Showing papers on "Schmidt number published in 1973"

Finite amplitude sideways diffusive convection

Abstract: We consider the flow in a differentially heated vertical slot filled with a stably stratified solution. The stability of the flow driven by the differential heating is investigated in the limits of small but finite amplitude disturbances and very large solute Rayleigh number RS = gβ(∂Sa/∂z)D4/KSv. If the Schmidt number H = KT/KS is of order 1, the growth of an initial perturbation at the neutral point is balanced by horizontal advection of solute and heat, and a steady equilibration amplitude is attained. The Nusselt number is independent of all fluid properties and is directly proportional to the Rayleigh number excess e = (Ra – Rac)/Rac. If H is much greater than |RS|⅙, or if the disturbance wave-number is slightly less than the critical wavenumber, subcritical instabilities are possible. In particular a resonant instability is possible. These theoretical predictions are consistent with previous experimental results and with the laboratory results described in this paper. In the experiments we find that the mixing of the initial sugar gradient is accomplished by convection cells which undergo transitions to larger wavelengths. The breakdown of the interfaces between convection cells is described.

Analytical and experimental investigation of a turbulent mixing layer of different gases in a pressure gradient

Abstract: An analytical and experimental study has been made of the turbulent mixing layer in a pressure gradient. Theory predicts the possible existence of equilibrium flows, and this was confirmed experimentally for turbulent shear layers between streams of helium and nitrogen. The only case for which similarity is possible is for ρ_2U_2%2 = ρ_1U1^2, since then P_2(x) = P_1(x). These equilibrium flows are of the form U_1 ~ x^α and δ ~ x where α = u/U-1 dU_1/dx is a non-dimensional pressure gradient parameter. The experimental investigation was conducted in the facility designed by Brown to produce turbulent flows at pressures up to 10 atmospheres. The adjustable walls of the test section of the apparatus were modified in order to set the pressure gradient. Shadowgraphs of the mixing zone for α = 0 and α = - 0.. 18, at different Reynolds numbers, revealed a large scale structure noticeably different for each α. The similarity properties of the shear layer were established from mean profiles of total head and density. In addition, the rms density fluctuations were found to be self-preserving. From the mean profiles, the spreading rate, turbulent mass diffusion, Reynolds stress and Schmidt number distributions were calculated from the equations of motion. The experimental results show that the spreading rate for the adverse pressure gradient is 60% greater than for the α = 0 case. The maximum shearing stress is 70% larger and the maximum value of the turbulent mass diffusion is 20% larger than their α = 0 counterparts. The maximum rms density fluctuations are approximately O.2 in both flows. Surprisingly low values of turbulent Schmidt numbers were found; e.g. , at the dividing streamline Sc_t ~ 0.16 for α = 0 and Sc_t = 0.33 for α = -0.18.

Mass transfer to rotating cones

Abstract: The mass transfer of oxygen to a rotating cone has been measured in a quiescent fluid. Cones with vertex angles of 19.2°, 30°, 60°, 90°, 120° and 180° (disks) were used in both laminar and turbulent flow at a Schmidt number of 400. The laminar flow mass transfer data is in agreement with an equation derived for cones at high Schmidt numbers. The turbulent flow mass transfer data for cones with vertex angles greater than 19.2° is in agreement with the high Schmidt number expression of Deissler. The 19.2° cone angle, however, results in experimental values for the mass transfer which are greater than the predicted values. Lastly, the values of the Reynolds number for transition from laminar to turbulent flow, as determined directly from the mass transfer data, are in agreement with previous results.

Consecutive chemical reactions in a turbular reactor with turbulent flow

Abstract: Homogeneous consecutive chemical reactions in turbulent flow system is analyzed in this paper. Arbitrary chemical reaction order is considered. The governing nonlinear material balance equations are solved numerically on a digital computer. It is seen from the preliminary numerical results that high Reynolds and Schmidt numbers significantly increase both reaction velocities.

Transport to a Rotating Disk in Turbulent Flow at High Prandtl or Schmidt Number

Abstract: The eddy viscosity distribution near the surface of a rotating disk is determined from an analysis of the basic conservation equations. The results are applied to the high Schmidt number problem and good agreement is obtained with experimental data for the mass flux.

Eddy diffusion coefficients in the stable atmospheric surface layer

Abstract: The dependence of the ratio of the eddy heat diffusivity to the eddy momentum diffusivity on the Richardson number is examined in terms of the relationship between the Deacon numbers of paired wind and temperature profiles in the Antarctic surface layer. It is found empirically that for Ri? +0.1, the diffusivity ratio varies as the minus two-thirds power of the Richardson number, while for 0 < Ri < + 0.1 no clear empirical relationship exists. It is further shown that the representation of wind and temperature profiles by specific analytical expressions may involve implicit assumptions about the diffusivity ratio, and requires specific relationships between the wind and temperature profile Deacon numbers. Such relationships are not observed in this empirical study. DOI: 10.1111/j.2153-3490.1973.tb00620.x