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The energy loss of the vertical axial flow pump device increases due to the unstable internal flow, which reduces the efficiency of the pump device and increases its energy consumption of the pump device. The research results of the flow loss characteristics of the total internal conduit are still unclear. Therefore, to show the internal energy loss mechanism of the axial flow pump, this paper used the entropy production method to calculate the energy loss of the total conduit of the pump device to clarify the internal energy loss mechanism of the pump device. The results show that the energy loss of the impeller is the largest under various flow conditions, accounting for more than 40% of the total energy loss of the pump device. The variation trend of the volume average entropy production and the energy loss is similar under various flow coefficients (KQ). The volume average entropy production rate (EPR) and the energy loss decrease first and then increase with the increase of flow, the minimum volume average entropy production is 378,000 W/m3 at KQ = 0.52, and the area average EPR of the impeller increases gradually with the increase of flow. Under various flow coefficient KQ, the energy loss of campaniform inlet conduit is the smallest, accounting for less than 1% of the total energy loss. Its maximum value is 63.58 W. The energy loss of the guide vane and elbow increases with the increase of flow coefficient KQ, and the maximum ratio of energy loss to the total energy loss of the pump device is 29% and 21%, respectively, at small flow condition KQ = 0.38. The energy loss of straight outlet conduit reduces first and then increases with the increase of flow coefficient KQ. When flow coefficient KQ = 0.62, it accounts for 27% of the total energy loss of the pump device, but its area average entropy production rate (EPR) and volume average entropy production rate (EPR) are small. The main entropy production loss in the pump device is dominated by entropy production by turbulent dissipation (EPTD), and the proportion of entropy production by direct dissipation (EPDD) is the smallest.

The unstable flow of a shaft tubular pump device (STPD) leads to energy loss, thereby reducing its efficiency. The aim of this study is to investigate the distribution pattern of energy loss in STPDs. This paper reveals that the two components with the highest proportion of energy loss are the impeller and the outlet passage. Furthermore, turbulent entropy production is the primary cause of energy loss. Due to the wall effect, the energy loss in the impeller mainly occurs near the hub and shroud. Additionally, the presence of a tip leakage vortex near the shroud further contributes to the energy loss in the region near the shroud. This results in the energy loss proportion exceeding 40% in the region with a volume fraction of 14% near the shroud. In the outlet passage, the energy loss mainly occurs in the front region, with a volume fraction of 30%, and the energy loss in this part accounts for more than 65%. Finally, this study reveals the locations of the vortex in the STPD under different flow-rate conditions, and when the distribution of energy loss is visualized, it is found that the energy loss occurs high in the vortex regions.

The low head pump is widely used in many important water conservation projects for drainage and irrigation purposes. A new type of low head pump, the bidirectional shaft tubular pump, consists of an S-shaped impeller, a straight-guide vane, an inlet section, and an outlet section. As known from the practical project, the distance between the impeller and guide vane of the bidirectional shaft tubular pump greatly affects a pump’s performance; however, because of its unique impeller and guide vane structure, the distance between the two cannot be easily determined by general empirical formulas. Therefore, in this research, three-dimensional unsteady numerical simulations were performed for six guide vane positions under positive and negative rotation conditions, and the accuracy of the results was experimentally verified. The entropy production method based on numerical results was used to evaluate the effect of the distance on the internal flow-loss distribution and overall power loss, and as a result, a better understanding of the hydraulic loss mechanisms was obtained. The results show that the distance between the impeller and guide vane of a bidirectional shaft tubular pump can affect the pump’s efficiency under a positive rotation condition, and turbulence dissipation is the dominant loss. This study can provide theoretical guidance to improve the hydraulic efficiency of low head pumps.

The cavitation phenomenon significantly impacts the performance of pump turbines, necessitating in-depth research on their cavitation characteristics. This study investigates the performance characteristics of a pump turbine through experimental and numerical simulation methods, with consistent results verifying the accuracy of the numerical simulations. The cavitation flow field is numerically analyzed to compare the cavitation distribution and velocity streamlines at different stages of cavitation development. The Q criterion and entropy production method are employed to identify vortex structures and energy loss regions, respectively, exploring the correlation between vortices and energy losses in the cavitation flow field under low-flow pump conditions. The results demonstrate that intensified cavitation generates more multi-scale vortices in the flow field, leading to increased entropy production and reduced energy efficiency. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) methods were subsequently applied to extract vorticity characteristics from transient cavitation flow fields, revealing primary energy loss regions and elucidating the evolution and distribution patterns of vortices. The POD analysis shows that low-order modes represent dominant vortex structures, while intensified cavitation increases both the quantity of vortices and their complexity in scale, distribution, and evolutionary frequency. The DMD results further indicate distinct evolutionary patterns for vortices of different scales. This research provides insights into the instability characteristics of cavitation flow fields in pump turbines under low-flow pump conditions and offers theoretical support for optimizing the design of pump turbines to expand their high-efficiency operational range.

A nonlinear fourth-order parabolic equation with nonhomogeneous Dirichlet-Neumann boundary conditions in one space dimension is analyzed. This equation appears, for instance, in quantum semiconductor modeling. The existence and uniqueness of strictly positive classical solutions to the stationary problem are shown. Furthermore, the existence of global nonnegative weak solutions to the transient problem is proved. The proof is based on an exponential transformation of variables and new \"entropy\" estimates. Moreover, it is proved by the entropy-entropy production method that the transient solution converges exponentially fast to its steady state in the$L^1$norm as time goes to infinity, under the condition that the logarithm of the steady state is concave. Numerical examples show that this condition seems to be purely technical.

Accurate estimation of terrestrial evapotranspiration (ET) is vital for understanding global water and energy cycles. However, current global ET estimations are not well constrained. This study introduces an integrated framework combining the Maximum Entropy Production (MEP) theory with Random Forest (RF) model to improve global ET estimation. Specifically, in contrast to direct ET estimation by the RF model, the integrated framework (MEP‐RF) trains to predict error of MEP‐simulated ET. MEP‐RF outperforms RF in spatiotemporal extrapolation. Attribution analysis with in situ observations reveals that the inputs of MEP are the most critical variables for the ET process, including net radiation, vegetated area, soil moisture, and surface temperature. We further drive MEP‐RF with global reanalysis and satellite data sets of these four inputs, yielding a global mean terrestrial ET of 548 mm/year, with 77% attributed to transpiration. The global ET increased at a rate of 0.85 mm/year per year during 2003–2021, primarily due to vegetation greening rather than rising temperature, while decreasing soil moisture led to decreasing regional ET. The integrated framework provides a novel approach for the estimation of global ET without the need for hard‐to‐obtain and thus uncertain inputs, such as wind speed, surface roughness, aerodynamic and canopy stomatal resistance. Therefore, MEP‐RF offers an independent method on existing global ET products. It represents a promising physically based approach that can be incorporated into Earth System Models to enhance water and energy cycle simulations.

In this paper, we address the problem of multi-objective production planning in a hybrid manufacturing and remanufacturing system (HMRS), introducing several significant contributions. First, we propose a new formulation of the problem that extends the existing literature by introducing a multi-objective model. This model aims to minimize both total costs and C O 2 emissions within a hybrid system composed of various machines in charge of producing new and remanufactured products of different qualities. To efficiently solve this complex problem, we present an innovative approach that integrates several techniques, including NSGA-II, the entropy weight method and the TOPSIS technique. Our research focuses on the economic and environmental aspects of the remanufacturing process, seeking to determine the optimal manufacturing and remanufacturing plan. This plan aims to meet demand for new products and maximize satisfaction for remanufactured products of different qualities, while minimizing the total economic costs and C O 2 emissions incurred during the various manufacturing and remanufacturing stages, including set-up, production, inventory and disposal. To address the multi-objective nature of this problem, we develop a mathematical model and introduce an approach based on the non-dominated genetic sorting algorithm (NSGA-II). To help decision-making, we use the technique of performance ranking by similarity to the ideal solution (TOPSIS) in combination with the entropy weight method (EWM) to objectively obtain the optimal compromise solution from the Pareto front provided by NSGA-II. Finally, we conduct computational experiments to assess the environmental impact of carbon emissions associated with new, remanufactured and discarded products over a finite production horizon. We illustrate the adaptability of the proposed approach by applying it to two distinct remanufacturing strategies: one where remanufacturing is used to reduce waste, and one where demand for remanufactured products is critical, with a penalty cost associated with any shortfall in demand.

Early detection of agricultural drought can alert farmers and authorities, enhancing the resilience of the food sector. A framework is proposed for developing a novel regional agricultural drought index (RegCDI) by combining remotely sensed vegetation health, soil moisture and crop water stress via a transparent Shannon’s entropy weighting method. The framework consists of the selection of suitable datasets based on their regional performance, the aggregation of selected drought indicators, the validation of the combined index against crop yield, and the testing of predictive capabilities. The creation and performance of RegCDI are demonstrated for the drought prone Indian state of Odisha. MODIS surface reflectance is selected for crop water stress and GLDAS-2 for assessing soil moisture deficits and vegetation health. Three selected indicators (SMCI, TCI, and SIWSI-1) are combined into RegCDI for Odisha. The performance of RegCDI is evaluated (a) against other popular drought indices and (b) by comparing with seasonal crop yields. RegCDI is used to identify drought hotspots based on drought severity, duration, and propensity over the study area. A reforecast evaluation of RegCDI (up to three months ahead) showed that the indicators based on soil moisture deficit and crop water stress could predict drought conditions up to two months ahead with no less than 80% accuracy. This demonstrated the potential of the RegCDI framework and its component indicators for early warning of drought in Odisha.

One of the most promising solutions to slow down CO2 emissions is the use of photocatalysis to produce hydrogen as a clean fuel. However, the efficiency of the photocatalysts is not at the desired level, and they usually need precious metal co-catalysts for reactions. In this study, to achieve efficient photocatalytic hydrogen production, a high-entropy oxide was synthesized by a mechano-thermal method. The synthesized high-entropy oxide had a bandgap of 2.45 eV, which coincided with both UV and visible light regions. The material could successfully produce hydrogen from water under light, but the main difference to conventional photocatalysts was that the photocatalysis proceeded without a co-catalyst addition. Hydrogen production increased with increasing time, and at the end of the 3 h period, 134.76 µmol/m2 h of hydrogen was produced. These findings not only introduce a new method for producing high-entropy photocatalysts but also confirm the high potential of high-entropy photocatalysts for hydrogen production without the need for precious metal co-catalysts.

High‐entropy alloys (HEAs) materials, as promising nanomaterials, have garnered significant attention from researchers due to their excellent performance in the field of hydrogen evolution reaction (HER). The four core effects of HEAs, including the high‐entropy effect, severe lattice distortion effect, sluggish diffusion effect, and cocktail effect, are pivotal in underpinning their remarkable mechanical and thermodynamic properties. Nevertheless, the intricate geometric and electronic structures of HEAs make their catalytic mechanisms exceptionally complex and challenging to decipher. In particular, a thorough analysis of the underlying factors responsible for the outstanding catalytic activity, selectivity, and the ability to maintain stable hydrogen production, even at high current densities, in HEAs is lacking. To provide a systematic exploration of the design and application of HEAs in HER systems, this review commences with an examination of the physicochemical properties of HEAs. It covers a wide range of topics, including the synthesis methods of HEAs, and the major reaction mechanisms of HERs, and presents innovative methods and approaches for designing HEAs specifically in the context of HERs. This paper provides a comprehensive review of the preparation methods for high‐entropy alloys (HEAs) and analyzes their application as catalysts in the hydrogen evolution reaction (HER).