Bowen Ratio Research Articles

Utility of single-source surface energy balance models in estimation of daily actual evapotranspiration in arid regions

Single-source surface energy balance (SS-SEB) models estimate daily actual evapotranspiration (ETa eb) in arid and semi-arid regions. A meta-analysis explored the impact of model types, upscaling methods, satellite data selection, topography, and validation methods on ETa eb accuracy. SEBAL outperformed other SS-SEB models, especially in arid areas. Clear-sky models were more precise than continuous ones. For SEBAL, the Constant Reference Evaporative Fraction (ETrF) method was best for upscaling, while Constant Evaporative Fraction (EF) was optimal for METRIC, SEBS, and S-SEBI. Multi-source remote sensing data enhanced SS-SEB model performance compared to single-source data, particularly with higher spatial resolution. Study area size didn’t affect accuracy, but SEBAL struggled in higher altitudes and complex terrains. Lysimeter or FAO-56 validation yielded the best results. Recommendations include developing continuous SS-SEB models using appropriate methods and considering SSEB/SSEBop as alternatives to SEBAL and METRIC in data-scarce regions.

Numerical Study on Combustion Behavior of Tuyere and Raceway in Blast Furnace with Oxygen-Rich Blast and Hydrogen Injection

The injection of hydrogen into a blast furnace is a promising technology to fulfill the low-carbon ironmaking purpose. A three-dimensional computational fluid dynamic (CFD) model is developed to investigate the effect of hydrogen injection rate and blast oxygen enrichment rate on the tuyere, raceway, and surrounding coke bed behaviors. It was found that hydrogen injection leads to a higher water vapor volume fraction in the raceway and a higher hydrogen fraction in the coke bed. The magnitude of velocity and temperature near the tuyere only increase slightly due to the cold inlet temperature of hydrogen, which also results in lower coke bed temperature. The volume-averaged temperature decreases from 2146 K to 2129 K when the injection rate increases from 0 to 1000 Nm3/h. Oxygen enrichment rate presents a highly positive correlation with temperature in the raceway and coke bed, water vapor and carbon dioxide volume fraction in the raceway, and pulverized coal burnout rate. Because more carbon participates in the raceway reaction with an increase in oxygen enrichment rate from 0% to 10%, the final carbon monoxide fraction in the coke bed increases from 0.29 to 0.40, and the final hydrogen fraction decreases from 0.15 to 0.13. With the increase in hydrogen injection, the temperature of the raceway and the coke bed decreased slightly. Pulverized coal burnout changes little with the hydrogen injection rate increasing from 500 Nm3/h to 1500 Nm3/h, which is because hydrogen combustion promotes pulverized coal at the front part of the raceway but inhibits it at the end due to the relative lack of oxygen. These results will help better understand the combustion behavior in the tuyere and raceway of the blast furnace with oxygen-rich blast and hydrogen injection.

COMPUTATIONAL FLUID DYNAMICS ANALYSIS OF NEW CONCEPT HEAT EXCHANGER FOR OTEC APPLICATION

This paper presents a comprehensive analysis of a new concept of heat exchanger for Ocean Thermal Energy Conversion (OTEC) applications. The study utilizes Computational Fluid Dynamics (CFD) simulations to evaluate the performance of different heat exchanger designs for extracting thermal energy from oceanic sources, specifically using water and R717 liquid. Key performance parameters including cold vapor fraction, temperature difference, and pressure drop are evaluated through a combination of numerical simulations and experimental validations. The analysis of the cold vapor fraction provides insights into evaporation rates and their distribution across multiple prototypes, highlighting the impact of the wetted area on heat transfer effectiveness. The evaluation of temperature differences reveals variations in discharge fluid temperatures, with some prototypes deviating from thermodynamic principles at a default evaporation frequency of 0.1. Various evaporation frequencies are simulated and compared with experimental data to select the optimal frequency for each prototype. The simulations and experiments, conducted under similar conditions, ensure accurate validation despite inconsistencies arising from variations in heat exchanger design and boundary conditions. The performance evaluation demonstrates the effectiveness of the three prototypes, with Prototype 2 achieving the highest effectiveness up to 59% for OTEC applications. The findings contribute to a better understanding of heat exchanger performance in OTEC and provide valuable insights for design optimization and future application development. This paper emphasizes the significance of efficient heat transfer and highlights the potential of ocean thermal energy as a renewable and sustainable resource.

Evaluation of the Maximum Evaporation and the Priestley‐Taylor Models for Inland Waterbodies

AbstractThe Priestley‐Taylor (PT) model is a classic model of potential evaporation of terrestrial and marine surfaces. It is now recognized that the Bowen ratio (β) implicit in the PT model is too sensitive to temperature. The model also requires the surface net radiation (Rn) as input even though Rn is not an independent external forcing. The maximum evaporation model (MEM) proposed by Yang and Roderick (2019, https://doi.org/10.1002/qj.3481) is a potential candidate for replacing the PT model. Past studies have evaluated the MEM for land ecosystems and for the global ocean. This study represents the first evaluation of the MEM for inland waterbodies. Results are based on eddy‐covariance observation at a large lake and at a small fishpond. Although there were complex error structures and error compensation patterns among its intermediate variables, the MEM was able to reproduce the observed monthly (R2 > 0.95) and interannual variability (R2 > 0.78) in the lake latent heat flux. A key assumption of the MEM, that the incoming and outgoing longwave radiation is coupled, was a reasonable approximation at both the monthly and the annual time scale for the large lake and at the monthly time scale for the small fishpond. This assumption allows the MEM to treat Rn as an intermediate variable instead of a prescribed forcing. These results support the MEM as an alternative to the PT model at locations where Rn measurements are not available. In situations where Rn data is available, a revised PT model with reduced β temperature sensitivity is recommended.

Heat wave: a new characterization in terms of energy

Heat waves (HW) are prolonged periods of excessively hot weather that can cause severe socioeconomic and environmental impacts. This study aims to evaluate the differences in stored heat and turbulent flux partitioning during a heat wave event in Mexico City, using observations from an eddy covariance tower during the period from 14 June to 21 June 2023. During this period, net radiation (Rn) and sensible heat flux (H) increased significantly, particularly from noon to evening, reflecting stable atmospheric conditions. The air temperature showed a noticeable increase in the afternoon and evening, whereas absolute humidity decreased. We found that during the heat wave, the Bowen ratio (β) increased by 80% during daylight hours and 65% over a full 24-hour period compared to the pre-heat wave period. This heat release at night prolonged warm conditions, intensifying heat stress. The partitioning of net radiation for latent heat (LE), sensible heat (H), and heat storage (ΔQs) showed significant changes; during the heat wave, 51% of Rn was allocated to H and 34% to ΔQs, compared to pre-heat wave values of 49% and 27%, respectively. This study introduces a new characterization of heat waves in terms of energy, emphasizing the significant shifts in energy flux partitioning and storage. The new characterization highlights the critical role of urban heat storage and its release in exacerbating heat stress during and after heat wave events. This approach provides a comprehensive understanding of the energy dynamics during heat waves, which is essential for developing effective mitigation strategies to combat the adverse effects of extreme heat in urban environments.

Improving time upscaling of instantaneous evapotranspiration based on machine learning models

ABSTRACT Evapotranspiration (ET) plays a crucial role in the global water and energy cycle. Upscaling instantaneous ET ( E T i ) to daily ET ( E T d ) is vital for thermal-based ET estimation. Conventional methods – such as the constant evaporative fraction method (ConEF), radiation-based method, and evaporative ratio method – often overlook environmental factors, leading to biased estimates of E T d from E T i . To resolve this issue, this study aimed to assess four machine learning (ML) algorithms—XGBoost, LightGBM, AdaBoost, and Random Forest—to integrate meteorological and remote sensing data for upscaling E T i across 88 global flux sites. Each ML model was tested with eight different variable combinations. Results indicated that XGBoost exhibited the best performance, with a root mean square error (RMSE) generally below 13 W m − 2 in estimating E T d from E T i . The best variable combination simultaneously considers evaporative fraction, available energy, meteorology factors, remote sensing albedo, normalized vegetation index, and leaf area index. Using this combination, the XGBoost model achieved an R 2 = 0.88 and an RMSE = 12.33 W m − 2 , outperforming the ConEF method ( R 2 = 0.71 and RMSE = 18.86 W m − 2 ) and its expansions. These findings support the application of ML models in ET upscaling, enabling ET estimation across large spatiotemporal scales.

Evaluating the Two-Source Energy Balance Model Using MODIS Data for Estimating Evapotranspiration Time Series on a Regional Scale

Estimating daily continuous evapotranspiration (ET) can significantly enhance the monitoring of crop stress and drought on regional scales, as well as benefit the design of agricultural drought early warning systems. However, there is a need to verify the models’ performance in estimating the spatiotemporal continuity of long-term daily evapotranspiration (ETd) on regional scales due to uncertainties in satellite measurements. In this study, a thermal-based two-surface energy balance (TSEB) model was used concurrently with Terra/Aqua MODIS data and the ERA5 atmospheric reanalysis dataset to calculate the surface energy balance of the soil–canopy–atmosphere continuum and estimate ET at a 1 km spatial resolution from 2000 to 2022. The performance of the model was evaluated using 11 eddy covariance flux towers in various land cover types (i.e., savannas, woody savannas, croplands, evergreen broadleaf forests, and open shrublands), correcting for the energy balance closure (EBC). The Bowen ratio (BR) and residual (RES) methods were used for enforcing the EBC in the EC observations. The modeled ET was evaluated against unclosed ET and closed ET (ETBR and ETRES) under clear-sky and all-sky observations as well as gap-filled data. The results showed that the modeled ET presented a better agreement with closed ET compared to unclosed ET in both Terra and Aqua datasets. Additionally, although the model overestimated ETd across all different land cover types, it successfully captured the spatiotemporal variability in ET. After the gap-filling, the total number of days compared with flux measurements increased substantially, from 13,761 to 19,265 for Terra and from 13,329 to 19,265 for Aqua. The overall mean results including clear-sky and all-sky observations as well as gap-filled data with the Aqua dataset showed the lowest errors with ETRES, by a mean bias error (MBE) of 0.96 mm.day−1, an average mean root square (RMSE) of 1.47 mm.day−1, and a correlation (r) value of 0.51. The equivalent figures for Terra were about 1.06 mm.day−1, 1.60 mm.day−1, and 0.52. Additionally, the result from the gap-filling model indicated small changes compared with the all-sky observations, which demonstrated that the modeling framework remained robust, even with the expanded days. Hence, the presented modeling framework can serve as a pathway for estimating daily remote sensing-based ET on regional scales. Furthermore, in terms of temporal trends, the intra-annual and inter-annual variability in ET can be used as indicators for monitoring crop stress and drought.

OilMixProp 1.0: Package for Thermophysical Properties of Oils, Common Fluids, and Their Mixtures

Abstract This work presents the first version of OilMixProp (short for oil mixture properties), which could be the first software package capable of calculating all the core thermophysical properties of fluids involving user-defined oils. Properties needed in thermodynamic cycle analysis are all included: density, phase equilibria, heat capacity, entropy, enthalpy, speed of sound, viscosity, and thermal conductivity. Approximately 632 pure fluids are available, and users can define their oil by determining its fluid constants using embedded fitting tools. Analogous to refpropm (Matlab interface of REFPROP 10.0), a function OilPropm is developed as the only interface for calculating thermophysical properties. Various input combinations (e.g., temperature and pressure, pressure and enthalpy, temperature and vapor fraction, etc.) are available to cater to the needs of thermodynamic cycle analysis. Sophisticated outputs are designed to deliver either complete information (phases and properties in each phase) or selected information about a fluid at the given condition. The package is written in Matlab and will be converted to other languages (e.g., C++) in the future.

Using an Isotope Enabled Mass Balance to Evaluate Existing Land Surface Models

AbstractLand surface models (LSMs) play a crucial role in elucidating water and carbon cycles by simulating processes such as plant transpiration and evaporation from bare soil, yet calibration often relies on comparing LSM outputs of landscape total evapotranspiration (ET) and discharge with measured bulk fluxes. Discrepancies in partitioning into component fluxes predicted by various LSMs have been noted, prompting the need for improved evaluation methods. Stable water isotopes serve as effective tracers of component hydrologic fluxes, but data and model integration challenges have hindered their widespread application. Leveraging National Ecological Observation Network measurements of water isotope ratios at 16 US sites over 3 years combined with LSM‐modeled fluxes, we employed an isotope‐enabled mass balance framework to simulate ET isotope values (δET) within three operational LSMs (Mosaic, Noah, and VIC) to evaluate their partitioning. Models simulating δET values consistent with observations were deemed more reflective of water cycling in these ecosystems. Mosaic exhibited the best overall performance (Kling‐Gupta Efficiency of 0.28). For both Mosaic and Noah there were robust correlations between bare soil evaporation fraction and error (negative) as well as transpiration fraction and error (positive). We found the point at which errors are smallest (x‐intercept of the multi‐site regression) is at a higher transpiration fraction than is currently specified in the models. Which means that transpiration fraction is underestimated on average. Stable isotope tracers offer an additional tool for model evaluation and identifying areas for improvement, potentially enhancing LSM simulations and our understanding of land‐surface hydrologic processes.

Global Terrestrial Water–Energy Coupling Across Scales

ABSTRACTTerrestrial water–energy coupling (WEC), in the form of a non‐linear relationship between Soil Moisture (SM) and evaporative fraction (EF, ratio of actual and potential evapotranspiration), controls critical ecohydrological processes. We investigate and parameterize the evolution of global SM–EF coupling from the field to remote‐sensing (RS)‐pixel. The field‐scale EF and SM were obtained from eddy covariance (EC) and SM sensors at the global FLUXNET and Texas Water Observatory sites. RS‐pixel‐scale EF and SM estimates were obtained from Moderate‐resolution Imaging Spectroradiometer (MODIS) and Soil Moisture Active Passive (SMAP) sensors, respectively. We estimate the effective thresholds of the WEC regimes from both EC and satellite datasets to highlight the influence of sub‐pixel‐scale heterogeneity, and, scaling and observational constraints on the evolution of WEC regimes from the field to RS‐pixel scale. We argue that the changes in land surface conditions add a temporal variability in the critical thresholds of terrestrial WEC at RS pixel scale. We compare the critical WEC thresholds of the water‐ and energy‐limited regimes with a SM drydown‐based approach and highlight the similarities between both methods in partitioning dominant WEC regimes. EF and SM are strongly coupled in dryland arid and semi‐arid regions compared to humid climates. WEC regimes and thresholds have strong interseason variability due to dynamic interactions between soil, vegetation and atmosphere at the RS‐pixel scale. In contrast, field‐scale SM‐EF coupling is influenced predominantly by soil conditions and land‐use/management practices. Hence, future development of Earth‐system/Land‐surface models must account for the inter‐scale differences in the coupling between terrestrial water and energy fluxes representative of the ‘effective’ processes at large spatial scales.

ENERGY ASPECTS OF CONILON COFFEE DEVELOPMENT IN NORTHERN FLUMINENSE. PART 2 - ENERGY BALANCE

Conilon coffee represents a large portion of Brazilian coffee production, and it is essential to understand how the crop relates to the energy available in the environment. Therefore, this study sought to determine the components of the energy balance of the Conilon coffee crop in the North Fluminense region during seven harvests. The experiment was conducted in a crop field in the area belonging to the Darcy Ribeiro State University of North Fluminense, in Campos dos Goytacazes, RJ, which contains a micrometeorological station that monitored environmental data between June 2015 and May 2022. Using this information, the energy balance was performed using the Bowen ratio method, which made it possible to determine the crop evapotranspiration (ETc), the reference evapotranspiration (ET0), and the crop coefficient (Kc). The Bowen ratio energy balance method performed satisfactorily and indicated that 66% of Rn was converted to LE, 24% to H and 10% to G. The average crop evapotranspiration was 3.81 mm.day-1 and the average Kc per harvest showed an increasing trend throughout the experiment and ranged from 0.82 to 0.92. Conilon coffee presented an average productivity of 3.43 t.ha-1 (57.16 sc.ha-1) and it was concluded that an average of 0.08 g per MJ of net energy was produced.

A Bowen ratio-informed method for coordinating the estimates of air-sea turbulent heat fluxes

Abstract Accurate quantification of turbulent heat fluxes [THF, comprising sensible heat flux (SHF) and latent heat flux (LHF)] and Bowen ratio (β, ratio of SHF and LHF) is essential for understanding the air-sea interaction. However, the biased estimates of SHF and LHF by widely applied bulk aerodynamic models, and the separate estimates of SHF and LHF by data-driven models, both may result in unrealistic β estimates. This study for the first time innovatively proposes a Bowen ratio-informed data-driven model (BrTHF) for coordinating the estimations of THF and β using the multivariate random forest technique and a combination of eddy covariance flux observations and meteorological and oceanic observations collected from 53 historical cruises. The result shows that the BrTHF model could not only achieve high-accuracy SHF and LHF estimates, but also avoid the outliers of β estimates that were commonly found in un-synergistic random forest and well-known COARE3.5 models.

Molecular characterization of condensates altered by thermochemical sulfate reduction and evaporative fractionation using high-resolution mass spectrometry

Conventional biomarkers are least available for the origin and formation mechanism investigation in condensates due to their extremely low concentrations. Heteroatomic compounds in condensates can provide unique insights for their origin and formation, but these compounds are with the low separation ability by conventional mass spectrometry tools. They can be characterized with the advance of the high-resolution mass spectrometry, but few study focuses on the altered condensate oil and their molecular-level compositions. In this study, a total of 19 condensates are analyzed to study the effects of thermochemical sulfate reduction and evaporative fractionation on the changes of molecular compositions characterized by Orbitrap mass spectrometry. The results show that thermochemical sulfate reduction (TSR) make the oils considerably enriched in S1 species (sulfur-containing compounds with one sulfur atom) (>90 %) and depleted in CH2s species (hydrocarbons compounds) (<3%) relative to the non-TSR altered oils due to the consumption of hydrocarbon and yield of sulfur-containing compounds. Relatively abundant S1 species with low DBE (Double Bond Equivalent) values (0–3) likely corresponding to thiols and thioethers in TSR-altered oils. However, the relative abundance of CH2s species in the oils undergoing evaporative fraction are much higher than that in non-evaporative fraction altered oils leading by the strong solubility of hydrocarbon in gas. Therefore, the relative contents of heteroatomic compounds are significant for the TSR alteration and evaporative fraction definition of condensates and their origin investigation.

Comparison of four upscaling methods to drive instantaneous evapotranspiration to daily values for maize in two climatic regions in China

Abstract Accurately converting satellite instantaneous evapotranspiration (λETi) over time to daily evapotranspiration (λETd) is crucial for estimating regional evapotranspiration from remote sensing satellites, which plays an important role in effective water resource management. In this study, four upscaling methods based on the principle of energy balance, including the evaporative fraction method (Eva-f method), revised evaporative fraction method (R-Eva-f method), crop coefficient method (Kc-ET0 method) and direct canopy resistance method (Direct-rc method), were validated based on the measured data of the Bowen ratio energy balance system (BREB) in maize fields in northwestern (NW) and northeastern (NE) China (semi-arid and semi-humid continental climate regions) from 2021 to 2023. Results indicated that Eva-f and R-Eva-f methods were superior to Kc-ET0 and Direct-rc methods in both climatic regions and performed better between 10:00 and 11:00, with mean absolute errors (MAE) and coefficient of efficiency (ɛ) reaching &lt;10 W/m2 and &gt; 0.91, respectively. Comprehensive evaluation of the optimal upscaling time using global performance indicators (GPI) showed that the Eva-f method had the highest GPI of 0.59 at 12:00 for the NW, while the R-Eva-f method had the highest GPI of 1.18 at 11:00 for the NE. As a result, the Eva-f approach is recommended as the best way for upscaling evapotranspiration in NW, with 12:00 being the ideal upscaling time. The R-Eva-f method is the optimum upscaling method for the Northeast area, with an ideal upscaling time of 11:00. The comprehensive results of this study could be useful for converting λETi to λETd.

Hysteresis in seasonal land-atmospheric interactions over India and its characteristics across croplands and forests

Abstract Satellite-derived vegetation optical depth and soil moisture (SM) data reveal the critical role of the soil-vegetation continuum in storing rainwater during the Indian Summer Monsoon and supporting evapotranspiration (ET) during the dry non-monsoon season. During the non-monsoon drier period, the climatologically estimated spatial mean of ET exceeds precipitation input, a phenomenon known as the soil–vegetation capacitor effect, which is pivotal in maintaining ecosystem productivity. Notably, our analysis reveals significant variations in the capacitor period between croplands and forests, with croplands exhibiting a ∼77 d longer due to dual crop seasons influenced by regional precipitation. The well-recognized hysteresis curves, observed in magnetization and soil–water characteristic curves, highlight phenomena where a system’s state is influenced by its historical inputs or states and are integral to our findings. We report a previously undocumented seasonal hysteresis in the relationship between the evaporative fraction (EVF) and SM for Indian croplands and forests. We further found that the croplands SM-EVF relation exhibits a reversal in hysteresis in the case of root-zone SM. The surface SM-EVF hysteresis is not present in forests with large root depths and reduced soil evaporation due to high canopy shading, and yet it is present for the root-zone SM. With its reversal for croplands, the newly found hysteresis must be addressed in redefining the critical SM threshold to demarcate the energy and water-limiting regimes. It should be incorporated in the land surface modeling parameterization. Additionally, we observed hysteresis in the SM-gross primary productivity relationship across both land covers and soil profiles (surface and root-zone), underscoring the need to investigate such processes to consider their dynamics in future ecological and hydrological models.

Water Transformation Relationship in Inner Mongolia Section of the Yellow River Basin Based on Stable Hydrogen and Oxygen Isotopes

By collecting the atmospheric precipitation, surface water, and groundwater in the Inner Mongolia section of the Yellow River Basin in July 2021 （wet season）, October （normal season）, and April 2022 （dry season）, stable isotope technology was used to analyze the temporal and spatial changes in hydrogen and oxygen stable isotopes in the "three rivers" of the basin, and the MixSIAR mixing model was used to reveal the water body transformation relationship. The results showed that the mean difference in the groundwater isotope was small in the abundance period, flat period, and dry period in the Mongolia section of the Yellow River Basin. The groundwater regeneration was slow, the retention time was long, the seasonal variation was not obvious, and the δD value of surface water was higher in the abundance period than in the normal period and dry period. According to the δ18O and δD diagrams, the slope and intercept of surface water lines in the three periods were smaller than those of local precipitation lines, and surface water was affected by evaporative fractionation after receiving precipitation recharge. The δD values of surface water on the north bank of the Yellow River showed a trend of first increasing and then decreasing from upstream to downstream, while the δD values of surface water on the south bank of the Yellow River showed a trend of gradually decreasing from upstream to downstream. The recharge contribution of groundwater in surface water in the high-water period accounted for 2.9%, precipitation accounted for 97.1%, surface water accounted for 5.0%, atmospheric precipitation accounted for 95.0%, surface water accounted for 56.6%, and precipitation accounted for 43.4%, and the recharge contributions of precipitation and surface water to groundwater in the high water period were 47.6% and 52.4%, respectively. Those in the normal period were 30.7% and 69.3%, and those in the dry period were 37.8% and 62.2%, respectively. Atmospheric precipitation was the main replenishment source of surface water, showing that the replenishment ratio in the wet season was larger than that in the normal season and dry season, which was closely related to the total precipitation and its distribution in each period. Surface water was the main replenishment source of groundwater, showing that dry season &gt; normal season &gt; wet season.

Numerical investigation on boiling crisis characteristic of a 7-rod HCF assembly in hexagonal lattice

Helical cruciform fuel (HCF) has the advantages of larger heat transfer area, enhanced coolant mixing and self-supporting, which contribute to increasing power density and safety margins. Compared with the square lattice configuration, the hexagonal arrangement of HCF assembly is more compact, which can help achieve a higher power density. In this paper, the flow characteristics and heat transfer behaviors of HCF in hexagonal lattice were predicted at high and low vapor quality during boiling crisis based on Eulerian two-fluid model. The influence of twist pitches and cross-sections of the fuel rod on heat transfer efficiency and fuel temperature was also studied. The cross-flow intensity changed periodically with a 30° cycle at low vapor quality, and did not fluctuate periodically at high vapor quality, which decreased with the increase of flow resistance. The highest heat flux of HCF rod was the at the blade root and the lowest was at the blade tip, and the maximum to average heat flux ratio was about 1.8. The peak vapor fraction and temperature occurred at leeside side of the fuel rods. The increase of the twist pitch reduced the critical heat flux (CHF), and the increase of blade length enhanced the non-uniformity of heat flux distribution. During boiling crisis, the maximum temperature of the fuel was lower than the phase transition temperature of U-50 wt%Zr alloy, which means the cladding meltdown caused by boiling crisis will occur before phase transition of the fuel.

New Two-Phase Multiplier Model for Phase-Change Flows in Plate Heat Exchangers

A complete thermo-hydraulic understanding of condensing and evaporating flows in heat exchangers requires predictive modeling and analysis of not just heat transfer but also the hydraulics of the flow. While modeling the friction factor and pressure gradient yields a quantitative understanding of the pressure drop, only the two-phase multiplier and void fraction, in combination with the Martinelli parameter, help better understand the relative contributions of the liquid and vapor fractions to the overall pressure drop. This article reports the empirical modeling, analysis, and meta-analysis of the two-phase multiplier for condensing and evaporating flows in plate heat exchangers. Over three thousand data compiled from forty-two sources were modeled using various regression techniques to develop correlations for predicting the two-phase multiplier for condensing and evaporating flows in plate heat exchangers. The Weber number for most studies was less than one, indicating that drop condensation and pool boiling were impossible. Further, the Bond number for most studies was also much higher than one, indicating that the buoyancy effects were significant during condensation and evaporation. Meta-analysis for evaporators was statistically significant and positive, strongly recommending plate heat exchangers.

Phase equilibrium calculations with specified vapor fraction

Phase equilibrium calculations have been extensively explored over the years, with numerous industrial applications, where pressure and temperature specifications are the most common. Different problems, however, may require different specifications for solving phase equilibrium. This article aims to develop a flash calculation with specified temperature or pressure and vapor fraction, termed ψβ-flash, which can be useful in studies of storage tanks and distillation columns. An algorithm is developed with an external loop for pressure or temperature optimization and an inner loop for the isobaric–isothermal-flash calculation. The method is efficient in predicting pressure for different binary and ternary mixtures, including refrigerants, hydrocarbons, and carbon dioxide, even in complex scenarios such as regions with retrograde condensation. The computational demand is investigated, revealing that calculations within the isobaric–isothermal-flash primarily contribute to the total computational cost, rather than pressure optimization. Finally, two case studies highlight the method’s efficiency: one involving a spherical storage tank, where we compute pressures based on liquid height to classify the safe operational region, and another focusing on a distillation tray, predicting temperatures driven by changes in liquid height to provide insights into separation performance.

Sensitivity of gross primary production and evapotranspiration to heat and drought stress in a young temperate plantation in northern China

Assessing the sensitivities of ecosystem functions to climatic factors is essential to understanding the response of ecosystems to environmental change. Temperate plantation forests contribute to global greening and climate change mitigation, yet little is known as to the sensitivity of gross primary production (GPP) and evapotranspiration (ET) of these forests to heat and drought stress. Based on near-continuous, eddy-covariance and hydrometeorological data from a young temperate plantation forest in Beijing, China (2012–2019), we used a sliding-window-fitting technique to assess the seasonal and interannual variation in ecosystem sensitivity (i.e., calculated slopes, SGPP-Ta, SET-Ta, SGPP-EF, and SET-EF) in GPP and ET to anomalies in air temperature (Ta) and evaporative fraction (EF). The EF was used here as an indicator of drought. Seasonally, daily SGPP-Ta, SET-Ta, and SGPP-EF were greatest in summer, reaching maxima of 1.12 ​± ​0.56 ​g ​C·m−2·d−1⋅°C−1, 1.36 ​± ​0.56 ​g H2O·m−2·d−1⋅°C−1, and 0.37 ​± ​0.35 ​g ​C·m−2·d−1, respectively. Evapotranspiration was constrained by drought, especially during the spring-to-summer period, SET-EF reaching −0.51 ​± ​0.34 ​g H2O·m−2·d−1. Variables EF, Ta, soil water content (SWC), vapor pressure deficit (VPD), and precipitation (PPT) were the main controls of sensitivity, with SGPP-Ta and SET-Ta increasing with Ta, VPD, and PPT (<50 ​mm·d−1) during both spring and autumn. Increased drought stress during summer caused the positive response in GPP and ET to decrease with atmospheric warming. Variable SET-EF intensified (i.e., became more negative) with decreasing EF and increasing Ta. Interannually, annual SGPP-Ta and SET-Ta were positive, SGPP-EF near-neutral, and SET-EF negative. Interannual variability in SGPP-Ta, SET-Ta, SET-EF, and SGPP-EF was largely due to variations in bulk surface conductance. Our study suggests that the dynamics associated with the sensitivity of ecosystems to changes in climatic factors need to be considered in the management of plantation forests under future global climate change.