Visualization and measurement of helicopter rotor flow with swept back tip shapes at hover flight using the “flow visualization gun” time line technique

The Flow Visualization Gun (FVG), a novel time line visualization technique, has been used to investigate the flow field of a helicopter rotor with swept back tip shape in hover flight condition. After introducing the FVG-technique, the paper presents some visualization photographs of the rotor blade tip vortices and the rotor downwash. Using orthogonal sets of flow photographs and digital image analysis, the 3-dimensional time line displacement within the flow and the tip vortex structure are determined. The data of 16 time line experiments are interpolated in space and time to obtain velocity data on an evenly spaced 3-dimensional grid. Vorticity contour plots of the flow field show the complex arrangement of the tip vortices of the blade itself and of the preceding blade and some additional vorticity in the direct wake which may form a secondary vortex. Understanding and control of this vorticity distribution is important for the design of new efficient tip shapes. While the FVG technique has been used so far for qualitative investigation of complex flow patterns at local velocities of up to 20 m/s, a good comparison to laser velocimetry data validates the technique as an interesting tool for both qualitative and quantitative investigation. This research was supported by a “Poste Rouge” grant by the Centre National de la Recherche Scientifique (C.N.R.S.). The authors would like to thank all members of the IRPHE for their help concerning the mechanical and electronical set up of the experiments.     

Processing,characterisation and rheology of transparent concentrated fibre-bundle suspensions

Highly concentrated planar fibre-bundle suspensions with a transparent PMMA matrix were processed with various initial bundle contents and orientations. They were submitted to simple compression and plane strain compression deformation modes. First rheological measurements are presented. They highlight the role of the bundle content and orientation on recorded stress levels. The transparent matrix allows the observation of fibrous microstructures before and after compressions: The in-plane deformation of bundles (flattening and bending) as well as the evolution of their orientation are analysed and discussed. This paper was presented at the 3rd Annual European Rheology Conference (AERC) 2006, held in Hersonisos, Crete, Greece, April 27–29, 2006.     

Improvement of tribological properties of co-acting elements by oil pockets creation on sliding surfaces

Sliding experiments were carried out using a block-on-ring friction machine. The tribosystem consists of the stationary block (counter-specimen) pressed at the required load P against the ring (specimen) rotating at the defined speed. The sliding was unidirectional. The block was a part of a bearing sleeve hardened EN-GJS 400-15 cast iron with a hardness value of 50 HRC. The ring samples, 35 mm in diameter, were made from hardened 42CrMo4 steel of hardness 32 HRC. Some variants of specimen surfaces were created by burnishing technique. Two kinds of experiments were done. Seizure tests were conducted at increasing pressure for sliding speeds in the range: 0.27–0.55 m/s. Wear resistance test was carried out under artificially increased dustiness conditions, too. It was found that surface texturing improved seizure resistance for the smallest sliding speed (0.27 m/s) comparing to untextured ground samples. The wear of steel rings with spherical dimples was smaller than of those having dimples of long drop shape for the pit-area ratio range of 7.5–20%.     

Analysis of Fractional Covering of Some Supply Management Problems

We study a supply management problem with a linear cost function and its mixed integer program. A parametric family of such problems, possessing exponential L _k -coverings, is constructed. Besides, the NP-hard expansion of the family, which has the same property, is formulated.     

Lubricated compression of BMC, a concentrated and fibre-reinforced granular polymer suspension

Bulk moulding compounds (BMCs) are thermoset polymer composites widely used in electric and automotive industries. During their processing by injection, BMCs look like fibre-reinforced granular suspensions in the form of pastes, the rheology of which is not well known. For that purpose, lubricated compression tests were performed on BMC samples with various formulations. Firstly, results show that samples flow without sticking to the rheometer’s plates, validating the efficiency of the lubricant. A correction, which requires few assumptions on the rheology of BMC, is then proposed to account for its contribution to the overall axial stress. Thereby, the influences of the axial strain rate, the loading path, the polydispersity of the mineral filler and the fibre content on the BMC flow are analysed. A 1D elementary non-linear viscoelastic model is proposed to capture the main observed trends.     

Hydrodynamics of ciliary propulsion

A numerical approach is developed to study the effect on a fluid of the regular oscillations of an array of flexible cilia which hinge around points on a wall. The specific application studied concerns the ctenophore Pleurobrachia pileus, a small marine invertebrate of quasi-spherical shape and diameter of the order of the centimeter which swims in water thanks to the rhythmic beating of eight rows of hair-like cilia aligned along its body. Only one row of cilia is studied here, in a three-dimensional setting. The technique presented is general enough to allow its application to a variety of fluid–structure interaction problems. The physical mechanisms of the propulsion are highlighted, by analysing the results of three-dimensional simulations. A parametric study involving natural and non-natural parameters leads to a better understanding of the propulsive characteristics of ctenophores; results show that the specific power expended increases with the increase of the beating frequency of the row of cilia, in agreement with experiments.     

WEIGHTED BEST LOCAL APPROXIMATION IN ORLICZ SPACE

We present a common fixed point theorem for generalized asymptotically non- expansive and noncommuting mappings in normed linear spaces.     

Second order partial differential equations for gradients of orthogonal polynomials in two variables

In this work, we introduce the classical orthogonal polynomials in two variables as the solutions of a matrix second order partial differential equation involving matrix polynomial coefficients, the usual gradient operator, and the divergence operator. Here we show that the successive gradients of these polynomials also satisfy a matrix second order partial differential equation closely related to the first one.     

Tilting Modules Arising from Ring Epimorphisms

We show that a tilting module T over a ring R admits an exact sequence 0?→?R?→?T ₀?→?T ₁?→?0 such that \(T_0,T_1\in\text{Add}(T)\) and Hom _R (T ₁,T ₀)?=?0 if and only if T has the form S?⊕?S/R for some injective ring epimorphism λ : R?→?S with the property that \(\text{Tor}_1^R(S,S)=0\) and pdS _R ?≤?1. We then study the case where λ is a universal localization in the sense of Schofield (1985). Using results by Crawley-Boevey (Proc Lond Math Soc (3) 62(3):490–508, 1991), we give applications to tame hereditary algebras and hereditary noetherian prime rings. In particular, we show that every tilting module over a Dedekind domain or over a classical maximal order arises from universal localization.     

Oxygenation of aromatic hydrocarbons with hydrogen peroxide catalyzed by rhodium carbonyl complexes

Hexanuclear rhodium carbonyl cluster, Rh₆(CO)₁₆, catalyzes benzene hydroxylation with hydrogen peroxide in acetonitrile solution. Phenol and (at lower concentration) quinone are formed with the maximum attained total yield and turnover number 17% and 683, respectively. Certain other rhodium carbonyl complexes, containing cyclopentadienyl ligands, Rh₂Cp₂(CO)₃ and Rh₃(CpMe)₃(CO)₃, are less efficient catalysts. Cyclopentadienyl derivatives of rhodium which do not contain the carbonyl ligands, Rh(CpMe₅)(CH₂?CH₂)₂, RhCp(cyclooctatetraene) and Rh₂Cp₂(cyclooctatetraene) turned out to be absolutely inactive in the benzene hydroxylation. Styrene is transformed into benzaldehyde and (at lower concentration) acetophenone and 1‐phenylethanol. Copyright © 2008 John Wiley & Sons, Ltd.