Characterisation of cross-flow above a railway bridge equipped with solid windbreaks

The flow field above a two dimensional model of a railway bridge equipped with solid windbreaks is analysed in a wind tunnel. Particle image velocimetry (PIV) is used to measure the flow velocity in planes perpendicular to the bridge span. The mean velocity components, the two-component turbulent kinetic energy, the turbulence intensities of the velocity fluctuation components and the Reynolds shear stress above the bridge deck are presented. The flow patterns based on the streamlines of the average flow field are analysed. The inclusion of a windbreak produces a separation bubble, that is locked to the bridge deck due to presence of the leeward fence. Special attention is paid to the analysis of the flow field characteristics along the vertical profiles above the railway tracks. The inclusion of the windbreak leads both to an increase of the mean velocity and the turbulence intensity around the catenary contact wires. On the other hand, the flow in the region close to the bridge deck is slowed-down. The effect of the size of the final interrogation window used in the PIV analysis is considered, more particularly on the determination of the mean velocity and turbulence intensity. The results show that a decrease of the final interrogation window leads to an increase of the turbulence intensity when there are no wind protection devices installed on the bridge

Use of calculus of variations to determine the shape of hovering rotors of minimum power and its application to micro air vehicles

In this paper, calculus of variations and combined blade element and momentum theory (BEMT) are used to demonstrate that, in hover, when neither root nor tip losses are considered; the rotor, which minimizes the total power (MPR), generates an induced velocity that varies linearly along the blade span. The angle of attack of every blade element is constant and equal to its optimum value. The traditional ideal twist (ITR) and optimum (OR) rotors are revisited in the context of this variational framework. Two more optimum rotors are obtained considering root and tip losses, the ORL, and the MPRL. A comparison between these five rotors is presented and discussed. The MPR and MPRL present a remarkable saving of power for low values of both thrust coefficient and maximum aerodynamic efficiency. The result obtained can be exploited to improve the aerodynamic behaviour of rotary wing micro air vehicles (MAV). A comparison with experimental results obtained from the literature is presented

Endpoint Estimates for N-dimensional Hardy Operators and Their Commutators

In this paper, it is proved that the higher dimensional Hardy operator is bounded from Hardy space to Lebesgue space. The endpoint estimate for the commutator generated by Hardy operator and (central) BMO function is also discussed.Comment: 8 page