Showing papers on "Schmidt number published in 1991"

Turbulent Free Shear Layer Mixing and Combustion

Abstract: : Some experimental data on turbulent free-shear-layer growth, mixing, and chemical reactions are reviewed. The dependence of these phenomena on such fluid and flow parameters as Reynolds number, Schmidt number, and Mach number are discussed, with the aid of some direct consequences deducible from the large-scale organization of the flow as well as from some recent models. The mixing of two or more fluids that are entrained into a turbulent region is an important process from both a scientific and an applications vantage point. Species can be transported by turbulence to produce a more uniform distribution than some initial mean profile. This process is sometimes also referred to as mixing, without regard to whether the transported species are mixed on a molecular scale or not. If the issue of mixing arises in the context of chemical reactions and combustion, however, we recognize that only fluid mixed on a molecular scale can contribute to chemical product formation and associated heat release. The discussion in this paper will be limited to molecular mixing.

Stochastic geometric properties of scalar interfaces in turbulent jets

Abstract: Experiments were conducted in which the behavior of scalar interfaces in turbulent jets was examined, using laser‐induced fluorescence (LIF) techniques. The experiments were carried out in a high Schmidt number fluid (water), on the jet centerline, over a jet Reynolds number range of 1000≤Re≤24 000. Both two‐dimensional scalar data, c(r,t) at fixed x/d, and one‐dimensional scalar data, c(t) at fixed x/d and r/x, were analyzed using standard one‐ and two‐dimensional fractal box‐counting algorithms. Careful treatment was given to the handling of noise. Both long and short records as well as off‐centerline measurements were also investigated. The important effect of threshold upon the results is discussed. No evidence was found of a constant (power‐law) fractal dimension over the range of Reynolds numbers studied. On the other hand, the results are consistent with the computed behavior of a simple stochastic model of interface geometry.

The effects of turbulent mixing on the correlation between two species and on concentration fluctuations in non-premixed reacting flows

Abstract: When two species A and B are introduced through different parts of the bounding surface into a region of turbulent flow, molecules of A and B are brought together by the combined actions of the turbulent velocity field and molecular diffusion. A random flight model is developed to simulate the relative motion of pairs of fluid elements and random motions of the molecules, based on the models of Durbin (1980) and Sawford & Hunt (1986). The model is used to estimate the cross-correlation between fluctuating concentrations of A and B, G, at a point, in non-premixed homogeneous turbulence with a moderately fast or slow second-order chemical reaction. The correlation indicates the effects of turbulent and molecular mixing on the mean chemical reaction rate, and it is commonly expressed as the ‘segregation’ or ‘unmixedness ’ parameter a( = c,C,/cA c,) when normalized by the mean concentrations CA and C,. It is found that a increases from near - 1 to zero with the time (or distance) from the moment (or location) of release of two species in highReynolds-number flow. Also, the model _- (and experiments) agrees with the exact results of Danckwerts (1952) that C,c,I(ci c;); = - 1 for mixing without reaction. The model is then extended to account for the effects on the segregation parameter a of chemical reactions between A and B. This leads to a eventually decreasing, depending on the relative timescales for turbulent mixing and for chemical reaction (i.e. the Damkohler number). The model also indicates how a number of other parameters such as the turbulent scales, the Schmidt number, the ratio of initial concentrations of two reactants and the mean shear affect the segregation parameter a. The model explains the measurements of a in previously published studies by ourselves and other authors, for mixing with and without reactions, provided that the reaction rate is not very fast. Also the model is only strictly applicable for a limited mixing time t, such that t 5 TL where TL is the Lagrangian timescale, because the model requires that the interface between A and B is effectively continuous and thin, even if highly convoluted. Flow visualization results are presented, which are consistent with the physical idea underlying the two-particle model.

Reynolds number dependence of scalar fluctuations in a high Schmidt number turbulent jet

Abstract: The scalar rms fluctuations in a turbulent jet were investigated experimentally, using high-resolution, laser-induced fluorescence techniques. The experiments were conducted in a high Schmidt number fluid (water), on the jet centerline, over a jet Reynolds number range of 3000 3000 or 6500.

Vorticity generation in jet diffusion flames

Abstract: A novel method to analyze the vorticity generation or destruction in jet diffusion Flames is presented. The analysis employs a generic flame structure and a single conserved scalar to examine the vorticity generation or destruction in jet diffusion flames. The analysis shows that the volumetric expansion and baroclinicity can result in vorticity destruction or generation depending on the flame structure, or the stoichiometry. Three regimes concerning vorticity generation or destruction are identified for jet diffusion flames. The analysis also defines a non-dimensional parameter, describing the relative importance of baroclinicity to volumetric expansion. The parameter is the ratio of Reynolds number to Froude number and multiplied by the square root of the Schmidt number.

Mixing in High Schmidt Number Turbulent Jets

Abstract: : This thesis is an experimental investigation of the passive scalar (species concentration) field in the far-field of round, axisymmetric, high Schmidt number (liquid phase), turbulent jets issuing into a quiescent reservoir, by means of a quantitative laser-induced fluorescence technique. Single-point concentration measurements are made on the jet centerline, at axial locations from 100 to 305 nozzle diameters downstream, and Reynolds numbers of 3,000 to 102,000, yielding data with a resolved temporal dynamic range up to 2.5 x 10 to the 5th power, and capturing as many as 504 large-scale structure passages. Long-time statistics of the jet concentration are found to converge slowly. Between 100 and 300 large-scale structure passages are required to reduce the uncertainty in the mean to 1%, or so. The behavior of the jet varies with Reynolds number. The centerline concentration pdf's become taller and narrower with increasing Re, and the normalized concentration variances correspondingly decrease with Re. The concentration power spectra also evolve with Re. The behavior of the spectral slopes is examined. No constant -1 (Batchelor) spectral slope range is present. Rather, in the viscous region, the power spectra exhibit log-normal behavior, over a range of scales exceeding a factor of 40, in some cases.

Double‐diffusive flow in enclosures

Abstract: Numerical calculations are conducted for two‐dimensional steady‐state double‐diffusive flow in enclosures, where both the temperature and solute gradients are imposed horizontally, and the two buoyancy effects can either augment or counteract each other. Important controlling parameters including the thermal and solutal Grashof numbers, Schmidt number, and Prandtl number, are varied and new insights into the solutions of both the augmenting and counteracting modes gained. Even though the relative directions of the two buoyancy mechanisms reverse between the augmenting and counteracting modes, qualitative similarities in convection characteristics emerge. For both modes, with fixed thermal and solutal Grashof numbers, convection strength increases as the ratio between the Schmidt and Prandtl numbers, i.e., the Lewis number, becomes higher. With appropriate combinations of the Grashof number and buoyancy ratio, multiple‐cell flow patterns also appear in both modes, where the length scale disparity due to a large Lewis number causes the convection to be largely controlled by the temperature field within the primary convection cell, and by the solute field either in the region across the cell interface or in the secondary cells. Effects of irregular geometry of the enclosure on the transport processes are also assessed.

Toward a mathematical model of oxygen transfer to and within bottom sediments

Abstract: A mathematical model of the benthic boundary layer and the porous bottom is presented and explored. Emphasis is placed on the transition between the Ekman layer flow and the Darcian flow deep in the sediments. The predicted flow field in the porous region is verified against analytical solutions. The effective exchange coefficient for a substance with a large Schmidt number, for example, oxygen, is calculated taking different physical processes like turbulence, diffusion and dispersion into account. It is found that vertical transport may be considerably enhanced in a thin layer near the sediment/water interface, i.e., within the Brinkman layer, due to a dispersion mechanism. The oxygen distribution in the sediment/water system has been investigated for different porosities and consumption rates.

Mass transfer in the liquid phase methanol synthesis process

Abstract: The mass transfer characteristics of the liquid phase methanol synthesis process were experimentally investigated using a one-liter, mechanically agitated slurry reactor. The CuO/ZnO/Al2O3 catalyst was crushed to -140 mesh and suspended in an inert mineral oil (Witco # 40). The catalyst loading was varied within limits of experimental feasibility. The effects of temperature, pressure, level of oil, impeller speed, and gas flow rate on the overall gas-liquid mass transfer coefficient KLiaB were studied The results obtained using a two-level, half-fractional factorial design of experiments indicated that the impeller speed, feed flow rate, and temperature had significant effects on the mass transfer coefficient at the experimental conditions examined. Correlations were developed for the Sherwood number based on the Reynolds number, the Schmidt number, the reciprocal gas flow number, the gas-liquid viscosity ratio, and the dimensionless temperature. A simplified power-law type approach was also used...

Effect of Gas Flow on Physical Absorption

Abstract: Air blowing over a liquid surface can greatly increase the rate of physical absorption of a gaseous component. This increase is associated with the initiation of waves and a change in the dependency of the mass transfer coefficient on Schmidt number. For sufficiently large interfacial stresses the mass transfer coefficient varies linearly with the product of the friction velocity and the Schmidt number raised to the -0.5 power. A remarkable finding is that the proportionality constant is roughly the same for experimental systems with a wide range of scales. This paper reviews these results and work done to interpret them in terms of the properties of the velocity field close to the interface.

Fragment Formation in the Break-up of a Drop Falling in a Miscible Liquid.

Abstract: When falling in a lighter miscible solvent, a drop of liquid deforms to a torus which then breaks up into several fragments or just disappears by diffusion. By using liquids of different compositions we show the universal behaviour of the phenomenon, and its dependence on two nondimensional numbers, the fragmentation number F, and the Schmidt number S. While F marks the transition from diffusion to splitting, here we show the role of S in controlling the number of horizontal fragments after the first break-up. The process is explained in terms of competitions of different time scales.

New mixing-length model for turbulent high-speed flows

Abstract: A modification of Prandtl's mixing-length model is presented which takes into account the effects of compressibility on turbulence for high speed flows A parameter is introduced into the turbulent transport formula which acts like an effective turbulent Schmidt number for mixtures of gases or a turbulent Prandtl number for a homogeneous gas Results presented for such cases as high Mach number turbulent boundary layer flows over a flat surface, tangential slot injection problems, and shock/turbulent shear-layer and boundary-layer interactions agree well with experimental data

Experimental study of aerosol deposition in stirred flow fields ranging from laminar to turbulent flows.

Abstract: The deposition of aerosol particles of 0.01–2 μm in diameter is investigated in laminar and turbulent flow fields, and deposition by air flow, particle diffusion and gravitational sedimentation is evaluated. In experiments, wall loss rates of monodisperse particles are measured in four stirred tanks (similar in form but different in size) with stirring Reynolds number Re ranging from 10 to 104. The result has shown that deposition velocities vd obtained for particles smaller than 0.1 μm, which range over several orders of magnitude, are almost proportional to Re0.56 when Re is larger than about 1500. At Re 1/2Sc1/3, where Sc is the Schmidt number. The deposition velocities for 200 vd with Re depends on Re, indicating the existence of a transitional regime concerning deposition. The influence of gravity is observed when the particle diameter exceeds 0.2 μm, and the deposition rate can be predicted well by summing the contributions of diffusive deposition and gravitational sedimentation of a particle.

Scaling properties of the viscous‐convective scalar spectral subrange in turbulent jets

Abstract: A recent analysis by Dimotakis and Miller [Phys. Fluids A 2, 1919 (1990)] of the power spectrum of a diffusive scalar in turbulent flow identified a difficulty with the k−1 viscous‐convective scaling in the limit of very large Schmidt number for finite‐Reynolds‐number flows with bounded scalar fluctuations. Here, a modified scaling of the form k−1−p is derived for the self‐similar round jet, where p∼Re−1/2 for Re≫1.

Centrifugal Convection due to Mass Transfer Near a Rotating Disk at High Schmidt Number

Abstract: The centrifugally-driven flow due to a density gradient between the surface of an infinite disk and the ambient fluid in a rotating system with mass transfer is studied for the case of high Schmidt number. Under certain assumptions the velocity and density fields exhibit a similarity like the classical von Karman disk flow, and the governing equations reduce to a nonlinear system of ordinary differential equations. These equations are solved by boundary layer technique or numerically, for high Schmidt number σ = v/D and finite or small density difference eρ = (ρd - ρ∞ )/ρ∞ . In the latter case it is shown that the major scaling parameter is the product σeρ . For σρ ≫ 1 the flow field consists of a constant density (ρ∞ ), linear Ekman layer driven by a buoyancy sublayer of relative thickness (σeρ )-1/4 in which ρ varies from ρd to ρ∞ . The representative Rossby number of the buoyancy driven flow is (σeρ )-1/2 . The general case eρ = O(1), σ ≫ 1 shows similar trends, i.e., a σ-1/4 sublayer. The case of simultaneous driving by density difference and angular velocity difference ev = (Ωd - Ω∞ )/Ω∞ is also discussed.