Showing papers on "Schmidt number published in 1987"

On the parameters influencing air-water gas exchange

Abstract: Detailed gas exchange measurements from two circular and one linear wind/wave tunnels are presented. Heat, He, CH4, CO2, Kr, and Xe have been used as tracers. The experiments show the central importance of waves for the water-side transfer process. With the onset of waves the Schmidt number dependence of the transfer velocity k changes from k ∝ Sc−⅔ to k ∝ Sc−½indicating a change in the boundary conditions at the surface. Moreover, energy put into the wave field by wind is transferred to near-surface turbulence enhancing gas transfer. The data show that the mean square slope of the waves is the best parameter to characterize the free wavy surface with respect to water-side transfer processes.

Prandtl Number Dependence of Natural Convection in Porous Media

Abstract: The effect of Prandtl number of a medium on heat transfer across a horizonal layer was measured. Stainless steel particles of diameters 1.6, 3.2, and 4.8 mm, glass particles of diameters 2.5 and 6.00 mm, and lead particles of diameter 0.95 mm were used with silicon oil, water and mercury as working fluids. The bed height was varied from 2.5 to 12 cm. Experimental results are presented showing Nusselt number as a function of medium Rayleigh number with the effective Prandtl number, defined as the product of medium Prandtl number and Kozeny--Carmen constant, serving as a parameter. Correlations for Nusselt number are given for effective Prandtl number less than 0.1 and for effective Prandtl number greater than 0.1, which corresponds to an infinite effective Prandtl number. For the steel--water case the wavenumber is shown as a function of medium Rayleigh number.

A two-equation model for heat transport in wall turbulent shear flows.

Abstract: A new proposal for closing the energy equation is presented at the two-equation level of turbulence modelling. The eddy diffusivity concept is used in modelling. However, just as the eddy viscosity is determined from solutions of the k- and e-equations, so the eddy diffusivity for heat is given as functions of temperature variance, ^-, and the dissipation rate of temperature fluctuations, et, together with k and e. Thus, the proposed model does not require any questionable assumptions for the "turbulent Prandtl number". Modelled forms of the ^-- and et-equations are developed to account for the physical effects of molecular Prandtl number and near-wall turbulence. The model is tested by application to a flat plate boundary layer, the thermal entrance region of a pipe, and the turbulent heat transfer in fluids over a wide range of the Prandtl number. Agreement with experiment is generally very satisfactory.

Shock wave structure in gas mixtures with large mass disparity

Abstract: The structure of normal shock waves is considered when the ratio of molecular masses mp/m of a binary mixture of inert monatomic gases is large and the density ratio ρp/ρ is of order unity or below. Generalized hydrodynamic equations, valid for arbitrary intermolecular potentials, are obtained from a hypersonic closure of the kinetic equation for the heavy gas and a near-equilibrium closure for the light component. Because the Prandtl number of the light gas and the Schmidt number of the mixture are nearly constant, the only independent transport coefficient arising in the model is the viscosity μ of the light gas, which is absorbed into a new independent position variable s. Knowledge of μ as a function of temperature thus determines the shock structure independently from the details of the intermolecular potential, allowing comparison with experiments in the complete absence of free parameters. In terms of the ratio M (frozen Mach number) between the speed of propagation and the sound speed of the light gas in the unperturbed medium, one finds that: (i) When M > 1, the behaviour is similar to that of a ‘dusty gas’, with a broad relaxation layer (outer solution) following a sharp boundary layer through which the speed of the heavy gas is almost constant (a shock within a shock). (ii) When (1 + ρp/ρ)s−½ 1, showing a failure of the Chapman–Enskog theory, even for weak shocks, when the heavy gas is dilute. Also, an algebraic explanation arises for the ‘double hump structure’ observed in He–Xe shocks. (iv) When M is nearly unity, the initial boundary layer spreads out, and the structure must be obtained by integration of a numerically unstable system of three differential equations. However, the reduction of order brought about by the weak variation of the light-gas entropy at the head of the shock, results in a stable system of equations that we integrate numerically. Excellent phase-space agreement with recent shock-tube experiments of Tarczynski, Herczynski & Walenta (1986) is found for both weak and strong shocks.

Numerical solution of laminar flow past a sphere with surface mass transfer

Abstract: The equations governing laminar flow past a sphere with surface mass transfer were solved numerically for low to moderate Reynolds numbers. The Reynolds number range considered was between 1 and 130. For mass transfer the Schmidt number was set equal to 1. Results of the calculations presented here include wake lengths, angles of separation, drag coefficients, and average Sherwood numbers. These predictions compare well with published experimental observations and other numerical results.

Numerical simulation of a plane turbulent mixing layer, with applications to isothermal, rapid reactions

Abstract: A hybrid method has been developed for the numerical prediction of turbulent mixing in a spatially-developing, free shear layer. Most significantly, the computation incorporates the effects of large-scale structures, Schmidt number and Reynolds number on mixing, which have been overlooked in the past. In flow field prediction, large-eddy simulation was conducted by a modified 2-D vortex method with subgrid-scale modeling. The predicted mean velocities, shear layer growth rates, Reynolds stresses, and the RMS of longitudinal velocity fluctuations were found to be in good agreement with experiments, although the lateral velocity fluctuations were overpredicted. In scalar transport, the Monte Carlo method was extended to the simulation of the time-dependent pdf transport equation. For the first time, the mixing frequency in Curl's coalescence/dispersion model was estimated by using Broadwell and Breidenthal's theory of micromixing, which involves Schmidt number, Reynolds number and the local vorticity. Numerical tests were performed for a gaseous case and an aqueous case. Evidence that pure freestream fluids are entrained into the layer by large-scale motions was found in the predicted pdf. Mean concentration profiles were found to be insensitive to Schmidt number, while the unmixedness was higher for higher Schmidt number. Applications were made to mixing layers with isothermal, fast reactions. The predicted difference in product thickness of the two cases was in reasonable quantitative agreement with experimental measurements.

Laminar boundary‐layer analysis of simultaneous mass and heat transfer in natural convection around A horizontal cylinder

Abstract: An analytical study is presented of the combined heat and mass transfer characteristics of natural convection flow around a horizontal circular cylinder. The surface of the cylinder is assumed to be at uniform temperature and uniform concentration. Specific cases of diffusion of water vapour and naphthalene into air are studied. The results indicate that the local Nusselt number and the local wall shear stress increase and decrease from the pure free convection values as the buoyancy force from species diffusion assists and opposes, respectively, the thermal buoyancy force. The local Nusselt number and the local wall shear stress are found to increase with the decrease of the Schmidt number, whereas the surface mass transfer increases with increasing Schmidt number. The Sherwood number is found to become more effective as the thermal buoyancy force increases. The cumulative tangential mass flow rate is found to increase with the increase of the polar angle from the lower pole and is strongly dependent on the nature and magnitude of the concentration to thermal buoyancy force ratio, especially at low Schmidt number.

Three‐dimensional numerical study of convection in a cylindrical thermal diffusion cell: Inclination effect

Abstract: The effect of the buoyancy‐driven convection on the separation of the two constituents of a binary mixture in a long cylindrical cell is considered. This cell is designed to measure the thermal diffusion (Soret) coefficient of that mixture in a spatial (microgravity) environment. Such a cell, heated from the ends, is subjected to a nearly constant axial temperature gradient that generally presents some inclination with respect to the gravity vector, giving rise to low but three‐dimensional motions. In space applications this inclination (with respect to residual gravity) is generally not known a p r i o r i. A three‐dimensional simulation based on a false transient scheme with finite difference techniques is carried out in order to study the influence of the cell inclination on low convective motions. Two small values of a Grashof number, relevant for space applications (Gr=1 and Gr=3), and three values of the Soret parameter (S=−0.5, S=0, and S=0.5) have been considered. Characteristics of the flow and of its influence on the separation of constituents are given for several inclinations. Particularly interesting results are discussed for the vertical situations. Attention is focused on a molten (AgI–KI) mixture with a Prandtl number of 0.6 and a Schmidt number of 60, contained in a cylinder with an aspect ratio of 6.

Mixing length equation for high schmidt number mass transfer at solid boundaries

Abstract: A simple modification of the Van Driest damping factor for mixing length calculations of mass and/or heat transfer coefficients at solid boundaries is proposed to increase mass eddy diffusivities in the near-wall region, without affecting velocity predictions. Calculated mass transfer rates with a constant Sct = 0.85 are in good agreement with present and previous experimental results obtained in pipe and duct flows at high Schmidt numbers. On propose une modification simple du coefficient d'amortissement de Van Driest pour les calculs de longueur de melange intervenant dans les coefficients de transfert de matiere et de chaleur a la paroi, pour augmenter les diffusivites massiques tourbillonaires dans la region proche de la paroi, sans modifier les predictions de la vitesse. Les flux de transfert de matiere calcules pour un nombre de Schmidt constant Sct = 0,85 sont en accord avec les resultats experimentaux actuels et anterieurs obtenus pour des ecoulements dans les tubes ou les canaux, a nombres de Schmidt eleves.

Effect of free convection on thermodiffusion in a liquid mixture filling an inclined rectangular cavity

Abstract: The convective motion which develops in an inclined cavity upon heating from above determines to a significant degree the form of the concentration field produced by thermodiffusion. The interaction of convective and thermodiffusion fluxes at small thermal Grashof numbers Gr causes the appearance of longitudinal jumps in concentration. Increase in temperature difference intensifies convection and encourages reduction in concentration gradients. The dominant role of convection for fixed Gr is determined by the angle of inclination of the liquid layer [1, 2]. A significant feature of liquid solutions is their low diffusion coefficient and thus high Schmidt number. This fact does not permit use of results obtained for gas mixtures, and greatly complicates numerical simulations. In contrast to [2], the present study will investigate thermodiffusion separation in a cavity with impermeable boundaries.

Pulsation characteristics of the process of mass exchange between a solid spherical particle and a turbulized liquid

Abstract: To intensify the process of mass exchange at an interface between liquid and solid phases, as a rule, one creates conditions such that the liquid is in a turbulent regime. Revealing the laws of mass transfer under these conditions makes it possible to choose the optimum regime of operation of a chemical apparatus, i.e., obtain the maximum coefficients of mass transfer for small energy costs. Vessels in which the liquid is mixed with agitators of the turbine or vane type are used as the working apparatus in industry. For this reason, many investigators occupied in studying mass-exchange processes in a liquid-solld system have fully modeled the actual conditions [1-4]. Another group includes papers in which mass exchange was studied in the flow of a liquid stream over a single spherical solid particle in channels of different configurations [5-10]. Two main methods used to study mass-exchange processs can be distinguished: dissolving solids in liquids [1-5, 9] and the electrochemical method [6-8, i0]. The first method is used only to obtain average values of the mass-exchange coefficient, and it is also characterized by variation of the shape and size of the investigated particles, which considerably lowers the accuracy of the results obtained. The electrochemical method has now become very popular; it provides a high measurement accuracy and also makes it possible to investigate both the integral and the pulsation characteristics of a process, which is important for systems in which the liquid is in a turbulent regime. In [ii] the problem of mass exchange of a turbulent liquid with a plane wall was considered and the question of correlations between pulsations of the liquid velocity and the mass-transfer coefficient on the basis of a spectral analysis was discussed. Itwas shown that in a turbulent regime of flow over the wall, the shape of the power spectrum of pulsations of the masstransfer coefficient does not depend on the Reynolds number, whereas a strong influence of the Schmidt number on the frequency of pulsations of the mass-transfer coefficient was noted. No noticeable influence of a change in the size of the electrode on the form of the spectral energy density of pulsations of the mass-transfer coefficient was found. Thus, the application of spectral analysis to the interpretation of results obtained using the electrochemical method to study mass-exchange processes allows one to estimate sufficiently precisely the influence of one or another factor on the process being studied. In the present paper a similar approach is used to study mass exchange between a fixed spherical solid particle and a turbulized liquid.

Study of mixing and reaction in the field of a vortex

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...

Mixing with diffusion and fast chemical reaction in simple shear flow: a comparison of stretch model to two-dimensional diffusion with periodic boundary conditions

Abstract: The lamellar stretch model for describing mixing with simultaneous diffusion and fast chemical reaction is evaluated for simple shear flow between two parallel plates by comparing the predicted concentration profiles to those computed from the governing partial differential equation. A direct algorithm is devised to solve the sparse matrix originating from the discretization of the PDE. Under conditions where initial striation thickness equals the characteristic dimension of the flow geometry, the lamellar stretch model turns out to be quite accurate for k ≥ 106 or k ≤ 1, where k is the product of the Reynolds number and the Schmidt number. In the intermediate range of k values, where mechanical and diffusional mixing are of comparable importance, the model is less accurate