Flow Variables Research Articles

Using froude and weber numbers to represent the changes in the flow pattern from stratified to stratified-wavy or plug for wire-on-tube condenser

According to manufacturing data, a theoretical study of condensation inside a heat exchanger with wires on tubes.examined flow patterns with variable refrigerant mass flow rates. Wire-on-tube condensers are adopted with tubes, which have multiple diameters (3.25, 4.83 and 6.29 mm). In addition to the use of two refrigerants (R-134a, R-600a) working at condensing temperatures of (54.4, 45, and 35 °C). The Equal Equation Solver software (EES) was used to obtain the results for the mass velocity range from 8 to 167 kg s−1m−2. Using the non-dimensionless numbers, the model determines the refrigerant flow pattern. Weber number (We) and Froude number (Fr) were used for mass velocity in a range below 100 kg s−1 m−2, which is recommended flow inside the wire-on-tube condenser. The initial transition of the two-phase flow pattern from stratified to stratified-wavy occurred at beginning of condensation for the quality range (0.78-0.42) was Fr (2.7-2.0) and We (6.1-4.0) for R-134a, while the quality range (0.85-0.39) was Fr (5.0-2.4) and We (7.0-4) for R-600a. Second, as the quality range approached, the stratified-wavy flow was replaced by a plug at quality (0.23-0.06) were Fr (1.5-0.4) and We (3.8-2.1) for R-134a and for R-600a the quality range (0.22-0.05) were Fr (1.7-0.55) and We (3.7-2.2).

Energy consumption analysis and operating characteristics research on small time scale of variable refrigerant flow air conditioning systems in public buildings

In order to analyze the energy consumption and operation characteristics of the variable refrigerant flow (VRF) air-conditioning system on small time scale and put forward effective energy-saving suggestions, the VRF system operation experiments are carried out under different indoor set temperatures, different indoor unit opening quantities and different indoor set air velocities. This experiment studies the main influencing factors of energy consumption and operation of the VRF system, such as indoor temperature difference, indoor air velocity, outdoor environment temperature and so on. The results show that the rated power of indoor unit is linearly related to the energy consumption of the VRF system. The total active power changes greatly when the VRF starts and stops, and the outdoor ambient temperature changes. The indoor set air velocities have a great influence on the energy consumption and operation of the VRF system. The performance parameters increase first and then decrease with the increase of compressor frequency and load rate. When the load rate is 40 %∼60 %, the performance parameters can reach 3.2 ∼ 4.2.

Numerical modeling of heat transfer mechanism in remote sensing bulb of thermal expansion valves

Thermal management of automotive systems has garnered a lot of focus in recent times to improve the energy efficiency of vehicles and address the challenge of global warming. In combustible fuel vehicles, the heat pump compressor is driven by the engine power which leads to changes in operating condition of the cycle while the vehicle is in motion. In electric vehicles, a combined thermal management strategy handles both cabin and battery pack cooling/heating depending on the ambient conditions and power requirements by adjusting refrigerant flow rates and flow directions with sophisticated valves. Irrespective of the vehicle type, effective variable refrigerant flow control is prerequisite to ensure optimum thermal comfort with minimum energy. Thermal expansion valves (TXV) are the most widely used method for regulating mass flow rate of refrigerant during the expansion step of the vapor compression cycle based on the principle of trying to maintain a fixed degree of superheat at the evaporator outlet. Conventional models of the thermal expansion valve ignore the time lag between fluctuation of temperature at the evaporator outlet and the corresponding change in pressure of the TXV remote sensing bulb, treating the valve as an instantaneous element during transient operation. This paper presents a novel method for determining the temperature profile and time constant of the remote sensing bulb response using numerical methods, in an attempt to capture the dynamics of thermal expansion valve in active heat pump cycle. Finite difference method was used to solve for the conduction heat transfer between the bulb and the heat exchanger outlet tube in perfect thermal contact applying the necessary boundary conditions. This improved modeling approach will be helpful in better prediction of the dynamic behavior of thermal expansion valves and how it influences the evaporative heat exchanger performance during transient operations to determine control algorithm and strategies.

Efficient cooling strategies for liquid hydrogen pipelines: A comparative analysis

Liquid hydrogen (LH2) stands out for its high energy density, efficient transportation, and safe low-pressure storage. However, the challenge lies in achieving rapid cooling of LH2 pipelines while minimizing hydrogen loss. This paper introduces a robust three-dimensional model for simulating the unsteady-state heat transfer and the gas-liquid two-phase flow within LH2 pipelines. Throughout the cooling cycle, the pipe undergoes transitions in flow patterns, including stratified smooth flow, wavy flow, and intermittent flow, in which wavy flow dominates due to the extremely low liquid-to-gas density ratio of hydrogen. A comprehensive comparative analysis is conducted for three cooling modes: constant flow, variable flow, and pulsing flow. Finally, an evaluative framework for distinct pipeline cooling modes has been proposed. A reasonable variable flow cooling mode exhibits certain advantages in both cooling time and liquid hydrogen consumption when compared with the constant flow cooling mode, and the pulse flow cooling method adeptly capitalizes on the performance benefits derived from intermittent flow. Specifically, within the cooling range of 40 K–20 K, it substantially economizes liquid hydrogen consumption (15%–20 %), albeit concomitant with an extended total cooling time (40%–60 %). This study can offer theoretical insights to guide the high-efficiency cooling of liquid hydrogen pipelines.

Effect of instantaneous local solid volume fraction on hydrodynamic forces in freely evolving particle suspensions

Particle Resolved Simulations (PRS) for freely evolving sphere suspensions at solid volume fractions (φ) between 0.1 and 0.4, Reynolds number Re from 10 to 300 and particle-fluid density ratios ρsρf of 2, 10 and 100 are used to investigate the effect of Voronoi tessellation based particle local solid volume fraction (φv)on particle drag and lateral forces. Findings reveal the instantaneous suspension mean drag force is positively correlated with the variance of φv among particles in the suspension. It is also shown that using the conditioned instantaneous φv of each particle in existing mean drag force correlations can significantly improve the prediction accuracy. Suspension mean lateral force ranges up to 60 % of the drag force while individual particles exhibit values as high as 90 % of the drag force. An instantaneous lateral force correlation is proposed based on suspension-averaged flow variables and φv.

Nitrogen use efficiencies, flows, and losses of typical dairy farming systems in Inner Mongolia

Dairy farming is a notable source of nitrogen (N) emissions, impacting both atmospheric and aquatic ecosystems, thus necessitating a detailed analysis of nutrient dynamics to curtail nutrient wastage. However, N flow variability and its environmental ramifications differ markedly among dairy farms, and a holistic understanding of these differences is lacking in Inner Mongolia, the biggest dairy production province in China. Utilizing data from 187 dairy farms and employing the NUFER-farm model, this study assessed N flows, N use efficiency (NUE), and N losses across four predominant dairy farming systems in Inner Mongolia. These systems include traditional pastoral dairy farms (PF), smallholder dairy farms with croplands (SF), industrial landless farms (IDF), and coupled dairy cattle and cropland-intensive farms (CDF). Our findings indicate considerable differences in N flows, NUE, and losses among the systems. On average, N deposition and N fertilizer were the primary N sources for PF and SF, respectively, whereas IDF and CDF derived over 90% of their N inputs from purchased feeds. PF and SF recycled all available manure N on-farm, whereas IDF and CDF recycled only approximately 36% of the total available manure N. N losses constituted 39–72% of total N outputs, with ammonia emissions accounting for 68–73% of total N losses across all farm types. In particular, PF had a higher N loss per kilogram of dairy product than other systems. Farm-level NUE ranged from 17 to 35%, with manure management practices showing significant variability, underscoring the potential for enhanced strategies to reduce N losses through improved manure treatment.

Multi-Parametric Investigations on White Etching Crack Formation in Deep Grove Ball Bearings

Research on White Etching Cracks (WEC) in multiple bearing applications has identified various drivers that cause them. Lubricants and electricity combined with contact mechanics have been proven to catalyze WEC significantly. However, none of these factors solely cause WEC on its own; instead, combinations of factors discretize whether WEC appears or not. Hence, the WEC phenomenon appears to be multidimensional, making WEC still unpredictable. The current paper is about a systematic study using a Deep Grove Ball Bearing test rig to investigate how lubricant chemicals, combined with electricity and variations in oil flow and pressure, lead to WEC formation. It becomes evident that even under critical conditions for WEC formation, increasing oil flow and decreasing contact pressure can prevent WEC.

Advanced, Cutting-Edge RP-HPLC Methodology for the Comprehensive Quantitative Analysis of Assay of Bictegravir, Emtricitabine, and Tenofovir Alafenamide in Co-Formulated Pharmaceutical Products.

In the current study, a simple and economic stability-indicating RP-HPLC method development and validation was carried out to estimate the bictegravir, emtricitabine and tenofovir from the pharmaceutical dosage form. 0.1M ammonium acetate in 0.5% v/v acetic acid solution and 1g of 1-octane sulfonic acid and adjustment of pH to 4.2 with dilute orthophosphoric acid done and methanol (40:60 v/v) was utilized as the mobile phase. The analysis was done using Inertsil ODS 3V (250 x 4.6 mm x 5 µm) column with column temperature kept at 30°C with an injection volume of 20 μL, flow rate of 1.0 ml/ minute and detection was carried out at 260 nm. The method was developed and it was validated according to ICH Q2 (R1) guidelines. The RT of bictegravir, emtricitabine and tenofovir were determined to be 12.23, 3.0 and 8.5 minutes, providing a reliable marker for its identification. The method was found linear from about 50 To 150% Of the target concentration of bictegravir emtricitabine and tenofovir with of 0.999. Significant degradation was observed in acidic, basic and peroxide stress conditions. Hence, it can be concluded that tablets are sensitive to acidic, basic and oxidation stress conditions. RSD for the peak area responses of emtricitabine, 0.03 and 0.03, respectively, indicating that the system is precise. The testing procedure was accurate from about 50 to 150%. Of the target concentration of emtricitabine, tenofovir alafenamide and bictegravir. The method was robust In relation to flow variation, column oven temperature variation, mobile phase variation and pH variation. In conclusion, our proposed RP-HPLC method provides a sensitive, accurate, and precise means of analyzing emtricitabine, tenofovir alafenamide and bictegravir from pharmaceutical dosage forms.

Mechanisms regulating trophic transfer in the Humboldt Upwelling System differ across time scales

Abstract The Humboldt Upwelling System hosts a highly productive ecosystem with central importance for global fisheries, yet with strong seasonal and interannual variability in the planktonic base of the food chain ultimately affecting fish yield. Understanding the variability in energy transfer within the plankton community in the contemporary climate can provide valuable insights for future projections of planktonic dynamics. Therefore, we use a regional physical-biogeochemical ocean model simulation (CROCO-BioEBUS) from 1990 to 2010 to investigate the underlying mechanisms of seasonal and interannual variability of the trophic transfer. Our model simulations suggest that, on an interannual scale, variations in trophic transfer are governed by variations in the offshore surface flow that modulate the plankton cross-shore distribution. Weak offshore surface flow, as simulated during the El Niño period, allows the zooplankton to stay relatively close to the shore, leading to more efficient grazing and trophic transfer compared to years with strong offshore flow. This mechanism differs from the seasonal one, where the mixed layer depth is the primary driver of variations in plankton dynamics, including trophic transfer. Our results highlight that mechanisms controlling plankton trophic transfer differ across time scales, and thus stress that extrapolating solely from seasonal findings to understand long-term trophic transfer changes in the context of climate change may be insufficient.

Analysis of flow regime classification in the Omo-Gibe River Basin: insights into fluid dynamics in Ethiopia

ABSTRACT The study investigates flow regime in the Omo-Gibe River Basin to address hydrological complexity caused by precipitation and catchment features. Despite employing various methodologies, daily flow data highlight the need for a more comprehensive understanding of flow variability. The study aims to scrutinize flow regime classification, emphasizing the challenges posed by the basin's unique hydrological dynamics, with the ultimate goal of improving water management practices in the region. Using XLSTAT (Excel statistics software), the average base flow index (60.66%), zero flow index (0.25%), coefficient of variation (1.56%), and flashiness index (0.276%) were determined to be the primary hydrological indices that contributed to streamflow characterization. Finally, flow regime classification was described as non-perennial (13%) or perennial (87%) using the shape of the flow duration curve and this hydrological index. However, the magnitude of extreme flow events was judged depending on flow duration curve and calibrated by the flashiness index computed in the study. The study's findings serve as an input for streamflow regionalization and the foundation for future research on the ecology and hydrology of Ethiopia's river basins as well as the management of the water resources throughout the Omo-Gibe River Basin.

Integrated optimization of the building envelope and the HVAC system in office building retrofitting

Increasing the energy efficiency of existing buildings is the major strategy to reach carbon neutral targets, given that the building sector is a major emitter. In particular, one major part of building energy usage is the building heating, ventilation and air-cooling system, which are highly depending on the thermal performance of building envelope and increase the challenge of selecting optimal packages of energy efficiency measures. This paper thereby presents a method for optimizing the building envelope and heating, ventilation and air-cooling system. The simulation-based NSGA-III approach developed in this paper is based on coupling the dynamic simulation models created in EnergyPlus software with the non-dominated sorting genetic algorithm, as the engine that performs an optimization process. A large domain of energy efficiency packages combined with heating, ventilation and air-cooling systems and building envelope are investigated to minimize energy consumption, retrofit cost and thermal discomfort in indoor environments, which including ideal loads air system, four pipe fan coil system and variable refrigerant flow system, insulation materials and insulation thickness for external walls and roof, different types of external windows, and window-wall ratio. An office building in Chongqing was chosen as a case study to demonstrate the practical implementation of the proposed method. The results show that the four pipe fan coil system was superior in the diversity and performance of the Pareto front. Then, the optimal packages were generated by a synthetic method, which have 58.57 kWh/m2 of energy consumption, 30.76 CNY/m2 of retrofit cost and 40.67 % of the percentage of thermal discomfort hours. The results also indicate that the yearly energy savings rates are 17.30 %, 23.05 % and 21.10 % separately for ideal loads air system, four pipe fan coil system and variable refrigerant flow system after performing optimization. These results highlight the importance and necessity of performing an optimization procedure for existing buildings to select the optimal retrofit measures.

Refractured Well Hydraulic Fractures Optimization in Tight Sandstone Gas Reservoirs: Application in Linxing Gas Field

Poorly producing wells in sandstone gas reservoirs are often refractured to enhance production. Considering the mutual interference of initial/refractured fractures, conductivity dynamic evolution, non-uniform inflow, and variable mass flow in the fracture comprehensively, a semi-analytical reservoir-fracture coupled production model fusing spatial and time separation methods is introduced to model refractured well performance. The proposed model is verified by CMG. The field applications indicate that the refracture job should be carried out when production is lower than the desired value. Restoring the Cf-ini and constructing the Cf-ref can increase productivity, which increases over 8 D•cm. The production growth rate just obtained a slight improvement. The production increased significantly with Lf-ini increasing from 120~270 m and Lf-ref increasing from 100~150 m. Hence, it is essential to extend the Lf-ini under engineering conditions. The ks/km = 10 can obviously increase production, but further enlarging ks does not contribute to well performance. Conversely, further producing larger bs is vital to enhancing production. Subsequently, the optimal parameter combinations (ds > Lf-ini > Lf-ref > Cf-ini > ks > Cf-ref) for well(X1) are carried out by orthogonal experiments. This work proposes a novel method to simulate refractured vertical well performance in tight gas reservoirs for refracture optimization.

Temporal dynamics of stream algae under the combined impacts of climate and land‐use stressors

Abstract Ecosystems are increasingly challenged by the multiple facets of climate change, coupled with intensifying land‐use pressures. These co‐occurring stressors can interact in complex ways, but we lack an empirical understanding of the impact of higher‐order interactions on temporal patterns. Using 128 flow‐through circular stream mesocosms, we investigated the individual and combined effects of two climatic stressors (CO2 enrichment, flow variability) and two land‐use‐related stressors (siltation, light—as lack of shading) on algal communities and net ecosystem productivity (NPP) in a full‐factorial design. The sediment pulses coincided with high flow to mimic erosion events, whereas CO2 and light disturbances were applied continuously, as they would in nature. Sediment emerged as a key stressor for algal biomass. Land‐use stressors had more pervasive individual effects, whereas climate‐change‐related stressors were more important in up to three‐way interactions with other stressors. However, CO2 was a key driver of NPP, followed by sediment and light, whereas flow variability was only important in interactions with other stressors. The effects of sediment and flow on algal biomass depended strongly on their temporal patterns. The combined effect of an increasing number of stressors on algal biomass appeared to reach saturation with three active stressors, with no apparent additional effect caused by the fourth stressor. Synthesis. Sediment emerged as a key stressor in streams. Despite the mounting evidence and the multitude of available mitigation strategies, this problem persists worldwide. The complex interactions uncovered in our study illustrate context‐dependency that can be masked in two‐factor experiments. Our findings also highlighted that temporal patterns of individual and co‐occurring stressors can determine the ecological outcome.

The interaction between vegetation patchiness and tidal flows in a shortleaf seagrass meadow

AbstractSeagrasses are critical coastal habitats that provide numerous ecosystem services. The inherent patchiness within meadows exerts a significant influence on the flow‐vegetation interaction, which, in turn, affects the array of services provided by these environments. We present field observations of vegetation distribution and hydrodynamic measurements within and surrounding an approximately 2 m diameter gap (bare sediment) in a fragmented seagrass meadow. We show that variability in mean flows and turbulence is correlated with meadow structure at small (O (100 m)) and large (O (102 m)) spatial scales. Our observations reveal that bare gaps within seagrass meadows lead to faster flows and lower bed elevations. Despite slower flow speeds above the dense seagrass adjacent to the gap, the rates of dissipation of turbulent energy above the vegetation are typically around an order of magnitude larger than above the bare bed. Associated with this enhanced dissipation of turbulent energy, we observed a dominance of down‐deceleration events promoting fluid exchange and mixing and driving mass flux into the canopy. Analysis of directional variograms demonstrates that the major continuity axis within NDVI (normalized difference vegetation index) imagery (used as a proxy for vegetation biomass) coincides with the major axis of flow on both gap and meadow scales. Conversely, along the axis of minor flow variance, vegetation remains dense and exhibits greater uniformity. These findings indicate a feedback mechanism between seagrass meadow patchiness and spatial structure through flow modification, which may be beneficial for plant development.

Evaluating the Impact of Casino-Shifts on Patient Flow in an Emergency Department: A Pilot Study.

Demand for emergency services has resulted in an increased number of physicians experiencing burnout. Burnout rates amongst emergency medicine physicians consistently exceed that of other specialties, with shift work being a large contributor to the phenomenon. Casino-shift scheduling has addressed this issue in several emergency departments (EDs). Casino-shift scheduling is modeled around circadian rhythm theory which shows that anchor sleep helps to preserve circadian rhythm and normalize sleep patterns. To account for this, casino-shift models schedule overnight coverage with two six-hour shifts, to allow both physicians to obtain some sleep within the 01:00 to 06:00 am anchor period. While the benefits of the model have been demonstrated concerning physician well-being, there is a paucity of evidence assessing if this model has any effect on quality measures such as patient flow. Given the importance of patient flows to ED functioning, the objective of our study was to determine the effect of a casino-shift trial on overnight patient flow variables in a tertiary ED. We performed a retrospective analysis of administrative data for overnight (10:00 pm to 10:00 am) patient flow variables during a two-month casino-shift intervention period (September 9, 2019, to November 4, 2019) compared with a control period at an ED in Eastern Canada. We analyzed various measures of patient flow for patients presenting overnight between 10:00 pm to 10:00 am during the study period. Primary outcome measures were wait time (WT), length of stay (LOS), and admission rates. Of the 19170 patient visits, 16787 met inclusion criteria. The median overnight WTs for the casino-shift intervention period were longer at 68 minutes (interquartile range (IQR) 31-154 minutes), compared with 51 minutes (IQR 21-104 minutes) in the control group. The LOS for the intervention was 217 minutes (IQR 132-358 minutes) compared with 195 minutes (IQR 112-336 minutes) for the control. There were 166 admissions/month during the trial, and 193 admissions/month during the 10-month control period. In our study, our patient flow indicators of median WT and LOS were longer in the casino-shift intervention period by an absolute difference of 17 minutes and 22 minutes respectively. As a relatively new concept in emergency medicine scheduling, the impact of the casino-shift model on both well-being and ED efficiency warrants further investigation given the potential benefits to an occupation prone to burnout.

Azimuthal and radial variations in sap flow and its effects on the estimation of transpiration for Picea mongolica.

In this study, we applied thermal dissipation probe technology to examine sap flow in various directions (east, south, west, and north) and at different depths (0-2, 2-4, 4-6 cm) within the stem of natural Picea mongolica trees in the eastern of Otindag Sandy Land to provide a scientific basis for accurately quantifying water consumption of P. mongolica forests through transpiration and to enhance the understanding of water relations. The results showed that the diurnal variation of sap flow in different directions displayed a unimodal curve, with the sap flow sequence being south>east>west>north. The sap flow at different sapwood depths exhibited an obvious unimodal curve, with a significant decrease as sapwood depth increased. Compared with that calculated from the mean sap flux density in four directions (23.57 kg·d-1), water consumption calculated using the mean value in south-east, east-west, south-west, north-east, north-south, and north-west was overestimated by 10.2%, 5.5%, 14.5%, and underestimated by 12.3%, 8.2%, 9.8%, respectively. The water consumption calculated using the values from the east, south, and west was overestimated by 6.1%, 14.4%, and 15.4%, respectively, and underestimated by 30.7% in the north. In addition, compared with the water consumption calculated from the mean value in three sapwood depths (48.51 kg·d-1), that calculated using sap flux density at sapwood depths of 0-2, 2-4, and 4-6 cm were overestimated by 18.8%, underestimated by 1.7%, and underestimated by 62.9%, respectively. These results indicated that sap flow of P. mongolica had significant azimuthal and radial variations, which considerably influence the estimation of tree water consumption. Installing probes at 0-2 cm simultaneously in both the north and east of the trunk could effectively reduce the estimation error of whole-tree water consumption by 4.2%. This approach enabled the accurate quantification of water consumption of individual P. mongolica trees in sandy areas, thereby improving the precision of transpiration water consumption estimates scaling up from individual level to stand level.

Phase fraction measurement of gas-liquid flow based on cyclonic capacitive sensor (CCS) and inverse drift flux method

Abstract As the demand for clean energy sources like natural gas increases, the need for methods to measure the phase fraction of gas-liquid two-phase flows, which have complex and variable flow patterns, becomes more pronounced. This study introduces a phase fraction measurement method based on a cyclonic capacitive sensor. An effective phase fraction prediction model for the gas-liquid flow measurement section is established based on the capacitive signals. Using the drift flux principle, the dimensionless drift velocity of the spiral annular flow is analyzed, and a volume gas fraction (GVF) prediction model based on the ‘inverse drift flux method’ is established. Experimental results show that this method is suitable for a wide range of phase fraction measurements and is highly accurate. When the liquid volume fraction (LVF) is less than 10%, the average relative error of the predicted GVF is 0.3%; for the LVF from 10% to 30%, the average relative error is 1.4%.

Observations of waves and currents on the fore-reef and reef flat of a coral reef atoll in the South China Sea

Understanding the wave and current conditions of coral reef ecosystems is essential for maintaining their health, as many reef processes are controlled by these hydrodynamic conditions. In this study, high-frequency measurements of tides, waves, and currents were made using acoustic, electromagnetic, and pressure instruments over a 28-d period on the fore-reef and reef flat of a coral reef atoll in the South China Sea. The research revealed wave transformation, tidal and wave modulation of flow, and wave setup conditions for the first time at this typical atoll. Three large wave processes dominated by gravity waves (GWs) are observed in the fore-reef. The GWs are significantly attenuated on the reef flat, whereas infragravity (IG) waves strengthened. The tidal modulation of GWs and IG waves on the reef flat is significant when the incident wave height exceeded 1 m. In the fore-reef, the modulation of progressive tidal waves and large waves leads to relatively stronger upper-layer currents, and weak near-bottom currents are primarily attributed to the dissipation of tidal wave energy by the rough coral terrain. In calm conditions, flow variations on the reef flat are modulated by tides, thereby allowing seawater flow to pass through the reef flat during spring tides. Conversely, during periods with large waves, tidal modulation of flow on the reef flat is less significant, and the cross-reef flow velocity increases with increasing incident wave height. The occurrence of wave setup on the reef flat enhances cross-reef flow towards the lagoon. The wave setup is positively linearly correlated with the incident wave height. The magnitude of wave setup is associated with the distance between the measurement sites on the fore-reef and reef flat.

Global optimization for large‐scale water network synthesis based on dynamic partition and adaptive bound tightening

AbstractThe synthesis of large‐scale integrated water networks is typically formulated as nonconvex mixed‐integer quadratic constrained programming (MIQCP) or QCP problems. With the complexity arising from bilinear terms in modeling mass flows of contaminants and binary variables representing the presence of units or streams, numerous local optima exist, thus presenting a significant optimization challenge. This study introduces a deterministic global optimization algorithm based on mixed‐integer programming (MIP) to tackle such problems. The approach involves dynamically strengthening the relaxed problems to converge towards the original problems. A simultaneous partition strategy is proposed combining locally uniform division with dynamic partitioned variables choosing. Furthermore, several adaptive bound contraction schemes are introduced to efficiently manage the size of the relaxed problems, assisting in accelerating the solution process. The algorithm's effectiveness and robustness are demonstrated with a large test set, showing superior performance compared to commercial solvers specifically on MIQCP problems.

Past, present, and future of the Hurst-Kolmogorov dynamics in Stochastics: A bibliometric analysis of the last 50 years in water resources

Hurst’s paper on the Nile’s flow variability marked a pivotal moment in hydrology and beyond by introducing what was called the Hurst phenomenon. Independently, Kolmogorov developed a mathematical model describing this behaviour a decade earlier. The Hurst-Kolmogorov dynamics (HKd) is used to express this phenomenon physically and mathematically, which is characterised by high uncertainty and persistence (across spatial and temporal scales) and challenges traditional analytical frameworks, particularly in water resources-related topics and implications in engineering designs. Given the importance of HKd, a bibliometric analysis of it in water resources is helpful to trace its historical development, current state, and (possible) future trajectories. The latter intends to offer a comprehensive perspective on HKd, serving as a guide for new readers seeking an entry point into this field. Using the Web of Science database, 617 publications from 1974 to 2023 are analysed, revealing a consistent growth trend in research outputs up to 2018. Collaborative efforts among researchers worldwide have been prominent, with the USA and China leading in international collaborations. High-impact journals on topics related to water resources and geosciences are primary outlets for research related to the HKd. Interestingly, only two journals published the 20 most cited papers on this topic. A clear pattern from “groundwater” to “streamflow” to “soil moisture” to “precipitation” was observed from the past to the present. Overall, this analysis provides a comprehensive overview of the past, present, and future trends in HKd research, and highlights its contribution to the scientific literature of water resources.