Diffusive Sublayer Research Articles

Small Particle Transport Across Turbulent Nonisothermal Boundary Layers

Based on the importance of thermophoretic drift in transporting small particles across a turbulent thermal boundary layer, and the relatively small Brownian diffusivity of such particles, we present a simple asymptotic theory of particulate transport to aerodynamically smooth, solid surfaces cooled below, Te, the mainstream gas temperature. Numerical calculations based on a law-of-the-wall equilibrium velocity profile, and the assumption that the effective eddy diffusivities for mass, energy, and momentum diffusion are equal, are well-represented by −m˙p″≈ρeueωp,e•Sth•(αTLe)w[(Te−Tw)/Tw]{1+[(Te−Tw)/Tw]•[0.07+0.93(αTLew]} where Sth is the local heat-transfer coefficient (Stanton number) and (αTLe)w is the ratio of the particle thermophoretic diffusivity to the gas mixture heat diffusivity. While currently being extended to cover particle size ranges for which (i) the Brownian diffusion sublayer is not negligible in thickness compared to the viscous sublayer, or (ii) eddy impaction sets in, the present theory provides a rational improvement over previous estimates, and explains several important features of the recent data of Nomura et al [1] on the fouling rate of internally air-cooled, gas turbine blades exposed to the products of combustion of Vanadium-containing residual fuel oil.

Theory for electric charging in turbulent pipe flow

Basec on somewhat simplified profiles of turbulent eddy diffusivity and mean vcLacity in turbulent flow, an expression is derived for the convection current in a pipe where electrification occurs at the wall. The expression is in explicit analytic form, and applies for all turbulent Reynolds numbers and all fluid conductivities, from conditions where the Debye length is small compared with the diffusion sublayer (typical aqueous solutions) to conditions where the Debye length is large compared with the sublayer (typical liquid hydrocarbons).

Wind‐water tunnel simulation of small‐scale ocean‐atmosphere interactions

Various results obtained at the Institut de Mecanique Statistique de la Turbulence wind‐water facility, where small‐scale dynamic and thermodynamic air‐sea exchange processes can be partially simulated, during the past 10 years are reviewed in the light of present ideas on ocean‐atmosphere interactions. The object here is to draw conclusions on both the validity and the usefulness of such laboratory studies. Large‐ and small‐scale turbulent velocity and temperature fields exhibit good similarity and general agreement with surface layer observations but also exhibit interesting departures from local isotropy. The spectral characteristics of waves in the laboratory are quite similar to short‐fetch field data. An inherently nonlinear ‘dominant wave’ is found to have a major influence upon properties and upon the dispersion relation of wind waves in the laboratory and in the field. Wind‐wave coupling is observed and investigated through linear and nonlinear methods. Turbulent heat and mass transfer processes, studied through different techniques, show that evaporation rates and diffusive sublayer thicknesses compare well with other estimates. Observed density stratification effects can be interpreted in terms of the accepted description for atmospheric surface layer. These data as a whole demonstrate that laboratory studies on small‐scales air‐sea interaction mechanisms can provide an insight into the naturally occurring physical processes.

Mass transfer to newtonian and non-newtonian fluids from rotating cylinders

Mass transfer from rotating cylinders to Newtonian and non-Newtonian fluids is investigated. Present and previous data are analysed and correlations are presented. Free convection mass transfer correlations for vertical cylinders are found to differ from those for horizontal cylinders available in previous literature. Modified Prandtl analogy is applied, by considering the eddy penetration of the diffusion sublayer, to obtain the following expression for forced convection mass transfer Sh Sc − 1 3 = 0.62 fRe which is found to correlate the present and previous data in the range of Sc, 2.6–32000, Pr, 0.72–676 and Re, 10 2–10 5 with a standard deviation of 14.6%. Differential viscosity is used to correlate mass transfer data to non-Newtonian fluids. Experimental results are seen to be lower than those predicted by the Newtonian correlation.

Use of Electrochemical Methods for the Study of Mass Transfer and Drag Reduction in Polymer Solutions Close to a Wall

Mass transfer to the surface of a rotating disk in the presence of a drag reducing polymer (PEO) has been studied by an electrochemical method. Mass transfer rates were predicted and measured for different electrode geometries: (i) thin ring, (ii) circular microelectrode, and (iii) the disk. A relation for friction velocity available up to maximum drag reduction conditions where the average flow is laminarized at the scale of the diffusion layer, has been proposed from the analysis of the experimental data on circular microelectrode and ring electrode. The comparison of these data with disk electrode measurements substantiated a sharp thickening of the diffusion sublayer at the lowest polymer concentrations.

Evaporation from a Warm, Wavy Surface: A Laboratory Study

The evaporation rates from small wind-waves by forced convection in a range where the spray of water by strong wind action is not important have been studied in the laboratory. The effects of free stream velocity, wave conditions and temperature differences between air and water (either stable or unstable stratified air flow) on evaporation are investigated. For stably stratified air flow, the evaporation rate correlates well with general dynamical parameters but not for unstably stratified flow. The buoyancy flux near the boundary appears to play an important role in moisture transfer at the air-sea interface. The effect of the buoyancy flux is considered important inside the diffusion sublayer. The thickness of the diffusion sublayer is not only a function of shear velocity and roughness but also a function of buoyancy flux. Based on this, the final form of evaporation rate can be given in a dimensionless form aswhere A is an empirical constant, Sh the Sherwood number, Cf the drag coefficient, B+ the buoyancy flux, and Re the Reynolds number. The above equation applies well to both stable and unstable stratified flow and indicates that the buoyancy flux from the boundary strongly affects the evaporation rate.

Structure and properties of nitrided binary Fe-Al, Fe-V, and Fe-Ti alloys

1. The formation of phases with nitrogen in the diffusion layer of binary alloys of iron with aluminum, vanadium, and titanium after nitriding at 500° for 1h occurs in the conformity with the Fe-N phase diagram. 2. With increasing amounts of aluminum in the alloy the amount of e phase decreases, while the amount of γ′ phase increases and it extends into the grains in the form of whiskers. 3. Aluminum has a slight effect on the hardness of the α solid solution; titanium and vanadium substantially increase the hardness after nitriding at 500°. 4. Sectioning and electron microscopic and electron diffraction analysis of the diffusion layer on nitrided Fe-Al alloys showed that the surface consists of e phase, with γ′ phase alloyed with aluminum beneath it. The sublayer contains two excess nitride phases-Fe4N and Fe16N2. 5. Besides e and γ′ phases on the surface of nitrided Fe-Al alloys, we observed separate crystals of Al2O3. 6. No precipitates of stable hcp AlN were observed on the surface of Fe-Al alloys after nitriding. 7. The diffusion sublayer of Fe-V and Fe-Ti alloys nitrided at 500° contains a second nitride phase-Fe16N2 — that is isomorphous with the matrix, in addition to precipitates of γ′ phase. The effect of diffusion scattering is noticeable on the matrix reflections in the form of streaks, indicating the formation of coherent GP zones.

Evaporation retardation by monomolecular layers

An analytical theory based on the kinetic theory of discrete particles has been developed to describe the movement of water molecules through a monolayer. A simplified model based on the theory shows the rate of evaporation through a monolayer to be a function of the length of the hydrocarbon chain molecules, the arrangement of the monolayer molecules, the thickness of the surface diffusion sublayer, and the temperature of the water.

A turbulent flow theory of electrodialysis

A hydrodynamic theory is presented of desalination by electrodialysis in a parallel channel system with unobstructed fully developed turbulent flow. A set of turbulent transport equations is derived for the mean salt concentration and electric field. Closure of the set is brought about by introducing a turbulent diffusion coefficient whose behavior is assumed known from empirical mass transfer considerations, and by making two different but phenomenologically reasonable assumptions about that part of the average ion flux which is due to the correlation between the concentration and electric field fluctuations. Estimates show both assumptions to lead to sensibly the same final results. From the equations and boundary conditions it is shown that there are five parameters which govern the system performance. Four are the same as for the corresponding laminar case, while the fifth measures the thickness of the concentration diffusion sublayer, the value of which is taken to be given by semi-empirical turbulent mass transfer results for high Schmidt numbers. The thickness of this diffusion layer is found to be the critical factor governing the salt removal rate. An integral method of solution is used to obtain the distributions of salt concentration and current density. A numerical quadrature is required for the complete solution. Analytic solutions are obtained in the unpolarized and fully polarized limits. Because of the very abrupt transition between these two limits, taken together the limiting analytic solutions are adequate to describe the system performance over the entire range of operating variables. For small fractional salt removal a universal correlation for the average current density embodying the five similarity parameters of the system is suggested based on the limiting solutions. Comparison of the theory is made with the experimental results of Cowan and Brown on average limiting current density and the agreement is found to be satisfactory.

An Experimental Study of Turbulent Diffusion of Drag-Reducing Polymer Additives

An experimental study of the mechanics of turbulent diffusion when uniformly injecting a drag-reducing polymer solution through a wall adjacent to a fully developed pipe flow of water is described. Experimental diffusion data were obtained using very low injection rates in a porous wall pipe test section designed on the basis of a prior theoretical diffusion analysis with uniform injection. The drag-reducing effectiveness of the polymer only in the wall region, discovered previously, is substantiated by detailed concentration profile, velocity profile and wall shear stress data. These data indicate that an increase in the viscous sublayer thickness is accompanied by an increase in the diffusion sublayer thickness for uniform drag-reducing polymer injection. Also, uniform polymer injection at the wall appeared to somewhat inhibit the turbulent diffusion away from the wall. This type of injection provided drag reduction with a much smaller supply of polymer than required to raise the concentration throughout the shear layer to the same drag-reducing level. (Author)