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Joseph Majdalani Sjoerd W. Rienstra 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(2):289-308
The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators
and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe
the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum
and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid,
rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three
possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying
the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex.
This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression
that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general
and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method
of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions
that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach
to other complex fluid motions that are easier to capture using spherical coordinates. 相似文献
44.
Reactions of the hydrated electron, H atoms, 2-propanol, and methanol radicals with the TiO2 nano-particles have been studied either directly or by competition kinetics. The radicals were produced by radiolysis of 2-propanol, t-butanol, or methanol aqueous solutions in acid pH's. The reactions involve electron injection to the conduction band. As expected, the t-butanol radical is inert towards TiO2 under our conditions, while the other reducing radicals react with TiO2. The reactivity decreases in the order: eaq−>H>CH3COHCH3>CH2OH. Two TiO2 nanocrystallite sizes, with average diameters of 1.0 and 4.7 nm were compared. For equal concentrations (in terms of TiO2 molecules), the rate of electron injection shows relatively little dependency on particle size. The rates of interfacial electron transfer and transfer coefficient are also reported. 相似文献
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Joseph Barback 《Mathematical Logic Quarterly》1997,43(1):83-91
In this paper we present a collection of results related to the comparability of summands property of regressive isols. We show that if an infinite regressive isol has comparability of summands, then every predecessor of the isol has a weak comparability of summands property. Recently R. Downey proved that there exist regressive isols that are both hyper-torre and cosimple. There is a surprisingly close connection between non-recursive recursively enumerable sets and particular retraceable sets and regressive isols. We apply the theorem of Downey to show that among the regressive isols that are related to recursively enumerable sets there are some with a new property. 相似文献
47.
This paper presents a few novel results, and collects together what is known and conjectured about the branching graph of a polyhex. 相似文献
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