Vortex Interaction in a Ducted Flow

The objective of this study is to describe the structure of pipe flow by considering it as a superposition of many axisymmetric vortex rings. In knowing the unsteady gross feature of pipe flow, the investigation on vortex interactions is important. As a first step to the goal, we investigate the nonlinear interaction among vortex rings whose number is three at most. The interaction among vortex rings of equal circulation is here investigated. Momentum and energy conservation of the present vortex ring system are also discussed to know a better understanding of the perturbed pipe flow. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper, we investigate the asymptotic validity of boundary-layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl’s boundary-layer solution to Navier-Stokes solutions with different Reynolds numbers. We show how Prandtl’s solution develops a finite-time separation singularity. On the other hand, the Navier-Stokes solutions are characterized by the presence of two distinct types of viscous-inviscid interactions that can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover, we apply the complex singularity-tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective.     

Uniform Flow Past an Axially Uniform Viscous Vortex

It is believed that the flow past a tornado causes the formation of smaller vortices which produce the “suction spots” observed along the path of destruction. Here we develop a greatly simplified mathematical model to investigate this phenomenon. An axially uniform vortex is developed by visualizing a circular tube with uniform surface suction of fluid possessing circulation at infinity. This vortex is then perturbed by a uniform flow past it. An inner asymptotic expansion of an E^1/3 radial boundary layer is matched to an outer expansion to obtain a solution. The results show that a stagnation point developing into a secondary vortex is formed in a free shear layer at critical flow conditions. However, it is difficult to apply our results quantitatively because of the difficulty in comparing the axially uniform vortex with a real tornado vortex.     

Turbulent Flow with Embedded Vortical Structures Induced by Vortex Generators in a Cascade

Presented work is the next step after several experimental examinations of vortex generator influence on a flow separation occurring on a model of the NACA 63A421 airfoil with deflected simple flap. In this stage of research the vortices produced by vortex generators (VGs) were studied using Particle Image Velocimetry technique (PIV) and numerical simulations. Vane type VGs with two spacings among VGs pairs in straight channel with turbulent flow were tested. The average velocity flow field, peak of vorticity and circulation decay downstream of VGs were evaluated. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flow over a Wing with an Attached Free Vortex

Exact solutions are constructed for two-dimensional inviscid potential flow over a wing with a free line vortex standing over the wing. The loci of positions of the free vortex are found, and the lift is calculated. It is found that the lift on the wing can be significantly increased by the free vortex.     

Dynamic Mode Decomposition for Swirling Jet Flow Undergoing Vortex Breakdown

Swirling jets undergoing vortex breakdown occur in many technical applications, e.g. vortex burners, turbines and jet engines. At the stage of vortex breakdown the flow is dominated by a conical shear layer and a large recirculation zone around the jet axis. We performed Large-Eddy Simulations (LES) of compressible swirling jet flows at Re=5000, Ma=0.6 in the high swirl number regime (S=1). A nozzle is included in our computational setup to account for more realistic inflow conditions. The obtained velocity fields are analyzed by means of temporal and spatial dynamic mode decomposition (DMD) to get further insight into the characteristic structures dominating the flow. We present eigenvalue spectra for the case under consideration and discuss the stability behaviour in time and space. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sublattices Generated by Polars

In an algebraic frame L, the complete sublattice CP(L) generated by the polars of L is studied, in comparison with FP(L), the subframe generated by the polars. It is shown, by an example from the theory of ?-groups, that these are distinct, in general. The relationship between FP(L), CP(L), and other established constructs, closely related to the boolean algebra of polars, is also studied.     

Large Eddy Simulations of Swirling Nozzle-Jet Flow Undergoing Vortex Breakdown

We developed a numerical setup to simulate swirling jet flow undergoing vortex breakdown. Our simulation code CONCYL solves the compressible Navier-Stokes equations in cylindrical coordinates using high-order numerical schemes. A nozzle is included in the computational domain to account for more realistic inflow boundary conditions. Preliminary results of a Re = 5000 compressible swirling jet at Mach number M a = 0.6 with an azimuthal velocity as high as the maximum axial velocity (swirl number S = 1.0 ) capture the fundamental characteristics of this flow type: At a certain point in time the jet spreads and develops into a conical vortex breakdown. A stagnation point-flow in the vicinity of the jet axis is clearly visible with the stagnation point located close to the nozzle exit. The stagnation point precesses in time around the jet axis, moving up- and downstream. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Posets Generated by Irreducible Elements

Let J be a fixed partially ordered set (poset). Among all posets in which J is join-dense and consists of all completely join-irreducible elements, there is an up to isomorphism unique greatest one, the Alexandroff completion L. Moreover, the class of all such posets has a canonical set of representatives, C ₀ L, consisting of those sets between J and L which intersect each of the intervals I _j =[j ,j ] (jJ), where j and j denote the greatest element of L less than, respectively, not greater than j. The complete lattices in C ₀ L form a closure system C L, consisting of all Dedekind–MacNeille completions of posets in C ₀ L. We describe explicitly those L for which C ₀ L, respectively, C L is a (complete atomic) Boolean lattice, and similarly, those for which C L is distributive (or modular). Analogous results are obtained for C L, the closure system of all posets in C ₀ L that are closed under meets of less than elements (where is any cardinal number).     

Semigroups Generated by Similarity Orbits

noindent We investigate the semigroups in M _n (smallbf F) generated by the similarity orbit of single matrices. February 11, 2000     

Algebras Generated by Semicentral Idempotents

Let be a unital K-algebra, where K is a commutative ring with unity. An idempotent is {\it left semicentral\/} if , and is {\it SCI-generated\/} if it is generated as a K-module by left semicentral idempotents. This paper develops the basic properties of SCI-generated algebras and characterizes those that are also prime, semiprime, primitive, or subdirectly irreducible. Minimal ideals and the socle of SCI-generated algebras are investigated. Conditions are found to describe a large class of SCI-generated algebras via generalized triangular matrix representations. SCI-generated piecewise domains are characterized. Examples are given that illustrate the breadth and diversity of the class of SCI-generated algebras.     

Varieties Generated by Standard BL-Algebras

If $ {\mathbb {V}} $ is a subvariety of $ {\mathbb {BL}} $ generated by a class of standard BL-algebras, then $ {\mathbb {V}} $ is generated by a finite class of standard BL-algebras.     

Vortex Generation in a Liquid Metal Duct Flow near a Magnetic Dipole

The generation of vortical structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces which act on the fluid elements. Our model uses the quasi-static approximation applicable in the limit of small magnetic Reynolds numbers. The analysis covers the stationary flow regime at smaller flow Reynolds numbers Re as well as the fully time-dependent regimes at higher values with a turbulent flow in the wake of the magnetic obstacle. We present a systematic study of these two basic flow regimes on Re and the Hartmann number Ha, a measure of the strength of the magnetic dipole field. Furthermore, three orientations of the dipole are compared, the streamwise, spanwise and wall-normal ones. The most efficient generation of turbulence at a fixed distance above the duct occurs for the spanwise orientation in which we can observe the formation of Hartmann layers at the top plate. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ginzburg-Landau Vortex and Mean Curvature Flow with External Force Field

This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a parabolic Ginzburg Landau system which simulates inhomogeneous type II superconducting materials and three-dimensional superconducting thin films having variable thickness. We will prove that the vortex of the problem is moved by a codimension k mean curvature flow with external force field. Besides, we will show that the mean curvature flow depends strongly on the external force, having completely different phenomena from the usual mean curvature flow.     

由Minkowski不等式生成的函数

定义一个与Minkowski不等式相关的二元函数,由它的单调性和准线性,可得出Minkowski不等式的一些加细.     

Permutations Generated by Stacks and Deques

Lower and upper bounds are given for the the number of permutations of length n generated by two stacks in series, two stacks in parallel, and a general deque.