Showing papers on "Schmidt number published in 1996"

Subgrid mixing and molecular transport modeling in a reacting shear layer

Abstract: The importance of molecular transport in high-Reynolds number reacting flows is now well accepted because of incontrovertible experimental evidence. However, most mixing models neglect this small-scale process and, as a result, fail to predict the observed variation of the mean mixed composition and the Reynolds number, Schmidt number, and Damkohler number dependence observed in the experiments. A mixing model that explicitly accounts for the small-scale mixing, molecular transport, and chemical kinetics processes was developed earlier as a stand-alone method by Kerstein. Here, this linear eddy model (LEM) is implemented as a subgrid model within a configuration-independent simulation methodology based on large eddy simulation (LES) and used to study scalar mixing in a low-heat release mixing layer. The ability of the present method to capture correctly the small-scale mixing and molecular transport effects is demonstrated by carrying out both qualitative and quantitative comparisons with experimental data obtained in high-Reynolds number flows. The present method provides a unique modeling capability to handle the small-scale processes within the context of a general LES approach without any ad hoc closure of the scalar equations.

Measurements of scalar power spectra in high Schmidt number turbulent jets

Abstract: Single-point, jet-fluid concentration measurements obtained from high Schmidt number (Sc ≃ 1.9 x 10^3) turbulent jets permit an investigation of temporal scalar power spectra, for jet Reynolds numbers in the range of 1.25 ≤ Re x 10^(-4)≤ 7.2. At intermediate scales, we find a spectrum with a logarithmic derivative (slope) that is increasing with Reynolds number, in absolute value, but less than 5/3 at the highest Reynolds number in our experiments. At the smallest scales, our spectra exhibit no k^(-1) power-law behavior, possessing a log-normal region over a range of scales exceeding a factor of 40, in some cases.

Effects of molecular diffusivities on counter-gradient scalar and momentum transfer in strongly stable stratification

Abstract: The effects of molecular diffusivities of heat and mass on the counter-gradient scalar and momentum transfer in strongly stable stratification are experimentally investigated in unsheared and sheared stratified water mixing-layer flows downstream of turbulence-generating grids. Experiments are carried out in two kinds of stably stratified water flows. In the case of thermal stratification, the difference between the turbulent fluxes of an active scalar (heat with the Prandtl number of Pr ≈ 6) and a passive scalar (mass with the Schmidt number of Sc ≈ 600) is investigated. In the case of salt stratification, the effects of the molecular diffusion of the active scalar (salt) with a very high Schmidt number of Sc ≈ 600 on the counter-gradient scalar transfer is studied. Comparisons of the effects of molecular diffusivities are also made between thermally stratified water and air ( Pr ≈ 0.7) flows. Further, the effects of mean shear on the counter-gradient scalar and momentum transfer are investigated for both stratified cases. Instantaneous temperature, concentration and streamwise and vertical velocities are simultaneously measured using a combined technique with a resistance thermometer, a laser-induced fluorescence method, and a laser-Doppler velocimeter with high spatial resolution. Turbulent scalar fluxes, joint probability density functions, and cospectra are estimated. The results of the first case show that both active heat and passive mass develop counter-gradient fluxes but that the counter-gradient flux of passive mass is about 10% larger than that of active heat, mostly due to molecular diffusion effects at small scales. The counter-gradient scalar transfer mechanism in stable stratification can be explained by considering the relative balance between the available potential energy and the turbulent kinetic energy as in Schumann (1987). In thermally and salt-stratified water mixing-layer flows with the active scalars of high Prandtl and Schmidt numbers, the buoyancy-induced motions with finger-like structures first contribute to the counter-gradient scalar fluxes at small scales, and then the large-scale motions, which bring fluid back to its original levels, generate the counter-gradient fluxes at large scales. The contribution of the small-scale motions to the counter-gradient fluxes in stratified water flows is quite different from that in stratified air flows. The higher Prandtl or Schmidt number of the active scalar generates both the stronger buoyancy effects and the longer time-oscillation period of the counter-gradient scalar fluxes. The time-oscillation occurs at large scales but the counter-gradient fluxes at small scales persist without oscillating. The mean shear acts to reduce the counter-gradient scalar and momentum transfer at large scales, and therefore the counter-gradient fluxes in sheared stratified flows can be seen only in very strong stratification. The behaviour of the counter-gradient momentum flux in strong stratification is quite similar to that of the counter-gradient scalar flux.

Maximal effective diffusivity for time-periodic incompressible fluid flows

Abstract: In this paper we establish conditions for the maximal, $Pe^2 $, behavior of the effective diffusivity in time-periodic incompressible velocity fields for both the $Pe \to \infty $ and $Pe \to 0$ limits. Using ergodic theory, these conditions can be interpreted in terms of the Lagrangian time averages of the velocity. We reinterpret the maximal effective diffusivity conditions in terms of a Poincare map of the velocity field. The connection between the $Pe^2 $ asymptotic behavior of the effective diffusivity and $t^2 $ asymptotic dispersion of a nondiffusive tracer is established. Several examples are analyzed: we relate the existence of accelerator modes in a flow with $Pe^2 $ effective diffusivity and show how maximal effective diffusivity can appear as a result of a time-dependent perturbation of a steady cellular velocity field. Also, three-dimensional, symmetric, time-dependent duct velocity fields are analyzed, and the mechanism for an effective diffusivity with Peclet number dependence other than $P...

Mass transfer effects on flow past an impulsively started infinite vertical plate with constant mass flux — an exact solution

Abstract: An exact solution to the problem of flow past an impulsively started infinite vertical plate in the presence of a foreign mass and constant mass flux at the plate is presented by the Laplace-transform technique. The velocity, the temperature and the concentration profiles are shown on graphs. The skin-friction and the Sherwood number are also shown on graphs. The effects of different parameters likeG (the Grashof number),Gc (the modified Grashof number),Pr (the Prandtl number) andSc (the Schmidt number) are discussed.

Modelling non-cohesive suspended sediment transport in 2D vertical free surface flows

Abstract: The mathematical model for simulating suspended sediment transport under equilibrium and non-equilibrium situations is described. Using the hydrodynamic variable field obtained from a refined turbulent free surface flow model, the suspension transport model involves bed boundary conditions for either the sediment flux to or from the bed, or an estimated concentration level, which are tested. The Schmidt number variability is also studied for several particle types. Some 2D vertical test cases for equilibrium situations or non-equilibrium situations with net erosion or net deposition flux to the bed are presented, and the predicted development of the concentration profiles is compared with measurements.

Bolus contaminant dispersion for oscillatory flow in a curved tube.

Abstract: The dispersion of a bolus of soluble contaminant in a curved tube during volume-cycled oscillatory flows is studied. Assuming a small value of delta (the ratio of tube radius to radius of curvature), the Navier-Stokes equations are solved by using a perturbation method. The convection-diffusion equation is then solved by expanding the local concentration in terms of the cross-sectionally averaged concentration and its axial derivatives. The time-averaged dimensionless effective diffusivity, , is calculated for a range of Womersley number alpha and different values of stroke amplitude A and Schmidt number Sc, where D is the molecular diffusivity of contaminant. For the parameter values considered, the results show that axial dispersion in a curved tube is greater than that in a straight tube, and that it has a local maximum near alpha = 5 for given fixed values of Sc = 1, A = 5 and delta = 0.3. Finally, it is demonstrated how the time history of concentration at a fixed axial position can be used to determine the effective diffusivity.

Convective transport about cylinder with surface reaction of arbitrary order

Abstract: Heat and mass transfer from a circular cylinder exposed to a convective environment with a surface reaction of arbitrary order is studied based on the stream function-vorticity formulation. A hybrid numerical scheme combining the Fourier spectral method in the angular direction and the spectral element method in the radial direction is used to solve the conservation equations along with an influence matrix technique to resolve the vorticity boundary conditions. Results showing the temporal evolution of the flow, temperature and concentration fields are presented for cases with and without vortex shedding with the latter triggered by the cylinder's rotation. A parametric study is also performed to examine the influence of the Reynolds number, Grashof number, Prandtl number, Schmidt number, Damkohler number, the reaction order, the flow alignment, the heat of reaction, the rotational velocity and the flow pulsation on the effectiveness of the reaction surface. With the exception rotation, they all exhibit strong dependence.

Modeling of saltation and turbulence effects in a horizontal gas-solid boundary layer

Abstract: This work is devoted to the study of the behavior of solid particles in a horizontal air boundary layer. A two-fluid model is selected to analyze the particle motion in the mixed regime where both saltation and turbulence effects are important. Boundary layer approximations are applied to the solid phase equations, using conventional space/time averaging. Resulting equations are shown to be in agreement with the phase averaged equations generally used in two-fluid models. Closure is achieved by means of a gradient law, however the particle diffusion and momentum transfer coefficients are distinguished using a variable particle Schmidt number. Turbulent particle diffusion is modeled using an available analytical model, which is modified to take the saltation effect into account in the particle r.m.s. velocity. Comparison between experimental and numerical results shows that the following analysis is acceptable within the experimental and numerical error. The model slightly underestimates the parti...

Simplified framework for description of mixing with chemical reactions (i) physical picture of micro- and macromixing

Abstract: 1 INTRODUCTION When a fluid is injected into a turbulence field to mix with another fluid,twohomogenization processes take place simultaneously:micromixing(on the molecularscale)and macromixing(on the mixer scale).For micromixing,three successive stages arerecognized at high Schmidt number(1)turbulent dispersion,in which the original ma-terial lumps are dispersed by turbulence into discrete elements with smallest eddy sizeλ_k;(2)viscous deformation,in which the size of the elements is further reduced

Combustion and Mixing Studies in Compressible Flows.

Abstract: : Single and two phase fuel injection into compressible flows was studied. Mixing was measured under a variety of injection conditions as governed by injector geometry and fuel chemistry, phase, velocity, temperature and pressure. The impact of flow conditions on the state of mixing was also investigated. Several diagnostic methods were used, including optical diagnostic techniques and mechanical probing. Combinations of mechanical probe measurements were used to calculate such flow properties as Mach number, velocity, static temperature, and species concentration. For mixing studies, both the scalar and vector quantities were measured to assess the Schmidt number effect Information obtained using laser diagnostic techniques was compared with the probe measurements. Results of the comparisons suggest that data obtained through laser diagnostic techniques and probe measurements can complement each other, contributing to the development of a broad understanding of the physical processes of running under a variety of conditions. These basic mixing studies have led to the successful development of several mixing enhancement schemes, which have been tested and reported elsewhere.

Analysis of Subgrid Eddy Diffusivity in Turbulence Using Direct Numerical Simulation Databases

Abstract: Direct numerical simulation data in isotropic turbulence at Taylor-scale Reynolds number 90 are used to compute subgrid transfer and spectral eddy diffusivities for passive scalars at Schmidt numbers 1 and 1/8. The results are consistent with spectral transfer processes dominated by a local forward cascade in wavenumber space which is a consequence of moderately nonlocal interactions in the scalar fields. Data decompositions show that resolvable-subgrid interactions make (in general) substantially stronger contributions than fully-subgrid interactions to the eddy diffusivity, which has a non-negligible inverse cascade, or backscatter, component. The eddy diffusivity has a strong cusp at wavenumbers close to the cutoff value separating resolvable and subgrid ranges. At low wavenumbers the eddy diffusivity is generally small, but there the details depend on Schmidt number. The behavior of the subgrid turbulent Schmidt number (the ratio of effective eddy viscosity to eddy diffusivity) is observed to depend strongly on Schmidt number. In interpreting the results at a given spectral cutoff it is important to note that the spectrum of less diffusive scalars (of higher Schmidt number) has more high-wavenumber content.

Some Effects of Density Variations in Turbulent Flows with Pressure Fluctuations

Abstract: To analyse the possible effects of density variations, which are induced by combustion and heat exchange processes, on turbulent flows with varying pressure field it is proposed to employ the balance equation for conditional probability density function (PDF) of velocity at concentration value fixed. The latter is derived from the governing set of Langevin’s type equations which replaces the commonly used Navier-tocks and molecular diffusion equations set. By using it the balance equations for conditionally averaged velocity and fluctuation intensity are obtained and these values have been shown to depend upon density and turbulent Schmidt number for uniform homogeneous turbulence, even when there is no pressure wave. And, naturally, lighter gas volumes have greater velocity fluctuation intensity.