Showing papers on "Schmidt number published in 2009"

Heat and mass transfer in stagnation-point flow towards a stretching surface in the presence of buoyancy force and thermal radiation

Abstract: In this paper an analysis has been made to study heat and mass transfer in two-dimensional stagnation-point flow of an incompressible viscous fluid over a stretching vertical sheet in the presence of buoyancy force and thermal radiation. The similarity solution is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential equations containing Prandtl number, Schmidt number and Sherwood number which are solved numerically with appropriate boundary conditions for various values of the dimensionless parameters. Comparison of the present numerical results are found to be in excellent with the earlier published results under limiting cases. The effects of various physical parameters on the boundary layer velocity, temperature and concentration profiles are discussed in detail for both the cases of assisting and opposing flows. The computed values of the skin friction coefficient, local Nusselt number and Sherwood number are discussed for various values of physical parameters. The tabulated results show that the effect of radiation is to increase skin friction coefficient, local Nusselt number and Sherwood number.

On MHD boundary‐layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux

Abstract: Purpose – The hydromagnetic mixed convection flow of an incompressible viscous electrically conducting fluid and mass transfer over a vertical porous plate with constant heat flux embedded in a porous medium is investigated.Design/methodology/approach – Using the Boussinesq and boundary‐layer approximations, the fluid equations for momentum, energy balance and concentration governing the problem are formulated. These equations are solved numerically by using the most effective Newton–Raphson shooting method along with fourth‐order Runge–Kutta integration algorithm.Findings – It was found that for positive values of the buoyancy parameters, the skin friction increased with increasing values of both the Eckert number (Ec) and the magnetic field intensity parameter (M) and decreased with increasing values of both the Schmidt number (Sc) and the permeability parameter (K).Practical implications – A very useful source of information for researchers on the subject of hydromagnetic flow in porous media.Originali...

High-Reynolds number Rayleigh-Taylor turbulence

Abstract: The turbulence generated in the variable density Rayleigh–Taylor mixing layer is studied using the high-Reynolds number fully resolved 30723 numerical simulation of Cabot and Cook (Nature Phys. 2 (2006), pp. 562–568). The simulation achieves bulk Reynolds number, Re = H [Hdot]/ν = 32,000, turbulent Reynolds number, Re t = [ktilde] 2/νϵ = 4600, and Taylor Reynolds number, R λ = 170. The Atwood number, A, is 0.5, and the Schmidt number, Sc, is 1. Typical density fluctuations, while modest, being one quarter the mean density, lead to non-Boussinesq effects. A comprehensive study of the variable density energy budgets for the kinetic energy, mass flux and density specific volume covariance equations is undertaken. Various asymmetries in the mixing layer, not seen in the Boussinesq case, are identified and explained. Hypotheses for the variable density turbulent transport necessary to close the second moment equations are studied. It is found that, even though the layer width becomes temporally self-similar re...

Measuring Qutrit-Qutrit Entanglement of Orbital Angular Momentum States of an Atomic Ensemble and a Photon

Abstract: Three-dimensional entanglement of orbital angular momentum states of an atomic qutrit and a single photon qutrit has been observed. Their full state was reconstructed using quantum state tomography. The fidelity to the maximally entangled state of Schmidt rank 3 exceeds the threshold 2/3. This result confirms that the density matrix cannot be decomposed into an ensemble of pure states of Schmidt rank 1 or 2. That is, the Schmidt number of the density matrix must be equal to or greater than 3.

Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. I. Comparison to experimental data

Abstract: A 1152×760×1280 direct numerical simulation (DNS) using initial conditions, geometry, and physical parameters chosen to approximate those of a transitional, small Atwood number Rayleigh–Taylor mixing experiment [Mueschke et al., J. Fluid Mech. 567, 27 (2006)] is presented. In particular, the Atwood number is 7.5×10−4, and temperature diffusion is modeled by mass diffusion with an equivalent Schmidt number of 7. The density and velocity fluctuations measured just off of the splitter plate in this buoyantly unstable water channel experiment were parametrized to provide physically realistic, anisotropic initial conditions for the DNS. The methodology for parametrizing the measured data and numerically implementing the resulting perturbation spectra in the simulation is discussed in detail. The DNS is then validated by comparing quantities from the simulation to experimental measurements. In particular, large-scale quantities (such as the bubble front penetration hb and the mixing layer growth parameter αb), ...

Effects of Viscous and Joules Dissipation on MHD Flow, Heat and Mass Transfer past a Stretching Porous Surface Embedded in a Porous Medium

Abstract: This paper investigates the influence of both viscous and joules dissipation on the problem of magnetohydrodynamic flow past a stretching porous surface embedded in a porous medium. Analytic solutions of the resulting nonlinear non-homogeneous boundary value problem in the case when the plate stretches with a velocity varying linearly with distance, expressed in terms of confluent hypergeometric functions, are presented for the case of prescribed surface temperature. Numerical calculations have been carried out for various values of suction parameter, magnetic field, Prandtl number, Eckert number and Schmidt number. The results show that increases in magnetic parameter decrease both the dimensionless transverse velocity, longitudinal velocity and also the skin friction coefficient. Also, formation of thin boundary layer is observed for higher value of magnetic parameter.

Direct measurement of transverse-mode entanglement in two-photon states

Abstract: We introduce and experimentally demonstrate a method to measure the Schmidt number of pure two-photon states entangled in transverse-mode structure. Our method is based on the connection between the Schmidt decomposition in quantum theory and the coherent-mode decomposition in classical coherence theory. We apply the method to two-photon states generated by spontaneous parametric down conversion and show that our results are in excellent agreement with numerical calculations based on the Schmidt decomposition.

Research on the Transport and Deposition of Nanoparticles in a Rotating Curved Pipe

Abstract: A finite-volume code and the SIMPLE scheme are used to study the transport and deposition of nanoparticles in a rotating curved pipe for different angular velocities, Dean numbers, and Schmidt numbers. The results show that when the Schmidt number is small, the nanoparticle distributions are mostly determined by the axial velocity. When the Schmidt number is many orders of magnitude larger than 1, the secondary flow will dominate the nanoparticle distribution. When the pipe corotates, the distribution of nanoparticle mass fraction is similar to that for the stationary case. There is a “hot spot” deposition region near the outside edge of bend. When the pipe counter-rotates, the Coriolis force pushes the region with high value of nanoparticle mass fraction toward inside edge of the bend. The hot spot deposition region appears inside the edge. The particle deposition over the whole edge of the bend becomes uniform as the Dean number increases. The corotation of pipe makes the particle deposition efficiency a reduction, while high counter-rotation of pipe only slightly affects the deposition efficiency. When two kinds of secondary flows are coexisting, the relative deposition efficiency is larger than that for the stationary case.

From dissipative particle dynamics scales to physical scales: a coarse-graining study for water flow in microchannel

Abstract: In the present work, dissipative particle dynamics (DPD) simulation of simple flows is studied based on coarse-graining parameter. Reference scales of DPD are expressed in terms of physical units and DPD parameters and equations are expressed in terms of Reynolds number and apparent Peclet number. DPD parameters for a given coarse-graining are calculated by matching the density and viscosity of water and Reynolds number of the flow. The formulation is applied to water flow in microchannels of height 5 and 10 μm and tested for a wide range of coarse-graining parameter varying from 107 to 109. The results are in a good agreement with the continuum formulation and simulated the correct hydrodynamics of water flow in microchannels. By inspecting the microscopic detail of the interaction between the DPD particles, it is found that diffusivity is low for high coarse-graining parameter, which results in higher values of Schmidt number. Parameters are tested within the continuum assumption. It is shown that correct Schmidt number can be achieved using small coarse-graining parameter. Also, it is observed that low diffusivity or high Schmidt number does not affect the hydrodynamics of water.

Thermal Radiation Effects on Heat and Mass Transfer over an Unsteady Stretching Surface

Abstract: The unsteady heat, mass, and fluid transfer over a horizontal stretching sheet has been numerically investigated. Using a similarity transformation the governing time-dependent boundary layer equations for the momentum, heat, and mass transfer were reduced to a sets of ordinary differential equations. These set of ordinary differential equations were then solved using the Chebyshev pseudo-spectral collocation method, and a parametric analysis was carried out. The study observed, among other observations that the local Sherwood number increases as the values of the stretching parameter 𝐴 and the Schmidt number 𝑆𝑐 increase. Also the fluid temperature was found to be significantly reduced by increases in the values of the Prandtl number 𝑃𝑟, the unsteadiness parameter 𝐴, and the radiation parameter 𝑅. The velocity and concentration profiles were found to be reduced by increasing values of the unsteadiness parameter 𝐴.

Oscillatory chemically-reacting mhd free convection heat and mass transfer in a porous medium with soret and dufour effects: finite element modeling

Abstract: The effects of thermo-diffusion (Soret effect) and diffuso-thermal gradients (Dufour effect) on the unsteady incompressible magneto-hydrodynamic (MHD) free convection flow with mass transfer past a semi-infinite vertical plate in a Darcian porous medium in the presence of significant thermal radiation, first order homogenous chemical reaction and viscous heating are analyzed. The governing differential equations are non-dimensionalized using a similarity transformation rendering a system of coupled, nonlinear partial differential equations which are solved numerically using the robust, extensively-validated finite element method. Dimensionless velocity ( U) is decreased with increasing magnetic parameter (M). An increase in Eckert number ( Ec ) causes greater mechanical energy to be dissipated as thermal energy and enhances fluid temperatures ( θ). An increase in chemical reaction parameter ( γ) increases velocity ( U), temperature ( θ) and also concentration value ( φ). Temperatures ( θ) are elevated substantially with decreasing Soret number ( Sr ) and simultaneous increasing Dufour number (Du ). Concentration values ( φ) are conversely enhanced with increasing Soret number ( Sr ) and a concurrent decrease in Dufour number ( Du ). Both temperature and velocity are suppressed with a rise in heat absorption parameter ( Φ ); On the other hand an increase in thermal radiation absorption parameter ( Q1) generates an increase in both velocity and temperature fields. Increasing Schmidt number (Sc) is found to cause a decrease in both temperature and concentration profiles. Finally, the numerical values of local skin friction, local rate of heat transfer parameter and local mass transfer parameter are also presented in tabular form. The present problem has significant applications in chemical engineering materials processing, solar porous wafer absorber systems and metallurgy.

Measurements of molecular mixing in a high-Schmidt-number Rayleigh-Taylor mixing layer

Abstract: Molecular mixing measurements are reported for a high-Schmidt-number (Sc ~ 103), small-Atwood-number (A ≈ 7.5 × 10−4) buoyancy-driven turbulent Rayleigh–Taylor (RT) mixing layer in a water channel facility. Salt was added to the top water 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 coloured 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 concentrations) can be combined to obtain a mathematical relationship between the coloured 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 probe resolution constraints. The dependence of molecular mixing on the Schmidt and Reynolds numbers is examined by comparing the current Sc ~ 103 measurements with previous Sc = 0.7 gas-phase and Pr = 7 (where Pr is the Prandtl number) liquid-phase measurements. This comparison indicates that the Schmidt number has a large effect on the quantity of mixed fluid at small Reynolds numbers Reh < 103. At larger Reynolds numbers, corresponding to later times in this experiment, 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 RT instability-induced mixing are discussed.

Numerical study of chemically reactive buoyancy-driven heat and mass transfer across a horizontal cylinder in a high-porosity non-Darcian regime

Abstract: We investigate the free convection boundary layer flow and heat and mass transfer across an isothermal cylinder embedded in an isotropic, homogenous, saturated porous regime with a first-order chemical reaction in the diffusing species. A Darcy-Forchheimer drag force model is implemented to simulate porous impedance effects in high-porosity media, which are encountered in various industrial and geophysical applications. The partial differential conservation equations are nondimensionalized and solved using a network simulation methodology. The effects of Darcy number, Forchheimer number, Schmidt number, and reaction parameter on dimensionless velocity, temperature, and species concentration distributions are studied in detail for the case of water of relevance to geohydraulic flows. Computations are also provided for the variation of local Nusselt number and local Sherwood number with various thermophysical parameters. Concentration is found to decrease continuously with distance into the boundary layer (y-coordinate) with an increase in chemical reaction parameter; values are markedly higher for the non-Darcian case than for the Darcian case. Temperatures are however increased by an increase in reaction parameter. Applications of the study include electrolysis processes, chemical filtration treatment systems, natural convection from buried waste canisters in geomaterials, geothermal systems, etc.

NSM analysis of time-dependent nonlinear buoyancy-driven double-diffusive radiative convection flow in non-Darcy geological porous media

Abstract: A network numerical simulator is developed and described to simulate the transient, nonlinear buoyancy-driven double diffusive heat and mass transfer of a viscous, incompressible, gray, absorbing–emitting fluid flowing past an impulsively started moving vertical plate adjacent to a non-Darcian geological porous regime. The governing boundary-layer equations are formulated in an (X *, Y *, t *) coordinate system with appropriate boundary conditions. An algebraic diffusion approximation is used to simplify the radiation heat transfer contribution. The non-dimensionalized transport equations are solved in an (X, Y, t) coordinate system using the network simulation model (NSM) and the computer code, Pspice. A detailed discussion of the network design is provided. The effects of Prandtl number, radiation–conduction parameter (Stark number), thermal Grashof number, species Grashof number, Schmidt number, Darcy number and Forchheimer number on the transient dimensionless velocities (U, V), non-dimensional temperature (T) and dimensionless concentration function (C) are illustrated graphically. Additionally, we have computed plots of U, V, T, C versus time and average Nusselt number and Sherwood number versus X, Y coordinate, for various thermophysical parameters. The model finds applications in geological contamination, geothermal energy systems and radioactive waste-repository near-field thermo-geofluid mechanics.

Prediction of mass transfer coefficients in a pulsed packed extraction column using effective diffusivity

Abstract: The volumetric overall mass transfer coefficients have been measured in a pulsed packed extraction column using diffusion model for two different liquid-liquid systems. The effects of operational variables such as pulsation intensity and dispersed and continuous phase flow rates on volumetric overall mass transfer coefficients have been investigated. Effective diffusivity is substituted for molecular diffusivity in the Grober equation for prediction of dispersed phase overall mass transfer coefficients. The enhancement factor is determined experimentally and therefrom an empirical correlation is derived for prediction of effective diffusivity as a function of Reynolds number, Schmidt number and viscosity ratio. Good agreement between prediction and experiments was found for all operating conditions that were investigated.

Hybrid Reynolds-Averaged/Large-Eddy Simulations of a Co-Axial Supersonic Free-Jet Experiment

Abstract: Reynolds-averaged and hybrid Reynolds-averaged/large-eddy simulations have been applied to a supersonic coaxial jet flow experiment. The experiment was designed to study compressible mixing flow phenomenon under conditions that are representative of those encountered in scramjet combustors. The experiment utilized either helium or argon as the inner jet nozzle fluid, and the outer jet nozzle fluid consisted of laboratory air. The inner and outer nozzles were designed and operated to produce nearly pressure-matched Mach 1.8 flow conditions at the jet exit. The purpose of the computational effort was to assess the state-of-the-art for each modeling approach, and to use the hybrid Reynolds-averaged/large-eddy simulations to gather insight into the deficiencies of the Reynolds-averaged closure models. The Reynolds-averaged simulations displayed a strong sensitivity to choice of turbulent Schmidt number. The initial value chosen for this parameter resulted in an over-prediction of the mixing layer spreading rate for the helium case, but the opposite trend was observed when argon was used as the injectant. A larger turbulent Schmidt number greatly improved the comparison of the results with measurements for the helium simulations, but variations in the Schmidt number did not improve the argon comparisons. The hybrid Reynolds-averaged/large-eddy simulations also over-predicted the mixing layer spreading rate for the helium case, while under-predicting the rate of mixing when argon was used as the injectant. The primary reason conjectured for the discrepancy between the hybrid simulation results and the measurements centered around issues related to the transition from a Reynolds-averaged state to one with resolved turbulent content. Improvements to the inflow conditions were suggested as a remedy to this dilemma. Second-order turbulence statistics were also compared to their modeled Reynolds-averaged counterparts to evaluate the effectiveness of common turbulence closure assumptions.

Schmidt-number effects on the flow past a sphere moving vertically in a stratified diffusive fluid

Abstract: The flow generated by a sphere moving vertically in a uniformly stratified fluid is investigated numerically for typical Schmidt numbers (or Prandtl numbers) which would be usually realized. For a high Schmidt number of Sc=700 typical to salt stratification, strong vertical round jet is formed in the lee of the sphere as has been demonstrated previously. On the other hand, with larger molecular diffusion typical to the heat conductivity in the water (Sc=7) and that in the air (Sc=0.7), the jet becomes much broader and the vertical velocity significantly decreases. This shows that the formation of the vertical jet is controlled by the diffusion processes of stratifying agents. Indeed, the thickness of the diffusive boundary layer along the obstacle surface determines the radius of the jet which becomes broader with larger molecular diffusion. The results demonstrate that a strong vertical jet is most likely generated in the high Schmidt-number fluid such as the sea water, suggesting that this phenomenon would be most intimately related to the phenomena in the ocean, such as the vertical movement of zooplanktons and buoys used for the ocean observation.

Turbulent heat and mass transfer over a rotating disk for the Prandtl or Schmidt numbers much larger than unity: an integral method

Abstract: Turbulent heat and mass transfer of a rotating disk for Prandtl and Schmidt numbers much larger than unity was modeled using an integral method validated against empirical equations of different authors for Sherwood numbers. As shown, decrease in relative thickness of thermal/diffusion boundary layers with increasing local radii entails additional increase of the exponent at the Reynolds number in expressions for Nusselt and Sherwood numbers in comparison with air flows.