One-dimensional Mathematical Model Research Articles

Hydraulic Transport of Large Solid Particles in Inclined Pipes Under Pulsating Flow Conditions

Abstract The pressure loss due to the hydraulic transport of large solid particles should be predicted for the design of subsea mining systems. The mixture flow in a flexible jumper is expected to be unsteady during lifting operations in an actual mining system. The authors develop a one-dimensional mathematical model that predicts such pressure loss under pulsating mixture flows in a static inclined pipe assuming that the flow in the jumper is fully developed. An experiment is performed on the hydraulic transport of solid particles to obtain data for model validation. In this experiment, several kinds of solid particles are used: alumina beads, glass beads, and gravel. The experimental parameters are mixture velocity, solid concentration, pulsation period and amplitude of water velocity, and pipe inclination angle. The proposed model is validated through a comparison with experimental data. The validation confirms that the model is applicable for the prediction of the pressure loss in inclined pipes under pulsating flow conditions. Furthermore, we calculate the pressure loss due to the hydraulic transport of polymetallic sulfide ores using the proposed model. The calculation results show that the time-averaged pressure loss drastically varies with the pipe inclination angle, reaching its maximum value between the pipe inclination angles of 30 deg and 60 deg, at which the flow is inclined upward. The results also show that the amplitude of pressure loss pulsation differs little between pipe inclination angles and that the pulsation component of pressure loss should be considered in designing lifting systems.

The 1D model of hybrid heat pump system designed and prototyped for electric vehicles

In this paper, a one-dimensional mathematical model of a hybrid heat pump system was developed to improve the driving range of electric vehicles considering energy consumption. The generated one-dimensional model was performed in four different heating modes under various scenarios to satisfy the heating demand considering both the driving range and the target temperature. This model was run in recirculation mode in all analyses for energy efficiency. The electric heater capacity can be reduced to prevent overheating in the cabin. The fastest proposed cases reached the target temperature in 300 s. In this case, the vehicle range was lowest and varied between 72.3 % and 77.5 %. The highest vehicle range varied between 81.3 % and 86.1 % and provided sufficient heating in approximately 900 s. In addition, the effect of preheating by different capacities electric heaters, it was observed that preheating with a low-capacity electric heater had advantages. As a result, the present study shows that the dynamic behavior of the hybrid heat pump systems allows researchers to improve electric vehicles thermal management system which had a crucial role. The results of the model were in good agreement with the experimental data presented with similar boundary conditions in available literature.

The Water Hammer Characteristics of Long-Distance Water Pipelines under Different Water Supply Modes

The pressure characteristics of long-distance water pipelines during hydraulic transient processes are crucial for ensuring the safe, stable, and long-term operation of water transfer projects. This paper establishes a one-dimensional mathematical model based on sections of the Yinjiangjihuai long-distance water diversion project in China. The water supply requirements of the pipelines are categorized into two replenishment modes as follows: gravity supply and pump-pressurized water supply. The opening and closing strategies of the water pipelines under different flow conditions are simulated and analyzed to explore the hydraulic transient processes under various water supply modes. The transient variations of key hydraulic parameters during valve closure are clarified. Simulation results indicate that the water pipeline design is reasonable, meeting the water supply demands at relatively low Manning values and that it has the capability for long-term supply. Due to the excessive head provided by the pumps, pump-pressurized water supply and gravity supply modes cannot operate simultaneously. Under gravity supply mode, the minimum pressure in the downstream pipeline is relatively higher overall, while the maximum pressure in the upstream pipeline is relatively lower overall. In the pump-pressurized water supply mode, the safety and stability of the water supply can be ensured by adjusting the closing time of individual pumps and the interval time between adjacent pumps. The research findings provide technical guidance and scientific basis for the construction of national water networks and water transfer projects.

An analytical approach for designing sCO2 centrifugal compressors using the loss-integrated throughflow method

Several studies have focused on the analytical modeling of centrifugal compressors. These models are commonly used in design, optimization and evaluation of rotor geometry. Existing models, which rely on either the meanline method (1D model) or the streamline curvature-based throughflow method (2D model) combined with semi-empirical pressure loss relations, are closed-loop models that do not account for pressure loss distribution along the blade channel. Additionally, these models simplify the rotor’s three-dimensional geometry, focusing primarily on the β angle and meanline length. To address these limitations, we introduce an open-loop analytical approach called the’loss-integrated throughflow method’ (LITM). This method computes pressure losses step-by-step along the blade’s channel geometry using the three-dimensional cross-section of the rotor as input data. The motivation behind this new approach is to develop an alternative tool for the preliminary design of supercritical CO2 (sCO2) compressors, providing insight into the relation between losses and rotor geometry beyond just the β angle and meanline length. In the present work we compare simulation results with a one-dimensional (1D) mathematical model that has been validated against experimental for sCO2. We compare three sets of rotors, where each set shares identical β angles and meanline lengths. When compared against the 1D model, our model yields deviations ranging from 2.8% to 21.9% for rotors with matching meanline lengths and β angles. This suggests that factors other than the variables previously considered influence pressure losses. As a result of this study, we conclude that the proposed analytical model offers potential to refine the preliminary design for sCO2 rotors.

Multizone Modeling for Hybrid Thermal Energy Storage

This study presents a one-dimensional mathematical model developed to simulate multi-zone thermal storage systems using phase change materials (PCMs). The model enables precise analysis of temperature distribution in the layered storage based on several PCM configurations and properties. It is distinguished by its adaptability to various tank geometries and the number of PCM capsules, enabling its application under diverse operating conditions. By simplifying the implementation of heat transfer processes that depend on the shape of the capsule and the thermal properties of the PCM, the computation time can be reduced to a level that makes simulations over longer periods feasible. Experimental validation confirmed the accuracy of the model, with deviations below 6%, underscoring its practical applicability. The study demonstrates that individual layering in the storage tank can be achieved by filling it with PCMs of different melting points without compromising the maximum storage capacity. It is shown that including a PCM layer can maintain the outlet temperature 20% longer while storing 14% more energy. The results point out the model’s potential to improve the performance of thermal storage systems through targeted PCM layer configurations. The model serves as the basis for the planning and optimization of these systems.

Modelling spatio-temporal interactions between second messengers Ca and cAMP in a pancreatic -cell.

Calcium serves as a widespread second messenger in almost every human and animal cell. The regulation of various cellular processes, such as transcriptional control and the kinetics of membrane channels, is significantly influenced by intracellular calcium ions (Ca ), and linkages between Ca and other second messengers should activate signaling networks. The passage of ions across the cell membrane regulates Ca levels in pancreatic -cells and requires the coordinated interaction of various ion transport mechanisms and organelles. The signaling of Ca in -cells and its interactions with the intracellular dynamics of cyclic adenosine monophosphate (cAMP) is poorly understood. Therefore, the current investigation proposes a mathematical model to illustrate the spatiotemporal dynamical interaction between Ca and cAMP. In order to construct a one-dimensional mathematical model, the fundamental initial and boundary conditions derived from the physiological characteristics of the -cell are incorporated. The numerical results were obtained by MATLAB simulations using the finite element method and the Crank-Nicolson method. The current study aims to offer an update on regulation between Ca and cAMP signaling circuits, with a focus on interactions that occur in localized areas of the -cell. The model gives the individual effect of each parameter on the regulation of Ca and cAMP profiles in a -cell. Evidently, impairments in the regulation of messenger pathways contribute to the pathological conditions, as demonstrated by the results obtained.

Modeling mass transfer limitations driven by electrowetting in electrochemical CO2 reduction at silver gas diffusion electrodes

A one-dimensional mathematical model of a silver gas diffusion electrode (GDE) in electrochemical CO2 reduction (eCO2R) is presented. A Leverett approach is utilized to describe the coexistence of gaseous and liquid phases in the porous GDE, accounting for the potential-dependent contact angle of silver influenced by electrowetting. The model is fit to a set of experimental steady state results for sprayed electrodes with a range of diluted feeds (25−100vol%CO2). The model results ascertain a high electrolyte saturation in the GDE as the main cause for the inherent mass transfer limitations during eCO2R at elevated current densities. Furthermore, precipitation as a result of increased local K2CO3 concentration that surpasses the solubility limit is determined as degradation mechanism at current densities >3kAm−2. It is demonstrated how the model can be used to examine the effects of design parameters, indicating benefits of more hydrophobic and thinner GDEs.

A one-dimensional mathematical model for shear-induced droplet formation in co-flowing fluids

A one-dimensional mathematical model for shear-induced droplet formation in co-flowing fluids

Assessing dissolved oxygen dynamics in Pasig River, Philippines: A HEC-RAS modeling approach during the COVID-19 pandemic

Abstract The water quality in Pasig River has been impacted by urbanization, industrialization, and the pandemic conditions. This study involved comparative analysis of dissolved oxygen (DO) levels before and during the pandemic. Field measurements, including water temperature, salinity, and DO, were conducted during neap and spring tides. To further understand and simulate DO distribution, a one-dimensional mathematical model, specifically Hydrologic Engineering Center-River Analysis System, was employed. Results showed that DO increased during the pandemic, ranging from 3.26 to 7.25 and 1.08 to 5.69 mg/L during neap and spring tide. From the minimum standard DO level, out of eight stations, seven passed during neap tide, while one station passed during spring tide. Salinity levels were higher during spring tide, which may have affected the DO. Salt intrusion was evident until 4 km from the confluence. The hydraulic model yielded average water level differences of 5.1 and 8.3 cm during calibration and validation, respectively. The DO calibration and simulation exhibited very good statistical evaluation outcomes, with values of 0.9 for Nash-Sutcliffe Efficiency and 0.3 for Root Mean Standard Deviation Ratio. These findings hold significant potential for formulation of water quality enhancement plans and implementation of solid waste management and pollution policies.

Coupling of sediment transport phenomena with turbulent surface flows: mathematical modeling, finite volume approximation and test simulations

Several sediment transport models coupled with shallow water equations have been developed in the literature over the past few decades. The water flow in the presence of abrupt bottom slopes distorts and cause turbulence. This phenomenon is well-known in the sediment transport theory. Sediment transport models based on shallow water equations do not include turbulence effects or the phase-lag between water velocity and bottom velocity. In this study, we consider a one-dimensional free surface turbulent water flow with sediment and morphodynamic. We propose a new one-dimensional acceleration-dissipation mathematical sediment transport model that considers the distortion of horizontal profile velocity in transport. The model is an improved version of existing averaged sediment transport models. In the new model, there is a distinction between fluid velocity and bottom velocity through a new bedload equation. The mathematical model is a system of nonlinear hyperbolic partial differential equations that are approximated by a stable and robust finite volume scheme presented in the path-conservative framework. Numerical tests are performed to demonstrate the efficiency of the developed theory.

Pollution Load Coordination and Eco-Compensation for Trans-Boundary Water Pollution Control: The Case of the Tri-Border Region of the Yangtze Delta

A partitioned governance mode, in the absence of multilateral cooperation, always culminates in recurring instances of trans-boundary conflicts and critical degradation of water bodies in border regions. Addressing the existing gaps in quantitative trans-boundary pollution control research in extensive river network, a new approach was designed to strategically guide water pollution control initiatives throughout the entire tri-border region of the Yangtze Delta (TBYD) via the following steps: (1) Building upon an analysis of the trans-boundary river hydrodynamics, the tri-border effective coordination scope (TECS), i.e., a strategic coordination scope for coordinated pollution control, was delineated, and 13 county-level administrative districts were identified as effective contributing regions for detailed coordination. (2) Considering water quality standard (WQS) attainment in the trans-boundary cross-sections, a one-dimensional mathematical model covering the complex river network was established. Then, the load capacities for all the contributing administrative regions were determined to facilitate coordinated pollution load reduction across the TECS. (3) Leveraging from the sewage treatment costs within the TECS, a standardized eco-compensation criterion was established to guide the coordinated compensation practices across the TECS. (4) By comparing the practical pollution discharging amount, the coordinated load reduction rates and eco-compensation payments of all 13 contributing administrative districts for trans-boundary pollution control were assessed. These assessments will guide policy promulgation and provide quantitative data support for harmonizing pollution control policymaking and addressing intricate trans-boundary pollution issues in complex river networks.

Conflict between urbanization and water environmental protection: Lessons from the Xiangjiang River Basin in China

China, the largest developing country, has experienced rapid urbanization since its reform and opening-up. However, the increasing pollution load from urban areas has deteriorated urban river water quality, contradicting the concept of sustainable and green development promoted by the Chinese government. This situation elucidates governmental shortcomings in systematic environmental protection. Our study revealed that the current wastewater treatment plant (WWTP) discharge standards in urban areas are insufficient for attaining the desired urban river water quality and thus intensify the conflict between urbanization and water environmental protection. As urbanization continues, the urban population will grow, further exacerbating pollution and conflict. Our focus was the Xiangjiang River basin in Zunyi, a typical urbanized city in China. Using a validated one-dimensional mathematical model, we compared the water quality in the Xiangjiang River between current and upgraded WWTP discharge standards. The results showed that the water quality in the Xiangjiang River falls short of the standards, with more than 60 % of the river exceeding limits. However, upgrading WWTP discharge standards significantly reduces the proportion of river sections exceeding limits, with only 0.4 % exceeding standards during specific periods. This enhancement greatly improved the Xiangjiang River's water quality, aided in restoring the entire water environment in the basin, and supported water environmental protection goals. Our research findings offer crucial support for local governments in shaping comprehensive water environmental protection policies and insights for addressing similar environmental challenges caused by rapid urbanization in other developing regions.

Theoretical performance assessment of a multi-effect distillation system integrated with thermal vapour compression unit running on solar energy

Abstract Mathematical models can be successfully applied to predict the multi-effect distillation system integrated with thermal vapour compression unit (MED-TVC) performance under different operating conditions. In this work, a one-dimensional (1-D) mathematical model was developed to perform the theoretical analysis of a small-scale parallel feed MED-TVC desalination system driven by solar heat. A parametric study was conducted allowing the ejector motive steam temperature, first effect temperature, between effects temperature difference and ejector compression ratio to vary within an expectable range. The results showed that higher motive steam temperatures, had a positive impact on the water yield up to an optimal point. Any additional increase of driving steam temperature reduced water yield. Gain output ratio ($GOR$) was maximum at the highest considered motive temperature. It was found that the calculated specific heat transfer area does not depend on the motive temperature variation. Water yield, $GOR$ and specific heat transfer area decrease with the ejector compression ratio. The temperature difference between the evaporator effects had no effect on the water yield and $GOR$. It only decreases the specific heat transfer area. First effect temperature should be as low as possible with respect to operational constraints. Based on the parametric study, the optimal design operating conditions, corresponding to the maximum water yield is identified for a small-scale three-effect desalination system. The unit can produce up to 204 l/h drinking water with a gain output ratio of 8.6 and specific heat transfer area of 575 m2/kg/s using about 22 kW of solar heat.

Modelling sludge dewatering in treatment reed bed considering sludge deposit formation

AbstractThe accumulation of sludge deposits is a crucial factor in the dewatering efficiency of sludge treatment reed bed (STRB). This paper presents an improved one-dimensional process-based mathematical model to simulate the dewatering mechanism in STRBs, in which the compressible cake filtration (CCF) theory was implemented to simulate the sludge deposits accumulation on the surface of the reed bed, while the varying sludge deposit thickness was accounted for using the moving mesh method. The proposed model also included the dual porosity variably saturated flow model and the Penman–Monteith equation to describe the dewatering through gravity drainage and evapotranspiration, respectively. The results from the model were validated with experimental data from laboratory-scale STRBs treating septage. The simulation results showed that considering the sludge deposit layer as a specific flow resistance effectively avoids the overprediction of water infiltration rate in the reed bed. The predicted results showed excellent agreement with the actual data, where only five cases of the root mean square error were above 10% compared to the average effluent flux. Further, the effect of evapotranspiration was found to be insignificant within a short-term simulation. The consideration of the influence of sludge deposit formation on drainage dewatering using the CCF model and moving mesh model has delivered a more robust simulation for sludge dewatering in STRBs, and the proposed model is capable of facilitating the understanding of the interactions between the sludge dewatering in STRB with respect to the bed characteristics, hydraulic load, and solid load.

Semi-batch extraction of phenolic compounds from Rosmarinus officinalis: Kinetic study and dimensionless modeling

A transient and one-dimensional mathematical model with two partial differential equations is developed to simulate the extraction of de-oiled rosemary plant in a vertical fixed-bed reactor. The effect of the dimensionless numbers which appear in the final governing equations (Peclet and Damköhler numbers) is studied. The influence of solvent composition, solid particle size and temperature is also investigated. The process is controlled by internal diffusion effects, with the smallest particle size exhibiting the smallest internal diffusion coefficient. Among the different solvents, 80% ethanol shows the highest total phenolics recovery. The antiradical activity is also enhanced by increasing the temperature and the smaller particle size leads to an improvement in the extraction selectivity. Peclet number has a small effect on the results, while Damköhler number strongly affects the process. An increase in bed porosity causes a significant increase in the internal diffusion time.

Transient Process Analysis of Oscillating Motion in Oscillating Heat Pipes

Abstract During the startup phase, oscillating heat pipes (OHPs) exhibit a transient process in which the working fluid moves erratically until a steady-state oscillatory flow is attained. Understanding the transient process is important to predict how long it takes an oscillating heat pipe to reach normal operation and realize its heat transfer potential after it is started. In this paper, we perform a theoretical study of the transient process of oscillating heat pipes. Based on a one-dimensional mathematical model, we obtain an analytic solution that allows us to predict transient process characteristics of oscillating motions in an oscillating heat pipe, as well as the impact that different design and operating parameters have on this transient process.

A Tutorial on the One-Dimensional Theory of Electron-Beam Space-Charge Effect and Steady-State Virtual Cathode

The space-charge effects of pulsed high-current electron beams are very important to high-power particle beam accelerators and high-power microwave devices. The related physical phenomena have been studied for decades, and a large number of informative publications can be found in numerous scientific journals over many years. This review article is aimed at systematically summarizing most of the previous findings in a logical manner. Using a normalized one-dimensional mathematical model, analytical solutions have been obtained for the space-charge-limited current of both planar diode and drifting space. In addition, in the case of a beam current higher than the space-charge-limited current, the virtual cathode behavior and beam current reflection are quantitively studied. Furthermore, the criteria of steady-state virtual cathode formation are investigated, which leads to the physical understanding of the unstable nature of the virtual cathode. This review article is expected to serve as an integrated source of related information for young researchers and students working on high-power microwaves and pulsed particle beams.

Methods for increasing the efficiency of climate control systems for electric buses

Increasing the range of an electric bus on a single battery charge is an important task facing electric bus developers. The auxiliary system that consumes the largest amount of electricity is the air conditioning system. This paper examines the main methods for increasing the efficiency of a climate control system and evaluates them using numerical methods using a verified one-dimensional mathematical model. The following methods were chosen to improve efficiency: the most suitable refrigerants, the use of an internal heat exchanger of a vapor compression unit, the recovery of heat from the air removed from the interior electric bus in the evaporator of a vapor compression unit, and the use of heat from electrical equipment in the climate control system. The greatest efficiency in cooling and heating modes is shown by the use of refrigerants R404a, R410a and R507a in the vapor compression unit. The use of an internal heat exchanger in a vapor compression unit allows an increase in coefficient of performance by 11%. The combined use of cabin heat in the evaporator of the vapor compression unit and the internal heat exchanger allows the coefficient of performance to be increased by 27%. Using the heat of electrical equipment allows you to increase the coefficient of performance in heat pump mode by 20%. The most promising is the combined use of the above methods to reduce the cost of air conditioning in the cold season.

DESIGN AND VERIFICATION OF THE MODEL OF STRUCTURE FORMATION AND HEAT TRANSFER IN A FLUIDIZED BED APPARATUS WITH A HEAT JACKET

A one-dimensional mathematical model of the formation of a fluidized bed and the evolution of its thermal state during the heating of an ensemble of particles is proposed based on the mathematical apparatus of the Markov chain theory. When describing the thermal state of the system, the processes of interfacial heat exchange between the gas flow and particles, as well as between the wall of the apparatus and the gas suspension, were taken into account. The results of previous studies and known empirical regularities for the material constants of the process were used to identify the parameters of the model. The parametric identification made it possible to adapt and apply the mathematical model for calculating the process of heat treatment of the suspension of silicate sand particles in an apparatus with a fluidized bed of a periodic principle of operation equipped with a heating jacket. Verification of the predictive capabilities of the physicomathematical model adapted in this way was carried out by comparing the forecasts obtained by calculation with the results of the full-scale experiment conducted during the study. To conduct the full-scale experiment, a sample of sand particles was placed in the apparatus, which was previously output to the established thermal regime of operation. After loading the material, a set of thermocouples equidistant from each other was placed in the apparatus and temperature readings were taken at different heights from the level of the gas distributor. The temperature distributions obtained in this way along the bed height were in good agreement with the calculated forecasts and show a significant heterogeneity of the gas phase temperature fields. The temperature of the particles was estimated only as an integral characteristic by measurements of the heat content of the bulk medium after unloading from the apparatus. The integral temperature of the particles also turned out to be close to the predicted values. In addition, during the computational and experimental study, the kinetic characteristics of the heating of the suspension of the material were clarified. Thus, the proposed mathematical model has sufficient predictive efficiency for engineering tasks and can be considered as a basis for constructing a computer method for calculating heat exchangers with a heating jacket using the fluidization technique of bulk media.

Topological optimization hybrid algorithm for the adhesive joint

The subject of this study is a topological optimization algorithm for a lapped symmetric adhesive joint. The purpose of this research is to create a hybrid optimization algorithm that combines the advantages of a genetic algorithm and a particle swarm algorithm and, at the same time, reduces the time required to solve the problem. Task: to create a methodology for solving the optimization problem for a symmetric double-sided lapped adhesive joint, which consists of a main plate and two patches (the main plate has a constant thickness, and the thickness of the patches varies along the length of the joint, this is required to reduce the stress concentration in the joint and reduce its weight) with satisfaction of the optimality criterion, namely, to minimize the mass of the structure with the strength and thickness restrictions for the patch. The optimization problem is that we must find the optimal patch form, namely, the length of the patch and the thickness-on-length dependence for the patch. Methods: the modified Goland-Reissner model was used to describe the deflected mode of the joint. The finite difference method was used to solve the direct stress state problem for the structure. For the numerical solution of the optimization problem, a combination of the multi-population model of the genetic optimization algorithm and the particle swarm algorithm was used. To improve the performance of the genetic algorithm, a multi-population model with migration of the best individuals between populations was applied. The introduction of individuals from other populations into the population avoids homogenization of the genotype in a separate population and premature stopping of the optimization process. To describe the shape of the patch, the Fourier series expansion of the patch thickness dependence was used. Results: A hybrid algorithm is proposed based on the sequential application of a genetic algorithm and a particle swarm algorithm for three populations of solutions. The particle swarm algorithm makes it possible to improve the value of the objective function achieved at the previous stage by 20%. Conclusions: the scientific novelty lies in the improvement of the optimization algorithm compared with the known ones. To reduce the calculation time, a one-dimensional adhesive joint stress state mathematical model was used in this paper. The methods used made it possible to create a combined topological optimization algorithm that combines the advantages of both methods and allows us to find a solution to the problem quite quickly. The Python program run time is only a few minutes.