Mass Transfer Velocity Research Articles

Development and application of the entropy production diagnostic model to the cavitation flow of a pump-turbine in pump mode

A novel mathematical model, entropy production diagnostic model (EPDM) with phase transition (EPDMS), was developed, which is practical to analyze the irreversible loss for cavitation flow in hydraulic machinery by including mass transfer and slip velocity. To model the corresponding flow, two-fluid model with main interphase forces was employed. Compared with the EPDM in homogeneous model, two extra contributions, diffusion and interface entropy production (DifE, IntE), are added in EPDMS. Then, EPDMS was validated by experiments of a pump-turbine in pump mode at three off-design conditions. The improved numerical model is more accurate in capturing the typical cavitation points, while the original one is obviously lower due to poor consideration of phase interaction. Therefore, the loss predicted by EPDMS is more rational. A detailed comparison among four overlapping items of EPDM and EPDMS was performed. It shows that these items merely interpret the accumulative effect of cavitation on the flow, while as a key part of EPDMS, IntE is closely related to the evolution of cavitation. Moreover, low-frequency excitation that caused by cavitation-induced vortex is captured by the probe at the edge of the cavity, which is consistent with the frequency-domain characteristics of IntE instead of other items.

Optimization of lanthanum extraction in asymmetric rotation pilot plant column by using central composite methodology

ABSTRACTThe present work aimed to optimize the lanthanum extraction efficiency in the pilot-scale asymmetric rotating disc contactor. Optimal batch-scale extraction conditions were determined for the preparation of feed for extraction column (D2EHPA 0.08 mol/L; pH~8). In continuous mode, the optimization with the central composite design approach was performed by using three main parameters, such as continuous phase flow rate, agitation intensity, dispersed phase flow rate. Three responses studied were slip velocity, dispersed phase holdup, and extraction efficiency. The higher value of extraction efficiency for lanthanum extraction shows the main effect of agitation intensity on the dispersed phase holdup, slip velocity, and rate of mass transfer. The optimum conditions for extraction efficiency equal 98.5% were obtained at a rotation speed equal to 7.75 1/s, and phase flow rates equal to 1.25 × 10−5 m3/s. The new correlations are estimated to describe the holdup of the dispersed phase and the slip velocity with high accuracy and R-square values equal to 0.9734 and 0.9670, respectively. The results showed that the pilot plant asymmetric rotating disc column could be used as an appropriate column for the lanthanum extraction from aqueous solution as an example of rare earth metals.

Entropy analysis in nonlinearly convective flow of the Sisko model in the presence of Joule heating and activation energy: the Buongiorno model

This investigation deals with entropy generation optimization and an activation energy mechanism for nonlinear convective flow of a Sisko nanofluid due to a stretchable rotating disk. Heat transfer analysis is accomplished through nonlinear thermal radiation and non-uniform heat generation/absorption. The Joule heating effect is also considered with viscous dissipation. The nanofluid model includes Brownian motion and thermophoresis. Apposite transformations are endorsed to obtain the nonlinear-coupled ordinary differential equation system. The attained system endeavors for series solutions by the homotopy technique. Total entropy generation is analyzed through numerous flow variables. A comparative study of shear-thickening and shear-thinning fluids is also presented for the Bejan number, heat transfer rate, mass transfer Nusselt number, entropy generation, temperature, velocity and concentration. Here the entropy generation rate (irreversibility rate) is enhanced for the thermal radiation parameter while the reverse behavior is noted for the material parameter and Brinkman number. Furthermore, the behavior of the temperature profile and nanoparticle concentration will be displayed through a Brownian motion parameter and an activation energy parameter.

Simulation of air–water interfacial mass transfer driven by high-intensity isotropic turbulence

Previous direct numerical simulations (DNS) of mass transfer across the air–water interface have been limited to low-intensity turbulent flow with turbulent Reynolds numbers of $R_{T}\leqslant 500$. This paper presents the first DNS of low-diffusivity interfacial mass transfer across a clean surface driven by high-intensity ($1440\leqslant R_{T}\leqslant 1856$) isotropic turbulent flow diffusing from below. The detailed results, presented here for Schmidt numbers $Sc=20$ and $500$, support the validity of theoretical scaling laws and existing experimental data obtained at high $R_{T}$. In the DNS, to properly resolve the turbulent flow and the scalar transport at $Sc=20$, up to $524\times 10^{6}$ grid points were needed, while $65.5\times 10^{9}$ grid points were required to resolve the scalar transport at $Sc=500$, which is typical for oxygen in water. Compared to the low-$R_{T}$ simulations, where turbulent mass flux is dominated by large eddies, in the present high-$R_{T}$ simulation the contribution of small eddies to the turbulent mass flux was confirmed to increase significantly. Consequently, the normalised mass transfer velocity was found to agree with the $R_{T}^{-1/4}$ scaling, as opposed to the $R_{T}^{-1/2}$ scaling that is typical for low-$R_{T}$ simulations. At constant $R_{T}$, the present results show that the mass transfer velocity $K_{L}$ scales with $Sc^{-1/2}$, which is identical to the scaling found in the large-eddy regime for $R_{T}\leqslant 500$. As previously found for a no-slip interface, also for a shear-free interface the critical $R_{T}$ separating the large- from the small-eddy regime was confirmed to be approximately $R_{T}=500$.

Re-Aeration on Stepped Spillways with Special Consideration of Entrained and Entrapped Air

As with most high-velocity free-surface flows, stepped spillway flows become self-aerated when the drop height exceeds a critical value. Due to the step-induced macro-roughness, the flow field becomes more turbulent than on a similar smooth-invert chute. For this reason, cascades are oftentimes used as re-aeration structures in wastewater treatment. However, for stepped spillways as flood release structures downstream of deoxygenated reservoirs, gas transfer is also of crucial significance to meet ecological requirements. Prediction of mass transfer velocities becomes challenging, as the flow regime differs from typical previously studied flow conditions. In this paper, detailed air-water flow measurements are conducted on stepped spillway models with different geometry, with the aim to estimate the specific air-water interface. Re-aeration performances are determined by applying the absorption method. In contrast to earlier studies, the aerated water body is considered a continuous mixture up to a level where 75% air concentration is reached. Above this level, a homogenous surface wave field is considered, which is found to significantly affect the total air-water interface available for mass transfer. Geometrical characteristics of these surface waves are obtained from high-speed camera investigations. The results show that both the mean air concentration and the mean flow velocity have influence on the mass transfer. Finally, an empirical relationship for the mass transfer on stepped spillway models is proposed.

Slip Flow of an Unsteady Nanofluid Past a Stretching Surface in a Transverse Magnetic Field Using SRM

A theoretical and numerical examination has been completed to talk about the unsteady, two dimensional slip flow of a nanofluid of heat and mass transfer with transverse magnetic field was investigated in this paper. A stretching surface is used to investigate the flow. Obtained nonlinear equations are solved by Spectral Relaxation Method (SRM) technique and the results are verified by comparing the results obtained by using the Matlab in-built boundary value problem solver bvp4c, and the outcomes which are published in previous papers. The outcomes are exhibited pictorially and talked about difference coming about parameters. Expanding heat transfer rate, mass transfer rate and velocity slip raises velocity yet to be diminishes temperature and skin friction (surface shear stress).

Optical determination of oxygen mass transfer in a helically-coiled pipe compared to a straight horizontal tube

The gas-liquid mass transfer of oxygen has been examined experimentally in a helically-coiled pipe using an optical colorimetric method. Two tracer redox-reactions have been used for this purpose: (i) methylene blue and (ii) resazurin. The gas hold-up has been varied from 0.1 to 0.6, and liquid flow rate from 0.37 to 0.68 l/min, both leading to plug-flow conditions in the helix for all parameter combinations. A progress variable has been defined to measure the advancement of the reaction and thus, oxygen transfer to the liquid. The resazurin reaction turned out to be more appropriate for mass transfer studies, due to the bigger time constant difference of oxidation and reduction. Therefore, it can be adapted more easily to the specific conditions of the set-up. It also possesses more intense colours and higher fluorescence intensity, which might be useful for other mass transfer studies. As expected, the oxygen mass transfer increases with gas hold up, but liquid flow rate has little influence. A comparison with a horizontal tube of the same diameter shows the drastically increased mass transfer in the helix, due to better radial mixing and different flow pattern. Depending on the experimental conditions, oxygen concentration in the helix was up to twice that of the horizontal tube. This can be explained by the much higher liquid side mass transfer velocity, which is determined in this study from the experimental kla-values and specific bubble surface per turn of the helix. For this purpose, bubble dimensions and gas-liquid cell volumes have been determined from the experimental images. The paper thus presents a locally resolved characterization of gas-liquid mass transfer in a helically coiled reactor. The high mass transfer especially during the first turns of the helix shows its advantages compared to a straight tube.

Instantaneous mass transfer measurement and its relation to large-scale structures in pipe flow

The flow field and mass transfer rate in a straight pipe are measured simultaneously using particle image velocimetry (PIV) and an electrochemical method, respectively. Turbulence structures of length scales larger than 2.4R in the log region are studied in relation with the mass transfer fluctuations in the near-wall region. The time-series contours of the fluctuations in mass transfer and stream-wise velocity are compared, and their correlation coefficient is discussed. Using the time-series contour, it can be confirmed that the footprint of the large-scale turbulent structures in the log region affects the near-wall region, which enhances the mass transfer rate. By comparing the two-point correlations of the stream-wise velocity fluctuation and mass transfer fluctuation, the mass transfer rate at the wall is observed to be related with the large-scale velocity structures in the log region.

Effect of surface contamination on interfacial mass transfer rate

The influence of surface contamination upon the mass transfer rate of a low diffusivity gas across a flat surface is studied using direct numerical simulations. The interfacial mass transfer is driven by isotropic turbulence diffusing from below. Similar to Shen et al. (J. Fluid Mech., vol. 506, 2004, pp. 79–115) the surface contamination is modelled by relating the normal gradient of the horizontal velocities at the top to the horizontal gradients of the surfactant concentrations. A broad range of contamination levels is considered, including clean to severely contaminated conditions. The time-averaged results show a strong correlation between the gas transfer velocity and the clean surface fraction of the surface area. In the presence of surface contamination the mass transfer velocity $K_{L}$ is found to scale as a power of the Schmidt number, i.e. $Sc^{-q}$, where $q$ smoothly transitions from $q=1/2$ for clean surfaces to $q=2/3$ for very dirty interfaces. A power law $K_{L}\propto Sc^{-q}$ is proposed in which both the exponent $q$ and the constant of proportionality become functions of the clean surface fraction.

Experimental investigation of terminal velocity and Sherwood number of rising droplet in an extraction column

Mass transfer and terminal velocity of toluene drops rising in an extraction column was studied experimentally. The impact of packing was investigated by inserting a structured packing in three different heights of 10, 25 and 40 cm inside the column. The effect of packing height, flow rate and drop size on terminal velocity and Sherwood number were investigated and the results were also compared with the case of non-packed column. It was discussed that a 30% increase in Sherwood number could be achieved using the packing with 40 cm in height. It was also found that for Eotvos number, Eo, higher than 0.4, the deformation of drops and velocity oscillation appeared, which affected the terminal velocity. Finally, two correlations were proposed, which permitted the prediction of deformation and extraction ratio versus the dimensionless numbers of Reynolds, Eotvos and the packing height ratio.

Calcium carbonate deposition drives nutrient cycling in a calcareous headwater stream

AbstractCalcium carbonate (CaCO3) deposition is common in aquatic ecosystems and may reduce phosphorus availability via coprecipitation of phosphate, an impact with broad implications for ecosystem processes. To determine if CaCO3 deposition in streams increases phosphorus (P) retention in minerals while reducing P availability to organisms, we studied paired streams (with and without active CaCO3 deposition) subjected to experimental shading and monitored changes in ecosystem attributes (e.g., periphyton biomass content, nutrient spiraling, periphyton nutrient limitation, and leaf litter decomposition). Shading reduced rates of CaCO3 deposition by over 50%, suggesting that a substantial proportion of CaCO3 deposition is supported by photosynthetically induced changes in alkalinity. Shading‐induced reductions in CaCO3 deposition led to increases in epilithon biomass P content (P < 0.05) and periphyton growth (F2,12 = 5.79, P < 0.05). Reductions in CaCO3 deposition also relieved P limitation of periphyton growth (F3,16 = 59.32, P < 0.001), extended P uptake lengths at least an order of magnitude, and reduced both P mass transfer velocity and areal uptake rates by over 80% (F2,3 = 22.62, P < 0.05 and F2,3 = 13.19, P < 0.05, respectively). Finally, while shading caused reductions in leaf litter decomposition in the non‐CaCO3 depositing stream (F5,7 = 22.45, P < 0.001), shading had no effect on leaf litter decomposition in the stream with active CaCO3 deposition. These results indicate that CaCO3 deposition can regulate P bioavailability and retention in streams and may drive streams to be P limited, as has been suggested in lake and wetland ecosystems.

Estimation of Uncertainty in Air-Water Exchange Flux and Gross Volatilization Loss of PCBs: A Case Study Based on Passive Sampling in the Lower Great Lakes.

Compared with dry and wet deposition fluxes, air-water exchange flux cannot be directly measured experimentally. Its model-based calculation contains considerable uncertainty because of the uncertainties in input parameters. To capture the inherent variability of air-water exchange flux of PCBs across the lower Great Lakes and to calculate their annual gross volatilization loss, 57 pairs of air and water samples from 19 sites across Lakes Erie and Ontario were collected using passive sampling technology during 2011-2012. Error propagation analysis and Monte Carlo simulation were applied to estimate uncertainty in the air-water exchange fluxes. Results from both methods were similar, but error propagation analysis estimated a smaller uncertainty than Monte Carlo simulation in cases of net deposition. Maximum likelihood estimations (MLE) of wind speed and air temperature were recommended to quantify the site-specific air-water exchange flux. An assumed 30-40% of relative uncertainty in overall air-water mass transfer velocity was confirmed. MLEs of volatilization fluxes of total PCBs across Lakes Erie and Ontario were 0.78 and 0.53 ng m-2 day-1, respectively, and gross volatilization losses of total PCBs over the whole lakes were 74 kg year-1 for Lake Erie and 63 kg year-1 for Lake Ontario. Mass balance analysis across Lake Ontario indicated that volatilization was the uppermost loss process of aqueous PCBs.

Holdup and flooding measurements in an asymmetric rotating disc column

Dispersed phase holdup and flooding rates have been measured in a 113mm diameter asymmetric rotating disc contactor (ARDC) of pilot plant scale for three different liquid–liquid systems. The effects of operating variables including mass transfer conditions, rotor speed and continuous and dispersed phase velocities on hydrodynamic parameters are investigated. The results showed that the maximum capacity of the column decreases with increase in the rotor speed and flow ratio, while it increases with increase in interfacial tension. There was a significant increase in the holdup at the flooding points with an increase in the rotor speed because of the smaller drops formation. The dispersed phase holdup was influenced mainly by mass transfer direction, agitation speed and velocity of the dispersed phase. The new unified correlations were proposed in this study to prediction for the flooding velocities, holdup at flooding and holdup data of the ARDC column used in this study.

Mathematical modeling of humidification process by means of hollow fiber membrane contactor

Modeling and simulation of air humidification by hollow fiber membrane contactors are investigated in the current study. A computational fluid dynamic model was developed by solving the k-epsilon turbulence 2D Navier.Stokes equations as well as mass conservation equations for steady-state conditions in membrane contactors. Finite element method is used for the study of the air humidification under different operating conditions, with a focus on the humidity density, total mass transfer flux and velocity field. There has been good agreement between simulation results and experimental data obtained from literature. It is found that the enhancement of air stream decreases the outlet humidity from 0.392 to 0.340 (module 1) and from 0.467 to 0.337 (module 2). The results also indicated that there has been an increase in air velocity in the narrow space of shell side compared with air velocity wide space of shell side. Also, irregular arrangement has lower dead zones than regular arrangement which leads to higher water flux.

Fatty acid methyl ester production from wet microalgal biomass by lipase-catalyzed direct transesterification

The aim of this work was to optimize the production of fatty acid methyl ester (FAME, biodiesel) from wet Nannchloropsis gaditana microalgal biomass by direct enzymatic transesterification. This was done in order to avoid the high cost associated with the prior steps of drying and oil extraction. Saponifiable lipids (SLs) from microalgal biomass were transformed to FAME using the lipase Novozyme 435 (N435) from Candida antarctica as the catalyst, and finally the FAME were extracted with hexane. t-Butanol was used as the reaction medium so as to decrease lipase deactivation and increase mass transfer velocity. A FAME conversion of 99.5% was achieved using wet microalgal biomass homogenized at 140 MPa to enhance cell disruption, a N435:oil mass ratio of 0.32, methanol added in 3 stages to achieve a total of 4.6 cm3 g−1 of oil and 7.1 cm3 g−1 oil of added t-butanol, with a reaction time of 56 h. The FAME conversion decreased to 57% after catalyzing three reactions with the same lipase batch. This work shows the influence of the polar lipids contained in the microalgal biomass both on the reaction velocity and on lipase activity.

Dispersion of VOC vapours in the surface treatment workspace: influence of variability in diffusivity, mass transfer and air velocity

Wherever solvents are allowed to disperse into the workspace it is necessary to be able to predict and determine their concentration and the effect of air velocity variations. Models developed to predict dispersion for assessing ventilation efficiency and worker exposure are validated against measured data with varying success. In numerical convection–dispersion models, including computational fluid dynamics methods, the transport coefficient effective diffusivity is used as a turbulence closure parameter and air velocities are used to define convective mass transport. This study shows how transport coefficient values, empirically estimated from airborne volatile organic carbon vapour concentrations from a solvent source, vary in a ventilated workspace. Variability in effective diffusivity values demonstrates non-Fickian dispersion from the source along the length of a one-dimensional axis. An important finding was that a correlation between air velocity and vapour transport data was not found. This suggests that air velocity should not be used a priori to represent mass transport in the determination of vapour dispersion in the workplace.

Chemical Enrichment of Nickel Sulfide

The availability of polymetallic ores is getting leaner in grade and is larger but inferior in volumes than in the past, making the extraction of copper, nickel and other non-ferrous metals metallurgically more difficult to produce. The standard technologies, including enrichment and concentration, do not provide methods for obtaining monometallic concentrates and high extraction of metals into the commercial product. Pyrometallurgical processing of large volumes of poor raw materials is not economical and is complicated from the technological point of view. Conditions of chemical enrichment of poor natural materials have been studied with the use of technology of salt exchange leaching. The main impurity in sulfide ores of nonferrous metals is iron present in the forms of pyrite and pyrrhotite and the properties of chemical enrichment for nickel in pyrite concentrates has been investigated in this work. On the basis of thermodynamic analysis carried out with the use of Potential-pH Pourbaix’s Diagrams, it has been established that, with the use of nickel salt, it is possible to leach iron sulfides from ores. Based on the study of the mechanism and kinetics of the process of dissolution of iron sulfides with nickel salts, it was established that during the dissolution, the chemical composition and thermodynamic characteristics of the dissolved iron sulfides change—the residues from leaching are enriched with iron sulfides that are rich in sulfur and also result with elemental sulfur formation. Enrichment of leaching residues with sulfide iron with increased sulfur content and formation on the surface of nickel sulfide leads to increase of diffusional resistances and the process is limited by the velocity of mass transfer. To increase the velocity of the process and completeness of the reaction, it is necessary to activate the process, in particular, by grinding the solid phase.

Diffusion of Chemically Reactive Species in Stagnation-Point Flow of a Third Grade Fluid: a Hybrid Numerical Method

The boundary layer flow of a third grade fluid and mass transfer near a stagnation-point with diffusion of chemically reacting species on a porous plate is investigated. Due to a porous plate the suction is taken into an account. Using suitable transformations, the momentum and concentration equations are first transformed into nonlinear ordinary ones and then solved using a hybrid numerical method. This method combines the features of finite difference and shooting methods. The effects of various controlling parameters on the flow velocity, concentration profile, skin friction and rate of mass transfer on surface are analyzed graphically and in tabular form. Comparison of the present results with the previous reported results has been found in excellent agreement.

Unified new correlation for prediction of dispersed phase holdup in agitated extraction columns

Abstract Dispersed phase holdup data have been obtained for Kuhni and ORC columns with investigation on three different systems (toluene–water, n-butyl acetate–water, n-butanol–water). The effects of operational variables such as mass transfer directions with acetone transfer, rotor speed and dispersed and continuous phase velocities have been investigated. The dispersed phase holdup was influenced mainly by mass transfer direction, agitation speed and velocity of the dispersed phase. Calculations with the literature equations cannot predict experimental data, thus a unified correlation considering the geometric parameter was provided to predict holdup. The correlation involving Froude number, phase velocities, modified property group along with those of geometry factor fits the experimental data well. The results of the proposed correlation were compared with the experimental data obtained from the literature and the present investigation. Findings of this study demonstrated that the proposed correlation leads to an accurate prediction for the dispersed phase holdup.

Three-dimensional double diffusive natural convection across a cubical enclosure partially filled by vertical porous layer

This paper reports a numerical study with two and three-dimensional flows, in an enclosure domain partially filled with a vertical porous media layer saturated by a mixture of air with another gaseous component, the Prandtl number Pr is kept at 0.7. The domain right and left vertical walls are considered at uniform different temperature and concentration, the other walls are adiabatic and impermeable. The results of two-and three-dimensional models were compared. The influence of the main parameters of double diffusive convection is investigated, namely the buoyancy ratio, (−0.1 ≤ N ≤ −4) and Lewis number (0.1 ≤ Le ≤ 10) on the flow structure and heat and mass transfer rate are depicted. The temperature and concentration effect (on density) could be opposing (N < 0). By The resulting flow is consequence of buoyancy forces (density) field affected by the relative conductivity and the porous media permeability. The complex obtained flow structure and corresponding heat and mass transfer (velocity, temperature profiles) are discussed at steady state. The numerical results are reported and analyzed in terms of stream trace, streamlines, isotherms, isoconcentrations lines and averaged Nusselt and Sherwood numbers.