Showing papers on "Schmidt number published in 2000"

A turbulence scheme allowing for mesoscale and large‐eddy simulations

Abstract: The paper describes the turbulence scheme implemented in the Meso-NH community research model, and reports on some validation studies. Since the model is intended to perform both large-eddy and mesoscale simulations, we have developed a full three-dimensional scheme, based on the original method of Redelsperger and Sommeria. A prognostic equation for the turbulent kinetic energy is used, together with conservative variables for moist non-precipitating processes. A particularity of the scheme is the use of variable turbulent Prandtl and Schmidt numbers, consistently derived from the complete set of second-order turbulent-moment equations. The results of three idealized boundary-layer simulations allowing detailed comparisons with other large-eddy simulation (LES) models are discussed, and lead to the conclusion that the model is performing satisfactorily. The vertical flux and gradient computation can be run in isolation from the rest of the scheme, providing an efficient single-column parametrization for the mesoscale configuration of the model, if an appropriate parametrization of the eddy length-scale is used. The mixing-length specification is then the only aspect of the scheme which differs from the LES to the mesoscale configuration, and the numerical constants used for the closure terms are the same in both configurations. The scheme is run in single-column mode for the same three cases as above, and a comparison of single-column and LES results again leads to satisfactory results. It is believed that this result is original, and is due to the proper formulation of the parametrized mixing length and of the turbulent Prandtl and Schmidt numbers. In fact, a comparison of the parametrized mixing length with the length-scale of the energy-containing eddies deduced by spectral analysis of the LES shows interesting similarity.

Schmidt number for density matrices

Abstract: We introduce the notion of a Schmidt number of a bipartite density matrix. We show that k-positive maps witness the Schmidt number, in the same way that positive maps witness entanglement. We determine the Schmidt number of the family of states that is made from mixing the completely mixed state and a maximally entangled state. We show that the Schmidt number does not necessarily increase when taking tensor copies of a density matrix $\ensuremath{\rho};$ we give an example of a density matrix for which the Schmidt numbers of $\ensuremath{\rho}$ and $\ensuremath{\rho}\ensuremath{\bigotimes}\ensuremath{\rho}$ are both $2.$

Mixing in coaxial jets

Abstract: The stirring and mixing properties of one-phase coaxial jets, with large outer (annular) to inner velocity ratio ru = u2/u1 are investigated. Mixing is contemplated according to its geometrical, statistical and spectral facets with particular attention paid to determining the relevant timescales of the evolution of, for example, the interface area generation between the streams, the emergence of its scale-dependent (fractal) properties and of the mixture composition after the mixing transition. The two key quantities are the vorticity thickness of the outer, fast stream velocity profile which determines the primary shear instability wavelength and the initial size of the lamellar structures peeled-off from the slow jet, and the elongation rate γ = (u2 − u1)/e constructed with the velocity difference between the streams and the gap thickness e of the annular jet. The kinetics of evolution of the interface corrugations, and the rate at which the mixture evolves from the initial segregation towards uniformity is prescribed by γ−1. The mixing time ts, that is the time needed to bring the initial scalar lamellae down to a transverse size where molecular diffusion becomes effective, and the corresponding dissipation scale s(ts) areformula herewhere Re and Sc denote the gap Reynolds number and the Schmidt number, respectively. The persistence of the large-scale straining motion is also apparent from the spectra of the scalar fluctuations which exhibit a k−1 shape on the inertial range of scales.

Combined heat and mass transfer along a vertical moving cylinder with a free stream

Abstract: The mixed convection flow over a continuous moving vertical slender cylinder under the combined buoyancy effect of thermal and mass diffusion has been studied. Both uniform wall temperature (concentration) and uniform heat (mass) flux cases are included in the analysis. The problem is formulated in such a manner that when the ratio λ(= u w/(u w + u ∞), where u w and u ∞ are the wall and free stream velocities, is zero, the problem reduces to the flow over a stationary cylinder, and when λ = 1 it reduces to the flow over a moving cylinder in an ambient fluid. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. We have also obtained the solution using a perturbation technique with Shanks transformation. This transformation has been used to increase the range of the validity of the solution. For some particular cases closed form solutions are obtained. The surface skin friction, heat transfer and mass transfer increase with the buoyancy forces. The buoyancy forces cause considerable overshoot in the velocity profiles. The Prandtl number and the Schmidt number strongly affect the surface heat transfer and the mass transfer, respectively. The surface skin friction decreases as the relative velocity between the surface and free stream decreases.

The onset of magnetoconvection at large Prandtl number in a rotating layer I. Finite magnetic diffusion

Abstract: This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress-Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of unit order. In Part I of this series, it was also supposed that the ratio thermal diffusivity diffusivity/magnetic diffusivity is O(1), but here we suppose that this ratio is large. The character of the solution is changed in this limit. In the case of main interest, when the layer is confined between electrically-insulating no-slip walls, the solution is significantly different from the solution when the mathematically simpler, illustrative boundary conditions also considered in Part I are employed. As in Part I...

Natural convection flow from a vertical permeable flat plate with variable surface temperature and species concentration

Abstract: Concerns the laminar flows from a permeable heated surface which arise in fluids due to the interaction of the force of gravity and density differences caused by the simultaneous diffusion of thermal energy and of chemical species. Species concentration levels in air are assumed to be small in many processes in the atmosphere. Under the usual Boussinesque approximations, a set of non‐similar equations for combined buoyancy effects and the permeability of the surface are obtained. The resulting equations have been integrated by four distinct methods: perturbation method for small transpiration rate; asymptotic solutions for large transpiration rate; Keller‐box methods; and local non‐similarity method for any transpiration rate. Effects of various practical values of the Schmidt number, of the multiple buoyancy parameter and that of the transpiration rate of fluid through the surface on the local skin‐friction, the local Nusselt number and the local Sherwood number are shown graphically as well as in tabular form.

Direct numerical simulation of differential diffusion with Schmidt numbers up to 4.0

Abstract: Highly resolved direct numerical simulations are used to study the differential diffusion of passive scalars of above-unity Schmidt number in low Reynolds number turbulence. Both the coherency and the spectrum of the two-scalar difference obey Batchelor scaling based on the parameters of the less diffusive scalar. A reverse spectral transfer effect due to velocity modes in the far dissipation range is identified, which may be important at very high Schmidt numbers.

Convective--Diffusive Transport with Chemical Reaction in Natural Convection Flows

Abstract: A study of laminar natural convection flow over a semi-infinite vertical plate at constant species concentration is examined. The plate is maintained at a given concentration of some chemical species while convection is induced by diffusion into and chemical reaction with the ambient fluid. In the absence of chemical reaction, a similarity transform is possible. When chemical reaction occurs, perturbation expansions about an additional similarity variable dependent on reaction rate must be employed. Two fundamental parameters of the problem are the Schmidt number, Sc, and the reaction order, n. Results are presented for the Schmidt number ranging from 0.01 to 10000 and reaction order up to 5. In the presence of a chemical reaction, the diffusion and velocity domains expand out from the plate. This results in a larger, less distinct convection layer.

Global stability in the Bénard problem for a mixture with superimposed plane parallel shear flows

Abstract: The Lyapunov direct method is used to study the non-linear stability of parallel convective shear flows of a mixture heated and salted from below for any Schmidt and Prandtl numbers. Global non-linear exponential stability for small values of Reynolds number R is found and conditional stability results up to the criticality which are independent of R are given for rigid and stress-free boundaries. Copyright © 2000 John Wiley & Sons, Ltd.

LES of turbulent channel flow of a binary electrolyte

Abstract: The turbulent diffusion boundary layer in a binary electrolyte was considered at Schmidt numbers of 1, 10 and 100 and exchange current densities between 10−4 A m−2 and 10−2 A m−2. A numerical scheme was developed for efficient investigation of the dynamics by means of large eddy simulations. The methodology was examined by detailed comparisons with documented data from earlier large eddy and direct numerical simulations and good agreement was found. Application of the methodology to electrochemical mass transfer indicated that the exchange current density seems to have negligible effect on the mean concentration profile but it influences the structure of the fluctuating field in a visible manner.

Characteristics of fluorescein dye and temperature fluctuations in a turbulent near-wake

Abstract: The Laser Induced Fluorescence (LIF) technique was used to determine a few characteristics of a high Schmidt number (Sc) passive scalar (fluorescein) in the near-wake of a circular cylinder. The mean and rms concentration indicate that increasing the Reynolds number (Re) improves the large-scale mixing and accelerates the homogenisation of the scalar. As Re increases, the intensity of segregation decreases because of turbulent diffusion but the scale of segregation increases due to dispersion. Comparison between concentration and temperature rms profiles indicates that molecular diffusion has a much smaller effect on the decay of the scalar variance than the Reynolds number. The ratio of mean-squared values of lateral and streamwise spatial derivatives of the scalar fluctuation deviates from isotropy, the departure increasing with Re. This reflects more the effect of dispersion by the turbulent velocity field rather than any molecular diffusion effect. At a given Re, the ratio decreases as the distance from the cylinder increases. This trend is more accentuated near the edge of the wake than at the centreline.

Similarity analysis for natural convection from a vertical plate with distributed wall concentration

Abstract: Steady laminar natural convection flow over a semi-infinite vertical plate is examined in this paper. It is assumed that the concentration of a species along the plate follows some algebraic law with respect to chemical reaction. Similarity solutions may then be obtained for different orders of reaction. The fundamental parameters of this problem are the Schmidt number, Sc, and reaction order, n. Numerical results, based on the fourth order Runge-Kutta method, for Schmidt number ranging from 0. 0t o 100.0 and reaction order from 0. 0t o 1.5 are presented. When chemical reaction occurs, diffusion and velocity domains are seen to expand out from the plate. For large values of n, one may expect a smaller diffusion layer which, at fixed Schmidt number, is associated with increased velocity and reduced convection-layer.

Theoretical solution of flow past an impulsively started vertical plate with variable temperature and mass diffusion

Abstract: An exact solution to the problem of flow past an impulsively started infinite vertical plate in the presence of variable temperature and mass diffusion is considered. The dimensionless governing equations are solved using the Laplace-transform technique. The velocity, temperature and concentration profiles are studied for different parameters like thermal Grashof number, Prandtl number, Schmidt number and for multiple buoyancy effects aiding and opposing. The values of the skin-friction are tabulated.

Experimental Investigation of the Relationship between Strain and Scalar Dissipation in Gas-Phase Turbulent Jets

Abstract: A study is described that is aimed at investigating the strain/scalar dissipation layer relationship in unity Schmidt number turbulent flows This analysis makes use of simultaneous PIV/acetone PLIF data that were acquired in a previous study of turbulent planar nonreacting jets In particular, we seek to investigate the extent to which the measured strain field can be used to predict the structure of the measured scalar dissipation layers A comparison of the strain/dissipation layer relationship with the theoretical, 1-D opposed flow solution corresponding to a steady uniform strain field was made, and the results suggest that it is not possible to correctly predict dissipative layer length scales based on this simplified theory Several different reasons for the lack of agreement with the simple theory are considered, but we believe that unsteady effects are the dominant reason To investigate unsteady effects, the unsteady scalar transport equation was solved numerically, where a uniform strain field was imposed that varied sinusoidally in time The results of this simplified model appear to capture the qualitative trends seen in the measured data

Experimental determination of mass transfer at the active surface of a membrane pervaporation cell

Abstract: This work is dedicated to an experimental study of overall mass transfer at the bottom of a rectangular cavity subjected to forced convective flow at its mouth. Mass transfer coefficients have been measured using an electrochemical method for different aspect ratios, H/h, between the depth of the cavity to the height of the upstream channel, range between 0.5 and 1.67. Reynolds number, based on the hydraulic diameter of the upstream duct, has been varied from 1 to 3000 and Schmidt number between 1010 and 8400. Overall mass transfer at the bottom edge of the cavity is found to increase with both Reynolds and Schmidt numbers and to decrease with the aspect ratio, H/h. General correlations taking into account these different parameters have been established in order to predict mass transfer at the bottom of the cavity. This work is the first part of a global investigation of a pervaporation membrane separation cell involving mass transfer in liquid phase at one side of the membrane surface, followed by a transfer of the species across the membrane and finally vaporization on the downstream side of the membrane occurs.

Effect of Interaction between Diffusion Fluxes on Evaporation or Condensation of Binary Solution Drop under Forced Convection

Abstract: In order to investigate the effect of interaction between diffusion fluxes on mass transfer from a binary solution drop, numerical analyses of mass transfer around a binary solution drop under forced convection are made by using a finite difference method for driving force ratios Δω B /Δω A =-10-10, diagonal Schmidt number Sc AA =1-3, Sc BB =0.5-3, nondiagonal Schmidt number Sc AB =1-10, Sc BA =1-10 and Reynolds number Re P =1-200. The effect of driving force ratios, Reynolds numbers, and multicomponent Schmidt numbers on the concentration profiles and the diffusion fluxes of a binary solution drop are discussed. A new correlation is proposed for the effect of interaction between diffusion fluxes on mass transfer around a binary solution drop under forced convection.

Unconditional nonlinear exponential stability of the motionless conduction-diffusion solution

Abstract: Nonlinear stability of the motionless state of a heterogeneous fluid with constant temperature-gradient and concentration-gradient is studied for both cases of stress-free and rigid boundary conditions. By introducing new energy functionals we have shown that for τ=PC/PT≤1,\(\hat \alpha = C/R \geqslant 1\) the motionless state is always stable and for τ≤1,\(\hat \alpha< 1\) the sufficient and necessary conditions for stability coincide, wherePC,PT,C andR are the Schmidt number, Prandtl number, Rayleigh number for solute and heat respectively. Moreover, the criteria guarantees the exponential stability.

Bifurcation in a buoyant horizontal laminar jet

Abstract: The trajectory of a laminar buoyant jet discharged horizontally has been studied The experimental observations were based on the injection of pure water into a brine solution Under certain conditions the jet has been found to undergo bifurcation The bifurcation of the jet occurs in a limited domain of Grashof number and Reynolds number The regions in which the bifurcation occurs has been mapped in the Reynolds number{Grashof number plane There are three regions where bifurcation does not occur The various mechanisms that prevent bifurcation have been proposed Buoyant jets are encountered in many engineering situations such as discharge of euents and maintenance of solar ponds In solar ponds, an internal convective layer can develop within the non-convective zone of the pond To remove the internal convective layer, a brine solution is injected into it To inject the brine at the correct location, a precise knowledge of the jet trajectory is needed The velocity of the brine that is injected must be kept low so that the flow is laminar The trajectory of a laminar horizontal buoyant jet in a still fluid depends upon the discharge velocity, the jet diameter and the dierence in density between the jet and the environment In this paper we present experimental observations which indicate that a horizontal buoyant laminar jet can bifurcate Consider a buoyant fluid issuing horizontally into still fluid from a tube with diameter d The jet fluid density is j, its average velocity is Vj; and the ambient fluid density is a Both the fluids have kinematic viscosity The diusivity of the species causing the buoyancy is D The trajectory of the buoyant jet will depend on the Reynolds number (Re = Vjd=), Grashof number (Gr = g(a j)d 3 =(j 2 )), Schmidt number (Sc = =D), or alternatively Prandtl number (Pr) for a heated jet, and on the initial conditions, ie the velocity prole at the exit of the tube In particular, the coordinates of the jet trajectory non-dimensionalized by d will also depend only on these parameters In the present paper we consider fresh water issuing into brine, ieSc = 740) Thus, to rst order we may neglect the dependence onSc That is, we assume jet fluid does not diuse into the ambient; only the momentum does Our experiments were performed with fully developed laminar flow at the tube exit and hence the jet prole at the inlet is same in all experiments Therefore, the trajectory of the buoyant jet will depend on Re and Gr only Froude number (Fr = Re=Gr 1=2 = Vj=[(gd(a j)=j) 1=2 ]), a ratio of inertia to buoyancy forces, is another useful non-dimensional parameter; thus, alternativelyFr andRe can be taken as the parameters determining the trajectory The trajectory of an inviscid buoyant jet will depend just on Fr During the experiment we discovered that for certain values of Re and Gr the jet was not a single entity, but split into two parts One part {

軸対称乱流噴流中の速度およびスカラー量の同時測定 : 第2報, 速度とスカラー量のスペクトルおよび相関の構造

Abstract: The axial velocity and concentration of a high Schmidt number matter were measured simultaneously in an axisymmetric turbulent jet. The diffusing fluid is a water solution of the commercial dye (Schmidt number Scs3800), and an issuing Reynolds number is 6300. A combined probe of a fiber optic concentration sensor and a sigle hot film was used to measure the axial velocity and the concentration simultaneously. The axial velocity and concentration power spectra show the log-normality in the scale region smaller than the integral scale of velocity. The decreases of the correlations of the axial velocity and the concentration are observed in the same region as the power region of the velocity spectra. And they have almost no correlation in the scale region smaller than that region.