Hot Water Flow Research Articles

Estimation and Control of WRRF Biogas Production

The development of resource-efficient digital technologies is a critical challenge in the wastewater sector. This industrial case study, conducted in collaboration with the Veas Water Resource Recovery Facility in Norway, focused on creating data pre-processing methods and resource-efficient control strategies. Using data from the Veas biogas plant, dynamic models were developed to compare control outcomes. The primary objective was to maximize biogas production and hot water usage while maintaining optimal temperature and hydraulic retention time by adjusting inlet sludge and hot water flow rates. Sequential operations were approximated as continuous operations using a 30-min moving minimum/maximum for bimodal data and a 2-h moving average for noisy data. The data-driven dynamic models achieved an accuracy of up to R2 of 0.85. The control strategy, which included one feedback controller, one ratio controller, and flow rate restrictions, was compared to real production data (baseline) and tested across six scenarios. The best improvement over the baseline scenario resulted in a 3% increase in total biogas production, a 6% increase in total organic loading, a 13% increase in hot water use, and a one-day reduction in hydraulic retention time. Future work should focus on control studies using extended datasets and nonlinear models.

Hybrid Energy (Thermoelectric Generator-Archimedes Screw Turbine) Study and Experiment as a Green Energy Generator Based on the Internet of Things (IoT)

The heat energy from the hot water source of Mount Sinabung can be used as a source of electrical energy before being channeled as a source of hot water baths. The hot water flow has a fairly high temperature and a flow rate that can be converted into a source of electricity generation using a Micro Hydro Power Plant (PLTMH) and Thermoelectric Generator (TEG). This data collection was simulated using a heat source designed in a reservoir and a cold water flow that is channeled into the PLTMH-TEG system space as a source of temperature delta. This paper aims to study the TEG series TEG1-199-1.4-0.5 and the Archimedes screw Turbine (PLTMH) as a Hybrid Generator (Green Energy). Data analysis was carried out to calculate the system power output, battery charging time, and efficiency of the TEG and PLTMH. Data analysis in this study applies the Internet of Things (IoT). Test data shows that the maximum output parameter of the PLTMH during testing, obtained a maximum voltage of 20.42 Vdc. The maximum current is 759.75 mA and the maximum water discharge is 2.31 m3/s. In the TEG system, the power generated by the TEG is 20.64 watts at a temperature difference of 70.5˚C. It is concluded that the higher the amount of discharge flowing into the Archimedes turbine system and the temperature difference absorbed by the TEG, the greater the power that will be generated and vice versa.

Pre-Roman U-Th datings of an aqueduct near ancient Lebedos (Aegean Region, Türkiye)

In the vicinity of the ancient city of Lebedos, known as one of the twelve Ionian cities, located south of İzmir in W. Anatolia (Türkiye), the NE-SW-trending active Tuzla Fault zone is characterized by numerous hot springs and associated travertine-type carbonate deposits (sinter). Among these, the active Doğanbey bath features an approximately 560 m-long hot water aqueduct, called the “Roman Aqueduct”. This structure is distinct from the well-known Roman (Byzantine) ruins (Karakoç bath) in the area in terms of its materials and construction techniques. Despite the absence of detailed archaeological or geochronological studies in this region, the Doğanbey bath and aqueduct have conventionally been attributed to the Roman era.The trough and sidewalls of the Doğanbey aqueduct are covered with a 5–25 cm-thick, laminated sinter crust, formed by the flow of hot water. Each sinter lamina comprises radial structures of calcite and/or aragonite, resembling feather-like shrub structures. This study employs the U-Th chronometry to determine the age of sinter layers covering the Doğanbey bath aqueduct. Two layers from a single sinter sample of the ancient Doğanbey aqueduct yielded U-Th ages of 2717 ± 106 and 2528 ± 106 years (BP). These dates indicate a pre-Roman phase of settlement in the Lebedos area, a finding documented for the first time through this study.

Novel heavy fuel oil based IGCC polygeneration system based on integration with ejector cooling and heat recovery of the solid oxide fuel cell in adsorption desalination

An innovative polygeneration system based on the gasification of heavy fuel oil including Orimulsion, Mazut, and Asphaltene has been proposed. In this system, electricity, hot water, cooling, hydrogen, fresh water, and nitrogen are produced in an innovative way to improve the system. In this regard, the integration of an Integrated Gasification Combined Cycle-Organic Rankine Cycle- Ejectero Refrigeration Cycle-Solid Oxide Fuel Cell-Adsorbation Deselination-Polyer Electron Electrolyzer has been proposed. The proposed system was investigated from the points of view of energy, exergy, exergoeconomic, and exergoenvironmental. In addition, to model the air separation unit, machine learning techniques have been employed.The results show that if Mazut is used as a gasification material, the system will have 36.81 %, 33.3 %, and 66.22 mPts/kWh in terms of polygeneration energy efficiency, polygeneration exergy efficiency and Levelized environmental impact of electricity, respectively and if Orimulsion is used, the Levelized cost of electricity value will be 33.32$/MWh which are the best performance in three fuel. Nitrogen production in this system is 35.08 kg/s, and hydrogen production is 0.0051 kg/s. The value of specific daily water production in the AD unit is 8.40 m3watertonofsilicagelper day, and the flow of hot water produced is 7.37 kg/s.

Thermal Performance of a Laminar Flow Double Pipe Heat Exchanger with Spiral Airfoil Inserts

Objective: This study evaluates the thermal performance of a double-pipe heat exchanger using a spiral airfoil insert in the inner pipe. Methods: The enhancement technique is classified as a passive method, as it does not require the direct application of external power to improve the heat transfer coefficient. Spiral pitch ratios of P/D=7, 5, and 3 were used, with the Reynolds number (Re) varying within the laminar flow regime (Re ≤ 2,100). Cold water flows inside the inner pipe, while hot water flows counter to it in the annulus. Results: The experimental results show that the Nusselt number increased by 159%, 161%, and 171%, respectively, compared to a smooth pipe alone, for flow rates of 2L/min, 2.5L/min, and 3L/min. Additionally, the highest friction factor reached 142%. Conclusion: The results indicate that the best performance evaluation criterion (PEC) was achieved within the flow range of 2L/min to 3L/min, with a pitch insertion of 3, yielding a PEC of 158% to 152%, respectively.

Off-design performance optimization for steam-water dual heat source ORC systems

High-pressure steam and hot water often coexist as industrial waste heat. In this study, dual loop and single loop ORC systems are designed for 700 kPa, 4.1 kg/s steam, and 90 ℃, 122.36 kg/s hot water conditions to study the off-design performance when steam or hot water conditions change. To maximize net output power, we employ a particle swarm optimization algorithm to optimize the evaporation and condensation temperatures. The results show that within the specified hot water conditions, the evaporation and condensation temperatures of D-ORC's low-pressure loop and S-ORC increase with rising hot water inlet temperature and flow rate. The S-ORC demonstrates a higher net output power growth rate as hot water flow rate and temperature rise. Under specific steam conditions, when the steam outlet is in a gas-liquid two-phase state, D-ORC's maximum net output power is 1.7 % higher than that of the S-ORC, with little variation in optimal evaporation and condensation temperatures with respect to steam inlet pressure. At a 3.5 kg/s steam flow rate, the D-ORC's high-pressure loop becomes ineffective, whereas S-ORC efficiently adjusts heat exchange capacity under diverse steam-water conditions, Consequently, the D-ORC's average net output power is 34.2 % lower than that of the S-ORC.

Preparation of dodecahydrate disodium hydrogen phosphate shape-stabilized composite phase change materials and their experimental investigation in solar thermal storage and exothermic systems

To alleviate the mismatch between energy supply and demand caused by the spatial and temporal distribution mismatch and weather uncertainty during solar energy utilization, solar energy is combined with phase change thermal storage technology to improve the performance of solar thermal storage systems. In this study, a shape-stabilized composite phase change material with a highly absorbent resin structure is proposed as thermal storage material. This material exhibits a latent heat of phase change of 246.5 J/g, a thermal conductivity of 1.968 W/(m·K), and maintains good stability after 200 thermal cycles. Subsequently, a detachable experimental setup integrating solar energy with a phase change thermal storage tank was designed and constructed. The effects of inlet and outlet hot water flow rates and heat source temperature on heat storage time and the amount of stored water were investigated separately. The experiments show that increasing the heat source temperature during storage effectively shortens the storage time, and that the largest effective amount of hot water is obtained when the exothermic flow rate is 300 L/h. The study's results are significant for broadening solar energy utilization, alleviating the mismatch between solar energy supply and demand, and evaluating the thermal performance of latent heat storage systems.

Effect of the surface form of the herringbone aluminum plate in a plate heat exchanger on the boiling heat transfer performance of ammonia

In this study, ammonia boiling heat transfer coefficient and the overall heat transfer were measured in a plate evaporator for an ocean thermal energy conversion (OTEC) system using aluminum plates. The OTEC system used ammonia as the working and a plate heat exchanger (PHE) that combined titanium plates. In this study, we used an anodized aluminum herringbone plate with two chevron angles of 45 and 60° installed in a PHE and measured the boiling heat transfer coefficients of ammonia and overall heat transfer coefficients for both plates to compare their heat transfer performances. The experimental conditions included a hot water flow rate of 1 – 12 L/min, a working fluid mass flux of 7 – 30 kg/m2s, a hot water inlet temperature of 30 – 40 °C, and a system pressure of 700 kPa.It was observed that anodized aluminum can be used as a heat-transfer plate for the PHE. In addition, the maximum overall heat transfer coefficient of chevron angle of 45° was 4 kW/m2K, and that of 60° was 3.5 kW/m2K, respectively. The maximum ammonia boiling heat transfer coefficient of 45° was 12.5 kW/m2K, and that of 60° was 13 kW/m2K, respectively. The heat transfer coefficient values are similar. Additionally, the correlation between the nondimensional heat transfer and the Lockhart-Martinelli parameter of aluminum plates was also clarified for comparison with the previous ammonia plate heat transfer in a flat plate. By comparing the correlation equations, the aluminum plate exhibited a value twice that of the flat plate.

Experimental study of the optimal mixing ratio of metallic additives for improving the performance of the solar activated carbon-methanol adsorption refrigeration system

An activated carbon–methanol system can run on low heat (70–100°C). Methanol is dependable and works well with activated carbon because of several benefits, including an appropriate latent heat of evaporation, a low freezing point, and negligible copper corrosion and steel at temperatures below 100 °C. An experimental study of the thermal performance by increasing the adsorption bed thermal conductivity was conducted. Using0 10 % 20 and %30 % of metallic copper powder with activated carbon to improve the bed thermal conductivity. A sample is prepared with 20 % copper powder to find out the improvement of heat transfer characteristics to the cooling effect. The temperature gradient has been tested with two flow rates to examine the coolant performance and increase. Solar energy can be effectively utilized based on low-grade temperature consumption in such systems. This work aims to make an experimental investigation of the thermal performance of an activated carbon-methanol adsorption refrigeration system to study the effect of the enhanced thermal conductivity of the adsorbing bed. Using 0 %, 10 %, 20 %, 30 % of metallic copper powder with activated carbon to enhance the thermal conductivity of the bed, providing a significant improvement in the system efficiency, specific cooling power (SCP), and coefficient of performance of adsorption cooling. It is found that copper filing with a mass concentration of 20 % are appeared the optimal ratio metallic additive to enhance the thermal performance of the system. Moreover, the effect of the hot water flow rate is studied. Results indicated that the addition of 20 % metallic copper filings to the activated carbon lowered the evaporator temperature to reach -5 and -10 °C for heating water flow rates 3 and 2 LPM, respectively. Also, the addition of copper filing enhances the cycle COP of the system by 49 % and 46 % at hot water flow rates of 2and 3 LPM, respectively. The highest cycle COP of the current system reached was 0.92 for the condition 20 % additives at 3 LPM hot water flow rate. Owning the feature of great solar energy availability and the long daily sunny hours, solar-powered adsorption cooling systems have promising potential applications in Egypt. A mathematical model of the system performance is also studied.

Economic and Exergy Analysis of TiO2 + SiO2 Ethylene-Glycol-Based Hybrid Nanofluid in Plate Heat Exchange System of Solar Installation

This paper concerns an economic and exergetic efficiency analysis of a plate heat exchanger placed in a solar installation with TiO2:SiO2/DI:EG nanofluid. This device separates the primary circuit—with the solar fluid—and the secondary circuit—in which domestic hot water flows (DHW). The solar fluid is TiO2:SiO2 nanofluid with a concentration in the range of 0.5–1.5%vol. and T = 60 °C. Its flow is maintained at a constant level of 3 dm3/min. The heat-receiving medium is domestic water with an initial temperature of 30 °C. This work records a DHW flow of V˙DHW,in = 3–6(12) dm3/min. In order to calculate the exergy efficiency of the system, first, the total exergy destruction, the entropy generation number Ns, and the Bejan number Be are determined. Only for a comparable solar fluid flow, DHW V˙nf=V˙DHW 3 dm3/min, and concentrations of 0 and 0.5%vol. is there no significant improvement in the exergy efficiency. In other cases, the presence of nanoparticles significantly improves the heat transfer. The TiO2:SiO2/DI:EG nanofluid is even a 13 to 26% more effective working fluid than the traditional solar fluid; at Re = 329, the exergy efficiency is ηexergy = 37.29%, with a nanoparticle concentration of 0% and ηexergy(1.5%vol.) = 50.56%; with Re = 430, ηexergy(0%) = 57.03% and ηexergy(1.5%) = 65.9%.

Multi-objective optimization of solar-driven hollow fiber membrane dehumidification system based on MOPSO

The solar-driven hollow fiber membrane dehumidification (SHFMD) system is a renewable, energy-saving, and highly effective dehumidification system. It provides an effective solution to the problem of air-entrained liquid droplets during the traditional solution dehumidification process. The system's mathematical model was established and the reliability of the mathematical model was verified by experimental data. To enhance the comprehensive performance of the system, the multi-objective particle swarm optimization (MOPSO) algorithm is used in this paper to optimize the multi-objective parameters of the system. The objective function is the total exergy destruction of the system and the dehumidification capacity of the system. The optimization variables are cold water temperature, cold water flow rate, solution flow rate, air flow rate, and hot water flow rate. The optimization is performed using the multi-objective particle swarm optimization (MOPSO) algorithm to obtain the Pareto front, and the points of the Pareto front are normalized. Finally, the optimal trade-off point of the Pareto frontier is obtained. Each operating parameter of the optimal point of the Pareto front is also analyzed. The results show that the air flow rate and cold water flow rate have the most influence on the conflict between the total exergy destruction of the system and the dehumidification capacity of the system.

A new model for predicting pressure traverse in two phase flow geothermal well

The complexity associated with the two phase or multiphase flow system have been a long-time challenge in the modelling of the flowing pressure in the production channel which includes geothermal well. The flow of hot water and its vapour ensued all throughout the geothermal system producing from the reservoir source to the wellbore and later to the surface. The performance of geothermal system is primarily dependent on the ability to accurately predict the flowing pressure in the production well. Several models derived from the fundamental thermodynamic energy equation to handle the complexity of two-phase flow in geothermal well have demonstrated diverse discrepancy when compared with real time measurement. It has been conceived in the study that the inclusion of pressure drop due to accumulation in the thermodynamic energy equation reduces the discrepancy between the predicted pressure and the field measurement. It is pertinent to the geothermal energy industry to assess the accurate model that consider all constituent terms that impact the two-phase flow behaviour in a geothermal production well. A more exact numerical model for evaluating the flowing pressure in geothermal has been derived in this study where the right constituent terms that practically impact the two-phase flow behaviour in a geothermal vertical well are considered. The present model has the capacity to predict flowing pressure accurately as the flow transit from one regime to another. Likewise, the present model was able to capture the transient period that usually occurs when the geothermal well is put to production. The present model was validated using data from KE1-22 and Mesa 6-1 wells reported in literature. The present model gave the least mean absolute relative error of 0.033 when applied to measured field data from KE1-22 Well while Hassan and Kabir, Ansari, Orkiszewski and Homogenous models gave errors of 0.12, 0.33, 0.41 and 0.38 respectively. Similarly, relative to data from Mesa 6-1 the present model gave a mean absolute relative error of 0.052 while Hassan and Kabir, Ansari, Orkiszewski and Homogenous models gave errors of 0.17, 1.46, 1.37 and 2.53 respectively. The newly derived model is reliable for assessing the performance of the geothermal system and evaluating flowing pressure at every difference transition period.

Identifying the structure as a hot water outflow path using gravity in Jatimulyo, South Lampung

Abstract Geothermal manifestations have been utilized as a tourist attraction (geo-tourism) worldwide. Geothermal manifestation systems could be found in many forms such as hot springs. The path of the hot water flow is controlled by the existence of geologic structures such as faults as the medium. Geophysical methods in general have been used to image and characterize subsurface layers. The gravity method using the natural source has been employed to determine the geological structure, such as faults. This study aims to identify the structure related to the outflow path which is part of the geothermal system using gravity method in Jatimulyo Village, Jati Agung, South Lampung. The result shows the contrast anomaly indicating the existence of a fault that could be a hot water path. An outflow zone which is characterized by low temperatures because it is far from heat sources. The complete Bouguer Anomaly is used to create 2D forward modelling where the model is divided in 2 layers. The first layer is indicated as Lampung Formation (QTl) with density of 1.8 g/cc, and second layer recognized as bedrock with denser rock of 2.78 g/cc representing Tertiary Paleozoic (Pzg) Gunung Kasih Complex Formation.

Experimental investigation of two-bed adsorption thermophysical battery with mass recovery technology

This paper developed a novel semi-continuous two-bed Adsorption Thermophysical Battery (ATB), utilizing silica gel RD/water as the adsorption pair. The Absorber Bed Unit (ABU) was designed and manufactured using finned tubes, while the condenser and evaporator are incorporated under a single Evaporator-Condenser Unit (ECU). The study investigated the impact of mass recovery, hot and cooled water temperature, and the chilled, cooled, and hot water flow rate on the system performance. The results of the study revealed that the ATBwith mass recovery demonstrated a higher Coefficient of Performance (COP) and Refrigeration Capacity (RC) in comparison to the system without mass recovery. The average COP for the cycles with and without mass recovery were 0.228 and 0.2, respectively. The present study determined that the most favorable duration for mass recovery was 60 s. A substantial reduction in the COP can be observed as the hot and cooled water temperature increases. Also, the COP of the ATB was found to be directly related to the flow rates of chilled and cooled water but not to the flow rates of hot water. In addition, the COP of the two-bed ATB with mass recovery was improved by 14 % compared with the single-bed ATB. Finally, the adsorption uptake rose by 24 % when the cooled temperature was decreased from 313 K to 303 K.

Experimental study of a novel in-tube spray evaporative condenser for geothermal power generation

To enhance the efficiency of medium to low-temperature geothermal power systems, we designed a novel in-tube spray evaporative condenser. Experimental setups for single-tube heat exchange were devised, examining both water-water and working fluid-water configurations. The study analyzed the impact of air volume and hot water flow rate on heat transfer. Economic comparisons were made in laboratory conditions among the novel evaporative condenser, traditional evaporative condenser, water-cooled condenser, and air-cooled condenser. Results indicated: (1) The novel evaporative condenser exhibited 1.5–1.7 times higher heat flux density and 2.0–2.7 times higher mass transfer coefficient, indicating superior heat transfer performance compared to the traditional one. (2) Variations in hot water flow rate within a certain range had minimal impact on condenser performance when the condenser size was constant, providing valuable insights for condenser selection and structural design. (3) Both total power and water consumption of the novel evaporative condenser were lower than the other three types. Its daily operating cost was approximately 3/4 of the traditional evaporative condenser, 1/2 of the air-cooled condenser, and 1/4 of the water-cooled condenser, demonstrating superior economic feasibility.

Numerical investigation on assessing the influence of diverse-shaped hybrid nanofluids on thermal performance of triple tube heat exchanger

The present study explored the effects of hybrid nanofluids, composed of water-based nanoparticles in various shapes (MWCNT-cylindrical, Al2O3-blade, Graphene-platelet, and Fe3O4-brick), within a triple concentric tube heat exchanger (TCTHX). Theoretical and computational modeling was conducted for the flow of hot water and hybrid nanofluids at varying inner annulus mass flow rates (0.1 kg/s to 0.5 kg/s and at a fixed temperature of 70 °C) in the TCTHX; their influence was analyzed by the energetic and exergetic performance and revealing the findings to enhance the heat transfer efficiency.The key finding of the work is that the thermal performance factor (TPF) of the brick-blade hybrid nanofluid in the TCTHX is 4.26, which is the maximum as compared to brick-platelet, brick-cylindrical, blade-platelet, blade-cylindrical, and platelet-cylindrical hybrid nanofluids for all mass flow rates. The brick-blade hybrid nanofluid is the most economical in the TCTHX system, followed by the brick-cylindrical hybrid nanofluid. Overall, the combination of brick-blade hybrid nanofluid performs best in the TCTHX system in terms of performance index, TPF, and CBR. Brick-platelet hybrid nanofluid is 7.20% less efficient than water at a mass flow rate of 0.1 kg/s. Platelet-cylindrical hybrid nanofluid exhibits 12.71% and 5.09% lower heat transfer rate and performance index than delaminated (DI) water at the lowest mass flow rate in the TCTHX system. Brick-platelet hybrid nanofluids show a reduced Nusselt number ratio for the tested mass flow rates. Entropy generation in blade-platelet hybrid nanofluid is 19.49% lower than in (DI) water.

Fuzzy System to Control a Liquid Mixing Tank

This paper aims to develop a fuzzy system to control the level and temperature of a fluid in a mixing tank by dynamically adjusting the flow rates of cold and hot liquids. The system involves a temperature and level loop, with the control variables being the rates of cold water and hot water flow, while also considering the outlet flow from the reservoir as a disruptive factor. The main goal of this control strategy is to maintain the liquid level and temperature within specified reference values. The system is a multivariable process that uses a fuzzy control system to develop a technique that, based on the state variables, can adapt the controller to achieve optimal control performance. In the development of this application, some linear controllers were tested, each implemented around specific regions within the phase plane. The designed controllers are then employed in conjunction with the fuzzy system to evaluate the system’s state variables. Therefore, an interpolation of these linear controllers is conducted, allowing for their application in a nonlinear system, with the aim of enhancing control performance near the boundaries between regions. The results show that the fuzzy approach is promising and provides convergence to the reference values of the liquid level and temperature in the mixing tank.

Case study of design and construction of dehydration for paddy by heat exchanger rectangular two-phase closed thermosyphon(DP-HE/RTPCT)

The purpose of this research was to design and produce a dehydration system for paddy using a heat exchanger rectangular two-phase closed thermosyphon (DP-HE/RTPCT), which is a modified version of the rectangular two-phase closed thermosyphon (RTPCT). The working fluids used in this study were R11 and methanol at 50% addition rate of the evaporator volume while evaporator temperatures of DP-HE/RTPCT were set at 60 and 80 °C. The evaporator and condenser of the DP-HE/RTPCT were of equal length, the hot water flow rate into the evaporator was 1.5 L/min whereas the initial moisture content of the paddy was 21.50% of the wet basis. Using methanol as a working fluid at the evaporator temperature of 80 °C reduced the moisture content of the paddy to 14% of the wet basis in 390 min, which yielded the highest DP-HE/RTPCT efficiency of 0.62. This was the shortest time in all cases while the internal heat of the paddy pile peaked at A-depth and decreased at B-depth and C-depth, respectively. Paddy germination rate was 90% in the DP-HE/RTPCT that used R11 as the working fluid, at the evaporator temperature of 60 °C. The design and construction of DP-HE/RTPCT demonstrated a novel application of thermosyphons with a modified cross-sectional area. This study could serve as a foundation for future research on heat exchangers.

Multi-criteria evaluation of novel multi-objective model predictive control method for indoor thermal comfort

We proposed a novel multi-objective model predictive control (MPC) approach based on a straightforward internal prediction model to achieve building energy efficiency and maintain the indoor temperature within a predetermined comfort range. Using the CARNOT Toolbox, we built a detailed room model based on a real room with water-circulated radiator heating. We developed an MPC controller using MATLAB and combined it with the room model in the CARNOT Toolbox to tune the controller parameters and evaluate its performance. Based on the co-simulations, a control step of 15 min and a prediction horizon of 90 min were found to be suitable for room level indoor thermal comfort control. The performance of the controller was evaluated in terms of multiple criteria, including control accuracy, hydrodynamic stability, and energy consumption. Compared with the traditional proportional-integral-derivative (PID) control, the MPC demonstrated a 16.4 % improvement in control accuracy, 2.8 % lower energy consumption, and a 50 % reduction in the hot water flow change rate, improving the system’s hydrodynamic stability. A significant advantage of the MPC is that it is possible to compute different efficient solutions by modifying the parameters, among which the decision-makers can choose their most preferred compromise solution considering multiple criteria.

Physics-informed neural network combined with characteristic-based split for solving Navier–Stokes equations

This paper presents a novel approach for solving the shallow-water transport equation using a physics-informed neural network (PINN) combined with characteristic-based split (CBS). Our method separates the variables, so it is no need to consider the weight coefficients between different loss functions. As not all partial derivatives are involved in the gradient backpropagation, our method can save half of the memory occupation without losing accuracy, and resulting in a significant reduction in computation time compared to traditional PINN. We solving the progress of the dispersion of hot water under known flow fields. Furthermore, we propose a boundary condition that accounts for the second-order partial derivative term, which is more appropriate for solving the diffusion equation with open domains than the commonly used assumption of zero boundary values. Our numerical results demonstrate that this boundary condition leads to improved convergence of the network. In addition, we introduce a parameter estimation method to estimate the diffusion coefficient of hot water flow, which requires information from the field at only two different times. We observe that excessive participation of variables in gradient backpropagation can lead to neural networks getting trapped in local optima. We use PINN combined with CBS method to solve 3-D incompressible flow. As the number of variables involved in gradient backpropagation increases, the accuracy of the solution decreases, which can partially support our viewpoint. The source codes for the numerical examples in this work are available at https://github.com/double110/PINN-cbs-.git.