Discontinuous Conditions Research Articles

Unlocking glycerol Potential: Novel pathway for hydrogen production and Value-Added chemicals

In the global fight against climate change, the bio-based supply chain represents an interesting solution as it offers the potential to produce high-value-added products and bioenergy through the utilization of waste and by-products. In this work, a new route is proposed for the conversion of bio-based glycerol to H2/CO2 and high value-added liquid and solid products. The innovative process used pure or crude glycerol or ethanol-glycerol mixture along with water and sodium metaborate as reagents at 300 °C under discontinuous conditions. The gas stream consists mainly of hydrogen, followed by biogenic CO2 (31–54 %), CO (4–13 %) and CH4 in traces. The presence of water in the tested crude glycerol improved the hydrogen selectivity to 55 %. Characterization of the liquid reaction products revealed the synthesis of products such as 1,2-propanediol, propanoic acid, acetic acid, cyclopentenones and cyclic diglycerol. In the solid phase, an aliphatic hydrocarbon resin with oxygenated carbon along the saturated chain and an aromatic cluster were also characterized by NMR, FTIR and TG analyses. Based on these findings, the global reaction route to the general reaction products was proposed.

Performance evaluation of ALIP applying fully enclosed slot

ABSTRACT In nuclear energy systems, annular linear induction pump (ALIP) is regarded as an ideal device for transporting liquid metal. Developed pressure and efficiency are crucial indicators for evaluating performance of an ALIP, and enhancing these fac- tors is of utmost importance. This paper presents a 2D axisymmetric finite element method (FEM) model for efficiently predicting the performance of ALIP and a 3D FEM model to explore the implementation of a fully enclosed slot structure. The accuracy of the proposed models is validated by comparing the results with experi- mental data, complemented by empirical formulas in the post-processing phase. The continuous and discontinuous conditions of the pole pieces are analyzed using the 3D FEM, demonstrating that the fully enclosed slot structure can significantly enhance both developed pressure and efficiency, thereby improving the overall performance of the ALIP.

Whitham modulation theory and Riemann problem for the Kundu–Eckhaus equation

In this paper, the Riemann problem for the defocusing Kundu–Eckhaus equation is investigated by Whitham modulation theory. First, we study the dispersion relation for linear waves. Then, the zero-phase and one-phase periodic solutions of the Kundu–Eckhaus equation along with the corresponding Whitham modulation equations are derived by the finite-gap integration method. Further, employing the Whitham equations parametrized by the Riemann invariants, the main fundamental wave structures induced by the discontinuous initial data are found. Analytical and graphic methods are utilized to provide the wave structures of rarefaction waves and dispersive shock waves, and thus for a complete classification of solutions under general step-like conditions of initial discontinuity.

Stepwise Alternating Direction Implicit Method of the Three Dimensional Convective-Diffusion Equation

A stepwise alternating direction implicit method of the three dimensional convective-diffusion equation is considered in this paper. We constructed an implicit difference scheme and analyzes it's truncation error, convergence and stabilities. The theoretical and numerical analysis shows that the implicit difference scheme is unconditional stable. Then the Greedy Algorithm is proposed to solve the numerical solution on x,y and z axis separately by using implicit difference scheme and the numerical solution is convergent theoretically, however with no physical meaning. The Stepwise Alternating Direction Implicit Method (SADIM) is proposed, which uses the implicit difference scheme in this paper. Using Sauls scheme to pretreat the initial-boundary condition before iterating, thus eliminate the numerical oscillation caused by discontinuous initial boundary conditions. This SADIM is at least six ordered convergent, and is one of high ordered numerical methods for three dimensional problem. Our implicit difference scheme is more ideal than the standard Galerkin centered on finite difference scheme, quicker than SOR iteration method. The convergence of our implicit scheme is better than finite element method, characteristic line method, and mesh-less method. Our method eliminates the numerical oscillation caused by the convection dominant, resists the dispersion effectively and addresses dissipation caused by diffusion dominant.The implicit difference scheme has good theoretical and practical value.

Construction of mathematical models of thermal conductivity for modern electronic devices with elements of a layered structure

This paper considers a heat conduction process for isotropic layered media with internal thermal heating. As a result of the heterogeneity of environments, significant temperature gradients arise as a result of the thermal load. In order to establish the temperature regimes for the effective operation of electronic devices, linear and non-linear mathematical models for determining the temperature field have been constructed, which would make it possible to further analyze the temperature regimes in these heat-active environments. The coefficient of thermal conductivity for the above structures was represented as a whole using asymmetric unit functions. As a result, the conditions of ideal thermal contact were automatically fulfilled on the surfaces of the conjugation of the layers. This leads to solving one heat conduction equation with discontinuous and singular coefficients and boundary conditions at the boundary surfaces of the medium. For linearization of nonlinear boundary value problems, linearizing functions were introduced. Analytical solutions to both linear and nonlinear boundary value problems were derived in a closed form. For heat-sensitive environments, as an example, the linear dependence of the coefficient of thermal conductivity of structural materials on temperature, which is often observed when solving many practical problems, was chosen. As a result, analytical relations for determining the temperature distribution in these environments were obtained. Based on this, a numerical experiment was performed, and it was geometrically represented depending on the spatial coordinates. This proves that the constructed linear and nonlinear mathematical models testify to their adequacy to the real physical process. They make it possible to analyze heat-active media regarding their thermal resistance. As a result, it becomes possible to increase it and protect it from overheating, which can cause the destruction of not only individual nodes and their elements but also the entire structure

Traveling wave vibration characteristic analysis of FRC sandwich cylindrical shells with FGP-GPLRC core under discontinuous elastic boundary conditions

In this study, a fiber-reinforced composite (FRC) sandwich cylindrical shell with a functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) core is investigated, and the traveling wave vibration characteristics of this new sandwich cylindrical shell under discontinuous elastic boundary conditions are analyzed for the first time. The influences of centrifugal and Coriolis forces are introduced into the model. By employing the first-order shear deformation theory (FSDT) and the continuity assumption of the layerwise theory, the governing equations of the rotating sandwich shell are obtained. The artificial springs are implemented at the ends of the sandwich shell to represent the discontinuous elastic boundary conditions. The natural frequency of the shell is solved via the Rayleigh-Ritz method and the state space method. Then, the approach proposed is validated by comparing the present results with those reported in the literature and the finite element method. Finally, the effects of various parameters on the traveling wave frequency of the shell are evaluated. It was found that in practical engineering, the appropriate thickness of the FGP-GPLRC core should be selected according to the boundary conditions and other factors, and the ply angle should be adjusted to obtain more stability of vibration.

PARAMETER-UNIFORM HYBRID NUMERICAL SCHEME FOR SINGULARLY PERTURBED PARABOLIC CONVECTION-DIFFUSION PROBLEMS WITH DISCONTINUOUS INITIAL CONDITIONS

This article presents a parameter-uniform hybrid numerical technique for singularly perturbed parabolic convection-diffusion problems (SPPCDP) with discontinuous initial conditions (DIC). It utilizes the classical backward-Euler technique for time discretization and a hybrid finite difference scheme ( which is a proper combination of the midpoint upwind scheme in the outer regions and the classical central difference scheme in the interior layer regions(generated by the DIC)) for spatial discretization. The scheme produces parameter-uniform numerical approximations on a piecewise- uniform Shishkin mesh. When the perturbation parameter ε(0 < ε ≪ 1) is small, it becomes difficult to solve these problems using the classical numerical methods (standard central difference or a standard upwind scheme) on uniform meshes because discontinuous initial conditions frequently appear in the solutions of this class of problems. The method is shown to converge uniformly in the discrete supremum with nearly second-order spatial accuracy. The suggested method is subjected to a stability study, and parameter-uniform error estimates are generated. In order to support the theoretical findings, numerical results are presented.

Modeling heat conduction with dual-dissipative variables: A mechanism-data fusion method.

Many macroscopic non-Fourier heat conduction models have been developed in the past decades based on Chapman-Enskog, Hermite, or other small perturbation expansion methods. These macroscopic models have achieved great success in capturing non-Fourier thermal behaviors in solid materials, but most of them are limited by small Knudsen numbers and incapable of capturing highly nonequilibrium or ballistic thermal transport. In this paper, we provide a different strategy for constructing macroscopic non-Fourier heat conduction modeling, that is, using data-driven deep-learning methods combined with nonequilibrium thermodynamics instead of small perturbation expansion. We present the mechanism-data fusion method, an approach that seamlessly integrates the rigorous framework of conservation-dissipation formalism (CDF) with the flexibility of machine learning to model non-Fourier heat conduction. Leveraging the conservation-dissipation principle with dual-dissipative variables, we derive an interpretable series of partial differential equations, fine tuned through a training strategy informed by data from the phonon Boltzmann transport equation. Moreover, we also present the inner-step operation to narrow the gap from the discrete form to the continuous system. Through numerical tests, our model demonstrates excellent predictive capabilities across various heat conduction regimes, including diffusive, hydrodynamic, and ballistic regimes, and displays its robustness and precision even with discontinuous initial conditions.

Lipid Quality Changes in French Fries, Chicken Croquettes, and Chicken Nuggets Fried with High-Linoleic and High-Oleic Sunflower Oils in Domestic Deep Fryers.

The quality of fried products greatly depends on the changes occurring during frying. The purpose of this work was to study the lipid quality changes taking place in selected frozen foods after domestic deep-frying. Conventional, high-linoleic sunflower oil (HLSO) and high-oleic sunflower oil (HOSO) were used, and the frozen foods selected were French fries, croquettes, and nuggets. The foods were fried in domestic fryers under discontinuous conditions. Analyses included fatty acid composition, sterols, tocopherols, squalene, and lipid alteration levels. In all fried foods, the content of lipids increased after frying, which is consistent with previous findings. However, the lipid exchange between the food and the oil greatly depended on the food characteristics. Specifically, the levels of frying oil in the food lipids were about 90, 40, and 58% for French fries, croquettes, and nuggets, respectively. The main results obtained showed that lipid alteration levels considerably decreased and amounts of sterols and tocopherols significantly increased in French fries' lipids after frying. In both chicken products, croquettes and nuggets, the best quality improvement observed was a significant decrease in cholesterol in food lipids due to the lipid exchange. Overall, frying with HLSO and HOSO improved the quality and nutritional properties of all products tested.

A robust B-spline method for two parameter singularly perturbed parabolic differential equations with discontinuous initial condition

A robust B-spline method for two parameter singularly perturbed parabolic differential equations with discontinuous initial condition

Semi-analytical modeling and analysis on traveling wave vibration characteristics of spinning FGP-GPLRC stepped cylindrical shells under discontinuous boundary conditions

Semi-analytical modeling and analysis on traveling wave vibration characteristics of spinning FGP-GPLRC stepped cylindrical shells under discontinuous boundary conditions

Random and harmonic responses of plain woven carbon fiber reinforced conical-conical shell based on machine learning multiscale modelling

This study analyzes the frequency-response characteristics under non-stationary base random acceleration and harmonic points force excitations of plain woven carbon fiber reinforced polymers (PW-CFRP) conical-conical shells comprehensively. Artificial neural network (ANN) based machine learning multiscale modelling strategy is introduced in the process of predicting the mechanical properties of PW-CFRP. The dataset is generated by randomization, linear fitting and two-step homogenization and then trained to generate an ANN to predict the mechanical properties of PW-CFRP. The governing equations of the conical-conical shell under random acceleration excitation are obtained according to the first order shear deformation theory (FSDT) and Hamilton's principle. After the structure is split along the circumference at the excitation points, the harmonic points force excitations are introduced based on the discontinuity condition between conical segments. Generalized differential quadrature (GDQ) is applied during the solving procedure. After comparison studies focusing on the frequency-response characteristics under two types of excitations, two examples on harmonic and random responses of conical-conical shell and conical-cylindrical shell are carried out separately. In this process, the effects of excitation type, excitation and response points, geometric parameters on the frequency-response characteristics are extensively analyzed, which proves efficiency and accuracy of the ANN based machine learning multiscale modelling strategy and the constructed GDQ based computational strategy.

A mixed finite element spatial discretization scheme and a higher‐order accurate temporal discretization scheme for a strongly discontinuous electromagnetic interface condition in ideal sliding electrical contact problems

AbstractSliding electrical contact involves multiple conductors sliding in contact at different speeds, with current flowing through the contact surfaces. The Lagrangian method is commonly used to describe the electromagnetic field in order to overcome the trouble of convective dominance, especially in high‐speed sliding electrical contact problems. However, to maintain correct field continuity, magnetic vector potential and scalar potential taken as variables cannot be continuous simultaneously at the ideal sliding electrical contact interface. This involves a strongly discontinuous condition for variables. Further, commonly used spatial–temporal discretization algorithms are invalid, for example, the classic finite element (CFEM) framework does not allow discontinuous variables, and the backward Euler method in time domain introduces a significant interface error source associated with the velocity of relative motion. To accurately handle strongly discontinuous conditions in numerical calculations, a mixed nodal finite element scheme and a higher‐order accurate temporal discretization scheme are introduced. In this scheme, classical finite element method is performed in each subdomain, and the derivative terms at the boundary are added as new variables. The effectiveness and accuracy of the above methods are verified by comparing them with a standard solution in a two‐dimensional railgun model and analyzing the current density distribution in a three‐dimensional railgun model.

Modeling groundwater redox conditions at national scale through integration of sediment color and water chemistry in a machine learning framework

Redox conditions play a crucial role in determining the fate of many contaminants in groundwater, impacting ecosystem services vital for both the aquatic environment and human water supply. Geospatial machine learning has previously successfully modelled large-scale redox conditions. This study is the first to consolidate the complementary information provided by sediment color and water chemistry to enhance our understanding of redox conditions in Denmark. In the first step, the depth to the first redox interface is modelled using sediment color from 27,042 boreholes. In the second step, the depth of the first redox interface is compared against water chemistry data at 22,198 wells to classify redox complexity. The absence of nitrate containing water below the first redox interface is referred to as continuous redox conditions. In contrast, discontinuous redox conditions are identified by the presence of nitrate below the first redox interface. Both models are built using 20 covariate maps, encompassing diverse hydrologically relevant information. The first redox interface is modelled with a mean error of 0.0 m and a root-mean-squared error of 8.0 m. The redox complexity model attains an accuracy of 69.8 %. Results indicate a mean depth to the first redox interface of 8.6 m and a standard deviation of 6.5 m. 60 % of Denmark is classified as discontinuous, indicating complex redox conditions, predominantly collocated in clay rich glacial landscapes. Both maps, i.e., first redox interface and redox complexity are largely driven by the water table and hydrogeology. The developed maps contribute to our understanding of subsurface redox processes, supporting national-scale land-use and water management.

Effects of real gas models on the wave dynamics and refrigeration of gas wave rotor

The gas wave rotor was usually designed and performed on the ideal gas model. However, the real gas effect could not be ignored anymore under high-pressure ratio conditions. In this study, for the first time, a two-dimensional computational model of a double-opening gas wave refrigerator (GWR) using a multi-parameter Benedict–Webb–Rubin equation of state is established and the influence of the real gas effect on gas wave dynamics and energy transfer processes in the GWR with discontinuous boundary conditions is thoroughly investigated. The numerical results show that the wave dynamics of the ideal gas and the real gas are similar under different operating conditions, but compression waves and expansion waves in real gas obviously lag behind the ideal gas. In addition, the low-temperature real gas is completely discharged earlier than the ideal gas and the difference between them gradually increases as the pressure ratio gets higher, which benefits the GWR compact structure design and cost reduction. At the same time, the temperature of the real gas being discharged is lower than that of the ideal gas. Therefore, the refrigeration efficiency of the isentropic expansion of the real gas will be improved compared with the operation in ideal gas. The research results on the real gas effect reveal the mechanism of wave dynamics and energy transfer, providing support for the optimization design of GWR.

Use of whey through anaerobic codigestion for biomethane production

The whey generated by cheese production is the main by-product generated by the dairy industry, which causes considerable impact on the environment if it is not treated properly. This potential contaminant is mainly due to its high content of organic matter. In recent years, numerous studies have been carried out with the objective of using whey more efficiently, using innovative technological methods for the treatment of wastewater such as the anaerobic digestion method, and thereby being able to obtain derived products such as biogas or biofuels, which generate less environmental impact and develop economic activities. The objective of this study is to collect studies on the use of whey to obtain biogas through the anaerobic digestion technique. The review allowed us to know the wide application of the anaerobic digestion method for the production of biogas from whey and other agri-food substrates, demonstrating the high efficiency of the method in association with biological media in semi-continuous and discontinuous conditions. Likewise, it was also possible to know that the anaerobic co-digestion method is a promising alternative for small and medium-sized industries that could replace fossil fuels with biogas and that in turn contribute to environmental conservation by avoiding pollution and environmental problems due to the effect of the poor serum management.

Modeling of contact resistivity and simplification of 3D homogenization strategy for the H formulation

The finite element method (FEM) provides a powerful support for the calculations of superconducting electromagnetic responses. It enables the analysis of large-scale high-temperature superconducting (HTS) systems by the popular H formulation. Nonetheless, modeling of contact resistivity in three-dimensional (3D) FEM is still a matter of interest. The difficulty stems from the large aspect ratio of the contact layer in numerical modeling. Nowadays, an available solution is to model the contact layer with zero thickness but requires the discontinuity conditions of the magnetic field. In this paper, the energy variational method is utilized to incorporate the contribution of contact resistivity into the H formulation. From the perspective of energy transfer, the contact resistivity is related to the energy dissipation of the radial current flowing through the contact interface. In terms of applications, this method can be employed to calculate the charging delay of no-insulation coils and the current sharing behaviors of CORC cables. One advantage of this model is that the magnetic field is continuous and hence can be easily implemented in FEM. Additionally, it requires fewer degrees of freedom and hence presents advantages in computational efficiency. Moreover, this method can be employed to simplify the 3D H homogeneous model for insulated coils. The above discussions demonstrate that the proposed model is a promising tool for the modeling of contact resistivity.

A Study of Singular Similarity Solutions to Laplace’s Equation with Dirichlet Boundary Conditions

A Study of Singular Similarity Solutions to Laplace’s Equation with Dirichlet Boundary Conditions

High-efficiency thermal reduction of CO2 to high-valued carbon nanotubes

To reduce the amount of carbon dioxide (CO2) already emitted into the atmosphere, various carbon capture, utilization, and storage (CCUS) technologies have been developed for climate and economic reasons in recent years. However, the state of art CCUS techniques suffer from deficiencies such as high cost, low yield, and harsh and discontinuous production conditions. In this work, we report a new thermal reduction method for continuously conversing CO2 to methane (CH4) by introducing sodium borohydride (NaBH4) as a reductant under catalyst-free conditions. Experimental results show that CO2 can be fully captured and converted to CH4 and carbon monoxide (CO) and the selectivity efficiency of CO2 to CH4 can be achieved to be as high as 90% with the optimization of experimental conditions. Such a result originates from the high activity of NaBH4 and high selectivity of the thermal reduction of CO2. To demonstrate one of the potential usages of the reduction products, we integrated the thermal reduction of CO2 with the production of carbon nanotubes (CNTs). As long as CO2 is supplied at the source end, the reduction products can undergo catalytic decomposition to produce a CNT fiber or film continuously at the final end. The present technique is featured with simple equipment setup, low cost, and continuous thermal reduction, thus providing a new pathway for the large-scale conversion of CO2 into high-valued products for wide applications.

Mechanics of inner core debonding of composite sandwich beam with CFRP hexagonal honeycomb

The inner core debonding of composite sandwich beams with carbon fiber reinforced polymer (CFRP) hexagonal honeycomb core is investigated theoretically and experimentally. Based on the principle of minimum potential energy, a theoretical model is established to reveal the core debonding mechanism with Timoshenko’s beam theory and Extended High-Order Sandwich Panel Theory (EHSAPT) for composite face sheets and CFRP hexagonal honeycomb core, respectively. The theoretical approach of core debonding simulation is based on the framework of the cohesive zone model (CZM). By constructing the constitutive relation of the core interface as the discontinuous stress and displacement boundary conditions, the vertical core debonding can be simulated overcoming the singularity of equilibrium equations. The crack propagation process is decomposed into three stages with the consideration of the double crack propagation mechanism. In experiments, the regular and reinforced hexagonal honeycomb sandwich beams are designed and fabricated, and the quantification of the defect degree of the core bonding interface is achieved by equivalent energy release rate obtained from the homogenized hexagonal honeycomb. The double cantilever beam (DCB) experiments are performed to determine the equivalent energy release rate and reveal the core debonding mechanism of CFRP hexagonal honeycomb sandwich beams. Comparing the load–displacement curves and debonding deformation patterns indicates that the established theoretical model can effectively predict the core debonding mechanical response. Finally, parametric analysis is carried out to discuss the impact of structural dimension parameters, defect location and defect degree on the debonding modes of CFRP hexagonal honeycomb sandwich beams.