Trailing Edge Noise Reduction by Passive and Active Flow Controls

This paper presents the results on the use of porous metal foams (passive control) and dielectric barrier surface plasma actuations (active control) for the reduction of vortex shedding tonal noises from the nonflat plate type trailing edge serration in a NACA0012 airfoil previously discussed in Chong et al. (AIAA J. Vol. 51, 2013, pp. 2665-2677). The use of porous metal foams to fill the interstices between adjacent members of the sawtooth can almost completely suppress the vortex shedding tonal noise, whilst the serration effect on the broadband noise reduction is retained. This concept will promote the nonflat plate type serrated trailing edge to become a genuine alternative to the conventional flat plate type serrated trailing edge, which is known to have drawbacks in the structural stability, aerodynamic performances and implementation issues. For the plasma actuators, configuration which produces electric wind in a tangential direction is found to be not very effective in suppressing the vortices emanated from the serration blunt root. On the other hand, for the plasma configuration which produces electric wind in a vertical direction, good level of vortex shedding tonal noise reduction has been demonstrated. However, the self noise produced by the plasma actuators negates the noise benefits on the tonal noise reduction. This characteristic illustrates the need to further develop the plasma actuators in a two pronged approach. First is to increase the electric wind speed, thereby allowing the plasma actuators to be used in a higher free jet velocity which naturally produces a larger level of jet noise. Second, the self noise radiated by the plasma actuators should be reduced

Self-noise produced by an airfoil with nonflat plate trailing-edge serrations

This paper represents the results of an experimental study aimed at reducing the airfoil self-noise by the trailing edge serration of four different sawtooth geometries (defined in the serration angle and length). These serrations have a common feature: all of the sawtooth patterns are cut directly into the trailing edge of a realistic airfoil. This configuration offers better structural strength and integrity. For the sawtooth trailing edges investigated here, the radiation of the extraneous vortex shedding noise in a narrowband frequency due to the partial bluntness at the serration roots is unavoidable. However, this narrowband component tends to be less significant provided that the serration angle is large and the serration length is moderate. Sound power was measured, and some of the sawtooth geometries have been shown to afford significant boundary-layer instability tonal noise and moderate turbulent broadband noise reductions across a fairly large velocity range. This paper demonstrates that a nonflat plate serrated trailing edge can also be effective in the self-noise reduction. Some experimental results are also presented in order to explain the self-noise mechanisms.This work is partly supported by the Brunel Research Initiative and Enterprise fun

Unique Minimal Liftings for Simplicial Polytopes

For a minimal inequality derived from a maximal lattice-free simplicial polytope in $\R^n$, we investigate the region where minimal liftings are uniquely defined, and we characterize when this region covers $\R^n$. We then use this characterization to show that a minimal inequality derived from a maximal lattice-free simplex in $\R^n$ with exactly one lattice point in the relative interior of each facet has a unique minimal lifting if and only if all the vertices of the simplex are lattice points.Comment: 15 page

Positive Measure Spectrum for Schroedinger Operators with Periodic Magnetic Fields

We study Schroedinger operators with periodic magnetic field in Euclidean 2-space, in the case of irrational magnetic flux. Positive measure Cantor spectrum is generically expected in the presence of an electric potential. We show that, even without electric potential, the spectrum has positive measure if the magnetic field is a perturbation of a constant one.Comment: 17 page

On the Second Law of thermodynamics and the piston problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio $m/M$ is a very small parameter, where $m$ is the mass of one particle of the gaz and $M$ is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.Comment: 29 pages, 9 figures submitted to Journal of Statistical Physics (2003

Imaging morphological details and pathological differences of red blood cells using tapping-mode AFM

The surface topography of red blood cells (RBCs) was investigated under nearphysiological conditions using atomic force microscopy (AFM). An immobilization protocol was established where RBCs are coupled via molecular bonds of the membrane glycoproteins to wheat germ agglutinin (WGA), which is covalently and flexibly tethered to the support. This results in a tight but noninvasive attachment of the cells. Using tappingmode AFM, which is known as gentle imaging mode and therefore most appropriate for soft biological samples like erythrocytes, it was possible to resolve membrane skeleton structures without major distortions or deformations of the cell surface. Significant differences in the morphology of RBCs from healthy humans and patients with systemic lupus erythematosus (SLE) were observed on topographical images. The surface of RBCs from SLE patients showed characteristic circularshaped holes with approx. 200 nm in diameter under physiological conditions, a possible morphological correlate to previously published changes in the SLE erythrocyte membrane

Influence of anisotropic next-nearest-neighbor hopping on diagonal charge-striped phases

We consider the model of strongly-correlated system of electrons described by an extended Falicov-Kimball Hamiltonian where the stability of some axial and diagonal striped phases was proved. Introducing a next-nearest-neighbor hopping, small enough not to destroy the striped structure, we examine rigorously how the presence of the next-nearest-neighbor hopping anisotropy reduces the $\pi/2$-rotation degeneracy of the diagonal-striped phase. The effect appears to be similar to that in the case of anisotropy of the nearest-neighbor hopping: the stripes are oriented in the direction of the weaker next-nearest-neighbor hopping.Comment: 9 pages, 3 figures, 1 tabl