One-dimensional Transient Model Research Articles

Simulation of Total Harmonic Distortion of Solid Oxide Fuel Cells for Carbon Deposition Detection

Abstract Identifying the degradation mechanisms at the early stage of operation is important for the long-term operation of solid oxide fuel cells (SOFCs). Compared to conventional methods, total harmonic distortion analysis (THDA) can significantly reduce the test time for identifying performance degradation during SOFC operation. In this study, a one-dimensional transient elementary reaction kinetic model of an SOFC fueled with syngas is developed. The model incorporates the coupling effect of elementary chemical and electrochemical reactions, the electrode microstructure, the charge and mass transport processes, and the detailed evolution reaction of surface adsorbed carbon. A THDA simulation calculation method was developed and applied to determine the failure mode of anode carbon deposition. The amplitude, duration, and harmonic number of the perturbation signal are determined to improve fault detection for THDs. The results show that the use of THD can not only detect carbon accumulation behavior at the early stage of SOFC operation but also distinguish the specific degradation mechanism caused by carbon deposition: the hindered SOFC charge transfer reaction can be detected in the frequency range of 100-4000 Hz, and the hindered gas diffusion process inside the anode can be detected in the frequency range of 0.01-10 Hz.

Design, analysis and optimisation of a novel adiabatic-isothermal CAES system with coupled stepped phase change energy storage unit

Compressed air energy storage (CAES) technology is one of the important technologies to address the instability of renewable energy sources. To further make full use of the system heat of compression and reduce the problem of energy grade dissipation inside the accumulator, this paper proposes a novel CAES system coupled with a graded phase change thermal energy storage unit (SP-TES) and near isothermal compression of a liquid piston. A combination of adiabatic compression and near-isothermal compression is used to reduce the generation of compression heat, while the graded storage of compression heat through SP-TES reduces the reduction of energy grade. The design of the proposed SP-TES is carried out through the binary eutectic theory, and a one-dimensional transient entransy dissipation model, a thermodynamic model and an economic model are developed to analyze the 4E performance (energy, exergy, entransy, and exergoeconomic) of the proposed SP-TES. Further, the effect patterns of key node parameters on the proposed system are investigated by developing system related models and the system is optimized with multiple objectives from the point of view of economic and thermodynamic performances. The results show that the 4E performance of SP-TES is in between that of high and low temperature single-stage accumulators, and that SP-TES combines the advantages of higher economic performance of single-stage low-temperature accumulators and higher thermal performance of single-stage high-temperature accumulators. The SP-TES with a temperature range of 350 K-451 K is gradually stabilized with the number of charging and discharging, and the efficiency of the system in the stabilization stage is 73.24 %. The SP-TES with a temperature range of 407 K-440 K has the best economic performance with exergoeconomic parameter of 360.05 kJ/USD. The thermal storage performance and power output of the SP-TES decreases with the increase in the number of stages. The multi-objective optimization results show that the new CAES system efficiency is 63.03 % and the design is optimal when the unit energy cost is 0.2217 $/kWh.

Modelling and Design of a Novel Integrated Heat Exchange Reactor for Oxy-Fuel Combustion Flue Gas Deoxygenation

The concentration of residual O2 in oxy-fuel combustion flue gas needs to be reduced before CO2 transportation, utilization, or storage. An original application of the printed circuit heat exchanger (PCHE) for catalytic combustion with natural gas (catalytic deoxygenation) is described for reducing the residual O2 concentration. The PCHE design features multiple adiabatic packed beds with interstage cooling and fuel injection, allowing precise control over the reaction extent and temperature within each reaction stage through the manipulation of fuel and utility flow rates. This work describes the design of a PCHE for methane–oxygen catalytic combustion where the catalyst loading is minimized while reducing the O2 concentration from 3 vol% to 100 ppmv, considering a maximum adiabatic temperature rise of 50 °C per stage. Each PCHE design differs by the number of reaction stages and its individual bed lengths. As part of the design process, a one-dimensional transient reduced-order reactor model (1D ROM) was developed and compared to temperature and species concentration axial profiles from 3D CFD simulations. The final design consists of five reaction stages and four heat exchanger sections, providing a PCHE length of 1.09 m at a processing rate of 12.3 kg/s flue gas per m3 PCHE.

Tuning mono-divalent cation water composition by the capacitive ion-exchange mechanism

Soil salinization poses a significant challenge to agricultural activities. To address this, the agricultural industry seeks an irrigation water solution that reduces both ionic conductivity and sodium adsorption rate (SAR), thereby diminishing the risks of soil sodification and fostering sustainable crop production. Capacitive deionization (CDI) is an attractive electrochemical technology to advance this search. Recently, a one-dimensional transient CDI model unveiled a capacitive ion-exchange mechanism presenting the potential to adjust the treated water composition by modifying monovalent and divalent cation concentrations, thereby influencing the SAR index. This behavior would be achieved by using electrodes rich in surface functional groups able to efficiently capture divalent cations during conditioning and releasing them during charging while capturing monovalent ions. Beyond the theoretical modelling, the current experimental research demonstrates, for the first time, the effectiveness of the capacitive ion-exchange mechanism in a CDI pilot plant using real water samples spiked with solutions containing specific mono and divalent ions. Electrosorption experiments and computational modeling, specifically Density-Functional Theory (DFT), were used along with the analysis of the surface functional groups present in the electrodes to describe the capacitive ion-exchange phenomenon and validate the steps involved on it, highlighting the conditioning as a critical step. Various operational and flow modes confirm the versatility of CDI technology, achieving separation factors (RMg/Na) of 5–6 in batch, raising production from 0.5 to 0.8 L m−2 h−1 (batch) to 8.0–8.1 L m−2 h−1 when using single pass although reducing RMg/Na to 2. The reliability of the CDI technology in reducing SAR was also successfully tested with different influent compositions, including magnesium and calcium. Finally, the robustness of the capacitive ion-exchange mechanism was validated by a second CDI laboratory 9-cell stack cycled over 350 cycles. Our results confirm the reported theoretical model and expands the conclusions through the experiments in a pilot plant showing direct implications for employing CDI in agricultural applications.

A comprehensive examination of the linear and numerical stability aspects of the bubble collision model in the TRACE-1D two-fluid model applied to vertical disperse flow in a PWR core channel under loss of coolant accident conditions

The one-dimensional Two-Fluid concept uses an area-average approach to simplify the time and phase-averaged Two-Fluid conservation equations, making it more suitable for addressing difficulties at an industrial scale. Nevertheless, the mathematical framework has inherent weaknesses due to the loss of details throughout the averaging procedures. This limitation makes the conventional model inappropriate for some flow regimes, where short-wavelength perturbations experience uncontrolled amplification, leading to solutions that need to be physically accurate. The critical factor in resolving this problem is the integration of closure relations. These relationships play a crucial function in reintroducing essential physical characteristics, thus correcting the loss that occurs during averaging and guaranteeing the stability of the model. To improve the accuracy of predictions, it is essential to assess the stability and grid dependence of one-dimensional formulations, which are particularly affected by closure relations and numerical schemes. The current research presented in the text focuses on improving the well-posedness of the TFM, specifically within the TRACE code, which is widely utilized for nuclear reactor safety assessments. Incorporating a bubble collision model in the momentum equations is demonstrated to enhance the TFM's resilience, especially in scenarios with high void fractions where conventional TFMs may face challenges. The analysis presents a linear stability analysis performed for the transient one-dimensional Two-Fluid Model of system code TRACE within the framework of vertically dispersed flows. The main emphasis is on evaluating the stability characteristics of the model while also acknowledging its susceptibility to closure relations and numerical techniques.

Exploration of Temperature Inversion in Intermediate Joints of 10 kV Three-Core Cable

In order to precisely ascertain the temperature at the hot spot within the intermediate joint of a three-core cable, this study focused on a 10 kV three-core cable joint as its primary subject. A three-dimensional finite element model of the cable joint was constructed, enabling the calculation of both the steady-state hot spot temperature field distribution and the transient temperature rise curve of the joint. Employing a one-dimensional transient thermal path model for the cable body, a radial inversion model for the cable core temperature was established. Through simulating the transient temperature field of the cable joint under varying currents, a fitting relationship was determined for the axial temperature points of the cable core. Subsequently, an inversion perception model was devised to calculate the hot spot temperature of the cable joint based on temperature measurements at specific points on the outer surface of the cable. Under both continuous and periodic loads, the inversion results revealed a consistent trend in the temperature at the joint crimping point with the finite element calculation outcomes, demonstrating a maximum error of within 3 degrees Celsius. This verification underscores the precision of the temperature combination inversion method when applied to three-core cable joints.

ONE-DIMENSIONAL TRANSIENT MODEL OF FOOD PRODUCT TEMPERATURE AND WEIGHT LOSS EVOLUTION IN A VACUUM COOLER WITH MEMBRANE HUMIDIFICATION

A one-dimensional, transient model was developed to predict the temperature and weight loss evolution of a food product cooled using a vacuum cooling system with membrane humidification. The model included the following: (1) a sub-model based on the mass conservation of air and vapor inside the vacuum chamber; (2) a sub-model based on the coupled mass and heat transfer with inner vapor and heat generation; and (3) a sub-model based on the mass conservation of water vapor along the flow channels inside the humidifier. The vacuum chamber pressure was reduced from 1 atm to 2200 Pa using a vacuum pump with deflating speed of 500 m3/hr and condenser and membrane humidifier operating temperatures of 13°C and 60°C, respectively. A meat joint with a weight of 5.30 kg was cooled from an initial core temperature of 74°C to below 10°C. The conventional and modified models both cooled the food product to 10°C in 25 minutes. It was found out that increasing the chamber relative humidity reduced the surface water evaporation while the internal evaporation rate remained the same. Thus, the meat's moisture content, which was initially at 73.51%, was reduced to only 65.44%-an improvement from the conventional vacuum cooling system's 64.31%. This translated to product weight loss of only 10.98%, which represented significant progress compared to the conventional system's 12.51%. The simulation results indicated that employing humidification in a vacuum cooling system reduces the product total moisture loss while maintaining the rapid cooling rate.

A one-dimensional transient temperature prediction model for Chinese assembled solar greenhouses

The prediction of the thermal environment of greenhouses has always been an essential component of greenhouse development. In this paper, a one-dimensional transient temperature prediction model is constructed based on the principle of energy balance for Chinese assembled solar greenhouses (CASG). The daily temperature trends for each surface in the greenhouse were obtained by solving the model using MATLAB. The performance of the model was assessed by comparing the measured and predicted values. The mean absolute errors for the temperature of air, back roof, front roof, heat collector plate, north wall, ground and water storage tank were computed to be 1.4 °C, 1.89 °C, 1.98 °C, 2.07 °C, 2.26 °C, 1.44 °C and 0.68 °C, respectively. The results demonstrate a high level of concurrence between the simulated and measured values, indicating that the model is proficient in predicting the thermal environment of CASG. Based on this, predictions were made regarding the internal environment of CASG on both sunny and cloudy days, which contributes to a comprehensive understanding of the thermal environment. The research provides theoretical support for regulating environmental conditions of CASG.

Investigation of modeling challenges of PEM fuel cells cold start operation

In this study a one-dimensional transient isothermal model was implemented in MATLAB to conduct an in-depth evaluation of available modeling framework for cold start simulation of PEMFC. In this regard, several shortcomings were addressed and a combination of modifications introduced by other researchers and assumptions made in this study was used to improve modeling accuracy; reaction kinetics variation with temperature and ionomer water content was investigated and incorporated in the model; dynamics of nucleation and subcooling was described by Johnson-Mehl-Avrami-Kolmogorov (JMAK) and Classical Nucleation theories; effect of temperature on ECSA loss was examined and assumptions were made regarding electro-osmotic drag in catalyst layer under low load conditions. The results showed high fidelity to experiments in the early stage of cold start and the model was able to capture the effect of all three influential parameters, i.e. temperature, initial ionomer water content, and current density on performance evolution and failing time in isothermal cold starts with acceptable accuracy. Moreover, the linear performance drop at low subcooling and the nonlinear relation between cold start duration and initial ionomer water content were properly reproduced by the model.

Mathematical model of unsteady flow in a natural circulation helium loop

This article presents a one-dimensional transient mathematical model of a helium thermosyphon, which was validated experimentally and shows agreement with measurement. The novelty stems mainly from its complexity, ability to cover real-world scenarios and a large variety of (not only) large-scale thermosyphon devices. The model uses scenario-driven boundary conditions that replicate the operation of the physical model, including the accumulation of heat energy in the solid parts of the heat exchangers and changes in mass of the flowing medium. The model is implemented using both the Eulerian fixed control volume approach and the Lagrangian particle moving approach, along with the pressure correction algorithm, which is innovative too. This paper contains a comprehensive description of the model algorithm, testing of numerical properties, such as sensibility to time step value and grid density; and the heat accumulation effect. The optimal model settings are presented. In addition, a comparison with experimental data is provided. The best agreement between model and measurement was obtained for pressure values (97% of data samples were below 5% of relative error), followed by temperature values (71% of data samples were below 5% of relative error). The model and measurement exhibited the poorest agreement in velocity values, with only 33% of data samples falling below the 5% relative error threshold.

Partially transient one-dimensional thermal-flow model of a heat exchanger, upwind numerical solution method and experimental verification

Partially transient one-dimensional thermal-flow model of a heat exchanger, upwind numerical solution method and experimental verification

Extreme Monovalent Ion Selectivity Via Capacitive Ion Exchange

Capacitive deionization (CDI) is an emerging technology applied to brackish water desalination and ion selective separations. A typical CDI cell consists of two microporous carbon electrodes, where ions are stored in charged micropore via electrosorption into electric double layers. For typical feed waters containing mixtures of several cations and anions, some of which are polluting, models are needed to guide cell design for a target separation, given the complex electrosorption dynamics of each species. An emerging application for CDI is brackish water treatment for direct agricultural use, for which it is often important to selectively electrosorb monovalent Na+ cations over divalent Ca2+ and Mg2+ cations. Recently, it was demonstrated that utilizing constant-voltage CDI cell charging with sulfonated cathodes and short charging times enabled monovalent-selective separations. Here, we utilize a one-dimensional transient CDI model for a flow-through electrode CDI cell to elucidate the mechanisms enabling such separations. We report the discovery that an asymmetric CDI cell with a chemically functionalized cathode induces electric charges in the pristine anode at 0 V cell voltage, which has important implications for monovalent cation selectivity. Leveraging our mechanistic understanding, with our model we uncover a novel operational regime we term “capacitive ion exchange”, where the concentration of one ion species increases while competing species concentration decreases. This regime enables resin-less exchange of monovalent cations for divalent cations, with chemical-free electrical regeneration.

Numerical Simulation of the Carbon Deposition Mechanism of Solid Oxide Fuel Cells Based on Total Harmonic Distortion Analysis

Identifying the corresponding degradation mechanisms at the early stage of operation is important for the long-term stable operation of solid oxide fuel cells (SOFCs). This paper uses total harmonic distortion analysis (THDA) to identify the anode carbon deposition mechanism in the early stage of SOFC operation with carbon-containing fuels. An accelerated calculation model for the electrochemical impedance spectrum (EIS) and a total harmonic distortion calculation model were constructed to study the carbon deposition mechanism and carbon removal strategy of SOFC anodes based on a one-dimensional transient elementary reaction kinetic model of an SOFC fueled by a CH4/H2O mixture. It is shown that the THDA calculation model can identify the primary stages of carbon deposition on SOFC anodes at specific frequencies. The THDA profiles at frequencies greater than 2 kHz contain essentially the same key information as at lower frequencies, suggesting that THDA can significantly reduce the test time for identifying performance degradation in the early stages of SOFC operation compared to EIS. Using a mixture of hydrogen and water vapor to remove the solid carbon generated by the cell anode and restore it to its initial performance, the THDA computational model can successfully respond to this process.

Heat Transfer in a Silo Containing Rice: Solution by the Explicit Method of the Finite Differences with Approximations of Order 2 and 4 for a One-Dimensional Transient Model

Rice is one of the most consumed cereals in the world, and the cultivation of this crop has significant relevance in the southern region of Brazil. When subjected to inadequate conditions of temperature and humidity, rice becomes susceptible to attacks from pests and fungi and, therefore, care in the storage process is of paramount importance, since this is largely responsible for the quality of the harvest. Such care allows the food to arrive without harm to the consumer. In this sense, the mathematical modeling, among numerous possibilities, allows for evaluating the internal temperature of a silo and, through this, taking preventive measures so that the grains maintain their quality. The objective of this work is to model the heat transfer process in a silo prototype containing rice in husk through the explicit finite difference method for a one-dimensional and transient model considering two approaches centered on the spatial derivative: error of order 2 and 4. In addition, the thermal diffusivity of the grain with average value was analyzed. The results obtained by the solutions were analyzed through graphs and statistical indexes comparing with the experimental data of the literature, and the computer simulation was performed through the Google Colab platform. The chosen methodology proved effective for the work, and the predicted temperatures for the approximations of order 2 and 4 denote similarities both graphically and in the precision of the statistical indexes.

Numerical modeling of transient cuttings transport in deviated wellbores

Hole-cleaning optimization is one of the major challenges while drilling long-reach horizontal wells. Accumulation of cuttings can affect the equivalent circulating density (ECD) by decreasing the open flow area and increasing the average density of the drilling fluid. The transient development or removal of cuttings bed due to variation of operating parameters are often ignored in the majority of prior numerical studies. In this paper, it is aimed to develop a transient cutting transport model to predict ECD while drilling. A one-dimensional transient two-phase hydraulic model based on the drift-flux approach is developed to predict the cuttings transport considering cuttings deposition and entrainment. The numerical method employs an upwind scheme to discretize the governing equations. To account for the effect of operating parameters on the cuttings bed, two empirical correlations were employed from the literature. A new empirical correlation is also developed for the prediction of cuttings bed hold-up through regression analysis of the experimental results of a published study. A computer program is developed to solve the governing equations and predict the ECD taking into account the effect of suspended cuttings and cuttings bed along the wellbore trajectory. The numerical model is validated by comparing the predicted return weight of cuttings with measured data in the literature for the cases of no pipe rotation and pipe rotation. The effects of employed empirical correlations on predicted ECD profiles are also examined for a hypothetical well. It is realized that the predicted cuttings bed area of the proposed correlation falls between the predictions of the existing empirical correlations. It is concluded that the most conservative prediction in terms of cutting accumulation in the wellbore cannot necessarily yield a conservative prediction in terms of ECD for early times.

Door to diuretics time is longer among heart failure patients with atrial fibrillation

Hole-cleaning optimization is one of the major challenges while drilling long-reach horizontal wells. Accumulation of cuttings can affect the equivalent circulating density (ECD) by decreasing the open flow area and increasing the average density of the drilling fluid. The transient development or removal of cuttings bed due to variation of operating parameters are often ignored in the majority of prior numerical studies. In this paper, it is aimed to develop a transient cutting transport model to predict ECD while drilling. A one-dimensional transient two-phase hydraulic model based on the drift-flux approach is developed to predict the cuttings transport considering cuttings deposition and entrainment. The numerical method employs an upwind scheme to discretize the governing equations. To account for the effect of operating parameters on the cuttings bed, two empirical correlations were employed from the literature. A new empirical correlation is also developed for the prediction of cuttings bed hold-up through regression analysis of the experimental results of a published study. A computer program is developed to solve the governing equations and predict the ECD taking into account the effect of suspended cuttings and cuttings bed along the wellbore trajectory. The numerical model is validated by comparing the predicted return weight of cuttings with measured data in the literature for the cases of no pipe rotation and pipe rotation. The effects of employed empirical correlations on predicted ECD profiles are also examined for a hypothetical well. It is realized that the predicted cuttings bed area of the proposed correlation falls between the predictions of the existing empirical correlations. It is concluded that the most conservative prediction in terms of cutting accumulation in the wellbore cannot necessarily yield a conservative prediction in terms of ECD for early times.

Numerical and experimental study on water-heat-salt transport patterns in shallow bare soil with varying salt contents under evaporative conditions: A comparative investigation

Soil salinization is aggravated by evaporation, resulting in salt crystallizing on the soil surface. Soil salinization is harmful to agriculture and has significant implications for the engineering and construction industry. Therefore, this paper investigates water and salt transport in saline soils through comparison of numerical simulations with indoor evaporation tests. Based on Darcy's law, ideal gas law, mass conservation law, and energy conservation law, a one-dimensional transient mathematical model of coupled water-heat-salt transport is derived. The bottom of the model represents a recharge boundary condition, the sides of the soil column are insulated and impermeable, and the top serves as a heat source. The results show that the greater the salinity of the soil, the more drastic the temperature change, and at the same time, the greater the water retention of the soil. The temperature gradient along the height of the soil column provides a tremendous driving force for water-salt transport, and although the volumetric water content of the soil column at 3 ∼ 4 cm dissipates quickly, there is a gradient of increasing salt concentration towards the ends and decreasing towards the middle. The modeled results agree with the experimental data, indicating that the model can effectively simulate the water-heat-salt transport process for different saline sites under evaporation conditions. The model is essential for the improvement of saline soils and for finding new methods to prevent further soil salinization.

One-dimensional transient numerical model and characteristic analysis for a double helix tube of conical J-T cryocooler

An open cycle miniature J-T cryocooler can provide a clear advantage over other cryocoolers in terms of the smaller size, faster cooling down, and no moving parts. In recent years, some experimental research has shown that the progress of heat exchanger technology promotes the application of miniature J-T cryocoolers in the field of infrared detection. Especially micro-finned double helix tube heat exchangers provide good performance for a conical J-T cryocooler. In order to study its rapid cooling mechanism, a one-dimensional numerical model is established for analyzing this unique flow and heat transfer characteristics in such a conical heat exchanger of J-T cryocooler, and the model algorithm is proved to be effective and efficient by the experiments for rapidly calculating entire J-T cryocooler. The simulated results show that the application of double layers conical helix tubes not only enhances heat transfer areas at the same mass flow rate but also optimizes the thermal mass distribution in the heat exchanger such that this part of thermal mass near the evaporator is reduced. Thus, the high-pressure working fluid can be cooled rapidly and throttled to a two-phase state, improving the heat transfer efficiency of the impact jet flow. On the other hand, excessively high vessel pressure will affect the saturation pressure in the evaporator, resulting in a cooling rate reduction. An appropriate vessel pressure can be found for a fast cooling rate by optimal evaporator pressure. In addition, studies revealed that the temperature drop resulting from the adiabatic discharge of the pressure vessel plays an indispensable role in the fast cooling process.

Investigation on the Flow Instability of Supercritical Hydrocarbon Fuels in Cooling Channels

Flow instability in regenerative cooling channels is an important issue for the thermal protection of hypersonic scramjet engines. Taking into account the dynamic process of the heat transfer and flow instability, a one-dimensional transient model with several modules (including the cracking reaction, convective heat transfer, and rapid calculation of thermal properties) has been developed to investigate the flow instability characteristics of supercritical hydrocarbon fuels in cooling channels. The calculated results were compared and validated against the available experiments and numerical benchmarks, attaining good agreements. By virtue of the transient simulations, the dynamic flow patterns under different flow rates were studied in a single cooling channel with -decane being the working substance. Then, the influences of the operating pressure and heated length on the in-tube flow were further investigated. In addition to the Ledinegg instability, several dynamic instability modes were detected under different external driving forces. It was also observed that under a specific range of pressure drop, the in-tube flow could transition from the density-wave oscillation to a new steady state. Moreover, this flow excursion was more likely to be triggered when decreasing the operating pressure or channel length.

Modelling of atmospheric water generation using desiccant coated heat exchangers: A parametric study

Water scarcity is a significant issue in developing countries and remote locations, however, atmospheric water vapour is a widely available and yet underutilised water reservoir. Desiccant coated heat exchangers are a potential sorption reactor for multicyclic atmospheric water generation due to the enhanced heat and mass transfer to the desiccant. This study utilised a transient one-dimensional mathematical model for a plate-fin desiccant coated heat exchanger and adapted the model for atmospheric water generation. From this, a heat and mass transfer analysis and parametric study were conducted to determine the effect of the operational and geometric parameters on the specific water production and specific energy consumption. The heat and mass transfer analysis found that the coating at the inlet and outlet regions of the channels were underutilised. The parametric study found that the adsorption and desorption cycle times should be optimised independently, the primary air velocity should be high during adsorption and low during desorption, and secondary channel cooling during adsorption did not significantly improve performance. The highest specific water production and the lowest specific energy consumption recorded in this study were 5.8 L kg−1 day−1 and 7.7 MJ L-1 respectively. The recorded specific water production values were higher than most desiccant based atmospheric water generators in the literature. However, the performance was significantly reduced at higher ambient temperatures.