Effect Of Nonuniform Density Research Articles

Oscillations of differentially rotating and tidally distorted gaseous spheres : Effect of non-uniform density

The original Strum-Liouville type of equation is tuned suitably to study the pulsational properties of gaseous spheres of non-uniform densities from centre to surface, which are non-rotating, have solid body rotation or are differentially rotating as well as those which are varying by tidal effects. The eign-frequencies of radial oscillations have been computed numerically for certain polytropic stellar models of non-uniform densities. In order to analyse the effect of non-radial modes of oscillations, the linearised system of differential equations that govern non-radial modes of oscillations, have also been developed and solved for certain polytropic models. It has been observed that with the exception of purely radial oscillations, which are unstable only when γ<4/3 (γ is the ratio of molar specific heats), there also exist non-radial modes of oscillations. It is necessary to consider radial as well as non-radial nodes of oscillations in order to ascertain the stabilities of the existence of any assumed model.

Spatio-temporal stability analysis of linear arrays of 2D density stratified wakes and jets

This paper investigates the spatio-temporal stability characteristics of multiple shear flow elements (wakes or jets) with density stratification. While the stability of single jets or wakes has been considered extensively, many applications exist where these canonical flow fields are aligned in multi-element configurations. A fundamental question is the relationship between the stability characteristics of a single element and the larger system. More fundamentally, this question involves the interaction of multiple regions of vorticity concentration and how they modify a system’s absolute stability as well as the manner in which density gradients influence the way these different regions of concentrated vorticity interact. This study presents a generalization of Yu and Monkewitz’s analysis [“The effect of nonuniform density on the absolute instability of two-dimensional inertial jets and wakes,” Phys. Fluids A 2, 1175 (1990)] for multiple jets and wakes, explicitly considering n = 2, 3, 4, and infinity elements. The velocity and density base profiles are parameterized by the density ratio, S, velocity shear ratio, λ, and the wake spatial separation parameter, L/D. The results show that the maximum absolute growth rate (ω0,i) exhibits a non-monotonic dependence on L/D. In addition, the most absolutely unstable mode switches between system-sinuous and system-varicose as the spatial separation parameter is varied, in agreement with prior experiments [I. Peschard and P. Le Gal, “Coupled wakes of cylinders,” Phys. Rev. Lett. 77, 3122 (1996)]. This transition in symmetry, as well as the specific L/D value at which a given mode dominates, can be approximately predicted using the resonant wave interaction model from Juniper et al. [“The effect of confinement on the stability of two-dimensional shear flows,” J. Fluid Mech. 565, 171 (2006)]. Furthermore, there are two distinct L/D regimes: a “near-wake regime” (L/D &amp;lt; ∼3) and a “far-wake regime.” In the near-wake regime, the system stability is a function of the number of elements, n, while in the far-wake regime, it is only the element spacing, not the number of elements that influences ω0,i.

Kinetic theory of heterogeneous nucleation; effect of nonuniform density in the nuclei

The heterogenous nucleation of a liquid from a vapor in contact with a planar solid surface or a solid surface with cavities is examined on the basis of the kinetic theory of nucleation developed by Nowakowski and Ruckenstein [J. Phys. Chem. 96 (1992) 2313] which is extended to nonuniform fluid density distribution (FDD) in the nucleus. The latter is determined under the assumption that at each moment the FDD in the nucleus is provided by the density functional theory (DFT) for a nanodrop. As a result of this assumption, the theory does not require to consider that the contact angle which the nucleus makes with the solid surface and the density of the nucleus are independent parameters since they are provided by the DFT. For all considered cases, the nucleation rate is higher in the cavities than on a planar surface and increases with increasing strength of the fluid-solid interactions and decreasing cavity radius. The difference is small at high supersaturations (small critical nuclei), but becomes larger at low supersaturations when the critical nucleus has a size comparable with the size of the cavity. The nonuniformity of the FDD in the nucleus decreases the nucleation rate when compared to the uniform FDD.

Ideal and resistive edge stability calculations with M3D-C1

Growth rates of edge localized modes for various benchmark equilibria, including a diverted equilibrium, are calculated using the nonideal fluid code M3D-C1. Growth rates calculated by M3D-C1 in the ideal limit are found to agree with those calculated by ideal magnetohydrodynamics codes. The effects of nonuniform density and resistivity profiles are explored, as well as the sensitivity of growth rates to the position of the ideal vacuum-plasma interface. Growth rates of the diverted equilibrium are found to be particularly sensitive to moving this interface inward from the separatrix, but less sensitive to extending the plasma region beyond the separatrix. The resistivity profile within the plasma is found not to affect growth rates significantly; however, growth rates may be greatly reduced by treating the outer region as a resistive plasma instead of an ideal vacuum. Indeed, it is found that for typical scrape-off layer (SOL) temperatures, the resistive SOL model behaves more like an ideal plasma than a vacuum.

The effects of non-uniform density and stagnation pressure on the breakdown characteristics of a vortex

This paper is concerned with the extension of the theory of vortex breakdown, that was presented in previous publications by the present author and others, to cases of non-uniform density and non-uniform stagnation pressure outside the vortex core. The effects of radial density and velocity variations play an essential role for the layout of modern low-emission burners for premixed combustion. Furthermore, these effects turn out to be important with respect to an improved understanding of the formation of zones of flow recirculation in tornado-like vortices. With the help of the extension of a variational principle for axisymmetric flow to the case of non-uniform density it is possible to discuss inviscid flows of non-uniform density and stagnation pressure in great generality. A numerical solution method is given for general axisymmetric vortex flows, including flows that undergo vortex breakdown. The influences of density and stagnation pressure variations on vortex breakdown are analyzed in detail, for the special case of a generalized Rankine vortex. It is found that a radially increasing density leads to a reduction of the swirl number at which vortex breakdown occurs, whereas a radially decreasing axial velocity component in the approach flow of a vortex breakdown bubble leads to a substantially enlarged bubble. Finally, a Richardson number criterion is proposed for the scaling of a vortex breakdown bubble in a tornado.

The effect of nonuniform density on the absolute instability of two-dimensional inertial jets and wakes

The boundary between absolute and convective (linear) instability of two-dimensional inertial jets and wakes is determined as a function of the ratio of jet/wake to ambient density, as well as the ratio of mixing layer thickness to jet/wake width, the velocity ratio, and the Reynolds number. For this, a viscous, heat-conducting ideal gas is taken as the fluid, a zero Mach number, no buoyancy and a parallel basic flow are assumed, and the density variation is achieved by specifying a mean temperature profile similar to the velocity profile. Considering both ‘‘varicose’’ and ‘‘sinuous’’ disturbances, results are obtained for the inviscid top-hat jet/wake bounded by two vortex sheets, the inviscid jet with continuous velocity and density profiles, and the viscous wake. For the latter, both constant and temperature-dependent viscosity are investigated. In all the cases it is found that low density of the high-speed fluid promotes absolute instability, while low density of the low-speed fluid has the opposite effect. By comparison with experiments it is shown that the present results provide useful information about the parameter range in which flow oscillations are self-excited.

Application of Sonic Moduli of Elasticity and Rigidity to Testing of Heavy Refractories

The application of A.S.T.M. C 215‐51 T (Tentative Method of Test for Fundamental Transverse Frequency of Concrete Specimens for Calculating Young's Modulus of Elasticity) to the nondestructive testing of 1‐ by 1‐ by 7‐in. laboratory fire‐clay specimens and standard 9‐in. fire‐clay and high‐alumina refractory brick is reviewed. Both room‐temperature measurements and hot sonic modulus of elasticity measurements to 1700°F. are analyzed. Sonic moduli of elasticity and rigidity are compared with modulus of rupture by a theory of measurements and statistical analysis. The limits of uncertainty of the average of modulus of rupture are shown to be a function of the degree of verification whereas in the case of both sonic moduli they are not. Limits of uncertainty of the average of sonic moduli data are usually of the same order as errors calculated from the precision of measurements. In the case of modulus of rupture of well‐vitrified clays, the uncertainty of the average is much greater than calculated error limits. Sonic moduli differentiate statistically between two samples of 60% alumina brick whereas modulus of rupture does not. If Poisson's ratio is assumed to be zero rather than the conventional one‐sixth, ratios of sonic modulus of elasticity to rigidity are shown to approximate the theoretical ratio more closely. Effects of nonuniform density to displace normal nodes are illustrated. Hot sonic modulus of elasticity is shown to reflect changes due to crystallographic inversions, deterioration of chemical bond in unfired brick, and development of sintered bond in unfired brick.