Fraction Distribution Research Articles

Segmented catalyst layer with varied catalyst loading to improve the cost performance of proton exchange membrane electrolysis cell, a numerical investigation

In this work, a steady-state, three-dimensional and non-isothermal numerical model for a proton exchange membrane electrolysis cell (PEMEC) is established. Based on this model, the distribution of catalyst loading is specifically designed according to the flow characteristics of both parallel and serpentine channels. In general, the catalyst loading is progressively reduced from inlet to outlet along the flow direction to match the local water content, leading to an innovative segmented catalyst layer which has not been studied yet for PEMEC applications. The electrochemical behavior of different segmentation schemes is investigated by comparing their polarization curves normalized by either electrode area or catalyst loading, while other physical fields such as velocity, pressure, water mole fraction and temperature distributions are also characterized. The numerical results reveal that a reasonable distribution of catalyst can reduce its amount of usage while still maintaining most of the PEMEC performance. In other words, the cost performance is significantly improved. This is mainly attributed to the full use of uneven water distribution in the flow channel, which improves the catalyst utilization efficiency significantly. This strategy is proved to be effective for both serpentine and parallel channels, ensuring a broad application prospect.

Convolution based fractional Wigner distribution and ambiguity function: theory and applications

Convolution based fractional Wigner distribution and ambiguity function: theory and applications

A review of polymeric heart valves leaflet geometric configuration and structural optimization

Valvular heart disease (VHD) is a major cause of loss of physical function, quality of life and longevity, and its prevalence is growing worldwide due to increased survival rates and an aging population. The most common treatment for VHD is surgical heart valve replacement with mechanical heart valves (MHVs) and bioprosthetic heart valves (BHVs), but with different limitations. Polymeric heart valves (PHVs) exhibit promising material properties, valve dynamics and biocompatibility, representing the most feasible alternative to existing artificial heart valves. However, inadequate fatigue performance remains a critical obstacle to their clinical translation. In this case, geometry and material design are essential to obtain the best mechanical properties of the PHV. In this study, we summarized the effects of optimal design of PHVs from geometrical configuration optimization (valve height, thickness and design curve) and structural material optimization (anisotropy, fiber reinforcement, variable thickness, microstructure and asymmetric optimization), and selected the parameters including Effective Orifice Area (EOA), Regurgitant fraction (RF), and Stress Distribution to compare the performance of valves. It would provide the theoretical support for the optimal design of PHVs.

Regularity of zinc, copper, and lead distribution in different size fractions of Rostov-on-Don urban soil aggregates

: The article is devoted to the study of zinc, copper, and lead content in the soils of Rostov-on-Don. Soil samples were collected from full-profile sections located in different districts of the city and suburbs of Rostov-on-Don. The group of anthropogenically disturbed soils included Urbic Technosol urbanstratozems and replantozems, as well as urbanized chernozems Calcic Chernozems (Technic). Natural soils of recreational areas are represented by migration-segregation chernozems Calcic Chernozems (Pachic). The study was carried out using atomic absorption spectrometry and X-ray fluorescence analysis to determine metal content. Soil structure was determined by the Savvinov method (dry sieving) (<0.25; 1–2; 3–5; 5–7; >10 mm). Statistical analysis of the Wilcoxon criterion for related samples was performed to identify relationships. The main objective of the study was to assess the heavy metal content in different size fractions of aggregates and the ability of structural fractions to accumulate zinc, copper, and lead. Structural aggregates of different sizes differ in their ability to accumulate zinc, copper and lead. Zinc, including its mobile compounds, is predominantly accumulated in microaggregates. The content of gross copper and especially lead is confined to larger aggregates. At the same time, mobile copper compounds are concentrated in microaggregates and in fractions larger than 10 mm. Mobile lead compounds are distributed in fractions of different sizes quite uniformly in all studied soils.

Generation of micrograph-annotation pairs for steel microstructure recognition using the hybrid deep generative model in the case of an extremely small and imbalanced dataset

Insufficient annotated samples coupled with class imbalance problem largely restrict the wide application of deep learning (DL)-based approach in microstructure recognition and quantification. In this work, we present a micrograph augmentation approach using the hybrid deep generative model to generate SEM image-annotation pairs for the establishment of a large-scale and well-balanced augmentation dataset. In this method, a generator is established to produce the desired annotations and then a translator is trained to translate these synthetic annotations into high-quality SEM images. The proposed method is successfully applied to an extremely small and imbalanced additively manufactured (AM) steel dataset containing only one SEM image-annotation pair with a very low martensite/austenite (MA) fraction, to significantly augment the initial dataset and achieve a more balanced distribution of phase fraction. The effectiveness of the present method is well demonstrated by the fact that the extensibility of microstructure recognition model to unseen micrographs is improved through the utilization of synthetic data. Furthermore, the impact of synthetic data proportion on the model's performance and the underlying reasons for synthetic data to improve the extensibility of trained models are also discussed in detail.

Sulphur Fractions, Distribution, and Connections with Soil Attributes in the Gopalpur and Ishwardi Soil Series of Bangladesh

The deficiency of soil sulfur (S) is a prevalent issue in Bangladesh soils, posing a significant obstacle to enhancing crop yield and overall productivity. This study aimed to evaluate the distribution of different sulfur fractions across various soil depths in the Gopalpur and Ishwardi soil series, along with their relationships with other soil parameters. In both soil series, the sulfur fractions were ordered as follows: organic > adsorbed > available forms, with organic sulfur being the most abundant. Additionally, soil attributes such as pH, organic carbon, texture, and EC were assessed to understand their relationships with sulphur fractions. Results indicate significant variations in sulphur distribution between the two soils series, with organic sulphur dominating in Gopalpur soils and sulphate-sulphur prevailing in Ishwardi soils. Correlation analysis reveals strong associations between sulphur fractions and soil attributes, highlighting the influence of soil properties on sulphur dynamics. These findings provide valuable insights into sulphur cycling in agricultural soils of Bangladesh and underscore the importance of soil management practices for optimizing sulphur availability and crop productivity.

Effect of metal-modified sewage sludge biochar tubule on immobilization of chromium in unsaturated soil: Groundwater table fluctuations induced by rainfall

Many studies have studied biochar immobilizing chromium (Cr) in soil. However, few studies were conducted to reduce the environmental risks due to biochar aging in soil. In this study, we adopt FeCl3, MgCl2, and AlCl3 to activate sewage sludge to form modified biochar and produce biochar tubules. Then, the column experiments were carried out to study the effect of fluctuating groundwater table on Cr leaching behavior, total Cr, and fractions distribution with the insertion of biochar tubule. Results showed that the Cr immobilization performance was improved by metal-modification biochar, the biochar tubules can significantly decrease the Cr leaching amounts, retard the Cr downward migration in the soil, and there was a better effect with slightly Cr-contaminated soil. In addition, the immobilization effect is also impacted by the biochar's application mode and the hydrodynamic conditions. Detailedly, the Cr leaching amounts maximally decreased by 33.39%, the residual amounts maximally increased by 10.05% in the soil column, and the exchangeable (EX) and carbonates-bound (CB) fractions were maximally increased by 85.18%, 151.78% at the equal depth of soil column, respectively. BET, SEM-EDS, XRD, and FTIR analyses revealed that biochars' immobilization mechanisms on Cr involved reduction(predominately), physisorption, precipitation, and complexation. Risk assessment demonstrated that the sewage sludge biochar has very low environmental risk. This study indicates that the biochar tubule applied to immobilize Cr in soil has potential and provides new insights into reducing environmental risks due to biochar aging.

A Stochastic FRET Study on the Core Dimension of Polystyrene-block-Poly(Polyethylene Glycol Monomethyl Ether Acrylate) Micelles.

Polystyrene-b-poly(polyethylene glycol monomethyl ether acrylate) (PSt-b-PPEGA) copolymers featuring pyrene and perylene as the Förster resonance energy transfer (FRET) donor (denoted as D-BCP) and acceptor (denoted as A-BCP), respectively, were synthesized via the reversible addition and fragmentation chain transfer (RAFT) polymerization. These copolymers were then used to form DA-mixed micelles via a dialysis method. The micelles consisted of D-BCP (mole fraction fD = 0.04), A-BCP (fA = 0.04), and label-free PSt-b-PPEGA (fN = 0.92). The decrease in fluorescence intensity of pyrene in the micelles confirmed the occurrence of FRET, with an observed efficiency of 0.32. A Monte Carlo approach was employed to estimate the expected FRET efficiency, assuming the random fractional distribution of D-BCP and A-BCP, along with the random spatial distribution of pyrene and perylene within the micellar core. The observed FRET efficiency suggested a core radius (Rc) of 0.95R0, where R0 was the Förster critical distance. With R0 calculated to be 3.2 nm based on Förster theory, Rc was determined to be approximately 3.0 nm, aligning closely with the dried-out core radius estimated from aggregation number and polystyrene density. This stochastic FRET methodology was further applied to investigate the swelling behavior of the polymer micelles in a mixture of N,N-dimethylformamide (DMF) and water. Dynamic light scattering analysis revealed minimal change in core dimension below 60 vol % DMF content. However, FRET analysis provided a deeper insight, showing an increase in core radius with DMF content up to 20 vol %, followed by saturation up to 50 vol %, offering a more comprehensive understanding of the micelle swelling behavior.

Effects of Ageing on Surface Properties of Biochar and Bioavailability of Heavy Metals in Soil

This study aims to explore the effects of biochar ageing on its surface properties and the bioavailability of heavy metals in soil. The biochar was subjected to chemical oxidation/dry–wet cycles (CDWs), chemical oxidation/freeze–thaw cycles (CFTs), and natural ageing (NT) to analyze changes in the elemental composition, pH, specific surface area, pore volume, and surface functional groups. Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM) were applied to characterize the functional groups and microstructure, and the BCR sequential extraction method was employed to demonstrate the fractionation distribution of Cu, Cd, and Pb. The results showed that the CDWs and CFTs treatments significantly reduced the carbon content of the biochar (with a maximum reduction to 47.70%), increased the oxygen content (up to 49.17%), and notably increased the specific surface area and pore volume. The pH decreased significantly from 9.91 to 4.92 and 4.99 for the CDWs and the CFTs, respectively. The FTIR analysis indicated notable changes in hydroxyl and carboxyl functional groups, and the SEM revealed severe microstructural damage in biochar after the CDWs and CFTs treatments. The heavy metal fractionation analysis indicated that exchangeable Cu, Cd, and Pb significantly increased after the CDWs treatment, reaching 31.40%, 5.25%, and 6.79%, respectively. In conclusion, biochar ageing significantly affects its physicochemical properties and increases the bioavailability of heavy metals, raising concerns about its long-term remediation effectiveness.

Modeling and 3-D simulation of petroleum coke calcination process: investigation of the effect of main operating variables

Abstract Coke calcination is a process that involves heating green petroleum coke to purify it and eliminate volatile materials for subsequent processing. Due to the complexity of the rotary kiln used in this process, conducting experimental studies can be challenging and restricted. However, quantitative analyses based on developed models can provide a foundation for optimizing and controlling the process, which can significantly enhance the design efficiency. A three-dimensional simulation model of a rotary calcining kiln for petroleum coke was created using COMSOL Multiphysics in a steady-state mode. This model accounted for all relevant physical and chemical phenomena in the gas stream and coke bed flow, including heat transfer, combustion, and the evolution of volatile matter and coke dust. The mathematical modeling yielded distributions of temperature and mass fractions within the kiln, as well as the velocity field. The results revealed two distinct peak temperatures in the gas phase: 1,780 K near the primary air injection point and 1,605 K near the tertiary air injection points. The findings were analyzed, and the impact of key variables was explored. The simulation data indicated that for every decrease of 10–15 m/s in air flow, the gas peak temperature dropped by approximately 100°. Additionally, an increase in the input oxygen concentration led to enhanced combustion, resulting in higher peak concentrations of CO2. The developed simulation model has proven to be a valuable and promising tool for the design and optimization of petroleum coke rotary kilns.

Detailed particle breakage of crushable granular materials under cyclic shearing conditions using dyed gypsum technique

Particle breakage of granular materials under cyclic shearing is related to a variety of engineering problems in geotechnical and transportation engineering. However, there is limited understanding regarding the detailed evolution law of breakage under cyclic shearing. To this end, a series of cyclic simple shear tests were conducted on artificially dyed gypsum particles. It was observed that, in contrast to the particle size distribution of the whole sample, the fractional particle size distributions of gap-graded samples followed a unified breakage evolution path as those of the uniformly graded ones and tended towards fractional fractal distributions. These results have inspired the introduction of the fractional breakage index. Moreover, the breakage-plastic work relationship was further extended to describe the breakage of fractional particles, incorporating the effect of the number of cycles on the plastic work distribution. Finally, based on the concept of breakage-packing, a predictive model for plastic work-breakage-deformation of crushable granular materials under cyclic shearing was proposed. These results have the potential in understanding the detailed particle breakage evolution and establishing a predictive framework for the breakage-induced deformation of crushable granular materials.

Simulation and design of a solar chimney integrated with phase change material layer for building ventilation

The development of modern life requires new energy sources, and one of this energy is renewable solar energy uses in solar chimney for natural ventilation, but at the present time it is not greatly invested, taking into account the weather conditions of the region and the physical characteristics of solar radiation and air in the area in which the study will be conducted. The current study was carried out in Basrah city- Iraq, at longitude 47.749° and latitude 30.568°, where the solar chimney was facing south. The investigation was conducted using both theoretical and experimental studied. In the theoretical study, the solar chimney with the room in the presence and absence of PCM was simulated numerically using the finite volume method using the soft package ANSYS-Fluent/2021/R2. The effect of different tilt angles (α = 30°, 45°, and 60°), solar chimney air gap (gab = 10 cm, 15 cm, and 20 cm), and PCM basin thickness (tPCM = 3 cm, 4 cm, and 5 cm) were investigated. The results were presented in the form of contours of the distribution of streamlines, velocity, temperature, and liquid fraction of the solar chimney with the room, rate of temperature of the absorber plate with time and the rate of temperature of the PCM (TPCM) with time, rate of air change per hour (ACH). As for the experimental side, the device was built, and the intensity of solar radiation was studied for several days on 30 Sep. and 15 Oct. 2023, the temperature distribution rate of the absorbent plate over time, the PCM temperature rate, and the air change per hour (ACH). The theoretical results were compared with the experimental results, where there was good agreement, and the theoretical comparison was also made with several researchers. Significant results showed that the optimal ratio of the air gap width of the solar chimney is 15 cm, the inclination angle of the solar chimney α = 30°, and the thickness of the PCM basin (tPCM = 4 cm) to obtain the maximum ventilation rate. The thickness of the PCM basin = 4 cm gives the largest liquid fraction along time and maximum average temperature of the absorber plate. On the experimental, it was found that PCM convert into the liquid phase after its melting point, which is 340 K, after 12 noon, and the highest value of ACH reached 37 on September 30/2023 at midday.

Uncertainty quantification of the inlet boundary conditions in a supercritical CO2 centrifugal compressor based on the non-intrusive polynomial chaos

Given the sensitivity of supercritical carbon dioxide centrifugal compressors performance to inlet boundary parameter fluctuations, this study focuses on the uncertainty quantification of the inlet boundary conditions. Non-intrusive polynomial chaos surrogate models were developed for both performance parameters and flow field of a supercritical carbon dioxide centrifugal compressor. Sensitivity and correlation analyses revealed that inlet total temperature is the primary influencing parameter. Fluctuations of 1.37 % in total temperature and 6.75 % in total pressure result in changes of 40.94 %, 18.57 %, and 1.77 % in mass flow rate, total pressure ratio, and total to total isentropic efficiency, respectively. Flow field statistical analysis shows that inlet uncertainties nonlinearly impact the dryness fraction and relative Mach number distributions near the blade leading edge, while the density in the condensation zone on the suction side of the leading edge is less affected. Error bands in static pressure on blade surfaces highlight significant variations, particularly at 90 % spanwise on the blade suction side, where shocks and supersonic flow induce prominent disturbances. This study offers a preliminary methodology and theoretical guidance for robust aerodynamic optimization and operational strategies of supercritical carbon dioxide centrifugal compressors.

Optimization of non-spherical particle flow in vertical waste heat recovery devices: Analyzing structural configurations

Vertical waste heat recovery devices are emerging but are immature. The vertical waste heat recovery devices of circular, square, and optimized designs were analyzed for a full capacity of 8 tons of sintered ore. Using DEM theory, the effects of particle size distribution, velocity, and wall forces on void fraction distribution and particle flow were examined. The circular device demonstrated superior mixed particle flow compared to the square device, achieving integrated flow for 50 % of particles in the cone, in contrast to 26 % for the square device. An optimized circular device achieved integral flow for 90 % of particles, significantly enhancing overall flow and reducing wall adhesion, attributed to its improved internal design. Through insert and distributor design, the overall particle flow within the device improved, with almost no particles remaining on the walls. These findings underscore the potential for enhanced heat recovery efficiency through optimized internal structures in waste heat recovery devices.

Numerical Simulation Studies on the Design of the Prosthetic Heart Valves Belly Curves

Prosthetic heart valves (PHVs) are employed to replace the diseased native valve as a treatment of severe aortic valve disease. This study aimed to evaluate the effect of curvature of the belly curve on valve performance, so as to support a better comprehension of the relationship between valve design and its performance. Five PHV models with different curvatures of the belly curve were established. Iterative implicit fluid–structure interaction simulations were carried out, analyzing in detail the effect of belly curvature on the geometric orifice area (GOA), coaptation area (CA), regurgitant fraction (RF), leaflet kinematics and stress distribution on the leaflets. Overall, GOA and CA were negatively and positively related to the curvature of the belly curve, respectively. Nevertheless, an excessive increase in curvature can lead to incomplete sealing of free edges of the valve during its closure, which resulted in a decrease in CA and an increase in regurgitation. The moderate curvature of the belly curve contributed to reducing RF and fluttering frequency. Valves with small curvature experienced a significantly higher frequency of fluttering. Furthermore, all stress concentrations intensified with the increase in the curvature of the belly curve. The valve with moderate curvature of the belly curve strikes the best compromise between valve performance parameters, leaflet kinematics and mechanical stress. Considering the different effects of the curvature of belly curve on valve performance parameters, the PHV design with variable curvature of belly curve may be a direction towards valve performance optimization.

FGM modeling considering preferential diffusion, flame stretch, and non-adiabatic effects for hydrogen-air premixed flame wall flashback

Preferential diffusion plays an important role especially in hydrogen flames. Flame stretch significantly affects the flame structure and induces preferential diffusion. A problematic phenomenon occurring in real combustion devices is flashback, which is influenced by non-adiabatic effects, such as wall heat loss. In this paper, an extended flamelet-generated manifold (FGM) method that explicitly considers the preferential diffusion, flame stretch, and non-adiabatic effects is proposed. In this method, the diffusion terms in the transport equations of scalars, viz. the progress variable, mixture fraction, and enthalpy, are formulated employing non-unity Lewis numbers that are variable in space and different for each chemical species. The applicability of the extended FGM method to hydrogen flames is investigated using two- and three-dimensional numerical simulations of hydrogen-air flame flashback in channel flows. The results of the extended FGM method are compared with those of detailed calculations and other FGM methods. The two-dimensional numerical simulations show that considering both preferential diffusion and flame stretch improves the prediction accuracy of the mixture fraction distribution and flashback speed. The three-dimensional numerical simulations show that the prediction accuracy of the flashback speed, backflow region, and distributions of physical quantities near the flame front is improved by employing the extended FGM method, compared with the FGM method that considers only the heat loss effect. In particular, the extended FGM method successfully reproduced the relationship between the reaction rate and curvature. These results demonstrate the effectiveness of the extended FGM method.Novelty and Significance Statement The novelty of this research is the development of a flamelet-generated mani-fold (FGM) method that explicitly considers preferential diffusion, flame stretch, and non-adiabatic effects. To the best of the authors’ knowledge, no studies have performed numerical simulations of pure hydrogen flames using such an FGM method. The developed FGM method was applied to numerical simula- tions of hydrogen-air premixed flame flashback at an equivalence ratio of 0.5 and reproduced the flashback speed of lean hydrogen-air premixed flame. The applicability of the FGM method to the numerical simulation of hydrogen-air flashback is reported first. This research is significant because the FGM method is one of the most widely used combustion models for premixed combustion, and the development of an accurate FGM method will contribute to the engineering field. The accurate prediction of the flame flashback attempted in this study is particularly important for the development of hydrogen-fueled combustion devices.

Crop rotation and green manure type enhance organic carbon fractions and reduce soil arsenic content

Green manure incorporation has recently emerged as a promising strategy for mitigating heavy metals (HMs) contamination and enhancing soil quality. However, there are still many uncertainties regarding the effects of crop rotation and the type of incorporated green manure on soil organic carbon fractions and arsenic (As) mitigation in As-contaminated soil. Thus, a two-phase experiment was conducted to determine the effects of crop rotation and green manure type on the distribution of organic carbon fractions and As accumulation in soil and brown rice plants. It was found that green manure incorporation increases soil nutrient content with an increase in total carbon of 18.64 %, 18.10 %, and 19.83 % under BC-R, AS-R, and LP-R respectively, and enhances organic carbon fractions. Furthermore, soil As concentration was significantly decreased by green manure incorporation for 20.65 %, 20.02 % and 19.99 % under BC-R, AS-R and LP-R respectively while As concentration in brown rice various parts was under permissible limits. This study highlights the complex interactions between green manure-brown rice rotation and green manure incorporation on soil organic carbon fractions, and As content in soil and brown rice, and emphasizes further research to elucidate optimal cultivation strategies of continuous crop rotation and green manure incorporation for sustainable remediation of As-contaminated soils while ensuring food safety.

SELECTION OF GAS MIXER PARAMETERS FOR DIESEL CONVERSION GENERATOR MOTOR IN GAS DIESEL

According to literary sources, options for converting diesel engines into dual-fuel engines for operation on any fuel, in particular, natural gas (NG), were analyzed. The conversion method with external mixture formation and an ignition dose of liquid fuel involves the preparation of a gas-air mixture of the required composition in a special device. The methodology for choosing the design parameters of the gas mixer for the organization of the work process of a V-shaped diesel engine type 12Ch 15/17.5, converted into a gas diesel, which works as part of a motor-generator unit of backup power supply, is given. The basic design of the diesel motor-generator was analyzed. A comparative calculation of the working processes of diesel and gas-diesel variants of execution (with an ignition dose of diesel fuel of 10%) was carried out. The requirements for the design and location of the gas mixer have been formed. In the work, using 3D modeling technologies, the geometry of the gas mixer and its flow part were formed. Using the method of finite volumes, the calculation grid was synthesized and its adaptation near solid walls was carried out. Next, a series of numerical experiments was conducted in a three-dimensional setting to evaluate the throughput and quality of mixing network methane with air (when the robot is operating at typical operating modes). The distribution of flow velocities in the vertical and horizontal planes of the flow part of the gas mixer was evaluated, the change in pressure along the height of the gas mixer and the distribution of the mass fraction of methane in the flow part of the engine intake tract were analyzed, and scientific and practical recommendations were developed to ensure the efficient operation of gas diesel as part of a motor-generator installation. It is shown that the proposed design of the gas mixer allows effective mixing of methane with air when operating in the entire power range of the considered engine. The use of 3D modeling technologies, with the use of modern numerical methods, allows you to assess the operating conditions of the mixture by macro indicators and in local sub-regions, which allows, in the future, to develop recommendations for increasing the efficiency of the process of preparing the fuel-air mixture.

Distribution of inorganic phosphorus fractions in different phosphorus level soil

Distribution of inorganic phosphorus fractions in different phosphorus level soil

An investigation of anisotropy in the bubbly turbulent flow via direct numerical simulations

We investigated the effects of bubble count, flow direction, and Eötvös number on deformable bubbles in turbulent channel flow. For a given shear Reynolds number Re = 180 and fixed bubble volume fractions (1.263% and 2.525%), we conducted a series of direct numerical simulations using a coupled level-set and volume-of-fluid solver to evaluate their impact on bubble volume fraction distribution, velocity fields, and turbulence characteristics. Each aspect was studied based on the microscopic equations of two-phase flow, and the accuracy of the modeling terms used in current Reynolds-averaged Navier–Stokes equation (RANS) models was assessed. The influence on the anisotropic state was analyzed using the Lumley triangle, and the anisotropy of Reynolds stresses was captured through the exact balance equations. The results indicate that in upward flow, bubbles tend to accumulate near the wall, with smaller Eötvös numbers leading to closer proximity to the wall and greater attenuation of the liquid-phase velocity. This distribution enhances energy dissipation and turbulence isotropy. In downward flow, bubbles cluster in the channel center, generating additional pseudo-turbulence and attenuating energy in the buffer layer. Moreover, the interfacial transfer of turbulent energy, as currently modeled in RANS, is found to be inadequate for upward flows.