Showing papers on "Schmidt number published in 1990"
TL;DR: In this paper, an experimental investigation of turbulent transport and molecular mixing of a Sc [dbl greater-than sign] 1 conserved scalar in the fully developed self-similar far field of a steady, axisymmetric, momentum-driven, free turbulent jet issuing into a quiescent medium is presented.
Abstract: We present results from an experimental investigation of turbulent transport and molecular mixing of a Sc [dbl greater-than sign] 1 conserved scalar in the fully developed self-similar far field of a steady, axisymmetric, momentum-driven, free turbulent jet issuing into a quiescent medium. Our experiments cover the axial range from the jet exit to 350 diameters downstream, and span the range of Reynolds numbers from 1500 to 20000. Flow visualizations of the scalar concentration field directly verify the presence of an underlying characteristic large-scale organization in the jet far field essentially consistent with a simplified conceptual picture proposed in an earlier study (Dahm & Dimotakis 1987). High-resolution imaging measurements of successive instantaneous scalar concentration profiles in the jet support the presence of such a large-scale organization and provide details of its implications for mixing. These results also establish the proper similarity scaling for the mean concentration in the jet far field and give the scaling constant on the jet centreline as 5.4. We also present conserved scalar concentration p.d.f.s throughout the jet far field, and introduce a chemical reaction method for measuring the p.d.f.s with potentially molecular resolution. The amount of unmixed ambient fluid that reaches the jet centreline is found to decrease with increasing Reynolds number over the range investigated. The distribution of mixed fluid compositions in the concentration p.d.f. also appears to change over this range of Reynolds numbers, indicating that some aspects of large Schmidt number mixing in the jet far field have not yet become Reynolds number independent.
166 citations
TL;DR: In this paper, an exact solution of the advection-diffusion equation for the simple model of divergent stagnation point flow is given, which shows the mass transfer coefficient (velocity) k to be proportional to (aD1/2) and surface diffusion boundary layer (DBL) thickness δ, where a is divergence, D diffusivity.
Abstract: Molecular diffusion sustains the flux of soluble gases on the water side of the air-sea interface. The “handover” of this flux to more efficient eddy mixing begins with the smallest eddies, of size l;, which interact with the surface diffusion boundary layer (DBL), of thickness δ. Owing to the discrepancy of the scales, δ ≪ l, the flow field on the δ scale consists of horizontal motions of a velocity constant with depth and varying horizontally on the l scale. The vertical velocity is proportional to the divergence of the horizontal flow and increases linearly with depth. An exact solution of the advection-diffusion equation for the simple model of divergent stagnation point flow shows the mass transfer coefficient (velocity) k to be proportional to (aD1/2) and DBL thickness δ to be proportional to (D/a1/2), where a is divergence, D diffusivity. Over a solid wall a similar model of Hiemenz flow yields a more complex relationship, also involving viscosity. These models reveal the mechanism by which the DBL is kept thin. The most intense surface divergences on a wind-blown sea surface are associated with rollers on breaking wavelets. Vorticity and divergence in the rollers are both proportional to u*2/v;, where u* is friction velocity and v is viscosity. The mass transfer coefficient resulting from divergences of this magnitude is then given by k = const u* Sc−1/2, where Sc is Schmidt number. Exact solutions of the advection-diffusion equation for model rollers reveal the details of the handover process. A thin DBL is maintained over divergences by the upward velocity. At convergences, narrow downward plumes convey DBL fluid into the turbulent interior. Flux lines (analogous to streamlines) are horizontal over divergences and dive down under convergences. Application to the sea surface requires a parameter quantifying the surface density of divergences. Laboratory data imply that a substantial fraction of the surface is covered by the divergences at higher wind speeds. However, in the open ocean straining by the large waves, and especially whitecapping, may significantly reduce the density of divergences and with it the area-average gas transfer rate. On the other hand, bubble and droplet production in whitecaps may diminish this effect or even reverse it.
114 citations
TL;DR: In this article, the authors used an electrochemical mass transfer technique to determine the asymptotic dependence of the Sherwood number (Sh) on Ra at high Schmidt number (Sc).
Abstract: A review of the literature on natural convection in a horizontal layer heated from below shows the need for reliable data at high Rayleigh number (Ra) to determine the asymptotic Nusselt number (Nu) variation with Rayleigh number. The present study expands the data base by the use of an electrochemical mass transfer technique to determine the asymptotic dependence of the Sherwood number (Sh) on Ra at high Schmidt number (Sc). The results of the present study give Sh = 0.0659 for Sc ≈ 2750, 3 × 109 < Ra < 5 × 1012. Using the heat-mass transfer analogy, this indicates the high Prandtl number variation of Nu with Ra.
104 citations
TL;DR: In this article, the authors examined the physical properties of the fractal interface of scalar-marked regions (scalar interface) in turbulent shear flows and derived fractal dimensions of these regions when the Schmidt number is small, unity and large.
Abstract: One of the recently established results concerns the fractal‐like properties of surfaces such as the turbulent/nonturbulent interface. Although several confirmations have been reported in recent literature, enough discussion does not exist on how various flow features as well as measurement techniques affect the fractal dimension obtained; nor, in one place, is there a full discussion of the physical interpretation of such measurements. This paper serves these two purposes by examining in detail the specific case of the interface of scalar‐marked regions (scalar interface) in turbulent shear flows. Dimension measurements have been made in two separate scaling regimes, one of which spans roughly between the integral and Kolmogorov scales (the K range), and the other between the Kolmogorov and Batchelor scales (the B range). In the K range, the fractal dimension is 2.36±0.05 to high degree of reliability. This is also the dimension of the vorticity interface. The dimension in the B range approaches (logarithmically) the value 3 in the limit of infinite Schmidt number, and is 2.7±0.03 when the diffusing scalar in water is sodium fluorescein (Schmidt number of the order 1000). Among the effects considered are those of (a) the flow Reynolds number, (b) developing regions such as the vicinity of a jet nozzle or a wake generator, (c) the free‐stream and other noise effects, (d) the validity of the method of intersections usually invoked to relate the dimension of a fractal object to that of its intersections, (e) the effect of intersections by ‘‘slabs’’ of finite thickness and ‘‘lines’’ of finite width, and (f) the computational algorithm used for fractal dimension measurement, etc. The authors’ previous arguments concerning the physical meaning of the fractal dimension of surfaces in turbulent flows are recapitulated and amplified. In so doing, turbulent mixing is examined, and by invoking Reynolds and Schmidt numbers similarities, the fractal dimensions of scalar interfaces are deduced when the Schmidt number is small, unity, and large.
88 citations
TL;DR: In this paper, it was shown that the maximum variance of the scalar field c(x,t) can be computed as a function of the mean value c. This was later shown to be the case in the limit of infinite Schmidt numbers (zero scalar species diffusivity).
Abstract: Values of the scalar field c(x,t), if initially bounded, will always be bounded by the limits set by the initial conditions. This observation permits the maximum variance ∼(c′^2) to be computed as a function of the mean value c. It is argued that this maximum should be expected in the limit of infinite Schmidt numbers (zero scalar species diffusivity). This suggests that c′/c on the axis of turbulent jets, for example, may not tend to a constant, i.e., independent of x/d, in the limit of very large Schmidt numbers. It also underscores a difficulty with the k^(−1) scalar spectrum proposed by Batchelor [J. Fluid Mech. 5, 113 (1959)].
60 citations
TL;DR: In this article, scaling laws controlling interference of buoyancy-induced convection with segregation during directional solidification of low Prandtl number melts with the gravity vector perpendicular to the growth surface are obtained.
42 citations
TL;DR: In this article, two species initially separated across a plane are allowed to diffuse and react in the presence of a line vortex situated at this separation plane, and the probability density distributions are calculated using Taylor's frozen flow approximation.
Abstract: Molecular mixing and finite rate chemical reactions in a two dimensional viscous vortex are examined analytically. Two species initially separated across a plane are allowed to diffuse and react in the presence of a line vortex situated at this separation plane. Solution of the species diffusion and reaction equations are obtained locally. From these solutions, the concentration field of the species is composed. The probability density distributions are calculated using Taylor's frozen flow approximation. They are determined for a range of vortex strengths and for several values of Schmidt number at different times during the growth of the vortex. An asymptotic analysis is presented with a favorable comparison of results in the high vortex strength limit. The reacting vortex is computed by use of Green's function solution of the species equation. The results for the reacting vortex are compared with those for the non-reacting vortex and some insight is gained concerning the form of the probabilit...
36 citations
TL;DR: In this article, a system simulating selective chemical etching of thin solid films for microelectronic device fabrication is presented, where the authors show that the formation of plumes result in effective communication between the external ‘fresh’ etching solution and the ‘contaminated’ solution within the cavity.
18 citations
TL;DR: In this paper, the effects of surface radiation heat transfer on the vapor transport process using a mathematical model was examined and isolated using a set of coupled nonlinear partial differential equations for conservation of mass, momentum, energy and species, and integrodifferential equations which represent radiative exchange.
Abstract: Growth of single crystals from vapor in closed ampoules is governed by an intricate interplay between mass, momentum and heat transfer processes. The objective of this study is to examine and isolate the effects of surface radiation heat transfer on the vapor transport process using a mathematical model. The model consists of a set of coupled nonlinear partial differential equations for conservation of mass, momentum, energy and species, and the integrodifferential equations which represent radiative exchange. It depends on five important physical parameters. These are Grashof number, Prandtl number, Schmidt number, aspect ratio and the radiation-conduction number. The effects of these dimensionless groupings are systematically investigated. From the cases examined, it is concluded that surface radiation can change the flow structure appreciably. This is especially true in microgravity environment where radiation competes primarily with conduction in modifying the thermal profiles. The numerical results also show that in the presence of radiation, the top heating configuration (source on top) is no longer stable and that near the growing crystal, radiation-induced vortices can introduce significant nonuniformities in the growth flux.
16 citations
TL;DR: In this paper, the mass transfer coefficient varies with the − 1/2 exponent of the Schmidt number for a large interfacial stress and a clean interface whereas it varies with − 2/3 exponent for weaker winds.
Abstract: Experiments of simultaneous absorption of carbon dioxide and helium, in transient absorption regimes, have been carried out in a gas-liquid flume for stratified-type cocurrent flows. There was a need to improve a method of chromatographic analysis for helium and CO2 titrations in the gaseous phase and the liquid phase; this led us to study simultaneous absorption of CO2 and He independent of dynamic conditions. In addition the dominant wave characteristics were studied and the interfacial friction velocity was measured. It was confirmed that, for two gases presenting a large contrast in diffusivities, gas absorption rates are related directly to the physical properties of the gases. The mass transfer coefficient varies with the − 1/2 exponent of the Schmidt number for a large interfacial stress and a clean interface whereas it varies with the − 2/3 exponent for weaker winds.
12 citations
TL;DR: In this paper, the authors examined particle drift induced by the nonuniform photon-produced heating of particles in a "host" gas, and showed that photophoresis is a significant transport mechanism for micronsized absorbing particles in high radiative transfer combustion environments.
TL;DR: In this article, a steady free convection in an aqueous solution of CuSO 4 with a large excess of H 2 SO 4 is considered, and the system is contained in a two-dimensional cavity with rectangular cross-section.
08 Jan 1990
TL;DR: In this article, a non-reacting supersonic combustor case is studied with a Navier-Stokes CFD code using a k F two-equation turbulence model.
Abstract: A non-reacting supersonic combustor case is studied with a Navier-Stokes CFD code using a k F two-equation turbulence model. The numerical scheme is based on a pressure correction algorithm solving the Full NavierStokes equations. The present combustor test section is configured with staged. transverse injectors located behind a rearward-facing step. The etiect of the tubulent Schmidt number on mixing, penetration and spreading rates associated with transverse injection is extensively investigated by comparing calculations with experimental data.
TL;DR: In this paper, the effects of liquid (0.03-0.12 m/s) and particle size (0-8.0 mm) on the volumetric mass transfer coefficients at the grid zone have been determined in a 0.152 mI.D. x 1.8 m high Plexiglas column.
Abstract: The effects of liquid (0.03-0.12 m/s) and as (0.04-0.20 m/s) velocities, and particle size (0-8.0 mm) on the volumetric mass transfer coefficients at the grid zone have been determined in a 0.152 mI.D. x 1.8 m high Plexiglas column. The volumetric mass transfer coefficient in the grid zone increases with increasing gas velocity and particle size. However, the coefficient exhibits a maximum value at an optimum bed porosity condition. The volumetric mass transfer coefficients in terms of the Sherwood number in three-phase fluidized beds have been correlated with the Schmidt number and particle Reynolds number which is related to the energy dissipation rate in the beds based on the local isotropic turbulence theory. Also, the coefficient has been correlated with the experimental variables.
TL;DR: In this paper, the boundary layer equations are transformed to ordinary differential equations, containing the magnetic parameterMn and the concentration parameter λ, and numerical results for different values of the Schmidt number are presented.
Abstract: Mass transfer over stretching surface with variable concentration in a transverse magnetic field is examined. The boundary layer equations are transformed to ordinary differential equations, containing the magnetic parameterMn and the concentration parameter λ. Numerical results for different values of the Schmidt number are presented. It is observed that the local mass transfer and concentration profile are very sensitive to the change in the values of the magnetic parameterMn and the concentration parameter λ.
TL;DR: In this article, the authors measured the limiting anodic current during dissolution of the tube wall in two position: in a short pipe section under fully developed flow; and downstream of a sudden contraction.
Abstract: The rate of diffusion controlled corrosion of copper tube in turbulently flowing 8M H3PO4 (Schmidt number Sc=49860) was studied by measuring the limiting anodic current during dissolution of the tube wall in two position: in a short pipe section under fully developed flow; and downstream of a sudden contraction. Also, the effect of drag reducing polymers on the rate of corrosion was tested. For a short pipe section, the data were described by the equation: Sh = 0·055Sc0.33Re0.8(d/L)0.33, where Sh is the Sherwood number, Re the Reynolds number, d pipe diameter, and L length of transfer section. This equation is useful in predicting the rate of local diffusion controlled corrosion. For a given Re, the mass transfer coefficient downstream of a sudden contraction was higher than the fully developed value by a factor in the range 1·19–1·57. Under the present conditions, where highly concentrated acid was used, the drag reducing polymer was found to have a negligible effect on the rate of dissolution. C...
TL;DR: In this paper, a two-dimensional geometry under isothermal conditions was used to study the consequences of laser-beam deposition mechanisms, and the results correspond in case (1) very well with boundary layer calculations and (2) a new dimensionless number was introduced to describe the dependence of the deposition rate on the Reynolds and on the Schmidt number.
TL;DR: In this article, three dimensionless parameters for a hot wall multiple-disk-in-tube LPCVD reactor have been presented, which are defined as the ratio of a gas dynamic to a diffusion characteristics time.
TL;DR: In this article, an analytical solution is presented which is valid at small values of time and this solution is extended to large values of times by using a modified Crank-Nicolson scheme.
Abstract: Unsteady mass transfer from a vertical plate in a transverse magnetic field is investigated assuming that all the fluid properties are constant. The solution is dependent on two parameters, namely the Prandtl number,Pr, and the Schmidt number,Sc. An analytical solution is presented which is valid at small values of time and this solution is extended to large values of time by using a modified Crank-Nicolson scheme.