Showing papers on "Schmidt number published in 2013"

Homogeneous-heterogeneous reactions in micropolar fluid flow from a permeable stretching or shrinking sheet in a porous medium

Abstract: The effects of a homogeneous-heterogeneous reaction on steady micropolar fluid flow from a permeable stretching or shrinking sheet in a porous medium are numerically investigated in this paper. The model developed by Chaudhary and Merkin (Fluid Dyn. Res. 16:311-333, 1995) for a homogeneous-heterogeneous reaction in boundary layer flow with equal diffusivities for reactant and autocatalysis is used and extended in this study. The uniqueness of this problem lies in the fact that the solutions are possible for all values of the stretching parameter , while for (shrinking surface), solutions are possible only for a limited range of values. The effects of physical and fluid parameters such as the stretching parameter, micropolar parameter, permeability parameter, Schmidt number, strength of homogeneous and heterogeneous reaction parameter on the skin friction, velocity and concentration are analyzed, and these results are presented through graphs. The solute concentration at the surface is found to decrease with the strength of the homogeneous reaction, and to increase with heterogeneous reactions, the permeability parameter and stretching or shrinking parameters. The velocity at the surface was found to increase with the micropolar parameter.

A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law

Abstract: We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive thermal drift term with diffusion coefficient obeying a Stokes-Einstein relation, in addition to the expected advection by a random velocity. The overdamped limit correctly reproduces both the enhanced diffusion in the ensemble-averaged mean and the long-range correlated giant fluctuations in individual realizations of the mixing process, and is amenable to efficient numerical solution. Through a combination of Eulerian and Lagrangian numerical methods we demonstrate that diffusion in liquids is not most fundamentally described by Fick's irreversible law; rather, diffusion is better modeled as reversible random advection by thermal velocity fluctuations. We find that the diffusion coefficient is effectively renormalized to a value that depends on the scale of observation. Our work reveals somewhat unexpected connections between flows at small scales, dominated by thermal fluctuations, and flows at large scales, dominated by turbulent fluctuations.

The Stokes-Einstein relation at moderate Schmidt number

Abstract: The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently developed minimally resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The mismatch arises because thermal fluctuations affect the drag coefficient for a particle due to the nonlinear nature of the fluid-particle coupling. The numerical data are in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

Heat and Mass Transfer with Free Convection MHD Flow Past a Vertical Plate Embedded in a Porous Medium

Abstract: An analysis to investigate the combined effects of heat and mass transfer on free convection unsteady magnetohydrodynamic (MHD) flow of viscous fluid embedded in a porous medium is presented. The flow in the fluid is induced due to uniform motion of the plate. The dimensionless coupled linear partial differential equations are solved by using Laplace transform method. The solutions that have been obtained are expressed in simple forms in terms of elementary function and complementary error function . They satisfy the governing equations; all imposed initial and boundary conditions and can immediately be reduced to their limiting solutions. The influence of various embedded flow parameters such as the Hartmann number, permeability parameter, Grashof number, dimensionless time, Prandtl number, chemical reaction parameter, Schmidt number, and Soret number is analyzed graphically. Numerical solutions for skin friction, Nusselt number, and Sherwood number are also obtained in tabular forms.

Statistical measurements of scaling and anisotropy of turbulent flows induced by Rayleigh-Taylor instability

Abstract: This work investigates several key statistical measurements of turbulence induced by Rayleigh-Taylor instability using data from well resolved numerical simulations at moderate Reynolds number with the goal of determining the degree of departure of this inhomogeneous flow from that of homogeneous, isotropic turbulence. The simulations use two miscible fluids with unity Schmidt number and moderate density contrast (3/2 to 9). The results of this study should find application in subgrid-scale modeling for large-eddy simulations and Reynolds-averaged Navier-Stokes modeling used in many engineering and scientific problems.

An approach for accurate simulation of liquid mixing in a T-shaped micromixer

Abstract: In this paper, we propose a new computational method for efficient evaluation of the fluid mixing behaviour in a T-shaped micromixer with a rectangular cross section at high Schmidt number under steady state conditions. Our approach enables a low-cost high-quality simulation based on tracking of fluid particles for convective fluid mixing and posterior solving of a model of the species equation for molecular diffusion. The examined parameter range is Re = 1.33 × 10−2 to 240 at Sc = 3600. The proposed method is shown to simulate well the mixing quality even in the engulfment regime, where the ordinary grid-based simulation is not able to obtain accurate solutions with affordable mesh sizes due to the numerical diffusion at high Sc. The obtained results agree well with a backward random-walk Monte Carlo simulation, by which the accuracy of the proposed method is verified. For further investigation of the characteristics of the proposed method, the Sc dependency is examined in a wide range of Sc from 10 to 3600 at Re = 200. The study reveals that the model discrepancy error emerges more significantly in the concentration distribution at lower Sc, while the resulting mixing quality is accurate over the entire range.

Influence of common modeling choices for high-speed transverse jet-interaction simulations

Abstract: Numerical simulations were carried out to determine the sensitivity of results to a variety of geometric and flow parameters commonly employed in high-speed transverse jet-interaction calculations. The configuration consisted of a single circular, flush-wall porthole injector inclined at 30 deg to the freestream in a Mach 4.0 crossflow. Injection was sonic with a jet-to-freestream momentum flux ratio of 2.1. The primary modeling parameters investigated include turbulence model, freestream turbulence intensity, turbulent Schmidt number, and several injector-pipe configurations. The simulations were conducted using the multispecies Reynolds-averaged Navier–Stokes equations with a number of popular turbulence models including the one-equation Spalart–Allmaras model and the two-equation Menter shear stress transport, two-equation realizable k-e, and two-equation nonlinear (cubic) k-e models. The results were found to be very sensitive to both the choice of turbulence model and value of the turbulent Schmidt n...

Evaluation of RANS turbulence models for simulating wind-induced mean pressures and dispersions around a complex-shaped high-rise building

Abstract: Re-ingestion of the contaminated exhaust air from the same building is a concern in high-rise residential buildings, and can be serious depending on wind conditions and contaminant source locations. In this paper, we aim to assess the prediction accuracy of three k-ɛ turbulence models, in numerically simulating the wind-induced pressure and indoor-originated air pollutant dispersion around a complex-shaped high-rise building, by comparing with our earlier wind tunnel test results. The building modeled is a typical, 33-story tower-like building consisting of 8-household units on each floor, and 4 semi-open, vertical re-entrant spaces are formed, with opposite household units facing each other in very close proximity. It was found that the predicted surface pressure distributions by the two revised k-ɛ models, namely the renormalized and realizable k-ɛ models agree reasonably with experimental data. However, with regard to the vertical pollutant concentration distribution in the windward re-entrance space, obvious differences were found between the three turbulence models, and the simulation result using the realizable k-ɛ model agreed the best with the experiment. On the other hand, with regard to the vertical pollutant concentration distribution in the re-entrant space oblique to the wind, all the three models gave acceptable predictions at the concentration level above the source location, but severely underestimated the downward dispersion. The effects of modifying the value of the turbulent Schmidt number in the realizable k-ɛ model were also examined for oblique-wind case. It was confirmed that the numerical results, especially the downward dispersion, are quite sensitive to the value of turbulent Schmidt number.

Extending the bejan number to a general form

Abstract: A modified form of the Bejan number (Be), originally proposed by Bhattacharjee and Grosshandler for momentum processes, is obtained by replacing the dynamic viscosity (m) appearing in the original proposition with the equivalent product of the fluid density (r) and the momentum diffusivity of the fluid (n). This modified form is not only more akin to the physics it represents but it also has the advantage of being dependent on only one viscosity coefficient. Moreover, this simple modification allows for a much simpler extension of Be to other diffusion processes, such as a heat or a species transfer process, by simply replacing the diffusivity coefficient. Consequently, a general Be representation for any process involving pressure-drop and diffusion becomes possible. It is shown that this general representation yields analogous results for any process satisfying the Reynolds analogy (i.e., when Pr = Sc = 1), in which case the momentum, energy and species concentration representations of Be turn out to be the same.

Large Eddy Simulation Requirements for the Richtmyer-Meshkov Instability

Abstract: The shock induced mixing of two gases separated by a perturbed interface is investigated through Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). In a simulation, physical dissipation of the velocity field and species mass fraction often compete with numerical dissipation arising from the errors of the numerical method. In a DNS, the computational mesh resolves all physical gradients of the flow and the relative effect of numerical dissipation is small. In LES, unresolved scales are present and numerical dissipation can have a large impact on the flow, depending on the computational mesh. A suite of simulations explores the space between these two extremes by studying the effects of grid resolution, Reynolds number, and numerical method on the mixing process. Results from a DNS are shown using two different codes that use a high- and low-order numerical method and show convergence in the temporal and spectral dependent quantities associated with mixing. Data from an unresolved, high Reynolds number LES are also presented and include a grid convergence study. A model for an effective viscosity is proposed which allows for an a posteriori analysis of the simulation database that is agnostic to the LES model, numerics, and the physical Reynolds number of the simulation. An analogous approximation for an effective species diffusivity is also presented. This framework is then used to estimate the effective Reynolds number and Schmidt number of future simulations, elucidate the impact of numerical dissipation on the mixing process for an arbitrary numerical method, and provide guidance for resolution requirements of future calculations in this flow regime.

Finite element solution of heat and mass transfer flow with Hall current, heat source, and viscous dissipation

Abstract: The aim of the paper is to investigate the effect of heat and mass transfer on the unsteady magnetohydrodynamic free convective flow with Hall current, heat source, and viscous dissipation. The problem is governed by the system of coupled non-linear partial differential equations whose exact solution is difficult to obtain. Therefore, the problem is solved by using the Galerkin finite element method. The effects of the various parameters like Hall current, Eckert number, heat source parameter, Prandtl number, and Schmidt number on the velocity components, the temperature, and the concentration are also examined through graphs.

Dissipative particle dynamics modeling of low Reynolds number incompressible flows

Abstract: This paper is concerned with the numerical modeling of a slow (creeping) flow using a particle-based simulation technique, known as dissipative particle dynamics (DPD), in which the particles' mass is allowed to approach zero to simultaneously achieve a high sonic speed, a low Reynolds number, and a high Schmidt number. This leads to a system of stiff stochastic differential equations, which are solved efficiently by an exponential time differencing (ETD) scheme. The ETD-DPD method is first tested in viscometric flows, where the particle mass is reduced down to 0.001. The method is then applied for the modeling of rigid spheres in a Newtonian fluid by means of two species of DPD particles, one representing the solvent particles and the other, the suspended particle. Calculations are carried out at particle mass of 0.01, with corresponding Mach number of 0.08, Reynolds number of 0.05, and Schmidt number of 6.0×103. Stokes results are used to determine the DPD parameters for the solvent-sphere interaction forces. The method obeys equipartition and yields smooth flows around the sphere with quite uniform far-field velocities.

Turbulent transport of a high-Schmidt-number scalar near an air–water interface

Abstract: We measure solute transport near a turbulent air–water interface at which there is zero mean shear. The interface is stirred by high-Reynolds-number homogeneous isotropic turbulence generated far below the surface, and solute transport into the water is driven by an imposed concentration gradient. The air–water interface is held at a constant concentration much higher than that in the bulk of the water by maintaining pure gas above a water tank that has been initially purged of dissolved . We measure velocity and concentration fluctuations below the air–water interface, from the viscous sublayer to the middle of the ‘source region’ where the effects of the surface are first felt. Our laboratory measurement technique uses quantitative imaging to collect simultaneous concentration and velocity fields, which are measured at a resolution that reveals the dynamics in the turbulent inertial subrange. Two-point statistics reveal the spatial structure of velocity and concentration fluctuations, and are examined as a function of depth beneath the air–water interface. There is a clear dominance of large scales at all depths for all quantities, but the relative importance of scales changes markedly with proximity to the interface. Quadrant analysis of the turbulent scalar flux shows a four-way balance of flux components far from the interface, which near the interface evolves into a two-way balance between motions that are raising and lowering parcels of low-concentration fluid.

The Stokes-Einstein Relation at Moderate Schmidt Number

Abstract: The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently-developed minimally-resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The numerical data is in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

Spectrum of passive scalars of high molecular diffusivity in turbulent mixing

Abstract: We consider the mixing of passive scalars transported in turbulent flow, with a molecular diffusivity that is large compared to the kinematic viscosity of the fluid. This particular case of mixing has not received much attention in experiment or simulation even though the first putative theory, due to Batchelor, Howells & Townsend (J. Fluid Mech., vol. 5, 1959, pp. 134–139), is now more than 50 years old. We study the problem using direct numerical simulation of decaying scalar fields in steadily sustained homogeneous turbulence as the Schmidt number (the ratio of the kinematic viscosity of the fluid to the molecular diffusivity of the scalar) is allowed to vary from to for two values of the microscale Reynolds number, and 240. The simulations show that the passive scalar spectrum assumes a slope of in a range of scales, as predicted by the theory, when the Schmidt number is small and the Reynolds number is simultaneously large. The observed agreement between theory and simulation in the prefactor in the spectrum is not perfect. We assess the reasons for this discrepancy by a careful examination of the scalar evolution equation in the light of the assumptions of the theory, and conclude that the finite range of scales resolved in simulations is the main reason. Numerical issues specific to the regime of very low Schmidt numbers are also addressed briefly.

Unsteady mhd radiative and chemically reactive free convection flow near a moving vertical plate in porous medium

Abstract: We have investigated an unsteady flow of a viscous, incompressible electrically conducting, laminar free convection boundary layer flow of a moving infinite vertical plate in a radiative and chemically reactive medium in the presence of a transverse magnetic field. The equations governing the flow are solved by Laplace transform technique. The expressions for velocity, temperature, concentration are derived and based on these quantities the expressions for skin friction; rate of heat transfer and the rate mass transfer near the plate are derived. The effects of various physical parameters on flow quantities, wise magnetic parameter, Grashof number, modified Grashof number, heat source parameter, the chemical reaction parameter, Schmidt number and radiation parameter are studied numerically and the results are discussed with the help of graphs. Some important applications of physical interest for different type motion of the plate like case (i) when the plate is moving with uniform velocity, case (ii) when the plate is moving with single acceleration and case (iii) when the plate is moving with periodic acceleration, are discussed.

Laboratory Investigations of Air-Sea Gas Transfer under a Wide Range of Water Surface Conditions

Abstract: Transfer velocities of 5 sparingly soluble gases were measured in two different wind wave tanks at wind speeds between u10=1.2 m/s and 67 m/s. Two different gas analysis techniques were used, FT-IR and UV spectroscopy. Additionally, a method was developed that allows the parallel measurement of gas transfer velocity and the solubility. The fast ’controlled leakage’ method for the measurement of gas transfer velocities was found to be not precise enough to measure Schmidt number exponents and transfer velocities in the Aeolotron. Gas transfer velocities measured spanned more than 3 orders of magnitude, lying between 0.5 cm/h and 1100 cm/h. At lower wind speeds, measured in the Heidelberg Aeolotron, the change of the Schmidt number exponent from 2/3 for a smooth to 1/2 for a wavy water surface was confirmed. A surfactant, which inhibits wave growth, was used in 3 of the 7 experiments. For all surfactant conditions, the change of the Schmidt number exponent spanned a wide range of wind speeds with the mid-point at u10=4.5 m/s for a clean, and at 9 m/s for a surface film covered water surface. It was confirmed that the mean square slope is suitable for the description of the transition of the Schmidt number exponent. The facet model could not reproduce the measured transfer velocities. The transfer velocities measured were found to scale very poorly with the commonly used parameter wind speed u10. The correlation between the mean square slope of the water surface and the transfer velocities was found to be good, except at the lowest mean square slopes. In the Kyoto high speed wind-wave tank, the effect of strong wave breaking and bubble entrainment on the gas transfer velocity was studied. Gas transfer velocities were split up into a purely wave induced part and a part caused by bubbles and wave breaking. The measured gas transfer velocities were found to be up to 350% larger than expected from waves alone at the highest wind speed. Three empirical parameterizations were tested on the bubble induced part, two successfully.

Heat and mass transfer effects on MHD flow of a couple‐stress fluid in a horizontal wavy channel with viscous dissipation and porous medium

Abstract: This paper looks at heat and mass transfer effects on an unsteady MHD flow of a couple-stress fluid in a horizontal wavy porous space with travelling thermal waves in the presence of a heat source and viscous dissipation. Initially the temperatures of the walls are maintained at different constant temperatures. The analytical expressions for velocity, temperature, and concentration field are obtained by the regular perturbation technique. The results are presented graphically for various values of emerging dimensionless parameters of the problem and are discussed to show interesting aspects of the solution. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 42(5): 403–421, 2013; Published online 8 April 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21040

Stability of a Gaussian pancake vortex in a stratified fluid

Abstract: Vortices in stably stratified fluids generally have a pancake shape with a small vertical thickness compared with their horizontal size. In order to understand what mechanism determines their minimum thickness, the linear stability of an axisymmetric pancake vortex is investigated as a function of its aspect ratio , the horizontal Froude number , the Reynolds number and the Schmidt number . The vertical vorticity profile of the base state is chosen to be Gaussian in both radial and vertical directions. The vortex is unstable when the aspect ratio is below a critical value, which scales with the Froude number: for sufficiently large Reynolds numbers. The most unstable perturbation has an azimuthal wavenumber either , or depending on the control parameters. We show that the threshold corresponds to the appearance of gravitationally unstable regions in the vortex core due to the thermal wind balance. The Richardson criterion for shear instability based on the vertical shear is never satisfied alone. The dominance of the gravitational instability over the shear instability is shown to hold for a general class of pancake vortices with angular velocity of the form provided that everywhere. Finally, the growth rate and azimuthal wavenumber selection of the gravitational instability are accounted well by considering an unstably stratified viscous and diffusive layer in solid body rotation with a parabolic density gradient.

A novel forcing technique to simulate turbulent mixing in a decaying scalar field

Abstract: To realize the full potential of Direct Numerical Simulation in turbulent mixing studies, it is necessary to develop numerical schemes capable of sustaining the flow physics of turbulent scalar quantities. In this work, a new scalar field forcing technique, termed “linear scalar forcing,” is presented and evaluated for passive scalars. It is compared to both the well-known mean scalar gradient forcing technique and a low waveshell spectral forcing technique. The proposed forcing is designed to capture the physics of one-time scalar variance injection and the subsequent self-similar turbulent scalar field decay, whereas the mean scalar gradient forcing and low waveshell forcing techniques are representative of continuous scalar variance injection. The linear scalar forcing technique is examined over a range of Schmidt numbers, and the behavior of the proposed scalar forcing is analyzed using single and two-point statistics. The proposed scalar forcing technique is found to be perfectly isotropic, preserving accepted scalar field statistics (fluxes) and distributions (scalar quantity, dissipation rate). Additionally, it is found that the spectra resulting from the three scalar forcing techniques are comparable for unity Schmidt number conditions, but differences manifest at high Schmidt numbers. These disparities are reminiscent of those reported between scaling arguments suggested by theoretical predictions and experimental results for the viscous-convective subrange.

Lattice Boltzmann simulation of viscous-fluid flow and conjugate heat transfer in a rectangular cavity with a heated moving wall

Abstract: In the present work, conjugate heat transfer in a rectangular cavity with a heated moving lid is investigated using the lattice Boltzmann method (LBM). The simulations are performed for incompressible flow, with Reynolds numbers ranging from 100 to 500, thermal diffusivity ratios ranging from 1 to 100, and Prandtl numbers ranging from 0.7 to 7. A uniform heat flux through the top of the lid is assumed. Results show that LBM is suitable for the study of heat transfer in conjugate problems. Effects of the Reynolds number, the Prandtl number and the thermal diffusivity ratio on hydrodynamic and thermal characteristics are investigated and discussed. The streamlines and temperature distribution in flow field, dimensionless temperature and Nusselt number along the hot wall are illustrated. The results indicate that increase of thermal diffusivity yields the removal of a higher quantity of energy from lid and its temperature decreases when increasing the Reynolds and the Prandtl numbers.

Effects of Chemical Reaction and Heat Generation on MHD Boundary Layer Flow of a Moving Vertical Plate with Suction and Dissipation

Abstract: In this paper, the study of the steady two-dimensional flow of an incompressible viscous fluid with heat and mass transfer and MHD heat generation past a moving vertical plate with suction in the presence of viscous dissipation and chemical reaction is investigated. Using similarity variables, the governing partial differential equations are transformed into non-linear ordinary differential equations. These equations are then solved numerically using fourth order Runge-Kutta method with shooting technique. The flow variables are presented graphically. The graphs showed that velocity rises for increasing Grashof number, mass Grashof numer, suction, heat generation and Eckert number while reducing with increasing magnetic parameter, Schmidt number, and chemical reaction parameter and Prandtl number. Comparisons with previously published work are performed and are found to be in an excellent agreement.