Two-dimensional Steady-state Model Research Articles

Optimization of tree-shaped fin structures towards enhanced discharging performance of metal hydride reactor for thermochemical heat storage based on entransy theory

Integrating fin structures into metal hydride (MH) bed can enhance heat discharging performance of the reactor for thermochemical heat storage. In this study, based on the entransy theory, the entransy dissipation rate (Eh,st) or the entransy dissipation (Eh,tr) of a simplified two-dimensional (2D) steady-state or transient heat conduction model for the MH bed was used to be an objective to optimize the tree-shaped fin (TSF) structures. Furthermore, response surface method (RSM) was adopted to explore the relationship between Eh,st or Eh,tr and structural parameters (i.e., branch number N, branch level M, length ratio α, width index β, and angle ratio γ). The results show that RSM can effectively predict influences of structural parameters of TSFs on heat discharging performance. Based on RSM with entransy theory, the obtained optimal combination parameters were N = 8, M = 3, α = 1, β = 0.5, and γ = 1, corresponding to the maximum gravimetric exergy-output rate (GEOR) of 20.98 W/kg. Furthermore, the GEOR with optimized fins was 11.5 % higher than that with unoptimized TSFs. The optimization method based on the entransy theory was effective to optimize the TSF structures by solving 2D model instead of three-dimensional model, and shorten the calculation time for optimization.

Approach to chemical equilibrium of water dissociation for modeling bipolar membranes in acid-base flow batteries

Understanding the behavior of bipolar membranes under forward and reverse bias in multi-ion solutions is essential for their application in acid-base flow batteries (ABFB). To this end, a two-dimensional steady-state model of the bipolar membrane is proposed based on the Nernst-Plank and Poisson equations coupled with water dissociation and acid-base neutralization reactions. The second Wien effect and catalytic activity are included in the water dissociation rate model at the bipolar junction. Experimental current-voltage curves were obtained using linear sweep voltammetry to validate the model. A commercial bipolar membrane was used in NaCl solutions at 0.25 and 0.5 mol L−1 concentrations, a mixture of NaCl-HCl and NaCl-NaOH solutions at different concentrations, and solutions of HCl and NaOH at 0.5 mol L−1 concentration. The catalytic activity coefficient was the only model parameter fitted to the experimental data; all other properties and parameters were obtained from the literature or calculated from the membrane supplier data. The numerical solution of the bipolar membrane model complements the experimental results. It shows a full view of conductivity, ion concentration, and potentials across the bipolar membrane as a function of its polarization.

Simulation of Heat and Mass Transfer in Pulverized Coal Boiler Based on Gaseous Combustion Through Phase Separation Technique

Abstract In order to meet the current environmental protection ultra-low pollutant emission requirements, one-step combustion is changed into two-step combustion by split-phase gasification combustion technology, and double-furnace structure, graded air distribution, calcium injection desulfurization, and combined denitrification with selective non-catalytic reduction (SNCR) and selective catalytic reduction (SCR) are adopted to reduce pollutant emissions. ansys was used to establish a two-dimensional steady-state structure model of pulverized coal boiler with a double-furnace. Finite element analysis was carried out on the combustion in 54 MW, 56 MW, and 58 MW working conditions under different calcium-sulfur (Ca/S) ratios. The results showed that the desulfurization efficiency increased gradually when the Ca/S ratio was between 1.0 and 2.6 under the three working conditions. The desulfurization efficiency has no noticeable change when it is between 2.6 and 2.8, and begins to decline when it is greater than 2.8. The optimal calcium-sulfur ratio is obtained when the calcium-sulfur ratio is 2.6, and the SO2 concentration at the outlet of the furnace is reduced to 0.0001 mg/m3. By controlling the highest temperature in the furnace and adjusting the amount of denitrification agent, the nitrogen oxide emission at the outlet of the furnace is reduced to 0.87 mg/m3.

A Novel Similarity Solution Approach Based Thermal Performance Prediction and Environmental Analysis of Evacuated U-Tube Solar Collector Employing Different Mono/Hybrid Nanofluids

In this article, a novel similarity function-based two-dimensional steady-state model is developed to analyze the thermal performance of an individual evacuated U-tube solar collector (EUTC). Using the developed model, the energy and environment assessments of a EUTC have been carried out employing different water-based mono/hybrid nanofluids as energy exchange fluids (EEF). The influence of nanoparticle volume concentration on energy gain, mass flow rate reduction, and efficacy has been analyzed. The influence of Reynolds number on energy gain is also investigated. The results show that Al2O3+MWCNT (multiwalled carbon nanotube) has high energy gain, whereas MgO has high mass flow reduction compared to water as a base fluid at 2% volume concentration. The efficacy of EUTC has been enhanced using nanoparticles as an additive. Employing Al2O3+MWCNT as EEF, the impact of EEF flow rate, EEF inlet temperature, ambient temperature, and solar intensity on the energy gain and efficacy of EUTC have been analyzed. It is observed that solar intensity and ambient temperature have major and minimum influence on EUTC performance.

Numerical simulation of inner characteristics in COREX shaft furnace with center gas distribution: influence of bed structure

Abstract The packed structure, such as packing density and particle size distribution, of COREX shaft furnace, directly affects the gas flow and reaction process. A two-dimensional steady-state mathematical model was developed to study the influence of five packed structures on the gas flow, pressure distribution, species composition, and solid metallization rate in a COREX shaft furnace with center gas supply. The results show that the gas velocity is relatively uniform along the radial direction under Case-P. Under Case-InV and Case-V, the gas velocity increases and decreases gradually from the center to the wall zone respectively. The gas velocity contour in the upper part of the shaft in Case-M is ‘M’ shape, while it shows ‘W’ shape in Case-W. The order of pressure drop under five packed structures is Case-P > Case-M > Case-W > Case-InV > Case-V, and for the solid metallization rate, the order is Case-V > Case-W > Case-P > Case-M > Case- InV. As Case-V has the lowest pressure drop and largest metallization rate, the charging matrix in practical production should develop towards a ‘V’ shaped burden profile in the upper of the packed bed in the COREX shaft furnace.

Optimization of SMR process for syngas production through a solar-assisted thermo-chemical reactor with a multi-layered porous core

A two-dimensional steady-state axisymmetric model is developed to analyze the performance of a thermo-chemical porous reactor used for syngas and subsequently hydrogen generation through the steam methane reforming (SMR) process. The finite volume method coupled with kinetics thermo-chemical reaction and local thermal non-equilibrium (LTNE) model with modified P1 approximation is employed to obtain the temperature distribution for both the fluid and porous zones. First, the effects of inlet mass flow rate, inlet steam to methane ratio, porosity, number of pores per inch (PPI), permeability, and reactor length on reactor performance are scrutinized. Next, to optimize the performance of the reactor, an artificial neural network (ANN) is developed to obtain the maximum hydrogen generation rate concerning the effective parameters. Finally, a two-layer porous foam is utilized as the catalyst zone to further improve the performance. Results show that increasing inlet flow rate leads to temperature decline and causes an incomplete reaction. Also, increasing porosity enhances heat absorption at the inlet and decreases radiative heat transfer through the porous foam. At a specified condition (ṁ= 0.25 kg.h−1, XCH4/XH2O = 1/3, and PPI = 10), increasing the porosity from 0.6 to 0.8 has increased hydrogen production by 27 %, while by a further increase of porosity to 0.9, hydrogen production decreased by 3 %. Results indicate up to 164 % increment in the performance of the optimal case compared to the base case. Furthermore, employing the two-layer porous foam with different PPIs could further increase hydrogen production, up to 20 %, and reduced the pressure drop.

Robust multi-objective optimization of methanol steam reforming for boosting hydrogen production

Methanol steam reforming (MSR) has been considered as a promising method for producing pure hydrogen in recent decades. A comprehensive two-dimensional steady-state mathematical model was developed to analyze the MSR reactor. To improving high purity hydrogen production, a triple-objective optimization of the MSR reactor is performed. Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is employed as a robust optimization approach to maximize the three objectives, termed as, methanol conversion, CO selectivity, and H2 selectivity. The Pareto optimal frontier has also been provided and the ultimate solution of the Pareto front has been found by the three decision-making methods (TOPSIS, LINMAP, and Shannon's Entropy). Among the three distinct decision-making approaches, LINMAP presents better results according to the deviation index parameter. It has been shown that a perfect agreement is available between the plant and simulation data. Operating under the optimum values based on the LINMAP method confirms an almost 47.04% enhancement of H2 mass fraction compared to the conventional industrial MSR reactor. The predicted results advocate that the key superiority of the optimized-industrial reactor is the remarkable higher production rate of hydrogen compared to the conventional MSR reactor which makes optimized-industrial reactor both feasible and beneficial.

CFD simulation of bubbly flow in a long coaxial heat exchanger

The numerical investigation of a two-phase bubbly flow inside a long vertical counterflow heat exchanger has been performed in this study. The heat transfer was running from the steam moving inside the tubing to the two-phase bubbly water in the annulus. A two-dimensional steady-state heat transfer and fluid flow model are based on the coupling of a probability density function (PDF) coupled with a k-epsilon turbulence model is determined to be the best computation technique in this large-scale case. The k-epsilon model was used to analyze the carrier fluid (water or steam) and the PDF model to calculate bubble flow. The authors desired to receive practical results of the heat transfer process rather than paying attention to the formation of bubbles, their coalescence, tracking flow regimes, and other turbulence-related features that are useless in industrial applications. The article explored two cases: short (800 m) and long heat exchanger (8000 m). Several thermodynamic parameters were on track: flow velocities, pressure, temperature, and concentration of the bubbles in the radial direction. Einstein's correction equation adjusted the viscosity of the bubbles. Solution converged with non-uniform grid spacing in the longitudinal and radial directions. The results gave satisfactory conclusions about the validity of the obtained data with theoretical and experimental results. This article opens a new way on computational fluid dynamics (CFD) application to a large-scale simulation of long vertical or horizontal pipelines and coaxial heat exchangers with the coupled bubbly flow and heat transfer applicable to geothermal and petroleum industry problems.

Optimization of tree-shaped fin structures towards enhanced absorption performance of metal hydride hydrogen storage device: A numerical study

Tree-shaped fins were introduced to improve the heat transfer of metal hydride reactor. A two-dimensional steady-state model was first applied to obtain the optimal geometric structures of tree-shaped fins using genetic algorithm with the constraint of fixed fin mass. Then, the hydrogen absorption performance of MH reactors with embedded radial fins and tree-shaped fins were numerically studied and compared using a multi-physical model. It was indicated that the hydrogen absorption time for 90% saturation for the reactor with optimized tree-shaped fins nearly decreases by 20.7% as compared with that for radial fins. The heat transfer and absorption performance of MH reactor were much sensitive to the length ratio of tree-shaped fins, which can be improved with increasing the length ratio. Besides, the performance of optimized tree-shaped fins reactor with variable angle ratio was only slightly better than that for fixing angle ratio at 1, indicating that the angle ratio of tree-shaped fins can be kept at 1 for simplifying the design. Moreover, the absorption performance of the reactor can be enhanced with increasing the maximum branch level of tree-shaped fins. Furthermore, it was shown that the optimized geometric structures of tree-shaped fins under different MHs thermal conductivities are nearly identical.

Mass transfer simulation of main species in swine biogas slurry in bipolar membrane electrodialysis

The aim of this model is to study the mass transfer of main species in swine biogas slurry in bipolar membrane electrodialysis. We developed a two-dimensional steady-state model composing three compartments. In this model, Nernst-Planck equation and Hagen-Poiseuille equation are combined for mass transfer and Faraday’s law is for the electrolyte current density. The model considers local electroneutrality condition and does allow cations and anions pass through membranes. The set of equations with boundary conditions and initial values are calculated by the finite element numerical method with COMSOL Multiphysics. This model can be able to predict the distribution of electrolyte potential, the ion flux and the ion concentration distribution. The two parameters, cell voltage and inlet velocity, are indicated to have influences on the process of bipolar membrane electrodialysis treatment on swine biogas slurry.

Two-dimensional comprehensive mathematical model for electroslag remelting process with pipe electrode

Taking the electroslag remelting with pipe electrode (ESR-PE) and electroslag remelting with solid electrode (ESR-SE) as the research objects, a two-dimensional steady-state mathematical model of coupled electromagnetic field equation, energy equation, and flow equation was established. The distribution of its current density, Joule heat, flow field, and temperature field was compared and the difference of their molten metal pool was analyzed. The results show that compared with those of ESR-SE, current density distribution and Joule heating area of ESR-PE are mainly concentrated in the inner and outer wall areas of the electrode tip, while the Joule heat generated in the central area of the slag pool is less. In the ESR-PE, the slag flows from the outside of the electrode to the hollow area of the electrode, which makes the temperature distribution in the slag pool is more uniform. Affected by the Joule heating area and flow field, the heat of ESR-SE is concentrated below the electrode in the slag pool area and it transfers from the center to the periphery. However, in the ESR-PE, the heat is concentrated near the inner and outer walls of the electrode tip, and the heat is transferred from the periphery to the center of the slag pool. The molten metal pool depth of ESR-SE is 0.1188 m and that of ESR-PE is 0.0962 m. Compared with that of ESR-SE, the molten metal pool of ESR-PE is shallower and flatter.

Prediction of the cohesive zone in a blast furnace by integrating CFD and SVM modelling

ABSTRACT High efficiency and clean emission operation of a blast furnace are mainly determined by its operating stability, which is closely related to the position of the cohesive zone (CZ) in the blast furnace. In order to monitor the CZ position in real time, a prediction model of the CZ was proposed by combining an off-line computational fluid dynamics (CFD) calculation and support vector machine (SVM) modelling. An axisymmetric two-dimensional steady-state CFD model was established to simulate the fluid flow, heat and mass transfer in the blast furnace shaft. The sample dataset of the CZ information was established based on the CFD off-line calculation, and the prediction of the CZ position was realized by SVM modelling. The results show that the established model can predict the CZ position in real time with high accuracy, providing effective guidance to the blast furnace operation and control.

Performance simulation and optimization of COREX shaft furnace with central gas distribution

To improve the distribution of the reducing gas inside the shaft furnace, recently, a central gas distribution (CGD) device is installed at the bottom of the shaft furnace in Bayi Steel. In this work, a two-dimensional steady-state mathematical model, including momentum, heat and mass transfers and chemical reaction, is developed to study the performance of the furnace with CGD. The model is validated by industrial production data of COREX-3000, and then it is used to study the detailed phenomena in the furnace with CGD. The results show that, compared with the traditional COREX shaft furnace without CGD, the CGD device has a positive effect on improving the solid metallization rate (MR) and gas utilization rate (UR). The solid metallization rate (MR) increases from 0.601 to 0.628, the gas utilization rate (UR) increases from 0.3437 to 0.3519 and the standard deviation (STDEV) of solid MR decreases from 0.0820 to 0.0037, which means that the MR of the DRI from the furnace with CGD is more uniform than that without CGD. In addition, the effects of operation conditions and the CGD design on the solid MR, gas UR and STDEV of MR are discussed and the optimized conditions are suggested.

Development of a Multiphysical 2-D Model of a PEM Fuel Cell for Real-Time Control

This paper presents a computationally efficient two-dimensional (2-D) steady-state model for fuel cell real-time control implementation. Both the fluid and electrochemical physical domains are considered in the proposed real-time model. The fuel cell under-rib convection is fully described by considering the geometry of serpentine channel. In addition, in order to solve the implicit activation voltage loss and further explore the computational performance, three numerical root-searching algorithms: bisection, secant, and Newton-Raphson methods are applied to the proposed implicit iterative solver and compared. The preferred secant method has been proven to effectively improve both the efficiency and robustness performance of the proposed real-time fuel cell model. Moreover, a computational fluid dynamic based COMSOL fuel cell model is used to validate the calculation accuracy. Furthermore, the practical feasibility of the presented real-time model has been verified using an RT-LAB simulator platform from Opal-RT.

Heat and mass transfer in a polymeric electrolyte membrane-based electrochemical air dehumidification system: Model development and performance analysis

In this paper, a two-dimensional steady-state theoretical model was established, to model the internal transport phenomena in a polymeric electrolyte membrane-based (PEM-based) air dehumidification element. The influences of electrochemical reactions, activation and concentration over-potentials, and Ohmic and electro-osmotic effects were considered. The model was solved by the finite difference method with conjugate boundary conditions. So, with this model, the heat, mass and current transfer through the five layers of the element (diffusion layers, catalyst layers and a PEM) could be described theoretically, as well as the convective heat and mass exchange with adjacent airflows. Compared with the results from previous models, this model showed a much closer trend to the experimental data. The overall error was less than 15%, with an acceptable average error of 8.6%. However, greater deviations were observed under larger airflow conditions, probably due to the assumption of laminar airflow and steady-state heat conduction. Furthermore, by the performance analysis, the maximum moisture gradient was found inside the PEM, so the PEM’s parameters could largely affect the system performance. With the increase in PEM water content, the dehumidification was significantly enhanced, especially when the air humidity was high. If the PEM water content was doubled, the dehumidification rate was increased by 42%. Then, decreasing the PEM thickness also improved the performance. However, the effect became minor if the thickness was less than 100 μm. It was also helpful by increasing the PEM conductivity, although the effect of this variable was relatively small. This study provided theoretical guidance for further system improvement and material preparation for PEM-based dehumidification systems.

Computational fluid dynamics study on the anode feed solid polymer electrolyte water electrolysis

A steady-state two-dimensional model for the anode feed solid polymer electrolyte water electrolysis (SPEWE) is proposed in this paper. Finite element procedure was employed to calculate the multicomponent transfer model coupled with fluid flow in flow channels and gas diffusion layers and electrochemical kinetics in catalyst reactive surface. The performance of the anode feed SPEWE predicted by this model was compared with the published experimental results and reasonable agreement was reached. The results show that oxygen mass fraction increases because of the water oxidation when water flows from the import to the export on the anode side. On the cathode side, hydrogen mass fraction varies little since hydrogen and water mix well. The flux of water across the electrolyte increased almost linearly with the increase of the applied current density. Since the ohmic overpotential loss increasing as the solid polymer electrolytes’ thickness increasing, the performance of the anode feed SPEWE with Nafion 112, 115, 117 decreases at the same applied current density.

A novel integrated thermally coupled moving bed reactors for naphtha reforming process with hydrodealkylation of toluene

Due to the importance of catalytic naphtha reforming process in refineries, development of this process to attain the highest yield of desired products is crucial. In this study, continuous catalyst regeneration naphtha reforming process with radial flow is coupled with hydrodealkylation of toluene to prevent energy loss while enhancing aromatics and hydrogen yields. In this coupled process, heat is transferred between hot and cold sections (from hydrodealkylation of toluene to catalytic naphtha reforming process) using the process integration method. A steady-state two-dimensional model, which considers coke formation on the catalyst pellets, is developed and 32 pseudo-components with 84 reactions are investigated. Kinetic model utilized for HDA process is homogeneous and non-catalytic. The modeling results reveal an approximate increase of 19% and 23% in aromatics and hydrogen molar flow rates, respectively, in comparison with conventional naphtha reforming process. The improvement in aromatics production evidently indicates that HDA is a suitable process to be coupled with naphtha reforming.

Modeling of the Flue Gas Condensation for the PM2.5 Removal Efficiency of a Integrated Technology

A combined pseudo-homogeneous and fractal geometry model was developed to simulate the process of a integrated technology. The technology was proposed to replace heat pipes and WFGD, which is based on the theory that liquid membrane and droplets grow in size by vapor heterogeneous condensation with they acting as nucleation centers and then the grown droplets are removed efficiently by using integrated diverse combinations of condenser pipes and a highly efficient scrubber. The model has been approached useful for both analyzing results and aiding in design of the technology by conducting a two-dimensional steady-state model by means of infinitesimal analysis, incorporating with the models of whole fine particles absorption efficiency of a regularly arranged liquid membrane and droplets column group, and the models of geometric classifications for liquid and solid based on the fractal dimension identified by different structural of radius of gyration of liquid–solid interface transition zone. The predicted values were also compared with the experimental results, and they are in excellent agreement. The results showed that: When the fractal dimension df is 0.3, the calculation result is the most closer to actual experiment parameter. The PM2.5 diffusion volume flux value Vw ranges from 22 and 45 mm/s.

Formulation and validation of a two-dimensional steady-state model of desiccant wheels

Desiccant wheels are rotary desiccant dehumidifiers used in air-conditioning and drying applications. The modeling of simultaneous heat and mass transfer in these components is crucial for estimating their performances, as well as for simulating and optimizing their implementation in complete systems. A steady-state two-dimensional model is formulated and implemented, aiming to obtain good accuracy and short computational times with the purpose of inclusion in complete system models. The model includes mass and energy balances and correlations for heat and mass transfer based on empirical relations from the scientific literature. Convective heat and mass transfer coefficients are computed locally accounting for the entrance length effects. Mass diffusion inside the desiccant material is neglected. Comparison with experimental data from the literature shows that the model reproduces the physical behavior of desiccant wheels satisfactorily, as the deviation between the computed results and available data is always within 12%. The simulation time is as low as 3 s for a model with 200 control volumes. It is found that for the applied case, the model provides accurate results for the overall flow using an equiangular control volume discretization with 200 control volumes and no axial discretization. More computationally expensive configurations with axial discretization give more accurate results and information on local flow and desiccant conditions inside the wheel.

Performance characteristics of cross-flow membrane contactors for liquid desiccant systems

Membrane based indirect contact liquid desiccant dehumidification technology subsides the serious concern of liquid desiccant droplet carryover observed in conventional direct contact liquid desiccant systems. In the membrane contactor the air and liquid desiccant streams flow in alternate channels in cross-flow arrangement, separated by micro-porous semi-permeable hydrophobic membranes. Only water vapor can pass through the membranes but liquid desiccant cannot permeate. A two-dimensional steady-state mathematical model for semipermeable membrane based indirect contactors as dehumidifiers for liquid desiccant dehumidification applications has been developed. The model can predict the air and desiccant parameters inside the dehumidifier and the outlet parameters for a given input parameters. Five different membrane contactors have been fabricated and series of experiments have been conducted to validate the mathematical model. Aqueous solution of lithium chloride has been used as desiccant. The maximum deviations between experimental and predicted values are within ±10% for outlet specific humidity and outlet enthalpy of air, ±15% deviation in dehumidification effectiveness and ±20% deviation in enthalpy effectiveness. The distributions of major parameters viz. temperature, humidity, concentration, etc., within the contactor have been presented. Parametric analysis has been carried out to study the effects of membrane characteristics, contactor design, fluid flow rates, ambient conditions and desiccant concentration on the performance of the contactors.