Showing papers on "Schmidt number published in 1970"

Relation of turbulent mass transfer to a wall at high Schmidt numbers to the velocity field

Abstract: Turbulent mass transfer to a wall at high Schmidt numbers is controlled by the velocity field within the viscous sublayer. Measurements have been obtained of the root-mean-square fluctuating mass transfer coefficient and the frequency spectrum of the fluctuating mass transfer coefficient for a Schmidt number of about 2300. From an order-of-magnitude analysis it is concluded that flow fluctuations in the direction of mean flow have little effect on the mass transfer fluctuations. A comparison of the mass transfer spectrum with the spectrum of the component of the velocity gradient in the transverse direction sz reveals that the high-frequency portion of the sz spectrum is not effective in transferring mass. Approximate relations between the mass transfer spectrum and the sz spectrum are developed for high frequencies and for low frequencies.

Simultaneous heat and mass transfer in free convection boundary layers

Abstract: Expressions are derived for the heat and mass transfer coefficients for laminar free convection driven by simultaneous differences in temperature and composition for the asymptotic cases of equal Schmidt and Prandtl numbers approaching zero, equal Schmidt and Prandtl numbers approaching infinity, Schmidt number approaching infinity and Prandtl number approaching zero, and Schmidt number larger than Prandtl number and Prandtl number approaching infinity. The results are applicable for horizontal cylinders or vertical axisymmetric bodies with arbitrary body contours insofar as the approximations of boundary-layer theory are valid. The results compare favorably with existing solutions and experimental results for particular conditions.

Chemical reaction in a turbulent flow field with uniform velocity gradient

Abstract: A simplified statistical theory is developed which describes the chemically reacting, turbulent shear flows in a tractable manner. This theory, which is based on the concept of the generalized Brownian motion, instead of Navier‐Stokes equation, is completely self‐containing provided that the molecular Schmidt number is of order one and that the local turbulence Reynolds number is sufficiently large. The latter requirement restricts the theory to the flow region outside of the laminar sublayers. The homologous flow and concentration fields are first analyzed for the chemically frozen case. From the analyses, the relationships between the mean velocity and concentration gradients, and the Reynolds stress, turbulence energy, turbulent transport of chemical species, and the mean square fluctuation of the species concentration are established. Comparison of the present results with the available experimental data is made, which shows a satisfactory agreement. The nonequilibrium chemical reaction is then analyzed and is found to create an inhomogeneity in the concentration field which, among other things, causes the mean square fluctuation to vary nonuniformly with respect to the Damkohler number and the flow region.

Distribution of a trace element in a boundary layer with mass transfer

Abstract: A theory is presented for the downstream distribution of a tracer injected into a boundary layer of a flat plate or cone with self-similar mass transfer. The tracer, which is injected over a finite length of the surface, is assumed to be chemically inert. Its behavior is controlled by a frozen diffusion equation. The assumption of constant density-viscosity product, and unit Schmidt number results in a linear partial differential equation for the seed mass fraction. This is solved analytically in series form by separation of variables, and numerically by a finite difference technique. It is shown that far downstream of the tracer injection region the analytical results reduce to a simple form; namely, the mass concentration profile is proportional to the local shear even in the presence of mass transfer. However, near the tracer injection region, even the first ten terms are insufficient to yield profiles comparable to those produced by the numerical integration scheme.

Free convection from a horizontal surface with mass diffusion

Abstract: The flow due to free convection and mass diffusion of the steady laminar flow of an incompressible fluid on upper side of a hot horizontal surface has been studied. Similar solutions have been obtained for the boundary layer equations under certain restricting assumptions. The effects of mass diffusion on the free convection flow field have been analyzed. Numerical solutions have been obtained for some particular cases of gases with Prandtl number and Schmidt number close to unity.

The Enhancement of Turbulent Diffusion in a Parallel-Wall Duct

Abstract: Experiments were carried out on the diffusion of nitr ous oxide from a line source in a turbulent flow in a parallel-wall duct over a range of Reynolds number 104to 105. Eddy diffusivity was derived from the concentration profiles in th e lateral direction, with and without obstructions of various shapes in the centre of the duct. Without obstructions the velocity profiles and friction factors agreed well with previous measurements and, for the central portion where the turbulence appears homogeneous, the turbulent Schmidt number was found to be 0·64. Turbulence enhancement caused by obstructions was mainly dependent on the blockage ratio and the shape of the trailing edge.

Similarity Analysis For Laminar Natural Convection Flow

Abstract: This paper deals with a theoretical study of laminar natural convection over a semi-infinite vertical plate. It is assumed that the plate is maintained at a given concentration in some chemical species and convection is induced by diffusion into and chemical reaction with the ambient fluid. The fluid is assumed to be viscous and the induced fluid flow, steady. A similarly transform to one variable is possible in the absence of chemical reaction. However, when the chemical reaction takes place between the plate and the ambient fluid, a similarity solution is not available. Thus to obtain an analytical solution of the problem, perturbation expansions about an additional similarity variable which is dependent on the reaction rate must be employed. It has been found that the Schmidt number Sc and the reaction order n are the two fundamental parameters of the problem.