Showing papers on "Schmidt number published in 2007"

Hydrodynamic interaction in polymer solutions simulated with dissipative particle dynamics.

Abstract: The authors analyzed extensively the dynamics of polymer chains in solutions simulated with dissipative particle dynamics (DPD), with a special focus on the potential influence of a low Schmidt number of a typical DPD fluid on the simulated polymer dynamics. It has been argued that a low Schmidt number in a DPD fluid can lead to underdevelopment of the hydrodynamic interaction in polymer solutions. The authors' analyses reveal that equilibrium polymer dynamics in dilute solution, under typical DPD simulation conditions, obey the Zimm [J. Chem. Phys. 24, 269 (1956)] model very well. With a further reduction in the Schmidt number, a deviation from the Zimm model to the Rouse model is observed. This implies that the hydrodynamic interaction between monomers is reasonably developed under typical conditions of a DPD simulation. Only when the Schmidt number is further reduced, the hydrodynamic interaction within the chains becomes underdeveloped. The screening of the hydrodynamic interaction and the excluded volume interaction as the polymer volume fraction is increased are well reproduced by the DPD simulations. The use of soft interaction between polymer beads and a low Schmidt number do not produce noticeable problems for the simulated dynamics at high concentrations, except for the entanglement effect which is not captured in the simulations.

Stability of miscible core–annular flows with viscosity stratification

Abstract: The linear stability of variable viscosity, miscible core-annular flows is investigated. Consistent with pipe flow of a single fluid, the flow is stable at any Reynolds number when the magnitude of the viscosity ratio is less than a critical value. This is in contrast to the immiscible case without interfacial tension, which is unstable at any viscosity ratio. Beyond the critical value of the viscosity ratio, the flow can be unstable even when the more viscous fluid is in the core. This is in contrast to plane channel flows with finite interface thickness, which are always stabilized relative to single fluid flow when the less viscous fluid is in contact with the wall. If the more viscous fluid occupies the core, the axisymmetric mode usually dominates over the corkscrew mode. It is demonstrated that, for a less viscous core, the corkscrew mode is inviscidly unstable, whereas the axisymmetric mode is unstable for small Reynolds numbers at high Schmidt numbers. For the parameters under consideration, the switchover occurs at an intermediate Schmidt number of about 500. The occurrence of inviscid instability for the corkscrew mode is shown to be consistent with the Rayleigh criterion for pipe flows. In some parameter ranges, the miscible flow is seen to be more unstable than its immiscible counterpart, and the physical reasons for this behaviour are discussed. A detailed parametric study shows that increasing the interface thickness has a uniformly stabilizing effect. The flow is least stable when the interface between the two fluids is located at approximately 0.6 times the tube radius. Unlike for channel flow, there is no sudden change in the stability with radial location of the interface. The instability originates mainly in the less viscous fluid, close to the interface.

Flow and heat transfer in a moving fluid over a moving flat surface

Abstract: In this paper, a numerical analysis of the momentum and heat transfer of an incompressible fluid past a parallel moving sheet based on composite reference velocity U is carried out. A single set of equations has been formulated for both momentum and thermal boundary layer problems containing the following parameters: r the ratio of the free stream velocity to the composite reference velocity, σ (Prandtl number) the ratio of the momentum diffusivity of the fluid to its thermal diffusivity, and E c (E ck ) (Eckert number). The present study has been carried out in the domain 0 ≤ r ≤ 1. It is found that the direction of the wall shear changes in such an interval and an increase of the parameter r yields an increase in temperature.

Scalar Fluctuation Modeling for High-Speed Aeropropulsive Flows

Abstract: A Reynolds-averaged Navier-Stokes-based scalar-variance model is described that extends a previous low-speed nonreacting jet model to more generalized high-speed compressible reacting flows. The model is cast in a k-e turbulence model framework. Transport equations for energy variance and its dissipation rate are solved to predict temperature fluctuations and provide a thermal time scale for use in calculating a variable turbulent Prandtl number. For multispecies problems, mixture-fraction variance and dissipation rate equations are solved that predict species concentration fluctuations and provide a species mixing time scale for use in calculating a variable turbulent Schmidt number. The formulation accounts for compressibility and near-wall damping effects. A series of high-speed flow simulations are presented for both nonreacting and reacting configurations and the predictions are compared to available measured data and companion LES calculations. Results demonstrate the models' capabilities over a range of conditions and suggest that the proposed formulation will provide improved predictions in practical high-speed aeropropulsive configurations of interest, such as scramjet combustors, where turbulent Prandtl and Schmidt numbers vary substantially.

Turbulent mixing in temporal compressible shear layers involving detailed diffusion processes

Abstract: Direct numerical simulations (DNS) of temporally evolving weakly compressible shear layers with gradients of species and temperature have been performed to investigate the influence of detailed diffusion processes on turbulent mixing. As an exact modeling of the mixing process is a prerequisite of correct combustion prediction, this study aims at exploring the necessity of considering detailed diffusion processes of active scalars. The results comprise a demonstration of the strength of the Soret and Dufour effect and of their impact on the scalar and temperature gradients. The erroneous assumption of a spatially and temporally constant Schmidt number, equal for all species, is discussed. Furthermore, the scalar dissipation rate which is responsible for the smoothening of scalar fluctuations in the smallest scales is investigated. As this quantity is controlling the molecular mixing, it is clear that an influence on it by detailed diffusion processes has a direct impact on the chemical reaction and heat r...

Numerical solutions for micropolar transport phenomena over a nonlinear stretching sheet

Abstract: We present a numerical study for the steady, coupled, hydrodynamic, heat and mass transfer of an incompressible micropolar fluid flowing over a nonlin ear stretching sheet. The governing differential equations are partially decoupled usin g a similarly transformation and then solved by two numerical techniques - the finite elem ent method and the finite difference method. The dimensionless translational velocity, microrotation (angular velocity), temperature and mass distribution function are computed for the different thermophysical parameters controlling the flow regime, viz the nonlinear (stretching) parameter, b, Grashof number, G and Schmidt number, Sc. All results are shown graphically. Additionally skin friction and Nusselt number, which provide an estimate of the surface shear stress and the rate of cooling of the surfac e, respectively, are also computed. Excellent agreement is obtained between both numerical methods. The dimensionless translational velocity (f ' ) for both micropolar and Newtonian fluids is shown to decrease with an increase in nonlinear parameter b. Dimensionless micro- rotation (angular velocity), g, generally increases with a rise in nonlinear parameter b (in particular in the vicinity of the wall) and decreases with a rise in convective pa rameter, G. The effects of other parameters on the flow variables are also discuss ed. The flow regime has significant applications in polymer processing technology and metallurgy.

Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel

Abstract: A numerical study of pulsatile flow and mass transfer of an electrically conducting Newtonian biofluid via a channel containing porous medium is considered. The conservation equations are transformed and solved under boundary conditions prescribed at both walls of the channel, using a finite element method with two-noded line elements. The influence of magnetic field on the flow is studied using the dimensionless hydromagnetic number, Nm, which defines the ratio of magnetic (Lorentz) retarding force to the viscous hydrodynamic force. A Darcian linear impedance for low Reynolds numbers is incorporated in the transformed momentum equation and a second order drag force term for inertial (Forchheimer) effects. Velocity and concentration profiles across the channel width are plotted for various values of the Reynolds number (Re), Darcy parameter (λ), Forchheimer parameter (Nf), hydro-magnetic number (Nm), Schmidt number (Sc) and also with dimensionless time (T). Profiles of velocity varying in space and time are also provided. The conduit considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. Increasing the hydromagnetic number (Nm) from 1 to 15 considerably depresses biofluid velocity (U) indicating that a magnetic field can be used as a flow control mechanism in, for example, medical applications. A rise in Nf from 1 to 20 strongly retards the flow development and decreases the velocity, U, across the width of the channel. The effects of other parameters on the flowfield are also discussed at length. The flow model also has applications in the analysis of electrically conducting haemotological fluids flowing through filtration media, diffusion of drug species in pharmaceutical hydromechanics, and also in general fluid dynamics of pulsatile systems.

Phase-field modeling of transport-limited electrolysis in solid and liquid states

Abstract: A phase-field model of electrochemical interface dynamics is developed to study cathode shape and topology change in transport-limited electrolysis in two and three dimensions under conditions of rapid charge redistribution. A case study for the binary model is carried out for an Fe-FeO system. Stability behavior of the model is in good agreement with linear stability theory for small amplitude sinusoidal perturbation in electrodeposition. When there is no convection, a high electric field and low surface tension cause the cathode interface to be unstable, leading to growth of dendrites which break into powders. When the electrodes and electrolyte are low-viscosity fluids, flow provides an additional mechanism for stabilizing the interface. A new stability criterion for this liquid situation based on the Schmidt number is derived from dimensional analysis and model results. For an unstable cathode interface, a streamer morphology (liquid dendrites) is observed in two and three dimensions. This binary model is extended to a ternary system and a representative case is carried out for the Ti-Mg-Cl system. One- and two-dimensional ternary simulations show qualitatively correct interface motion and electrical potential behavior.

Modeling Scramjet Flows with Variable Turbulent Prandtl and Schmidt Numbers

Abstract: A complete turbulence model, where the turbulent Prandtl and Schmidt numbers are calculated as part of the solution and where averages involving chemical source terms are modeled, is presented. The ability of avoiding the use of assumed or evolution Probability Distribution Functions (PDF’s) results in a highly ecient algorithm for reacting flows. The predictions of the model are compared with two sets of experiments involving supersonic mixing and one involving supersonic combustion. The results demonstrate the need for consideration of turbulence/chemistry interactions in supersonic combustion. In general, good agreement with experiment is indicated.

Simultaneous velocity and concentration field measurements of passive-scalar mixing in a confined rectangular jet

Abstract: Simultaneous velocity and concentration fields in a confined liquid-phase rectangular jet with a Reynolds number based on the hydraulic diameter of 50,000 (or 10,000 based on the velocity difference between streams and the jet exit dimension) and a Schmidt number of 1,250 were obtained by means of a combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system. Data were collected at the jet exit and six further downstream locations. The velocity and concentration field data were analyzed for flow statistics such as turbulent fluxes, turbulent viscosity and diffusivity, and turbulent Schmidt number (Sc T ). The streamwise turbulent flux was found to be larger than the transverse turbulent flux, and the mean concentration gradient was not aligned with the turbulent flux vector. The average Sc T was found to vary both in streamwise and in cross stream directions and had a mean value around 0.8, a value consistent with the literature. Spatial correlation fields of turbulent fluxes and concentration were then determined. The R u′ϕ′ correlation was elliptical in shape with a major axis tilted downward with respect to the streamwise axis, whereas the R v′ϕ′ correlation was an ellipse with a major axis aligned with the cross-stream direction. Negative regions of R u′ϕ′ were observed in the outer streams, and these negatively correlated regions decayed with downstream distance and finally disappeared altogether. The R ϕ′ϕ′ correlation field was found to be an ellipse with the major axis inclined at about 45° with respect to the streamwise direction. Linear stochastic estimation was used to interpret spatial correlation data and to determine conditional flow structures. It is believed that a vortex street formed near the splitter plate is responsible for the negatively correlated region observed in the R u′ϕ′ spatial correlations of turbulent fluxes. A positive concentration fluctuation event was observed to correspond to a finger of nearly uniform concentration fluid reaching out into the outer stream, whereas a negative event corresponds to a pocket of nearly uniform fluid being entrained from the outer stream into the center jet region. Large-scale vortical structures were observed in the conditional velocity fields with an elliptical shape and a streamwise major axis. The growth of the structure size increased linearly initially but then grew more slowly as the flow transitioned toward channel flow.

Measurements of Molecular Mixing in a High Schmidt Number Rayleigh-Taylor Mixing Layer

Abstract: Molecular mixing measurements are performed for a high Schmidt number (Sc {approx} 10{sup 3}), small Atwood number (A {approx} 7.5 x 10{sup -4}) buoyancy-driven turbulent Rayleigh-Taylor mixing layer in a water channel facility. Salt was added to the top stream to create the desired density difference. The degree of molecular mixing was measured as a function of time by monitoring a diffusion-limited chemical reaction between the two fluid streams. The pH of each stream was modified by the addition of acid or alkali such that a local neutralization reaction occurred as the two fluids molecularly mixed. The progress of this neutralization reaction was tracked by the addition of phenolphthalein - a pH-sensitive chemical indicator - to the acidic stream. Accurately calibrated backlit optical techniques were used to measure the average concentration of the colored chemical indicator. Comparisons of chemical product formation for pre-transitional buoyancy- and shear-driven mixing layers are given. It is also shown that experiments performed at different equivalence ratios (acid/alkali concentration) can be combined to obtain a mathematical relationship between the colored product formed and the density variance. This relationship was used to obtain high-fidelity, quantitative measures of the degree of molecular mixing which are independent of probemore » resolution constraints. The dependence of such mixing parameters on the Schmidt and Reynolds numbers is examined by comparing the current Sc {approx} 10{sup 3} measurements with Sc = 0.7 gas-phase and Pr = 7 liquid-phase measurements. This comparison indicates that the Schmidt number has a large effect on the bulk quantity of mixed fluid at small Reynolds numbers Re{sub h} < 10{sup 3}. At late times, all mixing parameters indicated a greater degree of molecular mixing and a decreased Schmidt number dependence. Implications for the development and quantitative assessment of turbulent transport and mixing models appropriate for Rayleigh?Taylor instability-induced mixing are discussed.« less

Mass transfer from circulating liquid drops

Abstract: Mass-transfer coefficients for partially miscible binary liquid–liquid systems have been measured from single drops. Four systems were studied, furfural-water, water-isobutanol, water-ethyl acetate and benzyl alcohol-water; the drop phase is the first mentioned and the drops were saturated with the other phase. These systems have low interfacial tensions and the drops circulate internally. Circulation will reduce the boundary layer thickness from that for a solid sphere towards that for a gas bubble or a sphere in potential flow and correspondingly affect the index of the Schmidt number. The mass transfer for circulating drops should correlate with Re1/2. Sc1/2 and for stagnant drops with Re1/2.Sc1/2. The present systems are intermediate in character, approximating to Re1/2. Sc0.42. The results are higher than those from spray columns and appear to represent the maximum mass-transfer rates obtainable from droplets in free motion.

2-D preplanetary accretion disks I. Hydrodynamics, chemistry, and mixing processes

Abstract: Aims. We outline a numerical method to calculate spatially two-dimensional (2-D) reactive flows and mixing processes in preplanetary accretion disks and present first results. The numerical e ciency and robustness is demonstrated by following the hydrodynamical and chemical evolution of the disk from a highly non-stationary dynamical “switch-on” phase asymptotically into the quasi-stationary, viscous accretion regime. One major question we address is the C-, H-, O-chemistry. The leit-motif of our investigation is the attempt to preserve as much consistency as possible when modelling the hydrodynamical, chemical, transport/mixing processes and their mutual interactions in preplanetary disks. Methods. We use an explicit scheme for solving the Navier-Stokes equations combined with an implicit solver for the energy equation. The viscosity coe cient is modelled according to the so-called -prescription of “turbulent” viscosity. In contrast to the well-known -viscosity, the -parameterization of the viscosity warrants physical consistency if self-gravitation of the disk material is to be taken into account. However, up to now we have neglected self-gravitation. For the radiative energy transport we have adopted the (grey) Eddington approximation. The opacity is assumed to be caused by microscopic dust particles. Di usive mixing of the various chemical species is modelled by taking the di usion coe cient, D, proportional to the (turbulent) viscosity, turb. For comparison purposes, we have considered two extreme choices of the Schmidt number,S := turb=D, that is,S = 1 (D = turb) andS =1 (D = 0, i. e., no di usive mixing at all), respectively. We have not yet included coagulation processes and grain growth. Results. The main outcome of the 2-D simulations so far carried out is a characteristic circulation pattern of the quasi-stationary accretion flow: Near the disk’s equatorial plane which is assumed to be a plane of symmetry the material moves in the outward direction, whereas the accretion flow proper develops in higher altitudes of the disk. Species that are produced or undergo chemical reactions in the warm inner zones of the disk are advectively transported into the cool outer regions. At the same time, they either di usively mix up with the surrounding material or freeze out on the dust grains to form “ice”-coated particles. By virtue of the large-scale circulation, which is driven by viscous angular momentum transfer, advective transport dominates di usive mixing in the outer part of the disk.

Direct numerical simulation of salt sheets and turbulence in a double‐diffusive shear layer

Abstract: [1] We describe three-dimensional direct numerical simulations (DNS) of double-diffusively stratified flow interacting with inflectional shear. The extreme difference in diffusivity (and thus minimum length scale) between heat, salt and momentum in seawater is replicated for the first time in a three-dimensional simulation. The primary instability generates salt sheets, which are oriented parallel to the direction of the sheared background flow. Subsequently, two distinct mechanisms of secondary instability combine to lead the flow to a turbulent state. In this state, the effective saline diffusivity is smaller than that calculated by previous investigators for the unsheared case. The Schmidt number is much smaller than unity, indicating that salt sheets are less effective at transporting momentum than is often assumed.

Chemical Reaction, Heat and Mass Transfer on MHD Flow over a Vertical Isothermal Cone Surface in Micropolar Fluids with Heat Generation/Absorption

Abstract: An analysis has been carried out to obtain the nonlinear MHD ∞ow with heat and mass transfer characteristics of an incompressible, viscous, electrically conducting and Boussinesq ∞uid on a vertical isothermal cone surface in micropolar ∞uids with chemical reaction and heat generation/absorption. A discussion is provided for the efiects of the micropolar parameters ‚;¢, chemical reaction parameter ∞,heat generation absorption parameter fi, Schmidt number Sc, and buoyancy parameter A on the friction factor, heat transfer rate, mass transfer rate and wall couple stress.

Instability and Diapycnal Momentum Transport in a Double-Diffusive, Stratified Shear Layer

Abstract: The linear stability of a double-diffusively stratified, inflectional shear flow is investigated. Doublediffusive stratification has little effect on shear instability except when the density ratio R is close to unity. Double-diffusive instabilities have significant growth rates and can represent the fastest-growing mode even in the presence of inflectionally unstable shear with a low Richardson number. In the linear regime, background shear has no effect on double-diffusive modes except to select the orientation of the wave vector. The converse is not true: double-diffusive modes modify the mean shear via momentum fluxes. The momentum flux driven by salt sheets is parameterized in terms of a Schmidt number (ratio of eddy viscosity to saline diffusivity) Scs. In the oceanic parameter regime, Scs is less than unity and can be approximated as Scs 0.08 ln[R /(R 1)]. Enhanced molecular dissipation by unstable motions is quantified in terms of the dissipation ratio , and the results are compared with observations. Corresponding results are given for diffusive convection in an inflectional shear flow, though linear theory is expected to give a less accurate description of this mechanism.

Pulsatile Blood Flow and Oxygen Transport Past a Circular Cylinder

Abstract: The fundamental study of blood flow past a circular cylinder filled with an oxygen source is investigated as a building block for an artificial lung. The Casson constitutive equation is used to describe the shear-thinning and yield stress properties of blood. The presence of hemoglobin is also considered. Far from the cylinder, a pulsatile blood flow in the x direction is prescribed, represented by a time periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest for the characterization of the flow and transport are the steady Reynolds number (Re), Womersley parameter (alpha), pulsation amplitude (A), and the Schmidt number (Sc). The Hill equation is used to describe the saturation curve of hemoglobin with oxygen. Two different feed-gas mixtures were considered: pure O(2) and air. The flow and concentration fields were computed for Re=5, 10, and 40, 0< or =A< or =0.75, alpha=0.25, 0.4, and Schmidt number, Sc=1000. The Casson fluid properties result in reduced recirculations (when present) downstream of the cylinder as compared to a Newtonian fluid. These vortices oscillate in size and strength as A and alpha are varied. Hemoglobin enhances mass transport and is especially important for an air feed which is dominated by oxyhemoglobin dispersion near the cylinder. For a pure O(2) feed, oxygen transport in the plasma dominates near the cylinder. Maximum oxygen transport is achieved by operating near steady flow (small A) for both feed-gas mixtures. The time averaged Sherwood number, Sh, is found to be largely influenced by the steady Reynolds number, increasing as Re increases and decreasing with A. Little change is observed with varying alpha for the ranges investigated. The effect of pulsatility on Sh is greater at larger Re. Increasing Re aids transport, but yields a higher cylinder drag force and shear stresses on the cylinder surface which are potentially undesirable.

Concentration profiles of particles settling in the neutral and stratified atmospheric boundary layer

Abstract: An expression for the vertical equilibrium concentration profile of heavy particles, including the effects of canopy on the eddy diffusivity as well as corrections for atmospheric stability, is proposed. This expression is validated against measurements of vertical concentration profiles of corn pollen above a corn field. The fitted theoretical profiles show that particle settling is correctly accounted for. The sensitivity to variations in the turbulent Schmidt number, settling velocity and stability corrections are explicitly characterized. The importance of independent measurements of the surface flux of pollen in future experiments is noted.

Mass Transfer from Ensembles of Newtonian Fluid Spheres at Moderate Reynolds and Peclet Numbers

Abstract: In this work, the rate of mass transfer from an ensemble of mono-size spherical Newtonian droplets (free from surfactants) to a Newtonian continuous phase has been numerically studied at moderate Reynolds and Peclet numbers. A simple spherical cell model (so-called free surface cell model) has been used to account for inter-drop hydrodynamic interactions. Extensive numerical results have been obtained to elucidate the effects of the Reynolds number (Reo), the ratio of internal to external fluid viscosity (k), the volume fraction of the dispersed phase (ɛ) and the Schmidt number (Sc) on the local and average Sherwood number (Sh) over the ranges of conditions: 1 ≤ Reo ≤ 200, 0.2 ≤ ɛ ≤ 0.6, 0.1 ≤ k≤ 50 and 1 ≤ Sc ≤ 10 000. It has been observed that the effects of viscosity ratio on the local and average Sherwood number is less significant for small values of the Peclet number (Pe) for all values of dispersed phase concentration. As the value of the viscosity ratio increases, the average Sherwood number decreases for all values of the droplet concentration and the Reynolds number. Based on the present numerical results, a simple predictive correlation is proposed which can be used to estimate the rate of inter-phase mass transfer in a liquid–liquid system in a new application. However, it is also appropriate to add here that at higher concentrations, fluid spheres interact significantly, deform and coalesce. All these effects are neglected in this study. Therefore, the present results are valid only for dilute to moderate concentration of the dispersed phase.