Various industrial applications require the use of common pipelines or tubing to simultaneously or sequentially deliver multiple types of liquids. Dependent upon the application, long pipelines or tubing can range from several meters to several kilometers in length, composed of significant horizontal and vertical sections. Axial mixing is an important aspect of such flows of liquids in succession from a safety and reliability point of view. It is anticipated that mixing is due to turbulence and buoyancy, with the latter as a result of density differences of the mixing fluids. This paper sets out a numerical simulation model based on computational fluid dynamics (CFD) to fundamentally understand the mixing behavior of two miscible fluids under actual industrial-project-specific conditions. To benchmark its accuracy, the simulation model is first verified with respect to its numerical parameters using a short, 10 m pipe. Subsequently, a 100 m horizontal pipe is modeled, and we show that these results can be used to extrapolate longer length pipes. Finally, the sensitivity of mixing with respect to the Reynolds and Richardson numbers (characterizing buoyancy) has been investigated.
In this paper, we show the regularity criteria for three-dimensional nematic liquid crystal flows. More precisely, we prove that the strong solution ( u, d) can be extended beyond T, provided ∇ u3 ∈ L s(0, T; L q( R3)), ∇ h d ∈ L α(0, T; L p( R3)), where s, q, α, p satisfy [Formula: see text] if [Formula: see text] or [Formula: see text] if [Formula: see text].
In this article, we consider the numerical method for solving the Schrödinger equations via Phragmén-Lindelöf inequalities under the order induced by a symmetric cone with the function involved being monotone. Based on the Phragmén-Lindelöf inequalities, the underlying system of inequalities is reformulated as a system of smooth equations, and a Schrödinger-type method is proposed to solve it iteratively so that a solution of the system of the Schrödinger equations is found. By means of the Schrödinger type inequalities, the algorithm is proved to be well defined and to be globally convergent under weak assumptions and locally quadratically convergent under suitable assumptions. Preliminary numerical results indicate that the algorithm is effective.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.