Numerical analyis of turbulent flow in a Coanda ejector

The task of this study is to investigate the influence of various geometric parameters and pressure ratios on the Coanda ejector performance. For numerically investigations we use an implicit formulation of the compressible Reynolds-average Navier-Stokes equations (RANS) for axisymmetric flow with a shear stress transport k − ω (SST model) turbulence model. The numerically results was obtained for a total pressure range 1-5 Bars, imposed at the reservoir inlet. The effect of various factors, such as, the pressure ratio, primary nozzle and ejector configurations on the system performance has been evaluated based on defined performance parameters. The numerical results have been compared with theoretical and experimental results for a given Coanda ejector configuration. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On conic-line arrangements with nodes,tacnodes, and ordinary triple points

Journal of Algebraic Combinatorics - In the present paper, we study conic-line arrangements having nodes, tacnodes, and ordinary triple points as singularities. We provide combinatorial constraints...     

Graph-theoretical analysis of the bonding topology in polyhedral organic cations

It is shown that in several cases where planar delocalisation in organic cations would result in the formation of an anti-aromatic system, polyhedral delocalisation is the form of bonding actually preferred. This explains, for instance, why organic cations in such cases adopt cage-like structures. A full graph-theoretical analysis, similar to one previously published¹² for polyhedral boranes, carboranes and metal clusters, indicates that the nido structure for (CH)₅⁺ may readily be accounted for. Moreover, in the case of the dication (CH)₆²⁺ the fact that its energy minimum also corresponds to a nido structure is explained. In fact, no closo- or arachno-type structures appear to be possible for organic cations. A number of structural predictions concerning these species are given in the conclusion.     

On a Problem of Brocard

It is proved that, if P is a polynomial with integer coefficients,having degree 2, and 1 > > 0, then n(n – 1) ...(n – k + 1) = P(m) has only finitely many natural solutions(m,n,k), n k > n, provided that the abc conjecture is assumedto hold under Szpiro's formulation. 2000 Mathematics SubjectClassification 11D75, 11J25, 11N13.     

Lipscomb's space

It is known that Lipscomb's space can be imbedded in Hilbert's space . Let be the imbedded version of endowed with the -induced topology. We show how to construct as the attractor of an iterated function system containing an infinite number of affine transformations of . In this way we answer an open question of J.C. Perry.

     

A Central Limit Theorem for Star-Generators of $${S}_{infty }$$ S ∞ , Which Relates to the Law of a GUE Matrix

Journal of Theoretical Probability - It is well known that, on a purely algebraic level, a simplified version of the central limit theorem (CLT) can be proved in the framework of a non-commutative...     

Influence of pitching on performance of VAWTs

Self- starting is the major obstacle to be overcome for successful design of a vertical axis wind turbine (VAWT). In the past has been suggested that pitching the turbine blades such that pitch angle is not 90 degrees allows for self-starting. To understand the physics surrounding pitching, an analysis is carried out for a common airfoil profile, NACA 0012. The vortex model is used to predict aerodynamic performance of VAWT with pitched blades at various angles. As a result of the analysis carried out for the airfoil at various pitch angles, it was shown that the “dead band” phenomenon could be overcome, but only slightly. At the same time, to overcome the “dead band” with a level on confidence, torques in the tip speed ratio (TSR ) range of 0.75 to 2.75 must be increased to values further above zero. The paper aimed at giving an insight into the small wind turbine starting behavior and its influence parameters. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients

^** Email: todor{at}math.ethz.ch^*** Corresponding author. Email: schwab{at}math.ethz.ch A scalar, elliptic boundary-value problem in divergence formwith stochastic diffusion coefficient a(x, ) in a bounded domainD ^d is reformulated as a deterministic, infinite-dimensional,parametric problem by separation of deterministic (x D) andstochastic ( ) variables in a(x, ) via Karhúnen–Loèveor Legendre expansions of the diffusion coefficient. Deterministic,approximate solvers are obtained by projection of this probleminto a product probability space of finite dimension M and sparsediscretizations of the resulting M-dimensional parametric problem.Both Galerkin and collocation approximations are considered.Under regularity assumptions on the fluctuation of a(x, ) inthe deterministic variable x, the convergence rate of the deterministicsolution algorithm is analysed in terms of the number N of deterministicproblems to be solved as both the chaos dimension M and themultiresolution level of the sparse discretization resp. thepolynomial degree of the chaos expansion increase simultaneously.