Non-isothermal Model Research Articles

Numerical study on the cavitation flow characteristics of high-pressure fuel in injector orifices based on compressible non-isothermal model

The flow inside the orifices in diesel injector largely determines the injection characteristics, which further affects the performance of the diesel engine. In this paper, numerical simulation is conducted to characterize the fuel flow with characteristics of two-phase cavitation, high speed, high pressure, high turbulence intensity, and high viscosity in two crucial orifice locations. The OZ orifice is selected as a benchmark to select the appropriate turbulence model and cavitation model. The simulation results from different turbulence and cavitation models are analyzed, and the combination of the realizable k–ɛ turbulence model and the Zwart–Gerber–Belamri cavitation model proves to be superior. Then, based on the validated models, the compressibility and non-isothermal characteristics of the fuel and two geometric parameters of the nozzles in an injector are emphatically discussed to depict the cavitation flow. The results suggest that the compressibility and non-isothermal characteristics of fuel affect the mass flow rate, fuel flow velocity, and cavitation extent within the orifices with a maximum deviation of the mass flow rate of 7.1%. However, their influence on the orifice flow coefficient is relatively minor with a maximum deviation of 0.8%. The mass flow rate and flow coefficient are both positively correlated with the rounded edge radius and taper coefficient. A greater rounded edge radius and taper coefficient can lead to a better fuel flow capacity in the nozzle orifice.

Explicit–implicit schemes for non-isothermal filtration problem: Single-temperature model

In this paper, we consider a non-isothermal filtration model for a two-phase immiscible incompressible fluid, for the numerical implementation of which an explicit–implicit algorithm is proposed. The problem is presented in a mixed generalized formulation, and an explicit–implicit method of the IMPES type is used to calculate the pressure, full velocity and water saturation, and an explicit–implicit scheme is built to calculate the temperature and heat flux with explicit consideration of convective heat transfer. At the beginning of the article, the mechanism of temperature homogenization of according to temperature heterogeneous system is considered. In computational experiments, special attention is paid to the comparison of the non-isothermal model with the isothermal one, including the discussion of fingering instability.

Numerical Investigation of the Heat Transfer Characteristics of Liquid Lithium Metal in Spiral Tubes

Abstract The application of liquid lithium as a coolant for the forthcoming era of space nuclear reactors exhibits significant potential, and spiral tube heat exchanger components are commonly used in steam generators for reactors. However, the heat transfer characteristics of liquid lithium in spiral tubes are not yet fully understood. This research establishes a non-isothermal heat transfer model incorporating a modified turbulent Prandtl number to analyze the flow of liquid lithium through spiral tubes with varying geometries. Numerical analysis is carried out focusing on the influence of inlet velocity, the distribution of related parameters, and the geometry of spiral tubes. The results demonstrate that in the range of the dimensionless Dean number 8165–13,063, the Nusselt number and the pressure drop present approximately linear relations with the Dean number. For the distribution law of relevant physical quantities, the inner side of the tube displays an eye-anatomy low-flowrate area and a high-temperature area, while a low-pressure area forms on the inner pipe wall. Finally, the pitch and spiral radius are found to be reduced as much as possible to ensure high liquid lithium-based heat transfer performance with a small pressure drop. The optimized design parameters reveal that within the actual design range of non-dimensional pitch of 0.667–10.667 and curvature of 0.0556–0.1667, the non-dimensional pitch and curvature are 0.667–2.667 and 0.1667, respectively. This study offers valuable insights into the heat transfer properties of liquid lithium within heat exchangers of the spiral tube design, promoting its application in space nuclear reactor power supply.

The main features of compositional modeling algorithms of modern reservoir flow simulators

Modern industrial reservoir flow simulators are integrated software products consisting of several packages. Modeling of gas injection with various compositions, or hydrocarbon recovery from gas-condensate and oil-gas-condensate reservoirs, or thermal recovery methods requires a detailed account for composition of the fluid system. In these cases, compositional (multi-component) flow simulation is used to calculate component distribution between the coexisting phases, the number and the fractions of the phases, together with the flow equations for fluid components.. For this purpose, the flow simulator solves the thermodynamic subproblem using basic methods and algorithms analogous to the fluid modeling (PVT modeling) packages. The paper describes the main principles and specific features of implementation of the compositional modeling algorithms in several modern reservoir flow simulators. Keywords: compositional modeling; multicomponent flow model; reservoir flow simulator; isothermal and non-isothermal compositional modeling.

CFD investigation of the effect of flow field channel design based on constriction and enlargement configurations on PEMFC performance

In this study, a three-dimensional CFD, non-isothermal model was developed to identify an optimal layout for key geometrical parameters of PEMFC flow field designs with constriction and enlargement cross-sections located at the middle of the channel. For this purpose, the effect of channel configurations with both constriction and enlargement cross-sections was explored and compared with a conventional constant channel segment, under varying hydraulic diameter and lengths. As results, the constriction configuration channel with a hydraulic diameter reduction of 50% has shown the best performance among the enlargement and straight channels for all considered lengths. The constriction configuration enhances fluid velocity, resulting in improved flow distribution and relatively increased pressure drop across the flow channels. Moreover, a better temperature distribution, higher oxygen consumption, improved membrane humidification, and water removal were observed. This leads to an increased net power output of the PEMFC. However, considering different hydraulic diameters of the constriction geometry, the best performance of the cell was achieved at a hydraulic diameter reduction of 60%, combined with a length of 4/7 of the total channel length. This optimal balance between pressure drops and reactants’ flow has enhanced the net power of the proposed geometry by 26.30 %, compared to the straight channel. The novel proposed single-channel configuration based on a simple constriction, is a low-cost design that has significantly improved cell performance compared to the straight one. Since operating conditions are crucial for cell performance, the effects of operating temperature and relative humidity were investigated, and the optimum conditions were determined.

Investigation of output performance and temperature distribution uniformity of PEMFC based on Pt loading gradient design

Temperature distribution uniformity within the cathode catalyst layer (CCL) and power density are two crucial parameters to characterize the durability and output performance of proton exchange membrane fuel cells (PEMFCs), which are affected by the Pt distribution within the CCL. Therefore, the temperature distribution uniformity within the CCL and the output performance at different operating voltages for a PEMFC with various Pt loading gradient distributions along the in-plane (IP) direction are investigated in this paper. Moreover, a two-dimensional, two-phase, non-isothermal model is developed, and the concepts of high power density range (HPDR) and temperature uniformity index (TUI) are defined in this study. The results indicate that gradient Pt distribution has the opposite effect on output performance and temperature distribution uniformity at low and medium operating voltages; the improvement of one indicator means the deterioration of another. Besides, the optimal output performance is obtained with the uniform Pt distribution at high operating voltages, while the ideal temperature distribution uniformity is achieved by loading more Pt under the channel. Consequently, the output performance and temperature distribution uniformity must be traded off to obtain optimal comprehensive performance of PEMFC at different operating voltages when designing the Pt loading gradient distribution.

Effects of cathode gas channel design on air-cooled proton exchange membrane fuel cell performance

In the study, the impact of cathode gas channel (CGC) structure on the operation of air-cooled PEMFCs is investigated by a multiphase nonisothermal model. First, the influences of tapered channel configuration on the distribution of key variable distributions are studied. The distributions of these variables are found to be coupled with the reactive transport process within the catalyst layer (CL). The variation of local current density is found to be positively correlated with the dissolved water content. Although the tapered channel design can improve the current density, the weight of the bipolar plates (BPs) will be inevitably increased. Finally, the trapezoidal channel design is proposed aiming at improving the performance without increase of fuel cell weight. Several performance indexes are employed to comprehensively evaluate the different CGC designs, and the results demonstrate that the inverted trapezoidal CGC design, with which good thermal and water management are achieved, presents the best performance among the different CGC designs studied, leading to 18.9 % increase of the mass power density and 18.6 % increase of volume power density compared with the base case design.

Balanced Fast-SpaciMS capillary configurations provide practically noninvasive channel-average measurements in catalytic monoliths

Spatially resolved capillary-inlet mass spectrometry (SpaciMS) provides a detailed picture of the spatiotemporal evolution of reaction network in catalytic monoliths. In the present work, we combine the SpaciMS experiments with a newly developed non-isothermal 3D CFD model for heterogeneously catalyzed reactive flows, including diffusion and permeation through the coated catalyst and channel wall. We explore how the capillary size and sampling rate can be balanced to minimize the impact on probed-channel conversions and provide species concentration measurements representative of the free channel average. In all studied configurations, the balanced sampling-rate fraction is noticeably higher than the corresponding capillary occlusion fraction. For a typical 350-micron capillary that occupies 11% of the channel cross- section, the balanced sampling rate represents 43% of the channel flow. The present work shows that together, a balanced SpaciMS configuration and numerical simulation provide accurate channel-averaged information of a monolithic catalyst under realistic operation conditions.

Mathematical Modeling of the Performance-Degradation Mechanisms of Cation-Contaminated Proton-Exchange-Membrane Water Electrolysis

The role of hydrogen as a commercial energy carrier is dependent on the development of robust processes to convert hydrogen into usable electricity as well as produce hydrogen at large scales. Proton-exchange-membrane water electrolysis (PEMWE) is a leading technology with the potential to produce hydrogen at projected consumption rates. In PEMWE, water is electrochemically split into hydrogen and oxygen gas using a membrane—electrode assembly, which uses a membrane capable of transporting both water and protons. Reactant water containing cationic impurities have been observed to degrade cell performance. Thus, developing an understanding of the influence of cationic contaminants is important to developing mitigation and recovery strategies for PEMWE systems.In the current work, mathematical models were developed to provide insight into the mechanisms of performance degradation due to cationic contaminants. The models are non-isothermal continuum models that describe multi-phase porous flow, electrochemical reactions, and concentrated-species transport in both the gas membrane, and ionomer phases. Simulations were performed in steady-state and transient operational modes for various cationic species at several ionic concentrations. The calibration and fitting of the models were performed using experimental measurements performed by the National Renewable Energy Laboratory. The mathematical models suggest that gradients facilitate the adsorption of cationic contaminants in reactant water, which subsequently accumulate in the cathode catalyst layer, as shown in Figure 1(a), and inhibit the PEMWE hydrogen-evolution reaction (HER) that consume protons and electrons to produce hydrogen gas. The models suggest that protonic conductivity is not significantly affected by low-concentration cationic species, but access to the catalyst active sites in the cathode catalyst layer is severely impeded. As a result, the evolution of hydrogen then proceeds by an alkaline mechanism, where water and electrons combine to produce hydrogen gas and hydroxide ions. An interpolated polarization curve shown in Figure 1(b) suggests that cell operation at high current densities favor the alkaline HER reaction due to the lack of protons in the cathode catalyst layer.This research is supported by DOE Hydrogen and Fuel Cell Technologies Office, through the H2NEW Consortia. Figure 1

Isothermal and non-isothermal computer simulation of a stretch blow molding process and comparison with experiments

Environmental pollution by plastic waste has become a serious problem, and there is increasing demand to reduce the weight of PET bottles. To fabricate reduced weight PET bottles, research on the PET blow molding process is essential. In this study, experiments and computer simulations were performed on the stretch blow molding process used to fabricate carbonated soft drink PET bottles. The computer simulations were performed under the same conditions as the experiment using isothermal and non-isothermal models to analyze the blowing phenomena, thickness and temperature distributions, stretch ratio, and the stretching path of PET bottles. Experimental and simulation results were compared, confirming that the stretch blow molding simulation was useful for designing and fabricating improved PET bottles through the stretch blow molding process.

Characterization and modelling of the crystallization behavior of PEEK for polymer processing techniques

This study examines the crystallization behavior of high-performance thermoplastics under both isothermal and non-isothermal conditions. The accurate prediction of the crystallization kinetics in conjunction with process simulation tools can create new methods for defining the key process parameters in various polymer processing techniques. By simulating the thermal history of the materials, optimal process parameters can be assigned at specific time points, resulting in a more homogeneous process and improved material properties, while avoiding costly and time-consuming trial-and-error experimentation or post-processing. Here, flash differential scanning calorimetry (DSC) was used to capture the rapid crystallization of Luvocom 3F PEEK 9581 NT, and various isothermal and non-isothermal models were applied to mimic its crystallization behavior, highlighting the differential form of the dual Nakamura model as the most suitable option. To accurately predict the absolute crystallinity, the maximum achievable enthalpy was introduced in the model, and weight factors were assigned to the primary and secondary crystallization mechanisms. The differential form of the model is suitable for efficient implementation in process simulation tools, because it is independent of the total crystallization time. This research has the potential to significantly improve the selection of proper process parameters in complex polymer processing techniques, e.g., material extrusion.

Multi-objective optimization of channel structure for a proton exchange membrane water electrolysis cell

The flow field dominates the process of mass transport and distribution inside the proton exchange membrane water electrolysis cell (PEMEC). Initially, a three-dimensional and non-isothermal PEMEC channel model was estimated to investigate the impact of channel height and width. Based on these results, a complete PEMEC model with a parallel flow-field pattern was developed, and the channel heights and widths of the model were optimized using a genetic algorithm (GA). Compared to the original model, the optimized model decreased the pressure drop by 34.97% at a lower voltage. In addition, because of the optimized flow-field pattern, the optimized model improves the current density on the proton exchange membrane as well as the gas holdup situation in a partial position in the cathode gas diffusion layer.

Isothermal and non-isothermal growth of a vapor bubble in pool boiling – Effect of translational velocity of bubble

In the present work, we have numerically simulated the effect of bubble translation on the growth of a vapor bubble in a pool of superheated liquid based on the isothermal and non-isothermal model. The isothermal growth uses the ODE solver and the non-isothermal growth the PDE-ODE solver. The overall model at present considers the forces acting on the bubble to compute the bubble motion and the energy balance at the bubble surface to include the effect of bubble size on its motion. Thus, it computes equivalent bubble radius and bubble velocity simultaneously. The numerical simulation shows a remarkable improvement by our method over the previous numerical model while validating with the experimental and numerical results on bubble growth with the phase motion. The improved model has significantly reduced the deviation from the experiments reported in literature on the growth of a moving bubble. The aspect ratio of the bubble is computed to see the shape change of the bubble and is used to model the drag force accurately. It has been shown that the model of the isothermal growth can better explain the bubble growth at the initial stage, and the model of the non-isothermal growth at the final stage. The non-isothermal growth of bubble is accompanied by the slowdown of the bubble translation in the superheated liquid.

Mass transfer and water management in proton exchange membrane fuel cells with a composite foam-rib flow field

Mass transfer capability of reactants and hydrothermal management is important for the performance and durability of proton exchange membrane fuel cells. In the conventional rib flow field, the oxygen transport is affected by the accumulation of under-rib liquid water which causes excessive concentration loss and limits cell performance. To improve the cell performance, a composite foam-rib flow field structure is proposed by combining the metal foam flow field and the conventional rib flow field. The proposed design is simulated by using a three-dimensional homogeneous non-isothermal numerical model. The results show that the composite foam-rib flow field, by improving the oxygen transfer and water removal capabilities under the ribs, can improve the oxygen concentration and current density without increasing the pumping power, thus improving the cell performance under different conditions. The key parameters of the composite foam-rib flow field are optimized. With the optimal metal foam filling ratio of 0.75 and porosity of 0.85, the peak power density and the limiting current density for the composite foam-rib flow field are higher than the conventional rib flow field by 5.20% and 22.68%.

A Non-Isothermal Pore Network Model of Primary Freeze Drying.

In this work, a non-isothermal pore network (PN) model with quasi-steady vapor transport and transient heat transfer is presented for the first time for the application of primary freeze drying. The pore-scale resolved model is physically based and allows for the investigation of correlations between spatially distributed structure and transport conditions. The studied examples were regular PN lattices with a significantly different structure, namely a spatially homogeneous PN, also denoted as monomodal PN, and a PN with significant structure variation, referred to as bimodal PN because of its bimodal pore size distribution. The material properties selected for the solid skeleton in this study are equivalent to those of maltodextrin. The temperature ranges applied here were -28 °C to -18 °C in the PN and -42 °C in the surrounding environment. The environmental vapor pressure was 10 Pa. The PNs were dried with constant temperature boundary conditions, and heat was transferred at the top side by the vapor leaving the PN. It is shown how the structural peculiarities affect the local heat and mass transfer conditions and result in a significant widening of the sublimation front in the case of the bimodal PN. The possibility of spatially and temporally resolved front structures is a unique feature of the PN model and allows the study of situations that are not yet described by classical continuum approaches, namely heterogeneous frozen porous materials. As demonstrated by the thin layers studied here, the pore-scale simulations are of particular interest for such situations, such as in lyomicroscopes or collagen scaffolds, where a length-scale separation between dry and ice-saturated regions is not possible.

Environmental Temperature Effect on Hydraulic Behavior and Stability of Shallow Slopes

This study established a study framework to quantify the safety factors of unsaturated shallow slopes at different temperatures. This study is based on a non-isothermal soil water characteristic curve model quantifying the temperature-dependent hydraulic properties of soils. The hydraulic coupling analysis models HYDRUS 2D and The Slope Cube Module were used for finite element modeling. A slope stability analysis was performed based on the local factor of safety (LFS) theory. An increased temperature decreased the soil matric suction, suction stress, effective stress, and LFS, weakening the soil strength. Slope modeling analysis showed that soils were dominated by different water retention mechanisms before and after rainfall infiltration, and the trends caused by temperature changes also changed accordingly. This study provides insights into the relationship between soil mechanical properties and temperature, which is valuable for maintaining soil stability and preventing geological hazards.

A non-isothermal phase-field hydraulic fracture modeling in saturated porous media with convection-dominated heat transport

This research aims to extend the isothermal continuum mechanical modeling framework of hydraulic fracturing in porous materials to account for the non-isothermal processes. Whereas the theory of porous media is used for the macroscopic material description, the phase-field method is utilized for modeling the crack initiation and propagation. We proceed in this study from a two-phase porous material consisting of thermomechanically interacting pore fluid and solid matrix. The heat exchange between the fluid in the crack and the surrounding porous environment through the diffusive fracture edges is carefully studied, and new formulations here are proposed. Besides, temperature-dependent solid and fluid material parameters are taken into account, which is of particular importance in connection with fluid viscosity and its effect on post-cracking pressure behavior. This continuum mechanical treatment results in strongly coupled partial differential equations of the mass, the momentum, and the energy balance of the thermally non-equilibrated constituents. Using the finite element method, two-dimensional initial-boundary-value problems are presented to show, on the one hand, the stability and robustness of the applied numerical algorithm in solving the emerged strongly coupled problem in the convection-dominated heat transport state. On the other hand, they show the capability of the modeling scheme in predicting important instances related to hydraulic fracturing and the role of the temperature field in this process. Additionally, they show the importance of using stabilization techniques, such as adding an artificial thermo-diffusivity term, to mitigate temperature fluctuations at high flow velocity.

A Super Uniform Hydrophobic Gas Diffusion Layer for a Proton Exchange Membrane Fuel Cell.

The design and optimization of the gas diffusion layer (GDL) play a crucial role in the improvement of proton exchange membrane fuel cell performance. Hydrophobic treatment of a GDL is an important method for facilitating mass transfer, while conventional Teflon treatment is not uniform and leads to an increase in ohmic and heat resistance. Herein, a homogeneous molecular hydrophobic GDL was prepared by liquid phase synthesis, and a two-dimensional non-isothermal model was developed to investigate the transfer mechanism. The peak power density of cells with the GDL described above was improved by 46% compared to that of the conventional GDL. The ohmic and mass transport resistance decreased by 15% and 52%, respectively, under a current density of 1 A cm-2 using the uniform hydrophobic GDL. The simulation results proved that the uniform hydrophobic GDL eliminates the hydrophilic dots, which prevents the formation of water pools and reduces the resistance to gas flow. The water saturation of the conventional GDL reaches 0.19 at a current density of 1 A cm-2, and the saturation of a modified GDL under the same conditions is only 0.13. A dimensionless parameter, Tf, is proposed to characterize the resistance of oxygen diffusion. In conclusion, molecular-level uniform hydrophobic treatment can effectively reduce the ohmic and mass transfer resistance of a GDL and effectively improve the performance of fuel cells.

Investigation of water effects on hydrogen dissolution, diffusion, and reaction in high temperature proton exchange membrane fuel cell

High-temperature proton exchange membrane fuel cell with phosphoric acid-doped polybenzimidazole membrane is typically utilized with a methanol steam reformer due to its high CO tolerance. However, methanol reformate commonly contains 20 % water, and its effect on the high temperature fuel cell is unclear. A comprehensive 3D multiphase non-isothermal model with an enhanced electrochemical kinetics model considering the water influence mechanism is developed. The water influence mechanism includes the proton conductivity, hydrogen dissolution on the pore-ionomer interface, hydrogen diffusion inside the ionomer, and hydrogen surface reaction on the platinum. The sensitivity analysis found that hydrogen dissolution on the pore-ionomer and hydrogen surface reaction on the platinum significantly affect cell performance. The influences of water on ionomer hydrogen concentration, platinum surface hydrogen concentration, and surface reaction rates are investigated under the voltage range of 0.9–0.4 V. The increase of water content can improve the net adsorption rate and benefit electrochemical reaction. Besides, the anode water is better for the uniformity of surface reaction rate distributions while not affecting the hydrogen distributions inside the ionomer and on the platinum surface. Additionally, the positive influence of water on CO poisoning is investigated in terms of surface reaction. The water's beneficial effect on decreasing platinum loading is also discussed. The results show that 20 % water can reduce the platinum loading by 20 %.

Hydrogen production from low pressure coke oven gas by vacuum pressure swing adsorption

Hydrogen is a major component of coke oven gas (COG) and can be used in gas-based direct reduction iron processes to help the steel industry achieve the carbon peaking and carbon neutrality goals. However, the high compression power consumption is the main drawback of the current PSA cycle since the COG needs to be compressed from atmospheric pressure to ∼18 bar to achieve a hydrogen production with purity >99.9% and recovery < 85%. Here in this study, we experimentally demonstrate by using a 4-bed 12-step lab-scale VPSA rig filled with activated carbon RB3 and can obtain a hydrogen product with a purity of 99.67% and a recovery of 91.97% at a feed pressure of only 5.17 bar. We then constructed a non-isothermal non-adiabatic VPSA model using our in-house code and validated the model against experimental breakthrough and VPSA cycles. Parametric optimization produced a H2 product of 99.995% purity and 92.29% recovery at a slightly increased adsorption pressure of 6 bar and a vacuum pressure of 0.02 bar with 10.21 mol.H2/kg.ads/hr productivity and 7.09 kJ/mole.H2 specific power. We also confirmed that light product purge at vacuum pressure can effectively improve the H2 purity and the gas flow direction of the pressure equalization step has a significant effect on the mass transfer front. Our research presents the success of low-pressure hydrogen production from COG, which will greatly accelerate the transformation of COG utilization and promote the decarbonization of the iron and steel industry.