Showing papers on "Schmidt number published in 1986"

Mixing and chemical reactions in a turbulent liquid mixing layer

Abstract: An experimental investigation of entrainment and mixing in reacting and non-reacting turbulent mixing layers at large Schmidt number is presented. In non-reacting cases, a passive scalar is used to measure the probability density function (p.d.f.) of the composition field. Chemically reacting experiments employ a diffusion-limited acid–base reaction to directly measure the extent of molecular mixing. The measurements make use of laser-induced fluorescence diagnostics and high-speed, real-time digital image-acquisition techniques. Our results show that the vortical structures in the mixing layer initially roll-up with a large excess of fluid from the high-speed stream entrapped in the cores. During the mixing transition, not only does the amount of mixed fluid increase, but its composition also changes. It is found that the range of compositions of the mixed fluid, above the mixing transition and also throughout the transition region, is essentially uniform across the entire transverse extent of the layer. Our measurements indicate that the probability of finding unmixed fluid in the centre of the layer, above the mixing transition, can be as high as 0.45. In addition, the mean concentration of mixed fluid across the layer is found to be approximately constant at a value corresponding to the entrainment ratio. Comparisons with gas-phase data show that the normalized amount of chemical product formed in the liquid layer, at high Reynolds number, is 50% less than the corresponding quantity measured in the gas-phase case. We therefore conclude that Schmidt number plays a role in turbulent mixing of high-Reynolds-number flows.

A model of gas transfer across air‐water interfaces with capillary waves

Abstract: The transfer of weakly soluble gases between the atmosphere and seas or lakes is controlled by liquid-phase molecular and turbulent diffusion mechanisms, which essentially depend on wind velocity and gas Schmidt number. A distinct change in regime is observed around 2–3 m s−1, when capillary waves appear, which present models cannot explain. We suggest relating turbulent diffusivity with (1) possible motions close to a “free” liquid-gas interface, (2) mean current distribution in that region, and (3) capillary wave spectra. Resulting transfer velocities explain laboratory and field data at low and moderate wind speeds.

Turbulent reactive mixing with a series-parallel reaction: Effect of mixing on yield

Abstract: The yield of a nonpremixed series-parallel reaction at complete conversion was measured in a turbulent, tubular-flow reactor with single and multijet feeds. The yield of the intermediate decreased as mixing was slowed relative to the chemical kinetics, either by decreasing the Reynolds number, or by using a less efficient mixing device, or by increasing the feed concentration. Four models, a modified slab model, a modified stretch model, the Harada mass transfer model, and a new closure model, adequately predict the yield when chemical and mixing kinetics are known from independent measurements of the conversion of acid-base reactions. Without modification, the original slab and stretch models are unable to account for the earlier observed invariance of conversion to Schmidt number of very rapid, single-step reactions or to satisfactorily predict the yield of the series-parallel reaction.

Stability of lifted laminar round gas-jet flame

Abstract: The exact solution of the concentration field of jet fluid in a round laminar jet is presented. This analytical solution, which assumes constant kinematic viscosity and molecular diffusivity, establishes the dependence of the concentration field on the Schmidt number. This solution and a kinematic argument were used to calculate the shape of the lifted flame front in a round laminar jet. The observed shape of the lifted laminar propane flame front was compared with the prediction of this formulation. A spatial-stability criterion of the flame was developed and applied to examine the stability of the lifted flame in the flow field of the round laminar jet. The laminar flame blowout height and the corresponding Reynolds number were calculated from the stability criterion. The predictions agree well with the experimental values. The flame blowout Reynolds number of laminar fuel jets of pure fuels discharging from round pipes with fully developed laminar flow is shown to be directly proportional to the pipe diameter. At blowout the fuel concentration in the vicinity of the flame is found to attain a constant value which lies between the lean flammability limit and the fuel concentration at which the laminar flame speed is maximum. This stability criterion is generalised to laminar gas-jet flames of different fuels using three experimentally determined parameters describing their flame speed-concentration characteristics. The general form can account for dilution of fuel jets with inert gases. That flames can be lifted and blow out while they are still laminar is also demonstrated experimentally.

Validation of an Aerothermochemical Model for Graphite Nozzle Recession and Heat-Transfer Processes

Abstract: Abstract-An aerothermochemical model for graphite nozzle recession and heat-transfer processes in solid-propellant rocket motors has been developed. The model considers the turbulent boundary-layer flow in the nozzle, heterogeneous reactions at the nozzle surface, and transient heat-conduction processes in the nozzle material. Mass transfer across the highly-accelerated turbulent boundary layer shows only a weak dependence on the Schmidt number of the diffusing species. Both frozen and chemical equilibrium boundary-layer assumptions were considered. H2O is found to be the dominant oxidizing species, with CO2 being of secondary importance. Concentration profiles of H2O across the boundary layer are not significantly affected by gas-phase reactions, implying that the graphite recession process is relatively independent of gas-phase reactions. The model has been verified with experimental data. Good agreement has been obtained for both recession and temperature measurements.

Three‐dimensional numerical study of convection in a cylindrical thermal diffusion cell: Its influence on the separation of constituents

Abstract: The convection arising in a cylindrical container, heated from the ends and designed for a measurement of Soret coefficient, is examined. A three‐dimensional method using a pseudostationary scheme with a finite differences technique is used. Attention is focused on a horizontal cylinder with an aspect ratio of 6, a Prandtl number of 0.6, and a Schmidt number of 60. The influence of convection on the separation and on the mass fraction profiles is examined for moderate Grashof numbers (0.01≤GrH≤10) and realistic Soret parameters (−0.75≤S≤1). A domain is found where the flow has no influence on the separation, corresponding to a ‘‘separation’’ regime. Extensions of the results to different Prandtl and Schmidt numbers and to larger aspect ratios are proposed.

Effects of mass transfer and free convection on the unsteady mhd flow past a vertical porous plate with constant suction

Abstract: Effects of free convection currents and mass transfer on the unsteady flow of an electrically conducting and viscous incompressible fluid past an infinite vertical porous plate subjected to uniform suction, in the presence of transverse magnetic field, have been studied taking into account that the external flow velocity varies periodically with time in magnitude but not in direction. The effect of the induced magnetic field has been neglected. Approximate solutions to the transient flow, the amplitude and the phase of the skin-friction and the rate of heat transfer have been derived. During the course of the discussion, the effects of the Grashoff number Gr, the modified Grashoff number Gc (depending on the concentration difference), the Schmidt number Sc, the Eckert number Ec, the magnetic field parameter M, and the frequency ω have been discussed.

Partition characteristics of close-boiling components in a chromatographic column

Abstract: Partition characteristics of three close-boiling components (dichloromethane, diethylether, and dimethoxymethane) were investigated with dinonylphthaiate-coated Chromosorb A and helium as the carrier The outlet stream from the Chromatographic column was monitored continuously Partition coefficients were experimentally determined at various column temperatures for the three components With the assumption of uniform film thickness, two parameters were estimated by Fourier analysis of the response curves The Peclet number for particle was expressed in terms of the Reynolds number and the Schmidt number as: $$\frac{1}{{Pe,p}} = \frac{{087}}{{\operatorname{Re} \cdot Sc}} + 05$$ Intraparticle diffusion coefficient of each component was also determined in the form of the dimensionless group Pi The theoretical response curve in time domain was in good agreement with the observed one From the sensitivity analysis, it is concluded that the liquid film resistance was small and the diffusion in the liquid phase was not a rate-determining step

Linear stability of a binary fluid layer with freezing

Abstract: The linear convective instabilities of a fluid layer of binary alloy, cooled from above and consequently frozen at the bottom, are considered. Due to the density jump across the freezing interface, some light material is then released and diffused by pressure and composition gradients. As a result of a low cooling rate, the effect of thermal buoyancy is insignificant and the freezing interface advances upward at a slow speed by accumulating the solidified binary alloy. As Schmidt number PL approaches infinity, instabilities set in stationarily at the marginal state. Cellular convective modes are possible, provided a destabilizing compositional profile occurs in the fluid layer, while morphological modes, associated with non‐cellular convection, require a constitutional supercooling near the freezing interface. In the absence of a constitutional supercooling, morphological modes are not important and cellular convective modes become dominant.

Transient ignition on a flat plate

Abstract: In this study, transient ignition on a hot plate is analyzed numerically. In addition to the transient energy and species equations, the transient momentum equation is also considered. A comparison is made between the results of transient velocity field and those of steady velocity field. It is found that the transient velocity field has the effect of increasing the ignition length and ignition time. The effects of wall temperature, Prandtl number and Schmidt number are also studied.

Numerical modeling of physical vapor transport in a vertical cylindrical ampoule, with and without gravity

Abstract: Numerical modeling has been performed of the fluid dynamics in a prototypical physical vapor transport crystal growing situation. Cases with and without gravity have been computed. Dependence of the flows upon the dimensionless parameters aspect ratio and Peclet, Rayleigh, and Schmidt numbers is demonstrated to a greater extent than in previous works. Most notably, it is shown that the effects of thermally-induced buoyant convection upon the mass flux on the growth interface crucially depend upon the temperature boundary conditions on the sidewall (e.g., whether adiabatic or of a fixed profile, and in the latter case the results depend upon the shape of the profile assumed).

Effects of the external temperature-dependent heat sources on the unsteady free convective and mass-transfer hydromagnetic flow in the Stokes problem

Abstract: There have been considered the effects of external temperature-dependent heat sources and mass transfer on free convection flow of an electrically conducting viscous fluid past an impulsively starting infinite vertical limited surface in presence of a transverse magnetic field as considered. Solutions for the velocity and skin-friction, in closed form are obtained by using the Laplace transform technique and the results obtained for various values of the parametersSc (Schmidt number),M (Hartmann number), andS (Strength a Source or Sink) are given in graphical form. The paper is concluded with a discussion on the obtained results.

The concentration fields of disperse impurity are calculated on the basis of a k-e model of turbulence in a wide range of Stokes numbers.

Abstract: Calculating the concentration fields of disperse impurity is one of the most important problems in the numerical modeling of two-phase turbulent jets. The character of the impurity distribution in the jet for the case of solid particles is determined by two basic mechanisms: turbulent diffusion of particles and their migrational transfer, which is due to the initial rotation of the particles, acquired in impacts on the tube wall, and the presence of phase slipping. One characteristic of the first mechanism is the Schmidt number Sc = 9t/ Dp, for which a theoretical dependence was obtained for the first time in [i] within the framework of the theory of Prandtl mixing paths. In [2], it was shown that, in taking account of the initial particle velocity of the particles incident in a turbulent mole, an analog of the Schmidt number may be obtained for a two-phase flow, permitting transition in the limit to the Schmidt number for a gas with reduction in particle size. However, calculation by this model gives an underestimate of the damping rate of the axial concentration distribution of the impurity, which has prompted the construction of various approaches determining the diffusional properties of a heavy impurity in a turbulent jet [3]. As shown by experiment [4], migrational transfer of impurity, causing the phenomena of concentration and dispersion, dominates in the initial section of the jet, and may be described by taking account of Magnus forces and radial phase slipping [5]. Nevertheless, the calculation scheme for a two-phase turbulent jet proposed in [5] is sufficiently cumbersome: calculation of the two-phase jet is preceded by solution of the problem of the emission of a one-phase jet, and then the turbulent transfer coefficients are found, taking account of the influence of particles on the theory [2]. Models of second-order turbulence are promising for the calculation of two-phase jets. In the present work, the distribution of concentration fields of the disperse phase in a turbulent jet on the basis of a two-parameter model is investigated numerically, using the transfer equations of pulsational energy and the rate of its dissipation. The dynamic phase interaction is determined, as in [5], by the drag force and the Magnus force. The system of equations for the mean quantities describing the emission of an axisymmetric turbulent gasdisperse jet, taking account of phase slipping and particle rotation, takes the form aug + I a