Showing papers on "Schmidt number published in 1998"

Unsteady flow past an impulsively started vertical plate with heat and mass transfer

Abstract: Finite difference solution of the transient free-convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with heat and mass transfer is presented here. The steady state velocity, temperature and concentration profiles are shown graphically. Velocity profiles are compared with exact solution. It has been observed that there is a rise in the velocity due to the presence of a mass diffusion. An increase in Schmidt number, leads to a fall in the velocity. Stability and the convergence of the finite difference scheme are established.

Microphysical and turbulent measurements of the Schmidt number in the vicinity of polar mesosphere summer echoes

Abstract: During the ECHO campaign in 1994 neutral and electron density fluctuations were measured together with charged aerosols on the same sounding rocket launched close to a VHF radar detecting polar mesosphere summer echoes (PMSE). For the first time this combination of measurements allows for an independent test of the microphysical and the turbulence interpretations of the Schmidt number (Sc). The Schmidt number characterizes the reduction of the electron diffusivity by charged aerosols, which leads to an enhancement of the electron density fluctuations at small spatial scales. In one of the flights charged aerosols were observed at ∼83–89km together with correlated depletions in electron density (‘biteouts’). We have applied a model of aerosol charging to the measured plasma profiles and determined a mean aerosol radius of ∼8nm and a mean aerosol charge of 1e-. In the microphysical description of electron diffusion these parameters correspond to Sc∼420. Spectral analysis of the electron density fluctuations showed enhancements of spectral densities at small scales suggesting likewise a Schmidt number much larger than unity. Using an energy dissipation rate of 67mW/kg as derived from neutral air turbulence measurements on the same rocket we get from the electron spectra Sc=385 which is in excellent agreement with the microphysical result. Apart from this turbulent layer we observe no significant disturbances in neutral air number densities below ∼87km which confirms earlier indications that processes must exist to create PMSEs which are not directly coupled to neutral air turbulence.

Transient natural convection along vertical cylinder with Heat and Mass transfer

Abstract: A numerical solution for the transient natural convection flow over a vertical cylinder under the combined buoyancy effect of heat and mass transfer is presented. The velocity, temperature and concentration profiles, local and average skin-friction, Nusselt number and Sherwood number are shown graphically. It is observed that time taken to reach steady state increases with Schmidt number and decreases as combined buoyancy ratio parameter N increases. Stability and convergence of the finite difference scheme are established.

Effective axial dispersion coefficients in packed beds under supercritical conditions

Abstract: Effective axial dispersion coefficients Dax in packed beds were measured by the chromatographic method at 313.2 K both for supercritical CO2 in the pressure range from 11 to 35 MPa and for organic solvents at atmospheric pressure. The Dax values were correlated with the Reynolds number, Schmidt number, binary diffusivity and bed void fraction. The correlation was consistent for all solvents, irrespective of pressure.

Mixing and particle dispersion in the wavy vortex regime of Taylor–Couette flow

Abstract: Fluid flow and particle dispersion were investigated numerically in the wavy vortex regime of Taylor-Couette flow. The flow field for wavy vortex flow is stationary when viewed in a frame rotating with the azimuthal wave velocity. These steady flow fields are used to track fluid particles and to estimate the effective axial difision resulting from chaotic fluid aduection. The effective diffusion coefficient for a fixed wave state is a function of the Reynolds number. Particle dispersion is a strong function of wave state, showing that a universal relationship between dispersion and Reynolds number cannot be found in this regime of cylindrical Taylor-Couette flow. The effectiue Schmidt number of chaotic advection is less than unity for all wavy vortex flows examined, indicating that chaotic advection plays an important role in fluid mixing in these flow regimes. Fluid particle retention in the cores of the wavy vortices is also predicted for some parameter regimes, although not all. Particles trapped in vortex cores are only poorly mixed within the core and play no role in global mixing. A preliminary examination of inertial particle settling suggests that the fluid flow does not prevent settling in the mean, although the magnitude of the settling velocity significantly affects the dispersion of inertial particles.

Differential diffusion in low Reynolds number water jets

Abstract: Experimental data on differential diffusion between two species with large and quite disparate Schmidt numbers were obtained in a turbulent water jet by optically measuring the two species concentrations simultaneously. Experimental conditions were chosen so that the species were dilute and did not affect the water density thereby avoiding inertial effects. Differential diffusion was found to be significant in magnitude, even in the absence of these effects. Schmidt number ratios of 4 and 18 were considered. Differential diffusion was found to be statistically significant and to manifest at scales larger than the computed Batchelor scale. In some instances the concentration signal for the species with larger diffusivity was simply a blurred version of the other, while in other instances structures present in one signal were completely absent from the other. This second observation, presumably a more complex effect due to diffusion across velocity gradients, is discussed.

Similarity solution of mixed convection with diffusion and chemical reaction over a horizontal moving plate

Abstract: The mixed convective heat and mass transfer over a horizontal plate has been investigated. A diffusion equation with a chemical reaction source term is taken into account. By applying transformation group theory to the analysis of the governing equations, we obtain a similarity solution of the problem in the case that the temperature and concentration at the wall and the moving speed of the plate are proportional to power distributions along the distance from the leading edge. Furthermore the similarity equations have been solved numerically by a fourth-order Runge-Kutta scheme. The numerical results obtained for various values of the Schmidt number, chemical reaction parameter and buoyancy parameters reveal the influence of the parameters on the flow, heat and mass transfer behavior.

Dispersion of solute in a fluid flowing through a curved tube with absorbing walls

Abstract: The dispersion of solute in a fluid flowing through a curved tube with absorbing walls is studied using a mathematical model of an infinitely long conduit defined by two concentric curved circular pipes. The annular wall is comprised of a stationary homogeneous medium, and the inner cylinder is the flowing fluid phase. The solute is soluble in the annular region and is assumed to satisfy a linear equilibrium relationship at the interface. A series expansion is derived for the effective longitudinal diffusivity, D eff , valid when both the Dean number N 1 /2 and the product σ N (σ is the Schmidt number) are sufficiently small. The theory is extended numerically using a spectral finite-difference method to widen the validity of the results to more realistic problems in which σ N can take large values although N remains small. The results are consistent with the experimental findings of Kaye et al. that the influence of secondary flows on dispersion is reduced if the tracer is very soluble in the wall

Diffusivity of CFC-11 and CFC-12 in pure water and seawater

Abstract: JOURNAL OF GEOPHYSICAL Measurements RESEARCH, VOL. 103, NO. C1, PAGES 1375-1379, JANUARY 15, 1998 of the diffusion coefficients of CFC-11 and CFC-12 in pure water and seawater Min Zheng, Warren J. De Bruyn, and Eric S. Saltzman Rosenstiel School of Marine and Atmospheric Sciences, University of Miami, Miami, Florida Abstract. Trichlorofluoromethane (CC13F; CFC-11) and dichlorodifluoromethane (CC12F2; CFC-12) have been widely used as tracers of oceanic circulation and mixing on decadal timescales. In order to estimate their transfer rate across the air-sea interface, liquid-phase diffusion coefficients are needed. In this study the difthsivities of CFC- 11 and CFC-12 in pure water were measured over the temperature range 0.6-30oC. Diffusivities of CFC-11 in pure -6 cm 2 s -• at 0.6 o C to (1. 1 3+0.05)xl 0 '5 cm water ranged from (5.24_0.25)x10 2 s '• at 30.3 oC and a fit to the data yielded the equation DcFc-•= 0.015 exp (-18.1/RT), where R is the universal gas constant in kJ mol '• K '• and T is 6 the 2 temperature in Kelvin. Diffusivities of CFC-12 in pure o o water ranged from (5.38+0.22)xl 0' cm s' at 0.6 C to (1.26+0.05)x10' cm s' at 30.3 C and the temperature dependence can be expressed as DcFc.12 = 0.036 exp (-20.1/RT). The estimated uncertainty in both equations is <3%. Experiments were also carried out in seawater for each compound. For CFC-11 the diffusivity in seawater was not significantly different from that in pure water. However, the diffusivity of CFC-12 in seawater was found to be 7.2+3.0% lower than that in pure water. Schmidt numbers for both CFC-11 and CFC-12 in pure water and seawater were estimated from the data. 1. Introduction the gas in the liquid phase. Molecular diffusivities for CFC-ll and CFC-12 in water and seawater have not been determined Industrially produced CFC-11 (CC13F) and CFC-12 (CC12F2) experimentally. In this study the diffusivities of CFC-11 and have well-known time histories of emissions and inferred CFC-12 in pure water and seawater were measured over the atmospheric concentrations. In seawater they are chemically temperature range of 0.6o-30oC. The results were compared to inert and have been shown to be useful tracers in the study of predictions from semiempirical formulae. oceanic circulation and mixing on decadal timescales [Gammon et al., 1982; Bullister and Weiss, 1983; Weiss et al., 1985; Fine et al., 1988; Fine, 1993; Molinari et al., 1992; Rhein, 1991, 1994]. They have also recently been found to be useful as tracers and age-dating tools for groundwater [Busenberg and Plutnmer, 1992; Busenberg et al., 1993]. In most regions of the oceans, CFC-11 and CFC-12 concentrations in surface seawater are close to being in equilibrium with atmospheric concentrations [Bullister, 1984; Weiss et al., 1985; Pickart et al., 1989]. However, this is not always the case. Measurements in newly formed Labrador Sea water [Wallace and Lazier, 1988], the Greenland Sea [Rhein, 1991], the Weddell Sea [Bullister, 1989, the Ross Sea [Trumbore et al., 1991], and the eastern Mediterranean Sea [Schlitzer et al., 1991] have shown that equilibrium saturation is not achieved in high-latitude deep water formation areas and upwelling regions. In these cases, the oceanic uptake of CFC-11 and CFC-12 is controlled by their air-sea exchange rate. Air-sea gas transfer rates are determined by the air-sea concentration gradient and the transfer velocity, which reflects the physical state of the interface and the physical/chemical properties of the gas. Gas transfer velocities are commonly parameterized in terms of the Schmidt number of the gas [Holmen and Liss, 1984; Jahne et al., 1987b]. The Schmidt number (Sc) is the ratio of the kinematic viscosity of seawater to the molecular diffusivity of 2. Experimental Method The experimental approach is based on the agar gel technique developed by Barrer [1941] and modified by Jahne et al. [1987a] and Saltznmn et al. [1993]. The diffusion cell used in this experiment is a stainless steel housing, consisting of two chambers on either side of an aqueous gel membrane. Details of cell construction and operation were given by Saltznmn et al. [1993]. In this experiment, CFC-11 or CFC-12 is passed continuously over one side of an aqueous gel membrane while helium flows across the other side. The concentration of CFC-11 or CFC-12 increases on the helium (low-concentration) side of the gel as the gas diffuses across the gel membrane. At. steady state the gas flux (•) through the gel is given by [Crank, 1975; Saltzman et al., 1993] •= DC• L where D is the diffusivity, L is the gel thickness, and C• is the aqueous gel concentration on the high-concentration side of the membrane. In terms of measurable parameters, the diffusivity can be expressed as [Saltzman et al., 1993] D= C2sf2 L C•sotA Copyright 1998 by the American Geophysical Union. Paper number 97JC02761. where C•g and C2g are the gas-phase concentrations on the high- concentration side and low-concentration side of the gel, 0148-0227/98/97JC-02761 respectively, f2 is the gas flow through the low-concentration

The viscous-convective subrange in nonstationary turbulence

Abstract: The similarity form of the scalar-variance spectrum at high Schmidt numbers is investigated for nonstationary turbulence. Theoretical arguments show that Batchelor scaling may apply only at high Reynolds numbers. At low Reynolds numbers, Batchlor scaling is not possible unless the turbulence is stationary or the enstrophy decays asymptotically as t−2. When this latter condition is satisfied, it is shown from an analysis using both the Batchelor and Kraichnan models for the scalar-variance transfer spectrum that the k−1 power law in the viscous-convective subrange is modified. Results of direct numerical simulations of high Schmidt number passive scalar transport in stationary and decaying two-dimensional turbulence are compared to the theoretical analysis. For stationary turbulence, Batchelor scaling is shown to collapse the spectra at different Schmidt numbers and a k−1 viscous-convective subrange is observed. The Kraichnan model is shown to accurately predict the simulation spectrum. For nonstationary t...

Current Distribution on a Rotating Disk Electrode below the Mass‐Transfer‐Limited Current Correction for Finite Schmidt Number and Determination of Surface Charge Distribution

Abstract: The two-dimensional model for the current distribution on a rotating disk below the mass-transfer-limited current developed by Newman is extended here to account for the influence of a finite Schmidt number and to provide the charge distribution in the diffuse part of the double layer. A polynomial expansion in terms of Sc -1/3 is developed for the dimensionless concentration derivative at the electrode surface. The charge distribution is estimated under the assumption that specific adsorption can be neglected. This approach requires introduction of only one additional parameter corresponding to the distance between the metal surface and the plane of closest approach for solvated ions. Zero-frequency asymptotes for the local impedance values, determined from the steady-state calculations, are used to establish the need for a two-dimensional model for the impedance response of a disk electrode.

A Correlation for Mass Transfer Coefficients in Elbows

Abstract: Mass transfer can have a significant effect on corrosion rates depending on the solution chemistry and flow conditions. Therefore, knowledge of the distribution of mass transfer coefficients along the flow geometry can be useful in determining the severity of corrosion rates in situations where mass transfer is a factor. In this investigation, mass transfer in 90 elbows was examined. A computational fluid dynamic (CFD) code was used to model the flow in an elbow and compute mass transfer coefficients. Results were compared to available experimental data to verify the model. Although the number of variables involved in corrosion process is large, only two dimensionless parameters, namely, the flow Reynolds number and the Schmidt number are important for characterizing the mass transfer process. Mass transfer in elbows is also influenced by elbow geometry parameters such as the elbow radius to pipe diameter ratio (r/D). Based on these three dimensionless parameters, mass transfer between the elbow wall and the fluid was simulated and a correlation was developed to predict the maximum elbow mass transfer coefficient as a function of the flow Reynolds number, the Schmidt number and the elbow r/D. This investigation was motivated by a need to predict mass transfer coefficientsmore » in elbows for use in conjunction with a comprehensive model for calculating CO{sub 2} corrosion rates in oil and gas pipelines.« less

Computational analysis of confined jet flow and mass transport in a blind tube.

Abstract: A computational analysis of confined nonimpinging jet flow in a blind tube is performed as an initial investigation of the underlying fluid and mass transport mechanics of tracheal gas insufflation. A two-dimensional axisymmetric model of a laminar steady jet flow into a concentric blind-end tube is put forth and the governing continuity, momentum, and convection-diffusion equations are solved with a finite element code. The effects of the jet diameter based Reynolds number (Re(j)), the ratio of the jet-to-outer tube diameters (epsilon), and the Schmidt number (Sc) are evaluated with the determined velocity and contaminant concentration fields. The normalized penetration depth of the jet is found to increase linearly with increasing Re(j) for epsilon = O(0.1). For a given epsilon, a ring vortex that develops is observed to be displaced downstream and radially outward from the jet tip for increasing Re(j). The axial shear stress profile along the inside wall of the outer tube possesses regions of fixed shear stress in addition to a local minimum and maximum in the vicinity of the jet tip. Corresponding regions of axial shear stress gradients exist between the fixed shear stress regions and the local extrema. Contaminant concentration gradients develop across the ring vortex indicating the inward diffusion of contaminant into the jet flow. For fixed epsilon and Sc and Re(j) approximately 900, normalized contaminant flow rate is observed to be approximately twice that of simple diffusion. This model predicts modest net axial contaminant transport enhancement due to convection-diffusion interaction in the region of the ring vortex.

Mass Transfer to Finite Areas at the Wall in Swirling Pipe Flow in the Transition Region

Abstract: This paper presents a work on mass transfer to finite areas at the wall in decaying swirl flow in a circular pipe, generated by short helical swirl generators. Four swirl generators with angles at the outer edge between 15 and 60° to the duct axis were used to introduce a tangential velocity component to the axial flow. The experiments were carried out in the Reynolds number range 1730−8650 and at a Schmidt number of 1692. The axial distribution of the mass transfer to circular finite areas at the wall was measured using the electrochemical limiting current technique. Flow visualization observations showed that no circulation nor dead zone occurs from the leading edge of the swirlers to the end of the system. The local mass transfer data were correlated in the form of Sh Sc-1/3 = 0.3058Re0.759(x/d)-0.400(1 + tan θ0)0.271, for the whole range of experimental conditions.

Rotating Hemispherical Electrode Accurate Expressions for the Limiting Current and the Convective Warburg Impedance

Abstract: The laminar boundary layer equations describing the steady-state axisymmetric fluid motion near a spherical surface are solved numerically by considering a series expansion of the colatitude θ limited to ten terms for each velocity component. The velocity expansions are used in the steady-state mass balance equation to obtain concentration as a series expansion of θ with ten terms. This calculation also provides the Schmidt number correction to the steady-state current density. Finally, the unsteady state mass balance equation is solved to obtain the convective Warburg impedance of an hemispherical electrode, taking into account the Schmidt number correction. The impedance results are experimentally confirmed over a wide range of dimensionless frequency (6 × 10 -3 ≤ p ≤ 1).

Mathematical modeling of turbulent combustion of hydrogen in a boundary layer

Abstract: Turbulent flow in a boundary layer with injection of hydrogen through a permeable plate into an external air flow is modeled. To calculate turbulence characteristics the Lam-Bremhorst modification of the k-e model is employed. Calculations are made both with and without account for the non-unity of the Lewis number. In determining the concentrations of the intermediate and end combustion products and the temperature the assumption of chemical equilibrium is made. The obtained distribution of turbulent pulsations allows the conclusion of flow laminarization under combustion conditions to be made.

Correction for Finite Schmidt Number and Determination of Surface Charge Distribution

Abstract: The two-dimensional model for the current distribution on a rotating disk below the mass-transfer-limited current developed by Newman is extended here to account for the influence of a finite Schmidt number and to provide the charge distribution in the diffuse part of the double layer. A polynomial expansion in terms of Sc -1/3 is developed for the dimensionless concentration derivative at the electrode surface. The charge distribution is estimated under the assumption that specific adsorption can be neglected. This approach requires introduction of only one additional parameter corresponding to the distance between the metal surface and the plane of closest approach for solvated ions. Zero-frequency asymptotes for the local impedance values, determined from the steady-state calculations, are used to establish the need for a two-dimensional model for the impedance response of a disk electrode.

Large eddy simulations of two-dimensional turbulent inclined plumes

Abstract: The motions of starting plumes traveling down slopes are investigated by large eddy simulations. The formulation of the model is based on the filtered two-dimensional Navier-Stokes equations and transport equation for density excess which is deduced from the conservation of mass. The subgrid-scale turbulent stress is evaluated by the Smagorinsky model. It is found that the model can give a good description of the front of inclined plumes over a wide range of slope angle (10°≤θ≤ 90°), when the following empirical relationships for the Smagorinsky constant Cs=0.06+0.1 sin θ and for the subgrid turbulent Schmidt number Scs=0.4-0.3 sin θ are used. The computational results further revealed the flow pattern, the density distribution as well as the mechanism of entrainment at the head of inclined plumes.

High Schmidt Number Passive Scalar in a Turbulent Near-Wake

Abstract: Quantitative measurements of the instantaneous concentration field of a high Schmidt number passive scalar (fluorescein : Sc = v/D ≈ 2000, v and D are respectively the fluid viscosity and the scalar diffusivity) in the near-wake of a cylinder are made using the Laser Induced Fluorescence (LIF) technique. These measurements are relevant to the study of turbulent mixing, in particular for elucidating the role of molecular diffusion. The experiment is carried out in a closed circuit constant head water tunnel. The cylinder (aspect ratio of 40) is inserted in the working section with both ends supported on opposite walls of the test section. The tracer is injected through a slit (less than 0.5 mm thick) machined along the full cylinder length, at the forward stagnation point of the cylinder. The Reynolds number based on the free stream velocity, U 0, and the cylinder diameter, d, varies from Re ≈ 100 (laminar) to Re ≈ 500 (turbulent). The spatial resolution of the images, essentially fixed by the laser sheet thickness (≈250µm) is of the order of the Kolmogorov scale for Re ≈ 500. At Re ≈ 100, most of the dye resides at the centres of the Karman vortices. The concentration at the centres remains approximately equal to C 0, the concentration of the dye at the injection location. Similarly, the rms concentration C’ remains almost constant further downstream because both the dye molecular diffusion and the dilution effect by entrainment of the ambient clear fluid are quite weak (Figure la). At Re ≈ 500 and beyond one diameter downstream of the cylinder, the maximum mean and rms concentration values are reached on the wake axis. This is mainly due to the strong dispersion of the scalar created by the turbulent velocity field (Figure lb). The mean gradient of the concentration fluctuations normal to the axis (y direction) is typically twice as large as that in the x direction.

High Rayleigh Number Turbulence of a Low Prandtl Number Fluid

Abstract: We have studied the scaling properties of thermal turbulence in a low Prandtl number, Pr, fluid using liquid Hg (Pr = 0.024). The length scale of thermal and viscous boundary layers are analyzed from time series of movable thermistors near the boundary. It revealed that the thermal and viscous layer had crossed over the observed range of Rayleigh numbers (106 < Ra < 108). The frequency spectrum of the temperature fluctuations and the scaling of the cutoff frequency differed from those of He. The cascade range was smaller than expected. Characters of high Rayleigh number flow of a low Prandtl number fluid is discussed.