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Showing papers on "Schmidt number published in 1997"


Journal ArticleDOI
TL;DR: In this article, mass transfer through the solid boundary of a turbulent channel flow is analyzed by means of large-eddy simulation (LES) for Schmidt numbers Sc=1, 100, and 200.
Abstract: Mass transfer through the solid boundary of a turbulent channel flow is analyzed by means of large-eddy simulation (LES) for Schmidt numbers Sc=1, 100, and 200. For that purpose the subgrid stresses and fluxes are closed using the Dynamic Mixed Model proposed by Zang et al. [Phys. Fluids A 5, 3186 (1993)]. At each Schmidt number the mass transfer coefficient given by the LES is found to be in very good quantitative agreement with that measured in the experiments. At high Schmidt number this coefficient behaves like Sc−2/3, as predicted by standard theory and observed in most experiments. The main statistical characteristics of the fluctuating concentration field are analyzed in connection with the well-documented statistics of the turbulent motions. It is observed that concentration fluctuations have a significant intensity throughout the channel at Sc=1 while they are negligible out of the wall region at Sc=200. The maximum intensity of these fluctuations depends on both the Schmidt and Reynolds numbers ...

160 citations


Journal ArticleDOI
TL;DR: In this paper, heat and mass transfer along a vertical plate under the combined buoyancy force effects of thermal and species diffusion, in the presence of the magnetic field is investigated and the boundary layer equations are transformed to ordinary differential equations.

109 citations


Journal ArticleDOI
TL;DR: Measurements of the geometric shape, perimeter, and cross-sectional area of the human oral passage is presented and relates them through dimensionless parameters to the depositional mass transfer of ultrafine particles to heat transfer in the human upper airways.
Abstract: This paper presents measurements of the geometric shape, perimeter, and cross-sectional area of the human oral passage (from oral entrance to midtrachea) and relates them through dimensionless parameters to the depositional mass transfer of ultrafine particles. Studies were performed in two identical replicate oral passage models, one of which was cut orthogonal to the airflow direction into 3 mm elements for measurement, the other used intact for experimental measurements of ultrafine aerosol deposition. Dimensional data were combined with deposition measurements in two sections of the oral passage (the horizontal oral cavity and the vertical laryngeal-tracheal airway) to calculate the dimensionless mass transfer Sherwood number (Sh). Mass transfer theory suggests that Sh should be expressible as a function of the Reynolds number (Re) and the Schmidt number (Sc). For inhalation and exhalation through the oral cavity (O-C), an empirical relationship was obtained for flow rates from 7.5-30.0 1 min-1: Sh = 15.3 Re0.812 Sc-0.986 An empirical relationship was likewise obtained for the laryngeal-tracheal (L-T) region over the same range of flow rates: Sh = 25.9 Re0.861 Sc-1.37 These relationships were compared to heat transfer in the human upper airways through the well-known analogy between heat and mass transfer. The Reynolds number dependence for both the O-C and L-T relationships was in good agreement with that for heat transfer. The mass transfer coefficients were compared to extrathoracic uptake of gases and vapors and showed similar flow rate dependence. For gases and vapors that conform to the zero concentration boundary condition, the empirical relationships are applicable when diffusion coefficients are taken into consideration.

105 citations


Journal ArticleDOI
TL;DR: Local flow velocities were correlated with local mass transfer coefficients using a semi-theoretical mass transfer equation and the relationship between the Sherwood number, the Reynolds number, and the Schmidt number was found using the experimental data to find the dimensionless empirical constants.
Abstract: The relationship between local mass transfer coefficient and fluid velocity in heterogenous biofilms was investigated by combining microelectrodes and confocal scanning laser microscopy (CSLM). The biofilms were grown for up to 7 days and consisted of cell clusters separated by interstitial channels. Mass transfer coefficient depth profiles were measured at specific locations in the cell clusters and channels at average flow velocities of 2.3 and 4.0 cm/s. Liquid flow velocity profiles were measured in the same locations using a particle tracking technique. The velocity profiles showed that flow in the open channel was laminar. There was no flow at the top surface of the biofilm cell clusters but the mass transfer coefficient was 0.01 cm/s. At the same depth in a biofilm channel, the flow velocity was 0.3 cm/s and the mass transfer coefficient was 0.017 cm/s. The mass transfer coefficient profiles in the channels were not influenced by the surrounding cell clusters. Local flow velocities were correlated with local mass transfer coefficients using a semi-theoretical mass transfer equation. The relationship between the Sherwood number (Sh,) the Reynolds number (Re,) and the Schmidt number (Sc) was found using the experimental data to find the dimensionless empirical constants (n1, n2, and m) in the equation Sh = n(1) + n(2)Re(m) Sc(1/3). The values of the constants ranged from 1.45 to 2.0 for n(1), 0.22 to 0.28 for n(2), and 0.21 to 0.60 for m. These values were similar to literature values for mass transfer in porous media. The Sherwood number for the entire flow cell was 10 when the bulk flow velocity was 2.3 cm/s and 11 when the bulk flow velocity was 4.0 cm/s. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 681-688, 1997.

78 citations


Journal ArticleDOI
TL;DR: In this paper, Lagrangian pdf methods are employed to extend the spectral relaxation (SR) model of the scalar dissipation of an inert, passive scalar (1⩽Sc) in homogeneous turbulence.
Abstract: Lagrangian pdf methods are employed to extend the spectral relaxation (SR) model of the scalar dissipation of an inert, passive scalar (1⩽Sc) in homogeneous turbulence. The Lagrangian spectral relaxation (LSR) model divides wavenumber space into a finite number (the total number depending on the Taylor-scale Reynolds number Rλ and the Schmidt number Sc) of wavenumber bands whose time constants are determined from the mean turbulent kinetic energy and instantaneous turbulent energy dissipation rate. The LSR model accounts for the evolution of the scalar spectrum (viz., pdf) from an arbitrary initial shape to its fully developed form. The effect of turbulent-frequency fluctuations on the instantaneous scalar dissipation rate following a Kolmogorov-scale fluid particle is incorporated into the LSR model through a Lagrangian pdf model for the turbulent frequency. Model results are compared with DNS data for passive scalar mixing in stationary, isotropic turbulence. Two distinct causes of non-Gaussian scalar s...

59 citations


Journal ArticleDOI
TL;DR: In this article, a detailed parametric study of dispersion and polydispersity of liquid drops in stationary isotropic turbulence via direct numerical simulation is conducted, where both non-evaporating and evaporating drops are simulated; in the latter both constant and variable rates of evaporation are considered.

49 citations


Journal ArticleDOI
TL;DR: In this article, the effects of differential diffusion on the low-order moments of the differential diffusivity variable (Z), the normalized scalars' variance difference (ζ), the scalar's cross correlation coefficient (ρ), and the moments of reacting scalars are investigated under both nonreacting and reacting nonpremixed conditions.

35 citations


Journal ArticleDOI
TL;DR: In this article, a comprehensive composite database for distillation sieve-tray efficiency is used to develop point efficiency and entrainment correlations based on a model that considers the fluid on the distillation tray to be contained in a liquid-continuous region near the tray deck and a vapor-continous region on top of the liquid continuous region.
Abstract: A comprehensive composite database for distillation sieve-tray efficiency is used to develop point efficiency and entrainment correlations based on a model that considers the fluid on the distillation tray to be contained in a liquid-continuous region near the tray deck and a vapor-continuous region on top of the liquid-continuous region. This model allows estimates of the portion of the mass transfer that occurs in each region and the mass-transfer resistance that occurs on the liquid side and vapor side of the interface. For most cases, most of the mass transfer occurs within the liquid-continuous region. The liquid side resistance is often significant. The entrainment correlation is consistent with the work of Bennett et al., which relates entrainment to the ratios of the liquid to vapor density and the froth height to the tray spacing. A simple liquid continuous-only mass-transfer model containing only four empirical parameters correlates the point efficiency data to within 6.4%. Despite a twofold change in vapor Schmidt number, no dependency on vapor Schmidt number is seen. Important dimensionless groupings are the Reynolds number based on the hole velocity, effective froth density, ratio of the liquid inventory to the perforation diameter, and fraction of the tray area perforated. Mathematically simple and accurate methods allow the prediction of the section efficiency for trays operating in cross or parallel flow. They address vapor and liquid mixing, entrainment and a criterion to avoid significant degradation of the tray efficiency due to weeping.

29 citations


Journal ArticleDOI
TL;DR: In this paper, a model of the absorption process in a vertical tubular bubble absorber working with R22-DMF, R 22-DMA, R22 -DMETEG and R 22 -NMP is developed using finite element method employing Galerkin's technique.
Abstract: A model of the absorption process in a vertical tubular bubble absorber working with R22-DMF, R22-DMA, R22-DMETEG, R22-DMEDEG and R22-NMP is developed using finite element method employing Galerkin's technique. The objective of this paper is to study the influence of the liquid and gas properties on the volumetric mass transfer coefficient. Analysis have also been done using ammonia-water as working fluid, the results obtained are compared with those in the literature and the agreement is found to be good. A correlation for mass transfer coefficient is proposed as a function of Reynolds number, Schmidt number and length to diameter ratio. The correlation can be used either in estimating the mass transfer rates or in fixing up any of the major design parameters namely length required for complete absorption and diameter.

28 citations


Journal ArticleDOI
TL;DR: In this paper, an experimental study of liquid/solid mass transfer at the wall of a trickle-bed reactor is presented, in which three flow regimes are mainly analyzed: trickling, pulsing and dispersed flows.

21 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the non-uniformity of the surface tension is due to the dependence of surface tension on a scalar quantity, either surfactant concentration or temperature, and the surface-tension induced velocity redistributes the scalar forming a closed-loop interaction.
Abstract: The free surface of a viscous fluid is a source of convective flow (Marangoni convection) if its surface tension is distributed non-uniformly. Such non-uniformity arises from the dependence of the surface tension on a scalar quantity, either surfactant concentration or temperature. The surface-tension-induced velocity redistributes the scalar forming a closed-loop interaction. It is shown that under the assumptions of (i) small Reynolds number and (ii) vanishing diffusivity this nonlinear process is described by a single self-consistent two-dimensional evolution equation for the scalar field at the free surface that can be derived from the three-dimensional basic equations without approximation. The formulation of this equation for a particular system requires only the knowledge of the closure law, which expresses the surface velocity as a linear functional of the active scalar at the free surface. We explicitly derive these closure laws for various systems with a planar non-deflecting surface and infinite horizontal extent, including an infinitely deep fluid, a fluid with finite depth, a rotating fluid, and an electrically conducting fluid under the influence of a magnetic field. For the canonical problem of an infinitely deep layer we demonstrate that the dynamics of singular (point-like) surfactant or temperature distributions can be further reduced to a system of ordinary differential equations, equivalent to point-vortex dynamics in two-dimensional perfect fluids. We further show, using numerical simulations, that the dynamical evolution of initially smooth scalar fields leads in general to a finite-time singularity. The present theory provides a rational framework for a simplified modelling of strongly nonlinear Marangoni convection in high-Prandtl-number fluids or systems with high Schmidt number.

Journal ArticleDOI
TL;DR: In this paper, a numerical model has been developed to simulate time-dependent turbulent flows in open channels, including the transport of dissolved materials The turbulence closure is provided by two algebraic eddy viscosity models.
Abstract: A numerical model has been developed to simulate time-dependent turbulent flows in open channels, including the transport of dissolved materials The turbulence closure is provided by two algebraic eddy viscosity models This paper's main focus is on the assessment of those two models' predicting capabilities for an open channel with compound cross section A three-dimensional turbulent flow field and the transport of a neutrally buoyant solute are modeled The results of the simulation are compared with experimental data and with similar calculations obtained using more advanced turbulence models Considerations are made regarding the choice of the appropriate Schmidt number for the modeling of turbulent mass transport, and the use of anisotropic eddy diffusivity to account for different mixing rates along the vertical and transverse directions Conclusions are drawn regarding the accuracy of the two models and their advantages and drawbacks when compared with more advanced turbulence models

Journal ArticleDOI
TL;DR: In this article, a simulation of two turbulent mixing layers starting from low and high-gradient laminar profiles has been performed, to assess the transitional and long time characteristics of these flows.
Abstract: Direct numerical simulations of two turbulent mixing layers starting from low- and high-gradient laminar profiles have been performed, to assess the transitional and long time characteristics of these flows. The simulations include a passive scalar with Schmidt number of 0.7, and were conducted using a grid resolution of 512×256×257 implemented in parallel on 128 nodes of the Intel Paragon supercomputer. The two mixing layers at their final turbulent condition achieved Reynolds number of ≈11 000. It is found that although the self-similarity appears to have been achieved early in the evolution of these flows, long time development is necessary for the mixing characteristics and the statistical content of these flows to become similar to the mixing layers that start from turbulent boundary layers.

Journal ArticleDOI
Sinan Yapici1, G. Yazici1, C. Özmetin1, H. Ersahan1, Ö. Çomakli1 
TL;DR: In this paper, mass transfer to local electrodes at the wall and wall friction factor behavior in decaying swirl flow in a circular duct generated by short helical swirl generators were investigated, where five swirl generators with angles between 15-70° to the duct axis were employed.

Journal ArticleDOI
TL;DR: In this paper, the effects of thermal creep on the growth process in axisymmetric, binary component PVT systems were investigated, and it was shown that thermal creep can result in recirculating bulk flows within the ampoule.

Journal ArticleDOI
TL;DR: The difference between mass and momentum transport in longitudinal vortical structures is shown in this paper, where experiments and numerical simulations are performed in order to compare the velocity field of the Gortler instability with the mass distribution of a passive scalar.
Abstract: The difference between mass and momentum transport in longitudinal vortical structures is shown in this paper. The patterns observed by visualization using laser induced fluorescence are the signature of the mass transport, while the flow structures revealed by anemometry show the momentum transport. Experiments and numerical simulations are performed in order to compare the velocity field of the Gortler instability with the mass distribution of a passive scalar. The typical scales involved in this problem are discussed with relation to the Schmidt number, in order to compare the size of the observed “mushrooms” with the size of the longitudinal Gortler vortices. It is found that the nonlinearities which strongly influence the velocity perturbation do not modify the shape and the size of the scalar structures.

Journal ArticleDOI
TL;DR: In this article, particle concentration and particle size distributions have been measured for two-phase (solid/air) turbulent coaxial jets using the Laser Diffraction Method (LDM) and a tomography data transform technique.
Abstract: Particle concentration and particle size distributions have been measured for two-phase (solid/air) turbulent coaxial jets using the Laser Diffraction Method (LDM) and a tomography data transform technique. Effects of velocity ratio, particle loading ratio, and particle size on the dispersions of gas and particles were determined. Experimental results show that the gas disperses much more rapidly than the particles and particle dispersion decreases with increasing in particle size. Increasing velocity ratio significantly increases gas dispersion, while effects of other variables are less significant. The mean particle size at the jet edge is about 15-20% smaller than that at the jet centerline. The turbulent Schmidt number Scp for two-phase turbulent coaxial jets ranges from 1.4 to 1.5.

Journal ArticleDOI
TL;DR: In this paper, the Schmidt number for supersaturated solutions is restricted to Sc ∞ ⪢ 4 9, and only under this restriction the generalized momentum and mass transfer equations have simultaneous consistent solutions.

Journal ArticleDOI
TL;DR: In this article, two types of annular developing flows are studied and both experimental and numerical studies are performed with the aim of establishing suitable assumptions for the numerical resolution of mass transfer problems characterized by high Schmidt number.

Journal ArticleDOI
TL;DR: In this article, a Peclet number Pe is introduced, representing the ratio of the velocities characterizing transverse and longitudinal transport, with transverse transport being by film diffusion of some reacting species and longitudinal transfer corresponding to film flow as with wetting processes.
Abstract: Heterogenous reactions under transport control can be modelled in terms of a film of reaction products covering the reaction surface. Such a surface defines a unique direction in space which may be used to classify transport processes as transverse or longitudinal. Since crossed-gradient transport occurs, a Peclet number Pe is introduced, representing the ratio of the velocities characterizing transverse and longitudinal transport, with transverse transport being by film diffusion of some reacting species and longitudinal transport corresponding to film flow as with wetting processes. If the influence of viscosity is taken into account in terms of a Schmidt number Sc, the long-wave approximation for the evolution of thin films on reaction surfaces is shown to be equivalent to a distinguished limit Pe → 0, Sc → ∞, while keeping 1/ $$(Sc{\text{ }}Pe^2 ) = O(1)$$ . The long-wave approximation is derived by an application of the method of strained variables which leads to a film equation for the spatio-temporal evolution of the film thickness h which represents the crucial element for a complete solution of the thermo-hydrodynamics of the layer. Since film generation due to chemical reaction and film removal due to evaporation may compensate for certain thicknesses h, surface phases are found to occur which correspond to stationary layers of uniform thickness. The evolution of the surface layer is shown to be a generalized reaction-diffusion process, with surface waves representing dynamical transitions between surface phases.

Journal ArticleDOI
TL;DR: In this article, particle concentration and particle size distributions have been measured for two-phase (solid/air) turbulent coaxial jets using the laser diffraction method (LDM) and a tomography data transform technique.
Abstract: Particle concentration and particle size distributions have been measured for two-phase (solid/air) turbulent coaxial jets using the laser diffraction method (LDM) and a tomography data transform technique. Effects of velocity ratio, particle loading ratio, and particle size on the dispersions of gas and particles were determined. Experimental results show that the gas disperses much more rapidly than the particles and particle dispersion decreases with increasing in particle size. Increasing velocity ratio significantly increases gas dispersion, while effects of other variables are less significant. The mean particle size at the jet edge is about 15–20% smaller than that at the jet centerline. The turbulent Schmidt number Scp for two-phase turbulent coaxial jets ranges from 1.4 to 1.5.

Book ChapterDOI
01 Jan 1997
TL;DR: In this paper, the authors measured the streamwise evolution of the highest concentration Cmax of a passive scalar in a turbulent round jet in the range (0 ≤ x/d ≤ 20).
Abstract: The streamwise evolution of the highest concentration Cmaxof a passive scalar in a turbulent round jet is measured in the range (0 ≤ x/d ≤ 20). The Schmidt number was Sc≅5.104 and the jet Reynolds number Red ≅ 13340. Beyond the near field of the jet nozzle (x/d ≤ 4) the Cmaxdecreases. This finding needs to be taken into account in scalar probability density function (PDF) modeling.

01 Jan 1997
TL;DR: In this article, the authors measured the streamwise evolution of the highest concentration Cmax of a passive scalar in a turbulent round jet in the range (0 ~ x/d ~ 20).
Abstract: The streamwise evolution of the highest concentration Cmaxof a passive scalar in a turbulent round jet is measured in the range (0 ~ x/d ~ 20). The Schmidt number was Sc=:5.104 and the jet Reynolds number Red =: 13340. Beyond the near field of the jet nozzle (x/d ~ 4) the Cmaxdecreases. This finding needs to be taken into account in scalar probability density function (pDF) modeling.