling and simulation capabilities to improve the accuracy of reactor safety analyses, reduce modeling uncertainties, and eliminate the modeling distortions that can occur when simultaneously applying conservatisms. In the past decade there have been large investments in the pursuit of new, higher-fidelity modeling and simulation tools. However, GOTHICTM, which has been developed and maintained by Zachry Nuclear Engineering (formerly Numerical Applications, Inc.) since the mid-1980s, already provides these capabilities. GOTHIC is an industry-trusted, computationally efficient, coarse-grid multiphase CFD tool that also includes the important attributes of traditional system-level modeling tools, such as component-level models, control system capabilities, and neutron point kinetics models. GOTHIC applies a domain decomposition approach, allowing various levels of fidelity from 0-D to full 3-D to be applied in a single model, giving the user the ability to focus computational resources in the regions of interest while still capturing the integrated system response and important feedback effects. The result is a general-purpose, multiphysics engineering design and analysis tool that can be used for both light water reactor (LWR) and non-LWR designs. This paper provides an overview of 3-D finite volume modeling in GOTHIC, including the governing equations, turbulence model, and solution methods. Additionally, a few of the verification and validation tests from GOTHIC’s full test suite are presented to demonstrate fundamental capabilities, including laminar flow in a channel of parallel plates, square and rectangular cavity natural convection, natural convection through vertical and horizontal openings, and natural convection associated with a heated horizontal cylinder in a rectangular cavity. Based on the comparisons with the analytical solutions and experimental results, it is demonstrated that the multidimensional model can perform very well for a wide range of applications.

Henry’s law constants and hydration equilibrium constants of n-hexanal and their temperature dependence as determined by the rectangular pulse method

The Henry’s law constants of n-hexanal are needed to predict its rate of mass transfer between gas and aqueous phases. However, information on these constants is limited because the mass transfer of n-hexanal involves a reversible hydration reaction in water; therefore, Henry’s law constants are difficult to obtain experimentally and cannot be deduced only from the gas-to-water equilibrium. Here, we conducted stimulus–response experiments using a rectangular input pulse and a double-mixing gas–liquid contactor to simultaneously determine Henry’s law constants and hydration equilibrium constants for n-hexanal in deionized water, aqueous sodium chloride, or aqueous sodium sulfate in the temperature range of 5.3–22.5 °C. The change in the concentration of a mixture of n-hexanal in nitrogen gas after passing through the contactor was examined, and simulation-based optimization was conducted to optimize parameters that included Henry’s law constants and hydration rate constants. In the simulation, convolution using the rectangular input pulse was used to determine the input signal, and perfect gas-phase mixing and two-film layer mass transfer were assumed. This approach, which we called the rectangular pulse method, was validated by performing similar investigations for toluene, ethyl acetate, and ethyl trifluoroacetate. As a result, Henry’s law constants and rate constants for the reversible hydration reactions of n-hexanal and their temperature dependence were obtained, and the calculated effective Henry’s law constant agreed with some, but not all, of the values reported in the literature. A potential reason for the disagreement was discussed from the viewpoint of long time-constants used for the hydration equilibrium. In addition, a salting effect by the aqueous salt solutions was found to affect the Henry’s law constants, but not the hydration equilibrium constants. The overall liquid‐side mass‐transfer coefficient was found to be correlated with the diffusion coefficient, based on the Higbie penetration theory.

Non-uniform mixing of hepatic venous flow and inferior vena cava flow in the Fontan conduit.

Fontan patients require a balanced hepatic blood flow distribution (HFD) to prevent pulmonary arteriovenous malformations. Currently, HFD is quantified by tracking Fontan conduit flow, assuming hepatic venous (HV) flow to be uniformly distributed within the Fontan conduit. However, this assumption may be unvalid leading to inaccuracies in HFD quantification with potential clinical impact. The aim of this study was to (i) assess the mixing of HV flow and inferior vena caval (IVC) flow within the Fontan conduit and (ii) quantify HFD by directly tracking HV flow and quantitatively comparing results with the conventional approach. Patient-specific, time-resolved computational fluid dynamic models of 15 total cavopulmonary connections were generated, including the HV and subhepatic IVC. Mixing of HV and IVC flow, on a scale between 0 (no mixing) and 1 (perfect mixing), was assessed at the caudal and cranial Fontan conduit. HFD was quantified by tracking particles from the caudal (HFDcaudal conduit) and cranial (HFDcranial conduit) conduit and from the hepatic veins (HFDHV). HV flow was non-uniformly distributed at both the caudal (mean mixing 0.66 ± 0.13) and cranial (mean 0.79 ± 0.11) level within the Fontan conduit. On a cohort level, differences in HFD between methods were significant but small; HFDHV (51.0 ± 20.6%) versus HFDcaudal conduit (48.2 ± 21.9%, p = 0.033) or HFDcranial conduit (48.0 ± 21.9%, p = 0.044). However, individual absolute differences of 8.2–14.9% in HFD were observed in 4/15 patients. HV flow is non-uniformly distributed within the Fontan conduit. Substantial individual inaccuracies in HFD quantification were observed in a subset of patients with potential clinical impact.

GPU-enhanced DEM analysis of flow behaviour of irregularly shaped particles in a full-scale twin screw granulator

During twin screw granulation (TSG), small particles, which generally have irregular shapes, agglomerate together to form larger granules with improved properties. However, how particle shape impacts the conveying characteristics during TSG is not explored nor well understood. In this study, a graphic processor units (GPUs) enhanced discrete element method (DEM) is adopted to examine the effect of particle shape on the conveying characteristics in a full scale twin screw granulator for the first time. It is found that TSG with spherical particles has the smallest particle retention number, mean residence time, and power consumption; while for TSG with hexagonal prism (Hexp) shaped particles the largest particle retention number is obtained, and TSG with cubic particles requires the highest power consumption. Furthermore, spherical particles exhibit a flow pattern closer to an ideal plug flow, while cubic particles present a flow pattern approaching a perfect mixing. It is demonstrated that the GPU-enhanced DEM is capable of simulating the complex TSG process in a full-scale twin screw granulator with non-spherical particles.

Performance evaluation of free cyanide control strategies in a simulated gold leaching circuit

AbstractA phenomenological dynamic model of gold ore leaching process in agitated tanks is derived and calibrated with a set of industrial data. This model is used to simulate the dynamic behaviour of a three‐tank industrial plant and to test the performance of 12 different free cyanide feedback control strategies. The performance of the control strategies faced to step disturbances is quantified using an economic objective criterion, for both steady‐state and dynamic operating regimes. The results of set‐point changes for the three‐tank cascade show responses like those of a linear system for first, second, and third orders, since the tanks behave as perfect mixers. The steady‐state and dynamic results for the uncontrolled plant show large losses of gold at low cyanide consumption, while regulatory control of the cyanide concentrations in the first tank helps improve the economic efficiency. However, in the presence of disturbances other than those related to cyanide concentrations, the control of cyanide at constant set‐points might be detrimental to the plant economic performance and would require a supervisory optimal control of the set‐point values.

Rayleigh–Taylor instability between unequally stratified layers

In this article, we explore the development and mixing that results from Rayleigh–Taylor instability between two layers. Unlike the classical problem, one of the two layers initially has a stable density stratification, while the density of the fluid in the other is uniform. The results presented here are from low-Atwood-number experiments with incompressible fluids, although there is an analogy between this case and low accelerations of compressible fluids that result in hydrostatic gradients that differ significantly. In both scenarios, the instability growth is asymmetric. For the present case, mixing will occur throughout the region initially occupied by the layer of uniform density but, depending on the strength of the stratification compared with the density difference across the initial Rayleigh–Taylor-unstable interface, the mixing may be arrested by the stratification before it reaches the lower boundary of the domain. We propose a simple model for the growth of the instability and see that it captures the qualitative behaviour. The final state comprises a weakly stratified layer bounded on one side by the remnant of the initially stratified layer. The structure of this weak stratification is seen to be consistent with the idea of maximal configurational entropy for the mixing zone. Ultimately, the efficiency of this mixing process is found to follow the pattern expected for the ‘perfect mixing’ equivalent, but achieves only 94% of the corresponding value.

An approach to measuring and modelling the residence time distribution of cement clinker in vertical roller mills

ABSTRACT This paper presents an experimental approach to measure and model the residence time distribution of vertical roller mill in cement clinker grinding circuit. The dispersion model, tank-in-series model, and a perfect mixer with a bypass model were employed to describe the residence time distribution. A perfect mixer with a bypass model was found to a tolerable fitting to describe the RTD of solids in VRM. The result shows 43% of the fine fraction of fresh feed as an existing bypass without spending adequate time within the VRM. The result also shows that the grinding occurs in 54% of the table surface and about 46% of the table surface can be called the dead zone.

Residence time distribution (RTD) of water flooding activity in oil recovery using vertical sand column: Radiotracer approach

Waterflooding is a common secondary recovery oil extraction method that can enhance oil recovery up to 45 percent overall recovery factor. Waterflooding is commonly used due to its availability, cost effectiveness and simplicity. Radioactive tracer was introduced to get the optimum Residence Time Distribution (RTD) model which indicates the mechanism of the system. Radiotracer Gallium-68 (Ga-68) is a positron emitting radioactive material, which is eluted from parent Germanium-68 (Ge-68) generator to study the water flooding activity inside the 15 μm grain size of sand pack column oil recovery study. The sand was cleaned, occupying a Perspex sand pack column of 30 cm length and 5 cm diameter arranged in vertical position. The water inlet and tracer were injected from the bottom of the column, assisted by a syringe pump, with the flow rate optimized at 3.5 ml/min in order to push the saturated oil inside the column. Four Sodium Iodide (NaI) scintillation detectors were installed accordingly and attached to 12-channel data analyzer (DAS) to acquire signals of the emitted positron from the Ga-68 solution and monitored by a laptop. The activity utilized was 766 μCi/3ml and the half-life of Ga-68 was 68 minutes with penetrative energy of 511 keV. Initial experience of using Ga-68 was eluting it with 0.05 M HCl for 90μCi/3ml and directly inject it using pulse injection at the upstream of the column. Nonetheless, there was no indication of tracer arrival at the output after several hours which indicated the sole Ga-68 behaves as sand tracer thus, some modification was made to the respective Ga-68 solution. Chelating with DOTA-NHS solution was the second experience with Ga-68, which produced satisfactory result. A very vivid signal was retrieved at the output and RTD model analysis was carried out. The results indicated that the vertical sand pack column behaved as a Perfect Mixer with Parallel Model.

Application of Cholette’s model in non-ideal mixing CSTR: a simulation study on dynamic behavior

Abstract Non-ideal mixing phenomena are widely found in industrial chemical reactors. In this work we derived the bifurcation formulas for a non-adiabatic CSTR with an irreversible exothermic first order reaction with the non-ideal mixing effect. This is investigated via dynamic behavior simulations based on Chollete’s model. The results show that the non-ideal mixing parameter n (the fraction of the feed entering the perfect mixing zone) determines the variation between six classified regions and dominates the dynamic behavior patterns in the steady-state response diagram. On the other hand, the phase portraits of examples verify the formulas derived in this work. We note that the non-ideal mixing effect has significant importance in CSTR design and control steps. For example, in the safe operating region for an ideal mixing CSTR, non-linear dynamics are obtained by the system under non-ideal mixing conditions (n ≠ 1). The present study has significance and help for chemical reactor design and CSTR control.

Effect of ethanol-gasoline blends on SI engine performance and emissions

Negative effects of using traditional engine fuels on climate change and global warning have produced a scenario of high competition to find an alternative fuel more friendly and unharmful to the environment. Alcohol fuel was found very practical to be mixed with engine designed fuel. In the present work, ethanol was mixed with gasoline in different proportions (10% ethanol + 90% gasoline, 20% ethanol + 80% gasoline, 30% ethanol +70% gasoline, 40% ethanol + 60% gasoline) by utilizing ultrasonic bath to ensure perfect mixing which in turn will increase the fuel energy content.A one-cylinder, four-stroke and spark ignition engine was used to study and analyze the effect of ethanol's/gasoline blend on power, efficiency and exhaust gases. Results showed that power, brake specific fuel consumption and thermal efficiency are improved with the increase of ethanol concentration. On the other hand, ethanol was found to have negative effect on volumetric efficiency.Furthermore, adding ethanol reduce harmful exhaust gasses. It is found that more ethanol is an accompanied with less exhaust gasses. Finally, research octane number and motor octane number are found to be much with ethanol blends. Although lower heating value was found to be higher for pure gasoline, it's found that all other parameters are enhanced with adding ethanol to the engine fuel.

Manipulation of Interfacial Diffusion for Controlling Nanoscale Transformation.

The unprecedented development of inorganic nanostructure synthesis has paved the way toward their broad applications in areas such as food science, agroforestry, energy conversion, and biomedicine. The precise manipulation of the nucleation and subsequent growth has been recognized as the central guiding principle for controlling the size and morphology of the nanostructures. However, conventional colloid syntheses based on direct precipitation reactions still have limitations in their versatility and extendibility. The crystal structure of a material determines the limited number of possible morphologies that its nanostructures can adopt. Further, as nucleation and growth kinetics are sensitive to not only the nature of the precipitation reactions but also ligands and ripening effect, rigorous control of reaction conditions must be established for every specific synthesis. In addition, multiple experimental parameters are entangled with each other, thereby requiring rigorous control of all reaction conditions. As a result, it is usually challenging to extend a synthetic recipe from one material to another. As an alternative method, the direct transformation of existing nanostructures into target ones has become an effective and robust approach capable of creating various complex nanostructures that are otherwise challenging to obtain using conventional methods. To this end, an in-depth understanding of nanoscale transformation toward the synthesis of inorganic nanostructures with diverse properties and applications is highly desirable.In this Account, we aim to reveal the critical effect of the interfacial diffusion on controlled nanoscale transformation. We first discuss how the interdiffusion rates determine the morphology and properties of bimetallic nanostructures. While equal interdiffusion rates lead to perfect mixing and generate fully alloyed nanostructures, interdiffusion at unequal rates creates vacancies in the fast diffusion side, which may cause dramatic morphological transformation to the nanostructures. Then, we introduce interfacial reactions, including the Kirkendall cavitation process, elimination reaction, and solid-state reaction, to promote the unbalanced interdiffusion and generalize nanoscale transformations in materials of various compositions, morphologies, and crystal structures. Finally, we discuss the use of capping ligands to inhibit the diffusion of atoms on one side of the interface in order to enable selective etching or transformation of the nanostructures. By modifying the nanostructured surface with specific capping ligands, the diffusion of surface atoms is restricted. When nanoparticles undergo chemical reactions (such as etching or heating), the outward diffusion of substances dominates, thereby successfully achieving chemical and morphological transformations. We believe that controlled interfacial diffusion can effectively manipulate nanoscale transformations, thus providing new strategies for the custom synthesis of multifunctional nanomaterials for various specific applications.

The multi-patch logistic equation

<p style='text-indent:20px;'>The paper considers a <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula>-patch model with migration terms, where each patch follows a logistic law. First, we give some properties of the total equilibrium population. In some particular cases, we determine the conditions under which fragmentation and migration can lead to a total equilibrium population which might be greater or smaller than the sum of the <inline-formula><tex-math id="M2">\begin{document}$ n $\end{document}</tex-math></inline-formula> carrying capacities. Second, in the case of perfect mixing, i.e when the migration rate tends to infinity, the total population follows a logistic law with a carrying capacity which in general is different from the sum of the <inline-formula><tex-math id="M3">\begin{document}$ n $\end{document}</tex-math></inline-formula> carrying capacities. Finally, for the three-patch model we show numerically that the increase in number of patches from two to three gives a new behavior for the dynamics of the total equilibrium population as a function of the migration rate.</p>

Mathematical and numerical predictions for optimum perfect mixing by bulk convective oscillatory exchange

The mixing quality for bulk convective oscillatory exchange are analyzed, modeled, and simulated for 24 cases mathematically and numerically. A new mathematical model has been derived for heat and mass transfer between two reservoirs to predict the perfect and optimum mixing quality. Two-dimensional axisymmetric simulations are carried out for incompressible viscous oscillatory flows. The computations are run for two reservoirs that are connected by a short duct over a unique range of the fluid’s axial displacements. From the mathematical model, two new equations for the instantaneous temperature in each reservoir have been derived to predict the perfect mixing quality for any bulk convective oscillatory exchange. According to the computational predictions, the mass exchange between the two reservoirs has been classified into five different regions depending on their mixing quality. Optimum perfect mixing conditions were obtained at a normalized fluid’s axial tidal displacement S¯=4.9 with mixing ratio ranged from 97%to100%. A new correlation for predicting the rate of heat transfer enhancement by the bulk convective oscillatory exchange is suggested. It is observed that the effective thermal conductivity has been enhanced by up to O(106) compared with the molecular conductivity of the fluid. Also, the mixing quality for specific mass exchange conditions has enhanced up to160% compared with the perfect mixing case.

Covid‐19: Where We Are, What Got Us Here, and Where We Are Likely to Be Going—A Review Essay*

Covid‐19: Where We Are, What Got Us Here, and Where We Are Likely to Be Going—A Review Essay*