Showing papers on "Schmidt number published in 1968"

Compressible Turbulent Magnetohydrodynamic Boundary Layers

Abstract: A closed analytical model for compressible magnetohydrodynamic boundary layers is formulated by using transport equations for the turbulent fluctuations of species mass density, velocity, and temperature, and thus avoiding a priori relations between turbulent fluxes and mean flow quantities. The equations for both the mean and the fluctuating motion are simplified according to the boundary‐layer approximation, and closure of the system is achieved by the introduction of “universal turbulence structure parameters” that only relate turbulent correlations among themselves. This model accounts for convection and diffusion of turbulent fluxes as well as for the effect of turbulence suppression by applied magnetic fields. It is shown that if convection, diffusion, and electromagnetic effects were omitted in the equations of fluctuating motion, the latter would reduce to algebraic forms defining the concepts of mixing length, turbulent Prandtl number, and turbulent Schmidt number in terms of turbulence structure parameters.

Dynamically Similar Motion of Two Miscible Constituents in Porous Mediums

Abstract: This study concerns the simultaneous motion of pairs of miscible constituents in porous mediums. Geometrically similar porous mediums are considered, and conditions for dynamic similarity are sought. It is found that in general the constituent pairs must have the same Schmidt number. Fortunately, this restriction does not apply if the inertial terms in the Navier-Stokes equations are negligible. Two special cases are considered: (1) steady, creeping mean motion, and (2) oscillatory mean motion. It is pointed out that the dispersion arising in the first case can often be described macroscopically in terms of a dispersivity, and it is shown that such a dispersivity must be a unique function of the microscopic Peclet number. Some theoretical and experimental examples of this dependency are discussed. In the second case, the dispersion at appropriately scaled positions and times will also depend upon the dimensionless amplitude of the displacement.

Decompositional burning of a droplet in a small Peclet number flow.

Abstract: Asymptotic results for chemical-reaction and forced-convection effects on the quasi-steady adiabatic vaporization of a rigid uniform spherical droplet immersed in an unbounded expanse of gas are obtained by inner-and-outer expansions. The zeroth-order approximation is the radially symmetric solution yielding the classical logarithmic mass transfer rate. The perturbation introduces the corrections arising from 1) first-order decompositional burning for reaction rates small relative to flow rates (small first Damkohler similarity parameter); and 2) the possible wake-generating role of a slight relative flow past the droplet (small Peclet number). For tractable closed-form solution the flow is taken as incompressible with constant properties; the Lewis number is restricted to unity in the perturbational analysis. The first perturbation to the Sherwood number (normalized mass transfer rate) is found to be independent of Schmidt number, but dependent on the reaction rate. The first modification to the Stokes drag (owing to mass transfer) is found to be independent of the reaction rate, but dependent on the Schmidt number. For indefinitely large Schmidt number the Stokes drag is always increased because of mass transfer, and streamlines display no wake; for orderunity Schmidt number entirely different results are anticipated.

An experimental study of some base injection techniques and the effect of large pressure gradients on turbulent diffusion processes.

Abstract: : Results of an experimental study of some base injection techniques and the effect of large pressure gradients on turbulent diffusion processes in an axisymmetric flow past a slender body at Mach number 3.92 and Reynolds number 3.85 x 10 to the 7th power ft. are presented. Base injection techniques were studied using gaseous hydrogen, helium, nitrogen, and argon as injectants. In each case, it is noticed that the base pressure reaches its peak value much faster (i.e., for a smaller injection rate) with a low molecular weight gas and that a larger increase in base pressure is accomplished with the lighter gas. Some schemes show very irregular behavior in the variation of base pressure with injection. In the study of diffusion processes it is found that the mass diffusion process is not affected at all by the pressure gradients produced in the flow field and that mass, momentum, and thermal diffusion are not the same. This leads to the conclusion that assumptions of Lewis number, Prandtl number, and Schmidt number equal to unity are not correct, especially for problems with large pressure gradients. (Author)

Laminar Diffusion Flame in the Core of a Vortex

Abstract: A steady laminar diffusion flame burning in the core of a vortex is studied. Solutions of the full Navier‐Stokes equation and the mass‐transfer equation are obtained to study the effect of the swirling motion on the flame and its flow field for different values of the Schmidt number. The flow conditions depend on two parameters: Γ∞, the circulation of the vortex and Re, the Reynolds number based on the velocity at the axis of symmetry. The velocity distribution is strongly affected by the circulation. As Γ∞ increases when Re remains constant the width of the jet flow in the core region also increases. However, the mass concentration distribution and the position of the flame depend principally on Re, and on Γ∞ only slightly.