Showing papers on "Schmidt number published in 1993"

Linear eddy simulations of mixing in a homogeneous turbulent flow

Abstract: The linear eddy mixing model is used to predict the evolution of a decaying scalar field in statistically steady homogeneous turbulent flow over a wide range of Reynolds and Schmidt numbers. Model results at low Reynolds number and order unity Schmidt number are shown to be in good overall agreement with direct numerical simulations. Results at higher Schmidt and Reynolds numbers reproduce conventional scaling properties of the scalar statistics. Predictions of Schmidt number and Reynolds number sensitivity of the evolution of the scalar concentration probability density function are presented and interpreted.

Probability distributions of concentration fluctuations of a weakly diffusive passive plume in a turbulent boundary layer

Abstract: Results are presented from an experimental investigation of turbulent dispersion of a saline plume of large Schmidt number (Sc=830) in a turbulent boundary-layer shear flow simulated in a laboratory water channel The dispersion measurements are obtained in a neutrally buoyant plume from an elevated point source over a range of downstream distances, where both plume meandering and fine-structure variations in the instantaneous plume are important High-resolution measurements of the scalar fluctuations in the plume are made with a rake of conductivity probes from which probability distributions of concentration at various points throught the plume are extracted from the time series

Depostition of submicron aerosol particles in turbulent and transitional flow

Abstract: Brownian and turbulent diffusive deposition of submicron aerosol particles from pipe flow is studied experimentally and theoretically. A theoretical model for evaluating the turbulent diffusive deposition is presented in which a turbulent flow in a circular pipe is numerically calculated based on the k-[epsilon] turbulent flow model and deposition velocities are derived by solving the convection-diffusion equation. Deposition velocities of monodisperse aerosol particles, 0.01-0.04 [mu]m in diameter, are obtained experimentally by measuring the decrease in the particle number concentration of an aerosol at two cross-sections of a circular test pipe through which the aerosol is flowing. The deposition velocities obtained when Re is larger than about 3,000 agree well with those predicted by the present analysis which are proportional to the 0.92nd power of Reynolds number and the 0.33rd power of Schmidt number. The particle deposition rates are measured when 1,000 [approx lt]Re[approx lt]2,000 suggest a transitional state for particle deposition which cannot be explained by the present analysis nor by the laminar pipe flow deposition theory.

Unsteady three-dimensional boundary layer flow due to a stretching surface

Abstract: In this numerical study, the unsteady laminar incompressible boundary-layer flow over a continuously stretching surface has been investigated when the velocity of the stretching surface varies arbitrarily with time. Both the nodal and the saddle point regions of flow have been considered for the analysis. Also, constant wall temperature/concentration and constant heat/mass flux at the stretching surface have been taken into account. The quasilinearisation method with an implicit finite-difference scheme is used in the nodal point region (0≦c≦1) wherec denotes the stretching ratio. This method fails in the saddle point region (−1≦c≦0) due to the occurrence of reverse flow in they-component of velocity. In order to overcome this difficulty, the method of parametric differentiation with an implicit finite-difference scheme is used, where the values atc=0 are taken as starting values. Results have been obtained for the stretching velocities which are accelerating and decelerating with time. Results show that the skin friction, the heat transfer and the mass transfer parameters respond significantly to the time dependent stretching velocities. Suction (A>0) is found to be an important parameter in obtaining convergent solution in the case of the saddle point region of flow. The Prandtl number and the Schmidt number strongly affect the heat and mass transfer of the diffusing species, respectively.

Power Law Fluids in a Circular Curved Tube. Part II. Axial Laminar Dispersion

Abstract: The application of Taylor's dispersion theory to non-Newtonian laminar dispersion in a circular curved pipe wrapped in a coil is discussed. An analytical expression for the dispersion coefficient in laminar flow under two conditions, viz. Dean's constraint and relaxing Dean's constraint, is discussed along with system parameters. The present expression of dispersion coefficient under two different conditions reduces to the reported results in the literature for Newtonian fluids. The effect of power law index in combination with other process parameters on dispersion coefficient is studied. It is found that the dispersion coefficient decreases with decrease in power law index, and that it decreases with increase in Reynolds number and Schmidt number at a fixed curvature ratio.

Finite-Rate Diffusion-Controlled Reaction in a Vortex

Abstract: The influence of a vortex on a gaseous diffusion reaction is examined. The vortex is taken to be two dimensional, and the species are initially assumed to occupy adjacent half spaces. In the flame-sheet limit, thermal expansion and the effects of variable diffusion are taken into account. A global similarity solution exists for this problem, and a simple expression for the solution is determined in the asymptotic limit of large Schmidt number. The problem is also analyzed for finite-rate chemistry, appropriate for an isothermal, bimolecular reaction. The problem depends upon three parameters, Reynolds number, Schmidt number and the equivalence ratio, with the Damkohler number equal to the dimensionless time. The structure of the reaction region normal to the flame front is examined as a function of time. The evolution of the reaction to a state relation, dependent only upon the mixture-fraction variable, is demonstrated as the Damkohler number becomes large.

Eddy Diffusivity Based Comparisons of Turbulent Prandtl Number for Boundary Layer and Free Jet Flows With Reference to Fluids of Very Low Prandtl Number.

Abstract: It is shown that turbulent Prandtl numbers for turbulent boundary layer and jet flows correlate well if compared on the basis of eddy diffusivity. Experimental data for liquid sodium (Pr= 0.0058) lead to a universal expression relating turbulent Prandtl number to eddy diffusivity of heat with the same expression applying to boundary layer and jet flows. This suggests that the length and velocity scale dependence of the turbulent Prandtl number is associated predominantly with the eddy diffusivity of momentum. Since turbulent flow codes generally include eddy diffusivity of momentum calculations, simple and accurate estimates of eddy diffusivity of heat are possible without reliance on a variety of turbulent Prandtl number functional relationships for prediction of the temperature field. Available results also indicate that turbulent Prandtl number can be set at 0.9-1.0 irrespective of molecular Prandtl number, provided that ϵ/v > 3 Pr and the structures of the mean temperature gradient and mean shear are similar.

Transient heat and mass transfer in a natural circulation loop

Abstract: Comprehensive work has been performed by theoretical and numerical methods in order to study the steady state, transient and stability characteristics of a double diffusive natural circulation loop. It was found that the behavior of the flow in the system depends on the initial conditions and on the location of the state in the seven-parameter space of the thermal and saline Rayleigh numbers,Ra T ,Ra S , the modified Prandtl and Schmidt numbers,Pr, Sc, the dimensionless heat and mass transfer coefficients,H T ,H S , and the “aspect ratio” (between the height and width) of the loop, γ. Numerical results are presented here, showing the flow in each of the five regions formed in the stability chart. The steady state solutions include convection (constant velocity flow), conduction (no-flow) and periodic with constant amplitude and frequency. Two main new results were obtained: long term periodic oscillations where the amplitude is not symmetric around the conduction solution, and an overshoot of the velocity in transients before reaching the stable convection solutions. In the monotonic instability region of the conduction solution, convection solutions (constant velocity flow) develop, and in the global stability region the flow decays to the conduction solution (no flow), regardless of the initial conditions.

Desorption from concentrated polymer solutions in good and poor solvents

Abstract: The objective of the study was to investigate the effects of the nature of solvent and polymer concentration on the mass-transfer coefficients in desorption of solvents and to develop a correlation to predict them. Desorption was experimentally studied in a Lewis cell with concentrated binary solutions of polymer in good and poor solvents. The range of parameters covered are polymer weight fraction between 0.25 and 0.6, Reynolds number between 3 and 100; Schmidt number between 1.4 X lo6 and 2.5 X lo8, and Sherwood number between 3.5 X lo2 and 1.2 X lo4. Desorption from moderately concentrated solutions (polymer weight fraction -0.25) is gas-phase controlled. Studies with more concentrated solutions showed that the effects of solvent and concentration were such that corrections due to concentration-dependent diffusivity and viscosity as well as high flux had to be applied to the mass-transfer coefficients before they could be correlated.

The effect of gravitational modulation on convection in vertical Bridgman growth

Abstract: During vertical directional solidification of a binary alloy at constant velocity, buoyancy-driven solutal convection may occur due to the solute gradient associated with the solidification process. This problem is further complicated if time-periodic forcing is considered, which is relevant to materials processing in a microgravity environment or as a means of dynamic control of flow instabilities. The effect of time-periodic modulation is studied by introducing a gravitational acceleration which is a sinusoidal function of time. The onset of solutal convection is treated by a stability analysis of the linearized governing equations and boundary conditions. Solutions are obtained numerically employing two distinct computational implementations of Floquet theory. Results are presented for materials with large Schmidt number, and an analysis for large frequency and large Schmidt number yields a more complete description of the behavior in this relevant limit.