Showing papers on "Schmidt number published in 2004"

MHD free convective flow and mass transfer over a stretching sheet with chemical reaction

Abstract: The effect of chemical reaction on free convective flow and mass transfer of a viscous, incompressible and electrically conducting fluid over a stretching surface is investigated in the presence of a constant transverse magnetic field. The non-linear boundary layer equations with the boundary conditions are transferred by a similarity transformation into a system of non-linear ordinary differential equations with the appropriate boundary conditions. Furthermore, the similarity equations are solved numerically by using a fourth order Runge-Kutta scheme with the shooting method. Numerical results of the skin friction coefficient, the local Nusselt number Nu, the local Sherwood number Sh, as will as the velocity, temperature and concentration profiles are presented for gases with a Prandtl number of 0.71 for various values of chemical reaction parameter, order of reaction, magnetic parameter and Schmidt number.

Heat and mass transfer in MHD flow by natural convection from a permeable, inclined surface with variable wall temperature and concentration

Abstract: An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a permeable, inclined surface with variable wall temperature and concentration, taking into consideration the effects of ohmic heating and viscous dissipation. Power-law temperature and concentration variations are assumed at the inclined surface. The resulting governing equations are transformed using suitable transformations and then solved numerically by an implicit finite-difference method. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Eckert number, the buoyancy ratio between species and thermal diffusion, Prandtl number, Schmidt number, wall temperature and concentration exponent, the inclination angle from the vertical direction, and the injection parameter. A parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for the velocity, temperature, and concentration distributions as well as the local friction coefficient, local Nusselt number, and the local Sherwood number.

Simulation of flow and mass dispersion in meandering channels

Abstract: This paper reports the development of an enhanced two-dimensional (2D) numerical model for the simulation of flow hydrodynamics and mass transport in meandering channels The hydrodynamic model is based on the solution of the depth-averaged flow continuity and momentum equations where the density of flow varies with the concentration of transported mass The governing equation for mass transport model is the depth-averaged convection and diffusion equation The dispersion terms arisen from the integration of the product of the discrepancy between the mean and the actual vertical velocity distribution were included in the momentum equations to take into account the effect of secondary current Two laboratory experimental cases, flow in mildly and sharply curved channels, were selected to test the hydrodynamic model The comparison of the simulated velocity and water surface elevation with the measurements indicated that the inclusion of the dispersion terms has improved the simulation results A laboratory experiment study of dye spreading in a sine-generated channel, in which dye was released at the inner bank, centerline, and outer bank, respectively, was chosen to verify the mass transport model The simulated concentration field indicated that the Schmidt number can be used as a calibration parameter when dispersion is computed using a 2D approach with a simplified turbulence model

Numerical study of scalar mixing in curved channels at low Reynolds numbers

Abstract: A computational study has been performed to determine the rates of mixing in a curved square duct at low Reynolds numbers of interest to microfluidic applications. Two flow streams with inlet scalar concentrations of zero and unity in the two halves of a duct perpendicular to the plane of curvature were allowed to mix by convection and diffusion. Concentration distributions and unmixedness coefficients are presented for several Reynolds and Schmidt numbers and are compared with values for a straight channel of equivalent length. It is seen that for large Schmidt number fluids, mixing is considerably enhanced at moderately low Reynolds numbers (Re ∼ 10), but is not enhanced at Reynolds numbers of the order of 0.1. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2359–2368, 2004

Simulations of three-dimensional turbulent mixing for Schmidt numbers of the order 1000

Abstract: We report basic results from new numerical simulations of passive scalar mixing at Schmidt numbers (Sc )o fthe order of 1000 in isotropic turbulence. The required high grid-resolution is made possible by simulating turbulence at very low Reynolds numbers, which nevertheless possesses universality in dissipative scales of motion. The results obtained are qualitatively consistent with those based on another study (Yeung et al., Phys. Fluids 14 (2002) 4178-4191) with a less extended Schmidt number range and a higher Reynolds number. In the stationary state maintained by a uniform mean scalar gradient, the scalar variance increases slightly with Sc but scalar dissipation is nearly constant. As the Schmidt number increases, there is an increasing trend towards k −1 scaling predicted by Batchelor (Batchelor, J. Fluid Mech. 5 (1959) 113-133) for the viscous-convective range of the scalar spectrum; the scalar gradient skewness approaches zero; and the intermittency measured by the scalar gradient flatness approaches its asymptotic state. However, the value of Sc needed for the asymptotic behavior to emerge appears to increase with decreasing Reynolds number of the turbulence. In the viscous-diffusive range, the scalar spectrum is in better agreement with Kraichnan's (Kraichnan., Phys. Fluids 11 (1968) 945-953) result than with Batchelor's. Ke yw ords: turbulence, mixing, passive scalars, schmidt number, numerical simulation, scaling

Chebyshev finite difference method for the effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate with temperature dependent viscosity

Abstract: The effect of variable viscosity, chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate has been analyzed. The fluid viscosity is assumed to vary as an inverse linear function of temperature. By means of the similarity solutions, deviation of the velocity, concentration and temperature fields as well as the skin friction and heal transfer results from their constant values are determined numerically by using Chebyshev finite difference method. The effects of variable viscosity, chemical reaction and Schmidt number parameters on the velocity, concentration and temperature profiles have been studied.

On the use of the active infrared technique to infer heat and gas transfer velocities at the air‐water free surface

Abstract: [1] A comparison study of the experimental and theoretical transfer velocities of heat ands gas transfer at a wavy air-water interface is undertaken using an active infrared technique and two gas tracers. Applying the surface renewal model formalism [Danckwerts, 1951], we find that the experimentally evaluated heat transfer velocity is roughly a factor of 2 higher than the transfer velocity of a gas with a low solubility in water when both are referenced to Sc = 600. Potential origins of such a discrepancy are investigated and we propose the use of the random eddy model [Harriott, 1962] to explain our results. The model is an extension of surface renewal to include the eddy approach distance as a new parameter. Numerical simulations of the random eddy model have been performed using a timescale evaluated from the Active Controlled Flux Technique (ACFT) and the characteristics of heat as well as the two gases used in the experiments (He and SF6). The simulation results show that the transfer velocities of two species, referenced to the same Schmidt number, are different and that their ratio depends on the average value of the approach distance and its distribution. The model as implemented in the present work also predicts changes in the Schmidt number exponent when the hydrodynamics conditions are varied.

Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective flow and mass transfer over an accelerating surface with a heat source in the presence of suction and blowing in the case of variable viscosity

Abstract: An analysis has been carried out to obtain the thermal-diffusion and the diffusion-thermo effects on the mixed free-forced convective and mass transfer steady laminar boundary-layer flow over an accelerating surface with a heat source in the presence of suction and blowing. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equations which is solved numerically by applying the shooting method. The results for an impermeable accelerating surface are discussed. The effects of the variable viscosity parameter θr, the thermal diffusion parameter Sr, the diffusion-thermo parameter Df, suction or blowing parameter m, heat flux parameter s and Schmidt number Sc have been examined on the flow field of a hydrogen-air mixture as a non-chemical reacting fluid pair. The effects of varying these parameters are studied in the case of a surface with prescribed wall temperature and a surface with prescribed wall heat flux.

High Schmidt number scalars in turbulence: Structure functions and Lagrangian theory

Abstract: We demonstrate the existence of Batchelor’s viscous-convective subrange using direct numerical simulation (DNS) results to confirm the logarithmic dependence of the scalar structure function on the separation for the scalar field generated by stationary isotropic turbulence acting on a uniform mean scalar gradient From these data we estimate the Batchelor constant Bθ≈5 By integrating a piecewise continuous representation of the scalar variance spectrum we calculate the steady-state scalar variance as a function of Reynolds number and Schmidt number Comparison with DNS results confirms the Reλ−1 behavior predicted from the spectral integration, but with a coefficient about 60% too small In the large Reynolds number limit the data give a value of 25 for the mechanical-to-scalar time scale ratio The dependence of the data for the scalar variance on Schmidt number agrees very well with the spectral integration using the values of the Batchelor constant estimated from the structure function We also car

Validation of the Wilcox k-omega Model for Flows Characteristic to Hypersonic Airbreathing Propulsion

Abstract: Numerical results obtained with the WARP code solving the 1988 Wilcox k‐ω two-equation model are compared with experimental data of flowfields characteristic of hypersonic airbreathing propulsion. The problems chosen for the comparison include a shock/boundary-layer interaction case, a reacting and inert planar mixing case, and two ramp injector mixing cases. In addition, a comparison is performed with empirical correlations on the basis of skin friction for flow over a flat plate and shear layer growth for a free shear layer. The agreement between the numerical and experimental results varies between being reasonable and excellent, with a discrepancy generally not exceeding 20%. It is found that the grid-induced error can be reduced to an acceptable level for most problems with a reasonable mesh size. However, the free shear layer and the shock/boundary-layer interaction cases require a considerably finer mesh. The Wilcox dilatational dissipation correction is seen to be beneficial in predicting the growth of a free shear layer at a high convective Mach number, but its use is considered either questionable or detrimental for the other cases. A proper choice of the turbulent Schmidt number is observed to be crucial in predicting the injectant mole fraction contours for one of the ramp injector cases, with the best agreement obtained with Schmidt number Sct fixed to 0.25. For the inert planar mixing case, overall better agreement is obtained when setting both the turbulent Prandtl and Schmidt number to 0.5.

Effect of substance properties on the appearance and characteristics of repeated surface tension auto-oscillation driven by Marangoni force.

Abstract: The effect of substance properties (solution viscosity and density, surfactant bulk and surface diffusion coefficient, activity, and solubility) on the appearance and characteristics of surface tension auto-oscillation that occurs by dissolution of a surfactant drop under the water-air interface is considered in the framework of a simple mathematical model, taking into account the convection driven by the Marangoni effect and convective diffusion together with adsorption/desorption processes at the air-water interface. Numerical simulations show that apart from the Marangoni and Schmidt number, the system behavior is governed also by the exchange number, which determines the surfactant exchange with the interface. The criterion for the instability onset in a system with both normal and tangential (with respect to the interface) concentration gradient, the correlation between the global and local Marangoni numbers, as well as a comparison with experiment are discussed.

Double-Diffusive Convective Flow of a Micropolar Fluid Over a Vertical Plate Embedded in a Porous Medium with a Chemical Reaction

Abstract: The problem of steady, laminar, double-diffusive natural convection boundary-layer flow of a micropolar fluid over a vertical permeable semi-infinite plate embedded in a uniform porous medium in the presence of non-Darcian and thermal dispersion effects is investigated. Also, the model problem allows for possible heat generation or absorption and first-order chemical reaction effects. Both the wall temperature and wall concentration are assumed to have linear variations with the distance along the plate. Appropriate transformations are employed to transform the governing differential equations into a non-similar form that can be solved as an initial-value problem. The resulting equations are solved numerically by an efficient implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in good agreement. A parametric study illustrating the influence of the microrotation material parameter, concentration to thermal buoyancy ratio, chemical reaction parameter, Schmidt number, heat generation or absorption and the surface suction or injection effects on the fluid velocity, microrotation, temperature and solute concentration as well as the local skin-friction coefficient, local wall microrotation coefficient and the local wall heat and mass transfer coefficients is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed. * * * Nomenclature

Dynamics of Brownian particles in a turbulent channel flow

Abstract: Turbulent channel flows with suspended particles are investigated by means of numerical simulations. The fluid velocity is computed by large eddy simulation. Motion of small graphite particles with diameter of 0.01–10 μm, corresponding to the Schmidt number, Sc, of 2.87 × 102–6.22 × 106 and the particle relaxation time in wall unit, τ p +, of 9.79 × 10–5–4.51, is computed by Lagrangian particle tracking. Relation between the particle relaxation time and the computed deposition velocity is found to be in good agreement with an empirical relation. The statistics of the particle motion in the vicinity of the wall are studied. Clear differences are found in dynamical behavior of particles with different sizes. Medium size particles show a strong dependence on the structure of the fluid flow, while small and large particles are considerably less sensitive.

Diffusive boundary layer development above a sediment-water interface.

Abstract: A model to estimate the entry length to a fully developed diffusive boundary layer above a sediment bed, such as those found in lakes, reservoirs, rivers, and estuaries, is presented. The model is used to determine how the length of a sediment bed in mass-transfer experiments influences the measured vertical diffusive flux at the sediment-water interface. A nondimensional local mass flux is introduced in the form of a Sherwood number (Sh) and expressed as a function of both the distance from the leading edge of the sediment bed (x) and the Schmidt number (Sc). Similarly, a mean Sherwood number (Sh(ave)) for a sediment bed of length (L) is introduced. The diffusive boundary layer grows with distance, and its thickness depends on the Schmidt number (i.e., the diffusive boundary layer gets thicker and develops more quickly as the Schmidt number decreases). For Schmidt numbers greater than or equal to 100, the diffusive boundary layer begins to develop slowly but is fully developed when the nondimensional horizontal coordinate (x+) is approximately 1000. The Sherwood number is largest (i.e., infinity) near the leading edge of the sediment bed (i.e., at x = 0), decreases as the distance from the bed increases, and, finally, approaches a constant value for a fully developed diffusive boundary layer (Sh(infinity)). In this paper, the distance to a fully developed diffusive boundary layer (L99) and the required length of a sediment bed are related explicitly to Sc, sheer velocity (U*), and the relative errors of local or average Sherwood numbers (Sh or Sh(ave), respectively) against the Sherwood number for the fully developed diffusive boundary layer (Sh(infinity)). The lengths L99 and L decrease as the Schmidt number increases and become independent of the Schmidt number when Sc is greater than 1000. A longer sediment bed is needed when the shear velocity or the Schmidt number is small (e.g., L99 and L approximately 1.0 m and 8.0 m, respectively, for Sc = 500, U* = 0.1 cm/s, and a 3% acceptable error). Experimental studies may not be able to meet these requirements and an adjustment of measured mass-transfer rates at a sediment-water interface may be necessary. The magnitude of that adjustment is up to 50%. Its dependence on the Schmidt number, shear velocity, and bed length is given in this paper.

Multifractal nature of plume structure in high Rayleigh number convection

Abstract: The geometrically different plan forms of near wall plume structure in turbulent natural convection, visualised by driving the convection using concentration differences across a membrane, are shown to have a common multifractal spectrum of singularities for Rayleigh numbers in the range $10^{10}- 10^{11}$ at Schmidt number of 602. The scaling is seen for a length scale range of $2^5$ and is independent of the Rayleigh number, the flux, the strength and nature of the large scale flow, and the aspect ratio. Similar scaling is observed for the plume structures obtained in the presence of a weak flow across the membrane. This common non trivial spatial scaling is proposed to be due to the same underlying generating process of the near wall plume structures.

Oscillatory Marangoni convection in binary mixtures in square and nearly square containers

Abstract: Three-dimensional simulations of oscillatory convection in binary mixtures driven by the Marangoni effect have been performed. The upper surface of the fluid is heated by a constant heat flux while the bottom is maintained at a constant temperature. Surface deflection is ignored. Oscillations are the result of concentration-induced changes in the surface tension due to the presence of an anomalous Soret effect. In domains with a square horizontal cross section and aspect ratio Γ=1.5 these take the form of either a standing wave with left–right reflection symmetry or a discrete rotating wave, depending on the separation ratio and the Schmidt number. Standing oscillations with reflection symmetry in a diagonal are unstable. When the cross section is slightly rectangular only the former bifurcate from the conduction state, and the transition to stable rotating waves with increasing Marangoni number proceeds via a sequence of secondary local and global bifurcations. The results are interpreted in terms of predictions from equivariant bifurcation theory.

Thermal plasma flow modeling: A simple model for gas heating and acceleration

Abstract: A simple model of gas heating and acceleration in a plasma torch is proposed. With simple conditions, easy to get from the torch operating parameters, this model leads to apprehend the gas behavior interacting with the surrounding atmosphere outside the torch, in steady or unsteady state. To better apprehend the air introduction into the plasma flow, different values of the Schmidt number have been investigated according to a classic k–e turbulence model. Comparisons between velocity, temperature and Nitrogen percentage measurements and calculations were made in steady state.

On the Large Eddy Simulation of High Prandtl Number Scalar Transport Using Dynamic Subgrid-Scale Model

Abstract: The present study investigates passive scalar transport using an eddy viscosity/diffusivity model in turbulent channel flow with Prandtl number range 1-10. Dynamic subgrid-scale model (DSM) was applied to the transport equation for passive scalar to determine the eddy diffusivity dynamically. To assess the feasibility of the DSM model applied for passive scalar,a priori test on direct numerical simulation data was conducted and the results are compared with those obtained from a large eddy simulation that uses DSM modela posteriori. As the Prandtl number increases, the discrepancy in subgrid-scale (SGS) heat flux amplifies but the shape of SGS temperature dissipation profiles shows reasonable agreement. This suggests that energy transfer between resolved and subgrid-scales are reasonably predicted regardless of the accuracy in SGS heat flux vectors. Whilea priori test shows that SGS turbulent Prandtl number changes significantly with Prandtl number, the actual LES results are found to be insensitive to Prandtl number away from the wall. Thus, the DSM model has some limitations in the prediction of high Prandtl number flows.

Scalar mixing in a forced non-reactive plane shear layer using a thermal analogue to species concentration

Abstract: Scalar composition and mixing rates within a non-reactive plane shear layer between two uniform water streams were manipulated by surface actuators on the highspeed side of the flow partition. The scalar concentrations were assessed using a thermal analogue by maintaining a time-invariant temperature difference between the uniform streams upstream of the flow partition. The ratio of the smallest velocity and temperature scales was governed by the Prandtl number. Because in water Pr 7 while the Schmidt number Sc for dyes and reactants is O(1000), temperature concentrations in water are a better representation of scalar mixing in air in which Sc = O(1). The effects of spanwise-uniform and -non-uniform actuation programs were investigated using arrays of discrete, individually controlled thin-film resistive heating elements that were surface-mounted on the flow partition. Spatial and temporal temperature distributions were measured phase-locked to the actuation waveform using a cross-stream array of closely spaced cold-wire sensors. These data were used to infer both the mixedness and the composition through the onset of mixing transition and quantify local and integral cross-stream mixing performance measures