ZGB Model Research Articles

CFD Simulation of Pressure, Temperature and Rotational Speed Influence on the Cavitation in Centrifugal Pump Impeller

The impeller is a critical rotating part of a centrifugal pump where the energy transfer to the fluid takes place. The complex nature of the fluid flow inside the impeller can give rise to cavitation which is highly undesirable. Design and operating conditions in the impeller influence the extent of cavitation. The effect of the outlet pressure, temperature and rotational speed of the impeller was studied using ANSYS CFX Computation Fluid Dynamics (CFD) software. The impeller geometry was meshed with high-quality hexahedral meshes and the y + values around the blade surface are less than 2. The k - omega turbulence model was used along with the ZGB model of cavitation. The effects of the variable parameters on the cavitation volume and the head developed were extensively studied. The numerical trends are similar to those presented in the literature. By carefully controlling the outlet pressure, the effects of increased temperature can be mitigated. Thus, it is possible to operate a centrifugal pump at higher working fluid temperatures by operating the pressure above 275 kPa.

Effects of temporal disorder in the continuous phase transition of a catalytic reaction system

We analyze through Monte Carlo simulations the continuous phase transition between the active and the absorbing phase of the ZGB model in the presence of temporal disorder. In order to employ the disorder we allow the control parameter to be time dependent, working as an environmental noise. We consider four different disorder strengths. Although the critical value of the control parameter does not shift as we change the disorder strength, the values of the static critical exponents ratio β/ν⊥ at the critical point are affected by the disorder. Same behavior is observed for different ratios between moments of the order parameter. Considering the time-dependent aspect we looked at the mean time required for the system to enter into the absorbing state. From this analysis we calculated the ratio ν∥/ν⊥ for different disorder strengths. As well as for the static scenario, the values are affected by the presence of temporal disorder. Besides, the mean lifetime of a sample scales generically as a power-law of the system size at criticality, and in the active phase, producing continuously varying critical values of the critical exponent ratio ν∥/ν⊥.

Validation and simulation of cavitation flow in a centrifugal pump by filter-based turbulence model

The simulation of cavitation flow is sensitive to the turbulence model and cavitation model. To improve the accuracy of numerical simulation, a centrifugal pump with specific speed of 56.5 is taken as the research object, and the Filter-Based Model (FBM) was used to correct the RNG turbulence model. Zwart-Gerber-Belamri (ZBG) cavitation model, Kunz model and Schnerr-Sauer model were employed for the simulation of cavitation flow in a centrifugal pump. According to the comparison, the results calculated by the ZGB model were 8% closer to the experimental results in cavitation predictions. The cavitation occurs around the impeller ring and balance holes firstly, and then the vapor develops and cover 80% of the blade suction side. By using Q-criterion, the distribution of the vortex core region under different cavitation conditions were investigated. The volume of high intensity vortex under severe cavitation condition is 30%∼50% higher than that under other conditions. Furthermore, the distribution of the radial force of the impeller corresponds to the number of blades, and the cavitation affects the resultant force direction of the impeller. With the intensification of cavitation, the radial force of impeller increases gradually, and the regularity of radial force direction will be disorder.

Improved model of lattice gas in the adsorption of carbon monoxide and oxygen

The adsorption and subsequent oxidation of carbon monoxide (CO) on a platinum (Pt) surface has been studied using computational methods. The Monte Carlo method is used to this end through the lattice model. This study focuses on the improvement of this first theoretical model (ZGB) proposed for the oxidation of CO. In this work, four different models are revised in detail with the objective of establishing a comparison between the obtained results on the oxidation of CO on the Pt with an orientation (111) surface. The variance between the models lies on the nature of the sticking coefficient of the CO and oxygen (O2) molecules on Pt (111). This adsorption depends on the initial concentration of CO in the gas phase and the number of vacant sites on the platinum surface. The results obtained in these simulations show that the first model, the ZGB model, differs considerably from the other models, and thus the results with the second and third model have a better adjustment to the adsorption of the CO and O2 molecules, since they take into account the gas concentration, the sticking coefficient and the interaction with the neighboring particles. In this sense, the oxidation reaction occurs in a wider theoretical range around 0.5 mole fraction of CO and 0.2 mole fraction of O atomic, and the poisoning of the platinum catalytic surface can be inhibited if the concentration of carbon monoxide is included as a control parameter.

Effects of sediment diameter and concentration on cavitation characteristics and mechanism

The synergistic erosion caused by cavitation and abrasion is a common and severe problem for hydraulic machinery. In order to explore the mechanism of particles size and concentration effect on cavitation, taking the rotating disk as the research object. The solid-liquid-gas three-phase flow was calculated based on the non-homogeneous multiphase flow model, modified RNG k−εturbulence model, and ZGB model. The increase of particles size firstly inhibited the bubbles (0.02 mm ≤ d ≤ 0.1 mm) and then promoted the bubbles (0.1 mm <d ≤ 0.4 mm); When 0.27 mm < d ≤ 0.4 mm, both cavitation area and cavitation damage intensity are more significant than those of cavitation alone. When d = 0.1 mm, 1% ≤ Cv ≤ 10%, the increase of particles concentration promotes bubbles. However, that only enhances the cavitation area, but has little effect on the cavitation damage intensity. When particles severely inhibit the bubbles, the vortex rotation effect is the strongest, and the mainstream promotion and re-entrant jet inhibition effect are the strongest. The purpose of this paper is to provide some theoretical basis for exploring the mechanism of synergistic erosion.

Mapping the phase transitions of the ZGB model with inert sites via nonequilibrium optimizing methods

In this paper, we revisit the ZGB model and explore the effects of the presence of inert sites on the catalytic surface. The continuous and discontinuous phase transitions of the model are studied via time-dependent Monte Carlo simulations. In our study, we are concerned with building a refinement procedure, based on a simple concept known as coefficient of determination r, in order to find the possible phase transition points given by the two parameters of the model: the adsorption rates of carbon monoxide, y , and the density of inert sites, . First, we obtain 106 values of r by sweeping the whole set of possible values of the parameters with an increment 10−3, i.e. and with . Then, with the possible phase transition points in hand, we turn our attention to some fixed values of and perform a more detailed refinement considering larger lattices and increasing the increment by one order of magnitude to estimate the critical points with higher precision. Finally, we estimate the static critical exponents , , and , as well as the dynamic critical exponents z and .

A cavitation model considering thermodynamic and viscosity effects

PurposeThis study aims to develop and validate a new cavitation model that considers thermodynamic effects for high-temperature water flows.Design/methodology/approachThe Rayleigh–Plesset equation and “B-factor” method proposed by Franc are used to construct a new cavitation model called “thermodynamic Zwarte–Gerbere–Belamri” (TZGB) by introducing the thermodynamic effects into the original ZGB model. Furthermore, the viscous term of the Rayleigh–Plesset equation is considered in the TZGB model, and the model coefficients are formulated as a function of temperature. Cavitating flows around the NACA0015 hydrofoil under different water temperatures (25°C, 50°C and 70°C) at the angle of attack of 5° are calculated.FindingsResults of the investigated temperatures show good agreement with the available experimental data. Given that the thermodynamic and viscosity effects are included in the TZGB model and the model coefficients are treated as a function of temperature, the TZGB model shows better performance in predicting the pressure coefficient distribution and length of cavity than the original ZGB cavitation model and other models do. The TZGB model aims to determine the thermodynamic and viscosity effects and perform better than the other models in predicting the mass transfer rate, particularly in high-temperature water.Originality/valueThe TZGB model shows potential in predicting the cavitating flows at high temperature and the computational cost of this model is similar to that of the original ZGB model.

Comparison between different models for the catalytic oxidation of CO on a surface in the presence of non-desorbing impurities in the gas phase

We apply kinetic Monte Carlo simulations to study the catalytic oxidation of CO on a surface in the presence of contaminants in the gas phase. The dynamic behavior of the process is simulated by models based on the Ziff-Gulari-Barshad model ZGB. We analyze three ways in which the entrance mechanism of the oxygen atoms can be modified such that the unphysical oxygen poisoned phase that characterizes the ZGB model disappears. We study the behavior of these models in the presence of impurities in the gas phase. Once on the surface, the impurities cannot be desorbed and do not react. We calculate the phase diagrams of the three cases for different percentages of impurities and study the behavior of the CO_2 production. We found that the non-desorbing impurities have the effect of eliminating the discontinuous phase transition to a CO poisoned phase, and that in the steady state there is no production of CO_2. However in the transient phase there can be an important CO_2 production that depends on the model.

Coupling of kinetic Monte Carlo simulations of surface reactions to transport in a fluid for heterogeneous catalytic reactor modeling

We have developed a method to couple kinetic Monte Carlo simulations of surface reactions at a molecular scale to transport equations at a macroscopic scale. This method is applicable to steady state reactors. We use a finite difference upwinding scheme and a gap-tooth scheme to efficiently use a limited amount of kinetic Monte Carlo simulations. In general the stochastic kinetic Monte Carlo results do not obey mass conservation so that unphysical accumulation of mass could occur in the reactor. We have developed a method to perform mass balance corrections that is based on a stoichiometry matrix and a least-squares problem that is reduced to a non-singular set of linear equations that is applicable to any surface catalyzed reaction. The implementation of these methods is validated by comparing numerical results of a reactor simulation with a unimolecular reaction to an analytical solution. Furthermore, the method is applied to two reaction mechanisms. The first is the ZGB model for CO oxidation in which inevitable poisoning of the catalyst limits the performance of the reactor. The second is a model for the oxidation of NO on a Pt(111) surface, which becomes active due to lateral interaction at high coverages of oxygen. This reaction model is based on ab initio density functional theory calculations from literature.

Comparison between different oxygen adsorption mechanisms for the catalytic oxidation of CO on a surface

We study by kinetic Monte Carlo simulations the dynamic behavior of a Ziff-Gulari-Barshad ZGB model for the catalytic oxidation of CO on a surface. It is well known that the ZGB model presents a continuous transition between an oxygen poisoned state and a reactive state that it is not observed in nature. Based on some experimental results that indicate that the oxygen atoms move away from each other upon dissociation at the surface, we modify the standard ZGB model by changing the entrance mechanism of the oxygen molecule. We study three different ways in which the oxygen atoms can be adsorbed at the surface such that the nonphysical continuous phase transition disappears. We calculate the phase diagram for the three cases and study the effects of including a CO desorption mechanism.

Effect of Droplet Size on the First Order Ziff-Gulari-Barshad (ZGB) Phase Transition

We introduce a new method to analyze the coexistence region of the constant rate ensemble ZGB discontinuous transition. The method clearly delineates the spinodal and coexistence points in the constant rate ZGB model. Increase in system size reduces the gap between the spinodal and coexistence points. Next we quantify the effect of metastability by introducing a droplet/nucleus of CO occupied sites in the initial system. In systems with initial nucleus of increasing size the distance between the spinodal and the coexistence point decreases, until for a large enough droplet spanning the initial system, the spinodal and the coexistence points become indistinguishable.

Hysteretic effects in the first-order irreversible phase transition of the ZGB model

The first-order irreversible phase transition (FOIPT) of the ZGB model [Ziff, Gulari, Barshad, Phys. Rev. Lett. 56 (1986) 2553] for the catalytic oxidation of carbon monoxide is studied numerically by using the constant-coverage (CC) ensemble. The CC method allows us to study hysteretic effects close to coexistence, as well as the location of the coexistence point. Also, evidence that the FOIPT exhibits a condensation/evaporation pseudo-transition (in finite samples), as observed in its reversible counterparts, is presented and discussed.

Surface reconstruction in reactive dynamics: A kinetic Monte Carlo approach

The oscillatory CO oxidation reaction on the restructuring surface of Pt(1 0 0) is studied through a mesoscopic kinetic Monte Carlo (KMC) approach. The present model is an extension of the standard ZGB model with specific attention to the emergence of oscillations in surface reactions. A square and a purely hexagonal lattice are used as substrates on which the CO oxidation reaction steps take place. The dynamics of the reaction on the two substrates exhibit the ZGB kinetic phase transitions, at different kinetic parameter values for each substrate. Surface reconstruction is modelled through switching between the two lattice types. Oscillations are produced in those parametric areas where the steady state concentrations on the two substrates are considerably different. The parametric area where notable oscillations are observed is narrow, but is greatly enhanced when different sticking coefficients of oxygen are taken into account. CO diffusion introduced microscopically to the model on the hexagonal lattice shifts the kinetic transition points and increases considerably the time needed to reach the steady state.

A non-thermal lattice gas model for a dimer–trimer reaction on a catalytic surface: A computer simulation study

The kinetics of an irreversible dimer–trimer reaction of the type 3A2+2B3→6AB have been studied using a non-thermal (precursor mechanism) model on a square as well as on a hexagonal lattice surface by Monte Carlo simulation. When the range of the precursors (A atoms) is increased, the model gives production rates (reactive window widths) that are quite large as compared with those for thermal (Langmuir–Hanshelwood mechanism) model. The phase diagrams qualitatively resemble with the standard ZGB model except that the continuous transition point is eliminated when the range of the precursors is extended up to the third nearest neighbourhood. The diffusion of A atoms on the surface as well as their desorption from the surface with a certain probability is also considered to see their effects on the reaction mechanism.

Quasi-stationary distributions for models of heterogeneous catalysis

We construct the quasi-stationary (QS) distribution for two models of heterogeneous catalysis having two absorbing states: the ZGB model for the oxidation of CO, and a version with noninstantaneous reactions. Using a mean-field-like approximation, we study the quasi-stationary surface coverages, moment ratios and the lifetime of the QS state. We also derive an improved, consistent one-site mean-field theory for the ZGB model.

Quasi-stationary distributions for models of heterogeneous catalysis

We construct the quasi-stationary (QS) distribution for two models of heterogeneous catalysis having two absorbing states: the ZGB model for the oxidation of CO, and a version with noninstantaneous reactions. Using a mean-field-like approximation, we study the quasi-stationary surface coverages, moment ratios and the lifetime of the QS state. We also derive an improved, consistent one-site mean-field theory for the ZGB model.

A NONTHERMAL MODEL FOR CATALYTIC SURFACE REACTION OF THE TYPE A2+B2→2AB: A MONTE CARLO SIMULATION STUDY

The kinetics of irreversible dimer–dimer reaction of the type A2+B2→2AB has already been studied through Monte Carlo simulation via a model based on Langmuir–Hinshelwood (thermal) mechanism. The results of this study are well known. There is single transition point (yC) at yB=0.5 (where yBis partial pressure of B2dimer in gas phase), which separates the two poisoned states from each other. Here, we have studied this reaction on the basis of a nonthermal model, which involves the precursor motion of B2molecule. The most interesting feature of this model is that it yields a steady reactive window. The phase diagram is similar to the ZGB model. The reactive window is separated by continuous and discontinuous irreversible phase transitions. The width of the reactive window depends upon the mobility of the precursors. The dependence of production rate on partial pressure of B2is shown by simple mathematical equations in our model. Some interesting results are observed when reaction between precursors and chemisorbed B atoms is considered.

Kinetic phase transitions in the reaction CO+O→CO2 on Ir(111) surfaces

The oxidation of CO on Ir(111) surfaces was investigated under UHV conditions in the temperature range 360 K to 700 K by CO2 rate measurements utilizing mass spectroscopy. Steady-state CO2 rates were measured at constant total CO+O2 gas flux and variable gas composition (YCO=Y, YO2=1−Y) using mass flow controllers which allowed changes in the CO/O2 gas composition down to 0.1%. Between 360 K and 450 K the CO2 rates initially increase proportional to Y (T&amp;lt;400 K) or to Y1.5 (420 K&amp;lt;T&amp;lt;450 K) and exhibit a sudden drop to a negligible value at a temperature-dependent critical value Y*. The rate drop indicates a kinetic phase transition induced by CO poisoning of the surface. This behavior is similar to the features described by the ZGB and more recently developed lattice gas (LG) models of the CO+O reaction on surfaces. However, in contrast to the ZGB model but in accordance with LG models and experimental results on other platinum metal surfaces, no oxygen poisoning was observed at small Y, i.e., the surface was reactive even at the lowest attainable values of Y. Between 450 K and 530 K the initial CO2 rates remain proportional to Y1.5 up to critical Y* values but the kinetic phase transition softens due to the onset of CO desorption. Accordingly, CO poisoning is not complete and the CO2 rates do not attain the zero level beyond the transition. Above 530 K a kinetic phase transition is no longer seen since substantial CO desorption prevents poisoning, in accordance with conclusions from LG modeling. The kinetic phase transitions, their dependence on Y and temperature, and the measured CO2 rates can be excellently reproduced by simple kinetic modeling.

Monte Carlo simulations of the short time dynamics of a first-order irreversible phase transition

The ZGB model (Ziff–Gulari–Barshad, Phys. Rev. Lett. 56 (1986) 2553) for the catalytic oxidation of carbon monoxide has a single parameter given by the normalized partial pressure of CO molecules ( P CO). For P CO⩾ P CO Coex≃0.52583 the surface of the catalyst becomes irreversibly covered by CO molecules and the system cannot escape from this state. However, for P CO slightly below P CO Coex the system reaches an active stationary state. So, just at P CO Coex a sharp first-order irreversible phase transition is observed. It is shown that a study of the short time dynamics of the ZGB model allows to obtain a fairly accurate evaluation of the upper spinodal point given by P CO Usp≃0.52675(5). This figure is in excellent agreement with extensive simulations performed using the constant coverage ensemble.

Catalytic formation of ammonia: a lattice gas non-thermal Langmuir–Hinshelwood mechanism

The catalytic formation of ammonia synthesis through dimers N 2 and H 2 has been studied through Monte-Carlo simulation via a model based on lattice gas non-thermal Langmuir–Hinshelwood mechanism, which involves the precursor motion of H 2 molecule. The most interesting feature of this model is it yields a steady reactive window, which is separated by continuous and discontinuous irreversible phase transitions. The phase diagram is qualitatively similar to well-known ZGB model. The width of the window depends upon the mobility of precursors. The continuous transition disappears when mobility of precursors is extended to third nearest neighbourhood. The dependence of production rate on partial pressure of hydrogen is predicted by simple mathematical equations in our model. Some more interesting results are observed when reaction between precursors and chemisorbed hydrogen atoms is considered.